Linchevsky theory of metallurgical processes. Textbook: Theory of metallurgical processes. Chapter XVII. Seamless and welded pipe production

Federal Agency for Education

GOU VPO "Ural State Technical University - UPI"

A.M. Panfilov

Educational electronic text edition

Prepared by the Department of Theory of Metallurgical Processes

Scientific editor: prof., Doct. chem. M.A. Spiridonov

Methodical instructions for laboratory work in the disciplines "Physicochemistry of metallurgical systems and processes", "Theory of metallurgical processes" for students of all forms of training in metallurgical specialties.

The rules for organizing work in the workshop "Theory of metallurgical processes" of the Department of TMP (specialized audience

MT-431 named after O.A. Esina). The methodology and procedure for performing laboratory work are described, requirements for the content and preparation of reports on laboratory work in accordance with the current GOST and recommendations for their implementation are given.

© GOU VPO USTU-UPI, 2008

Ekaterinburg

Introduction ................................................. .................................................. .................................................. . 4

1 Organization of work in a laboratory workshop on the theory of metallurgical processes ............. 4

1.1 Preparation for laboratory work ............................................. .................................................. .. 5 1.2 Recommendations for processing measurement results and preparing a report .............................. 5

1.3.1 Construction of graphs ............................................. .................................................. ................... 5

1.3.2 Smoothing experimental data ............................................ ................................... 7

1.3.5 Numerical differentiation of a function given by a set of discrete points ................ 8

approximating some data set .............................................. .................................. nine

1.3.7 Presentation of results ............................................. .................................................. ....... ten

2 Description of laboratory work .............................................. .................................................. ............. eleven

2.1 Study of the kinetics of high-temperature oxidation of iron (Work No. 13) ......................... 12

2.1.1 General laws of iron oxidation ........................................... .................................. 12 2.1.2 Description of the installation and the procedure for carrying out experiments ... .................................................. ..... fourteen

2.1.3 Processing and presentation of measurement results .......................................... ................... 15

Control questions................................................ .................................................. ..................... 17

2.2 Study of the temperature dependence of the electrical conductivity of oxide melts

(Work No. 14) ............................................. .................................................. .......................................... 19

2.2.1 General information on the nature of electrical conductivity of slags ...................................... 19

2.2.2 Description of the installation and measurement procedure .......................................... ................................ 21

2.2.3 The order of performance of work ............................................ .................................................. ..... 23

2.2.4 Processing and presentation of measurement results .......................................... ................... 24

Control questions................................................ .................................................. ..................... 25

2.3 Study of the kinetics of metal desulfurization by slag on a simulation model (Work No.

15) ............................................................................................................................................................ 26

2.3.1 General information on the kinetics of metal desulfurization by slag ........................................ ..... 26

2.3.2 Mathematical model of the process ............................................ ............................................... 29

2.3.3 The order of work ............................................ .................................................. ...... thirty

2.3.4 Processing and presentation of measurement results .......................................... ................... 31

Control questions................................................ .................................................. ..................... 32

2.4 Thermographic study of the processes of dissociation of natural carbonates (Work No. 16) 33

2.4.1 General regularities of carbonate dissociation ........................................... ...................... 33

2.4.2 Installation diagram and work procedure ......................................... ......................... 39

2.4.3 Processing and presentation of measurement results .......................................... ................... 39

Control questions................................................ .................................................. ..................... 41

2.5 Study of the temperature dependence of the viscosity of oxide melts (Work No. 17) ............. 42

2.5.1 The nature of the viscous resistance of oxide melts .......................................... ................ 42

2.5.2 Description of the installation and the procedure for measuring the viscosity ......................................... .................. 43

2.5.3 The order of work ............................................ .................................................. ...... 45

2.5.4 Processing and presentation of measurement results .......................................... ................... 45 Test questions ............................ .................................................. ......................................... 46

2.6 Reduction of manganese from oxide melt to steel (Work No. 18)

2.6.1 General laws of the electrochemical interaction of metal and slag ............... 47

2.6.2 Process model ............................................. .................................................. ........................ 49

2.6.3 The order of work ............................................ .................................................. ...... 50

Control questions................................................ .................................................. ..................... 52 References .......................... .................................................. .................................................. ..... 53

STP USTU-UPI 1-96	Enterprise standard. General requirements and rules for the design of diploma and course projects (works).
GOST R 1.5-2002	GSS. Standards. General requirements for construction, presentation, design, content and designation.
GOST 2.105-95	ESKD. General requirements for text documents.
GOST 2.106-96	ESKD. Text documents.
GOST 6.30 2003	USD. Unified system of organizational and administrative documentation. Requirements for paperwork.
GOST 7.32-2001	SIBID. Research report.
GOST 7.54-88	SIBID. Representation of numerical data on the properties of substances and materials in scientific and technical documents. General requirements.
GOST 8.417-2002	GSOEE. Units of quantities

Abbreviations and abbreviations

	State standard of the former USSR or interstate standard (currently).
	The standard adopted by the State Committee of the Russian Federation for Standardization and Metrology (Gosstandart of Russia) or the State Committee of the Russian Federation for Housing and Construction Policy (Gosstroy of Russia).
	State system of standardization.
	State system for ensuring the uniformity of measurements.
	Information Technology
	Least square method
	Personal Computer
	Enterprise standard
	Theory of metallurgical processes

Introduction

Performing laboratory work to study the properties in the metal-slag system and the processes occurring in metallurgical units, allows you to better understand the capabilities of the physicochemical method of analysis and gain skills in its practical application. Additionally, the student gets acquainted with the implementation of some methods of experimental and model research of individual physical and chemical properties and metallurgical processes in general, acquires the skills of processing, analysis and presentation of experimental information.

1 Organization of work in a laboratory workshop on the theory of metallurgical processes

In a laboratory workshop on the theory of metallurgical processes, the main thing is the computer collection of experimental information. This determines a number of features of the organization of work:

Each student receives an individual task, performs the experiment in whole or a specified part of it, and processes the information received. The result of the work includes the obtained numerical characteristics of the phenomenon under study and errors in their determination, graphs illustrating the identified features, and conclusions obtained from the entire set of information. The discrepancy between the quantitative results of work, given in student reports, in comparison with the control marks should not exceed 5%.

The main options for presenting the results are processing experimental data, plotting graphs and formulating conclusions in Microsoft.Excel or OpenOffice.Calc spreadsheets.

With the permission of the teacher, it is temporarily allowed to present a handwritten report with the necessary illustrations and graphs made on graph paper.

The report on the laboratory work performed is sent to the teacher leading the laboratory practice no later than on the working day preceding the next laboratory work. The order of transmission (by e-mail, during a break to any teacher or laboratory assistant leading the class at the moment) is determined by the teacher.

Students who have not submitted a report on previous work in time and have not passed the colloquium (testing) are not allowed to the next laboratory work.

Only students who have undergone an introductory briefing on safe work measures in a laboratory practice and signed the instruction sheet are allowed to perform laboratory work.

Work with heating and measuring electrical devices, with chemical glassware and reagents is carried out in accordance with the safety instructions in the laboratory.

After completing the work, the student tidies up the workplace and hands it over to the laboratory assistant.

1.1 Preparation for laboratory work

The main sources in preparation for the lesson are this manual, textbooks and teaching aids recommended by the lecturer, lecture notes.

Preparing for laboratory work, the student during the week preceding the lesson must read and understand the material related to the phenomenon under study, understand the diagrams given in the manual in the design of the installation and the measurement technique and the processing of their results. If difficulties arise, it is necessary to use the recommended literature and consultations of the lecturer and teachers conducting laboratory studies.

The student's readiness to perform the work is controlled by the teacher through an individual survey of each student, or by conducting computer testing. An insufficiently prepared student is obliged to study the material related to this work during the lesson, and to perform the experimental part of the work in an additional lesson after re-checking. The time and procedure for conducting repeated classes is regulated by a special schedule.

1.2 Recommendations for processing measurement results and preparing a report

According to GOST 7.54-88, experimental numerical data should be presented in the form of titled tables. Sample tables are provided for each lab.

When processing the measurement results, it is necessary to use statistical processing: apply smoothing of experimental data, use the least squares method when evaluating the parameters of dependences, etc. and it is imperative to evaluate the error of the obtained values. Special statistical functions are provided in spreadsheets to perform this processing. The necessary set of functions is also available in calculators designed for scientific (engineering) calculations.

1.3.1 Plotting

When performing experiments, as a rule, the values ​​of several parameters are fixed simultaneously. By analyzing their relationship, one can draw conclusions about the observed phenomenon. The visual representation of numerical data makes it extremely easy to analyze their relationship - which is why graphing is such an important step in working with information. Note that among the fixed parameters there is always at least one independent variable - a value whose value changes by itself (time) or which is set by the experimenter. The rest of the parameters are determined by the values ​​of the independent variables. When building graphs, you should follow some rules:

The value of the independent variable is plotted on the abscissa (horizontal axis) and the value of the function is plotted on the ordinate (vertical axis).

The scales along the axes should be chosen so as to use the area of ​​the graph as informative as possible - so that there are fewer empty areas on which there are no experimental points and lines of functional dependencies. To meet this requirement, you often need to specify a non-zero value at the origin of the coordinate axis. In this case, all experimental results must be presented on the graph.

The values ​​along the axes should, as a rule, be multiples of some integer (1, 2, 4, 5) and be evenly spaced. It is categorically unacceptable to indicate the results of specific measurements on the axes. The scale units you select should not be too small or too large (they should not contain multiple leading or trailing zeros). To ensure this requirement, you should use a scale factor of the form 10 X, which is taken out in the axis designation.

The line of functional dependence should be either straight or smooth curve. It is permissible to connect experimental points with a broken line only at the stage of preliminary analysis.

Many of these requirements will be automatically met when charting with spreadsheets, but usually not all and not fully, so you almost always have to adjust the resulting representation.

Spreadsheets have a special service - Chart Wizard (Main menu: Insert Chart). The simplest way to access it is to first select an area of ​​cells that includes both an argument and a function (several functions), and activate the "Chart Wizard" button on the standard panel with the mouse.

Thus, you will get a draft chart that you still need to work with, since the automatic selection of many of the default chart parameters will most likely not ensure that all requirements are met.

First of all, check the size of the numbers on the axes and the letters in the axis labels and function labels in the legend. It is desirable that the font size be the same everywhere, no less than 10 and no more than 14 points, but you will have to set the value for each label separately. To do this, move the cursor over the object of interest (axis, label, legend) and press the right mouse button. In the context menu that appears, select "Format (element)" and in the new menu on a piece of paper labeled "Font" select the desired value. When formatting the axis, you should additionally look at and, possibly, change the values ​​on the sheets with labels "Scale" and "Number". If you do not understand what changes the proposed choice will lead to, do not be afraid to try any option, because you can always discard the changes made by pressing Ctrl + Z, or by selecting the Main menu item "Edit" - Undo, or by clicking on the button "Undo" on the standard toolbar.

If there are a lot of points, and the spread is small and the line looks smooth enough, then the points can be connected with lines. To do this, move the cursor over a point on the chart and press the right mouse button. In the context menu that appears, select the "Format data series" item. In a new window, on a piece of paper labeled "View", you should select the appropriate color and line thickness, and at the same time check the color, size and shape of the dots. This is how the dependences are constructed that approximate the experimental data. If the approximation is performed by a straight line, then two points on the edges of the range of the argument are sufficient. It is not recommended to use the "smoothed curve" option built into spreadsheets due to the inability to adjust the smoothing parameters.

1.3.2 Smoothing experimental data

The experimental data obtained on high-temperature experimental installations are characterized by a large value of the random measurement error. This is mainly due to electromagnetic interference from the operation of a powerful heating device. Statistical processing of the results can significantly reduce the random error. It is known that for a random variable distributed according to the normal law, the error of the arithmetic mean determined from N values ​​in N½ times less than the error of a single measurement. With a large number of measurements, when it is permissible to assume that the random scatter of data over a small segment significantly exceeds the regular change in the value, an effective smoothing technique is to assign the next value of the measured value to the arithmetic mean calculated from several values ​​in a symmetric interval around it. Mathematically, this is represented by the formula:

(1.1)

and is very easy to implement in spreadsheets. Here y i is the measurement result, and Y i is the smoothed value used instead.

Experimental data obtained using digital data collection systems are characterized by a random error, the distribution of which differs significantly from the normal law. In this case, it may be more efficient to use the median instead of the arithmetic mean. In this case, the measured value in the middle of the interval is assigned the value of the measured value that turned out to be closest to the arithmetic mean. It would seem that a slight difference in the algorithm can change the result very significantly. For example, in the variant of the median estimate, some experimental results may turn out to be completely unused, most likely exactly those that really are

"Jumping out" values ​​with a particularly large error.

1.3.5 Numerical differentiation of a function given by a set of discrete points

The need for such an operation arises quite often when processing experimental points. For example, by differentiating the dependence of concentration on time, the dependence of the rate of the process on time and on the concentration of the reagent is found, which, in turn, makes it possible to estimate the order of the reaction. The operation of numerical differentiation of a function given by a set of its values ​​( y) corresponding to the corresponding set of argument values ​​( x), is based on the approximate replacement of the differential of a function by the ratio of its final change to the final change in the argument:

(1.2)

Numerical differentiation is sensitive to errors caused by inaccuracies in the original data, discarding members of a series, etc., and therefore should be performed with caution. To improve the accuracy of estimating the derivative (), they try to first smooth out the experimental data, at least on a small segment, and only then perform differentiation. As a result, in the simplest case for equidistant nodes (the values ​​of the argument differ from each other by the same value x), the following formulas are obtained: for the derivative in the first ( NS 1) point:

for the derivative at all other points ( x), except for the last one:

for the derivative in the latter ( x) point:

If there is a lot of experimental data and it is permissible to neglect several extreme points, you can use stronger smoothing formulas, for example, by 5 points:

or 7 points:

For an uneven arrangement of nodes, we restrict ourselves to the fact that we recommend using a modified formula (1.3) in the form

(1.8)

and do not calculate the derivative at the start and end points.

Thus, to implement numerical differentiation, you need to place suitable formulas in the cells of a free column. For example, unequally spaced argument values ​​are located in column "A" in cells 2 through 25, and function values ​​are in column "B" in the corresponding cells. The derivative values ​​are supposed to be placed in the "C" column. Then in the cell "C3" you should enter the formula (5) in the form:

= (B4 - B2) / (A4 - A2)

and copy (stretch) to all cells in the range C4: C24.

1.3.6 Determination by the method of least squares of the coefficients of the polynomial,

approximating some data set

When numerical information is presented graphically, it is often necessary to draw a line along the experimental points, revealing the features of the obtained dependence. This is done for a better perception of information and to facilitate further analysis of data that have some scatter due to the measurement error. Often, on the basis of a theoretical analysis of the phenomenon under study, it is known in advance what form this line should have. For example, it is known that the dependence of the rate of a chemical process ( v) from temperature must be exponential, and the exponential exponent represents the inverse temperature in an absolute scale:

This means that on the graph in coordinates ln v- 1 / T should be a straight line,

whose slope characterizes the activation energy ( E) process. As a rule, several straight lines with different slope can be drawn through the experimental points. In a sense, the best of them will be the straight line with the coefficients determined by the least squares method.

In the general case, the least squares method is used to find the coefficients approximating the dependence y (x 1 , x 2 ,…x n) a polynomial of the form

where b and m 1 …m n Are constant coefficients, and x 1 …x n- a set of independent arguments. That is, in the general case, the method is used to approximate a function of several variables, but it is also applicable to describe a complex function of one variable x... In this case, it is usually believed that

and the approximating polynomial has the form

When choosing the degree of the approximating polynomial n keep in mind that it must necessarily be less than the number of measured values x and y... In almost all cases, it should be no more than 4, rarely 5.

This method is so important that Excel spreadsheets have at least four options for obtaining the values ​​of the desired coefficients. We recommend using the LINEST () function if you work in Excel spreadsheets with Microsoft Office, or the LINEST () function in Calc spreadsheets with OpenOffice. They are presented in the list of statistical functions, belong to the class of so-called matrix functions and in this connection have a number of application features. First, it is entered not into one cell, but directly into a range (rectangular area) of cells, since the function returns multiple values. The size of the area horizontally is determined by the number of coefficients of the approximating polynomial (in this example, there are two of them: ln v 0 and E / R), and vertically from one to five lines can be highlighted, depending on how much statistical information is needed for your analysis.

1.3.7 Presentation of results

In a scientific and technical document, when presenting numerical data, an assessment of their reliability should be given and random and systematic errors should be highlighted. The given data errors should be presented in accordance with GOST 8.207–76.

When statistically processing a group of observation results, the following operations should be performed: exclude known systematic errors from observation results;

Calculate the arithmetic mean of the corrected observation results, taken as the measurement result; calculate the estimate of the standard deviation of the measurement result;

Calculate the confidence limits of the random error (random component of the error) of the measurement result;

Calculate the boundaries of the non-excluded systematic error (non-excluded residuals of the systematic error) of the measurement result; calculate the confidence limits of the error of the measurement result.

To determine the confidence limits of the error of the measurement result, the confidence probability R take equal to 0.95. With a symmetric confidence error, the measurement results are presented in the form:

where is the measurement result, ∆ is the margin of error of the measurement result, R Is the confidence level. The numerical value of the measurement result must end with a digit of the same digit as the value of the error ∆.

2 Description of laboratory work

In the first part of each of the sections devoted to specific laboratory work, information is provided on the composition and structure of phases, the mechanism of processes occurring within a phase or at the boundaries of its interface with neighboring phases, the minimum necessary to understand the essence of the phenomenon studied in the work. If the information given is not enough, you should refer to the lecture notes and the recommended literature. Without understanding the first part of the section, it is impossible to imagine what is happening in the system under study in the course of the work, to formulate and comprehend the conclusions based on the results obtained.

The next part of each section is devoted to the hardware or software implementation of a real installation, or a computer model. It provides information about the hardware used and the algorithms used. Without understanding this section, it is impossible to assess the sources of error and what actions should be taken to minimize their impact.

The last part describes the procedure for performing measurements and processing their results. All these questions are submitted to the colloquium prior to the work, or computer testing.

2.1 Study of the kinetics of high-temperature oxidation of iron (Work No. 13)

2.1.1 General laws of iron oxidation

According to the principle of the sequence of transformations of A.A. Baikov, on the surface of iron during its high-temperature oxidation with atmospheric oxygen, all oxides that are thermodynamically stable under these conditions are formed. At temperatures above 572 ° C, the scale consists of three layers: FeO wustite, Fe 3 O 4 magnetite, Fe 2 O 3 hematite. The wustite layer closest to iron, which is approximately 95% of the entire scale thickness, has p-semiconducting properties. This means that there is a significant concentration of ferrous iron vacancies in the FeO cation sublattice, and electroneutrality is provided due to the appearance of electron "holes", which are ferric iron particles. The anionic sublattice of wustite, consisting of negatively charged О 2– ions, is practically defect-free; the presence of vacancies in the cation sublattice significantly increases the diffusion mobility of Fe 2+ particles through wustite and reduces its protective properties.

The intermediate layer of magnetite is an oxide of stoichiometric composition, which has a low concentration of defects in the crystal lattice and, as a result, has increased protective properties. Its relative thickness is 4% on average.

The outer layer of scale - hematite has n-type conductivity. The presence of oxygen vacancies in the anionic sublattice facilitates the diffusion of oxygen particles through it, in comparison with iron cations. The relative thickness of the Fe 2 O 3 layer does not exceed 1% .

At temperatures below 572 ° C, wustite is thermodynamically unstable; therefore, the scale consists of two layers: magnetite Fe 3 O 4 (90% of the thickness) and hematite Fe 2 O 3 (10%).

The formation of a continuous protective film of scale on the surface of iron leads to its separation from the air atmosphere. Further oxidation of the metal occurs due to the diffusion of reagents through the oxide film. The considered heterogeneous process consists of the following stages: oxygen supply from the volume of the gas phase to the boundary with the oxide by molecular or convective diffusion; adsorption of O2 on the surface of the oxide; ionization of oxygen atoms with the formation of О 2– anions; diffusion of oxygen anions in the oxide phase to the interface with the metal; ionization of iron atoms and their transition to scale in the form of cations; diffusion of iron cations in oxide to the border with gas; crystal-chemical act of the formation of new portions of the oxide phase.

The diffusion mode of metal oxidation is realized if the most inhibited stage is the transport of Fe 2+ or O 2– particles through the scale. Molecular oxygen is supplied from the gas phase relatively quickly. In the case of the kinetic regime, the limiting stages are the stages of adsorption or ionization of particles, as well as the act of crystal chemical transformation.

The derivation of the kinetic equation of the iron oxidation process for the case of a three-layer scale is rather cumbersome. It can be significantly simplified, without changing the final conclusions, if the scale is considered homogeneous in composition and only the diffusion of Fe 2+ cations through it is taken into account.

Let us denote by D diffusion coefficient of Fe 2+ particles in scale, k- rate constant of iron oxidation, C 1 and WITH 2 equilibrium concentrations of iron cations at the interface with metal and air, respectively, h- the thickness of the oxide film, S Is the surface area of ​​the sample, is the density of the oxide, M- its molar mass. Then, in accordance with the laws of formal kinetics, the specific rate of the chemical act of the interaction of iron with oxygen per unit surface of the sample ( v r) is determined by the ratio:

In a stationary state, it is equal to the density of the diffusion flux of Fe 2+ particles.

Considering that the overall rate of the heterogeneous oxidation process is proportional to the rate of growth of its mass

(13.3)

can be excluded C 2 from equations (13.1) and (13.2) and obtain the dependence of the scale mass on time:

(13.4)

It can be seen from the last relation that the kinetic mode of the process is realized, as a rule, at the initial moment of oxidation, when the thickness of the oxide film is small and its diffusion resistance can be neglected. The growth of the scale layer slows down the diffusion of reagents, and the process mode changes over time to diffusion.

A more rigorous approach, developed by Wagner in the ion-electron theory of high-temperature oxidation of metals, makes it possible to quantitatively calculate the rate constant of the parabolic law of film growth using the data of independent experiments on the electrical conductivity of oxides:

where ∆ G- change in the Gibbs energy for the metal oxidation reaction, M- the molar mass of the oxide, - its electrical conductivity, t i- fraction of ionic conductivity, z- the valence of the metal, F- Faraday constant.

When studying the kinetics of the formation of very thin ( h < 5·10 –9 м) пленок необходимо учитывать также скорость переноса электронов через слой оксида путем туннельного эффекта (теория Хауффе и Ильшнера) и ионов металла под действием электрического поля (теория Мотта и Кабреры). В этом случае окисление металлов сопровождается большим самоторможением во времени при замедленности стадии переноса электронов, чему соответствует логарифмический закон роста пленок h = K Ln ( a τ+ B), as well as cubic h 3 = KΤ (oxides are semiconductors p-type) or inverse logarithmic 1 / h = C K Ln (τ) ( n- type of conductivity) when the stage of transfer of metal ions is slower.

2.1.2 Description of the installation and the procedure for conducting experiments

The kinetics of iron oxidation is studied using the gravimetric method, which makes it possible to record the change in the mass of the sample with time during the experiment. The installation diagram is shown in Figure 1.

Figure 1 - Schematic of the experimental setup:

1 - investigated iron sample; 2 - electric resistance furnace; 3 - mechanoelectric converter Э 2D1; 4 - personal computer with ADC board.

A metal sample (1), suspended on a nichrome chain to the beam of a mechanoelectric converter E 2D1 (3), is placed in a vertical tubular electric resistance furnace (2). The output signal E 2D1, proportional to the change in the sample mass, is fed to the ADC board of the computer as part of the installation. The constancy of the temperature in the furnace is maintained by an automatic regulator, the required temperature of the experiment is set by the appropriate dial on the dashboard of the furnace as instructed by the teacher (800 - 900 ° C).

Based on the results of the work, the rate constant of the oxidation reaction of iron and the diffusion coefficient of its ions in the oxide film and, if possible, the activation energies of the chemical reaction and diffusion are determined. Graphically illustrate the dependence of the change in the mass of the sample and the rate of the oxidation process on time.

2.1.3 Processing and presentation of measurement results

The mechanical-electric transducer is designed in such a way that part of the mass of the measured object is compensated by a spiral spring. Its magnitude is unknown, but it must remain constant during measurements. As follows from the description of the measurement technique, the exact time (0) of the beginning of the oxidation process is not known, since it is not known when the sample will acquire a temperature sufficient for the development of the oxidation process. Until the moment in time when the sample actually begins to oxidize, its mass is equal to the mass of the parent metal ( m 0). The fact that we do not measure the entire mass, but only its uncompensated part, does not change the essence of the matter. The difference between the current mass of the sample ( m) and the initial mass of metal represents the mass of scale, therefore, formula (13.4) for real experimental conditions should be presented in the form:

(13.6)

in which m- the measured value of the remaining uncompensated part of the sample mass, m 0- the same before the beginning of the oxidation process at a low temperature of the sample. It can be seen from this relationship that the experimental dependence of the sample mass on time should be described by an equation of the form:

, (13.7)

whose coefficients, according to the obtained measurement results, can be found by the least squares method. This is illustrated by a typical graph in Fig. The points are the measurement results, the line is obtained by approximating the data by equation 13.7

Points marked with crosses are outliers and should not be taken into account when calculating the coefficients of Equation 13.7 using the least squares method.

Comparing formulas (13.6) and (13.7), it is easy to relate the found coefficients with their determining physicochemical values:

(13.8)

In the given example, the value of m0 - the value on the ordinate at = 0, turned out to be 18.1 mg.

Using these values, the sample area values ​​obtained in preparation for the experiment ( S) and the density of wustite borrowed from the literature (= 5.7 g / cm 3) can be

to estimate and the ratio of the diffusion coefficient and the rate constant of the oxidation process:

(13.13)

This ratio characterizes the thickness of the scale film at which the diffusion rate constant is equal to the rate constant of the chemical reaction of metal oxidation, which corresponds to the definition of a strictly mixed reaction mode.

Based on the results of the work, all values ​​should be determined using the formulas (13.7, 13.11 - 13.13): b 0 , b 1 , b 2 , m 0, 0 and D /K... To illustrate the results, you should give a graph of dependence m-. Along with the experimental values, it is desirable to give an approximating curve.

Based on the measurement results, the following table must be filled in:

Table 1. Results of the study of the process of iron oxidation.

In the table, the first two columns are filled after the data file is opened, and the rest are calculated. Smoothing is performed at 5 points. When determining the coefficients of the approximating polynomial, the first, third and fourth columns are used simultaneously. The last column should contain the results of the approximation by the polynomial (13.7) using the coefficients found by the least squares method. The graph is built according to the first, third and fifth columns.

If the work is performed by several students, then each of them conducts the experiment at its own temperature. Joint processing of the results of estimating the thickness of the scale layer in a strictly mixed mode () makes it possible to estimate the difference between the activation energies of diffusion and chemical reaction. Indeed, the obvious formula is valid here:

(13.14)

Similar processing of coefficients b 2 makes it possible to estimate the activation energy of diffusion. Here the formula is valid:

(13.15)

If the measurements were carried out at two temperatures, then the estimates are carried out directly according to formulas (13.4) and (13.15), if the temperature values ​​are more than two, the method of least squares should be applied for the functions ln () – 1/T and ln (b 2) – 1/T. The resulting values ​​are given in the summary table and discussed in the conclusions.

The order of processing the results of work

2. Build a dependency graph on a separate sheet m-, visually identify and remove pop-up values.

3. Smooth out the measured weight values.

4. Calculate the squares of mass change

5. Find the coefficients by the least squares method b 0 , b 1 , b 2 equations approximating the dependence of the change in mass over time.

6. Calculate the mass estimate at the beginning of measurements in accordance with the approximating equation

7. Analyze the results of approximation using sorting and exclude incorrect values

8. Display the results of the approximation on the graph of dependence m – .

9. Calculate the characteristics of the system and process: m 0 , 0 , D /K .

Test results:

a. In cell "A1" - the surface area of ​​the sample, in the adjacent cell "B1" units of measurement;

b. In cell "A2" - the mass of the original sample, in cell "B2" - units of measurement;

c. In cell "A3" - the temperature of the experiment, in cell "B3" - units of measurement;

d. In cell "A4" - the thickness of the scale layer in a strictly mixed mode, in cell "B4" - units of measurement;

e. Starting with cell "A10", conclusions on the work should be clearly formulated.

In cells A6-A7 there should be references to cells on other sheets of the spreadsheet book on which calculations were performed to obtain the presented result, and not the numerical values ​​themselves! If this requirement is not met, the verification program displays the message "Information presentation error".

2. Correctly formatted dependence graph m- obtained experimentally (points) and approximated by a polynomial (line), on a separate sheet of spreadsheets with all the necessary signatures and designations.

Control questions

1. What is the structure of the scale obtained on iron during its high-temperature oxidation in air?

2. Why does the appearance of the wustite phase in the scale lead to a sharp increase in the rate of iron oxidation?

3. What are the stages of the heterogeneous iron oxidation process?

4. What is the difference between the diffusion mode of iron oxidation and the kinetic one?

5. What are the order and methodology of the work?

6. How to identify the mode of the oxidation process?

2.2 Study of the temperature dependence of the specific electrical conductivity of oxide melts (Work No. 14)

2.2.1 General information about the nature of electrical conductivity of slags

The study of the dependence of the electrical conductivity of slags on their composition and temperature is of great importance for metallurgy both in theoretical and applied terms. The value of electrical conductivity can have a significant effect on the rate of the most important reactions between metal and slag in steel production processes, on the productivity of metallurgical units, especially in electroslag technologies or arc furnaces for smelting synthetic slag, where the rate of heat release depends on the amount of electric current passed through the melt. In addition, electrical conductivity, being a structurally sensitive property, provides indirect information about the structure of melts, concentration and type of charged particles.

According to the concepts of the structure of oxide melts, formulated, in particular, by the scientific school of Professor O. A. Esin, uncharged particles cannot be present in them. At the same time, the ions in the melt differ greatly in size and structure. Basic oxide elements are present as simple ions, for example, Na +, Ca 2+, Mg 2+, Fe 2+, O 2-. On the contrary, elements with high valence, which form acidic (acidic) oxides, such as SiO 2, TiO 2, B 2 O 3, in the form of an ion have such a high electrostatic field that they cannot be in the melt as simple Si 4+ ions, Ti 4+, B 3+. They approach oxygen anions so much that they form covalent bonds with them and are present in the melt in the form of complex anions, the simplest of which are, for example, SiO 4 4, TiO 4 4-, BO 3 3-, BO 4 5-. Complex anions have the ability to complicate their structure, uniting in two- and three-dimensional structures. For example, two silicon-oxygen tetrahedra (SiO 4 4-) can be connected at the vertices, forming the simplest linear chain (Si 2 O 7 6-). This releases one oxygen ion:

SiO44- + SiO44- = Si2O76- + O2-.

In more detail, these questions can be found, for example, in the educational literature.

Electrical resistance R conventional linear conductors can be determined from the ratio

where is the resistivity, L- length, S Is the cross-sectional area of ​​the conductor. The quantity is called the specific electrical conductivity of the substance. From formula (14.1) it follows that

The unit of electrical conductivity is expressed in Ohm –1 m –1 = S / m (S - siemens). Specific electrical conductivity characterizes the electrical conductivity of the volume of the melt enclosed between two parallel electrodes having an area of ​​1 m 2 and located at a distance of 1 m from each other.

In a more general case (inhomogeneous electric field), electrical conductivity is defined as the coefficient of proportionality between the current density i in a conductor and an electric potential gradient:

The appearance of electrical conductivity is associated with the transfer of charges in a substance under the action of an electric field. In metals, electrons of the conduction band participate in the transfer of electricity, the concentration of which is practically independent of temperature. With an increase in temperature, there is a decrease in the specific electrical conductivity of metals, because the concentration of "free" electrons remains constant, and the decelerating effect of the thermal motion of the ions of the crystal lattice on them increases.

In semiconductors, the carriers of electric charge are quasi-free electrons in the conduction band or vacancies in the valence energy band (electron holes), arising due to thermally activated transitions of electrons from donor levels to the conduction band of the semiconductor. As the temperature rises, the probability of such activated transitions increases; accordingly, the concentration of electric current carriers and specific electrical conductivity increase.

In electrolytes, which also include oxide melts, ions, as a rule, participate in the transfer of electricity: Na +, Ca 2+, Mg 2+, SiO 4 4–, BO 2 - and others. Each of the ions ј -th grade can contribute to the total value of the electric current density in accordance with the known relation

where is the partial specific electrical conductivity; D ј , C ј , z ј- diffusion coefficient, concentration and charge of the ion ј -th grade; F- Faraday constant; T- temperature; R

Obviously, the sum of the quantities i ј is equal to the total current density i associated with the movement of all ions, and the conductivity of the entire melt is the sum of the partial conductivities.

The movement of ions in electrolytes is an activation process. This means that under the action of an electric field, not all ions move, but only the most active of them, possessing a certain excess of energy in comparison with the average level. This excess energy, called the activation energy of electrical conductivity, is necessary to overcome the forces of interaction of a given ion with the environment, as well as to form a vacancy (cavity) into which it passes. The number of active particles, in accordance with Boltzmann's law, increases with

increase in temperature exponentially. That's why ... Follow-

therefore, in accordance with (14.5), the temperature dependence of the specific electrical conductivity should be described by the sum of exponentials. It is known, however, that with an increase in the size of particles, their activation energy also increases significantly. Therefore, in relation (14.5), as a rule, the contribution of large low-mobile ions is neglected, and for the rest, partial values ​​are averaged.

As a result, the temperature dependence of the specific electrical conductivity of oxide melts takes the following form:

(14.6)

which is in good agreement with experimental data.

Typical values ​​for metallurgical slags containing oxides CaO, SiO 2, MgO, Al 2 O 3 are in the range 0.1 - 1.0 S cm –1 near the liquidus temperature, which is much lower than the electrical conductivity of liquid metals (10 5 –10 7 S cm –1). The activation energy of electrical conductivity is almost independent of the temperature in the basic slags, but it can slightly decrease with an increase in temperature in acidic melts, due to their depolymerization. Typically, the value lies in the range 40–200 kJ / mol, depending on the composition of the melt.

At elevated contents (over 10%) of iron oxides (FeO, Fe 2 O 3) or other oxides of transition metals (for example, MnO, V 2 O 3, Cr 2 O 3), the character of the electrical conductivity of the slags changes, since in addition to the ionic conductivity in them a significant fraction of electronic conductivity appears. The electronic component of conductivity in such melts is due to the movement of electrons or electron "holes" according to the relay mechanism from a transition metal cation with a lower valence to a cation with a higher valence through R-orbitals of the oxygen ion located between these particles.

The very high mobility of electrons in the combinations Ме 2+ - O 2– - Me 3+, despite their relatively low concentration, sharply increases the electrical conductivity of the slags. So the maximum value of æ for purely iron melts FeO - Fe 2 O 3 can be

10 2 S · cm –1, while remaining, nevertheless, much less metals.

2.2.2 Description of the installation and measurement procedure

In this work, the specific electrical conductivity of molten sodium tetraborate Na 2 O 2B 2 O 3 is determined in the temperature range 700 - 800 ° C. To eliminate the complications associated with the presence of the resistance of the metal - electrolyte interface, the study of electrical conductivity must be carried out under conditions when the resistance of the interface is negligible. This can be achieved by using a sufficiently high frequency (≈ 10 kHz) alternating current instead of direct current.

The electrical circuit diagram of the installation is shown in Figure 2.

Figure 2 Electric circuit diagram of the installation for measuring the electrical conductivity of slags:

ЗГ - sound frequency generator; PC - a personal computer with a sound card; Yach solution and Yach slag - electrochemical cells containing an aqueous solution of KCl or slag, respectively; R et - reference resistance of a known value.

An alternating current from an audio frequency generator is supplied to a cell containing slag and a reference resistance of a known value connected in series with it. The PC sound card measures the voltage drop across the cell and the reference resistance. Since the current flowing through R et and Yach is the same

(14.7)

The laboratory installation service program calculates, displays on the monitor screen and writes to the file the value of the ratio ( r) amplitude values ​​of alternating current at the output of the sound generator ( U hg) and on the measuring cell ( U bar):

Knowing it, you can determine the resistance of the cell

where is the cell constant.

For determining K cell in the experimental setup, an auxiliary cell is used, similar to the one investigated in terms of geometric parameters. Both electrochemical cells are corundum boats with electrolyte. In them, two cylindrical metal electrodes of the same cross-section and length, located at the same distance from each other, are omitted to ensure a constant ratio (L / S) eff.

The investigated cell contains a Na 2 O 2B 2 O 3 melt and is placed in a heating furnace at a temperature of 700 - 800 ° C. The auxiliary cell is at room temperature and is filled with a 0.1 N aqueous solution of KCl, the electrical conductivity of which is 0.0112 S cm –1. Knowing the conductivity of the solution and determining (see formula 14.9) the electrical resistance

auxiliary cell (

2.2.3 Work order

A. Operation using a real-time measuring system

Before starting measurements, the furnace must be preheated to a temperature of 850 ° C. The order of work on the installation is as follows:

1. After performing the initialization procedure in accordance with the instructions on the monitor screen, turn off the oven, put the "1 - reference resistance" switch in the "1 - Hi" position and follow the further instructions.

2. After the indication "Switch 2 - to the" solution "position appears, execute it and until the indication" Switch 2 - to the "MELT" position appears, record the resistance ratio values ​​that appear every 5 seconds.

3. Follow the second instruction and watch the temperature change. As soon as the temperature becomes less than 800 ° С, the command from the keyboard "Xs" should turn on the graph output and every 5 seconds record the temperature values ​​and resistance ratios.

4. After the melt has cooled to a temperature below 650 ° C, measurements should be initialized for a second student performing work on this installation. Switch "1 - reference resistance" to the position "2 - Lo" and from this moment the second student starts recording temperature values ​​and resistance ratios every 5 seconds.

5. When the melt is cooled to a temperature of 500 ° C or the value of the resistance ratio is close to 6, the measurements should be stopped by sending the “Xe” command from the keyboard. From this moment on, the second student must move switch 2 to the ‘solution’ position and write down ten values ​​of the resistance ratio.

B. Working with data previously written to a file

After activating the program, a message about the value of the reference resistance appears on the screen and several values ​​of the resistance ratio ( r) of the calibration cell. After averaging, this data will allow you to find the setting constant.

Subsequently, every few seconds, the temperature and resistance ratios for the measuring cell appear on the screen. This information is displayed on the graph.

The program automatically terminates the work and sends all the results to the teacher's PC.

2.2.4 Processing and presentation of measurement results

Based on the measurement results, fill in the table with the following heading:

Table 1. Temperature dependence of the electrical conductivity of the Na 2 O · 2B 2 O 3 melt

In the table, the first two columns are filled after the data file is opened, and the rest are calculated. They should be used to plot the dependence ln () - 10 3 / T and using the least squares method (the LINEST function in OpenOffice.Calc) to determine the value of the activation energy. The graph should show the approximating straight line. You should also build a graph of conductivity versus temperature. The order of processing the results

1. Enter records of measurement results into a spreadsheet file.

2. Calculate the average value of the resistance ratio for the calibration cell.

3. Calculate the setting constant.

4. Build a dependency graph r – t, visually identify and remove pop-up values. If there are a lot of them, apply sorting.

5. Calculate the resistance of the measuring cell, the conductivity of the oxide melt at different temperatures, the logarithm of the conductivity and the inverse absolute temperature

b 0 , b 1 of the equation approximating the dependence of the logarithm of electrical conductivity on the reciprocal temperature, and calculate the activation energy.

7. Construct a graph of the dependence of the logarithm of electrical conductivity on the reciprocal temperature on a separate sheet and give an approximating dependence Test results:

1. In a spreadsheet book submitted for review, the following information should be provided on the first page titled "Results":

a. In cell "A1" - initial temperature, in cell "B1" - units of measurement;

c. In cell "A3" - the activation energy of electrical conductivity, in cell "B3" - units of measurement;

d. In cell "A4" - the preexponential factor in the formula for the temperature dependence of electrical conductivity, in cell "B4" - units of measurement;

e. Starting with cell "A5", conclusions on the work should be clearly formulated.

In cells A1-A4 there should be references to cells on other sheets of the spreadsheet book on which calculations were performed to obtain the presented result, and not the numerical values ​​themselves! If this requirement is not met, the verification program displays the message "Information presentation error".

2. Correctly designed graph of the dependence of the logarithm of electrical conductivity on the reciprocal temperature, obtained from experimental data (points) and approximated by a polynomial (line), on a separate sheet of spreadsheets with all the necessary signatures and designations.

Control questions

1. What is called electrical conductivity?

2. What particles determine the electrical conductivity of slags?

3. What is the nature of the temperature dependence of the electrical conductivity of metals and oxide melts?

4. What determines the cell constant and how to determine it?

5. Why do you need to use alternating current for determination?

6. How does the activation energy of electrical conductivity depend on temperature?

7. What sensors and devices are used in the laboratory installation. What physical quantities do they allow to register?

8. What graphs (in what coordinates) should be presented based on the results of the work?

9. What physical and chemical values ​​should be obtained after processing the primary data?

10. Decide what measurements are carried out before the experiment, what values ​​are recorded in the course of the experiment, what data refer to the primary information, what processing it undergoes and what information is obtained in this case.

2.3 Study of the kinetics of metal desulfurization by slag on a simulation model (Work No. 15)

2.3.1 General information on the kinetics of metal desulfurization by slag

Sulfur impurities in steel, in amounts exceeding 0.005 wt. %, significantly reduce its mechanical, electrical, anti-corrosion and other properties, worsen the weldability of the metal, lead to the appearance of red and cold brittleness. Therefore, the process of desulfurization of steel, especially efficiently proceeding with slag, is of great importance for high-quality metallurgy.

The study of the kinetic laws of the reaction, the identification of its mechanism and mode of flow is necessary for effective control of the rate of desulfurization, since in the real conditions of metallurgical units, the equilibrium distribution of sulfur between the metal and the slag is usually not achieved.

Unlike most other impurities in steel, the transition of sulfur from metal to slag is a reduction process, not oxidative 1. [S] + 2e = (S 2–).

This means that for the continuous flow of the cathodic process, leading to the accumulation of positive charges on the metal, a simultaneous transition of other particles is necessary, capable of donating electrons to the metal phase. Such concomitant anodic processes can be the oxidation of oxygen anions of the slag or particles of iron, carbon, manganese, silicon and other metal impurities, depending on the composition of the steel.

2. (O 2–) = [O] + 2e,

3. = (Fe 2+) + 2e,

4. [C] + (O 2–) = CO + 2e, 5. = (Mn 2+) + 2e.

Taken together, the cathodic and any one anodic process makes it possible to write the stoichiometric equation of the desulfurization reaction in the following form, for example:

1-2. (CaO) + [S] = (CaS) + [O], H = -240 kJ / mol

1-3. + [S] + (CaO) = (FeO) + (CaS). H = -485 kJ / mol

The corresponding expressions for the equilibrium constants are

(15.1)

Obviously, selected processes and the like can occur simultaneously. From relation (15.1) it follows that the degree of desulfurization of the metal at a constant temperature, i.e. constant value of the equilibrium constant, increases with an increase in the concentration of free oxygen ion (O 2-) in the oxide melt. Indeed, the growth of the factor in the denominator must be compensated for by the decrease in another factor in order to correspond to the unchanged value of the equilibrium constant. Note that the content of free oxygen ions increases with the use of highly basic, calcium oxide-rich slags. Analyzing relation (15.2), we can conclude that the content of iron ions (Fe 2+) in the oxide melt should be minimal, i.e. slags should contain a minimum amount of iron oxides. The presence of deoxidizers (Mn, Si, Al, C) in the metal also increases the completeness of desulfurization of steel due to a decrease in the content of (Fe 2+) and [O].

Reaction 1-2 is accompanied by heat absorption (∆H> 0), therefore, as the process proceeds, the temperature in the metallurgical unit will decrease. On the contrary, reaction 1-3 is accompanied by the release of heat (∆H<0) и, если она имеет определяющее значение, температура в агрегате будет повышаться.

In the kinetic description of desulfurization, the following process steps should be considered:

Delivery of sulfur particles from the bulk of the metal to the interface with the slag, which is realized first by convective diffusion, and immediately near the metal-slag interface - by molecular diffusion; the electrochemical act of the addition of electrons to sulfur atoms and the formation of S 2– anions; which is an adsorption-chemical act, removal of sulfur anions into the slag volume, due to molecular and then convective diffusion.

Similar stages are characteristic of the anodic stages, with the participation of Fe, Mn, Si atoms or O 2– anions. Each of the stages contributes to the overall resistance of the desulfurization process. The driving force of the flow of particles through a number of specified resistances is the difference of their electrochemical potentials in a nonequilibrium metal-slag system or the difference in the actual and equilibrium electrode potentials at the interface, which is proportional to it, called overvoltage .

The speed of a process consisting of a number of successive stages is determined by the contribution of the stage with the greatest resistance - limiting stage. Depending on the mechanism of the rate-limiting stage, one speaks of a diffusion or kinetic mode of the reaction. If the stages with different flow mechanisms have comparable resistances, then they speak of a mixed reaction mode. The resistance of each stage depends significantly on the nature and properties of the system, the concentration of reagents, the intensity of phase mixing, and temperature. So, for example, the rate of the electrochemical act of sulfur reduction is determined by the value of the exchange current

(15.3)

where V- temperature function, C[S] and C(S 2–) - sulfur concentration in metal and slag, α - transfer coefficient.

The rate of the stage of delivery of sulfur to the phase boundary is determined by the limiting diffusion current of these particles

where D[S] is the diffusion coefficient of sulfur, β is the convective constant determined by the intensity of convection in the melt, it is proportional to the square root of the linear velocity of convective flows in the liquid.

The available experimental data indicate that under normal conditions of convection of melts, the electrochemical act of the discharge of sulfur ions proceeds relatively quickly, i.e. Desulfurization is inhibited mainly by the diffusion of particles in the metal or slag. However, with an increase in the concentration of sulfur in the metal, diffusion difficulties decrease and the process mode can change to kinetic. This is also facilitated by the addition of carbon to iron, because the discharge of oxygen ions at the carbonaceous metal - slag interface occurs with significant kinetic inhibition.

It should be borne in mind that the electrochemical concept of the interaction of metals with electrolytes makes it possible to clarify the mechanism of the processes, to understand in detail the phenomena occurring. At the same time, simple equations of formal kinetics fully retain their validity. In particular, for a rough analysis of the experimental results obtained with significant errors, the equation for the reaction rate 1-3 can be written in the simplest form:

where k f and k r - rate constants of the forward and reverse reaction. This ratio is fulfilled if solutions of sulfur in iron and calcium sulfide and wustite in slag can be considered infinitely dilute and the reaction orders for these reagents are close to unity. The contents of the remaining reagents of the considered reaction are so high that all the interaction time remains practically constant and their concentrations can be included in the constants k f and k r

On the other hand, if the desulfurization process is far from equilibrium, then the rate of the reverse reaction can be neglected. Then the rate of desulfurization should be proportional to the concentration of sulfur in the metal. This version of the description of experimental data can be verified by examining the relationship between the logarithm of the desulfurization rate and the logarithm of the sulfur concentration in the metal. If this relationship is linear, and the slope of the dependence should be close to unity, then this is an argument in favor of the diffusion mode of the process.

2.3.2 Mathematical model of the process

The possibility of several anodic stages greatly complicates the mathematical description of the desulfurization processes of steel containing many impurities. In this regard, some simplifications have been introduced into the model, in particular, the kinetic

For the half-reactions of the transition of iron and oxygen, in connection with the adopted limitation on diffusion control, the ratios look much simpler:

(15.7)

In accordance with the condition of electroneutrality in the absence of current from an external source, the relationship between currents for individual electrode half-reactions is expressed by a simple relationship:

Differences in electrode overvoltages () are determined by the ratios of the corresponding products of activities and equilibrium constants for reactions 1-2 and 1-3:

The time derivative of the sulfur concentration in the metal is determined by the current of the first electrode half-reaction in accordance with the equation:

(15.12)

Here i 1 , i 2 - current density of electrode processes, η 1, η 2 - their polarization, i n - limiting particle diffusion currents ј -that varieties, i o is the exchange current of the kinetic stage, C[s] is the concentration of sulfur in the metal, α is the transfer coefficient, P, K p is the product of activities and the equilibrium constant of the desulfurization reaction, S- the area of ​​the metal-slag interface, V Me is the volume of the metal, T- temperature, F- Faraday constant, R Is a universal gas constant.

In accordance with the laws of electrochemical kinetics, expression (15.6) takes into account the inhibition of the diffusion of iron ions in the slag, since, judging by the experimental data, the stage of discharge-ionization of these particles is not limiting. Expression (15.5) is the retardation of the diffusion of sulfur particles in the slag and metal, as well as the retardation of the ionization of sulfur at the interface.

Combining expressions (15.6 - 15.12), it is possible by numerical methods to obtain the dependence of the sulfur concentration in the metal on time for the selected conditions.

The following parameters were used in the model:

3)
Sulfur ion exchange current:

4) The equilibrium constant of the desulfurization reaction ( TO R):

5) The ratio of the area of ​​the interface to the volume of the metal

7) Convective constant (β):

The model makes it possible to analyze the influence of the listed factors on the rate and completeness of desulfurization, as well as to estimate the contribution of diffusion and kinetic inhibitions to the total resistance of the process.

2.3.3 Work procedure

The image generated by the simulation program is shown in Fig. ... In the upper part of the panel, selected numerical values ​​of the measured values ​​are shown, the graph shows all the values ​​obtained during the process simulation. In the designations of the components of metal and slag melts, additional signs adopted in the literature on metallurgical topics are used. Square brackets denote the belonging of the component to the metal melt, and the round brackets - to the slag. Component symbols are used only for plotting and should not be taken into account when interpreting values. During the operation of the model, at any given moment, only the value of one of the measured values ​​is displayed. After 6 seconds, it disappears and the next value appears. During this period of time, it is necessary to have time to write down the next value. To save time, it is recommended not to write fixed numbers, for example, the leading unit in the temperature value.

Five minutes after the start of measurements by the clock in the upper right corner of the setup panel, by simultaneously pressing the and [No.] keys, where No. is the setup number, intensify the phase stirring speed.

2.3.4 Processing and presentation of measurement results

The table of measurement results generated by the simulation program should be supplemented with the following calculated columns:

Table 1. Results of statistical processing of experimental data

In the table in the first column, calculate the time since the start of the process in minutes.

Further processing is performed after graphical construction - at the first stage of processing, a graph of temperature versus time should be plotted and the range of data should be estimated when the transition of sulfur is accompanied mainly by the transition of iron. In this range, two areas with the same mixing speeds are distinguished and the coefficients of the approximating polynomials are found using the least squares method:

which follows from equation (15.5) under the specified conditions. Comparing the obtained values ​​of the coefficients, conclusions are drawn about the mode of the process and the degree of approach of the system to the state of equilibrium. Note that there is no intercept in equation (15.13).

To illustrate the results of the experiment, graphs of the dependence of the sulfur concentration on time and the rate of desulfurization on the concentration of calcium sulfide in the slag are plotted.

The order of processing the results

2. Calculate the rate of the desulfurization process from the concentration of sulfur in the metal, the logarithms of the rate and the concentration of sulfur.

3. Plot on separate sheets the graphs of the temperature in the unit versus time, the mass of slag versus time, the desulfurization rate and time, and the logarithm of the desulfurization rate versus the logarithm of the sulfur concentration.

4. Using the least squares method, estimate separately for different mixing rates the kinetic characteristics of the desulfurization process in accordance with the equation () and the order of the reaction in terms of sulfur concentration.

Test results:

1. Correctly designed graphs of the dependence of the speed of the desulfurization process and the logarithm of this value on time, on a separate sheet of spreadsheets with all the necessary signatures.

2. Values ​​of the kinetic characteristics of the desulfurization process in all variants of the process, indicating the dimensions (and errors).

3. Conclusions on the work.

Control questions

1. What conditions are necessary for the most complete desulfurization of metal with slag?

2. What anodic processes can accompany sulfur removal?

3. What are the stages of the process of transition of sulfur across the interface?

4. In what cases is the diffusion or kinetic desulfurization mode implemented?

5. What is the order of the work?

2.4 Thermographic study of the processes of dissociation of natural carbonates (Work No. 16)

2.4.1 General laws of carbonate dissociation

A thermogram is the time dependence of the temperature of a sample. The thermographic method for studying the processes of thermal decomposition of substances became widespread after the characteristic features of such dependences were discovered: "temperature stops" and "inclined temperature areas".

1.4

Figure 3. Thermogram illustration:

dashed line - thermogram of a hypothetical reference sample in which dissociation does not occur; the solid line is a real sample with two-stage dissociation.

These are characteristic sections of the dependence, within which for some time () the temperature either remains constant (T = const), or increases by a small amount (T) at a constant rate (T /). Using numerical or graphical differentiation, it is possible to determine with good accuracy the moments of time and temperatures of the beginning and end of the temperature stop.

In the proposed laboratory work, such a dependence is obtained by continuous heating of natural calcite material, the main component of which is calcium carbonate. A rock consisting mainly of calcite is called limestone. Limestone is used in large quantities in metallurgy.

As a result of calcination (heat treatment) of limestone by an endothermic reaction

CaCO 3 = CaO + CO 2

get lime (CaO) - a necessary component of the slag melt. The process is carried out at temperatures below the melting point of both limestone and lime. It is known that carbonates and the oxides formed from them are mutually practically insoluble; therefore, the reaction product is a new solid phase and gas. The expression for the equilibrium constant, in the general case, has the form:

Here a- activity of solid reagents, - partial pressure of the gaseous reaction product. In metallurgy, another rock called dolomite is also widely used. It mainly consists of a mineral of the same name, which is a double salt of carbonic acid CaMg (CO 3) 2.

Calcite, like any natural mineral, along with the main component, contains a variety of impurities, the amount and composition of which depends on the deposit of natural minerals and even on a specific mining site. The variety of impurity compounds is so great that it is necessary to classify them according to some essential characteristic in this or that case. For thermodynamic analysis, an essential feature is the ability of impurities to form solutions with reagents. We will assume that there are no impurities in the mineral that, in the studied range of conditions (pressure and temperature), enter into any chemical reactions with each other or with the main component or product of its decay. In practice, this condition is not completely fulfilled, since, for example, carbonates of other metals may be present in calcite, but from the point of view of further analysis, taking these reactions into account will not provide new information, but will unnecessarily complicate the analysis.

All other impurities can be divided into three groups:

1. Impurities forming a solution with calcium carbonate. Such impurities, of course, must be taken into account in thermodynamic analysis and, most likely, in the kinetic analysis of the process.

2. Impurities dissolving in the reaction product - oxide. The solution to the question of taking this type of impurities into account depends on how quickly they dissolve in the solid reaction product and the closely related issue of the dispersion of inclusions of this type of impurities. If the inclusions are relatively large in size, and their dissolution occurs slowly, then they should not be taken into account in thermodynamic analysis.

3. Impurities insoluble in the original carbonate and its decomposition product. These impurities should not be taken into account in thermodynamic analysis, as if they did not exist at all. In some cases, they can influence the kinetics of the process.

In the simplest (rough) version of the analysis, it is permissible to combine all impurities of the same type and consider them as some generalized component. On this basis, we distinguish three components: B1, B2 and B3. The gas phase of the considered thermodynamic system should also be discussed. In laboratory work, the dissociation process is carried out in an open installation that communicates with the atmosphere of the room. In this case, the total pressure in the thermodynamic system is constant and equal to one atmosphere, and in the gaseous phase there is a gaseous reaction product - carbon dioxide (CO2) and air components, in simplified terms - oxygen and nitrogen. The latter do not interact with the rest of the components of the system; therefore, in the case under consideration, oxygen and nitrogen are indistinguishable and in what follows we will call them the neutral gaseous component B.

Temperature stops and sites have a thermodynamic explanation. With a known composition of the phases, the stopping temperature can be predicted by thermodynamic methods. The inverse problem can also be solved - by the known temperatures, the composition of the phases can be determined. It is provided for in this study.

Temperature stops and platforms can only be implemented if certain requirements for the kinetics of the process are met. It is natural to expect that these are requirements for practically equilibrium phase compositions at the site of the reaction and negligible gradients in the diffusion layers. Compliance with such conditions is possible if the rate of the process is controlled not by internal factors (diffusion resistance and resistance of the chemical reaction itself), but by external factors - by the rate of heat supply to the reaction site. In addition to the basic modes of a heterogeneous reaction defined in physical chemistry: kinetic and diffusion, this process is called thermal.

Note that the thermal regime of the solid-phase dissociation process turns out to be possible due to the peculiarity of the reaction, which requires the supply of a large amount of heat, and at the same time there are no stages of supplying the initial substances to the reaction site (since decomposition of one substance occurs) and removal of the solid reaction product from the boundary phase separation (since this boundary moves). There remain only two stages associated with diffusion: removal of CO2 through the gas phase (obviously with very low resistance) and diffusion of CO2 through the oxide, which is greatly facilitated by cracking of the oxide filling the volume previously occupied by volatilized carbon monoxide.

Consider a thermodynamic system at temperatures below the temperature stop. First, let us assume that there are no impurities of the first and second types in the carbonate. We will take into account the possible presence of an impurity of the third type, but only in order to show that this can not be done. Let us assume that a sample of the investigated powder calcite is composed of identical spherical particles with a radius r 0. We draw the boundary of the thermodynamic system at a certain distance from the surface of one of the calcite particles, which is small compared to its radius, and thus we include a certain volume of the gas phase in the system.

The system under consideration contains 5 substances: CaO, CaCO3, B3, CO2, B, and some of them participate in one reaction. These substances are distributed into four phases: CaO, CaCO3, B3, the gas phase, each of which is characterized by its inherent values ​​of various properties and is separated from other phases by a visible (at least under a microscope) interface. The fact that the B3 phase is represented, most likely, by a multitude of dispersed particles will not change the analysis - all particles are practically identical in properties and can be considered as one phase. The external pressure is constant, so there is only one external variable - temperature. Thus, all terms for calculating the number of degrees of freedom ( with) are defined: with = (5 – 1) + 1 – 4 = 1.

The obtained value means that when the temperature (one parameter) changes, the system will move from one equilibrium state to another, and the number and nature of the phases will not change. The parameters of the state of the system will change: temperature and equilibrium pressure of carbon dioxide and neutral gas B ( T , P CO2 , P B).

Strictly speaking, what has been said is true not for any temperatures below the temperature stop, but only for the interval when the reaction, which initially occurs in the kinetic regime, has passed into the thermal regime and one can really speak of the proximity of the parameters of the system to equilibrium ones. At lower temperatures, the system is not significantly equilibrium, but this is not reflected in the nature of the dependence of the sample temperature on time.

From the very beginning of the experiment - at room temperature the system is in a state of equilibrium, but only because there are no substances in it that could interact. This refers to calcium oxide, which under these conditions (the partial pressure of carbon dioxide in the atmosphere is about 310 –4 atm, the equilibrium pressure is 10 –23 atm) could carbonize. According to the isotherm equation for the reaction, written taking into account the expression for the equilibrium constant (16.1) at the activities of condensed substances equal to unity:

the change in the Gibbs energy is positive, which means that the reaction should proceed in the opposite direction, but this is impossible, since the system initially lacks calcium oxide.

With increasing temperature, the elasticity of dissociation (the equilibrium pressure of CO2 over carbonate) increases, as follows from the isobar equation:

since the thermal effect of the reaction is greater than zero.

Only at a temperature of about 520 C will the dissociation reaction become thermodynamically possible, but it will begin with a significant time delay (incubation period) necessary for the nucleation of the oxide phase. Initially, the reaction will proceed in the kinetic mode, but due to autocatalysis, the resistance of the kinetic stage will decrease quite quickly so that the reaction will go into a thermal mode. It is from this moment that the thermodynamic analysis given above becomes valid, and the temperature of the sample will begin to lag behind the temperature of the hypothetical reference sample, in which dissociation does not occur (see Figure 3).

The considered thermodynamic analysis will remain valid until the moment when the elasticity of dissociation reaches 1 atm. In this case, carbon dioxide is continuously released on the surface of the sample under a pressure of 1 atm. It displaces the air, and new portions come to replace it from the sample. The pressure of carbon dioxide cannot increase in excess of one atmosphere, since the gas freely escapes into the surrounding atmosphere.

The system is fundamentally changing, since there is no air in the gas phase around the sample and there is one less component in the system. The number of degrees of freedom in such a system with = (4 - 1) + 1 - 4 = 0

turns out to be equal to zero, and while maintaining equilibrium in it, no state parameters, including temperature, can change.

We now note that all conclusions (calculation of the number of degrees of freedom, etc.) remain valid if we do not take into account the component B3, which increases by one both the number of substances and the number of phases, which is mutually compensated.

A temperature stop sets in, when all the incoming heat is consumed only for the dissociation process. The system works as a very good temperature regulator, when a small accidental change in it leads to the opposite change in the dissociation rate, which returns the temperature to the previous value. The high quality of regulation is explained by the fact that such a system is practically inertial.

As the dissociation process develops, the reaction front shifts deeper into the sample, while the interaction surface decreases and the thickness of the solid reaction product increases, which complicates the diffusion of carbon dioxide from the reaction site to the sample surface. Starting from a certain point in time, the thermal regime of the process turns into a mixed one, and then into a diffusion one. Already in the mixed mode, the system will become significantly non-equilibrium and the conclusions obtained in thermodynamic analysis will lose their practical meaning.

Due to a decrease in the rate of the dissociation process, the required amount of heat will decrease so much that part of the incoming heat flux will again begin to be spent on heating the system. From this moment, the temperature stop will stop, although the dissociation process will still continue until the complete decomposition of the carbonate.

It is easy to guess that for the considered simplest case the value of the stopping temperature can be found from the equation

Thermodynamic calculation according to this equation using the TDHT database gives a temperature of 883 ° C for pure calcite, and 834 ° C for pure aragonite.

Now let's complicate the analysis. During the dissociation of calcite containing impurities of the 1st and 2nd types, when the activities of carbonate and oxide cannot be considered equal to unity, the corresponding condition becomes more complicated:

If we assume that the content of impurities is small and the resulting solutions can be considered as infinitely dilute, then the last equation can be written as:

where is the molar fraction of the corresponding impurity.

If an inclined temperature pad is obtained and both temperatures ( T 2 > T 1) above the stop temperature for pure calcium carbonate - K P (T 1)> 1 and K P (T 2)> 1, then it is reasonable to assume that impurities of the second type are absent, or do not have time to dissolve () and estimate the concentration of impurities of the 1st type at the beginning

and at the end of the temperature stop

An impurity of the first type should accumulate to some extent in the CaCO3 - B1 solution as the reaction front moves. In this case, the slope of the platform is expressed by the ratio:

where 1 is the proportion of component B1 returning to the original phase when it is isolated in pure form; V S- molar volume of calcite; v C- the rate of dissociation of carbonate; - the thermal effect of the dissociation reaction at the stop temperature; r 0 is the initial radius of the calcite particle.

Using reference data, this formula can be used to calculate v C- the speed of the solution

rhenium component B1 in calcite.

2.4.2 Installation diagram and work procedure

The work studies the dissociation of calcium carbonate and dolomite of various fractions.

The experimental setup is shown in Figure 4.

Figure 4 - Installation diagram for studying thermograms of carbonate dissociation:

1 - corundum tube, 2 - carbonate, 3 - thermocouple, 4 - furnace,

5 - autotransformer, 6 - personal computer with ADC board

A corundum tube (1) with a thermocouple (3) and a test sample of calcium carbonate (2) is installed in a furnace (4) preheated to 1200 K. A thermogram of the sample is observed on the monitor screen of a personal computer. After passing through the isothermal section, repeat the experiment with another carbonate fraction. When examining dolomite, heating is carried out until two temperature stops are detected.

The obtained thermograms are presented on the "temperature - time" graph. For ease of comparison, all thermograms should be shown on one graph. According to it, the temperature of the intensive development of the process is determined, and it is compared with that found from thermodynamic analysis. Conclusions are made about the influence of temperature, the nature of carbonate, the degree of its dispersion on the nature of the thermogram.

2.4.3 Processing and presentation of measurement results

Based on the results of the work, the following table should be filled in:

Table 1. Results of the study of the dissociation process of calcium carbonate (dolomite)

The first two columns are filled with values ​​when you open the data file, the last ones should be calculated. Smoothing is performed at five points, numerical differentiation of smoothed data is performed with additional smoothing, also at five points. Based on the results of the work, two separate dependency diagrams should be built: t- and d t/ d - t .

The obtained temperature stop value ( T s) should be compared with the characteristic value for pure calcite. If the observed value is higher, then it is possible to approximately estimate the minimum content of the first type of impurity according to equation (16.7), assuming that there are no second type impurities. If the opposite relationship is observed, then we can conclude that impurities of the second type have the main effect and estimate their minimum content provided that there are no impurities of the first type. Equation (16.6) implies that in the latter case

It is desirable to calculate the value of the equilibrium constant using the TDHT database according to the method described in the manual. In an extreme case, you can use an equation that approximates the dependence of the change in the Gibbs energy in the reaction of dissociation of calcium carbonate with temperature:

G 0 = B 0 + B 1 · T + B 2 T 2 ,

taking the values ​​of the coefficients equal: B 0 = 177820, J / mol; B 1 = -162.61, J / (mol K), B 3 = 0.00765, J · mol -1 · K -2.

Note ... If in the course "Physical Chemistry" students are not familiar with the TDHT database and did not perform the appropriate calculations in practical classes, then you should use the Shvartsman-Temkin equation and data from the reference book.

The order of processing the results

1. Enter the results of manual recording of information into a spreadsheet file.

2. Perform temperature smoothing.

3. Build a graph of temperature versus time on a separate sheet.

4. Perform time differentiation of temperature values ​​with 5-point smoothing.

5. Construct on a separate sheet a graph of the dependence of the derivative of temperature over time from temperature, determine the characteristics of the sites.

Test results:

1. In a spreadsheet book submitted for review, the following information should be provided on the first page titled "Results":

a. In cell "A1" - the value of the temperature stop (average for an inclined platform), in cell "B1" - units of measurement;

b. In cell "A2" - the duration of the temperature stop, in cell "B2" - units of measurement;

c. In cell "A3" - the slope of the platform, in cell "B3" - units of measurement;

d. In cell "A4" - the type of impurity or "0" if the presence of impurities was not detected;

e. In cell "A5" - the mole fraction of the impurity;

f. Starting with cell "A7", conclusions on the work should be clearly formulated.

In cells A1, A3 and A5, there should be references to cells on other sheets of the spreadsheet book on which calculations were performed to obtain the presented result, and not the numerical values ​​themselves! If this requirement is not met, the verification program displays the message "Information presentation error".

2. Correctly formatted graphs of temperature versus time dependences, temperature derivative versus time versus temperature and derivative temperature versus time on separate sheets of spreadsheets with all the necessary signatures and designations.

3. Values ​​of estimates of stop temperatures and their duration.

4. Conclusions on the work.

Control questions

1. What determines the temperature of the onset of carbonate dissociation in air?

2. Why does the elasticity of carbonite dissociation increase with increasing temperature?

3. What is the number of degrees of freedom of the system in which equilibrium has been established between the substances CaO, CO 2, CaCO 3?

4. How will the nature of the thermogram change if the dissociation product forms solid solutions with the original substance?

5. What regime of the heterogeneous reaction of dissociation of carbonates corresponds to the isothermal section of the thermogram?

6. How will the appearance of the thermogram change during the dissociation of polydispersed carbonate?

7. What is the difference between thermograms obtained at a total pressure of 101.3 kPa and 50 kPa?

2.5 Study of the temperature dependence of the viscosity of oxide melts (Work No. 17)

2.5.1 The nature of the viscous resistance of oxide melts

Viscosity is one of the most important physicochemical characteristics of slag melts. It has a significant effect on the diffusion mobility of ions, and hence on the kinetics of metal-slag interaction, the rate of heat and mass transfer processes in metallurgical units. The study of the temperature dependence of viscosity provides indirect information on structural transformations in oxide melts, changes in the parameters of complex anions. The composition, and hence the value of the viscosity, depends on the purpose of the slag. So, for example, to intensify the diffusion stages of the redox interaction of metal and slag (desulfurization, dephosphorization, etc.), the slag composition is selected so that its viscosity is low. On the contrary, in order to prevent the transfer of hydrogen or nitrogen into the steel through the slag, a slag with increased viscosity is introduced from the gas phase.

One of the quantitative characteristics of viscosity can be the coefficient of dynamic viscosity (η), which is defined as the coefficient of proportionality in Newton's law of internal friction

where F Is the force of internal friction between two adjacent layers of liquid, grad υ – speed gradient, S- the area of ​​the contact surface of the layers. Measurement unit of dynamic viscosity in SI: [η] = N · s / m 2 = Pa · s.

It is known that the flow of a liquid is a series of jumps of particles to an adjacent stable position. The process has an activation character. For the hopping to occur, the particle must have a sufficient supply of energy in comparison with its average value. Excess energy is required to break the chemical bonds of a moving particle and to form a vacancy (cavity) in the volume of the melt, into which it passes. With an increase in temperature, the average energy of particles increases and a larger number of them can participate in the flow, which leads to a decrease in viscosity. The number of such "active" particles grows with temperature according to the exponential Boltzmann distribution law. Accordingly, the dependence of the viscosity coefficient on temperature has an exponential form

where η 0 is a coefficient that depends little on temperature, Eη is the activation energy of viscous flow. It characterizes the minimum supply of kinetic energy of a mole of active particles capable of participating in the flow.

The structure of oxide melts has a significant effect on the viscosity coefficient. In contrast to the motion of ions under the action of an electric field, in a viscous flow, all particles of a liquid move in the direction of motion sequentially. The most inhibited stage is the motion of large particles, which make the largest contribution to the value of η. As a result, the activation energy of viscous flow turns out to be greater than that for electrical conductivity ( E η > E).

In acidic slags containing oxides Si, P, B, the concentration of large complex anions in the form of chains, rings, tetrahedra and other spatial structures (for example,

Etc.). The presence of large particles increases the viscosity of the melt, because moving them requires more energy than small ones.

The addition of basic oxides (CaO, MgO, MnO) leads to an increase in the concentration of simple cations (Ca 2+, Mg 2+, Mn 2+) in the melt. Introduced О 2– anions promote depolymerization of the melt; decomposition of complex anions, for example,

As a result, the viscosity of the slags decreases.

Depending on the temperature and composition, the viscosity of metallurgical slags can vary over a fairly wide range (0.01 - 1 Pa · s). These values ​​are orders of magnitude higher than the viscosity of liquid metals, which is due to the presence of relatively large flow units in the slags.

The reduced exponential dependence of η on T(17.2) describes well the experimental data for basic slags containing less than 35 mol. % SiO 2. In such melts, the activation energy of viscous flow Eη is constant and small (45 - 80 kJ / mol). As the temperature decreases, η changes, insignificantly, and begins to increase intensively only during solidification.

In acidic slags with a high concentration of complexing components, the activation energy can decrease with increasing temperature: E η = E 0 / T, which is caused by the downsizing of complex anions upon heating. In this case, the experimental data are linearized in coordinates « lnη - 1 / T 2 ".

2.5.2 Description of installation and method of measuring viscosity

A rotary viscometer is used to measure the viscosity index (Figure 5). The device and principle of operation of this device is as follows. The test liquid (2) is placed in a cylindrical crucible (1), into which the spindle (4), suspended on an elastic string (5), is immersed. During the experiment, the torque from the electric motor (9) is transferred to the disk (7), from it through the string to the spindle.

The viscosity of the oxide melt is judged by the twist angle of the string, which is determined by the scale (8). When the spindle rotates, the viscous resistance of the fluid creates a braking moment of forces that twists the string until the moment of elastic deformation of the string becomes equal to the moment of viscous resistance forces. In this case, the rotational speeds of the disk and the spindle will be the same. Corresponding to this state, the twist angle of the string (∆φ) can be measured by comparing the position of the arrow (10) relative to the scale: initial - before turning on the electric motor and steady - after turning on. Obviously, the angle of twist of the string ∆φ is the greater, the greater the viscosity of the liquid η. If the deformations of the string do not exceed the limiting ones (corresponding to the feasibility of Hooke's law), then the value of ∆φ is proportional to η and we can write:

Equation coefficient k, called the constant of the viscometer, depends on the dimensions of the crucible and the spindle, as well as on the elastic properties of the string. With a decrease in the diameter of the string, the sensitivity of the viscometer increases.

Figure 5 - Scheme of installation for measuring viscosity:

1 - crucible, 2 - investigated melt, 3 - spindle head,

4 - spindle, 5 - string, 6 - upper part of the installation, 7 - disc,

8 - scale, 9 - electric motor, 10 - arrow, 11 - oven, 12 - transformer,

13 - temperature control device, 14 - thermocouple.

To determine the constant of the viscometer k a liquid with a known viscosity is placed in the crucible - a solution of rosin in transformer oil. In this case, in an experiment at room temperature, ∆φ0 is determined. Then, knowing the viscosity (η0) of the reference fluid at a given temperature, calculate k according to the formula:

Found value k used to calculate the viscosity coefficient of the oxide melt.

2.5.3 Work procedure

To get acquainted with the viscosity properties of metallurgical slags in this laboratory work, the Na 2 O 2B 2 O 3 melt is studied. Measurements are carried out in the temperature range of 850–750 o C. After reaching the initial temperature (850 o C), the viscometer needle is set to zero. Then they turn on the electric motor and fix the stationary angle of twisting of the string ∆φ t . Without turning off the viscometer, repeat the measurement of ∆φ t at other temperatures. The experiment is terminated when the twist angle of the string begins to exceed 720 °.

2.5.4 Processing and presentation of measurement results

According to the measurement results, fill in the following table.

Table 1. Temperature dependence of viscosity

In the table, the first two columns are filled in according to the results of manual recording of the temperature readings on the monitor screen and the angle of twisting of the thread on the viscometer scale. The rest of the columns are calculated.

To check the feasibility of the exponential law of change in the viscosity coefficient with temperature (17.2), a graph is plotted in the coordinates "Ln (η) - 10 3 / T". The activation energy is found using the LINEST () (OpenOffice.Calc) or LINEST () (MicrosoftOffice.Exel) function by applying them to the fifth and sixth columns of the table.

In the conclusions, the obtained data η and E η are compared with those known for metallurgical slags, and the nature of the temperature dependence of viscosity and its relationship with structural changes in the melt are discussed.

The order of processing the results

1. Carry out measurements on the calibration cell and calculate the setting constant

2. Enter the results of manual recording of information into a spreadsheet file.

3. Calculate the viscosity values.

4. Construct a graph of viscosity versus temperature on a separate sheet.

5. Calculate the log viscosity and reciprocal absolute temperature for the entire set of measurements.

6. Find the coefficients by the least squares method b 0 , b 1 of the equation approximating the dependence of the logarithm of viscosity on the reciprocal temperature, and calculate the activation energy.

7. Construct a graph of the dependence of the logarithm of viscosity on the reciprocal temperature on a separate sheet and give an approximating dependence Test results:

1. In a spreadsheet book submitted for review, the following information should be provided on the first page titled "Results":

a. In cell "A1" - initial temperature, in cell "B1" - units of measurement;

b. In cell "A2" - the final temperature, in cell "B2" - units of measurement;

c. In cell "A3" - the activation energy of viscous flow at low temperatures, in cell "B3" - units of measurement;

d. In cell "A4" - the preexponential factor in the formula for the temperature dependence of electrical conductivity at low temperatures, in cell "B4" - units of measurement;

e. In cell "A5" - the activation energy of a viscous flow at high temperatures, in cell "B5" - units of measurement;

f. In cell "A6" - the preexponential factor in the formula for the temperature dependence of electrical conductivity at high temperatures, in cell "B6" - units of measurement;

g. Starting with cell "A7", conclusions on the work should be clearly formulated.

In cells A1-A6, there should be references to cells on other sheets of the spreadsheet book on which calculations were performed to obtain the presented result, and not the numerical values ​​themselves! If this requirement is not met, the verification program displays the message "Information presentation error".

2. Correctly designed plots of viscosity versus temperature and logarithm of viscosity versus reciprocal temperature, obtained from experimental data (points) and approximated by a polynomial (line), on separate sheets of spreadsheets with all the necessary designations. Control questions

1. In what form are the components of the oxide melt, consisting of CaO, Na 2 O, SiO 2, B 2 O 3, Al 2 O 3?

2. What is called the coefficient of viscosity?

3. How will the temperature dependence of the viscosity of the slag change when adding basic oxides to it?

4. In what units is viscosity measured?

5. How is the constant of the viscometer determined?

6. What determines the activation energy of a viscous flow?

7. What is the reason for the decrease in viscosity with increasing temperature?

8. How is the activation energy of a viscous flow calculated?

2.6 Reduction of manganese from oxide melt to steel

(Work No. 18)

2.6.1 General laws of the electrochemical interaction of metal and slag

The processes of interaction of liquid metal with molten slag are of great technical importance and occur in many metallurgical units. The productivity of these units, as well as the quality of the finished metal, is largely determined by the speed and completeness of the transition of certain elements across the phase boundary.

The simultaneous occurrence of a significant number of physical and chemical processes in different phases, high temperatures, the presence of hydrodynamic and heat flows make it difficult to experimentally study the processes of phase interaction in industrial and laboratory conditions. Such complex systems are investigated using models that reflect individual, but the most significant aspects of the object under consideration. In this work, a mathematical model of the processes occurring at the metal - slag interface allows one to analyze the change in the volume concentrations of components and the rate of their transition through the interface as a function of time.

The reduction of manganese from the oxide melt occurs by the electrochemical half-reaction:

(Mn 2+) + 2e =

The accompanying processes must be oxidation processes. Obviously, this could be the process of iron oxidation.

= (Fe2 +) + 2e

or impurities in the composition of steel, such as silicon. Since a four-charged silicon ion cannot be in the slag, this process is accompanied by the formation of a silicon-oxygen tetrahedron in accordance with the electrochemical half-reaction:

4 (O 2-) = (SiO 4 4-) + 4e

Independent flow of only one of the given electrode half-reactions is impossible, because this leads to the accumulation of charges in the electric double layer at the interface, which prevents the transition of the substance.

The equilibrium state for each of them is characterized by the equilibrium electrode potential ()

where is the standard potential, are the activities of the oxidized and reduced forms of the substance, z- the number of electrons participating in the electrode process, R- universal gas constant, F- Faraday constant, T- temperature.

The reduction of manganese from slag to metal is realized as a result of the joint occurrence of at least two electrode half-reactions. Their velocities are set so that there is no accumulation of charges at the interface. In this case, the potential of the metal takes on a stationary value, at which the rates of generation and assimilation of electrons are the same. The difference between the actual, i.e. stationary, potential and its equilibrium value, is called polarization (overvoltage) of the electrode,. Polarization characterizes the degree to which the system is removed from equilibrium and determines the rate of transition of components across the phase boundary in accordance with the laws of electrochemical kinetics.

From the standpoint of classical thermodynamics in the system in one direction or another, the processes of manganese reduction from the slag by silicon dissolved in iron take place:

2 (MnO) + = 2 + (SiO 2) H = -590 kJ / mol

and the solvent itself (oxidation of manganese with iron oxide in the slag

(MnO) + = + (FeO) =. H = 128 kJ / mol

From the standpoint of formal kinetics, the rate of the first reaction, determined, for example, by the change in the silicon content in the metal far from equilibrium in the kinetic regime, should depend on the product of the concentrations of manganese oxide in the slag and silicon in the metal to some degrees. In the diffusion mode, the reaction rate should linearly depend on the concentration of the component, the diffusion of which is difficult. Similar reasoning can be made for the second reaction.

Equilibrium constant of the reaction, expressed in terms of activities

is a function of temperature only.

The ratio of the equilibrium concentrations of manganese in slag and metal

is called the distribution coefficient of manganese, which, in contrast, depends on the composition of the phases and serves as a quantitative characteristic of the distribution of this element between the slag and the metal.

2.6.2 Process model

In the simulation model, three electrode half-reactions are considered, which can occur between the oxide melt CaO - MnO - FeO - SiO 2 - Al 2 O 3 and liquid iron containing Mn and Si as impurities. An assumption is made about the diffusion regime of their flow. The inhibition of diffusion of Fe 2+ particles in slag, silicon in metal, manganese in both phases is taken into account. The general system of equations describing the model has the form

where υ ј - rate of electrode half-reaction, η j- polarization, i j- the density of the limiting diffusion current, D j- diffusion coefficient, β - convective constant, C j- concentration.

The simulation model program allows you to solve the system of equations (18.4) - (18.8), which makes it possible to establish how the volume concentration of the components and the rate of their transition change with time when the metal interacts with the slag. The calculation results are displayed. The information received from the monitor screen includes a graphical representation of changes in the concentrations of the main components, their current values, as well as the values ​​of temperature and convection constants (Figure 8).

The block diagram of the program for the simulation model of the interaction of metal and slag is shown in Figure 7. The program runs in a cycle that stops only after the specified simulation time (approximately 10 minutes).

Figure 7 - Block diagram of the simulation model program

2.6.3 Work procedure

The image generated by the simulation program is shown in Figure 8 (right panel). In the upper part of the panel, selected numerical values ​​of the measured values ​​are shown, the graph shows all the values ​​obtained during the process simulation. In the designations of the components of metal and slag melts, additional signs adopted in the literature on metallurgical topics are used. Square brackets denote the belonging of the component to the metal melt, and the round brackets - to the slag. Component symbols are used only for plotting and should not be taken into account when interpreting values. During the operation of the model, at any given moment, only the value of one of the measured values ​​is displayed. After 6 seconds, it disappears and the next value appears. During this period of time, it is necessary to have time to write down the next value. To save time, it is recommended not to write fixed numbers, for example, the leading unit in the temperature value.

Fig 8. Image of the monitor screen when performing work No. 18 at different stages of the processes.

Four to five minutes after the start of the installation, add the preheated manganese oxide to the slag, which is realized by simultaneously pressing the Alt key and the numeric key on the main keyboard with the number of your installation. The order of processing the results:

1. Enter the results of manual recording of information into a spreadsheet file.

2. Calculate the rates of the processes of transition of elements through the interface and the logarithms of these values ​​before and after the addition of manganese oxide to the slag with the mass of the metal melt 1400 kg.

3. Construct on separate sheets graphs of temperature versus time, manganese transition rate versus time, logarithm of silicon transition rate versus logarithm of silicon concentration in metal.

4. Using the least squares method, estimate the kinetic characteristics of the silicon transition process.

Test results:

1. Correctly designed charts, listed in the previous section, on a separate sheet of spreadsheets with all the necessary signatures and designations.

2. Values ​​of the order of the silicon oxidation reaction before and after the introduction of manganese oxide with an indication of the errors.

3. Conclusions on the work.

Control questions

1. Why is there a need to model steel production processes?

2. What is the nature of the interaction of metal with slag and how is it manifested?

3. What potential is called stationary?

4. What potential is called equilibrium?

5. What is called electrode polarization (overvoltage)?

6. What is called the coefficient of distribution of manganese between metal and slag?

7. What determines the distribution constant of manganese between the metal and the slag?

8. What factors affect the rate of transition of manganese from metal to slag in the diffusion mode?

Bibliography

1. Linchevsky, B.V. Technique of metallurgical experiment [Text] / B.V. Linchevsky. - M .: Metallurgy, 1992 .-- 240 p.

2. Arsentiev, P.P. Physicochemical methods of research of metallurgical processes [Text]: textbook for universities / P.P. Arsentiev, V.V. Yakovlev, M.G. Krasheninnikov, L.A. Pronin and others - M .: Metallurgy, 1988 .-- 511 p.

3. Popel, S.I. Interaction of molten metal with gas and slag [Text]: study guide / S.I. Popel, Yu.P. Nikitin, L.A. Barmin and others - Sverdlovsk: ed. UPI them. CM. Kirov, 1975, - 184 p.

4. Popel, S.I. Theory of metallurgical processes [Text]: textbook / S.I. Popel, A.I. Sotnikov, V.N. Boronenkov. - M .: Metallurgy, 1986 .-- 463 p.

5. Lepinskikh, B.M. Transport properties of metal and slag melts [Text]: Handbook / B.М. Lepinskikh, A.A. Belousov / Under. ed. Vatolina N.A. - M .: Metallurgy, 1995 .-- 649 p.

6. Belay, G.E. Organization of a metallurgical experiment [Text]: textbook / G.E. Belay, V.V. Dembovsky, O. V. Sotsenko. - M .: Chemistry, 1982 .-- 228 p.

7. Panfilov, A.M. Calculation of thermodynamic properties at high temperatures [Electronic resource]: teaching aid for students of metallurgical and physical-technical faculties of all forms of education / А.М. Panfilov, N.S. Semenova - Yekaterinburg: USTU-UPI, 2009 .-- 33 p.

8. Panfilov, A.M. Thermodynamic calculations in Excel spreadsheets [Electronic resource]: guidelines for students of metallurgical and physical-technical faculties of all forms of education / A.M. Panfilov, N.S. Semenova - Yekaterinburg: USTUUPI, 2009 .-- 31 p.

9. A short reference book of physical and chemical quantities / Under. ed. A.A. Ravdel and A.M. Ponomarev. L.: Chemistry, 1983 .-- 232 p.

and the solvent itself (oxidation of manganese with iron oxide in the slag

(MnO) + = + (FeO) =. H = 128 kJ / mol

From the standpoint of formal kinetics, the rate of the first reaction, determined, for example, by the change in the silicon content in the metal far from equilibrium in the kinetic regime, should depend on the product of the concentrations of manganese oxide in the slag and silicon in the metal to some degrees. In the diffusion mode, the reaction rate should linearly depend on the concentration of the component, the diffusion of which is difficult. Similar reasoning can be made for the second reaction.

Equilibrium constant of the reaction, expressed in terms of activities

is a function of temperature only.

The ratio of the equilibrium concentrations of manganese in slag and metal

is called the distribution coefficient of manganese, which, in contrast, depends on the composition of the phases and serves as a quantitative characteristic of the distribution of this element between the slag and the metal.

2.6.2 Process model

In the simulation model, three electrode half-reactions are considered, which can occur between the oxide melt CaO - MnO - FeO - SiO 2 - Al 2 O 3 and liquid iron containing Mn and Si as impurities. An assumption is made about the diffusion regime of their flow. The inhibition of diffusion of Fe 2+ particles in slag, silicon in metal, manganese in both phases is taken into account. The general system of equations describing the model has the form

(18.4)

where υ ј - rate of electrode half-reaction, η j- polarization, i j- the density of the limiting diffusion current, D j- diffusion coefficient, β - convective constant, C j- concentration.

The simulation model program allows you to solve the system of equations (18.4) - (18.8), which makes it possible to establish how the volume concentration of the components and the rate of their transition change with time when the metal interacts with the slag. The calculation results are displayed. The information received from the monitor screen includes a graphical representation of changes in the concentrations of the main components, their current values, as well as the values ​​of temperature and convection constants (Figure 8).

The block diagram of the program for the simulation model of the interaction of metal and slag is shown in Figure 7. The program runs in a cycle that stops only after the specified simulation time (approximately 10 minutes).

Figure 7 - Block diagram of the simulation model program

2.6.3 Work procedure

The image generated by the simulation program is shown in Figure 8 (right panel). In the upper part of the panel, selected numerical values ​​of the measured values ​​are shown, the graph shows all the values ​​obtained during the process simulation. In the designations of the components of metal and slag melts, additional signs adopted in the literature on metallurgical topics are used. Square brackets denote the belonging of the component to the metal melt, and the round brackets - to the slag. Component symbols are used only for plotting and should not be taken into account when interpreting values. During the operation of the model, at any given moment, only the value of one of the measured values ​​is displayed. After 6 seconds, it disappears and the next value appears. During this period of time, it is necessary to have time to write down the next value. To save time, it is recommended not to write fixed numbers, for example, the leading unit in the temperature value.

Fig 8. Image of the monitor screen when performing work No. 18 at different stages of the processes.

Four to five minutes after the start of the installation, add the preheated manganese oxide to the slag, which is realized by simultaneously pressing the Alt key and the numeric key on the main keyboard with the number of your installation. The order of processing the results:

1. Enter the results of manual recording of information into a spreadsheet file.

2. Calculate the rates of the processes of transition of elements through the interface and the logarithms of these values ​​before and after the addition of manganese oxide to the slag with the mass of the metal melt 1400 kg.

3. Construct on separate sheets graphs of temperature versus time, manganese transition rate versus time, logarithm of silicon transition rate versus logarithm of silicon concentration in metal.

4. Using the least squares method, estimate the kinetic characteristics of the silicon transition process.

Test results:

1. Correctly designed charts, listed in the previous section, on a separate sheet of spreadsheets with all the necessary signatures and designations.

2. Values ​​of the order of the silicon oxidation reaction before and after the introduction of manganese oxide with an indication of the errors.

3. Conclusions on the work.

Control questions

1. Why is there a need to model steel production processes?

2. What is the nature of the interaction of metal with slag and how is it manifested?

3. What potential is called stationary?

4. What potential is called equilibrium?

5. What is called electrode polarization (overvoltage)?

6. What is called the coefficient of distribution of manganese between metal and slag?

7. What determines the distribution constant of manganese between the metal and the slag?

8. What factors affect the rate of transition of manganese from metal to slag in the diffusion mode?

Bibliography

1. Linchevsky, B.V. Technique of metallurgical experiment [Text] / B.V. Linchevsky. - M .: Metallurgy, 1992 .-- 240 p.

2. Arsentiev, P.P. Physicochemical methods of research of metallurgical processes [Text]: textbook for universities / P.P. Arsentiev, V.V. Yakovlev, M.G. Krasheninnikov, L.A. Pronin and others - M .: Metallurgy, 1988 .-- 511 p.

3. Popel, S.I. Interaction of molten metal with gas and slag [Text]: study guide / S.I. Popel, Yu.P. Nikitin, L.A. Barmin and others - Sverdlovsk: ed. UPI them. CM. Kirov, 1975, - 184 p.

4. Popel, S.I. Theory of metallurgical processes [Text]: textbook / S.I. Popel, A.I. Sotnikov, V.N. Boronenkov. - M .: Metallurgy, 1986 .-- 463 p.

5. Lepinskikh, B.M. Transport properties of metal and slag melts [Text]: Handbook / B.М. Lepinskikh, A.A. Belousov / Under. ed. Vatolina N.A. - M .: Metallurgy, 1995 .-- 649 p.

6. Belay, G.E. Organization of a metallurgical experiment [Text]: textbook / G.E. Belay, V.V. Dembovsky, O. V. Sotsenko. - M .: Chemistry, 1982 .-- 228 p.

7. Panfilov, A.M. Calculation of thermodynamic properties at high temperatures [Electronic resource]: teaching aid for students of metallurgical and physical-technical faculties of all forms of education / А.М. Panfilov, N.S. Semenova - Yekaterinburg: USTU-UPI, 2009 .-- 33 p.

8. Panfilov, A.M. Thermodynamic calculations in Excel spreadsheets [Electronic resource]: guidelines for students of metallurgical and physical-technical faculties of all forms of education / A.M. Panfilov, N.S. Semenova - Yekaterinburg: USTUUPI, 2009 .-- 31 p.

9. A short reference book of physical and chemical quantities / Under. ed. A.A. Ravdel and A.M. Ponomarev. L.: Chemistry, 1983 .-- 232 p.

Ministry of Education and Science of the Russian Federation

Federal Agency for Education

South Ural State University

Branch in Zlatoust

Department "General Metallurgy"

669. 02/ . 09 (07)

D463

THEORY OF METALLURGICAL PROCESSES

Tutorial

Chelyabinsk

SUSU Publishing House

INTRODUCTION

Metallurgical processes are a combination of physical phenomena and physicochemical transformations (movement of gases, liquid and solid materials, heat and mass transfer, phase transitions, oxidation and reduction of materials, etc.) occurring in metallurgical units (blast furnace, sintering machine , steel-making and heating furnace, converter) at high temperatures. The subject of study of the course "Theory of metallurgical processes" is the reactions occurring in the specified metallurgical units.

The TMP course occupies a special position among all metallurgical disciplines, in fact, it is applied physical chemistry in relation to the analysis of the phenomena occurring in the production of iron, steel and ferroalloys.

The theoretical foundations of metallurgical processes are considered in a certain sequence: first, on the basis of the laws of thermodynamics, the conditions of equilibrium of chemical processes are analyzed, then - the kinetics and features of the mechanism of the processes. These questions are the main tasks to be solved when studying the course of TMP.

1. COMPOSITION AND PROPERTIES OF HIGH-TEMPERATURE GAS ATMOSPHERE

1.1. Thermodynamics of gas atmospheres

Pyrometallurgical processes for the production of metallurgical melts (cast iron, steel, alloy) take place with the participation of gaseous atmospheres, which can be neutral, oxidizing and reducing.

The composition, pressure and temperature of the gas phase depend on the nature of its interaction with other phases formed during the production of metals and alloys. In this case, both the intermediate and the complete composition of the gas phase are very similar:

products of complete interaction of elements with oxygen - CO2, H2O (steam), SO3;

products of incomplete interaction with oxygen, dissociation of oxides and degassing of metals - CO, SO2, H2, O2, N2, CH4; inert gases - Ar, Kr.

The equilibrium composition of the gas phase can be calculated based on the thermodynamic analysis of chemical reactions, the most important of which are the reactions of interaction with oxygen of hydrogen, carbon monoxide, methane and sulfur dioxide.

These reversible reactions are described by the following chemical equations (per mole of O2):

2H2 + O2 = 2H2O (steam),	J;
2CO + O2 = 2CO2,	J;
2СH4 + O2 = 2СО + 4H2O,	J;
1 / 2СH4 + O2 = 1 / 2СО2 + Н2О,	J;	(1.4)
2SO2 + O2 = 2SO3,	J.

Thermodynamic analysis of these reversible reactions makes it possible to establish the equilibrium contents and partial pressures of molecular oxygen, as well as to characterize the redox properties of the gas phase in these reactions.

However, a more important thermodynamic characteristic that determines the direction of the course of chemical reactions is the change in the Gibbs energy D GT, the standard change of which D G ° T, depending on the temperature for reactions (1.1) - (1.5), has the form, J:

D G ° (1.1) = - + 108 T;

D G ° (1.2) = - + 175 T;

D G ° (1.3) = - + 370 T;

D G ° (1.4) = - + 2 T;

D G ° (1.5) = - + 196 T.

In fig. 1.1 graphs of these dependencies are presented.

Rice. 1.1. Standard Gibbs energy for combustion reactions

The indicated dependences are valid at temperatures up to 2500 K and total pressure in the system P = 1 atm., I.e., before the processes of dissociation of H2O, O2, H2 into atoms, their ionization and plasma formation.

From the analysis of the given dependences and graphs of the form D G ° T = f (T) in Fig. 1.1 it follows that with increasing pressure the equilibrium of reactions (1.1), (1.2) and (1.5) shifts in the forward direction, and with increasing temperature the completeness of these reactions decreases. A change in pressure does not affect the equilibrium of reaction (1.4), and the direct course of reaction (1.3) slows down with increasing pressure. With an increase in temperature, reactions (1.3) and (1.4) are characterized by a more complete flow.

The equilibrium composition of the formed atmosphere and the partial pressures of its constituent components will make it possible to determine and calculate the redox properties (ORS) of the gas phase affecting the materials of the heterogeneous system capable of oxidation or reduction.

The simplest quantitative characteristic of the OBC of any gas mixture is the equilibrium partial pressure of oxygen. However, a more accurate estimate of the OMC of a gaseous atmosphere is its oxygen potential p О, which is the value of the chemical potential of molecular oxygen when measured from the standard state, at which DIV_ADBLOCK144 ">

The value of p O depends on the temperature and on the composition of the gas phase, which is expressed through the ratio of the partial pressures of the reactants affecting.

In metallurgical plants, gaseous atmospheres consist of many components that are constantly involved in physical and chemical transformations. Thermodynamic analysis of such systems is based on the statement that a complex chemical equilibrium is achieved as a result of the simultaneous establishment of all possible partial equilibria in the system.

So, with the simultaneous occurrence of reactions (1.1) - (1.5) in the gas phase at T = const, the pressures of the indicated components will take values ​​corresponding to the equilibrium constants КР (1.1) –КР (1.5), and the oxygen potential of the gas mixture

can be calculated from any of these equilibria, for example, by the equation

In the considered eight-component gas mixture, in addition to reactions (1.1) - (1.5), other chemical interactions between the reagents are also possible. Of greatest interest is the so-called reaction of water gas (water gas is called a mixture of four gases H2 - H2O - CO - CO2):

H2 + CO2 = H2O + CO, D G ° (1.5) = - 33.5T J. (1.8)

The analysis of this reaction is extremely important in metallurgy for evaluating equilibria in gaseous atmospheres when using natural gas or humidified blast in a blast furnace and other metallurgical units.

To determine the equilibrium composition of the reaction system (1.8), it is necessary to specify not only the value of the equilibrium constant

(1.9)

and general pressure

(1.10)

but also by two other conditions, which follows from the analysis of the number of degrees of freedom:

С = p + 2 - Ф = 3 + 2 - 1 = 4.

In practice, the initial composition of the system or the partial vapor pressures in the initial mixture are most often set. In our case, in addition to P and T, as two variables, one can choose unchanging numbers of moles of carbon and hydrogen or unchanging sums of the partial pressures of hydrogen and carbon-containing gases:

(1.11)

(1.12)

The joint solution of equations (1.9) - (1.12) makes it possible to find the equilibrium composition of the gas mixture. The calculation results can be presented graphically, with the initial data being the ratios:

(1.13)

From the graph (Fig. 1..gif "width =" 69 "height =" 28 "> and vice versa. After calculating the equilibrium value of% CO /% CO2 (or% H2 /% H2O), you can determine the oxygen potential of the CO - CO2 - H2 - H2O and plot lines of constant values ​​of p O in Fig. 1.2.

Rice. 1.2. The ratio between% CO/% CO2 and% H2 /% H2O.

1.2. Homogeneous gas processes

Thermodynamic analysis of reactions proceeding in complex gaseous atmospheres allows only to judge the possibility of the reaction proceeding in the forward or reverse directions and to calculate the composition of the gas phase. However, in this case it is impossible to consider the mechanism of interaction processes and carry out their kinetic analysis.

The mechanism of interaction of valence-saturated molecules should include breaking or weakening of valence bonds. This requires large energy expenditures, which cannot be compensated for only by the energy of the thermal motion of molecules. Experimental data show that all combustion reactions have a chain mechanism characterized by the participation of active centers (particles) - atoms and radicals with free valences. The simplest acts of a multistage oxidation process begin after the formation of active centers and proceed as chemical reactions between them and molecules with low activity energies. A feature of such reactions is the reproduction of active centers. By the nature of their course, chain reactions are divided into unbranched, branched and degenerate branching.

In general, the model in the theory of chain reactions is the most studied reaction of hydrogen combustion, which is characterized by a small number of intermediate products and well-distinguished elementary acts. They are:

1) the reaction of the formation of active centers in the volume of the mixture and on the vessel wall:

E1.14 = 198.55 kJ / mol; (1.14)

E1.15 = 180.7 kJ / mol; (1.15)

Nads + O2 = HO2; (1.16)

2) chain continuation reaction:

https://pandia.ru/text/79/398/images/image020_45.gif "width =" 172 "height =" 48 src = "> E1.17 = 41.9 kJ / mol; (1.17)

3) chain branching reactions:

E1.18 = 63.27 kJ / mol; (1.18)

E1.19 = 25.14 kJ / mol; (1.19)

4) chain break (deactivation) reaction on the wall

; (1.20)

5) the reaction of chain termination in the volume of the gas phase (M is a neutral molecule):

E (1.21) "0; D Н1.20 = - 197 kJ / mol. (1.21)

The rate of each of these reactions is determined by the partial pressure P and the order of the reaction n and in general form can be represented as

V = const × https://pandia.ru/text/79/398/images/image029_30.gif "width =" 411 height = 267 "height =" 267 ">

Rice. 1.3. Ignition conditions of the gas mixture (H2 + O2)

2. ANALYSIS OF SOLID CARBON COMBUSTION PROCESSES

Let us consider the most important of the possible interactions of carbon with oxidants.

1. Reaction of incomplete combustion of carbon

2С + О2 = 2СО, D G ° Т (2.1) = - - 180Т J / mol. (2.1)

2. Reaction of complete combustion

C + O2 = CO2, D G ° T (2.2) = - - 2.3T J / mol. (2.2)

3. Reaction of carbon gasification with H2O steam to CO

2C + 2H2O = 2CO + 2H2, D G ° T (2.3) = - 288T J / mol. (2.3)

4. Reaction of carbon gasification with H2O steam to CO2

C + 2H2O = CO2 + 2H2, D G ° T (2.4) = - 110.6T J / mol. (2.4)

5. Reaction of carbon gasification

C + CO2 = 2CO, D G ° T (2.5) = - 177.7T J / mol. (2.5)

Of greatest interest is reaction (2.5), which is endothermic: D H ° = 172.6 kJ.

By the ratio, which is established by the reaction of carbon gasification, one can judge about the effect of solid carbon on the composition of the gas phase of the C - CO - CO2 system in a wide temperature range. The equilibrium composition of this gaseous atmosphere is shown in Fig. 2.1.

According to Le Chatelier's principle, an increase in pressure shifts the equilibrium of the carbon gasification reaction to the left, that is, at a constant temperature, the equilibrium gas mixture is enriched with CO2 dioxide. With decreasing pressure, the concentration of CO in the gas phase increases.

The heterogeneous process of interaction of carbon with an oxidizing agent consists of a number of stages:

2) molecular diffusion through a hydrodynamic layer of thickness d Г, where laminar flow is maintained;

3) adsorption of the oxidant on the carbon surface;

4) chemical interaction with the formation of adsorbed products (CO2 at low temperatures and CO at high);

5) desorption of reaction products;

6) diffusion (molecular and turbulent) of reaction products into the gas flow.

Rice. 2.1. The composition of the gas atmosphere (CO- CO2) in equilibrium with solid carbon

The limiting in the process of carbon oxidation is the adsorption-kinetic stage, which combines stages 3, 4, and 5. Molecular diffusion can also be limiting.

The diffusion rate per unit surface can be calculated using the formula

(2.6)

where D is the diffusion coefficient, b is the mass transfer coefficient, Co and Spov are the oxidant concentration in the volume of the gas phase and on the carbon surface, respectively.

The rate of chemical interaction is determined by the concentration of the adsorbed reagent Spov:

(2.7)

where K is the reaction rate constant, which depends exponentially on the temperature of the activation energy of the process, n is the order of the reaction (in this case, n = 1).

If the process of interaction of carbon with the gas phase occurs in a stationary mode, i.e., without changing the rate over time, then the rate of this process Vproc is defined as

Vprots = V x. p = VD. (2.8)

Substituting relations (2.6) and (2.7) into (2.8), we finally obtain the observed rate of the carbon oxidation process:

(2.9)

Depending on the ratio of the K and b values, the following oxidation modes are possible:

- kinetic at b >> K;

- diffusion at K >> b;

- diffusion-kinetic at K "b.

Thermodynamic analysis of reaction (2.5) makes it possible to reveal the conditions for the decomposition of carbon monoxide. This is possible in gaseous atmospheres with high ratios and with decreasing temperatures. D G ° T value for reaction

2CO = CO2 + C

decreases with decreasing temperature, but kinetically without a catalyst it is difficult to carry out this reaction, which is used, for example, in the cementation process.

For the oxidation of the "C - O" bond in the CO molecule, a catalytic solid surface is needed; the most powerful catalyst is iron. In this case, the main stages of the CO decomposition process with the formation of solid finely dispersed carbon will be as follows:

1) adsorption of a CO molecule on the catalyst surface, leading to a weakening of the "C - O" bond;

2) the process of decay upon impact of an active CO molecule of the gas phase on the adsorbed one according to the reaction

CO + Coads = CO2 + C.

3. EVALUATION OF STRENGTH OF CHEMICAL COMPOUNDS

The processes of dissociation of the most important compounds for metallurgy - oxides, nitrides, carbonates - are very important, since they are a direct method of obtaining metals. These processes are very similar, and depending on the temperature, they can be represented by equations of the form:

AVtv = Atv + Vgaz;

AVtv = Al + Vgaz;

AVzh = Atv + Vgaz;

AVzh = Al + Vgaz.

The value of the equilibrium partial pressure of the gaseous product of these reactions is called elasticity of dissociation connection AB and characterizes the strength of this connection. Dissociation reactions are endothermic, i.e., as the temperature rises, the equilibrium shifts towards the reaction products. Reducing the pressure while maintaining the composition of the gas phase has a similar effect.

According to the Gibbs phase rule, the number of degrees of freedom for dissociation reactions is defined as

C = K + 2 - F = 2 + 2 - 3 = 1,

i.e., for a quantitative characteristic, only one independent parameter is sufficient - the temperature, on which the process equilibrium constant depends:

Кр = РВ = ¦ (Т).

Rice. 3.1. Dependence of the dissociation elasticity of the AB compound on temperature

In fig. 3.1 shows the dependence of RV on temperature for the indicated reactions.

3.1. Dissociation of carbonates

In ferrous metallurgy, the analysis of the dissociation reaction of calcium carbonates CaCO3, magnesium MgCO3, manganese MnCO3, iron FeCO3 (siderite) and dolomite CaMg (CO3) 2 is of the greatest practical interest. The dissociation processes of these compounds are of the same type and proceed according to the equation:

MeCO 3 = MeO + CO 2,

The quantity is the dissociation elasticity of the carbonate and characterizes a measure of the chemical strength of the compound.

Of greatest interest is the reaction of dissociation of calcium carbonate, which is part of the charge materials of blast furnace and steel-making production, and is also used to obtain CaO through calcining limestone.

The dissociation reaction of CaCO3 is described by an equation of the form

CaCO 3 = CaO tv + CO 2, = J; (3.1)

D G ° T = - 150 T; Kp (3.1) =

The temperature dependence of the elasticity of carbonate dissociation is shown in Fig. 3.2.

Rice. 3.2. Elasticity of CaCO3 dissociation

Analysis of this graphical dependence using the isotherm of the chemical reaction shows that the dissociation of carbonate is possible when the actual value is less than the equilibrium value and at the same time D G ° T< 0. Температура, при которой возможен этот процесс, является температурой начала диссоциации ТНД.

Any figurative point 1 above the equilibrium line in Fig. 3.2 corresponds to the stable existence of CaCO3 carbonate. Any figurative point 2 below the line corresponds to the stable existence of CaO oxide.

The process of dissociation of carbonate proceeds at a high rate at temperatures above the chemical boiling point of TCA, at which the elasticity of dissociation becomes equal to the total external pressure of the gas phase.

3.2. Dissociation of iron oxides

The thermodynamics of the dissociation of oxides is similar to the dissociation of carbonates, the peculiarities are associated only with the presence of different degrees of valence in some metals, in particular, in iron oxides.

In accordance with Baykov's principle, the dissociation of iron oxides occurs sequentially, from higher to lower, up to the formation of a metal. Dissociation reactions are as follows:

6Fe2O3 = 4Fe3O4 + O2, D G ° T = - 281.3 T J; (3.2)

2Fe3O4 = 6FeO + O2, D G ° T = - 250.2 T J; (3.3)

2FeO = Fe + O2, D G ° T = - 130.7 T J; (3.4)

1 / 2Fe 3O 4 = 3 / 2Fe + O 2, D G ° T = - 160.2 TJ. (3.5)

These oxides exist in certain temperature ranges. In fig. 3.3 shows the graphs of the dependences D G ° T on the temperature of reactions (1) - (4).

Rice. 3.3. Standard Gibbs energy of dissociation reactions of iron oxides

The calculated values ​​of the dissociation elasticities were used to plot the dependences presented in Fig. 3.4.

Rice. 3.4. Areas of sustainable existence

iron and its oxides

This diagram shows the areas of stable existence of pure iron and its oxides in a wide temperature range. Point O corresponds to invariant equilibrium with parameters T = 575 ° C and "- 26 (there are four phases in equilibrium - solid Fe, FeO, Fe3O4 and O2). The rest of the lines are in invariant equilibrium. Any point between the lines corresponds to a fixed state of the bivariant system, which makes it possible to determine the conditions for the stable existence of a given condensed phase.

3.3. Mechanism and kinetics of dissociation processes

Distinctive features of the dissociation processes proceeding according to the reaction of the form

AVtv ® Atv + Vgaz,

are:

- the presence of the process of nucleation of a new solid phase;

- localization of the process at the interface between the "old" and "new" solid phases;

- the dependence of the rate of the process on the degree of conversion.

As a characteristic of this process, the degree of conversion is used a:

where mAB (p), mAB (out) - equilibrium and initial values ​​of compound AB.

Conversion rate a depends on the time of the process, which is confirmed by numerous experimental data (Fig. 3.5).

font-size: 13.0pt; letter-spacing: -. 1pt "> Fig. 3.5. Isothermal dependences of the degree of transformation a from time
and the rate of conversion versus the degree of conversion

In this case, three stages can be distinguished:

I - the induction period, characterized by low rates of the process due to the difficulties of nucleation of a new phase;

II - autocatalysis associated with the acceleration of the dissociation reaction;

III - the period of completion of the process, which is associated with a decrease in the amount of the old phase and the interface.

Experimental studies of dissociation processes indicate that such a process proceeds according to the scheme

AVtv ® Atv × Vgaz (ads) ® Atv + Vgaz.

In this case, the formation of a nucleus of a new phase in the depths of the old one should be accompanied by a decrease in the Gibbs energy of the system, calculated by the equation

D G = D GV + D GW,

where D GV and D GW are the volumetric and surface components of the total change in the Gibbs energy.

The D GV and D GW values ​​are defined as

D GV =

D GW = S × s,

where V and S are the volume and surface of the nucleus of the new phase, r and M are the density and molecular weight of the new phase, s is the surface tension, m 2 and m 1 are the chemical potentials of the AB compound in the new and old phases.

From the analysis of this ratio, it follows that the spontaneous process of the formation of a new phase is possible at a certain ratio of m 2 and m 1.

At T £ Tnd m 2 ³ m 1, and in this case the appearance of a nucleus of any size is thermodynamically impossible.

If T> Tind, then m 2> m 1, and the terms in the formula for DG have different signs, since with increasing r the first term increases in absolute value faster, then the curve DG = f (r) also has a maximum, the position of which determines the value of the critical nucleus, the growth of which is accompanied by a decrease in the energy of the system. Under certain conditions, the nucleus of a new phase becomes thermodynamically stable. The degree of overheating of the AVTV compound determines both the radius of the critical nucleus and its stability. To determine the size of the critical nucleus, it is necessary to investigate the function D G = f (r) for an extremum, after which we obtain

The value D m = m 1 - m 2 is called chemical satiety and is the driving force behind the dissociation process.

In fig. 3.6 shows the condition for the emergence and growth of a nucleus of a new phase.

It follows from the analysis of the dependences that, all other things being equal, the greater the overheating, the smaller the critical nucleus and the easier (faster) the process of dissociation of compounds.

Rice. 3.6. Growth conditions for a nucleus of a new phase

Thus, the growth of the nucleus of a new medium depends on the temperature, time, and mobility of the particles that form the new medium. The study of the mechanism of a specific transformation makes it possible to determine analytical dependences, however, they are acceptable, as a rule, only for the analyzed case. In this case, it is necessary to take into account the natural hindrance to growth associated with the "overlap" of the nucleus of a new phase and the limitation of the process by any of its elementary stages.

Real systems can differ significantly from the created models of dissociation, when creating which one should pay attention to the following features: at the initial moment of time, a slower growth of embryos is possible; the surface rate of advancement of the phase boundary may differ from the rate of penetration into the volume; the reactivity of the border changes over time; the volume of products and reagents may not match; with reversible reactions, adsorption of volatile reaction products is possible; possible manifestation of diffusion inhibition; kinetic characteristics, as a rule, depend on the particle size; there may be difficulties in transferring heat through the reaction products.

Some of the listed features of dissociation processes can be limiting links, which include:

1) the rate of chemical transformation (the so-called kinetic regime);

2) the rate of gas diffusion through the cover layer (diffusion mode);

3) mixed mode (comparability of the rates of chemical transformation and diffusion);

4) the rate of transfer of the heat of reaction through the cover layer.

Each of these stages can be expressed analytically in relation to the process of dissociation of a particular compound, taking into account its features.

3.4. Oxidation of hard metals

When Me is placed in an atmosphere containing O2 or other oxidizing gases (CO2, H2O), its surface becomes covered with oxides, dross, the thickness of which increases with time. At high temperatures, this process - high temperature corrosion- develops very quickly and leads to the loss of Me when it is heated before rolling, forging.

In total, 18 ... 20 million tons of Me are lost annually due to the oxidation of Me. Oxidation of Me is a spontaneous process, but it depends on a number of factors.

The oxidation process consists of the following stages:

1) external diffusion of oxidizing gas to the surface of the oxide;

2) internal diffusion in the scale layer;

3) a chemical act (reaction) at the phase boundaries.

Scale (MeO) of thickness y is between two media - between Me and gas; within its limits, the O2 concentration falls from the gas / MeO interface to the MeO / Me interface, and the Me content decreases in the opposite direction. Due to this, the diffusion of substances in the oxide layer is possible, which is shown in Fig. 3.7.

Rice. 3.7. Metal oxidation scheme

The diffusion coefficient in solid scale depends on its crystal structure, determined by the ratio of the molar fractions of oxide (VMeO) and Me (VMe).

For VMе> VMeO, porous oxide layer, through which the oxidizing gas easily penetrates to Me. The following Me have such properties.

MenOn		Na2O

If VMе< VMeO, то оксид покрывает Ме сплошным плотным покровом, который создает значительное диффузионное сопротивление и окисление затрудняется. К данной группе относятся следующие Ме:

MenOn	Al2O3		Cu2O	Cr2O3	Fe2O3

Under conditions of real metal oxidation, external diffusion of gas proceeds relatively quickly, therefore, the oxidation process of any metal can be represented in the form of two stages:

1) diffusion of O2 (another oxidizing agent) through the oxide film;

2) the direct act of chemical interaction at the interface.

Let us derive the equation for the dependence of the thickness of the oxide layer y on the oxidation time t at T = const.

Observed process speed

Vobl = dy / dt.

Internal diffusion rate is defined as

where "-" is the concentration gradient;

Spov, Sob - concentration of the oxidizing agent on the reaction surface and in the volume of the gas;

The rate of a chemical reaction is defined as

for n = 1, https://pandia.ru/text/79/398/images/image057_8.gif "width =" 115 height = 52 "height =" 52 ">

In the steady state, the speeds of the successive links K and the total speed are equal to each other:

in this case, Cp is substituted into the diffusion equation:

y = f (t) is a differential equation.

Let's move and split the variables:

Initial conditions: t = 0, y = 0.

The sought dependence of the thickness of the oxidized diffusion layer on time:

(*)

This function is parabolic.

For t = 0 and y ® 0, y2<< y, поэтому величиной y2/2 пренебрегаем:

y = Kx C rev × t. (3.6)

This dependence is linear.

This implies:

1) the thickness of the scale layer is ~ t, i.e. oxidation proceeds at a constant rate;

2) the oxidation rate is determined by the peculiarities of the Kx value, i.e., the reaction is in the kinetic region.

This applies to the metals of the 1st group.

For metals of the second group D< R; при этом t – велико. В этом случае слагаемым пренебрегаем и получаем:

. (3.7)

1) the thickness of the scale layer is proportional, i.e. the oxidation rate decreases with time;

2) the process takes place in the diffusion region.

This is shown graphically in Fig. 3.8.

Thus, in Me with dense scale, the oxidation reaction is initially in kinetic area and the oxide layer grows along a linear dependence (in Fig. 3.8 - zone 1).

With a significant layer thickness, the dependence becomes parabolic and the process is limited internal diffusion(zone 2). Between these extreme cases lies the transition zone - 3, where y and t are related by a differential equation (*), which takes into account the features of chemical transformation and diffusion.

Rice. 3.8. Dependence of the scale thickness on the process time: 1 - kinetic region;

2 - diffusion area; 3 - transition zone

4. METAL RESTORATION PROCESSES

4.1. Thermodynamic characteristics of reduction processes

Obtaining pure metals due to the dissociation of their oxides is thermodynamically unlikely due to the very low values ​​of the dissociation elasticity of the compounds.

The most expedient is the process of obtaining metals from their oxides by reduction. Such a process is essentially a redox process (the oxidized metal is reduced, and the reducing agent is oxidized) and can be generally described by the reaction

MeO + B = Me + BO, D G T (4.1), (4.1)

where both a solid and a gaseous substance (element) can be used as a reducing agent B.

Reaction (4.1) is essentially the sum of formation reactions of the form

B = = BO, D G T (4.2); (4.2)

Ме = = МеО, D G Т (4.3), (4.3)

which are exothermic.

Spontaneous occurrence of reaction (4.1) is possible if D G T (4.2)< D G Т(4.3).

4.2. Reduction of iron oxides with solid and gaseous

restorers

The universal reducing agent for iron oxides is solid carbon; when reducing with gaseous gases, CO and H2 are often used.

The thermodynamics of the processes of reduction of iron oxides with solid and gaseous reducing agents is, in principle, the same.

When using carbon monoxide CO, equilibria in the FemOn - CO - CO 2 system should be considered, which are described by the following reactions:

(4.4)

EN-US "> EN-US"> position: absolute; z-index: 5; left: 0px; margin-left: 234px; margin-top: 12px; width: 11px; height: 88px "> (4.8)

Rice. 4.1. Equilibrium composition of the gas phase of the system FemOn - CO - CO 2

The diagram does not show a zone of stable existence of the Fe 2O 3 phase, since, according to calculations, this phase is unstable in the considered temperature range even at a CO content> 0.01%.

Point O is a point of invariant equilibrium with the gas phase of three solid phases.

When using hydrogen or some other reducing agent as a reducing agent, the curves of the equilibrium gas composition will be calculated in a similar way.

When carbon oxides of iron are used as a reducing agent, the process can be described by reactions corresponding to equilibrium in the system
Fe 2O 3 - Fe 3O 4 - FeO - Fe - C - CO - CO 2 containing seven components.

However, taking into account the instability of Fe 2O 3, it is advisable to analyze the following chemical equilibria:

Fe3O4 + CO = 3FeO + CO2;

FeO + CO = Fe + CO2;

2CO = C + CO2.

In addition to partial equilibria, in accordance with the phase rule, a simultaneous equilibrium of five phases is possible - four solid and gaseous (mixtures of CO and CO2).

The equilibrium curves of these reactions are shown in Fig. 4.2.

font-size: 13.0pt "> Fig. 4.1. Equilibrium monoxide contents

carbon in the indirect reduction of oxides

iron and solid carbon gasification reactions

The quantitative characteristics of the equilibria in the system under consideration can be obtained by jointly solving the equations expressing the dependence of the constants on the composition of the gas phase. From the solution of the system of these equations, it follows that with increasing pressure in the system, the temperatures of the onset of reduction of iron oxides increase, and with decreasing pressure, vice versa.

Thus, phase equilibria in the Fe – O system in the presence of solid carbon are determined by the temperature and total pressure of the gas phase
(CO + CO2).

4.3. Mechanism and kinetics of recovery processes

The mechanisms for the reduction of metal oxides by gases and solid reducing agents are different and have their own characteristics.

When reducing with gases, this process takes place in at least three stages:

1) adsorption of reduction on the reaction surface;

2) the transition of oxygen from the oxide lattice and its combination with adsorbing reducing agent molecules with the simultaneous formation of a new solid phase.

3) desorption of gaseous reduction products.

This theory is called the adsorption-autocatalytic theory, and the mechanism itself can be represented by the following diagram:

MeO (tv) + B (gas) = ​​MeO (tv) × B (ads),

MeO (tv) × B (ads) = Me (tv) × VO (ads),

Me (tv) × VO (ads) = Me (tv) × VO (gas)

MeO (tv) + B (gas) = ​​Me (tv) × VO (gas).

There is also a two-stage scheme, consisting of a stage of oxide dissociation with the formation of molecular oxygen and a stage of combining with a reducing agent in the gas phase.

According to the adsorption-autocatalytic theory, the reduction process is autocatalytic - the formation of a solid reaction product accelerates the process of its formation. In this case, the adsorption of reducing gas molecules develops in different ways - depending on the structure, structure. At a certain stage of reduction, a maximum characteristic of autocatalysis is observed, which corresponds to the kinetic reduction mode.

In general, kinetically, the process of reduction of metal oxides by gases is heterogeneous, consisting of the following stages:

1) external diffusion of the reducing agent from the gas flow to the surface of the reduced oxide;

2) internal diffusion of the reducing agent to the reaction fraction through the pores and lattice defects of the solid product layer of the reducing agent;

3) chemical reaction followed by crystal-chemical transformation of the metal oxide into a lower one, down to metal;

4) removal of gaseous reduction products into the gas flow due to internal and external diffusion.

Any of these stages can be, in principle, limiting, that is, determine the speed of the recovery process. Depending on the rate of diffusion and chemical transformation, stepwise or zonal reduction is possible, which corresponds to the principle of sequence.

The stepwise type of the process is observed in the kinetic regime, zonal - in the diffusion regime. At comparable rates of diffusion and chemical reaction, the reduction process will proceed in a mixed, or diffusion-kinetic mode, which is the most complex.

The rate of reduction by gases is influenced by various factors, the main ones are the following: the size of the pieces of oxide material, the porosity of the ores, the rate of movement of the reducing gas flow, the composition of the gas, pressure and temperature.

Direct reduction reactions of metal oxides are more complex than reduction with gases.

The reduction of oxides with solid carbon can be estimated by the reaction

MeO (tv) + C (tv) = Me (tv) + CO2.

However, this equation does not reflect the actual mechanism of the process, which proceeds in several stages with the participation of gases as intermediate products.

There are several schemes for the carbon-thermal reduction of oxides.

The two-stage scheme is developed and represented by the equations

MeO + CO = Me + CO2

C + COg = 2CO

MeO + C = Me + CO.

According to the above scheme, the interaction of metal oxide with solid carbon is reduced to reduction with CO gas. This makes it possible to apply the adsorption-catalytic theory to explain the direct reduction processes, and the role of solid carbon is reduced to CO regeneration by the gasification reaction. Kinetically, according to this scheme, it is possible to restore those metals that are easily reduced by gases (Fe, Ni, Cu, etc.). The lower temperature limit of the interaction according to this scheme is associated with the low rate of the carbon gasification reaction at low temperatures, and this stage is often limiting. Therefore, the decisive factors for the direct reduction of metal oxides are factors that affect the rate of the gasification reaction - temperature, carbon activity, and the presence of catalysts.

There is a dissociative scheme, according to which the dissociation of the oxide is possible, followed by the interaction of oxygen with carbon according to the scheme

Me = Me + 1 / 2O2

C + 1 / 2Or = CO

MeO + C = Me + CO.

This scheme is acceptable for oxides with high dissociation elasticity (Mn О2, Pb О2, Cu О, Сo 3О4).

Oxide - sublimation scheme was developed, according to this hypothesis, the reduction of a number of oxides can pass through the sublimation (sublimation) of oxide, followed by condensation (adsorption) of its vapors on the carbon surface:

MeO (tv) = MeO (gas)

MeO (gas) + C (tv) = MeO (ads) C (tv)

MeO (ads) C (tv) = Me (tv) CO (ads)

Me (tv) CO (ads) = Me (tv) + CO (gas)

MeO (tv) + C (tv) = Me (tv) + CO (gas).

This scheme is typical both for volatile oxides (Mo О3, W О3, Cr 2О3) and explains their reduction at 630 ... 870K, when interaction according to other schemes is impossible due to low rates of the carbon gasification reaction and thermal dissociation of the oxide, and for strong oxides (Al 2O3, Mg O, Zn O2), the sublimation of which is accompanied by the formation of vapors of oxides and lower gaseous oxides (Al 2 O, Si O).

According to the contact reduction scheme, the interaction occurs at the points of contact of solid phases - oxide and carbon. After direct contact, a separating layer of the product is formed, and the reduction proceeds with the diffusion of reagents through this layer.

A number of regularities of carbothermal reduction are explained within the framework of the gas-carbide scheme: the effect of CO on the rate of the process, the presence of carbon in condensation products in zones remote from the reacting mixture, the effect of swelling of ore-coal pellets, and autocatalysis.

Thus, different oxides can interact with carbon according to different schemes, while others can be realized simultaneously with the main mechanism. The share of each mechanism in the recovery process varies depending on conditions - temperature, pressure, the degree of mixing of reagents and the degree of recovery, and other factors.

5 . METALLURGICAL ALLOYS

5.1. general characteristics

High-temperature metallurgical processes involve liquid phases: metal, oxide (slag), sulfide (matte), and salt. The interaction between liquid phases and with the obligatory participation of the gas phase depends on the structure (structure) and properties of metallurgical melts.

Taking into account the nature and structure, all liquids are classified as follows:

1) with hydrogen bonds (water, alcohols, organic acids);

2) with molecular bonds (benzene, paraffin);

3) with ionic bonds (oxide and sulfide melts, aqueous and other solutions of salts, alkalis, acids);

4) with metal bonds (interaction of cations with free electrons).

Oxide and sulfide melts participating in metallurgical processes are multicomponent liquids and have a complex structure. In molten salts related to ionic liquids, there is a strong interparticle interaction and a high concentration of particles per unit volume. Industrial metal melts are multicomponent liquids containing metallic and metalloid constituents.

When obtaining a metal melt of a given composition, an attempt is made to reduce the loss of alloying elements with slag and the gas phase. This is facilitated by knowing the regularities of the redistribution of elements between the contacting phases, the ability to calculate the thermodynamic activity of components in metallurgical melts.

To solve such problems, it is necessary to know the structure (structure) of melts and the nature of the forces acting between the structural units of the melt. To assess the rate of processes occurring in the system, it is necessary to know a number of physicochemical properties of melts.

The structure or structure of a melt is understood as a quantitative description of the mutual arrangement in space of their constituent particles. The structure of the melt is interconnected with the electronic nature of the particles, the magnitude of the forces of interaction between the particles and with its physicochemical properties, which are often called structure-sensitive properties.

5.2. Metal melts

Pure liquid metals are usually referred to as so-called simple liquids, which are liquefied inert gases with Vanderwaal forces of interaction. In liquid metals, interparticle communication is carried out by itinerant electrons; their presence explains electrical conductivity, thermal conductivity, as well as viscosity and adsorption, along with other properties of metals.

At temperatures close to the crystallization temperature, the structure of liquid metals is close to the structure of solid crystalline bodies. This similarity lies in the comparability of the nature of the interparticle interaction and thermodynamic properties. In the liquid state, atoms (ions) are at close distances, but do not form a strictly periodic regular structure, that is, long-range order, characteristic of solid crystalline bodies.

The introduction of various impurity elements (including alloying elements) into the metal changes the electronic structure of the melts, while, depending on the nature of the impurity, the form of its existence in the melt differs from the form of existence of the solvent.

Thus, elements such as manganese, chromium, nickel, and other metals that differ little from iron in electronic structure have unlimited solubility in liquid iron and high solubility in solid iron. They form solid substitutional solutions with iron, while occupying part of the sites in the crystal lattice.

Elements such as carbon, nitrogen and hydrogen form interstitial solutions with iron, while being located in the interstices of the iron crystal lattice.

Silicon and phosphorus in liquid iron dissolve indefinitely, and in solid iron - their solubility is limited. In iron melts, they form separate groups of iron atoms with silicon and phosphorus, with a predominance of covalent bonds.

Dissolved in liquid iron (or other solvent) impurities change the properties of metal melts and affect the nature of the course of steelmaking processes. These properties include viscosity, surface properties, density, electrical conductivity and thermal conductivity.

5.3. Thermodynamic properties of metallic melts.

Interaction parameters

Metallic melts, which are in essence solutions, are characterized by a complex physicochemical interaction between the particles of which they are composed. The reliability of the thermodynamic description of metallurgical systems is determined by the degree of development of one or another thermodynamic theory. In this case, depending on the nature of the adopted certain assumptions, statistical theories are divided into rigorous theories (for example, quantum mechanical); theories based on a numerical experiment; model theories.

The latter have become quite widespread - these are the theory of perfect solutions, the theory of ideal dilute solutions, the theory of regular solutions, and others. One of the reasons for the introduction of such theories is the absence of a general thermodynamic model of solutions.

In describing the thermodynamic properties of metal melts, the most frequently used model is the method of interaction parameters.

This method is used to take into account the effect of all components of the solution on the activity of the component under consideration (for example, component A is the solvent, components B, C and D are added impurities). The interaction parameters are determined as a result of the Taylor expansion of the excess free energy for component B near the point corresponding to the pure solvent:

https://pandia.ru/text/79/398/images/image083_4.gif "width =" 39 "height =" 25 "> by mole fractions of impurity elements are called molar interaction parameters of the first order, the second - of the second order https: / /pandia.ru/text/79/398/images/image086_4.gif "width =" 28 "height =" 28 ">.

Taking this into account, expression (5.1) for solutions with low values ​​of dissolved components (B, C, D, ...) can be written in the form

Or for the i-th component

. (5.2)

For multicomponent solutions, a 1% diluted solution is usually taken as the standard state of a substance. In this case, instead of (5.2), write

or in general (5.3)

here

5.4. Slag melts. Composition, structure, thermodynamic properties

Metallurgical slag is a multicomponent (mainly oxide) solution that interacts with the metal melt and the gas phase of the metallurgical unit. The slag may contain sulfides, fluorides, and other non-metallic inclusions. In the course of metal melting, the slag performs the most important technological functions (for example, such as protecting the metal from the atmosphere of the unit; absorption of harmful impurities from the metal; participation in oxidative processes; diffusional deoxidation of the metal).

The structure of the slag melt is determined by the nature of structural units and their distribution in space. A comprehensive study of the main physicochemical properties of slag melts - viscosity, diffusion, adsorption, carried out, inter alia, using X-ray diffraction studies of solid and liquid slags, showed that in a molten state the slag melt consists of ions - cations and anions.

The composition of slags significantly affects their main properties, among which basicity should be distinguished - the ratio of the concentration of oxides with pronounced basic properties, and oxides with acidic properties. Further, depending on the composition, slags are subdivided into basic (they are dominated by basic oxides - CaO, MgO, MnO, etc.) and acidic (SiO 2, Al 2O 3, TiO 2).

The composition of the slag and its structure affects the physicochemical properties: density, surface properties, viscosity, diffusion.

Density and molar volume are structurally sensitive properties; these characteristics are used to calculate the kinetic properties of ionic melts. The influence of the composition is determined by a change in the coordination number and is characterized by a change in the free volume. The temperature dependence is associated with a change in the interatomic distance due to an increase in the atomic vibration amplitude.

When analyzing the surface properties, it was found that for most binary systems, the surface tension changes linearly with a change in composition.

Another important characteristic of slag melts is the viscosity, which varies within 0.1 ... 1.0 Pa · s (due to the presence of large structural units such as silicon-oxygen complexes), which is higher compared to metal melts.

Dynamic viscosity η and kinematic ν are related by the relation η = 1 / ν.

The dependence of viscosity on temperature is expressed by the equation

η = Аехр (Еη / RT),

where Eη is the activation energy of the viscous flow.

The thermodynamic properties of slag melts are described using various theories - molecular and ionic, which are based on the results of studies of the mineralogical composition of the crystallized slag and the generalization of experimental data.

The variant of the molecular theory of the structure of liquid slags, developed by G. Schenck, is simple and is based on the statement that molecules of free oxides (CaO, SiO 2, FeO ...) and their compounds are considered as single slag structures.

From the variety of oxide compounds, 5 were selected: 2FeO · SiO 2, 3CaO · Fe 3O 4, 2MnO · SiO 2, CaO · SiO 2, 4 CaO · P2O5. These compounds satisfactorily describe a wide range of slag properties, including the distribution of elements between the metal and the slag based on the equilibrium constants of the dissociation reactions of the given compounds.

However, the main feature and disadvantage of the molecular theory of slag melts is the lack of taking into account the real structure of slag melts. Nevertheless, the accumulated material allows one to evaluate some thermodynamic characteristics - for example, the activity of ai components.

The theory of perfect ionic solutions (author) is based on the statement that the slag solution completely dissociates into ions (cations and anions); ions of the same sign are energetically equal; the nearest neighbors of each ion are ions of the opposite sign; the solution is formed without changing the volume; during thermal motion, permutations between ions of the same sign are possible. The activity of the components of such a melt is calculated as the product of the ionic fractions of cations and anions.

For example, the activity of calcium sulfide CaS will be determined by the ratio

where хСа, хS - ionic fractions of calcium cation and sulfur anions, respectively.

The theory of perfect ionic solutions can be used to determine the activities of components in strongly basic slags, however, an increase in the proportion of SiO 2 and Al 2O 3 to 20% gives a strong discrepancy between theory and experiment; therefore, this theory is not used in practical calculations of equilibria.

However, the main static provisions of this model are applicable in the theory of regular ionic solutions, developed and tested.

The features of this theory include the following provisions: the entropy of a solution is not considered ideal and is calculated as according to the theory of perfect ionic solutions; the solution consists of the simplest atomic ions (cations - metal ions Ca2 +, Fe 2+, Al 3+, and anions - metalloid ions O2–, F -, S 2–); the nearest neighbors of ions are ions of the opposite sign; the solution is formed without changing the volume, with the release or absorption of heat.

When calculating the chemical potentials of the components of a solution - as well as when determining the activity of the components; in this theory, it is necessary to take into account the mixing energy of the components Qij, which is found on the basis of the results of experimental studies of solutions from compounds containing cations i and j. This theory is characterized by the fact that the relationship between the composition and thermodynamic functions is established more strictly and reasonably, therefore the accuracy and reliability of calculations is higher.

In the polymerization theory of slag melts, it is assumed that the ions forming the solutions are energetically unequal, while polymerized complexes are formed, in which the binding energy of the complexes with other structural units of the solution is formed.

According to the theory of solutions as phases with a collective system of electrons (the main provisions have been developed), not chemical compounds are selected as a component of the slag solution, but the elements of the periodic system, therefore the composition of the solution is expressed in atomic fractions. In this case, the electrons of all atoms of the solution form a single quantum mechanical system. The activity of the compound Аm Вn in the slag solution is determined as

,

where https://pandia.ru/text/79/398/images/image095_3.gif "width =" 23 "height =" 25 src = "> - activities of elements A and B.

The activity of an element of type i is determined by the atomic fraction of this component and the energy of interaction with component j. In this case, the interaction energy Еij is defined as

Еij = 1/2 (χ1 / 2 - χ1 / 2) 2,

where χi and χj are the atomic parameters of atoms i and j, determined from the values ​​of the standard enthalpies of formation for various compounds.

6. GASES IN STEELS. NITRIDE FORMATION PROCESSES

High-temperature metallurgical processes are characterized by the interaction of the metal melt with the slag and gas phases. The completeness and rate of interaction of gases primarily with liquid metals determines the quality of metal products.

The dissolution of diatomic gases (oxygen, hydrogen and nitrogen) in a liquid metal is the same, obeys the law of A. Sieverts (known as the square root law) and occurs according to the reaction

The equilibrium constant of reaction (6.1) has the form

, (6.2) where

The equilibrium concentration of gas [Г] in a metal at = 1 atm is called solubility and is numerically equal to the equilibrium constant of reaction (6.1) for a two-component "metal-gas" system.

At a temperature of 1600 ° C, the limiting solubility of oxygen in liquid iron is 0.22%, for nitrogen - 0.044%, for hydrogen - 0.0026%.

The processes of dissolution of gases in most metals (iron, nickel, etc.) are endothermic, therefore, with an increase in temperature, the solubility of gases increases. An exception is the solubility of nitrogen in -Fe, which decreases with increasing temperature at the points of phase transitions of iron from one modification to another (-Fe -Fe, -Fe https://pandia.ru/text/79/398/images/image102_2.gif "width =" 13 "height =" 20 src = "> - Fe) and during melting (-Fe EN-US"> Fe -l) the equilibrium concentration of gases in the solution change abruptly.

According to (6.2), the solubility of gases is also influenced by pressure. With increasing pressure, the equilibrium of reaction (6.1) shifts towards a smaller number of gas moles, i.e., to the right. Satisfaction of Sieverts' law indicates the ideality of the resulting solution. In the presence of other components dissolved in the metal, the equilibrium gas concentrations become different. This influence can be taken into account using the parameters of the interaction of the component with the dissolved gas.

In the case when<0, происходит снижение коэффициента активности газа в расплаве и повышение его растворимости. Например, элементами, повышающими растворимость водорода в железе, являются титан, ниобий, ванадий. Снижению растворимости водорода в железе способствуют такие элементы, как углерод, алюминий , кремний (для них >0).

In almost the same sequence, these components affect the activity coefficient of nitrogen and its solubility.

A strong decrease in the solubility of hydrogen and nitrogen during the crystallization of iron and its alloys is accompanied by a number of undesirable phenomena. Hydrogen in molecular form is isolated in the defective places (microvoids) of the crystallized metal. With a decrease in the size of these microdefects during subsequent plastic processing, it creates high pressures, as a result of which stresses arise in the metal, leading to a decrease in plasticity, as well as discontinuity.

The influence of alloying elements on the solubility of nitrogen in melts based on iron or nickel can be estimated using the experimentally established ones.

When nitrogen interacts with melts doped with nitride-forming elements, the formation of an Fe-R-N solution in equilibrium with the gas phase is possible, and with an increase in the R content, the solubility of nitrogen increases.

At certain contents of the R component, a refractory compound, RN nitride, can be released from the melt. The elements Iva of the Ti, Zr, Hf subgroups have the highest affinity for nitrogen, which are used mainly for binding nitrogen in liquid metal.

Dispersed carbides released from the solution cause a strong decrease in the ductility of the metal and increase its hardness.

The specific features of the interaction of nitrogen with metal melts are reflected in the Me-R-N phase diagram, a fragment of the isothermal section of which in the regions rich in metal is shown in Fig. 6.1.

The lines bounding the regions of phase stability are described by the corresponding equations of equilibrium thermodynamics.

As can be seen from the diagram, with small amounts of a nitride-forming element, there is a two-phase region of stability of the liquid phase with gaseous nitrogen. The coordinates of the AB line separating this region (I) and the region of liquid stability (II) can be determined by analyzing the equation:

At atm, the nitrogen activity is equal to the equilibrium constant of reaction (1). The concentration of nitrogen at point A is equal to its solubility in the binary system Me-N.

Figure 6.1. Isothermal section diagram of the state diagram of the Me-R-N system

In fig. 6.1 shows the following regions of phase stability:

I - w + N2,

II - f,

III - w + RN,

IV - g + RN + N 2.

The intersection of the nitride formation isotherm (BCD) and the line (AB) corresponding to the solubility of nitrogen in the Fe-RN melt at font-family: Symbol "> - [R] of the concentration triangle at the point corresponding to the RN compound, and the BE line at the point corresponding to the pure nitrogen at atm.

7. OXIDATION OF METAL ALLOYS

During the oxidizing period of steel melting in the steelmaking unit, oxygen entering the metal (from the oxidizing slag blown into the metal bath by a gas jet) is spent mainly on the oxidation of impurities (C, S, P, Si) and some alloying components, but some of it remains in the metal melt.

The solubility of oxygen in iron under pure ferrous slag is estimated based on the reaction

(FeO) = +. (7.1)

.

Chipman found that for react (7..gif "width =" 176 height = 47 "height =" 47 ">.

At T = 1600 ° C (1873K), the limiting oxygen solubility in iron is 0.21%.

However, in real melting conditions, steel-making slags, in addition to FeO, contain numerous oxides and other inclusions, therefore. Therefore, the oxygen content in liquid steel does not reach the solubility limit and is at the level of 0.06 ... 0.08. In this case, when the content in the metal melt is more than 0.05 ... 0.06% C, the oxygen content in the metal is determined by the development of the carbon oxidation reaction

+ = (CO). (7.2)

When the metal melt reaches an equilibrium state at T = 1873 K, the ratio · = 0.0025 should be fulfilled, however, under real conditions of steel melting in industrial units, the carbon oxidation reaction does not reach equilibrium, in particular, because of the conditions for the formation of CO bubbles. In this regard, in the course of steel melting under the oxidizing slag, the oxygen content in the metal is higher than the equilibrium one and approaches it when the carbon content is less than 0.15%. In fig. 7.1 shows the dependence of the oxygen content in the metal melt on the carbon content.

Rice. 7.1 Change in oxygen content in iron-carbon melts: 1 - equilibrium curve; 2 - area of ​​actual concentrations of steel melting

The actual oxygen concentration in steel for all types of processes fits into one area. This indicates that at> 0.05 ... 0.06, the carbon oxidation reaction has a decisive effect on the oxygen content in steel. At< 0,05…0,06 содержание кислорода в металле соответствует равновесному с углеродом и бывает ниже его. Следовательно, равновесное со шлаком содержание кислорода в Me достигает величин, соответствующих равновесию с углеродом или даже меньше их.

Reaction (7.2) is exothermic, therefore, upon cooling and crystallization of the metal melt, the value · at Р = const decreases; excess oxygen concentrations are even higher, which leads to the formation of gas bubbles, which reduce the density of the ingot, and the release of inclusions of iron oxides and its solutions with sulfides along the grain boundaries of the crystallizing metal. These oxysulfides impart red brittleness to the metal due to their low melting points.

The liquation of elements, especially oxygen, also has a strong effect: during crystallization, its content in the initial solution at the front of growing crystals is much higher than the average in the volume of liquid metal, which causes intense oxidation of carbon.

In this regard, one of the main tasks of the final melting period is to remove excess oxygen from the liquid stage, which is achieved by deoxidizing the metal melt.

Deoxidation is understood as a set of operations to reduce the oxygen content in liquid steel.

The main tasks of deoxidation are:

- a decrease in the oxygen content in liquid iron by additives of elements with a higher affinity for oxygen than that of iron, to a level that ensures the production of a dense metal;

- creation of conditions for more complete removal of deoxidation products from liquid steel.

If the first problem is considered using the laws of chemical thermodynamics, then the second is solved using the apparatus of chemical kinetics.

The thermodynamic approach makes it possible to reveal the relationship between the oxygen content in liquid steel and the content of the deoxidizing element R, to determine the degree of influence of temperature on the nature of this relationship, and also to calculate the minimum oxygen content in the metal melt when it is deoxidized with the element R.

The most common method of deoxidation is the precipitation, or deep method, according to which elements with a higher affinity for oxygen (Si, Al, Ca) than iron are introduced into the depths of the metal. These elements bind oxygen into strong non-metallic inclusions (usually oxides), the solubility of which in iron is several orders of magnitude lower than the solubility of FeO. These inclusions separate into a separate phase in the form of a fine suspension, which, having a lower density compared to steel, partially floats into the slag, and partially remains in the crystallized metal in the form of non-metallic inclusions, deteriorating its quality.

Precipitating (deep) deoxidation can be described by a reaction of the form

. (7.3)

Under the condition, the equilibrium constant of this reaction will take the form

(7.4)

where ai is the activity of the ith component in the melt.

To calculate the activities of the melt components, a 1% diluted solution is usually taken as the standard state.

Diffusive deoxidation is achieved when equilibrium is established according to the reaction

(FeO) = + [O]

The method is based on the idea of ​​striving for an equilibrium distribution of matter between immiscible liquid phases - Me and slags. In this case, the relation

(7.5)

With a decrease in the activity of iron oxides in the slag, oxygen diffuses in the metal to the interface and, in the form of pairs of Fe 2+ and O 2– ions, passes into the slag.

The advantage of this method is the absence of any reaction products in the metal after removal of oxygen.

This method is implemented in an EAF with a small amount of slag and a low oxygen content in the gas phase. In other steel-making units, diffusion deoxidation is not used today because of the low process speeds.

Most often, diffusion deoxidation is used as a concomitant process when processing liquid steel in a ladle with synthetic lime-alumina slags with a low FeO content (less than 1%). When metal is crushed into small droplets, the surface of the metal-slag contact increases thousands of times, the presence of convective currents accelerates the process of not only deoxidation, but also desulfurization of steel.

Another method of deoxidation is vacuum deoxidation, which is based on the decarburization reaction C (7.2).

A decrease in pressure shifts the equilibrium of this reaction in the forward direction. The advantage of this method is the absence of deoxidation products in the metal. This method is implemented in out-of-furnace steel processing.

There is a complex deoxidation based on the use of complex deoxidizers - alloys of two or more components (silicocalcium, silicomanganese, etc.). The advantages of using such deoxidizers are predetermined by a significant improvement in the thermodynamic conditions for deoxidation and more favorable kinetic conditions for the nucleation, enlargement and removal of nonmetallic inclusions.

Thus, the addition of Mn to Fe during its deoxidation with silicon leads to an increase in the deoxidizing ability of the latter.

The effect of an increase in the deoxidizing ability under the influence of the second component is explained by a decrease in the thermodynamic activity of the formed oxide in complex deoxidation products, which differ significantly from products with separate deoxidation.

The deoxidizing ability of an element is understood as the equilibrium concentration of oxygen dissolved in iron (metal), corresponding at a given temperature to a certain content of this element. Obviously, the lower this concentration at a given deoxidizing agent content, the higher the deoxidizing ability of the element.

M / n lg [R] - m / n lg fR - lg fO. (7.9)

Equating the right-hand side of equation (7.10) to zero and solving it with respect to R, we find the concentration of the deoxidizer R, corresponding to the minimum oxygen content in the metal; in this case, the values ​​of the activity coefficients of the components are found by the relations (7.7) and (7.8):

(7.11)

(7.12)

Substituting the value [R] from relation (7.12) into equation (7.9), we determine the minimum oxygen concentration in the metal melt deoxidized by the element R:

(7.13)

In fig. 7.2 shows the deoxidizing ability of some elements in liquid iron at T = 1600 ° C.

The oxygen content is difficult to depend on. At low concentrations of the deoxidizing agent, the oxygen content decreases with increasing R. A further increase leads to an increase in the oxygen concentration in the metal. However, with an increase in the oxygen content caused by a decrease in the activity coefficient, the oxygen activity decreases, which is also confirmed by experimental data. Fractures on the curves of the oxygen content in liquid iron in Fig. 7.1 are a consequence of the formation of different deoxidation products with a change in the content of the deoxidizer.

The nucleation of deoxidation products can be carried out in a homogeneous phase (the so-called spontaneous nucleation) or on finished surfaces (surfaces of the walls of the unit, slag, suspended inclusions, oxide films on deoxidizers).

In all cases, the nucleation of new phases occurs as a result of fluctuations - a random accumulation of particles (atoms, ions) differing in composition from the average content in the metal. These fluctuations, depending on their magnitude and external conditions, can disappear or, having overcome some energy barrier, develop, developing into inclusions.

Rice. 7.2 Deoxidizing ability of elements in liquid iron at T = 1600 ° C

It has been experimentally confirmed that in a homogeneous system, during the formation of nuclei of a new phase, they initially have an increased affinity for oxygen and cause the highest surface tension at the "metal - nucleus of a new phase" interface. With the subsequent growth of inclusions, the concentration of active components involved in the formation of a new phase decreases. Those components of the melt that contribute to a decrease in the thermodynamic activity of oxides that separate in fluctuations facilitate the formation of nuclei, and those that contribute to a decrease in the activity of the deoxidizer and oxygen in the metal make it difficult to separate them.

In the case of the nucleation of inclusions on gas surfaces, in addition to those noted above for homogeneous phases, the effect of surface wetting by the segregating phase is significant. The smaller the contact angle, the smaller the fluctuations become nuclei. The formation of nuclei is facilitated with the predominant separation of substances that are capillary-active at the interface.

In the case of a significant deviation from the equilibrium state, homogeneous nucleation is decisive. With a decrease in the supersaturation of one or another component, the role of finished surfaces as nucleation centers increases. The effect of finished surfaces, especially when separating solid inclusions, is the more effective, the closer the orientational and dimensional correspondence of the crystals of the separating inclusion and the existing substrate is.

The nucleated inclusions (their initial size is of the order of 1 nm) enlarge as a result of coagulation (joining) of particles upon collision and the release of matter on these particles from the metal melt due to oversaturation of the solution. The rate of coagulation is influenced by the frequency and efficiency of particle collisions, which occurs due to Brownian motion, as well as due to the difference in speed of movement, which is caused by unequal sizes and densities of particles and the presence of convective currents

Convective currents ensure the delivery of deoxidation products from the depth of the metal to the metal-slag interface. The displacement of the inclusion at the metal-slag boundary is determined by the direction and magnitude of the resultant of a number of forces: buoyancy (Archimedean) F A, due to the difference in the densities of the metal and slag and directed vertically upward; capillary F cap, caused by the concentration gradient of capillary-active substances and directed towards their higher concentration; inertial - centrifugal F Ц, caused by the curvature of the trajectory and directed into the depth of the metal, since the density of inclusions is less than the density of steel, and the inertial force F and, the direction of which depends on the direction of movement of particles: for freely floating inclusions, it is directed vertically upward, and for those carried by flows - coincides with the direction of flow.

Depending on the size and shape of the inclusions, the deoxidation of the metal and slag, and the hydrodynamics of flows, the effect of each of these forces on the speed of approach of a particle to the surface of the slag is different. Large inclusions approach the boundary mainly under the action of a buoyant force, smaller ones - under the action of capillary ones, especially with a large gradient of oxygen concentration.

With a decrease in the surface on which these forces act, the pressure increases and the breakthrough of the metal layer is realized faster. It is easier to overcome such resistance by solid inclusions of irregular shape with sharp edges, more difficult - with flat ones.

Thus, the more completely the steel is deoxidized and the inclusions are removed from it, the higher the quality of the finished metal.

8. DISTRIBUTION OF ELEMENTS BETWEEN METAL AND SLAG

The distribution of impurity elements of a liquid metal or any metal (element) between the metal and slag phases depends on the chemical affinity of the elements for oxygen, the composition of the slag, the interaction of the elements with each other in the metal and slag, and temperature.

The influence of the chemical composition of the slag is associated with the chemical properties of the oxide formed during the oxidation of the impurity element.

The influence of temperature manifests itself depending on the sign of the heat effect of the oxidation reaction of the impurity and the transition of the oxide to the slag, which, as a rule, is positive (ΔН< 0).

The distribution of elements that occurs as a result of a chemical reaction between the metal and the slag can be characterized using the distribution coefficient of the substance L i.

Under certain conditions, this indicator can be a quantitative characteristic of the distribution of an impurity due to an oxidative reaction with a change in the electronic state of this impurity during the transition from one phase to another.

The equilibrium distribution index can be expressed from the equilibrium constant of the oxidation reaction of an element, which occurs, for example, during the interaction of contacting phases of metal and slag melts:

X [E] + y (FeO) = (Ex O y) + y; (8.1)

. (8.2)

Taking into account (8.2), the distribution coefficient of the element [E] will be expressed in the form:

. (8.3)

Analysis of equation (8.3) makes it possible to identify the conditions for the transfer of elements from one phase to another: from metal to slag or vice versa. Below are examples of the distribution of some elements between metal and slag.

For silicon, the equilibrium of the interphase distribution reaction is expressed as

2 (FeO) = (SiO 2) + 2; (8.4)

. (8.5)

The conditions for the maximum transition of silicon from metallic to slag melt will be as follows:

1) lowering the temperature, which makes it possible to increase the value of КSi, since for a given chemical reaction ΔН< 0;

2) an increase in the activity (FeO) in the slag and the oxidation of the metal [% O];

3) a decrease in the activity coefficient of particles containing Si in the slag;

4) an increase in the activity of Si in the metal melt.

Conditions 2 and 3 are fulfilled at a certain basicity of the slag: an increase in% CaO decreases the activity coefficient of particles containing Si due to their groups with Ca 2+ ions.

Silicon has a high affinity for oxygen, for it EN-US "> 2 [P] + 5 (FeO) + 4 (CaO) = (4 (CaO) · (P 2 O 5)) + 5; (8.6)

(8.7)

The activity of particles containing phosphorus in the slag decreases with increasing CaO content, which is associated with the formation of groups of the type 4CaO · P 2O 5. From the analysis of (8.6) and (8.7) it follows that for a more complete transfer of phosphorus from metal to slag, it is necessary to increase EN -US "> FeO, as well as CaO. In this case, the greatest influence of one of these quantities is manifested at increased values ​​of the other.

The conditions for the maximum transfer of phosphorus from metal to slag are:

1) an increase in the activity of FeO (ions Fe 2+ and O2-) in the slag, which makes it possible to obtain the oxidized form of phosphorus (P 2O 5);

2) an increase in the CaO content and basicity of the slag, which makes it possible to reduce the activity of the particles in the oxide melt containing phosphorus;

3) lowering the temperature: this factor should be taken into account, all other things being equal, since an increase in temperature in modern oxidative processes does not reduce the possibility of removing phosphorus when receiving more basic pre-phosphoric slags;

4) the presence in the metal melt of elements that have positive parameters of interaction with phosphorus (carbon, silicon, oxygen).

BIBLIOGRAPHIC LIST

1. Theory of metallurgical processes: textbook for universities /, etc. - M .: Metallurgy, 1989. - 392 p.

2. Popel, metallurgical processes: a textbook for universities /,. - M .: Metallurgy, 1986 .-- 463 p.

3. Paderin, and calculations of metallurgical systems and processes: a textbook for universities /,. - M .: MISIS, 2002 .-- 334 p.

4. Grigoryan, the basics of electric steel-smelting processes: a textbook for universities /,. - M .: Metallurgy, 1989 .-- 288 p.

5. Kazachkov, on the theory of metallurgical processes: a textbook for universities /. - M .: Metallurgy, 1988 .-- 288 p.

Introduction ……………………………………………………… ... ………… ...... …… 3
1. Composition and properties of high-temperature gas atmosphere

1.1. Thermodynamics of gas atmospheres ………………………………………… 3
1.2. Homogeneous gas processes ………………………………………… .. 7
2. Analysis of combustion processes of solid carbon ………………………………… 9
3. Evaluation of the strength of chemical compounds ………………………………… .. 11
3.1. Dissociation of carbonates ……………………………………………… .. 12
3.2. Dissociation of iron oxides …………………………………………… ... 13
3.3. Mechanism and kinetics of dissociation processes ………………………… .. 15
3.4. Oxidation of hard metals ………………………………………… ... 18
4. Metals recovery processes

4.1. Thermodynamic characteristics of reduction processes ... ... .... 21
4.2. Reduction of iron oxides with solid and gaseous

reducing agents ………………………………………………………… .. 21
4.3. Mechanism and kinetics of reduction processes ……………………… .. 23
5. Metallurgical melts

5.1. General characteristics …………………………………………………… .. 26
5.2. Metallic melts. …………………………………………………. 27
5.3. Thermodynamic properties of metallic melts. Options

interactions …………………………… .. ……………………………… 28
5.4. Slag melts. Composition, structure, thermodynamic properties ... 29
6. Gases in steels. Nitride formation processes ………………………. ……… 31
7. Deoxidation of metal melts ………………………………………. 34
8. Distribution of elements between metal and slag ……………… .. …… 40
Bibliographic list …………………………………………………… 43

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n1.doc

FGOU VPO

SIBERIAN FEDERAL UNIVERSITY

INSTITUTE OF NON-FERROUS METALS

AND MATERIALS SCIENCE

THEORY OF METALLURGICAL PROCESSES

LECTURES FOR STUDENTS SPECIALTIES

ENGINEER-PHYSICIST

KRASNOYARSK 2008

UDC 669.541

BBK 24.5

Reviewer
Approved as a study guide
I.I.Kopach
C 55 Theory of metallurgical processes: Textbook. Manual for the specialty "Engineer-Physicist" / SFU. Krasnoyarsk, 2008 .-- 46 p.

ISBN 5-8150-0043-4
The manual sets out the theoretical provisions of the main processes of metallurgical production, such as: dissociation, redox processes, chemical and physical methods of refining, metallurgical production slags and sulfide metallurgy.
Siberian Federal University, 2008

INTRODUCTION

1. 
   DISSOCIATION OF CHEMICAL COMPOUNDS
2. 
   COMPOSITION AND PROPERTIES OF THE GAS PHASE AT HIGH TEMPERATURES.
3. 
   OXIDATING-REDUCING PROCESSES.
   1. 
      Hydrogen reduction
   2. 
      Reduction with solid carbon
   3. 
      Recovery with CO gas
   4. 
      Metal recovery

4. REFINING OF METALS

4.1. Pyrometallurgical refining methods

4.2. Physical methods of refining

1. 
   Upholding
2. 
   Crystallization
3. 
   Vacuum refining

5. PROCESSING OF SULFIDE MATERIALS.

1. 
   Separation melting.
2. 
   Converting mattes.

6. METALLURGICAL SLAGS.

1. 
   The structure of slag melts

IN E D E N I E

The theory of metallurgical processes is physical chemistry that describes the behavior of chemically reacting systems at high temperatures, in the range from 800 to 2500 K and more.

The accelerated progress of mankind began after people learned to use metals. The level of development of the country and at present is largely determined by the level of development of the metallurgical, chemical and extractive industries. At present, the paths of extensive development are practically exhausted and the question of the intensive development of all branches of production, including metallurgy, has come to the fore. The last ten years have been characterized by qualitatively new approaches to all production processes, these are:

1. 
   energy and resource saving,
2. 
   deep processing of raw materials and industrial waste,
3. 
   the use of the latest scientific achievements in production,
4. 
   the use of micro- and nanotechnology,
5. 
   automation and computerization of production processes,
6. 
   minimization of harmful effects on the environment.

The listed (and many others) requirements make high demands on the level of fundamental and special training of a modern engineer.

The proposed textbook on the theory of metallurgical processes is an attempt to present the discipline at the first, lowest level of complexity, i.e. without mathematical proofs, with minimal justification of the initial positions and analysis of the results. The manual consists of 6 chapters, covering almost the entire process of obtaining metals from ores and concentrates.

First, let us recall the blast furnace process of smelting pig iron from iron ore or iron ore concentrates known from the school chemistry course. There are three phases in a blast furnace:

1. 
   gas phase, consisting of gases CO, CO 2, metal and oxide vapors,
2. 
   slag phase consisting of molten oxides CaO, SiO 2, Al 2 O 3, FeO, MnO, etc.
3. 
   a metallic phase consisting of liquid iron and impurities dissolved in it, such as carbon, manganese, silicon, phosphorus, sulfur, etc.

All three phases interact chemically and physically. Iron oxide is reduced in the slag phase and passes into the metallic phase. Oxygen dissolved in the slag phase passes into the metal phase and oxidizes impurities in it. Drops of oxides float up in the metal phase, and drops of metal settle in the slag phase. The transition of components from one phase to another is associated with their transfer across the phase boundaries, therefore, an engineer  metallurgist works with multicomponent, heterogeneous, chemically reactive systems.

Currently, metallurgy receives about 70 metals, which are usually subdivided into non-ferrous and ferrous. The latter include only 4 metals: iron, manganese, vanadium and chromium. The group of non-ferrous metals is more numerous, therefore it is divided into the following subgroups.

1. 
   Heavy: copper, lead, zinc, nickel, tin, mercury, 18 elements in total.
2. 
   Light metals: aluminum, magnesium, titanium, silicon, alkali and alkaline earth metals, 12 elements in total.
3. 
   Noble: gold, silver, platinum, etc., there are only 8 elements, they got their name due to the lack of affinity for oxygen, therefore, in nature they are in a free (non-oxidized) state.
4. 
   Rare metals: refractory - 5 elements, rare earth - 16 elements and radioactive - 16 elements.

According to the method of production, the processes for obtaining metals are divided into three groups:

pyrometallurgical,

hydrometallurgical and

electrometallurgical processes.

The first of them occur at temperatures of the order of 1000 - 2500 K, while the components are in the molten and dissolved states.

The latter occur in aqueous, less often organic, solvents, at temperatures of 300-600 K. Many hydrometallurgical processes also occur at elevated pressures, i.e. in autoclaves.

Electrometallurgical processes take place on electrodes both in aqueous solutions and in molten salt at different temperatures. For example, the electrolysis of alumina in a cryolite-alumina melt proceeds at 1230 K, and the electrolysis of platinum from an aqueous electrolyte - at 330 K.

The raw materials for the production of many metals are, first of all, oxidized ores, from which aluminum, iron, chromium, manganese, titanium, partly copper, nickel, and lead are obtained. Metals such as copper, lead, nickel, cobalt, and precious metals are obtained from the less common sulfide ores. Magnesium, calcium and alkali metals are obtained from chloride ores (from the waters of seas and lakes).

Metallurgical production has a harmful effect on the environment, namely:

1. 
   emissions of reaction gases such as CO, SO 2, SO 3, Cl, CS 2 and many other gases,
2. 
   moss and liquid particles of various sizes and composition,
3. 
   discharge of large volumes of industrial water polluting water bodies, including drinking water supply.
4. 
   large discharge of excess, low-value energy, which can be used to heat greenhouses, etc.

These factors have a negative impact. First of all, for workers of enterprises, as well as for nearby cities and towns. Therefore, one of the most important tasks of an engineer is to organize and plan production in such a way as to minimize harmful effects on the environment. Environmental problems should be in the first place not only in social production, but also in the personal self-restraint of each person, in the form of complete or partial rejection of personal transport, excessive consumption of energy resources, etc.

A rough estimate shows that a person commuting to work in public transport uses about an order of magnitude less fuel and oxygen, compared to comfort lovers traveling alone in a car with a displacement of several liters. The future of humanity, as a thinking community, is on the path of conscious self-limitation in the sphere of consumption of goods, services and, ultimately, energy resources.

 

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