Thermodynamic computations and analysis of the phase diagrams of multicomponent systems

№ 2725    МИНИСТЕРСТВО ОБРАЗОВАНИЯ И НАУКИ РФ
ФЕДЕРАЛЬНОЕ ГОСУДАРСТВЕННОЕ АВТОНОМНОЕ ОБРАЗОВАТЕЛЬНОЕ УЧРЕЖДЕНИЕ ВЫСШЕГО ПРОФЕССИОНАЛЬНОГО ОБРАЗОВАНИЯ
   «НАЦИОНАЛЬНЫЙ ИССЛЕДОВАТЕЛЬСКИЙ ТЕХНОЛОГИЧЕСКИЙ УНИВЕРСИТЕТ «МИСиС»

  Кафедра металловедения цветных металлов




                А.В. Поздняков
                В.В. Чеверикин
                О.А. Яковцева




  THERMODYNAMIC
  COMPUTATIONS AND ANALYSIS
  OF THE PHASE DIAGRAMS
  OF MULTICOMPONENT SYSTEMS





  Учебное пособие



   Рекомендовано редакционно-издательским советом университета


Москва 2015

УДК 536.717 П47


Рецензент канд. техн. наук А.Н. Алабин




            Поздняков А.В.


П47 Thermodynamic computations and analysis of the phase diagrams of multicomponent systems : учеб. пособие / А.В. Поздняков, В.В. Чеверикин, О.А. Яковцева. - М. : Изд. Дом МИСиС, 2015. -37с.- Текст англ.
          ISBN 978-5-87623-935-8

          В пособии представлены возможности программы Thermo-Calc, которая позволяет проводить термодинамические расчеты двойных, тройных и многокомпонентных фазовых диаграмм, фазового состава сплавов, состава фаз, неравновесной кристаллизации. Показано применение программы для расчета фазового состава промышленных сплавов, а также даны рекомендации по выполнению курсовой работы.
          Содержание пособия соответствует программе дисциплины «Thermodynamic computations and analysis of the phase diagrams of multicomponent systems» для студентов, обучающихся по магистерской программе «Advanced Metallic Materials and Engineering».

УДК 536.717

          This tutorial presents the program features Thermo-Calc, which allows to carry out thermodynamic calculations of binary, ternary and multicomponent phase diagrams, phase composition of the alloys, composition of the phases, the non-equilibrium crystallization, the application program to calculate the phase composition of industrial alloys and recommendations for implementation of course work.
          The content of the tutorial corresponds to the program of discipline “Thermodynamic computations and analysis of the phase diagrams of multicomponent systems”, for students studying on master’s program “Advanced Metallic Materials and Engineering”.

© А.В. Поздняков,
                                                      В.В. Чеверикин,
                                                      О.А. Яковцева, 2015
ISBN 978-5-87623-935-8                             © НИТУ «МИСиС», 2015

CONTENT


Introduction                                                       4
1  Calculations of binary and ternary phase diagrams                7
2  Calculation of polythermal sections                            12
3  Calculation of isothermal sections                             17
4  Calculation of phase composition and composition of the phases 20
5  Calculation of non-equilibrium crystallization                 22
6  Application of Thermo-Calc to calculate phase composition
of industrial alloys                                              26
7  Recommendations for implementation of course work              33
References                                                        36

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                Introduction




      To provide the required mechanical and technological properties of alloys need to choose their composition. In this case it is useful to use the phase diagram of systems. Using phase diagrams allow for analysis of the phase composition, structure and properties of materials in specific operating conditions. Currently, binary and ternary the phase diagram of metallic systems have been well studied. But only knowledge of binary and ternary phase diagrams is not enough for a complete representation of the phase composition of industrial alloys that can contain up to ten or more elements. Respectively, it is necessary to investigation of the multicomponent phase diagrams and for their investigations we can use the Thermo-Calc software.
      Thermo-Calc software is a software package that contains a large number of thermodynamic data for calculations of phase diagrams. Calculations based on thermodynamic databases, an assessment of the experimental data using the CALPHAD method.
      CALPHAD (CALculation of PHAse Diagrams) - method of calculation of phase diagram.
      Under the equilibrium phase diagram usually understand diagrams depending on the composition of the chemical system of the temperature. The phase diagram of the areas of existence are marked compounds and solutions (i.e. phases) and the area of their coexistence.
      Phase diagrams - a very powerful tool to predict the state of the system under different conditions. They first appeared as a graphic method of generalization of experimental data on the equilibrium.
      In the CALPHAD method one collects and assesses all available experimental and theoretical information available on phase equilibria and thermochemical properties in a system. Thus it is possible to calculate the phase diagram by an initial assessment of the thermodynamic properties of all phases of the system.
      CALPHAD method brings together all experimental information on the phase equilibria in the system and all the thermodynamic information obtained during the thermochemical and thermophysical investigations. Further set of thermodynamic properties of each phase is described by a mathematical model containing adjustable parameters. These parameters are evaluated by optimizing the fit of the model to all the assessed information, also involving coexisting phases. Following this it is possible to recalculate the phase diagram, as well as the thermodynamic

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properties of all the phases and the system as a whole. The philosophy of the CALPHAD method is to obtain a consistent description of the phase diagram and the thermodynamic properties so to reliably predict the set of stable phases and their thermodynamic properties in regions without experimental information and for metastable states during simulations of phase transformations.
      A core ingredient of the CALPHAD method is the development of models to represent thermodynamic properties for various phases which permit prediction of properties of multicomponent systems from those of binary and ternary subsystems. This is accomplished by considering physical and chemical properties of the system in the thermodynamic model, for example, account is taken for crystallography, type of bonding, order-disorder transitions, and magnetic properties.

      1 Thermodynamic modeling of phase
      There are two critical factors for successful use of the method CALPHAD. The first factor - is finding a realistic and convenient mathematical model of the Gibbs energy for each phase. Gibbs energy is used because most of the experimental data obtained under certain temperature and pressure. In addition, any other thermodynamic quantities can be obtained on the basis of the Gibbs energy. A complete description of the Gibbs energy of a multicomponent system in analytic form is impossible. Therefore it is necessary to identify the main features of which are based mathematical model. Discrepancy between the modeled system and the real system in finite form is submitted power series expansion of temperature, pressure and composition of the phases. Adjustable parameters of the model description specified to reproduce the experimental data. Power of CALPHAD method is that the description of the subsystems constituting the multicomponent system can be combined for a complete description of its.
      2  Calculation of equilibrium
      Another critical factor is the availability of computer programs for calculating the equilibrium of various types of schemes and database with expert information. Currently there are many different types of models used for various types of phases, there are several thermodynamic databases (both commercial and freeware) of different materials (steel, superalloys, solid materials, aqueous solutions, oxides, etc.). There are also several different types of programs using different types of algorithms

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for calculating the equilibrium. The most advanced of them allow you to use in the calculation of the equilibrium not only the temperature, pressure and composition but also many other types of conditions for the existence of the system, because equilibrium may be determined using a constant volume, or specified chemical potential element or composition of particular phase and others.
      3 Using
      CALPHAD method developed slowly from the 1960s to the 1980s. In the 1980s have appeared complex systems on the basis of thermodynamic databases. Today there are several of commercial software (FactSage, MTDATA, PANDAT, Thermo-Calc, NUCLEA / GEMINI et al.). They are used for research and production. The use of these software allows to reduce essentially time and costs by optimization of experimental work as a result of the thermodynamic prediction of the behavior of multicomponent systems (it would have been impossible without the use CALPHAD method).

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Calculations of binary and ternary phase diagrams




      Thermo-Calc program widely used for a variety of calculations including calculating: Stable and meta-stable heterogeneous phase equilibria; amounts of phases and their compositions; thermochemical data such as enthalpies, heat capacity and activities; transformation temperatures, such as liquidus and solidus; driving force for phase transformations; phase diagrams (binary, ternary and multi-component); solidification applying the Scheil-Gulliver model (Sheil simulation); thermodynamic properties of chemical reactions and much more. The program contains database alloys based on Fe, Ni, Al, Ti, Mg, by solders, slags, etc.
      Figure 1.1 show main window of Thermo-Calc program. This window is always open when Thermo-Calc is running. On the Toolbar can be identified 4 main buttons needed to work with the program: 1 - define a binary system and calculate a binary phase diagram, Gibbs energy curves, Activity curves or Phase fraction diagram; 2 - define a ternary system and calculate isothermal section, monovariant lines or liquidus projection diagrams; 3 - simulate a solidification processes using the Scheil-Gulliver model (Scheil simulation); 4 - “Elements” - opens the THERMO-CALC DATA window where a system can be set up by choosing elements, phases and a database.


Figure 1.1 - Thermo-Calc main window

      For the calculation of phase diagrams of binary systems Press E the key to the right on the toolbar in the Main window to start the Binary

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Phase Diagram Module (figure 1.1). In the opened window (figure 1.2, а) on Toolbar “Periodic Table” on line “Database” select the database (database on binary systems - TCBIN) and select two the elements from the periodic table (selected elements are displayed in the window “Selected Elements”).
       The window “Phases”. In this window it’s possible to specify the phases that the calculation will be based upon by rejecting undesired phases.


b

Figure 1.2 - Calculation of binary systems: a - the choice of elements; b - adding (removal) phases

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      After selecting the elements click on the button “Phase Diagram” and binary phase diagram will be calculated and plotted automatically (figure 1.3). Also, the program allows the calculation of the function of the Gibbs energy (button “G-curves” (figure 1.2)) and Activity (button “A-curves” (figure 1.2)) from the concentration of the element at specified temperature and from the fraction of phases at a predetermined temperature at specified concentration of elements (button “Phase Fraction” (figure 1.2)). Figure 1.4, a shows as an example calculation function the Gibbs energy (G, J/mol) of the silicon concentration in the system Al-Si at 550 °C for the phases which may be present in the system ((Al), Si and Liquid).


а

b

Figure 1.3 - The calculated Al-Si binary phase diagram: a - main window; b - aluminum corner

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       For a more detailed view calculations by pressing the button Al, distinguish the area of interest (figure 1.3, b). To designate the phase areas click on the button “Add Label” and then click on the field in the area of interest in the diagram (figure 1.3, b).


Figure 1.4 - The calculation of the Gibbs energy function of the concentration of Si in the Al-Si at 550 °C

      The final graphical property or phase diagram can be saved in the following graphical formats: Portable Network Graphics (.png), Windows Bitmaps (.bmp), Portable Document Format (.pdf), Joint Photographic Experts Group (JPEG) Format (.jpg), Tagged Image File Format (.tif), PostScript File (.ps), Microsoft Windows Enhanced Metafile (.emf) or Thermo-Calc’s own experimental format (.exp) for later edit or inclusion/ combination with other calculated diagrams.
      To save the calculation phase diagrams of “Menu” tab, click “Save”, and save the file in JPG format save the file in a folder “DOC” on the desktop.
      For the calculation of phase diagrams of ternary systems open the window “TERNARY” by pressing the button 2 A (figure 1.1). In the opened window (figure 1.5) in the tab “Periodic Table” in the window “Database” select the database and then select the elements of the ternary system. The Ternary module enables quick calculations of: isothermal sections, projections of liquidus surfaces, monovariant lines.
      For the calculation of polythermal and isothermal sections, as well as the phase composition and the composition of the phases in the ternary and multicomponent systems more convenient to use the tab “Elements” (figure 1.1). Further will be discussed in more detail these issues.


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а

b

Figure 1.5 - Calculation of ternary systems: a - the choice of elements; b - liquidus projection

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