1. Computational Thermodynamics 1

2. Outline Theoretical background: thermodynamics of substitional solutions Introduction to thermodynamic database: element, specie, constitution, phase, function Introduction to Pandat software: phase diagram, line/propert and point calculation Pandat and database. Writing a database for Cu-Ni system

3. Theoretical background: thermodynamics of substitional solutions By definition, the phase is a homogeneous part of the space. The phase has the same structure, property and the phase is limited by phase boundary. Do you agree with this definition? We can see, that inside the glass We have 4 different phases: -Solid phases: ice and straw -Liquid phase: pepsi-cola -Gas phase: CO 2 But, of course, we can guess, those phases Are not in equilibrium!

4. Theoretical background: thermodynamics of substitional solutions Let’s re-define a phase: The phase is a homogeneous part of the space and the phase is limited by a phase boundary

5. Theoretical background: thermodynamics of substitional solutions A phase diagram is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium.

6. Theoretical background: thermodynamics of substitional solutions Condition for two phases to be in equilibrium

7. Theoretical background: thermodynamics of substitional solutions ΔG α Δμ A α =Δμ A β Δμ B α ΔG β = Δμ B β

8. Theoretical background: thermodynamics of substitional solutions AB L α+β L+β α+L β α

9. Theoretical background: thermodynamics of substitional solutions Substitutional solution A-B: atoms A can substitute atoms B and vice versa. Both phases (FCC and Liquid) are substitional solutions

10. Theoretical background: thermodynamics of substitional solutions In case of Face Centered Cubic FCC_A1 structure and Cu – Ni alloy, There are no restrictions and both types of atoms can occupied any position in crystal structure for whole concentration range. The Gibbs energy will, in this case, has 3 parts:

11. Theoretical background: thermodynamics of substitional solutions

12. Superposition of Gibbs energies of pure elements Gibbs energy mechanical mixing Excess Gibbs energy

13. Theoretical background: thermodynamics of substitional solutions For i=0 and B=C=0 we just have a regular solution x A x B Ω Redlich-Kister polynominal Value of i depends on thermodynamic properties of a given phase

14. Theoretical background: thermodynamics of substitional solutions Let’s take a look at the Gibbs energy function Using Excel and the values 0 A = 1 A = 2 A = 1000, 0 B = 1 B = 2 B = 0 C = 1 C = 2 C = 0, please make a graph of the Gibbs energy (separately for each L and their superposition)

15. Introduction to thermodynamic database: element, specie, constitution, phase, function The thermodynamic database is a text file with extension TDB For editing the file one should not use a word processor (i.e. MS Word) due to invisible information added by the word processor. The easiest way to edit the database is to use Notepad or other simple editor (personally, I like to use the Edit Plus)

16. Introduction to thermodynamic database: element, specie, constitution, phase, function Format of the database: -Information about elements -Information about species (if applicable) -Functions -Parameters

17. Introduction to thermodynamic database: element, specie, constitution, phase, function Se-Te database (part)

18. Introduction to thermodynamic database: element, specie, constitution, phase, function $ Database file written 2010-10-28 $ From database: User data 2010.10.28 ELEMENT /- ELECTRON_GAS 0.0000E+00 0.0000E+00 0.0000E+00! ELEMENT VA VACUUM 0.0000E+00 0.0000E+00 0.0000E+00! ELEMENT SE HEXAGONAL_A8 7.8960E+01 5.5145E+03 4.1966E+01! ELEMENT TE HEXAGONAL_A8 1.2760E+02 6.1212E+03 4.9497E+01! $ comment line ELEMENT SYMBOL Crystal structure SER ELEMENT [element name]*2 [ref. state]*24 [mass] [H298] [S298] ! Atomic mass Enthalpy and entropy difference between 0 and 298.15 K for the element in SI units. If they are unknown, the values can be set to zero.

19. Introduction to thermodynamic database: element, specie, constitution, phase, function H298 and S298 - the enthalpy and entropy difference between 0 and 298.15 K for the element in SI units. All these information (reference state, H298 and S298) precisely define the so-called SER (Stable Element Reference State).

20. Introduction to thermodynamic database: element, specie, constitution, phase, function SPECIES [species name]*24 [stoichiometric formula] ! This keyword defines species in the data structure. Every species name (maximum 24 characters) must be unique. The species are built from the already defined set of elements in the stoichiometric formula. The stoichiometric formula is written with a simplified chemical notation, in which the chemical elements should always be given in UPPER-cases and in any preferred order, and their stoichiometric coefficients can be written in either real numerical factor or integer digits. It is important that the numerical factor of 1 cannot be left out. SPECIES AL2O3 AL2O3 ! SPECIES Silica SI1O2 ! SPECIES NaSb_6OH NA1SB1O6H6 ! SPECIES FE+2 FE/+2 ! SPECIES SB-3 SB/-3 ! SPECIES AlCl2/3 AL.33333CL.666667 !

21. Introduction to thermodynamic database: element, specie, constitution, phase, function FUNCTION [function name]*8 [lowest temp. limit] [expression 1]; [upper temp. limit 2] Y [expression 2]; [upper temp. limit 1] Y [expression 3]; [upper temp. limit 2] Y.......... ;..... Y [expression n-1]; [upper temp. limit n-1] Y [expression n]; [upper temp. limit n] N {Ref. Index} !

22. Introduction to thermodynamic database: element, specie, constitution, phase, function TYPE_DEFINITION % SEQ *! DEFINE_SYSTEM_DEFAULT ELEMENT 2 ! DEFAULT_COMMAND DEF_SYS_ELEMENT VA /- ! PHASE HEXAGONAL_A8 % 1 1.0 ! CONSTITUENT HEXAGONAL_A8 :SE,TE : ! PARAMETER G(HEXAGONAL_A8,SE;0) 2.98150E+02 +GHSERSE#; 1.00000E+03 N REF0 ! PARAMETER G(HEXAGONAL_A8,TE;0) 2.98150E+02 +GHSERTE#; 1.60000E+03 N REF0 ! PARAMETER G(HEXAGONAL_A8,SE,TE;0) 2.98150E+02 -9.9498291E+02 +2.7357836E+00*T; 1.60000E+03 N REF0 !

23. Introduction to thermodynamic database: element, specie, constitution, phase, function TYPE_DEFINITION [data-type code]*1 [secondary keyword with parameters] ! This keyword couples phases to an action performed by the TDB module when the TDB command GET_DATA is executed. The available secondary keywords and associated parameters in syntax for TYPE_DEFINITION are: SEQ [filename] RND# [filename] GES [valid GES command with parameters] POLY [valid POLY command with parameters] TDB [valid TDB command with parameters] IF [conditional statement] THEN [keyword with parameters] AFTER [valid GES command with parameters]

24. Introduction to thermodynamic database: element, specie, constitution, phase, function The secondary keyword SEQ specifies a sequential file that stores parameters belonging to the phases using the associated data type code (which is defined by this TYPE_DEFINTION keyword). A special case where the filename is given as an asterisk, *, implies that the database definition file also acts as a sequential data storage file. This case makes it possible to have a single file for a small database, which is especially suited for personal databases.

25. Introduction to thermodynamic database: element, specie, constitution, phase, function DEFINE_SYSTEM_DEFAULT [keyword] {G-ref. type index} ! Thermocalc software! This keyword sets the default value to ELEMENT or SPECIES in the TDB command DEFINE_SYSTEM. For a substance database, it might be appropriate to have ELEMENT as default value whereas a large solution database can benefit from having SPECIES as default value. A proper default value is beneficial for a beginner, but an advanced user will probably use the TDB commands DEFINE_ELEMENT and DEFINE_SPECIES to override the default value. {G-ref. type index} is an integer indicating the reference state type for an element when entering and listing data in the GES module. The following lists legal numbers and their corresponding meaning (the reference state type for an element): 1 ⇒ symbol: G 2 ⇒ symbol: H298 3 ⇒ symbol: H0

26. Introduction to thermodynamic database: element, specie, constitution, phase, function DEFAULT_COMMAND [secondary keyword and parameters] ! Thermocalc software The keyword specifies commands to be executed by the TDB module at database initialization. The syntax of the available commands is currently not the same as the user available TDB commands but the actions are similar. The available secondary keywords and parameters in syntax for DEFAULT_COMMAND are, DEFINE_SYSTEM_ELEMENT [element names] DEFINE_SYSTEM_SPECIES [species names] DEFINE_SYSTEM_CONSTITUENT [phase] [sublattice] [species] REJECT_SYSTEM_ELEMENT [element names] REJECT_SYSTEM_SPECIES [species names] REJECT_SYSTEM_CONSTITUENT [phase] [sublattice] [species] REJECT_PHASE [phase names] RESTORE_PHASE [phase names]

27. Introduction to thermodynamic database: element, specie, constitution, phase, function PHASE [phase name]*24 [data-type code]*8 [numb. subl.] [sites in subl. 1] [sites in subl. 2] etc... {auxiliary text string} ! This keyword defines a phase and its properties (except for what species are allowed to enter it and for its thermodynamic parameters). The data-type code consists of 1 to 8 characters where each character must stand for connecting to a specific database file The data entries [numb. subl.] [sites in subl. 1] [sites in subl. 2] etc... specify the total number of sublattices (always as an integer digit) and the sites (i.e., stoichiometric coefficients) of each of the sublattices (given in either integer digits or real numerical factors) for the phase. Optionally, an auxiliary text string (maximum 78 characters) may be given after the last [sites in sublattice #] but before the exclamation mark “!”; see examples below. This string will show up in connection with the phase name in some listings within the TDB module.

28. Introduction to thermodynamic database: element, specie, constitution, phase, function PHASE GAS:G % 1 1.0 ! PHASE LIQUID:L %ZCDQ 2 1.0 1.0 > Metallic liquid solution, modelled by CEF Model. ! PHASE IONIC-LIQ:Y %ZCDQ 2 1.0 1.0 > Ionic liquid solution, modelled by Ionic Two-Sublattice Model. ! PHASE SPINEL:I %ZA 4 1 2 2 4 > Complex Spinel Solution, by CEF model with ionic constraints. ! PHASE M23C6 % 3 20.0 3.0 6.0 ! PHASE FCC_A1 %&A 2 1 1 > Disordered FCC phase; also as MX carbides/nitrides. ! PHASE FCC_L10 %&AX 3 0.75 0.25 1 > Ordered FCC phase, modelled by 2-Sublattice Model for Ordering. ! PHASE FCC_L12:F %&AX 5 0.25 0.25 0.25 0.25 1.0 > Ordered FCC phase, modelled by 4-Sublattice Model for Ordering. ! PHASE AQUEOUS:A %HIJMR 1 1.0 > Aqueous Solution: using the Complete Revised HKF Model. !

29. Introduction to thermodynamic database: element, specie, constitution, phase, function Legal GES phase-type codes are (Thermocalc software): G ⇒ Bit set for a gaseous mixture phase. A ⇒ Bit set for an aqueous solution phase. Y ⇒ Bit set for an ionic liquid solution phase (that is specially treated by the Ionic Two- Sublattice Liquid Model). L ⇒ Bit set for a liquid solution phase [but not A (aqueous) or Y (ionic liquid)]. I ⇒ Bit set for a phase with charged species [but not G (gaseous), A (aqueous) or Y (ionic liquid)]. F ⇒ Bit set for an ordered FCC or HCP solution phase with 4 substitutional sublattices (additionally, such a phase can also have an interstitial sublattice). B ⇒ Bit set for an ordered BCC solution phase with 4 substitutional sublattices (additionally, such a phase can also have an interstitial sublattice).

30. Introduction to thermodynamic database: element, specie, constitution, phase, function CONSTITUENT [phase name]*24 [constituent description]*2000 ! This keyword (and the ADD_CONSTITUENT keyword for large solution phase) defines the phase-constitution as a list of constituents (for a substitutional phase with no sublattice) or of constituent arrays (for a sublattice phase).

31. Introduction to thermodynamic database: element, specie, constitution, phase, function PARAMETER [GES parameter name] [lowest temp. limit] [expression 1]; [upper temp. limit 1] Y [expression 2]; [upper temp. limit 2] Y [expression 3]; [upper temp. limit 2] Y.......... ;..... Y [expression n-1]; [upper temp. limit n-1] Y [expression n]; [upper temp. limit n] N {Ref. Index} ! GES parameters G Standard energy parameter (Gibbs energy of formation); L Excess energy parameter (Gibbs energy of interaction); TC Curie temperature for magnetic ordering; BMAGN or BM Bohr magneton number for magnetic ordering

32. Introduction to Pandat software: phase diagram, line/property and point calculation

35. Program Files->Computherm->Pandat 2012 Demo->Pandat 2012 Examples-> PanPhaseDiagram->Line

36. Introduction to Pandat software: phase diagram, line/property and point calculation

38. Right-click on a database

39. Introduction to Pandat software: phase diagram, line/property and point calculation

40. Point calculation Line calculation Phase diagram calculation Let’ start from phase diagram calculation

41. Introduction to Pandat software: phase diagram, line/property and point calculation

47. Edit Select Zoom Label Legend Text Line/Arrow Pan mode

48. Introduction to Pandat software: phase diagram, line/property and point calculation Double click

49. Introduction to Pandat software: phase diagram, line/property and point calculation

53. After that we have to deal with tables. However, a new version, Pandat 2013, has a new menu: Property

54. Introduction to Pandat software: phase diagram, line/property and point calculation

55. Lets calculate activity of components in liquid phase

56. Introduction to Pandat software: phase diagram, line/property and point calculation

57. It doesn’t look good, does it?

58. Introduction to Pandat software: phase diagram, line/property and point calculation As you see, we calculated activity of all phases. We have to delete everything what we don’t need

59. Pandat and database. Writing a database for Cu- Ni system

63. Right-click on database

64. Pandat and database. Writing a database for Cu-Ni system How many phases do we have in Cu-Ni system? How many phases do we have in the TDB file? Let’s delete everything what we don’t need!

65. Pandat and database. Writing a database for Cu-Ni system

66. Don’t forget to save the changes!

67. Pandat and database. Writing a database for Cu-Ni system Gibbs energies of pure elements. We need to add interaction parameters (excess Gibbs energy)

68. Pandat and database. Writing a database for Cu-Ni system Where are the parameters?

69. Pandat and database. Writing a database for Cu-Ni system Let’s calculate a phase diagram, activities of Cu and Ni in FCC (500K) and Liquid (1500K), enthalpy of mixing in Liquid (1400K) in respect (with reference state) to Liquid and FCC (2 pictures)

70. Pandat and database. Writing a database for Cu-Ni system Phase diagram Activities at 500KActivities at 1500K Enthalpy at 1400K, ref. state liquidEnthalpy at 1400K, ref. state FCC

71. Homework Base on the paper, prepare a TDB file for Te-Se system