THE CALPHAD METHOD AND ITS ROLE IN MATERIAL AND PROCESS DEVELOPMENT
O MÉTODO CALPHAD E SEU PAPEL NO DESENVOLVIMENTO DE MATERIAIS E PROCESSOS
Kattner, Ursula R.
http://dx.doi.org/10.4322/2176-1523.1059
Tecnol. Metal. Mater. Min., vol.13, n1, p.3-15, 2016
Abstract
Successful design of materials and manufacturing processes requires the availability of reliable materials data. Commercial alloys usually contain a large number of elements, and the needed data for the design of new materials and processes are rarely available. The CALPHAD (CALculation of PHAse Diagrams) method enables the development of thermodynamic and property databases, that in conjunction with extrapolation methods of the descriptions of binary and ternary systems to higher-order systems, allow the calculation of data for higher-order systems. The results obtained from CALPHAD calculations have been shown to be invaluable in the design of new materials. This review presents an overview of the CALPHAD method, software tools and databases and gives examples of its application.
Keywords
CALPHAD, Databases, Diffusion, Phase equilibria, Phase-based properties, Thermodynamics.
Resumo
O projeto bem sucedido de materiais e processos de fabricação exige a disponibilidade de dados confiáveis sobre os materiais. Ligas comerciais geralmente contêm um grande número de elementos, e os dados necessários para a concepção de novos materiais e processos raramente estão disponíveis. O método CALPHAD (CALculation of PHAse Diagrams) permite o desenvolvimento de bases de dados termodinâmicos e de propriedades que, em conjunto com métodos de extrapolação das descrições de sistemas binários e ternários para os sistemas de ordem superior, permite o cálculo de dados para sistemas de mais alta ordem. Os resultados obtidos a partir de cálculos CALPHAD tem se mostrado extremamente valiosos para a concepção de novos materiais. Esta revisão apresenta uma visão geral do método CALPHAD, ferramentas de software e bancos de dados e dá exemplos de sua aplicação.
Palavras-chave
CALPHAD, Bases de dados, Difusão, Equilíbrio de fases, Propriedades baseadas em fase, Termodinâmica.
Referências
1 Van Laar JJ. The melting and freezing curves of binary system when the solid phase is a mixture (amorphous or crystalline solid solution) of both components. Zeitschrift für physikalische Chemie. 1908;63:216-253. In German.
2 Meijering JL. Calculation of the nickel-chromium-copper phase diagram from binary data. Acta Metallurgica. 1957;5(5):257-264. http://dx.doi.org/10.1016/0001-6160(57)90099-8.
3 Kaufman L, Cohen M. The martensitic transformation in the iron-nickel system. Transactions of the Metallurgical Society of AIME. 1956;206:1393-1400.
4 Kaufman L, Bernstein H. Computer calculation of phase diagrams with special reference to refractory metals. New York: Academic Press; 1970.
5 Spencer PJ. A brief history of CALPHAD. Calphad. 2008;32(1):1-8. http://dx.doi.org/10.1016/j.calphad.2007.10.001.
6 Saunders N, Miodownik AP. CALPHAD (Calculation of phase diagrams): a comprehensive guide. Oxford: Pergamon; 1998.
7 Dinsdale AT. SGTE data for pure elements. Calphad. 1991;15(4):317-425. http://dx.doi.org/10.1016/0364-5916(91)90030-N.
8 National Research Council. Committee on Integrated Computational Materials Engineering. Integrated computational materials engineering: a transformational discipline for improved competitiveness and national security. Washington, DC: National Academic Press; 2008.
9 Office of Science and Technology Policy. Materials genome initiative for global competitiveness. Washington, DC: OSTP; 2011.
10 Ågren J. The materials genome and CALPHAD. Chinese Science Bulletin. 2014;59(15):1635-1640. http://dx.doi.org/10.1007/s11434-013-0108-2.
11 Kaufman L, Ågren J. CALPHAD, first and second generation: birth of the materials genome. Scripta Materialia. 2014;70:3-6. http://dx.doi.org/10.1016/j.scriptamat.2012.12.003.
12 Olson GB. Preface to viewpoint set on: the materials genome. Scripta Materialia. 2014;70:1-2. http://dx.doi.org/10.1016/j.scriptamat.2013.09.013.
13 Ågren J. Numerical treatment of diffusional reactions in multicomponent alloys. Journal of Physics and Chemistry of Solids. 1982;43(5):385-391.
14 Ågren J. Diffusion in phases with several components and sublattices. Journal of Physics and Chemistry of Solids. 1982;43(5):421-430.
15 Andersson J-O, Ågren J. Models for numerical treatment of multicomponent diffusion in simple phases. Journal of Applied Physics. 1992;72(4):1350-1355. http://dx.doi.org/10.1063/1.351745.
16 Grimvall G. Thermophysical properties of materials. Amsterdam: Elsevier; 1999.
17 Fernández Guillermet A, Gustafson P, Hillert M. The representation of thermodynamic properties at high pressures. Journal of Physics and Chemistry of Solids. 1985;46(12):1427-1429. http://dx.doi.org/10.1016/0022-3697(85)90082-4.
18 Lu X-G, Selleby M, Sundman B. Implementation of a new model for pressure dependence of condensed phases in Thermo-Calc. Calphad. 2005;29(1):49-55. http://dx.doi.org/10.1016/j.calphad.2005.04.001.
19 Brosh E, Makov G, Shneck RZ. Application of CALPHAD to high pressures. Calphad. 2007;31(2):173-185. http://dx.doi.org/10.1016/j.calphad.2006.12.008.
20 Jacobs MHG, Schmid-Fetzer R, van den Berg AP. An alternative use of Kieffer’s lattice dynamics model using vibrational density of states for constructing thermodynamic databases. Physics and Chemistry of Minerals. 2013;40(3):207-227. http://dx.doi.org/10.1007/s00269-012-0562-4.
21 Hillert M. Phase equilibria, phase diagrams and phase transformations: their thermodynamic basis. 2nd ed. Cambridge: Cambridge University Press; 2008.
22 Unland J, Onderka B, Davydov A, Schmid-Fetzer R. Thermodynamics and phase stability in the Ga-N system. Journal of Crystal Growth. 2003;256(1-2):33-51. http://dx.doi.org/10.1016/S0022-0248(03)01352-6.
23 Hickel T, Kattner UR, Fries SG. Computational thermodynamics: recent developments and future potential and prospects. Physica Status Solidi. B, Basic Research. 2014;251(1):9-13. http://dx.doi.org/10.1002/pssb.201470107.
24 Sundman B, Aldinger F. The Ringberg workshop 1995 on unary data for elements and other end-members of solutions. Calphad. 1995;19(4):433-436. http://dx.doi.org/10.1016/0364-5916(96)00001-6.
25 Chen Q, Sundman B. Modeling of thermodynamic properties for bcc, fcc, liquid, and amorphous iron. Journal of Phase Equilibria. 2001;22(6):631-644. http://dx.doi.org/10.1007/s11669-001-0027-9.
26 Ågren J. Thermodynamics of undercooled liquids and their glass transition. Physics and Chemistry of Liquids. International Journal (Toronto, Ont.). 1988;18:123-139.
27 Bigdeli S, Mao H, Selleby M. On the third generation CALPHAD databases. Physica Status Solidi. B, Basic Research. 2015;252(10):2199-2208. http://dx.doi.org/10.1002/pssb.201552203.
28 Xiong W, Chen Q, Korzhavyi PA, Selleby M. An improved magnetic model for thermodynamic modeling. Calphad. 2012;39:11-20. http://dx.doi.org/10.1016/j.calphad.2012.07.002.
29 Inden G. Approximate description of the configurational specific heat during a magnetic order-disorder transformation. In: Proceeding of the 5th project meeting CALPHAD; 21-25 jun. 1976; Max Planck Institute for Iron Research. Düsseldorf: Max-Planck-Institut für Eisenforschung GmbH; 1976. p. III-4.1-III-4.13.
30 Hillert M, Jarl M. A model for alloying effect in ferromagnetic metals. Calphad. 1978;2(3):227-238. http://dx.doi.org/10.1016/0364-5916(78)90011-1.
31 Hertzman S, Sundman B. A thermodynamic analysis of the Fe-Cr system. Calphad. 1982;6(1):67-80. http://dx.doi.org/10.1016/0364-5916(82)90018-9.
32 Gheribi AE, Rogez J, Mathieu JC. Magnetic contribution to the Gibbs energy of elements versus temperature and pressure. Journal of Physics and Chemistry of Solids. 2006;67(8):1719-1723. http://dx.doi.org/10.1016/j.jpcs.2006.03.019.
33 Lukas HL, Fries SG, Sundman B. Computational thermodynamics: the Calphad method. Cambridge: Cambridge University Press; 2007.
34 Redlich O, Kister AT. Algebraic representation of thermodynamic properties and the classification of solutions. Industrial & Engineering Chemistry. 1948;40(2):345-348. http://dx.doi.org/10.1021/ie50458a036.
35 Ansara I, Dupin N, Lukas HL, Sundman B. Thermodynamic modelling of the phases in the Ni-Al system. Journal of Alloys and Compounds. 1997;247(1-2):20-30. http://dx.doi.org/10.1016/S0925-8388(96)02652-7.
36 Sundman B. Modification of the two-sublattice model for liquids. Calphad. 1991;15(2):109-119. http://dx.doi.org/10.1016/0364-5916(91)90010-H.
37 Pelton AD, Chartrand P. The modified quasi-chemical model: part II multicomponent solutions. Metallurgical and Materials Transactions A. 2001;32A:1355-1360.
38 Pelton AD, Chartrand P. The modified quasi-chemical model: part IV two-sublattice quadruplet approximation. Metallurgical and Materials Transactions A. 2001;32A:1409-1416.
39 Oates WA, Zhang F, Chen S-L, Chang YA. Improved cluster-site approximation for the entropy of mixing in multicomponent solid solutions. Physical Review B: Condensed Matter and Materials Physics. 1999;59(17):11221-11225. http://dx.doi.org/10.1103/PhysRevB.59.11221.
40 Turchi PEA, Abrikosov IA, Burton B, Fries SG, Grimvall G, Kaufman L, et al. Interface between quantum- mechanical-based approaches, experiments, and CALPHAD methodology. Calphad. 2007;31(1):4-27. http://dx.doi.org/10.1016/j.calphad.2006.02.009.
41 Harvey J-P, Gheribi AE, Chartrand P. Thermodynamic integration based on classical atomistic simulations to determine the Gibbs energy of condensed phases: Calculation of the aluminum-zirconium system. Physical Review B: Condensed Matter and Materials Physics. 2012;86(22):224202. http://dx.doi.org/10.1103/PhysRevB.86.224202.
42 Lukas HL, Henig E-T, Zimmermann B. Optimization of phase diagrams by a least squares method using simultaneously different types of data. Calphad. 1977;1(3):225-236. http://dx.doi.org/10.1016/0364-5916(77)90002-5.
43 Marquardt DW. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. Journal of the Society for Industrial and Applied Mathematics. 1963;11(2):431-441. http://dx.doi.org/10.1137/0111030.
44 Königsberger E. Improvement of excess parameters from thermodynamic and phase diagram data by a sequential Bayes algorithm. Calphad. 1991;15(1):69-78. http://dx.doi.org/10.1016/0364-5916(91)90027-H.
45 Schmid-Fetzer R, Andersson D, Chevalier P-Y, Eleno L, Fabrichnaya O, Kattner UR, et al. Assessment techniques, database design and software facilities for thermodynamics and diffusion. Calphad. 2007;31(1):38-52. http://dx.doi.org/10.1016/j.calphad.2006.02.007.
2 Meijering JL. Calculation of the nickel-chromium-copper phase diagram from binary data. Acta Metallurgica. 1957;5(5):257-264. http://dx.doi.org/10.1016/0001-6160(57)90099-8.
3 Kaufman L, Cohen M. The martensitic transformation in the iron-nickel system. Transactions of the Metallurgical Society of AIME. 1956;206:1393-1400.
4 Kaufman L, Bernstein H. Computer calculation of phase diagrams with special reference to refractory metals. New York: Academic Press; 1970.
5 Spencer PJ. A brief history of CALPHAD. Calphad. 2008;32(1):1-8. http://dx.doi.org/10.1016/j.calphad.2007.10.001.
6 Saunders N, Miodownik AP. CALPHAD (Calculation of phase diagrams): a comprehensive guide. Oxford: Pergamon; 1998.
7 Dinsdale AT. SGTE data for pure elements. Calphad. 1991;15(4):317-425. http://dx.doi.org/10.1016/0364-5916(91)90030-N.
8 National Research Council. Committee on Integrated Computational Materials Engineering. Integrated computational materials engineering: a transformational discipline for improved competitiveness and national security. Washington, DC: National Academic Press; 2008.
9 Office of Science and Technology Policy. Materials genome initiative for global competitiveness. Washington, DC: OSTP; 2011.
10 Ågren J. The materials genome and CALPHAD. Chinese Science Bulletin. 2014;59(15):1635-1640. http://dx.doi.org/10.1007/s11434-013-0108-2.
11 Kaufman L, Ågren J. CALPHAD, first and second generation: birth of the materials genome. Scripta Materialia. 2014;70:3-6. http://dx.doi.org/10.1016/j.scriptamat.2012.12.003.
12 Olson GB. Preface to viewpoint set on: the materials genome. Scripta Materialia. 2014;70:1-2. http://dx.doi.org/10.1016/j.scriptamat.2013.09.013.
13 Ågren J. Numerical treatment of diffusional reactions in multicomponent alloys. Journal of Physics and Chemistry of Solids. 1982;43(5):385-391.
14 Ågren J. Diffusion in phases with several components and sublattices. Journal of Physics and Chemistry of Solids. 1982;43(5):421-430.
15 Andersson J-O, Ågren J. Models for numerical treatment of multicomponent diffusion in simple phases. Journal of Applied Physics. 1992;72(4):1350-1355. http://dx.doi.org/10.1063/1.351745.
16 Grimvall G. Thermophysical properties of materials. Amsterdam: Elsevier; 1999.
17 Fernández Guillermet A, Gustafson P, Hillert M. The representation of thermodynamic properties at high pressures. Journal of Physics and Chemistry of Solids. 1985;46(12):1427-1429. http://dx.doi.org/10.1016/0022-3697(85)90082-4.
18 Lu X-G, Selleby M, Sundman B. Implementation of a new model for pressure dependence of condensed phases in Thermo-Calc. Calphad. 2005;29(1):49-55. http://dx.doi.org/10.1016/j.calphad.2005.04.001.
19 Brosh E, Makov G, Shneck RZ. Application of CALPHAD to high pressures. Calphad. 2007;31(2):173-185. http://dx.doi.org/10.1016/j.calphad.2006.12.008.
20 Jacobs MHG, Schmid-Fetzer R, van den Berg AP. An alternative use of Kieffer’s lattice dynamics model using vibrational density of states for constructing thermodynamic databases. Physics and Chemistry of Minerals. 2013;40(3):207-227. http://dx.doi.org/10.1007/s00269-012-0562-4.
21 Hillert M. Phase equilibria, phase diagrams and phase transformations: their thermodynamic basis. 2nd ed. Cambridge: Cambridge University Press; 2008.
22 Unland J, Onderka B, Davydov A, Schmid-Fetzer R. Thermodynamics and phase stability in the Ga-N system. Journal of Crystal Growth. 2003;256(1-2):33-51. http://dx.doi.org/10.1016/S0022-0248(03)01352-6.
23 Hickel T, Kattner UR, Fries SG. Computational thermodynamics: recent developments and future potential and prospects. Physica Status Solidi. B, Basic Research. 2014;251(1):9-13. http://dx.doi.org/10.1002/pssb.201470107.
24 Sundman B, Aldinger F. The Ringberg workshop 1995 on unary data for elements and other end-members of solutions. Calphad. 1995;19(4):433-436. http://dx.doi.org/10.1016/0364-5916(96)00001-6.
25 Chen Q, Sundman B. Modeling of thermodynamic properties for bcc, fcc, liquid, and amorphous iron. Journal of Phase Equilibria. 2001;22(6):631-644. http://dx.doi.org/10.1007/s11669-001-0027-9.
26 Ågren J. Thermodynamics of undercooled liquids and their glass transition. Physics and Chemistry of Liquids. International Journal (Toronto, Ont.). 1988;18:123-139.
27 Bigdeli S, Mao H, Selleby M. On the third generation CALPHAD databases. Physica Status Solidi. B, Basic Research. 2015;252(10):2199-2208. http://dx.doi.org/10.1002/pssb.201552203.
28 Xiong W, Chen Q, Korzhavyi PA, Selleby M. An improved magnetic model for thermodynamic modeling. Calphad. 2012;39:11-20. http://dx.doi.org/10.1016/j.calphad.2012.07.002.
29 Inden G. Approximate description of the configurational specific heat during a magnetic order-disorder transformation. In: Proceeding of the 5th project meeting CALPHAD; 21-25 jun. 1976; Max Planck Institute for Iron Research. Düsseldorf: Max-Planck-Institut für Eisenforschung GmbH; 1976. p. III-4.1-III-4.13.
30 Hillert M, Jarl M. A model for alloying effect in ferromagnetic metals. Calphad. 1978;2(3):227-238. http://dx.doi.org/10.1016/0364-5916(78)90011-1.
31 Hertzman S, Sundman B. A thermodynamic analysis of the Fe-Cr system. Calphad. 1982;6(1):67-80. http://dx.doi.org/10.1016/0364-5916(82)90018-9.
32 Gheribi AE, Rogez J, Mathieu JC. Magnetic contribution to the Gibbs energy of elements versus temperature and pressure. Journal of Physics and Chemistry of Solids. 2006;67(8):1719-1723. http://dx.doi.org/10.1016/j.jpcs.2006.03.019.
33 Lukas HL, Fries SG, Sundman B. Computational thermodynamics: the Calphad method. Cambridge: Cambridge University Press; 2007.
34 Redlich O, Kister AT. Algebraic representation of thermodynamic properties and the classification of solutions. Industrial & Engineering Chemistry. 1948;40(2):345-348. http://dx.doi.org/10.1021/ie50458a036.
35 Ansara I, Dupin N, Lukas HL, Sundman B. Thermodynamic modelling of the phases in the Ni-Al system. Journal of Alloys and Compounds. 1997;247(1-2):20-30. http://dx.doi.org/10.1016/S0925-8388(96)02652-7.
36 Sundman B. Modification of the two-sublattice model for liquids. Calphad. 1991;15(2):109-119. http://dx.doi.org/10.1016/0364-5916(91)90010-H.
37 Pelton AD, Chartrand P. The modified quasi-chemical model: part II multicomponent solutions. Metallurgical and Materials Transactions A. 2001;32A:1355-1360.
38 Pelton AD, Chartrand P. The modified quasi-chemical model: part IV two-sublattice quadruplet approximation. Metallurgical and Materials Transactions A. 2001;32A:1409-1416.
39 Oates WA, Zhang F, Chen S-L, Chang YA. Improved cluster-site approximation for the entropy of mixing in multicomponent solid solutions. Physical Review B: Condensed Matter and Materials Physics. 1999;59(17):11221-11225. http://dx.doi.org/10.1103/PhysRevB.59.11221.
40 Turchi PEA, Abrikosov IA, Burton B, Fries SG, Grimvall G, Kaufman L, et al. Interface between quantum- mechanical-based approaches, experiments, and CALPHAD methodology. Calphad. 2007;31(1):4-27. http://dx.doi.org/10.1016/j.calphad.2006.02.009.
41 Harvey J-P, Gheribi AE, Chartrand P. Thermodynamic integration based on classical atomistic simulations to determine the Gibbs energy of condensed phases: Calculation of the aluminum-zirconium system. Physical Review B: Condensed Matter and Materials Physics. 2012;86(22):224202. http://dx.doi.org/10.1103/PhysRevB.86.224202.
42 Lukas HL, Henig E-T, Zimmermann B. Optimization of phase diagrams by a least squares method using simultaneously different types of data. Calphad. 1977;1(3):225-236. http://dx.doi.org/10.1016/0364-5916(77)90002-5.
43 Marquardt DW. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. Journal of the Society for Industrial and Applied Mathematics. 1963;11(2):431-441. http://dx.doi.org/10.1137/0111030.
44 Königsberger E. Improvement of excess parameters from thermodynamic and phase diagram data by a sequential Bayes algorithm. Calphad. 1991;15(1):69-78. http://dx.doi.org/10.1016/0364-5916(91)90027-H.
45 Schmid-Fetzer R, Andersson D, Chevalier P-Y, Eleno L, Fabrichnaya O, Kattner UR, et al. Assessment techniques, database design and software facilities for thermodynamics and diffusion. Calphad. 2007;31(1):38-52. http://dx.doi.org/10.1016/j.calphad.2006.02.007.
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