CALPHAD method

CALPHAD method

CALPHAD method, which stands for CALculation of PHAse Diagrams, has become a widely used method for effectively calculating phase diagrams of multi-component systems in the past a few decades.

A phase diagram is a graphical representation of the state of a material system in terms of temperature, composition, and pressure. The most familiar phase diagram of a binary system is the temperature-composition diagram, and common ternary phase diagrams include isothermal sections, isoplethal sections, and liquidus projection. Since phase diagrams are the starting point to understand the properties and phenomena of a material system, they are frequently referred as blueprints or road maps for alloy design and process development. While most binary phase diagrams and some sections for a number of ternary systems can be found in the handbook, multi-component phase diagrams needed by modern materials design are usually not available. This is because determination of multi-component phase diagrams purely by experimental approach is extremely expensive and time consuming.  

The CALPHAD method, which stands for CALculation of PHAse Diagrams, has become a widely used method for effectively calculating phase diagrams of multi-component systems in the past a few decades [1-4]. The essence of this approach is to obtain self-consistent thermodynamic descriptions of the lower-order systems in terms of known thermodynamic and phase equilibrium data. The advantage of this method is that the separately measured phase diagrams and thermodynamic properties can be represented by a self-consistent thermodynamic database of the material system in question. More importantly, a thermodynamic database for a higher-order system can be obtained from those of the lower order systems via an extrapolation method [5]. This thermodynamic database enables us to calculate phase diagrams and thermodynamic properties of a multi-component system that are experimentally unavailable. Currently, the CALPHAD approach is the only method that can be used to obtain multi-component phase diagrams with enough accuracy for practical applications without the need of exhaustive experimental work [6].

The success of the CALPHAD approach depends on the availability of both software and phase-base property databases developed by this method. Software packages and multi-component thermodynamic databases have become commercially available since 1990s. The features of the most widely used software packages in this field can be found in the special issue of CALPHAD journal, volume 33, published in 2009 [7]. These software packages, when integrating with suitable materials property databases, can be used to answer questions involving metallic systems with 10-plus components. Such results provide the fundamental underpinnings of evolutionary and revolutionary materials development and have been successfully applied to materials design programs [8-10].

Although the CALPHAD method was initially emerged as a method for understanding thermodynamics and phase equilibria of multicomponent systems, the method has been successfully applied to diffusion mobilities in multicomponent systems [11], and mobility databases have been developed using a similar way as that of a thermodynamic database [12]. Recently, the CALPHAD method has been expanded to other phase-properties, such as molar volumes, elastic constants, and thermal conductivity [13]. Therefore, the CALPHAD approach has in recent years been applied to a broader field of materials science and engineering beyond phase diagrams, such as solidification, coating, joining, and phase transformation. There is no doubt that CALPHAD has played an important role in ICME [14] to significantly reduce the time and cost to develop and deploy new materials.


[1] L. Kaufman, H. Bernstein, Computer Calculation of Phase Diagrams, ed., Academic Press, 1970

[2] N. Saunders, A.P. Miodownik, CALPHAD Calculation of Phase Diagrams: A Comprehensive Guide, Pergamon, 1998

[3] Y.A. Chang, S.L. Chen, F. Zhang, X.Y. Yan, F.Y. Xie, R. Schmid-Fetzer, W.A. Oates, Phase Diagram Calculation: Past, Present and Future, Progress in Materials Science, 49, 313-345 (2004)

[4] H.L. Lukas, S.G. Fries, B. Sundman, Computational Thermodynamics: The CALPHAD Method, Cambridge University Press, 2007

[5] Y.-M. Muggianu, M. Gambino, J.-P. Bros, Formation enthalpies of bismuth-tin-gallium liquid alloys at 723 k. Choice of an analytical representation of the quantities of integral and partial excess of mixture, Journal de Chimie Physique, 72, 83-88 (1975)

[6] U.R. Kattner, The CALPHAD method and its role in material and process development, Tecnol Metal Mater Min., 13(1), 3-15 (2016)

[7] Z.-K. Liu, Tools for Computational Thermodynamics, Calphad, 33(2), 265-440 (2009)

[8] G.B. Olson, Genomic materials design: The ferrous frontier, Acta Materialia, 61(3), 771-781 (2013)

[9] F. Zhang, W.S. Cao, C. Zhang, S.-L. Chen, J. Zhu, D.C. Lv, Simulation of Co-precipitation Kinetics of γ′ and γ″ in Superalloy 718, Proceedings of the 9th International Symposium on Superalloy 718 and Derivatives: Energy, Aerospace, and Industrial Applications, E.O.e. al. Ed., 2018, TMS, pp 147-161

[10] O.N. Senkov, S. Gorsse, D.B. Miracle, High temperature strength of refractory complex concentrated alloys, Acta Materialia, 175, 394-405 (2019)

[11] J.O. Andersson, J. Agren, Models for numerical treatment of multicomponent diffusion in simple phases, Journal Of Applied Physics, 72(4), 1350-1355 (1992)

[12] C.E. Campbell, W.J. Boettinger, U.R. Kattner, Development of a diffusion mobility database for Ni-base superalloys, Acta Materialia, 50(4), 775-792 (2002)

[13] C.E. Campbell, U.R. Kattner, Z.-K. Liu, The development of phase-based property data using the CALPHAD method and infrastructure needs, Integrating Materials and Manufacturing Innovation, 3(1), 12 (2014)

[14] National Research Council, Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security, The National Academies Press, 2008