Microstructure courtesy of George F. Vander Voort


This article describes how computational thermodynamics and kinetics can assist the metallurgist in making such predictions.

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CALPHAD - A Basis for Computational Thermodynamics and Kinetics

Computational thermodynamics, specifically the CALPHAD (Computer cALculation of PHAse Diagrams) approach,[1] allows for the prediction of the thermodynamic properties of multicomponent, multiphase systems based on mathematical models that describe the Gibbs energy as a function of temperature, pressure and composition for each individual phase in a system. Parameters in the numerical models capture the composition and temperature dependence in binary and ternary systems and are optimized in order to best correspond to the experimental data available.

Two benefits of this approach are that it ties together both thermodynamic properties and phase equilibria in a self-consistent framework, and it allows for the extrapolation to multicomponent systems based on data obtained from binary and ternary systems. The advantage of this is that data are not fitted to specific alloys of a nominal composition but are calculated for a specific user-defined input chemistry.

For more than 25 years, the CALPHAD method has been successfully applied by industry to assist in alloy design and process optimization for different alloy types including steels and ferrous-based alloys, Ni-Superalloys, Al, Ti, Mg, etc. The CALPHAD approach has also been extended to modeling other properties, such as atomic mobilities, which enable diffusion coefficients as a function of temperature and local compositions to be derived and allow the time dependence of phase transformations and microstructural evolution to be predicted.

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Fig. 1. Influence of temperature on phases formed for an M42 tool steel (NPM is the numeral of moles of a phase normalized to one mole.)

Thermo-Calc - Thermodynamic Modeling and Phase Equilibria

Thermo-Calc[2] is a software package for performing thermodynamic calculations for multicomponent systems and is used in conjunction with thermodynamic databases produced using the CALPHAD method. Databases are available for gas-phase calculations, steels, Ti, Al, Ni-superalloys and other materials. Thermo-Calc enables users to predict phases formed for equilibrium and metastable equilibrium conditions based on the composition of the system, temperature and pressure. Thermo-Calc is a very general tool, and it is not possible to cover the full range of applications here. However, some examples specifically of interest to the heat-treat community are described in the following subsections.

Gas-Phase Equilibria – Furnace Atmosphere
Thermo-Calc can be used to predict the activities, potentials and speciation of gas-phase systems as a function of composition, temperature and pressure. An article from the September 2010 issue of Industrial Heating by Winter and Torok[3] highlighted some different potentials that heat treaters need to control for a nitriding/nitrocarburizing treatment (Table 1). Each of these partial pressures, potentials and activities can be directly calculated from Thermo-Calc using a database such as the SGTE Substance database.[4]

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Fig. 2. Calculated isoplethal section for M42 tool steel


Alloy Chemistry – Phase EquilibriaPredictive calculations can also be made to see how the phases, the amounts of each phase and their composition vary with temperature or chemistry for a given alloy. For example, Figure 1 illustrates the phases that can form as temperature is varied for an M42 tool steel. Such calculations can be useful not only for alloy design but also for predicting whether deleterious phases could form prior to a heat treatment. This is based on the actual measured chemistry of a heat rather than discovering the phase during metallographic examination after the heat treatment has been performed.

The formation of certain phases can be extremely sensitive to alloy chemistry, even those that are within the specified range of composition. Therefore, these types of calculations (when combined with the metallurgist’s experience) can be useful in deciding whether to take mitigating actions prior to the heat treatment. Such calculations can be especially useful when heat treating alloys of unfamiliar specifications in order to understand the alloys much better. Also, these step calculations can predict phase-transformation temperatures based on the actual (not nominal) chemistry (e.g., Aecm, Ae1, Ae3) and, thus, provide information on the solution temperatures of the precipitates.

Compositional variation of alloys and the influence of this on their properties is another aspect that can be investigated. It can be difficult and time consuming to characterize an alloy completely, especially in terms of the tail effects attributed to the variation of alloy composition. Computationally, one can investigate this in a time-efficient and cost-effective manner. For example, the temperature where sigma phase first appears for SAF 2507 is calculated as 1030°C (1886°F) for the nominal chemistry, but with a possible range of ±60°C due to the variation in chemistry within its specified range.

Multicomponent phase diagrams (isothermal and isoplethal sections) can also be constructed for alloys, beyond binary and ternary systems. Figure 2 shows an isoplethal section for an M42 tool steel. Furthermore, so called Lehrer diagrams, which show what type of compound layer to expect for the respective nitriding potentials controlled in the furnace, can also be calculated not just for pure iron but for multicomponent alloys as well. The Center for Heat Treating Excellence (CHTE) at Worcester Polytechnic Institute has calculated the diagram in Figure 3 for AISI 4140 steel[5] using Thermo-Calc.

The examples given so far have all been related to steels, but heat treatment for other alloys, such as Al, Ni and Ti, can also be modeled using such tools. For example, Gupta et al[6] compared calculations made using Thermo-Calc with experimental observations for automotive alloy AA6111, which is a commercial sheet alloy.

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Fig. 3. Calculated Leher diagram for AISI 4140 steel[5]

DICTRA - Diffusion-Controlled Simulations

DICTRA[2] is a software package for accurate simulations of diffusion in multicomponent alloys. It is a general 1-D code and can treat diffusion-controlled phase transformations (moving boundary problems), diffusion in one-phase systems and reactions in dispersed systems. The code cannot, however, treat diffusionless transformations such as martensitic transformations. DICTRA uses thermodynamic data obtained from Thermo-Calc and atomic mobilities derived using a CALPHAD approach based on the critical evaluation of experimental diffusion data for binary and ternary systems. Two examples using DICTRA are given here – carburizing and homogenization – and other illustrations are available in the literature of nitriding, nitrocarburizing, post-weld heat treatment, etc.

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Fig. 4. AISI 1018 steel carburized at 899°C


CarburizingSince DICTRA considers fully coupled calculations between the thermodynamics of the system and the kinetics, it is possible to investigate the influence of the alloying chemistry on the diffusion coefficients (e.g., carbon) in the alloy.

However, DICTRA can also be used to predict the diffusion of carbon into an alloy directly. Boundary conditions can be defined as either the activity of the diffusing species at the surface, which can be predicted by Thermo-Calc, or the flux, which takes into consideration the mass transport of the diffusing species at the surface. Figure 4 illustrates a calculation of the carburization of AISI 1018 at 899°C (1650°F).

For highly alloyed steels, gas carburizing results in the formation of chromium-rich carbides that cause precipitation hardening in the surface. The precipitation of these carbides results in a decrease of chromium in the matrix phase, however, which has a detrimental effect on the corrosion resistance of the alloy. A compromise, therefore, needs to be made in order to maintain good corrosion resistance in the carburized layer.

Traditional methods to balance these objectives have been by experiment only, but computational tools that enable a number of parameters involved in the carburizing process to be assessed (such as alloying elements, temperature, carbon flux, etc.) offer alternatives to this approach. Turpin et al[7] have used Thermo-Calc and DICTRA to optimize an alloy chemistry and heat treatment for martensitic steel. Figure 5 illustrates the simulated growth and dissolution of such carbides as a function of time and distance for an alloy with the composition Fe-13Cr-5Co-3Ni-2Mo-0.07C.

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Fig. 5. Predicting the amount and types of carbides that will form in Fe-13Cr-5Co-3Ni-2Mo-0.07C


HomogenizationMany Ni-based superalloy castings and ingots are given homogenization treatments prior to further processing or hot working in order to evenly distribute the alloying elements throughout the microstructure. Jablonski and Cowen[8] used the Scheil model of Thermo-Calc to predict the as-cast segregation present within Nimonic 105 and then used DICTRA to refine the homogenization treatment of this alloy. Confirming their conclusions with experimental studies, they were able to propose an alternative two-step heat-treatment schedule that resulted in better solute redistribution and reduced heat-treatment times, potentially leading to significant time and cost savings. Samaras and Haidemenopoulos[9] made a similar study of the microsegregation and homogenization of 6061 extrudable Al alloy.


The use of computational thermodynamics and kinetic simulations are well established in the areas of alloy design and process optimization. Predictive calculations can complement the experience and understanding of the metallurgist or R&D engineer, provide a deeper understanding of the chemical behavior of both known and new alloys, and can lead to time and cost reductions through a better understanding of the science behind the alloys and processes. IH

For more information: Contact Paul Mason, Thermo-Calc Software Inc., 4160 Washington Road, Suite 230, McMurray, PA 15317; tel: 724-731-0074; fax: 724-731-0078; e-mail: paul@thermocalc.com; web: www.thermocalc.com