CALPHAD Methodology

CALPHAD Methodology

CALPHAD is a proven methodology for predicting thermodynamic, kinetic, and other properties of multicomponent material systems.  At Thermo-Calc Software, we use CALPHAD methodology to develop our databases, which, when used together with our software, can predict the properties of multicomponent systems corresponding to real materials.

Figure 1. CALPHAD methodology consists of four main steps for developing databases of materials systems. We follow these steps rigorously when developing our thermodynamic, kinetic, and properties databases.

About CALPHAD

CALPHAD is a phenomenological approach for calculating/predicting thermodynamic, kinetic, and other properties of multicomponent materials systems. It is based on describing the properties of the fundamental building blocks of materials, namely the phases, starting from pure elements and binary and ternary systems. With extrapolation from the binary and ternary systems, CALPHAD predicts the properties of higher order alloys. Over the last decades, the CALPHAD method has successfully been used for development of numerous “real” engineering materials.

A Phase-based Approach

It is important to understand that CALPHAD is a phase-based approach, in other words, the properties for the individual phases are modeled as a function of composition, temperature, and sometimes also pressure. This, along with various thermodynamic models adopted, is, in fact, the power of CALPHAD—it allows one to extrapolate from the data available on only binary and ternary systems into the higher order systems, information that is rarely available through experiments and handbooks. Since phases are the fundamental building blocks of a material, the CALPHAD method is truly a Materials Genome approach.

Predict Many Properties with CALPHAD

The applicability of this approach expands beyond the traditional thermochemistry. In other words, besides the thermodynamics of a system, it is possible to calculate other properties such as atomic mobility, molar volume, thermal conductivity and diffusivity, viscosity and surface tension of liquids, electrical resistivity, and more.

See Properties that Can be Calculated

CALPHAD Databases

The functions and parameters determined using the CALPHAD method are stored in a database. At Thermo-Calc Software, we use CALPHAD methodology to develop two types of databases. Our thermodynamic and properties databases generate thermodynamic data as well as additional properties data, such as molar volume, thermal conductivity, and more. We also develop mobility databases, which generate kinetic data and each correspond to a specific thermodynamic and properties database. All database development uses the same methodology, but there are differences in the models that are applied to the data.

Read about our Databases

See how We Develop Databases using the CALPHAD Method

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CALPHAD Step-by-Step

The core of the CALPHAD approach is transforming a variety of experimental data on materials systems into physical-based mathematical models. The methodology consists of four main steps, and the whole procedure is schematically summarized in Figure 1.

Figure 1. CALPHAD methodology consists of four main steps for developing databases of materials systems: i) collecting the available experimental data on the to-be-modeled properties, for example, in the case of thermodynamics these would be the data on phase equilibria, crystal structure, and thermochemical data, ii) critical assessment of the captured data and choosing the appropriate model based on this data, iii) optimizing the free parameters of the models and iv) appending the optimized model parameters of the investigated system to a library containing the model for other systems. Once the library of models is updated, the validations against the experimental data for higher order systems are performed.

Data Capture

The first step of CALPHAD modeling is to collect experimental data on the materials system of interest. In the case of thermodynamics, high quality experimental data on phase equilibria, thermochemical properties like enthalpy of mixing or formation energies and crystal structures are the essence of CALPHAD modeling.

In cases where we lack experimental data, we perform ab-initio calculations (or use previously calculated ab-initio values). We also make use of machine learning, empirical relations, and/or rule of thumb to estimate the model parameters for systems with little or uncertain data.

Critical Assessment and Model Selection

The next step in the CALPHAD process is the critical assessment and pre-processing of the collected data. This can also be referred to as Model Selection. For instance, in the case of a phase diagram assessment of a given thermodynamic system with elements A and B, there exists a number of thermodynamically distinct regions or so-called phases. For each of these phases, a model for the Gibbs energy is assigned by a human expert depending on its crystal structure. The Gibbs energy is a polynomial in the chemical composition and temperature (and pressure if it is not fixed in the experiments) of a material, and it is the crucial quantity in computational thermodynamics because it describes all the thermodynamic properties of a material.

This process is similar for all types of properties we include in our databases, but the models may vary. For instance, the Gibbs energy model is used for describing the thermodynamics of a system, while other models are used for describing the thermophysical properties, for example the surface tension of liquids has been described using the modified-Guggenheim model.

Read a detailed description of how we capture and assess thermodynamic data for our thermodynamic and properties databases.

Assessment of Thermodynamic Data

Optimization

After assigning the models to phases, the free parameters of the model are fitted to the input data that was collected in the first step. This step is called optimization and demands extensive human judgement at different stages, mainly due to the fact that the free parameters of all phases should be consistent with each other. In other words, our modeling task is a multi-objective optimization with constraints. This is analogous to training multiple-models in the machine learning context.

In Thermo-Calc, optimization is completed using the built-in PARROT Module, which is available in all Thermo-Calc and Diffusion Module (DICTRA) installations.

Read about the PARROT Module

Storage

Once the parameters for all phases are fitted to the experimental data, the Gibbs energy functions with their optimized free parameters are stored in a text file, or so-called database, with a format that is readable by Thermo-Calc.

Validation

The final step in the process of developing a CALPHAD database is to validate the predictions against experimental results. When developing a multicomponent database for a specific alloy system, validation against data (not used during the optimization of the individual subsystems) from commercial and other multicomponent alloys is critical. If the agreement with real multicomponent commercial alloys is not good for key data points, a re-optimization of one or more lower order systems is the only way to rectify this.

CALPHAD Calculations and Predictions

Once all of the steps are completed and the predictions have been validated, the models, with their fitted parameters, known as databases, are loaded into our computational package, Thermo-Calc, to calculate thermodynamic, kinetic, and other properties of the systems of interest. Typically, we optimize only binary and ternary systems and not for higher-order systems. This is in fact the power of the CALPHAD methodology and the reason is that the models have a physical basis and all the model parameters are intrinsically consistent with each other. Therefore, the extrapolation from binary and ternary systems to higher-order systems works very well. This is ensured by critical validation of the optimized model parameters against the experimental data for higher-order systems.

A Summary of the Process

A summary of the assessment process is illustrated in Figure 2 within the context of a thermodynamic assessment.

image2

Figure 2. The first panel shows the first step of the assessment process. The experimental data on a system is collected by materials experts. The diagram in this panel illustrates the phase equilibria data for the Al-Mg system. Note that the dashed-line is only a guide to the eye. After the materials scientist identifies all phases and their crystal structures for a given system, a model is assigned for the Gibbs energy of each phase. This model is basically a polynomial function of composition and temperature, and terms in the function varies from phase to phase. The free model parameters are fitted to the experimental data. This step is performed for all phases together, in other words, a multi-phase model optimization because the model parameters of all phases are interconnected to each other. A plot of Gibbs energy functions with optimized model parameters for three phases that exist at 730 K for the Al-Mg system is given in the second panel. With such critically optimized model parameters, we can then map the phase diagram through the minimization of the Gibbs energy function as shown in the third panel.

Learn More

Read a detailed description of how we capture and assess thermodynamic data for our thermodynamic and properties databases.
Assessment of Thermodynamic Data

Read about the module in Thermo-Calc we use to optimize the data, called the PARROT Module, also known as the Data Optimization Module.
Data Optimization Module (PARROT)

History of CALPHAD

Read about the history of CALPHAD through the scientists who made the discoveries in our Historic Note series.
Historic Note

Learn about the importance of CALPHAD to materials science in a presentation from the head of our database development team, Dr. Qing Chen.
Presentation: CALPHAD and Beyond – The True Story of Materials Genome

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