A method that models the Gibbs energy of each phase as a function of temperature and composition and calculates multicomponent phase diagrams and phase fractions from a database fitted to experimental and other data.
Japanese name: CALPHAD法
CALPHAD method appears in 2 practice questions across 1 topic, including Computational materials science.
In the CALPHAD method, the Gibbs energy of each phase, such as liquid, solid solutions and compounds, is written as a formula in temperature and composition. For a solid solution it is the sum of pure-substance terms, an ideal mixing entropy term and an excess term representing interactions between components, the excess term being expressed as a polynomial in composition (the Redlich–Kister expression). For phases in which atoms occupy fixed sites, such as compounds, sublattice models are used. For the pure-substance terms, common values for each element are defined as a database.
The parameters in the formulas are fitted to experimental data such as phase boundaries, heat capacities, heats of mixing and activities, and to formation energies obtained by first-principles calculations. This work is called thermodynamic assessment, and multicomponent thermodynamic databases are built up by accumulating assessments of binary and ternary systems. Interactions of quaternary and higher order are often neglected as small, which allows extrapolation to multicomponent compositions without experiments. Databases have been developed for practical alloy systems such as steels, nickel-based superalloys, aluminum alloys and solders.
Finding the combination of phases and the composition of each phase that minimize the Gibbs energy of the whole system at a given temperature, pressure and composition gives phase diagrams, phase fractions, liquidus temperatures and more. This can be used to narrow down the composition range in which harmful phases do not appear in multicomponent alloys. Combined with data on diffusion mobilities it can also calculate the rates of diffusion and precipitation, and combined with the phase-field method, microstructural change. What is obtained, however, is the equilibrium state, and the accuracy depends on the quality and range of the database assessment.
Answer: B. A method that fits Gibbs energy models of each phase to experimental and other data and calculates phase diagrams from the combination of phases that minimizes the total Gibbs energy
In the CALPHAD (CALculation of PHAse Diagrams) method, the Gibbs energy of each phase, such as liquid, solid solutions and compounds, is expressed as the sum of pure-substance terms, an ideal mixing term and an excess term representing interactions. Its parameters are fitted to experimental data such as phase diagrams, heat capacities and heats of mixing, and to formation energies obtained by first-principles calculations, and are compiled into a thermodynamic database. Finding the phases and compositions that minimize the Gibbs energy of the whole system at a given temperature and composition gives phase diagrams and phase fractions. Solving the electronic equations is first-principles calculation, whose results CALPHAD uses as one of its inputs. Because it uses thermodynamic models rather than interpolating phase diagram lines, it can extrapolate to temperatures and compositions without experiments.
Answer: C. The Gibbs energy of the multicomponent system is extrapolated by combining parameters assessed mainly for binary and ternary systems. What is obtained is the equilibrium state, and accuracy drops for compositions outside the assessed range
Experimenting at every composition of a multicomponent system is impossible, but with Gibbs energy models, parameters determined for binary and ternary systems can be combined to extrapolate to the multicomponent system. Interactions of quaternary and higher order are often neglected as small, and on this basis the liquidus temperatures of practical alloys, the kinds and fractions of precipitating phases, solubility limits and so on can be predicted, greatly reducing trial and error in alloy design. However, what is obtained is the thermodynamic equilibrium state; it does not tell whether the actual microstructure reaches equilibrium or how fast transformations proceed. To handle rates, data on diffusion mobilities and calculations of precipitation kinetics are combined. Pure-substance values alone cannot represent the interactions between components.
It stands for CALculation of PHAse Diagrams. It was originally the name of a method for calculating phase diagrams, but it now refers to the whole approach of building thermodynamic databases and using them to calculate phase equilibria and thermodynamic quantities.
First-principles calculation starts from the electronic states and gives quantities such as the energies of compounds at 0 K. The CALPHAD method uses those results and experimental data to determine Gibbs energy formulas and calculates phase equilibria of multicomponent systems at finite temperature. The two do not compete; rather, first-principles calculation supplies part of the data for CALPHAD.
For phases whose Gibbs energy models are in the database, metastable phase diagrams can be calculated by excluding stable phases from the calculation. An example is calculating equilibrium with cementite in steel by excluding graphite. Phases without models, however, cannot be calculated.
In the CALPHAD (CALculation of PHAse Diagrams) method, the Gibbs energy of each phase, such as liquid, solid solutions and compounds, is expressed as the sum of pure-substance terms, an ideal mixing term and an excess term representing interactions.
Which statement about the CALPHAD method is correct?Gibbs energy Density functional theory Nickel-based superalloy Finite element method Interatomic potential Materials informatics Molecular dynamics Monte Carlo method Phase-field method