Computational Thermodynamics of Materials

Lesson 1 • Thermodynamic Databases and Data Sources

Surveys critically assessed thermodynamic databases and standard data formats used in materials science. Students learn to evaluate data quality and select appropriate reference datasets.

Lesson 2 • Laws and State Functions

Covers internal energy, enthalpy, entropy, and Gibbs energy as state functions derived from the four laws. Establishes the mathematical language used throughout the course.

Lesson 3 • Chemical Potential and Partial Molar Quantities

Introduces chemical potential as the driving force for mass transfer and reaction. Partial molar quantities link single-component properties to multicomponent mixtures.

Lesson 1 • Magnetic and Order-Disorder Contributions

Adds magnetic Gibbs energy contributions using the Inden-Hillert-Jarl model and treats order-disorder transitions. Demonstrates how physical models improve extrapolation accuracy.

Lesson 2 • Ideal and Regular Solution Models

Derives ideal mixing entropy and introduces the regular solution model with a single interaction parameter. Provides the simplest baseline for comparing more complex models.

Lesson 3 • Models for Ionic and Ceramic Systems

Covers ionic liquid models and modified quasichemical approaches for oxide and salt systems. Addresses charge neutrality constraints in multicomponent ionic solutions.

Lesson 4 • Sublattice and Compound Energy Formalism

Introduces the compound energy formalism for phases with multiple sublattices, such as intermetallics and oxides. Connects site fractions to measurable thermodynamic quantities.

Lesson 1 • Binary Phase Diagram Calculation

Computes complete binary phase diagrams including eutectic, peritectic, and miscibility gap features. Demonstrates how model parameters control diagram topology.

Lesson 2 • Metastable and Constrained Equilibria

Calculates metastable phase diagrams by suspending stable phases and applying paraequilibrium constraints. Relevant to kinetically trapped microstructures in steels and alloys.

Lesson 3 • Ternary and Multicomponent Diagrams

Extends phase diagram calculation to ternary and higher-order systems using geometric and numerical methods. Introduces liquidus projection and monovariant line tracing.

Lesson 4 • Phase Rule and Gibbs Triangle

Applies the Gibbs phase rule to determine degrees of freedom in multicomponent systems. Introduces ternary composition space and isothermal section construction.

Lesson 1 • Extrapolation to Higher-Order Systems

Applies geometric extrapolation methods to predict ternary and quaternary properties from binary assessments. Evaluates when ternary interaction parameters are necessary.

Lesson 2 • Parameter Optimization Techniques

Applies least-squares and global optimization algorithms to fit thermodynamic parameters to experimental data. Covers convergence criteria and avoiding overfitting.

Lesson 3 • CALPHAD Philosophy and Workflow

Explains the hierarchical binary-to-ternary assessment strategy and the role of critical evaluation. Establishes the workflow from data collection to validated multicomponent database.

Lesson 4 • Experimental Data for Assessment

Identifies and weights experimental data types used in CALPHAD optimization, including calorimetry, EMF, and phase boundary data. Teaches critical evaluation of conflicting datasets.

Lesson 1 • Scripting and API-Based Workflows

Automates thermodynamic calculations using Python-based APIs and scripting interfaces to thermodynamic engines. Enables integration of thermodynamic data into larger materials informatics pipelines.

Lesson 2 • Scheil and Solidification Simulations

Simulates non-equilibrium solidification using the Scheil-Gulliver model to predict segregation and phase sequence. Compares Scheil results to equilibrium lever rule solidification.

Lesson 3 • Phase Diagram Mapping and Property Diagrams

Generates binary and ternary phase diagrams and property diagrams such as driving force and activity plots. Covers axis mapping, stepping, and mapping calculation modes.

Lesson 4 • Single-Point Equilibrium Calculations

Performs fixed temperature-composition equilibrium calculations to determine stable phases and their amounts. Introduces console and scripting interfaces for batch calculations.

Lesson 1 • Phonons and Vibrational Free Energy

Calculates vibrational contributions to Helmholtz free energy using harmonic and quasi-harmonic approximations. Demonstrates the importance of phonon contributions near phase transitions.

Lesson 2 • Special Quasirandom Structures

Uses special quasirandom structures to model disordered alloy configurations in DFT supercells. Enables calculation of mixing enthalpies for random solid solutions.

Lesson 3 • DFT Basics for Thermodynamics

Reviews density functional theory at the level needed to extract formation energies and elastic constants. Focuses on practical inputs and outputs rather than derivation of exchange-correlation functionals.

Lesson 4 • Integrating DFT Data into CALPHAD

Transfers DFT-calculated formation energies and heat capacities into CALPHAD parameter optimization as pseudo-experimental data. Addresses systematic DFT errors and correction strategies.

Lesson 1 • Phase Field and CALPHAD Integration

Introduces phase field models that use CALPHAD free energy functions as input for microstructure simulation. Demonstrates grain growth and precipitate coarsening simulations.

Lesson 2 • Multicomponent Diffusion Equations

Extends Fick's laws to multicomponent systems using the diffusivity matrix and off-diagonal terms. Demonstrates cross-diffusion effects in ternary alloys.

Lesson 3 • CALPHAD-Coupled Diffusion Simulation

Performs diffusion simulations using software that couples thermodynamic and mobility databases at each time step. Predicts composition profiles during homogenization and carburization.

Lesson 4 • Nucleation Theory and Driving Force

Applies classical nucleation theory with CALPHAD-derived driving forces to predict nucleation rates. Quantifies the effect of undercooling and interfacial energy on nucleation kinetics.

Lesson 1 • Corrosion and Oxidation Thermodynamics

Constructs Pourbaix and Ellingham diagrams computationally to predict corrosion and oxidation stability. Links thermodynamic stability windows to alloy protection strategies.

Lesson 2 • Ceramic and Refractory System Design

Applies thermodynamic calculations to oxide, carbide, and nitride systems for refractory and coating applications. Addresses challenges of limited experimental data in ceramic databases.

Lesson 3 • Process Simulation and Heat Treatment

Simulates industrial heat treatment cycles by coupling equilibrium calculations to time-temperature paths. Predicts phase fractions and compositions after annealing, quenching, and aging.

Lesson 4 • Integrated Computational Materials Design

Combines CALPHAD, diffusion simulation, and property models in an ICME framework for accelerated alloy development. Demonstrates a full design-to-validation case study.