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Computational materials science

Learn the ideas and limits of first-principles calculation (DFT), molecular dynamics and interatomic potentials, the Monte Carlo method, the CALPHAD method, the phase-field method, the finite element method and materials informatics through three-choice questions.

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Computational materials science: key points

In computational materials science, methods are chosen according to the scale of space and time to be handled. First-principles calculation (density functional theory, DFT), which starts from the electronic states, can obtain the structures and energies of up to a few hundred atoms without experimental data, but its approximations bring limits such as underestimating band gaps. Molecular dynamics, using interatomic potentials, follows the motion of many atoms for up to about nanoseconds, and the Monte Carlo method handles equilibrium states and long-time diffusion through probabilistic trials.

At the scale of microstructures and components, continuum methods take center stage. The CALPHAD method calculates multicomponent phase diagrams from Gibbs energy models of each phase, and the phase-field method follows changes in solidification and precipitation microstructures using diffuse interfaces. The finite element method finds the distributions of stress and temperature in components. Materials informatics, which predicts properties from data, has joined these, advancing materials development that combines computation and experiment.

All Computational materials science questions (15)
  1. Which pairing of a materials computation method with the range of space and time it can usually handle is most appropriate?
  2. Which statement about the ideas behind density functional theory (DFT) is correct?
  3. Which is a correct tendency of the results of standard DFT calculations using LDA or GGA exchange-correlation functionals?
  4. A 108-atom supercell (with periodic boundary conditions) of a metal calculated with DFT has a total energy of −405.00 eV. Removing one atom to create one vacancy and relaxing the structure gives −400.10 eV. Which is closest to the vacancy formation energy calculated as E_v = E(N−1) − [(N−1)/N]E(N)?
  5. In molecular dynamics, you want to integrate the equations of motion with a time step of 2 fs to calculate atomic motion over 1 ns. How many time steps are needed?
  6. Which statement about the interatomic potentials used in molecular dynamics is correct?
  7. Argon is described by the Lennard-Jones potential V(r) = 4ε[(σ/r)¹² − (σ/r)⁶] with σ = 0.34 nm. Which is closest to the interatomic distance r₀ at which the energy is a minimum?
  8. In a molecular dynamics calculation of a monatomic system, the average kinetic energy per atom was 0.0517 eV. Which is closest to the temperature of the system obtained from the equipartition theorem? Take the Boltzmann constant as k = 8.617×10⁻⁵ eV/K.
  9. In a Monte Carlo calculation by the Metropolis method, a trial move of an atom raises the energy of the system by 0.10 eV. At a temperature of 1000 K, which is closest to the probability of accepting this move? Take k = 8.617×10⁻⁵ eV/K.
  10. Which statement about the kinetic Monte Carlo (kMC) method is correct?
  11. Which statement about the CALPHAD method is correct?
  12. The CALPHAD method is used to predict the precipitating phases and their fractions in a nickel-based superalloy or steel containing close to ten elements. Which combination of the underlying idea and a caution is correct?
  13. Which statement about the phase-field method is correct?
  14. Which is the correct way of thinking when using the finite element method to calculate the elastic stresses in a component with holes or notches?
  15. In materials informatics, when a machine learning model is built from data on existing materials to predict the properties of new materials, which caution is correct?

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