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Computational materials science

Which pairing of a materials computation method with the range of space and time it can usually handle is most appropriate?

  1. ADensity functional theory (DFT) calculations following several million atoms, electronic structure included, for several microseconds
  2. BThe finite element method following the vibrations of individual atoms in femtosecond steps
  3. CClassical molecular dynamics following thousands to millions of atoms for times of the order of nanoseconds
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Answer: C. Classical molecular dynamics following thousands to millions of atoms for times of the order of nanoseconds

Computational methods are chosen according to the scale they can handle. DFT, which solves for the electronic states by quantum mechanics, usually handles tens to hundreds of atoms, and can follow time evolution only up to some tens of picoseconds. Classical molecular dynamics, which uses interatomic potentials, can follow thousands to millions of atoms for times of the order of nanoseconds. The phase-field method treats microstructural change from nanometers to micrometers, and the finite element method treats stress and temperature at the scale of components as a continuum. Following millions of atoms for microseconds with DFT is not realistic in computational cost, and the finite element method does not deal with atoms at all. Passing the results of smaller-scale calculations on to larger-scale ones is called multiscale modeling.

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More Computational materials science questions

  1. Which statement about the ideas behind density functional theory (DFT) is correct?
  2. Which is a correct tendency of the results of standard DFT calculations using LDA or GGA exchange-correlation functionals?
  3. 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)?
  4. 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?
  5. Which statement about the interatomic potentials used in molecular dynamics is correct?