English
Menu

Computational materials science

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)?

  1. AAbout 1.15 eV
  2. BAbout 4.90 eV
  3. CAbout 3.75 eV
Show answer and explanation

Answer: A. About 1.15 eV

E_v = −400.10 − (107/108)(−405.00) = −400.10 + 401.25 = 1.15 eV. The factor (N−1)/N is applied to compare with a state in which the removed atom is returned with the energy of one atom in the crystal (−405.00/108 = −3.75 eV), so that the numbers of atoms match. About 4.90 eV takes only the difference of the two total energies and leaves out the contribution of returning the removed atom to the crystal. About 3.75 eV is the magnitude of the energy per atom of the perfect crystal and is not the vacancy formation energy. The correct value can also be written as 4.90 − 3.75 = 1.15 eV. In real calculations, a small cell leaves interactions between the periodically repeated vacancies, so convergence with respect to cell size is checked.

Report an error

Practice this topic Back to topic

More Computational materials science questions

  1. 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?
  2. Which statement about the interatomic potentials used in molecular dynamics is correct?
  3. 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?
  4. 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.
  5. 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.