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Publication Figures

Publication Date:
2019-12-26

First Author:
P-W Ma

Title:
CALANIE: anisotropic elastic correction to the total energy, to mitigate the effect of periodic boundary conditions

Paper Identifier:
CP/19/193

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Figure Reference Title Description Number of Figure Data Items Identifier Download Figure Details
calanie_fig_1 Variation of the formation energy of a vacancy during its transition from an equilibrium position to a nearest neighbour equilibrium position. A small difference can be observed between the cases studied with and without applying the elastic correction. 1 CF/19/194 Download
calanie_fig_2_a Elastic dipole tensor of a vacancy moving along a migration pathway in the $y-z$ plane. Owing to the symmetry of the defect, $P_{22}=P_{33}$ and $P_{12}=P_{31}=0$. 0 CF/19/196 Download
calanie_fig_2_b Elastic dipole tensor of a vacancy moving along a migration pathway in the $y-z$ plane. Owing to the symmetry of the defect, $P_{22}=P_{33}$ and $P_{12}=P_{31}=0$. 0 CF/19/197 Download
calanie_fig_3 Atomic configuration of (left) a circular $frac{1}{2}langle 111 rangle$ and (right) a square $langle 100 rangle $ self-interstitial atom loop. Both loops contain 61 self-interstitial atoms. Bulk atoms were filtered out according to the centre of symmetry parameter criterion. (Data and figures are in the same zip file) 0 CF/19/198 Download
Calanie_fig_4 Elastic dipole tensors of $frac{1}{2}langle 111 rangle$ self-interstitial atom loops containing 7, 13, 19, 37, 55, and 61 atoms as functions of the simulation cell size. $P_{alphaalpha}$ are the diagonal terms, whereas $P_{alphabeta}$ are the off-diagonal terms. Elements of the elastic dipole tensor are computed using the condition that the simulation cell shape was fixed to match the perfect lattice case, or allowed to relax to a stress-free condition. 0 CF/19/199 Download
calanie_fig_5 Formation energy $E^F_{def}$ of $frac{1}{2}langle 111 rangle$ self-interstitial atom loops containing 7, 13, 19, 37, 55, and 61 atoms shown as a function of the simulation cell size. The $E^F_{def}$ is calculated with elastic correction applied, i.e. using Eq. ref{formation_energy_correction}, or without the correction, i.e. ignoring the $E^{app}$ and $E_{el}^{corr}$. Both are calculated under the condition that the simulation cell shape was fixed to match the perfect lattice case, or was allowed to relax to a stress-free condition. 0 CF/19/200 Download
calanie_fig_6 Elements of elastic dipole tensors of $langle 100 rangle$ self-interstitial atom loops containing 5, 13, 25, 41, and 61 atoms plotted as a function of teh simulation cell size. The off-diagonal terms of the dipole tensor vanish because of symmetry. The elastic dipole tensor is calculated under the condition that the simulation box shape was fixed to match the perfect lattice case, or was allowed to relax to a stress-free condition. 0 CF/19/201 Download
calanie_fig_7 Formation energy $E^F_{def}$ of $langle 100 rangle$ self-interstitial atom loops containing 5, 13, 25, 41, and 61 atoms shown as a function of the simulation cell size. Values of $E^F_{def}$ were calculated with elastic correction applied, i.e. using Eq. ref{formation_energy_correction}, or with no correction, i.e. ignoring $E^{app}$ and $E_{el}^{corr}$. Both were calculated under the condition that the simulation box shape was fixed to match the perfect lattice case, or was allowed to relax to a stress-free condition. 0 CF/19/202 Download