Dislocation properties of coesite from an ab-initio parametrized interatomic potential

Calculation of the properties of dislocations by computer simulations requires, among other things, the availability of accurate interatomic potentials, ideally with ab-initioquality. For crystals with large unit cells and complex crystal structures, such as most minerals, the number and size of the calculations may severely limit the applicability of a full ab-initio approach. In this paper we present an investigation of the dislocation properties of coesite, a mineral with a relatively large unit cell, carried out with a force field developed for silica based on a parametrization to ab-initio data. Two-dimensional generalized stacking fault energy surfaces for basal and prismatic planes are considered for a global search of the possible dissociation paths in partial dislocations. Test calculations show negligible differences between the energy surfaces calculated with the force field and with ab-initio methods. Five different coesite slip systems are investigated: [100](010), [001](010), [101](010), [010](001), and [010]($\overline{1}$01). Dislocation core structures and critical stresses are determined by using the Peierls-Nabarro-Galerkin approach. While [100] and [101] (screw) dislocations share a similar core structure, [001] differs substantially by showing a much larger split between partial dislocations. The lattice friction experienced by [001](010) is found to be close to those of [100](010) and [101](010), confirming the pseudohexagonal symmetry suggested by experiments.

Figure 1

Ball and stick model of the coesite primitive cell: view of the (010) basal plane. Silicon and oxygen atoms are shown with blue (large) and light gray (small) balls.

Figure 2

(i) Supercell used for the $\gamma$-surface calculation on the basal plane (010). (ii) Shear plane along which the $\gamma$ surface of Fig. 4a was calculated (1) and a test choice for the shear plane (2) are shown.

Figure 3

$\gamma$ line calculated by ab-initio method (dots), by ab-initio parametrized force field (solid), and by BKS force field (dashed) (Ref. 46). The adopted cell is shown in Fig. 2.

Figure 4

Contour plots of the $\gamma$ surfaces of (a) (010), (b) (001), (c) (100), and (d) ($\overline{1}$01).

Figure 5

$\gamma$ surfaces obtained for the two parallel shear planes shown in Fig. 2(ii). (a) corresponds to the shear plane (1) and (b) to the shear plane (2). A mesh of $20\times 20$ points was used.

Figure 6

(a) $\gamma$ lines of the slip systems [100](010) (dotted), [001](010) (solid), and [101](010) (dashed). (b) $\gamma$ lines of the slip systems [010](001) (dotted) and [010]($\overline{1}$01) (solid).

Figure 7

Dislocation profiles $S(x)$ and $\rho (x)=\mathit{dS}(x)/\mathit{dx}$ (dotted) for the [001](010) screw dislocation. $S(x)$ calculated by PNG method (disks) is superimposed on the fit through an expansion in a series of arctangent functions (solid).

Figure 8

Local dislocation densities for the screw [100](010) (dotted), [001](010) (solid), and [101](010) (dashed) dislocations.

Figure 9

Dislocation density profiles of the [010](001) (dotted) and [010]($\overline{1}$01) (solid) screw dislocations.

Figure 10

$\gamma$ surfaces (a) (001) and (b) ($\overline{1}$01) on which shear paths (line with filled squares) of the [010] screw dislocations have been superimposed.