Dislocation Mobility in a Quantum Crystal: The Case of Solid ${}^4\mathrm{He}$

We investigate the structure and mobility of dislocations in hcp ${}^4\mathrm{He}$ crystals. In addition to fully characterizing the five elastic constants of this system, we obtain direct insight into dislocation core structures on the basal plane, which demonstrates a tendency toward dissociation into partial dislocations. Moreover, our results suggest that intrinsic lattice resistance is an essential factor in the mobility of these dislocations. This insight sheds new light on the possible correlation between dislocation mobility and the observed macroscopic behavior of crystalline ${}^4\mathrm{He}$.

Figure 1

Degrees of freedom in the PN model. (a) Atomic rows on one side of slip plane (dashed line) are labeled by index $i$. Distance between adjacent rows in defect-free crystal is $\Delta x$. (b) Displacements of rows with respect to those on other side of slip plane are described by vector ${\overrightarrow{\delta }}_i$.

Figure 2

Fourier series representation of GSF surface on the basal plane of hcp ${}^4\mathrm{He}$ as modeled by the SWF. (a) GSF energy (in $\mathrm{mJ}/{\mathrm{m}}^2$) as a function of two-dimensional displacement $\overrightarrow{\delta }$ (in units of $b_p=\frac{1}{3}\sqrt{3}a=2.0996\AA$). (b) Contour plot of the GSF. It reflects the basal-plane symmetry of the hcp structure.

Figure 3

Optimized displacement profile ${\overrightarrow{\delta }}_i$ for screw dislocation on the basal plane: edge component (open circles) and screw component (filled squares) are measured in units of the Burgers vector $b=a=3.63668\AA$. Dashed lines indicate positions of partial dislocations.