Dislocation Structure and Mobility in hcp ${}^4\mathrm{He}$

Using path-integral Monte Carlo simulations, we assess the core structure and mobility of the screw and edge basal-plane dislocations in hcp ${}^4\mathrm{He}$. Our findings provide key insights into recent interpretations of giant plasticity and mass flow junction experiments. First, both dislocations are dissociated into nonsuperfluid Shockley partial dislocations separated by ribbons of stacking fault, suggesting that they are unlikely to act as one-dimensional channels that may display Lüttinger-liquid-like behavior. Second, the centroid positions of the partial cores are found to fluctuate substantially, even in the absence of applied shear stresses. This implies that the lattice resistance to motion of the partial dislocations is negligible, consistent with the recent experimental observations of giant plasticity. Further results indicate that both the structure of the partial cores and the zero-point fluctuations play a role in this extreme mobility.

Figure 1

(a) Cell geometry with two screw dislocations of opposite Burgers vectors placed on basal planes separated by half of the box height along the [0001] direction. (b) Path-centroid positions after PIMC relaxation viewed along the $[\overline{1}2\overline{1}0]$ direction. Colors represent ranges of common-neighbor analysis (see the text). Red and green depict hcp- and fcc-type atomic environments, respectively. (c) Centroids of two atomic planes containing one of the dislocations. Green represents the SF areas. Arrows depict partial dislocation Burgers vectors.

Figure 2

Configuration for the edge dislocation after PIMC relaxation. Colors represent ranges of the common-neighbor parameter (see the text). Red and green depict hcp- and fcc-type atomic environments, respectively. (a) Path-centroid positions viewed along the $[10\overline{1}0]$ direction. (b) Centroids of two atomic planes containing one of the dislocations. Green represents the SF area and arrows depict partial dislocation Burgers vectors.

Figure 3

Disregistry analysis for screw dislocation configuration. (a) Atoms in layers immediately below (circles) and above (dots) the slip plane. Screw disregistry is measured by monitoring the vertical position of the dot with respect to its enclosing triangle along eight horizontal rows of triangles (two are shown). Dashed lines depict spline fits through a set of eight core positions determined from fits to the PN model. (b) Representative fit of PIMC data for the disregistry $u$ (diamonds, in units of the full Burgers vector $b$) as a function of the horizontal position $x$ (also in units of $b$) to the PN model of Eq. (1) (the red line). Corresponding partial dislocation positions ($x_l$, $x_r$) and core widths ($2{\zeta }_l$, $2{\zeta }_r$) are also marked.

Figure 4

(a),(b) Centroid core positions for the left (diamonds) and right (squares) partial dislocations of the dissociated screw and edge dislocations as a function of the PIMC snapshot number. Vertical axes are in units of the perfect Burgers vector $b$. Shaded areas between partial positions denote the SF widths. Mean partial dislocation-core widths are also indicated. Mean confidence intervals for PN fits of the partial positions are $\sim \pm 0.3b$ and $\sim \pm 0.4b$ for the screw and edge dislocations, respectively. (c) Histogram of partial core positions relative to centroid partial core position as determined by fitting the PN expression to 50 displacement profiles per PIMC snapshot, each obtained from an average over three consecutive time slices.