Grain Boundary Diffusion in Yukawa Crystals

TL;DR

This work investigates grain boundary diffusion in Yukawa crystals to understand transport in neutron star crusts where bulk diffusion is suppressed at low temperatures. Using molecular dynamics with a Yukawa potential, diffusion along 11 grain boundaries across multiple orientations is characterized and shown to follow an Eyring activation form, behaving like a thin amorphous film with diffusion substantially faster than the bulk solid but slower than a corresponding supercooled liquid. The diffusion coefficients exhibit weak orientation dependence and depend on the screening parameter κ, indicating non-universal boundary landscapes shaped by Coulomb screening. The findings imply grain boundaries could dominate viscous dissipation in neutron star crusts and white dwarf cores, providing a practical scaling where GB diffusion is roughly one to two orders of magnitude smaller than bulk liquid and about 20 orders of magnitude larger than bulk solid diffusion, guiding future modeling of crustal creep and starquakes.

Abstract

We present calculations of diffusion coefficients in grain boundaries in Yukawa crystals for astrophysics. Our methods follow from our recent work calculating diffusion coefficients in perfect body-centered cubic crystals. These diffusion coefficients show only a weak dependence on the crystal orientations at the grain boundary and are consistent with those expected for a supercooled liquid scaled down by one to two orders of magnitude. We argue that the local disorder at the grain boundary produces a landscape of potential barriers similar to that of an amorphous liquid thin film, significantly reducing activation barriers to diffusive hops relative to the bulk solid. This also introduces a screening dependence, such that boundary diffusion does not exhibit the same universality as the bulk crystal. These diffusion coefficients suggest that grain boundaries may be a dominant source of viscous dissipation in neutron star crusts.

Figures (3)

• Figure 1: Grain Boundary: Initial MD configuration for a pure tilt GB viewed along the $xz$-plane, constructed from crystal A (bottom) and crystal B (top). There are two GBs, one in the middle and another at the top due to the periodic boundary.
• Figure 2: Diffusion analysis of the fiducial runs. We simulate the pure tilt $\Sigma5$ boundary (top) and a mixed boundary obtained by twisting the (001) crystal (bottom). (Top left) A histogram of displacement magnitudes $|\Delta \mathbf{r}|$ of all particles in the simulation show that about a thousand nuclei diffuse more than one $a_i$, consistent with the expectation that about a tenth of the particles are in a GB, and no diffusive hops are observed outside of a GB. For the thousand particles that diffuse by more than a lattice spacing, we show the displacement in (top center) $\Delta x$, (bottom left) $\Delta y$, and $\Delta z$ (bottom center). It is apparent that there are abundant diffusive steps in the $x$ and $y$ directions, but only incidental diffusion in $z$. To visualize diffusion at the two GBs, we plot displacement vectors for the particles that move (right). In the pure tilt crystal, diffusion in the $y$ direction dominates at both the top GB (top right) and central GB (bottom right) because particles move in the 'ridges' of crystal B; this is the into-the-page direction of Fig. \ref{['fig:xz_projection']}, while the twist destroys the $y$-axis symmetry. Few particles move vertically by more than one unit cell length (vector color).
• Figure 3: Grain Boundary Diffusion Coefficients: Diffusion coefficients for $\kappa=0.333$ (top) and $\kappa=0.666$ (bottom) for pure twist and CSL GBs (left) and tilt and mixed GBs (right). GB diffusion coefficients consistently show only weak sensitivity to the specific crystal orientation. The Eyring model slope is generally steeper for tilt and mixed GBs than pure twist and high symmetry GBs. The fit for a liquid (dotted) from Caplan et al. CaplanBauerFreeman has been extrapolated to supercooled temperatures, and shows that GB diffusion follows approximately the same Eyring model slope but rescaled down by one to two orders of magnitude.