Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0709.2726

Anisotropic step stiffness from a kinetic model of epitaxial growth

Dionisios Margetis·Russel E. Caflisch
View original source ↗Read source document ↗Export metadata ↓

Abstract

Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson type formula and the associated step stiffness as a function of the step edge orientation angle, $theta$. Basic ingredients of the model are: (i) the diffusion of point defects (``adatoms'') on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive laws that relate adatom fluxes, sources for kinks, and the kink velocity with densities via a mean-field approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, $\tbe(θ)$, is determined via perturbations of the kinetic steady state for small edge Peclet number, P, which is the ratio of the deposition to the diffusive flux along a step edge. In particular, $\tbe$ is found to satisfy $\tbe =O(θ^{-1})$ for $O(P^{1/3}) <θ\ll 1$, which is in agreement with independent, equilibrium-based calculations.

Explore related subjects

cond-mat.mtrl-sci

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dionisios Margetis, Russel E. Caflisch. 2007-09-17. Anisotropic step stiffness from a kinetic model of epitaxial growth. https://arxiv.org/abs/0709.2726

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Hidden Subsurface Oxygen Asymmetry Stabilizes Polaron Beneath the Polar CeO2(100) Surface

Polar oxide surfaces often reconstruct to compensate their intrinsic electrostatic instability, yet identifying the atomic-scale structural motifs that govern such reconstructions and their coupling with localized electronic states remains challenging because oxygen configurations are difficult to resolve. Here, we show that a hidden asymmetric arrangement of subsurface oxygen atoms is intimately coupled with the reconstruction of the polar CeO2(100) surface and the formation of subsurface small polarons. Global structure search and deep potential molecular dynamics identify a previously unknown asymmetric (1*2) reconstruction, where subsurface oxygen asymmetry creates anisotropic Ce-O coordination environments and elongated Ce-O bonds, stabilizing localized Ce3+ small polarons beneath the surface. Enabled by oxygen-sensitive integrated differential phase contrast scanning transmission electron microscopy (iDPC-STEM), we directly visualize the predicted asymmetric subsurface oxygen configuration, while high-angle annular dark-field (HAADF) STEM resolves the accompanying asymmetric cerium arrangement and expanded interlayer spacing. These findings establish hidden subsurface oxygen asymmetry as a key structural motif coupling oxygen rearrangement, lattice reconstruction, and polaron localization, revealing a coupled oxygen-lattice-electron mechanism governing the evolution of polar oxide surfaces.

cond-mat.mtrl-sci↗
arXiv2026

Peierls Transition and Magnetism in a Dirac Semimetal: CaMnBi$_2$

Dirac semimetals of the form $A$Mn$X_2$ ($A =$ alkaline-earth or divalent rare earth; $X =$ Bi, Sb) host conducting square-net Dirac-electron layers of $X$ atoms interleaved with antiferromagnetic Mn$X$ layers. Hypervalent pnictogen square nets have long been predicted to host an electronically driven Peierls instability, whereas low-temperature anomalies in CaMnBi$_2$ near $T^{*}\sim 50$~K have previously been discussed in terms of possible magnetic canting, TRS breaking, and a resulting Weyl-semimetal (WSM) state. Here we use polarized and unpolarized neutron diffraction, x-ray diffraction, and density functional theory (DFT) to investigate this transition in single-crystal CaMnBi$_2$. We observe a coupled structural/magnetic symmetry-lowering transition at $T^{*}=46(2)$ K from a tetragonal lattice with C-type antiferromagnetism to an orthorhombic phase with unit-cell doubling along the $c$ axis, minimal impact on magnetism, and no measurable uniform spin canting ($\lesssim 2^\circ$). Superlattice peak intensities and the lattice distortion reveal a continuous second-order transition governed by a single primary order parameter. The refined displacement pattern corresponds to a zigzag bond-order-wave (BOW) modulation of in-plane Bi--Bi bonds, providing direct diffraction evidence for a Peierls-type instability of the Dirac-electron Bi layer anticipated by Hoffmann and co-workers [W. Tremel and R. Hoffmann, J. Am. Chem. Soc. 109, 124 (1987); G. A. Papoian and R. Hoffmann, Angew. Chem. Int. Ed. 39, 2408 (2000)]. These results identify the $T^{*}$ anomaly as an intrinsic Dirac-electron-driven Peierls/BOW transition of the Bi square net.

cond-mat.mtrl-sci↗
arXiv2026

Diffusion coefficients of multi-principal element alloys from first principles

Vacancy-mediated diffusion in multi-principal element alloys (MPEAs) remains poorly understood. Existing computational methods face challenges in connecting electronic structure to macroscopic transport coefficients due to the large number of chemical elements. To address this, we introduce the embedded local cluster expansion (eLCE), which bridges first-principles calculations with kinetic Monte Carlo simulations to compute the matrix of multicomponent diffusion coefficients. Applying this approach to refractory MPEAs in the V-Cr-Nb-Mo-Ta-W system, we evaluate the complete mobility and diffusion tensors of a six-component alloy at finite temperatures. We find that local kinetic barriers, rather than thermodynamics or vacancy correlation factors, primarily control diffusion in these materials. Whether diffusion is sluggish or anti-sluggish depends on the mean vacancy migration barrier relative to the rule-of-mixtures estimate and on the availability of percolating pathways of fast-diffusing species. We use this insight to screen the senary composition space and identify compositions with anti-sluggish diffusion. This study presents a predictive, first-principles approach for computing non-dilute transport coefficients and designing MPEAs with targeted transport properties.

cond-mat.mtrl-sci↗