Analytic Formulas for the Orientation Dependence of Step Stiffness and Line Tension: Key Ingredients for Numerical Modeling

TL;DR

This paper provides explicit analytic formulas for the temperature-dependent anisotropic step line tension and stiffness on face-centered-cubic crystal surfaces, enhancing numerical modeling accuracy across a wider temperature range.

Contribution

It introduces improved, explicit, twice-differentiable formulas for step line tension and stiffness applicable to {001} and {111} surfaces, valid over broader temperature ranges.

Findings

Explicit formulas for step line tension and stiffness

Applicable to {001} and {111} crystal surfaces

Suitable for numerical simulations

Abstract

We present explicit analytic, twice-differentiable expressions for the temperature-dependent anisotropic step line tension and step stiffness for the two principal surfaces of face-centered-cubic crystals, the square {001} and the hexagonal {111}. These expressions improve on simple expressions that are valid only for low temperatures and away from singular orientations. They are well suited for implementation into numerical methods such as finite-element simulation of step evolution.