Line stress of step edges at crystal surfaces

Step edges at crystal surfaces interact elastically with the underlying bulk solid. The resulting attraction or repulsion between neighboring steps is well described by an established dipole model. Here, we focus on the average stress which a step edge generates in the bulk. This quantity represents an excess of surface stress due to the presence of the step. Within the standard dipole description of the stress field of steps, that excess is zero. Yet, atomistic simulation testifies to a significant variation in the apparent surface stress of vicinal surfaces with the number density of steps. We show how a line stress can be defined as an excess in surface stress per line length. The definition is analogous to that of line tension as an excess of surface tension. Even though the step edge may be viewed as a one-dimensional object, we show that the line stress cannot be represented by a vector along the line; it is also not adequately represented by dipole forces. The line stresses give rise to cusps, typically upward, in polar plots of the principal values of the surface stress tensor in the surface orientation domain. We present a continuum model that links the directionality and magnitude of the line stress to the surface stress at the inclined step face. ► We compute the mean bulk stress due to a step edge. ► An excess in surface stress per line length defines the ‘line stress’ on an edge. ► The line stress controls the surface stress polar dependence for vicinal surfaces. ► It has components parallel and perpendicular to the edge. ► Results of our continuum theory match atomistic simulation.