Depth-dependent critical behavior inV2H

Abstract

Using x-ray diffuse scattering, we investigate the critical behavior of an order-disorder phase transition in a defective "skin layer" of V 2 H. In the skin layer, there exist walls of dislocation lines oriented normal to the surface. The density of dislocation lines within a wall decreases continuously with depth. We find that, because of this inhomogeneous distribution of defects, the transition effectively occurs at a depth-dependent local critical temperature. A depth-dependent scaling law is proposed to describe the corresponding critical ordering behavior.

Anomalous ordering in inhomogeneously strained materials

“…Performing several simulations of systems with different sizes and using finite size scaling, we are able to measure the critical exponents characterizing the transition. The critical exponents found are comparable with exponents that have been measured experimentally in a variety of materials, and for different types of transitions [1,2,[7][8][9][10][11][12][13][14]. Notably, similar critical exponents have recently been measured for the magnetic ordering transition that accompanies the onset of the pseudogap state in high T c superconductors [15][16][17][18].…”

Depth-dependent ordering, two-length-scale phenomena, and crossover behavior in a crystal featuring a skin layer with defects

“…Thus, we find a depth-dependent critical temperature T c ͑y͒, where y is the effective scattering depth. 5 Furthermore, as shown in Ref. 4, there is a twolength-scale effect in the CDS from the skin layer.…”

“…Other kinds of defects are not found after the first 150 Å and the influence of this upper region on the scattering is negligible. 5 The arrangement of dislocation lines into walls, in the skin layer, is indicated by the mosaic spread. Walls occur inhomogeneously across the surface so that in planes parallel to the surface there is an inhomogeneous distribution of dislocation lines.…”

“…5 This mechanism provides an explanation as to why experimental measurements of at different depths yield different values even if taken at corresponding reduced temperatures, once the depth dependence of the critical temperature has been accounted for, and even though the critical exponent remains the same. A treatment to collapse the data onto a single curve, including corrections for the experimental method used, has been proposed and verified in Ref.…”

“…Indeed, with high-resolution x-ray diffraction measurements, we have previously found that V 2 H has two-length-scale and associated behavior that is depth dependent. 4,5 These measurements were performed in both reflection and transmission geometries, allowing us to compare the behavior of the crystal at different depths. In this paper, we propose a theoretical explanation of these experimental results that accounts for the depth dependence of the observed behavior.…”