Anomalous ordering in inhomogeneously strained materials

Abstract

We study a continuous quasi two-dimensional order-disorder phase transition that occurs in a simple model of a material that is inhomogeneously strained due to the presence of dislocation lines. Performing Monte Carlo simulations of different system sizes and using finite size scaling, we measure critical exponents describing the transition of β = 0.18 ± 0.02, γ = 1.0 ± 0.1, and α = 0.10 ± 0.02. Comparable exponents have been reported in a variety of physical systems. These systems undergo a range of different types of phase transitions, including structural transitions, exciton percolation, and magnetic ordering. In particular, similar exponents have been found to describe the development of magnetic order at the onset of the pseudogap transition in high-temperature superconductors. Their common universal critical exponents suggest that the essential physics of the transition in all of these physical systems is the same as in our simple model. We argue that the nature of the transition in our model is related to surface transitions although our model has no free surface.PACS numbers: 64.60. Cn, 61.72.Bb, 74.72.Kf Real solids are commonly in a strained state. This can be due to a variety of reasons, ranging from forces applied upon them to the presence of structural defects, to ongoing phase transformations. Such strains affect the ordering processes of the materials [1-6]. Therefore, understanding the extent of these effects is important. In this Communication, we study the continuous order-disorder phase transition in a model of a strained material. The strain field we consider results from a "wall of dislocations", that is, a linear array of parallel edge dislocation lines. This particular arrangement of defects is relatively common in crystals, as it often occurs because of surface treatments. The resulting strain is inhomogeneous, and order develops inhomogeneously in the material, with ordered regions growing in quasi two-dimensional layers around a central cylindrical rod-shaped nucleus [1]. Each layer orders at a different critical temperature. In order to study the critical behavior of this process, we consider a mesoscopic spin model in which the coupling between spins reflects the strain field induced by the dislocation walls. 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]. These exponents are also compatible with those found in multicritical surface transitions [19], although in our case the exponents describe bulk measurements.Assuming that atoms interact more strongly where they are pu...