Long-Range Ordered Phases without Short-Range Correlations

Abstract

We present results of Monte Carlo simulations of kinetics of spinodal ordering on a one-dimensional Ising chain with competing interactions up to third neighbors for Glauber and Kawasaki dynamics. Application of these results to the 2H-6H transformation in SiC shows that the arrested state of the transformation possesses long-range order but lacks short-range correlations.PACS numbers: 61.50. Ks, 64.70.Kb, 81.30.Kf Solid-state transformations from one close-packed modification to another in materials like SiC, ZnS, Cdh, cobalt and its alloys, 1 and martensites of copper-based alloys 2,3 take place through nucleation and propagation of stacking faults on the basal plane. These transformations often get arrested much before completion because of the formation of domains of the product phase in different orientations. 4,5 The arrested state has generally been described as a heavily disordered state because of the presence of extensive diffuse streaking along c* for HK.L reciprocal-lattice rows with H -A^0(mod3) (Ref. 6) on the diffraction patterns. The diffuse streaking does not disappear even after repeated annealings. Recently we have undertaken 7 a detailed Monte Carlo simulation study of the kinetics of domain formation and growth during the 2H to 6H transformation in SiC which is known 4,5 to take place above 1600°C. In this Letter, we show that the arrested state for the 2H to 6H transformation possesses long-range ordering but lacks any short-range correlation in the direction of stacking of the close-packed layers. As such, the arrested state for the 2H to 6H transformation cannot be categorized as a conventional crystal or glass.The stacking sequence of a close-packed structure, in which atoms may lie in one of the three positions A, B, or C, can also be described 8 in terms of two state variables + and -which represent relative orientations of the pairs of consecutive layers and which for our purpose correspond to up (|) and down (1) Ising spins. 9 In this notation, pairs like AB, BC, CA and BA, CB, AC are represented by + and -symbols, respectively. The 2H (AB,. . .) and 6H (ABCACB, . . .) stacking sequences may therefore be described as containing (1) and (3) bands, where the numeral within the angular brackets is obtained by addition of all the consecutive spins of the same orientation. 9 Consider the Hamiltonian given below with competing interactions between the Zhdanov-Ising spins in the direction of stacking: H--'L r T, i SiS i ± r Jr,s, = ±i.

∊-Machine spectral reconstruction theory: a direct method for inferring planar disorder and structure from X-ray diffraction studies

“…(2013). A69, 197-206 2 These are identical to the QðmÞ, RðmÞ and PðmÞ often referred to in the literature(Kabra & Pandey, 1988;Shrestha & Pandey, 1996).…”

Pairwise correlations in layered close-packed structures

“…Warren (1969) uses P 0 m ; P þ m and P À m ; Kabra & Pandey (1988) call these PðmÞ; QðmÞ and RðmÞ; and Estevez- Rams et al (2008) use P 0 ðÁÞ; P f ðÁÞ and P b ðÁÞ. Since we prefer to reserve the symbol 'P' for other probabilities previously established in the literature, here and elsewhere we follow the notation of Yi & Canright (1996), with a slight modification of replacing 'Q r ðnÞ' with 'Q a ðnÞ'.…”

“…In the following, we demonstrate how pairwise correlation functions can be calculated either analytically or to a high degree of numerical certainty for an arbitrary HMM and, thus, for an arbitrary "-machine. Previous researchers often calculated pairwise correlation functions for particular realizations of stacking configurations (Berliner & Werner, 1986;Kabra & Pandey, 1988;Shrestha & Pandey, 1997;Estevez-Rams, Martinez et al, 2001;Varn et al, 2013a) or from analytic expressions constructed for particular models (Tiwary & Pandey, 2007;Estevez-Rams et al, 2008;Varn & Crutchfield, 2004). The techniques developed here, however, are the first generally applicable methods that do not rely on samples of a stacking sequence.…”

“…Disordered layered materials are often studied via the pairwise correlations between layers, as these correlations are experimentally accessible from the Fourier analysis of a diffraction pattern (Estevez-Rams, Martinez et al, 2001;Estevez-Rams, Penton-Madrigual et al, 2001;Varn et al, 2002Varn et al, , 2013a, or directly from simulation studies (Kabra & Pandey, 1988Shrestha & Pandey, 1996a,b, 1997Shrestha et al, 1996;Varn & Crutchfield, 2004). Such studies yield important insights into the structural organization of materials.…”

Chaotic crystallography: how the physics of information reveals structural order in materials

“…1(h) represents the random deformation faulting (RDF) process as it models random deformation faults in the 2H crystal structure [55]. The introduction of deformation faults in 2H crystals is often modeled by Glauber dynamics [44,58] that corresponds to changing 1 to 0 or 0 to 1. The ε-machine for the RGF does this randomly, with some small probability α.…”