Reverse Monte Carlo Modeling of Local Structure using Short-Range and Medium-Range Order Parameters

Hiroshi ABE

Department of Materials Science and Engineering, National Defense Academy,
1-10-20 Hashirimizu, Yokosuka, Kanagawa 239-8686

Journal of the Physical Society of Japan 76 (2007) 094601.

Abstract

An expansion of a pair-correlation function is introduced to express medium-range order (MRO). The approximated correlation function is extended from conventional short-range order (SRO) parameters. SRO parameters are obtained by the conditional average of a pair-correlation function. It is demonstrated that the model can reconstruct SRO and MRO of atomic arrangements from an initial random state by Monte Carlo (MC) method. MRO parameters control cluster formations such as heterogeneous microstructures. On an approach of atomic pair- and triplet-interactions, approximated many-body interactions are estimated in the simulations. Moreover, the MC simulations are applied to ordering process on cooling in AgxTiS2 regarded as a typical two-dimensional material. Furthermore, cluster developments are visualized by the reverse Monte Carlo method.

Fig. 1 The combination of two sets of a pair-correlation function is illustrated by R0l and Rlm. This is extended from short-range order parameters.


Fig. 2 Monte Carlo simulations are performed by referring to (a) antiferro-like clusters and (b) ferro-like clusters as a target on the square lattice. (c) An initial atomic arrangement (random) for Monte Carlo simulations.


Fig. 3 On antiferro-like cluster model, (a) a final atomic arrangement only by short-range order (SRO) parameters (h=0). Final arrangements by the mixing effect between SRO and medium-range order (MRO) parameters with (b) h=0.2, (c) h=0.4, (d) h=0.6 and (e) h=0.8. (f) Pure MRO effect is calculated using h=1.0.


Fig. 4 On ferro-like cluster model, (a) a final atomic arrangement only by short-range order (SRO) parameters (h=0). Final arrangements by the mixing effect between SRO and medium-range order (MRO) parameters with (b) h=0.2, (c) h=0.4, (d) h=0.6 and (e) h=0.8. (f) Pure MRO effect is calculated using h=1.0.

Fig. 5 On ferro-like cluster model, final cluster distributions using (a) M=1, (b) M=2 and (c) M=3 at h=0.5. M is the degree of the second shell as MRO parameters (see text).

Fig. 6 Interaction energies are monitored during Metropolis Monte Carlo simulations using short-range order and medium-range order parameters.

Fig. 7 Arrangements of Ag atoms and vacancies are simulated on  two-dimensional hexagonal lattice by the reverse Monte Carlo method (RMC). (a) A random initial state. RMC simulation results are seen using the observed SRO diffuse intensities at (b) 350K, (c) 300K and (d) 280 K. Large closed and small open circles correspond to the Ag atoms and vacancies, respectively. Triangles stand for  R30o structure as antiferro-like order. With decreasing temperature, triangle clusters develop gradually.

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ab@nda.ac.jp
Department of Materials Science and Engineering
National Defense Academy

Last Modified: April 1, 2009