Relaxation dynamics in lattice reverse Monte Carlo

ABSTRACT

The reverse Monte Carlo (RMC) method is widely used in structural modelling and analysis of experimental data. More recently, RMC has been applied to the calculation of equilibrium thermodynamic properties and in dynamic problems. These studies require properly converged RMC calculations and an understanding of the relaxation behaviour in RMC. From our detailed lattice RMC calculations, we show that the relaxation comprises both fast and slow aspects. A metric is introduced to assess whether fast equilibration is achieved, i.e. detailed balance condition is satisfied. The metric is used as a test for quasi-equilibration. The slow evolution is analogous to glassy materials, i.e. it is characterised empirically in terms of the Kohlrausch-Williams-Watts (KWW) function, i.e. stretched exponentials. This feature can be exploited to estimate the convergence error or to extrapolate statistical quantities from short RMC calculations.

KEYWORDS:

• Reverse Monte Carlo
• convergence
• detailed balance
• short-ranged order
• stretched exponential

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data will be provided upon request to authors.

Supplementary material

The movie available as a Powerpoint presentation shows relaxation dynamics in reverse Monte Carlo (RMC) calculations. The starting arrangement is completely random. First frame is obtained at 0.5 million iterations. The target structure is reached at 7 s into the movie. Two SRO parameters are used. RMC parameters are: $x=0.2,z_1=0.9$, $z_2=0.85$ and $\theta =1$. Total number of trial moves are 200 million.

Additional information

Funding

This work was supported by National Supercomputing Mission India [grant number DST/NSM/R&D_HPC_Applications/2021/02]; Science and Engineering Research Board [grant number EMR/2017/001520, CRG/2022/008058, MTR/2019/000909].