Thermodynamic calculations using reverse Monte Carlo: convergence aspects, sources of error and guidelines for improving accuracy

ABSTRACT

The reverse Monte Carlo (RMC) method has been widely used to gain 3D structural ordering information from experimental scattering data. Recently, we have introduced a novel application of RMC, viz., calculating thermodynamic properties of crystalline materials, construction of phase diagram and rapid estimation of the local structural order [Agrahari and Chatterjee, Physical Review E, 104, 044129 (2021).]. The method has been shown to be accurate and orders-of-magnitude faster than standard Monte Carlo simulations – this makes the approach quite promising. However, the error in RMC has never been systematically quantified. The goal here is to perform a thorough investigation into the types of error in RMC-based thermodynamic calculations, assess the relative magnitude of these errors, and develop strategies to improve the accuracy. Some of the conclusions presented are also relevant to previous experiment-based RMC implementations.

KEYWORDS:

• Thermodynamics
• reverse Monte Carlo
• short range order
• lattice models
• error analysis

Disclosure statement

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

Notes

1 In general, relative entropy is calculated as $\sum pInp/q$ where $p$ is the reference/exact distribution, and $q$ s an approximate one.

Additional information

Funding

AC acknowledges support from Science and Engineering Research Board [Grant Nos. EMR/2017/001520 and MTR/2019/000909] and National Supercomputing Mission [DST/NSM/R&D_HPC_Applications/2021/02].