Reverse Monte Carlo refinement

To calculate the diffuse scattering intensity from a disordered structure, a supercell is first generated corresponding to the average structure. Next, initially random disorder is introduced with magnetic moments or site occupancies and/or atomic displacements. The diffuse scattering intensity is then calculated from the deviations from the average structure.

Illustration of generating a supercell with disorder

The reverse Monte Carlo refinement methodology is bases on the Metropolis algorithm. The chi-square goodness of fit is used as the system energy which is a measure of the closeness of the calculated to the experimentally obtained diffuse scattering intensity

\[\chi^2=\sum_{\pmb{Q}}\bigg[\frac{I_{\text{calc}}(\pmb{Q})-I_{\text{expt}}(\pmb{Q})}{\sigma_{\text{expt}}(\pmb{Q})}\bigg]^2.\]

The acceptance ratio \(\alpha\) follows a Boltzmann distribution

\[\alpha=e^{-\beta\Delta{\chi^2}}\]

which gives the likelihood of a bad move being accepted with energy change \(\Delta{\chi^2}\) with inverse system temperature \(\beta\). The temperature of the system is cooled according to a function analogous to Newton’s law of cooling

\[T=T_0e^{-\lambda t}\]

where \(T_0\) is the temperature prefactor and \(\lambda\) is the decay constant.