Reverse Monte Carlo techniques

Proffen T, Welbeny TR (1997) Analysis of diffuse scattering via the reverse Monte Carlo technique A systematic investigation. Acta Crystallogr Sect A 53 202-216 Proffen T, Welbeny TR (1998) Analysis of diffuse scattering of single ciystals using Monte Carlo methods. Phase Transit 67 373-397... 

Rosato, V., Lascovich, J.C., Santoni, A., and Colombo, L. (1998). On the use of the reverse Monte Carlo technique to generate amorphous carbon structures. Int. 

Random structure methods have proved useful in solving structures from X-ray powder diffraction patterns. The unit cell can usually be found from these patterns, but the normal single-crystal techniques for solving the structure cannot be used. A variation on this technique, the reverse Monte Carlo method, includes in the cost function the difference between the observed powder diffraction pattern and the powder pattern calculated from the model (McGreevy 1997). It is, however, always necessary to include some chemical information if the correct structure is to be found. Various constraints can be added to the cost function, such as target coordination numbers or the deviation between the bond valence sum and atomic valence (Adams and Swenson 2000b Swenson and Adams 2001). 

This paper does not intend to be a review rather comments and examples are given for some of the recent progress. The related literature is not searched exhaustively and the selection is rather arbitrary. Preliminary results of two new studies by the XD method are presented in order to demonstrate the capabilities of the method at new conditions. The reverse Monte Carlo (RMC) technique is also discussed in more detail to show a new perspective in the structural modelling of solutions. 

The main advance in recent years has been the development of methods to obtain models of structures that are consistent with the total diffraction pattern. One method is the Reverse Monte Carlo (RMC) method (McGreevy and Pusztai 1988, McGreevy 1995, Keen 1997, 1998). In this method, the Monte Carlo technique is used to modify a configuration of atoms in order to give the best agreement with the data. This can be carried out using either S Q) or T(r) data, or both simultaneously. We also impose a... 

Maxwell JC (1864) On the calculation of the eqnilibrium and stiffness of frames. Phil Mag 27 294-299 McGreevy RL, Pusztai L (1988) Reverse Monte Carlo simulation A new technique for the determination of disordered structures. Molec Simulations 1 359-367 McGreevy RL (1995) RMC - Progress, problems and prospects. Nuclear Instmments Methods A 354 1-16 Palmer DC, Finger LW (1994) Pressnre-induced phase transition in ciistobalite an x-ray powder diffraction study to 4.4 GPa. Am Mineral 79 1-8... 

In the investigation of Ortiz et al. [104], a stochastic method is presented which can handle complex Hermitian Hamiltonians where time-reversal invariance is broken explicitly. These workers fix the phase of the wave function and show that the equation for the modulus can be solved using quantum Monte Carlo techniques. Then, any choice for its phase affords a variational upper bound for the ground-state energy of the system. These authors apply this fixed phase method to the 2D electron fluid in an applied magnetic field with generalized periodic boundary conditions. 

McGreevy, R.L. and Pusztai, L. (1988). Reverse Monte Carlo simulation a new technique for the determination of disordered structures. Mol. SimuL, 1, 359-67. 

Petersen, T., Yarovsky, 1., Snook, 1., et al. (2004). Microstructure of an industrial char by diffraction techniques and Reverse Monte Carlo modelling. Carbon, 42, 2457-69. 

Several methods have been developed for generating models of the structure of amorphous materials at the atomic level. These include random network models (which may be made by hand or, as discussed later, generated on a computer), energy minimization (or relaxation) methods, Monte Carlo (MC), Molecular Dynamics (MD), Reverse Monte Carlo (RMC), and Quantum Mechanical (QM) methods. The aim of this chapter is to discuss the generation of models for amorphous solids mainly using the most widely used and successful MD and RMC techniques, giving examples from the literature. 

Other new variants of MD that have been developed in recent years. They include a MD version of the Reverse Monte Carlo, RMC, technique. RMC does not have an interaction potential as an input parameter but uses a sequence of biased molecule displacements based on criteria to minimise the difference between an experimental and calculated structure factor for the various species in the system. Toth and Baranyai have developed the MD equivalent of this. A fictitious potential field is introduced which is proportional to the mean square difference between the experimental and computed structure factors. 

McGreevy, R. L. Pusztai, L. (1988) Reverse Monte Carlo Simulation A New Technique for the Determination of Disordered Structures, Molecular Simulation 1, 359-367... 

One way to avoid assuming a potential is the Reverse Monte Carlo numerical method (Nield et al., 1991). This technique employs an algorithm... 

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