Reverse Monte Carlo Modeling of the Rigidity Percolation Threshold in Ge<SUB>x</SUB>Se<SUB>1-x</SUB> Glassy Networks

Abstract

Based on Maxwell’s constraint counting theory, rigidity percolation in Ge x Se 1-x glasses occurs when the mean coordination number reaches the value of 2.4. This corresponds to Ge 0.20 Se 0.80 glass. At this composition, the number of constraints experienced by an atom equals the number of degrees of freedom in three dimensions. Hence, at this composition, the network changes from a floppy phase to a rigid phase, and rigidity starts to percolate. In this work, we use reverse Monte Carlo (RMC) modeling to model the structure of Ge 0.20 Se 0.80 glass by simulating its experimental total atomic pair distribution function (PDF) obtained via high energy synchrotron radiation. A three-dimensional configuration of 2836 atoms was obtained, from which we extracted the partial atomic pair distribution functions associated with Ge-Ge, Ge-Se and Se-Se real space correlations that are hard to extract experimentally from total scattering methods. Bond angle distributions, coordination numbers, mean coordination numbers and the number of floppy modes were also extracted and discussed. More structural insights about network topology at this composition were illustrated. The results indicate that in Ge 0.20 Se 0.80 glass, Ge atoms break up and cross-link the Se chain structure, and form structural units that are four-fold coordinated (the GeSe 4 tetrahedra). These tetrahedra form the basic building block and are connected via shared Se atoms or short Se chains. The extent of the intermediate ranged oscillations in real space (as extracted from the width of the first sharp diffraction peak) was found to be around 19.6 ? . The bonding schemes in this glass are consistent with the so-called “8-N” rule and can be interpreted in terms of a chemically ordered network model.