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Rigidity percolation (mean-field) theory is a simple theory that can explain several anomalies in the thermodynamic properties of covalently bonded glasses such as chalcogenides. According to this theory, the atoms in covalent glasses are constrained by either bonds or bond angles. When the constituent atom has coordination number r, the bond constraint and bond angle constraint are r/2 and 2r-3 per atom, respectively. If the averaged sum of these constraints is equal to the degree of freedom of three in three dimensions, i.e., r = 2.4 at x = 0.40 for As_xSe_1-x glasses and x = 0.20 for Ge_xSe_1-x glasses, the glasses show excellent glass forming ability separated between rigid (r > 2.4) and floppy (r < 2.4) glasses. Further, calorimetric and Raman scattering experiments revealed that the transition occurred within a certain composition range of the intermediate phase (IP) of the unstressed rigid phase.

This article presents a series of structural studies using element-selective diffraction techniques with synchrotron X-rays and high-flux neutron sources to investigate the structural changes across the IP transition phase in chalcogenide glasses. Technical improvements were achieved by developing a new detection system with a curved graphite analyzer crystal and a 1-m-long detector arm at the beamline BM02 of the European Synchrotron Radiation Facility (ESRF). Experimental X-ray and neutron diffraction data and anomalous X-ray scattering (AXS) results close to the absorption edges of the constituent elements were analyzed using reverse Monte Carlo modeling to reveal changes in intermediate-range atomic configurations across the IP range from rigid to floppy. The As_xSe_1-xglasses have an IP range of x = 0.29-0.37, where a rapid decrease in the number of wrong As-As bonds is observed. However, other anomalies found in Ge-Se glasses were not clearly observed, such as a rapid decrease in the pre-shoulder positions in the Se-Se partial structure factor, S_SeSe(Q), a rapid decrease in the number of edge-sharing connections, and an exclusion tendency of the connections between the As (Ge) atoms sharing two Se atoms. These differences may be related to the anisotropic pyramidal AsSe₃ units in the As-Se glasses, in contrast to the isotropic tetrahedral GeSe₄ units around the Ge atoms in the Ge-Se glasses. This study was supported by a JSPS Grant-in-Aid for Transformative Research Areas (A) Hyper-Ordered Structures Science.

(Written by S. Hosokawa on behalf of all the authors.)