Raman thresholds and rigid to floppy transitions in calcium silicate glasses

TL;DR

This study investigates how calcium silicate glasses transition from rigid to floppy states, using Raman spectroscopy and advanced constraint counting methods to understand the structural conditions for an elastic intermediate phase.

Contribution

It introduces a size increasing cluster approximation for constraint counting, enabling a deeper analysis of the rigidity transition in calcium silicate glasses beyond mean-field models.

Findings

Identification of a Raman threshold linked to rigidity onset

Application of advanced constraint counting methods

Discussion of conditions for elastic intermediate phase

Abstract

Alkaline earth silicate glasses $xCaO-(1-x)SiO_2$ exhibit a well marked threshold in Raman lineshapes which can be related to the onset of network rigidity as the concentration of calcium oxide $x$ is decreased. The present results are analyzed by constraint counting algorithms and more deeply characterized by a size increasing cluster approximation that allows to perform Maxwell mechanical constraint counting beyond the usual mean-field treatment. This permits to discuss under which structural conditions an elastic intermediate phase can be obtained.