Raman thresholds and rigid to floppy transitions in calcium silicate glasses

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.