Fig. 10. Effect of disorder and temperature on the linewidths of silica polymorphs.

Increasing temperature yields an increase of the linewidths that account for third-order anharmonicity^88,89 and isotopic-mass disorder⁹² in both vitreous and crystalline materials: the left panel shows the 192(D) and 108(D) vitreous-silica model (both computed from first-principles and at q = 0 only), the central panel shows α-cristobalite, and the right panel shows α-quartz. The temperatures of 50, 300, and 500 K at which the linewidths distributions are reported are chosen to span the temperature range over which all these materials are stable. The 1300 K distribution shows the behavior at high temperature, and is reported only for vitreous silica since α-cristobalite and α-quartz are not stable at this temperature. The insets in the central and right panels show the linewidths at low vibrational energies for α-cristobalite and α-quartz, respectively. The purple area shows the overdamped regime characterized by ℏΓ > ℏω; the lack of linewidths in the purple region shows that there are no overdamped vibrations and thus the Wigner formulation can be employed^41,47. The gray lines represent the average spacing between the vibrational energy levels Eq. (6) (in the left panel only the average energy-level spacing for the 192-atom model is reported).