On the ratio between longitudinal and transverse Ioffe-Regel frequencies in glasses

Abstract

The temperature dependence of thermal conductivity in glasses differs characteristically from that in crystals, and is largely controlled by how sound waves are damped. The Ioffe-Regel (IR) frequency sets the high-frequency limit of well-defined sound waves. Although the transverse IR frequency has been established to coincide with the boson peak frequency and reported to be far below the longitudinal IR frequency, the quantitative relation between longitudinal and transverse IR frequencies has remained unknown. Here we examine this relation in two- (2D) and three-dimensional (3D) model glasses with vastly different stability. We observe that, in 3D glasses, the longitudinal-to-transverse IR frequency ratio is approximately equal to the ratio of the low-frequency transverse to longitudinal sound attenuation coefficient, whereas this correspondence is not observed in 2D glasses. Moreover, we find that the glass stability strongly controls the longitudinal-to-transverse IR frequency ratio in both 2D and 3D glasses: the ratio decreases significantly with increasing glass stability and approaches unity for the most stable glasses under study. Accordingly, in sufficiently stable glasses, the longitudinal sound attenuation should be comparable to the transverse attenuation, and therefore cannot be treated as negligible, challenging common assumptions adopted especially in theoretical studies. Our work is another demonstration of the glass stability as a key parameter for investigating glass properties, and cautions against simply extrapolating observations from poorly annealed glasses to stable glasses.