Sound velocities of PbTe to 14 GPa: evidence for coupling between acoustic and optic phonons

Abstract

Sound velocities of PbTe have been determined to 14 GPa using an ultrasonic interferometric method, which allowed for a detailed investigation of the characteristic variations of P and S wave velocities across the phase transitions from Fm3¯m (B1) to the orthorhombic Pbnm to Pm3¯m (B2). Elastic bulk and shear moduli and their pressure derivatives have been determined by fitting the measured velocities using a finite-strain approach. Based on the measured velocities and Debye theory, an estimate is made of the acoustic phonon contribution to the thermal conductivity, considering inter-phonon interactions only. By combining this result with previous determinations of the thermal conductivity due to electrons, the combination was found to have a significantly lower value than the previously determined total thermal conductivity. This is interpreted as evidence for coupling between the low-lying transverse optic (TO) and longitudinal acoustic (LA) modes, allowing the transfer of thermal energy from the acoustic to the optic modes. Possible explanations are discussed in the paper.

Thermostructural and Elastic Properties of PbTe and Pb0.884Cd0.116Te: A Combined Low-Temperature and High-Pressure X-ray Diffraction Study of Cd-Substitution Effects

“…For experimental data, see refs. [29,51,52,[61][62][63], for theoretical data for PbTe, see refs. [8,[45][46][47]53,[64][65][66][67][68][69] and for Pb 1−x Cd x Te, see refs.…”

“…For experimental studies, the ranges refer to the lower and upper limit of the experiment. References for experimental data: (a) [61], (b) [51], (c) [52], (d) [62], (e) [63], (f) [29], and for theoretical data: (g) [53], (h) [45], (i) [64], (j) [47], (k) [46], (l) [8], (m) [65], (n) [66,68], (o) [67], (p) [69]. (*)-this study refers to thin films; "amb" stands for ambient pressure.…”

“…The resulting bulk modulus value for PbTe K 0 is 45.6(2.5) GPa, which is consistent with previously reported values, in particular with those obtained from X-ray diffraction studies, 38.9 GPa [78,80] and 44(1) GPa [82] as well as with those from early ultrasonic wave velocity measurements of refs. [29,52,63,113], quoted in Table 10. second order equation, applied in the present study (an equation of the second order has also been used in a recently reported experimental diffraction study of PbTe [83]).…”

“…The resulting bulk modulus value for PbTe K0 is 45.6(2.5) GPa, which is consistent with previously reported values, in particular with those obtained from X-ray diffraction studies, 38.9 GPa [78,80] and 44(1) GPa [82] as well as with those from early ultrasonic wave velocity measurements of refs. [29,52,63,113], quoted in Table 10. References: (a) [78,80], (b) [83], (c) [52], (d) [113], (e) [63], (f) [29].…”

Phonon mode potential and its contribution to anharmonism

“…The remaining possible sources of the broad and anomalous line shape of the TO mode (not covered in the DFT calculations presented above) include mainly changes in the local potential due to the normal mode interactions 7,22 , possible ferroelectric effects like micro-domains breaking local symmetry of the crystal and coupling to the TO mode 8,16,31,34,41 , multi-phonon interactions 21,32 , electron-phonon interactions 17 or even phonon-strain coupling 15 . Finally we cannot also exclude possible dynamical effects not reproduced by the static (by definition) DFT calculation.…”