Ultrasonic investigation of amorphous As 2 S 3 from 1.5 to 480 K

The attenuation of longitudinal and shear ultrasonic waves with frequencies between 10 and 450 MHz has been measured in amorphous ${\mathrm{As}}_{2}$${\mathrm{S}}_{3}$ at various temperatures between 1.5 and 480 K. It is found that the attenuation is proportional to frequency except below about 30 K where it becomes less frequency dependent the lower the temperature. Below 50 K the attenuation is accounted for quantitatively using recent theory for the attenuation due to stress-relaxation processes each of which involves the thermal phonon-assisted tunneling of a sulfur ion between adjacent positions representable by a double potential-energy well. Tunneling times with a wide range of values occur indicating that there are double wells with various barrier heights and amounts of asymmetry. The probability for the occurrence of double wells is found to be proportional to the product of two Gaussian distributions depending, respectively, on the size of the barrier and the energy difference between the wells of a given pair. The number of double wells per unit volume deduced from fitting our ultrasonic data is consistent with the density of wells deducible from low-temperature specific-heat data of Stephens. Direct evidence that electronic tunneling is not responsible for the low-temperature attenuation has been obtained from measurements which revealed that the attenuation at 4.2 K increased only very slightly with magnetic field up to the highest value used, 133 kOe. Between 50 and 140 K the attenuation is almost independent of temperature and may be due to the combined effects of ions tunneling through and hopping over the potential barriers between the two wells of each of the many double wells in the material although no quantitative justification of this is presented. Above 140 K the attenuation is found to increase with temperature at an ever increasing rate and it is found that 30-MHz longitudinal-wave data can be fitted fairly well all the way up to 480 K by a three-term expression with two of the terms being exponential functions of the negative of the reciprocal temperature. Various possible interpretations of these results are presented but a unique and definitive explanation is not arrived at. However, it does seem that the attenuation involves more than one type of relaxation process and that each process is characterized by a wide range of relaxation times. Jumping of groups of ions over potential barriers may be involved. The velocites of 10-, 30-, and 50-MHz longitudinal waves and of 10- and 30-MHz shear waves have also been measured for $a\ensuremath{-}{\mathrm{As}}_{2}{\mathrm{S}}_{3}$ samples between 100 and 290 K. It is found that the velocities of both types of waves increase as the temperature decreases in a manner attributable to the anharmonicity of interatomic forces. The velocities increase slightly with frequency thereby providing additional evidence that the attenuation in $a\ensuremath{-}{\mathrm{As}}_{2}{\mathrm{S}}_{3}$ is not due to the Akhieser phonon viscosity mechanism which usually predominates in crystalline dielectric solids at the temperatures in question.