Measurement of Elastic Constants at Low Temperatures by Means of Ultrasonic Waves–Data for Silicon and Germanium Single Crystals, and for Fused Silica

Abstract

Ultrasonic waves (shear or longitudinal) in the 10–30 mc range are transmitted down a fused silica rod, through a polystyrene or silicone one-quarter wavelength seal, and into the solid specimen. Measurement of reflections within the specimen yields values for velocities of propagation and elastic constants. Data obtained over a temperature range of 78° to 300°K for silicon and germanium single crystals, and 1.6° to 300°K for fused silica are listed. For the latter, a high loss is noted, with an indicated maximum near 30°K.

High temperature indentation behavior of eutectic lead-free solder materials

“…In addition equations of the material properties as functions of temperature (in °C), resulting from linear regression lines, are also presented. The somewhat unusual behavior of fused silica according to which Young's modulus increases with temperature was reported in several references [7][8][9]. These results are compared to 40009-p. 5 our data in Fig.…”

Three terminal capacitance technique for magnetostriction and thermal expansion measurements

“…The Young's modulus of Si substrate was assumed to be temperature independent since elastic constants of Si do not change much with temperature. 23 Observed longitudinal and transversal stresses in Ni/Si(111) cantilever exhibit a positive sign in both cases. That agrees well with the previous room temperature data 24 thus confirming the reliability of our experiment.…”

Temperature dependence of Brillouin light scattering spectra of acoustic phonons in silicon

“…36 The phonon modes we observed agree with the frequencies predicted using an incident wave vector of 1.18 Â 10 7 m À1 and group velocities of 5.834 Â 10 3 m/s and 9.167 Â 10 3 m/s, for the TA and LA phonons, respectively. 37 In our temperature analysis of the BLS spectra, we choose to focus on the LA phonon mode over the TA mode because of its relatively high signal to noise ratio. In the Raman spectra, shown in Fig.…”

“…2, have an apparent upward shift in frequency as temperature increases, opposite to the downward shift predicted by the decreasing phonon group velocity. 37 The phonon frequency shifts are explicitly plotted as a function of temperature by extracting the centers from the Lorentzian fits. The temperature dependent BLS and Raman frequency both fit to linear functions quite well in the temperature range examined, as shown in Fig.…”

“…The measured temperature is affected by a range of phonons, coupled to the probed mode via the anharmonic terms in the interatomic potential, affecting the frequency of the probed phonon mode through the refractive index and the group velocity. 37,49 Similarly, anharmonic phonon interactions and possibly other factors determine the linewidth of the probed phonon mode. Consequently, the frequency and linewidth can be used as empirical temperature sensors, but this measured temperature represents the average temperature of a range of different phonon modes.…”