Determination of the single crystal Ge Young’s modulus between room temperature and melting temperature using the impulse excitation technique

Abstract

In the present study, the vibrational properties of single crystal Ge samples are studied between room and melt‐ing temperature using the impulse excitation technique (IET). From the IET measurements, the temperature dependent Young's moduli Eijk of single crystal Ge are extracted in the (100), (110) and (111) crystallographic directions in inert atmosphere. The results show an anomalous softening of an elastic constant around 890 °C temperature during the measure‐ment. The Young's moduli values between 88 to 132 GPa are obtained close to the melting temperature, depending on the crystallographic direction. Empiric expressions are derived for the temperature dependence of E(100), E(110) and E(111). (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Characterization of the thermo-mechanical properties of p-type (MnSi1.77) and n-type (Mg2Si0.6Sn0.4) thermoelectric materials

“…where F (N) is the applied force and c (mm) is the average length of the cracks created at the corners of the indentation and measured from its center. E measurements were conducted by impulse excitation technique (IET) [32][33][34]. The measurement is based on the theory of the propagation of mechanical waves in solids.…”

“…to 263 GPa at 500°C and from 90 GPa at 25°C to 82 GPa at 500°C for Mg 2 Si 0.6 Sn 0.4 . Several studies have revealed the temperature dependence of Young's modulus via IET [33,34]. Depending on the authors, Arrhenius or polynomial law are used to describe their temperature dependence.…”

Temperature Dependent Young's Modulus of Si and Ge

“…This decrease is probably due to free electron effects which occur in semiconductors and metals but not in isolators and which are not taken into account in Wachtman's equation. For practical application, an empirical polynomial fit of the measured E0<ijk> can also be used for the whole temperature range from room temperature to melting temperature (14,20). E<ijk> at 4.2 K should be a good approximation for E0<ijk> and can be calculated for Ge using the data of Bruner and Keyes (21), yielding the values listed in Table I.…”

Temperature Dependent Internal Friction Behavior of Single Crystal Germanium Studied by the Impulse Excitation Technique

“…The impulse excitation technique (IET) is a well-established mechanical spectroscopic technique analyzing the internal friction and Young's modulus (E) of materials as a function of temperature (16)(17)(18)(19)(20). IET is a resonance method and measures the resonant frequency of a specimen by exciting it mechanically with an impulse tool.…”

“…The IET does not require any prestress/strain before or during the measurement, which can lead to change the initial state of crystal lattice e. g. by causing plastic deformation. Recent results on the temperature dependent Young's modulus of single crystal Si and Ge in the <100>-, <110>-and <111>-crystallographic directions determined by IET have been published elsewhere (18)(19)(20).…”