Three independent single-crystal elastic constants of (a) and (b) plotted as a function of temperature.
Bulk, shear, and Young moduli of (a) and (b) plotted as a function of temperature.
(a) Anisotropic parameter and (b) Poisson ratio of and plotted as a function of temperature.
Thermal expansion of and plotted as the relative elongation with respect to the original specimen length at 300 K.
Stress-strain curves for single crystals of and .
(a) Schematic illustration of thermal stresses developed in the thermoelectric material in operation. Stresses that are caused by thermal expansion mismatch between the thermoelectric material (with the length and width ) and metal electrode, and stresses that are internally developed due to the temperature gradient between the heat source and sink. (b) Schematic illustration of the generation of internal shear stresses generated in the direction perpendicular to the thermal gradient due to the different thermal expansion at heat source and sink positions.
Internal shear stress developed in , , and calculated as a function of temperature gradient for various specimen widths .
Dimensions of specimens used for the measurements of elastic constants and coefficients of thermal expansion.
Values of single-crystal elastic constants extrapolated to 0 K and numerical constants obtained with Eq. (1).
Values of polycrystalline elastic moduli extrapolated to 0 K and numerical constants obtained with an equation similar to Eq. (1), and values of polycrystalline elastic moduli of pure germanium measured at 1.7 K.
Bulk modulus at 0 K, volume density of atoms, and melting temperature of and described by normalizing to the corresponding values for pure germanium. Numbers in parenthesis indicate the absolute values.
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