The second- and third-order elastic constants of amorphous arsenic

Abstract

The hydrostatic and uniaxial pressure and the temperature dependences of the ultrasonic wave velocities in bulk amorphous arsenic (a-As) have been measured by the pulse echo overlap and pulse superposition techniques. The results provide the first complete set of components of the second- and third-order elastic stiffness tensors of an amorphous element. The ultrasound velocities, and elastic stiffnesses of the amorphous material are appreciably smaller than those of the crystalline, rhombohedral allotropic form. The bulk, shear and Young's moduli and the pressure derivatives of the bulk and shear moduli of a-As conform well with trends noted previously for these properties in chalcogenide glasses in terms of the average number of covalent bonds per atom. In marked contrast to the anomalous behaviour of the insulating, silica-based glasses, the pressure derivatives of the bulk and shear moduli of a-As are found to be positive, while the temperature derivatives are negative. This more normal elastic behaviour is emphasized by the negative signs of the third-order elastic constants (with the exception of C ₁₄₄) of a-As. To extend the quantitative information on the anharmonicity, provided by the third-order elastic constants, two combinations of fourth-order constants have been calculated from the temperature dependences ∂C ₁₁/∂T and ∂C ₄₄/∂T of the second-order elastic constants.