Ultrasonic wave propagation in compounds containing ordered vacancies

Abstract

The compounds HgTe, Hg(_5)In(_2)□Te(_8), Hg(_3)In(_2)□Te(_6) and Hg(_5)Ga(_2)□Te(_8), Hg(_3)Ga(_2)□Te(_6) constitute a series in which the concentration of vacancies, sited regularly on the lattice, increases progressively from zero. To assess the effect of such vacancies on the mechanical properties, the propagation of 10MHz ultrasonic waves in single crystal samples of each compound has been studied over the temperature range 77 K to room temperature. The large single crystals required for the ultrasonic experiements have been grown, using a modified Bridgman technique, from stoichiometric melts. Single crystal grains within each boule produced, have been identified by the use of polishing, etching and back reflection x-ray techniques. Back reflection x-ray photographs have been used primarily to establish the Laue group of Hg(_3)In(_2)□Te(_6), Hg(_3)Ga(_2)□Te(_6) and Hg(_5)Ga(_2)□ Te(_8), which are shown to be cubic, and to align the samples in the specific direction required by the theory of ultrasonic wave propagation in solids; the│110│axis in a cubic material. The lattice parameter of each of these compounds has been found using Debye-Scherrer powder photographs each of which exhibits a superlattice imposed on the zincblende pattern of lines, because of this Hg(_5)In(_2)□Te(_8)(Hg(_5)Ga(_2)□Te(_8) was indexed using a 2 x 2 x 2 unit cell and Hg(_3)In(_2)□Te(_6)(Hg(_3)Ga(_2)□Te(_6) using 3 x 3 x 3 unit cell. An order-disorder transformation has been observed in quenched samples of the semiconducting compound Hg(_3)In(_2)□Te(_6); extinction of the superlattice lines indicates that a change from an ordered to a disordered state is complete above 595 ± 5 K. This effect has been further investigated by making resistivity, Hall voltage, thermoelectric power and differential thermal analysis measurements through the temperature region of the transition. In each case the order-disorder transformation had a marked effect on the results, especially in the transition region. The elastic constants of each compound have been determined from measurements of the ultrasonic velocity made by the pulse echo technique. These constants show a regular trend through each series, namely that the stiffness decreases as the vacancy concentration increases. In particular, there is a linear relationship between the reduced compressibility and the vacancy concentration. The elastic constants are also used to determine the anisotropy ratio, the Cauchy relationship and those parameters which can be related to interatomic binding such as the force constants of Bern's model, ionicity (Potters relationship) and Debye temperature. Finally, the elastic constant data in conjunction with the mathematical theory for wave propagation in cubic crystals enabled the phase velocity surfaces, and the particle displacement and energy flux vectors to be determined. Attenuation measurements - made over the same temperature range as the elastic constant data - exhibit Bordoni-type relaxation peaks on a background which is probably dominated by a resonance type loss mechanism associated with pinned dislocations. The peaks which occur in the compounds HgTe, Hg(_5)In(_2)□Te(_8) and Hg(_3)In(_2)□Te(_6) are consistent with dislocation motion on the (111) and (110) slip planes. In this series of compounds the activation energies for kink formation and the Peierls stresses, calculated on the basis of the kink nucleation theory, show that dislocation motion becomes easier with increased vacancy concentration and takes place more readily on the (111) slip planes.