Third order elastic constants and the acoustic mode vibrational anharmonicity in crystals.

  • Tu Hailing

Student thesis: Doctoral ThesisPhD


A number of different aspects of the vibrational anharmonicity of acoustic modes at the long wavelength limit, which relate to mode softening, thermal expansivity, the Gruneisen parameter and structural phase transition has been investigated. Thus the pressure dependences of the second order elastic constants (SOEC) for chalcopyrite CdGeAs2, the rare earth solid solution Sm0. 58Y0. 42S, vacancy compounds Hg5Ga2Te8, Hg3ln2Te6, HgIn2DTe4 and the third order elastic constants (TOEC) of the zincblende structure crystal CuGe2P3, the semimetal bismuth, rare earth monochalcogenide SmS and the hexahalometallate K2SnCl6 have been determined by employing pulse echo overlap and pulse superposition techniques. In tetrahedrally bonded ternary compounds, the bonding effect and influence of defects - sited vacancies - on the acoustic vibrational anharmonicity have been studied. There is a systematical trend between ionicity, shear mode third order elastic constants and phase transition pressures; the shear mode Gruneisen parameters of the vacancy compounds are found to be linearly dependent upon the concentration of the sited vacancies. These results provide a basis for the discussion of the dynamic mechanism of the densification structural phase transition in these materials. A complete set of the TOEC of bismuth has been obtained and is used to estimate the Gruneisen parameter components along the z-axis and in the x-y plane which show a considerable difference in the axial acoustic vibrational anharmonicity in this crystal which has some layer-like character. The anisotropy of the thermal expansivity is ascribed largely to the highly anisotropic nature of the second order elastic compliances. The importance of measurements of the higher order elastic constants in the vicinity of the structural phase transition is that they contain valuable information on the relation between the anharmonic interatomic forces and lattice instability. SmS undergoes an isostructural phase transition at 6.5 Kbar, then goes into an intermediate valence state. The pressure dependences of the ultrasonic wave velocities have been measured up to 6 Kbar. There is a large positive bulk TOEC combination (C111 +6C112 + 2C123)/9 near the transition which is associated with the reduction of the nearest-neighbour repulsive forces and the incipience of lattice instability. A negative C12 been observed in the Measurements on Sm0. 58Y0. 42S which is already in an intermediate valence state. The resultant negative Poisson's ratio is discussed. A phase transition driven by the softening of a rotary optic phonon mode takes place in K2SnCl6 at -11°C (Tc1). The nonlinear elastic properties have been assessed by the determination of nine sets of the TOEC between room temperature and Tc1. These data provide the first actually measured complete TOEC of a crystal in the vicinity of a structural phase transition. The TOEC combination (C111 -C123)/2 increases and (C111 -3C112 + 2C123)/8 decreases with temperature towards Tc1. Results indicate that the TOEC vary substantially with temperature near the transition point and therefore that there exists a strong influence of the optical rotary mode on the acoustic mode (N[110], U[110]) vibrational anharmonicity. Large negative mode Gruneisen parameters have been found in both SmS and K2SnCl6 in the vicinity of the transition.
Date of Award1983
Original languageEnglish
Awarding Institution
  • University of Bath

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