Temperature Variation of Anharmonic Properties of CdO, CoO and FeO Crystals

A theory for evaluating the temperature variation of second, third and fourth order elastic constants for face centred cubic crystal structure solids is developed on the basis of Coulomb and Born-Mayer potentials using nearest-neighbour distance and hardness parameter. The theory thus obtained is first applied to get the higher order elastic constants for CdO, CoO and FeO at different temperatures (50-500K). Also the computed elastic constants are used to evaluate the first order pressure derivatives of second and third order elastic constants and second order pressure derivatives of second order elastic constants. The graphical representations of results obtained have also been given to understand the effect of temperature on higher order elastic constants and their pressure derivatives. These parameters may be correlated with the optical and thermoelastic parameters in the broad temperature range. These results, together with other well-known physical properties of the materials, may be expanded as further prospects for the application of isostructural oxides. I. INTRODUCTION The elastic energy density for a deformed crystal can be expanded as a power series of strains using Taylor's series expansion. The second, third and fourth order elastic constants (SOECs, TOECs and FOECs) are the coefficients of quadratic, cubic and quartic terms respectively. In present investigation, some of the di-valent crystals, having face centered cubic crystal structure, are taken into account. Cadmium oxide, Cobalt oxide and Ferrous oxide are divalent in nature. Rocks are complicated heterogeneous materials with microstructures that scatter acoustic or seismic waves. At the ultrasonic scale, these microstructures are primarily cracks and grain boundaries. The scattering of waves from these boundaries is generally considered noise in geophysical applications, but these scattered wave fields may give insight into how the rock formed, the environment in which it formed, its state of stress, fluid saturation, etc. The anharmonic properties plays an important role in these type of studies. Several physical properties and crystal anharmonicities such as thermal expansion, specific heat at higher temperature, temperature variation of ultrasonic velocity and attenuation, Gruneisen numbers and temperature derivatives of second order elastic constants are directly related to second and third order elastic constants. An investigation of the higher- order elastic constants and their pressure derivatives provides useful information on the inter-atomic forces, inter-ionic potentials and anharmonic properties of crystalline solids. The evaluation of nature, choice of proper material for different researches and industrial applications, quality control and assurance can also well understood with the knowledge of anharmonic properties under different pressure and temperature conditions. Experimental as well as theoretical work on different aspects of anharmonic properties for several compounds has been reported in the recent years (1-3). Though compendiums of elastic constant data for several compounds exist, they are restricted to the room temperature. Current problems in material science often require values of elastic constants at elevated temperatures. In the last few years studies of anharmonic properties of monovalent compounds have attracted the attention of the physicists since they provide much valuable information regarding crystal dynamics (4, 5). Elastic properties of divalent compounds are also equally important because they relate to the various fundamental solid state phenomena such as inter- atomic potentials, equation of state and phonon spectra. If the values of second order elastic constants and density at a particular temperature are known for any substance, one may obtain ultrasonic velocities for longitudinal and shear waves (6, 7), which give an important information about its anharmonic properties. Elastic properties are linked thermodynamically with specific heat, thermal expansion, Debye temperature and Gruneisen parameters (8). A number of theoretical and experimental measurements have been made on the anharmonic properties, such as second, third and fourth order elastic constants, first order pressure derivatives (FOPDs) of SOECs and TOECs, second order pressure derivatives (SOPDs) of SOECs etc. of several ionic crystals (9, 10). The physical properties of materials are dependent on both temperature and pressure.The pressure derivatives of SOECs and TOECs are useful in understanding the effect of hydrostatic pressure on a cubic crystal. The elastic energy density for a deformed crystal can be expanded as a power series of strains using Taylor's series expansion. The coefficients of quadratic, cubic and quartic terms are known as SOECs, TOECs and FOECs respectively. Several physical properties and crystal anharmonicities such as thermal expansion, specific heat at higher temperature, temperature variation of acoustic velocity and attenuation, the FOPDs of SOECs and Gruneisen numbers are directly related to SOECs and TOECs.