Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO 2 glass

Abstract

A short survey has been made on the extensive work that is being done on the pressure derivatives of the second order elastic constants (SOEC) to ascertain various properties of substances. Hence an attempt has been made to correlate the pressure derivatives to some properties of the substances. Thus some equations have been derived to correlate the Grüneisen parameter which is evaluated from Schofield's equations and Bhatia-Singh's (BS) parameters. They have been used to compute the longitudinal ( γ g L) and transverse ( γ g T) Grüneisen constants. γ g L calculated by different methods agree well with experiment. γ g T obtained from BS parameters gives rather higher value while Schofield's equations give results in agreement with experiment. The DeLaunay–Nath–Smith (DNS) equation has been used to derive a relation to compute γ g el (elastic). A method has been extended to calculate the third order elastic constants (TOEC) and it is found to give excellent values of TOECs in agreement with experiment. The absorption band position of TeO 2 has been predicted to occur at 276 cm −1. The phonon dispersion curves have been calculated through BS equations for TeO 2. Several other properties of TeO 2 have been computed such as thermal Grüneisen parameter γ g th, its pressure derivatives ( γ g th)′≡(d γ g th/d P), the pressure variation of bulk modulus C 1≡(d K T /d P) T and its pressure derivatives that is (d C 1/d P) T which is in turn related to ( γ g th)′, the heat capacity at constant volume C V, and the second Grüneisen constant Q. In some cases we calculated these quantities by different methods and the agreement between them is good. Besides we evaluated δ T AG the Anderson Grüneisen parameter. Another important aspect of the present investigations is the formulation of the potential function (PF) of TeO 2 from which we calculated SOECs and these are found to be in excellent agreement with experiment. All other properties mentioned already have also been calculated through the use of the newly formulated PF and the calculated values obtained through various other equations are in good agreement with those obtained from PF. According to valence force field (VFF) all atomic forces can be resolved into bond bending β and bond stretching α forces. It is shown that TeO 2 does not satisfy Martins unity rule. Hence it is concluded that there is an effective dynamic charge on Te in TeO 2. Using the experimental elastic constants the bond bending force β and bond stretching force α and also their pressure derivatives have been evaluated. In addition the reststrauhlen optic frequency ω has been calculated. A self consistent check has been made by evaluating C 44 through the calculated values of α and β.