Application of valence force field theory, tight binding approximation andGirifalco potential in the study of thermodynamic and elastic properties of C-60 in detail

In this paper we calculated the second order elastic constants (SOECs) of C -60 using tight binding approximation (TBA) and valence force field theory (VFFT). To the SOECs obtained from Girifalco potential we added the contrib ution of Coloumb forces obtained through Mar-tins prescription and the corr ected values so obtained compare favorably with those of TBA and VFFT and a lso with literature values. We also derived the pressure derivatives of SOE Cs obtained through TBA and VFFT. In addition we calculated bond stretching force constant oc and bond bending force constants beta and also their pre ssure derivatives. The ratio proportional to /beta compares favorably with several compounds for which these calculations have been made. The longitudinal omega (L) and transverse omega (T) frequencies have been c alculated by two different methods. The calculated band positions are in sa tisfactory agreement with each other. Even though C-60 is not isotropic, sa mple calculations of gamma (L)(g) and gamma (T)(g) have been made so as to have an insight into these quantities. A second method due to Bhatia and Si ngh has also been applied to calculate these quantities. But this method gi ves a high gamma (T)(g) value while it gives a good gamma (L)(g) value. Rea sons for this high value of gamma (T)(g) have been discussed. The longitudi nal COL and transverse CUT frequencies Of C60 have been calculated through the use of calculated elastic constants. We also used the Nath-Smith-De Lau ney equation to calculate the band position. The calculated and observed ba nd absorption position agree well. The calculated wT value has been used to compute Kr the bulk modulus with a modified Szigete's equation taking into consideration the existence of a small amount of Coloumb forces and the ca lculated value is found to be in good agreement with Duclose value. The eff ective charge on C-60() has been obtained through Martin's equation and the elastic constant C-44 has been evaluated through Martin's prescription. Th e effective charge found to be 0.21 e is in satisfactory agreement with tha t of Lu et al. [24] who found the effective charge to be 0.27 e. The pressu re derivative of gamma (th)(g), the thermal Gruneisen constant has been eva luated and also through the second derivative of eta and delta, the Bhatia Singh's parameters and the value is found to be -0.01 Kbar(-1) and this val ue of gamma (g)' has been used to evaluate the second Gruneisen constant Q and the Anderson Gruneisen constant delta (AG)(T). A new equation has been derived through the use of the derivative of SOECs C-11 and eta ' to evalua te gamma (th)(g) which is found to be in good agreement with the measured v alue. The pressure derivative of bulk modulus (K-r) has been calculated. Th e estimated heat capacity is in fair agreement with experiment and the calc ulated value of K-T using the computed value Of WT is found to be in reason able agreement with that modified by Szigeti equation. (C) 2001 Elsevier Sc ience Ltd. All rights reserved.