Application of valence force field theory, tight binding approximation and Girifalco potential in the study of thermodynamic and elastic properties of C60 in detail Original Research Article

In this paper we calculated the second order elastic constants (SOECs) of C60 using tight binding approximation (TBA) and valence force field theory (VFFT). To the SOECs obtained from Girifalco potential we added the contribution of Coloumb forces obtained through Martins prescription and the corrected values so obtained compare favorably with those of TBA and VFFT and also with literature values. We also derived the pressure derivatives of SOECs obtained through TBA and VFFT. In addition we calculated bond stretching force constant ∝ and bond bending force constants β and also their pressure derivatives. The ratio ∝/β compares favorably with several compounds for which these calculations have been made. The longitudinal ωL and transverse ωT frequencies have been calculated by two different methods. The calculated band positions are in satisfactory agreement with each other. Even though C60 is not isotropic, sample calculations of γgL and γgT have been made so as to have an insight into these quantities. A second method due to Bhatia and Singh has also been applied to calculate these quantities. But this method gives a high γgT value while it gives a good γgL value. Reasons for this high value of γgT have been discussed. The longitudinal ωL and transverse ωT frequencies of C60 have been calculated through the use of calculated elastic constants. We also used the Nath–Smith–De Launey equation to calculate the band position. The calculated and observed band absorption position agree well. The calculated ωT value has been used to compute KT the bulk modulus with a modified Szigeteʹs equation taking into consideration the existence of a small amount of Coloumb forces and the calculated value is found to be in good agreement with Duclose value. The effective charge on C60 has been obtained through Martinʹs equation and the elastic constant C44 has been evaluated through Martinʹs prescription. The effective charge found to be 0.21 e is in satisfactory agreement with that of Lu et al. [24] who found the effective charge to be 0.27 e. The pressure derivative of γgth, the thermal Grüneisen constant has been evaluated and also through the second derivative of η and δ, the Bhatia Singhʹs parameters and the value is found to be −0.01 Kbar−1 and this value of γ′g has been used to evaluate the second Grüneisen constant Q and the Anderson Grüneisen constant δTAG. A new equation has been derived through the use of the derivative of SOECs C11′ and η′ to evaluate γgth which is found to be in good agreement with the measured value. The pressure derivative of bulk modulus (KT) has been calculated. The estimated heat capacity is in fair agreement with experiment and the calculated value of KT using the computed value of ωT is found to be in reasonable agreement with that modified by Szigeti equation.