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

Abstract

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 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 ω L and transverse ω T frequencies have been calculated by two different methods. The calculated band positions are in satisfactory agreement with each other. Even though C 60 is not isotropic, sample calculations of γ g L and γ g T 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 γ g T value while it gives a good γ g L value. Reasons for this high value of γ g T have been discussed. The longitudinal ω L and transverse ω T frequencies of C 60 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 ω T value has been used to compute K T the bulk modulus with a modified Szigete's 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 C 60 has been obtained through Martin's equation and the elastic constant C 44 has been evaluated through Martin's 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 γ g th, the thermal Grüneisen constant has been evaluated and also through the second derivative of η and δ, the Bhatia Singh's 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 δ T AG. A new equation has been derived through the use of the derivative of SOECs C 11 ′ and η′ to evaluate γ g th which is found to be in good agreement with the measured value. The pressure derivative of bulk modulus ( K T) has been calculated. The estimated heat capacity is in fair agreement with experiment and the calculated value of K T using the computed value of ω T is found to be in reasonable agreement with that modified by Szigeti equation.