Abstract
In the present study, four equations of state (EOSs) were used, namely Birch-Murnaghan, Dodson, Bardeen and modified Lenard Jones for evaluating relative compression volume Vp/Vo, isothermal bulk modulus B and spinodal pressure Psp for C60 under high pressure. Required constant parameters in the EOSs were taken from literature data. Starting from the definition of spinodal pressure, as the pressure at which bulk modulus of a material vanishes (i.e. B=0), A new approach for the evaluation of spinodal pressure have been established, in present work, by extrapolating variation of bulk modulus under high pressure data to the point where B=0, and formulate a new mathematical expression for spinodal pressure. With the aim of finding validity of these equations of state of applying on C60, the calculated results from the entire equations of state are compared with themselves and with other available experimental and theoretical published data. The results for Vp/Vo, B, and Psp are found to be in agreement with each other for whole pressure ranges. Some other theoretical and empirical data are brought in this study and give good agreements with our results. The new spinodal pressure approach and high pressure studies might represent a promising entrance to the formalism of universal equation of state for solids.
Highlights
Carbon C60 is a new crystalline form of solid Carbon; it is coincidently discovered in 1985
BB-M : Bulk modulus according to B-M EOS By the same method, expressions for the bulk modulus under high pressure according to Dodson, Bardeen and modified Lenard-Jones (mL-J) EOSs can be obtained and expressed in respectively
On substituting B0 and B0' values, for C60 from Table 1, into Dodson EOS, given in eq.2, Bardeen EOS, given in eq.3, and in mL-J EOS given in eq.4 respectively, variations of Vp/V0 with high pressure PDo, PBard and PmL-J for C60, have been evaluated
Summary
Carbon C60 is a new crystalline form of solid Carbon; it is coincidently discovered in 1985. (Goyal and Gupta [11]), have performed a comparative study of compression volume for C60 under high pressure using different equations of state such as Tait’s EOS, Murnaghan EOS, Vinet EOS, Suzuki EOS and (Sharma and Kumar) EOS to make comparison with the other experimental data obtained by (Duclos et al [10]). Where P : pressure according to Birch Murnaghan B-M calculated values using different equations of state in this work are found to be in good agreement with (Duclos et al [10]) measurements. This shows that B-M, Dodson, Bardeen and mL-J EOSs are conformed as standard.
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