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Pressure-dependent equation of state for nanomaterials
Monika Goyal and B. R. K. Gupta
In the present paper, it is shown that the equation of state (EOS) [10,11] described earlier on the basis of the Gruneisen theory of thermal expansivity is mathematically and thermodynamically inconsistent. This inconsistency is corrected by Kholiya  using the expansion of PV2 in powers of ( 1 – V/V0) up to the quadratic term. However, in the present study this inconsistency is overcome by assuming the pressure variation with respect to change in volume (∆V/V) and thermodynamically consistent EOS is obtained. The formulated EOS has been used for the study of compression behavior of nanomaterials such as SnO<sub>2</sub> (14 nm); α-Fe<sub>2</sub>O<sub>3</sub>; CuO (24 nm); Ge (49 nm); Ni (20 nm); Ni- filled and Fe- filled MWCNT under pressure. The results achieved using newly formulated are found to be in better agreement with the experimental data as compared to those calculated from previous EOS. The formulated EOS is further tested to verify its validity in extreme compression region and high pressure range using the Stacey Criteria [22,23]. It is found that newly formulated EOS also satisfies the Stacey’s criteria.
Keywords: Equation of state, Volume compression, bulk modulus, high pressure, Nanomaterials, Stacey Criteria