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H. P. Patel A*, Y. A. Sonvane A, P. B. Thakor A, P. N. Gajjar B and A. R.

Jani C A Deparment of Physics, Veer Narmad South Gujarat University,Surat - 395007, Gujarat India B Deparment of Physics, Gujarat University, Ahmedabad 380 009, Gujarat, India C Deparment of Physics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India 1. Introduction The theoretical basis for an understanding of the thermodynamics of simple liquid metals has been forged in recent years to a point where it can be used to calculate the thermodynamic properties with some success. This advance has been made possible due to the combination of the pseudopotential with thermodynamic perturbation theories. The pseudopotential theory enables one to formulate the energy in terms of the pseudopotential and structure factor. It is possible to write down closed form expressions for the thermodynamic quantities of hard sphere systems, including the structure factor, in the PercusYevick approximation [1]. A link between both theories is provided by a variational technique based on the GibbsBogoliubov (GB) inequality [2]. This GB inequality states that when the Hamiltonian of a given system is regarded as the Hamiltonian of a reference system plus a perturbation, the free energy of the system will always be smaller than that of the reference system plus the expectation values of the perturbation (calculated with the structure factors of the reference system)[3-8]. In our case, the reference system is one of the hard spheres, and the hard sphere diameters will be chosen to minimize the free energy. Present paper deals with the thermophysical properties of liquid lanthanides. The packing fraction is the variation parameter which is determined by minimizing the hard sphere system configurational Helmholtz free energy with our newly constructed model potential [2,9] along with Sarkar et al (S) [10] local field correction function. In the present studies, we have calculated isothermal compressibility (T), long wavelength limit S(0), thermal expansion coefficient (V), thermal pressure co-efficient (V), specific heat at constant volume (CV) and specific heat at constant pressure (CP) [11-12]. We found that our present results are in good agreement with the experimental data [13]. Lastly, we conclude that our model potential is capable to explain the thermophysical properties References [1] J. K. Percus, G. J. Yevick. Phys. Rev., 110, 1 (1958) [2] P. B. Thakor, Y. A. Sonvane and A. R. Jani, AIP. Conf. Proc., (2010) [3] J. K. Baria, A. R. Jani, Digs. J. Nano. and Biosci., 5, 317 (2010) [4] J. K. Baria, Chin. Phys. Lett., 20, 894 (2003) [5]A. M. Vora, Phys. Chem. Liq., 48, 723 (2010) [6] A. M. Vora, Phys. Chem. Liq., 46, 278 (2008) [7] G. M. Bhuiyan and M. A. Khalque, J. NonCryst. Solid, 226, 175 (1998) [8] V. G. Postovalov, E.P. Romanov, V. P. Kondratev, Phys. Met. Metallography, 103, 234 (2007) [9] P. B. Thakor, Y. A. Sonvane and A. R. Jani, Phys. Chem. Liq., 47, 653 (2009) [10] A. Sarkar, D. Sen, S. Haldar and D. Roy, Mod. Phys. Lett., B12, 639 (1998) [11] S. Tamaki and Y. Waseda, J Phys. F: Metal Phys., 6 (1976) [12]Y. Waseda, S. Tamaki and Y.Tsuchiya, Sci. Rep. Ritu, 159 (1976) [13] R. Hultgren, P. D. Desai, D. I. Hawkins, M. Gleiser, K. K. Kelly, D. Wagman, Selected Values of the Thermodynamic properties of the elements, Am. Soc. Met., Metals Park, (1973) *

Thermophysical Properties of Liquid Lanthanides