# Equation of state and thermal expansion of metals with FCC structure: Application to Cu, Al and Ni

## In present paper "Equation of state and thermal expansion of metals with FCC structure: Application to Cu, Al and Ni", by the statistical moment method (SMM) we obtain the equation of state for metals with cubic structure at temperature 0 K and pressure P and from that obtain the expressions of lattice parameter and thermal expansion coefficient for these metals at temperature T and pressure P. Applying to metals Cu, Al and Ni, we derive the equation of state, simple analytic expressions of lattice parameter and thermal expansion coefficient for each metal and our numerical results are in good agreement with the experimental data in the interval of temperature from 0 K to near the melting temperature. | October 7 2014 9 36 WSPC 147-MPLB S0217984914502091 1 6 Modern Physics Letters B Vol. 28 No. 26 2014 1450209 6 pages c World Scientiﬁc Publishing Company DOI S0217984914502091 Equation of state and thermal expansion of metals with FCC structure Application to Cu Al and Ni Pham Dinh Tam Le Qui Don University of Technology 100 Hoang Quoc Viet Street Cau Giay District Hanoi Vietnam Nguyen Quang Hoc and Bui Duc Tinh Department of Physics Hanoi National University of Education 136 Xuan Thuy Street Cau Giay District Hanoi Vietnam hocnq@ Nguyen Duc Hien Mac Dinh Chi Secondary School Chu Pah District Gia Lai Province Vietnam Received 5 March 2014 Revised 5 August 2014 Accepted 16 September 2014 Published 8 October 2014 The equation of state the expressions of lattice parameter and thermal expansion co- eﬃcient in general form are obtained by the statistical moment method. Applying to Cu Al and Ni metals we determine these properties in simple analytic form for each metal. Numerical results for the thermal expansion coeﬃcient of these metals in diﬀerent temperatures and pressures are in good agreement with experiments. Keywords The statistical moment method modiﬁed Lennard-Jones potential. 1. Introduction The equation of state of metal gives us many information on thermodynamic prop- erties such as the lattice parameter and the thermal expansion coeﬃcient at temper- ature T and pressure P etc. Finding the equation of state for metals is a complex problem. There are some equations of state which approximately describe states of metals and can be applied to study the thermal expansion. Examples of these equations are the Mie Gruneisen equation of state1 approximately in low temperatures and the Corresponding author. 1450209-1 October 7 2014 9 36 WSPC 147-MPLB S0217984914502091 2 6 P. D. Tam et al. Bradbam Furth equation of Many equations of state are calculated directly from approximate methods such as the Debye approximation 3 the Einstein Debye .

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