tailieunhanh - Investigation of the specific heat at constant volume of free electrons in metals using q-deformed fermi-dirac statistics

We obtained the analytic expressions of the specific heat at constant volume of metals which are dependent on the value of q-deformed parameters. Results calculated for the specific heat at constant volume for some kinds of alkali and transition metals show good agreement with those obtained by other theories and in experiments as well. | JOURNAL OF SCIENCE OF HNUE Mathematical and Physical Sci. 2013 Vol. 58 No. 7 pp. 117-124 This paper is available online at http INVESTIGATION OF THE SPECIFIC HEAT AT CONSTANT VOLUME OF FREE ELECTRONS IN METALS USING q-DEFORMED FERMI- DIRAC STATISTICS Vu Van Hung1 Duong Dai Phuong2 and Luu Thi Kim Thanh3 1 Viet Nam Education Publishing House Hanoi 2 Tank Armour Officers Training School Tam Duong Vinh Phuc 3 Faculty of Physics Hanoi University of Education No. 2 Xuan Hoa Vinh Phuc Abstract. The contribution of free electrons to the specific heat at constant volume of metals in low temperature was investigated using q-deformed Fermi-Dirac statistics. We obtained the analytic expressions of the specific heat at constant volume of metals which are dependent on the value of q-deformed parameters. Results calculated for the specific heat at constant volume for some kinds of alkali and transition metals show good agreement with those obtained by other theories and in experiments as well. Keywords Specific heat at constant volume q-deformed fermi-dirac statistics alkali metal transition metal. 1. Introduction In metals many electrons can move freely throughout the crystal which oftentimes makes the metal a high electrical conductivity candidate with an electrical conductivity of around 106 to 108 Ω 1 m 1 . For instance if each atom in a material contains only one free electron there would be about 1022 conduction electrons per cm3 . Depending on which distribution function is used to consider the free-electron gas different theories could be established i If free electrons are considered to be a simple classical gas settling on the same energy Drude s theory can be used to analyze issues arising related to the metal ii When using the Maxwell-Boltzmann distribution function for a classical gas the metal can be described in the framework of Lorentz s theory iii In the quantum feature with the Fermi-Dirac distribution function being used Sommerfeld s theory .