Study of thermo-elastic properties of nanomaterials under high pressure and high temperature
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Date
2008-05
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G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
T he study based on the EOS at high-pressure and high temperature is of fundamental interest because they permit interpolation and extrapolation in to the regions in which the experimental data are not available adequately. The Present work describes the theoretical study of thermo-elastic properties especially compression, thermal expansion, bulk modulus, thermal expansion coefficient of some of the nanomaterials by making use of Equation of State. For different class of solids a lot of numbers of equation of states are available. Among the number of isothermal and isobaric EOS described earlier, we prefer isothermal Usual Tait’s Equation of State (UTE) and isobaric Singh and Gupta Integral form of Equation of State (IFEOS) because of their simple and straightforward applications in high pressure and high temperature physics. We have reported the results obtained for thermo physical properties of nanomaterials i.e. n-SnO2, n-CeO2, n-PbS, n-MgO, nCuO, n-AlN, n-ZnO, n-NiO, n-TiO2, n-Ni, n-Ti, n-(Ni+Fe), n-Mo, individual single wall carbon nanotube (SWCNT), under effect of high temperatures and high pressures. The variation of compression (V/V0), isothermal bulk modulus (KT) and relative isothermal expansion coefficient ǂ(P)/ǂ0) with pressure have plotted and shown in tables, for nanocrystalline n-SnO2 with three particle sizes 3nm, 8nm and 14nm, n-CeO2, nanocrystalline MgO ( 100nm and 200nm), n-CuO, n-PbS ( 2.6nm, 5.4nm and 8.8nm), n-Ni(20nm and 62nm), n-Mo and n-AlN n-TiO2( 35nm and 6nm) and nZnO using Usual Tait’s equation of state. We have also calculated temperature dependence of thermal expansivity (ǂT), relative volume thermal expansion (V/V0) and bulk modulus (KT) of nanomaterials { n-ZnO, n-TiO2 anatase, n-NiO, n-Ni, n(Ni+Fe), n-Ti, and SWCNT(armchair CNT (5, 5), and zig-zag CNT (9, 0); both in axial as well as radial directions)}using IFEOS at different temperature and atmospheric pressure. The Integral form of Equation of State( IFEOS) is entirely free from the use of potentials and need only three input parameters such as Anderson Gruneisen parameter( 0 TDž ), volume thermal expansion coefficient(ǂ0) at zero pressure, reference temperature, and the thermo-elastic parameter k which can be calculated from the slope of the graph between log(DžT) and log(T/T0). The calculated values are plotted with temperature and compared to available experimental data in order to compare the present results. All the results have been presented graphically. It may be noted here that the calculated values are in close agreement to the experimental data. Thus it is emphasized here that the Integral form of Equation of State (IFEOS) and Usual Taits Equation of State(UTE) successfully explains the thermo-elastic properties nanomaterials.
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