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Two different approaches to study thermal expansion and compression of nanosystems are unified, which have been treated quite independently by earlier workers. We provide the simple theoretical analysis, which demonstrates that these two approaches may be unified into a single theory, viz. one can be derived from other. It is concluded that there is a single theory in the place of two different approaches. To show the real connection with the nanomaterials, we study the effect of temperature (at constant pressure), the effect of pressure (at constant temperature) as well as the combined effect of pressure and temperature. We have considered different nanomaterials viz. carbon nanotube, AlN , Ni , 80 Ni –20 Fe , Fe – Cu , MgO , CeO 2, CuO and TiO 2. The results obtained are compared with the available experimental data. A good agreement between theory and experiment demonstrates the validity of the present approach.

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In this paper, Gorter-Casimir (GC) two fluid model for low temperature normal superconductors is modified introducing phononic term along with electronic term in the normal phase free energy. The exponent corresponding to the normal phase fraction is changed from 1/2 to a general value n which can be different for different materials. n is a parameter which tunes how much portion of normal phase free energy will be reduced to form superconducting phase by condensation of normal electrons into super-electrons at some finite temperatures below superconducting transition temperature (T C) and the electron-phonon interaction is the controlling factor which calibrate the values of n. This present model describes the idea of different jump ratios of specific heat of different materials at T = T C , which GC model cannot predict. We have adopted a new concept of "Phase diagram" from which an idea of a new temperature T * has been obtained. Modified GC model explains well the resistivity behavior near T C. Moreover, for some high temperature superconductors along with the electronic and phononic contribution, a low temperature Schottky contribution is added to the free energy density. However, the contribution is negligible near T C .

PACS 64.30.-t -Equation of state of specific substances PACS 62.50.-p -High-pressure effects in solids and liquids PACS 65.40.-b -Thermal properties of crystalline solidsAbstract -A simple theoretical model is developed to study the properties of fullerites under varying conditions of pressure and temperature. The model is initially applied to study the compression behavior of C70 and C84 solids in the light of other relations as well as experimental data. The model performed in a better way as compared with the other relations. The results obtained are found to be encouraging. The model is therefore extended for the study of C70 and C84 solids under varying conditions of pressure and temperature. We have computed the pressure and temperature dependence of V /V0, the coefficient of volume thermal expansion and the bulk modulus. The results are compared with the available experimental data. There is a good agreement between theory and experiment, which supports the validity of the model developed for fullerites.