A nanomaterial equation of state has been combined with Grüneisen approximation in present work to investigate the influence of high pressure on phonon density of state function of C60 through evaluating variations of lattice vibration frequencies and variation of mode density. Furthermore, the effect of high pressure on Debye temperature has been determined by using a formula of volume dependence of Debye temperature. Volume compression ratio in C60 has been computed, using a nanomaterial equation of state. Expressions of pressure dependence of phonon density of state and Debye temperature have been combined with volume compression ratio value. The evaluated result of volume compression ratio and phonon density of state have been compared with the experimental observations and good agreement can be seen.
The present study is a theoretical calculation for the effects of high pressure on thermodynamic properties on GaN up to 40Gpa at room temperature. Volume compression ratio (V0/Vp), lattice constant (a) and elastic bulk modulus(B) have been established. Furthermore, lattice frequencies and disruptions function by analyzing phonon frequency spectrum (PFS) at (0 K). The entire calculations rely on using of two equation of state (EOS) "Birch-Murnaghan and modified Lennard-Jones" equation of state and with the integration of Grüneisen approximation theory. From the considered equations of state, formulation of bulk modulus was derived, that predicts a rising trend of bulk modulus. The large bulk modulus value of GaN has made a small fraction of change in volume (less than 15%) of the material even under an extreme pressure up to 45Gpa. It was also found that the results of phonon frequency spectrum obtained from Birch-Murnaghan equation of state in a better agreement with the experimental data than that of modified Lennard-Jones equation of state. Given that the Birch-Murnaghan equation of state developed according to Eulerian strain theory accounted as a universal equation of state. Moreover, good agreement between theoretically present calculations and experiment data of phonon frequency spectrum, reveals the validity of the equations of state used in the present study.
Surface effect and crystal structure lead to formulating a theoretical model to study the influences of size on thermodynamic parameters, such as melting temperature, Debye temperature, melting entropy and specific heat capacity, of nanoparticles. The cohesive energy as a thermodynamic quantity was used to relate the ratio of surface area to volume of nanomaterial with thermodynamic properties which depend on size of the nanomaterial. In this contribution, Si and Au nanoparticles were considered to study due to their potential applications in science and technology. It was found that melting temperature, Debye temperature, melting entropy of nanoscale size material is decreased with decreasing the size up to their critical sizes. Whereas, the specific heat capacity tends to enhance with reduction in nanoparticle size. The present results for melting temperature, melting entropy and Debye temperature are compared with experimental and theoretical observations and adequate agreements are observed.
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