The thermodynamics of three-dimensional, single-component elastic crystalline solids was developed by Slattery and Lagoudas (2005). Considering the in¯nitesimal deformations, the stress can be expressed as a function of the lattice vectors and density in the reference configuration and ¹(I;mn), which is defined as the derivative of specific Helmoholtz free energy with respect to the I(mn). Using the Cauchy - Born rule to connect the interatomic potential energy and the specific Helmholtz free energy, it is possible to calculate the elastic properties of both nano-scale materials such as carbon nanotubes and macro-scale materials such as diamond and silicon. In this study, we used Terso® (1988a) - Brenner (1990b) Potential, Terso® (1988b) potential and Finnis and Sinclair (1984) potential for carbon, silicon, and vanadium systems respectively. Using the interatomic potentials to describe the specific Helmholtz free energy, the elastic properties of graphite, diamond, silicon and vanadium were calculated. This method was also extended to the calculation of Young's modulus of single-walled carbon nanotubes (SWCNTs), which are composed of a two dimensional array of carbon atoms. For SWCNT, we get good agreement with the available experimental data. For diamond and silicon, C11 and C12 were consistent with both the superelastic model and the experimental data. The difference of C44 between the calculation and experimental data was due to accuracy of the potential functions.

Мы исследуем термодинамические свойства магнитных жидкостей с небольшими и умеренными значениями параметра диполь-дипольного взаимодействия в отсутствии внешнего магнитного поля. Магнитные жидкости моделируются монодисперсной системой дипольных твердых сфер. Построена теория, основанная на обратном кумулянтном преобразовании вириального разложения свободной энергии Гельмгольца в ряд по плотности. Методом компьютерного моделирования Mayer Sampling получены данные для пятого вириального коэффициента. По данным компьютерного моделирования получены аналитические выражения для четвертого и пятого вириальных коэффициентов. В работе были определены аналитические выражения для свободной энергии, давления, химического потенциала и коэффициента градиентной броуновской диффузии. Построенная теория хорошо согласуется с данными компьютерного моделирования в широкой области концентраций феррочастиц (φ≤4) и интенсивности межчастичного диполь-дипольного взаимодействия (λ≤4). / We investigate thermodynamic properties of ferrofluids with low and intermediate dipolar coupling constant. The model of dipolar hard spheres is observed. In this work a new theory is constructed based on the transformation of the virial expansion for the Helmholtz free energy into a logarithmic form. Analytical expressions of the forth and the fifth virial coefficients are obtained on the basis of numerical results of Mayer-sampling calculation. In this work analytical expressions for free energy, chemical potential, pressure and gradient diffusion coefficient were obtained. The comparison between theory and computer simulation shows good agreement for dipolar coupling constant λ≤4 and for particle volume fraction φ≤4.