Calculation of the bulk modulus of simple and complex crystals with the chemical bond method

The relation between the lattice energies and the bulk moduli on binary inorganic crystals was studied, and the concept of lattice energy density is introduced. We find that the lattice energy densities are in good linear relation with the bulk moduli in the same type of crystals, the slopes of fitting lines for various types of crystals are related to the valence and coordination number of cations of crystals, and the empirical expression of calculated slope is obtained. From crystal structure, the calculated results are in very good agreement with the experimental values. At the same time, by means of the dielectric theory of the chemical bond and the calculating method of the lattice energy of complex crystals, the estimative method of the bulk modulus of complex crystals was established reasonably, and the calculated results are in very good agreement with the experimental values.

Tensile modulus of polymer nanocomposites

Based on Takayanagi's two-phase model, a three-phase model including the matrix, interfacial region, and fillers is proposed to calculate the tensile modulus of polymer nanocomposites (E-c). In this model, fillers (sphere-, cylinder- or plate-shape) are randomly distributed in a matrix. If the particulate size is in the range of nanometers, the interfacial region will play an important role in the modulus of the composites. Important system parameters include the dispersed particle size (t), shape, thickness of the interfacial region (tau), particulate-to-matrix modulus ratio (E-d/E-m), and a parameter (k) describing a linear gradient change in modulus between the matrix and the surface of particle on the modulus of nanocomposites (E-c). The effects of these parameters are discussed using theoretical calculation and nylon 6/montmorillonite nanocomposite experiments. The former three factors exhibit dominant influence on E-c At a fixed volume fraction of the dispersed phase, smaller particles provide an increasing modulus for the resulting composite, as compared to the larger one because the interfacial region greatly affects E-c. Moreover, since the size of fillers is in the scale of micrometers, the influence of interfacial region is neglected and the deduced equation is reduced to Takayanagi's model. The curves predicted by the three-phase model are in good agreement with experimental results. The percolation concept and theory are also applied to analyze and interpret the experimental results.

Bulk modulus of ternary chalcopyrite A(I)B(III)C(2)(VI) and A(II)B(IV)C(2)(V) semiconductors

Based on the complex crystal chemical bond theory, the formula of Liu and Cohen's, which is only suitable for one type of bond, has been extended to calculate the bulk modulus of ternary chalcopyrite A(I)B(III)C(2)(VI) and A(II)B(IV)C(2)(V) which contains two types of bonds. The calculated results are in fair agreement with the previous theoretical values reported and experimental values. (C) 1998 Elsevier Science Ltd. All rights reserved.

Shear modulus of two-dimensional foams: The effect of area dispersity and disorder

Cox, S.J. and Whittick, E.L. (2006) Shear modulus of two-dimensional foams: The effect of area dispersity and disorder. Euro. Phys. J. E 21:49-56 Sponsorship: EPSRC