Explicit expressions for inverse of Young's modulus ( ) E n , inverse of shear modulus ( ) G , n m , and Poisson's ratio ( ) ν , n m for cubic media are considered. All these characteristics of elastic media depend on components 11 S , 12 S and 44 S of the compliance tensor S , and on direction cosines of mutually perpendicular vectors n and m with fourfold symmetry axes. These characteristics are studied for all mechanically stable cubic materials for vectors n belonging to the irreducible body angle subtended by three cubic high symmetry directions
Abstract. The Curie-Weiss model is an exactly soluble model of ferromagnetism that allows one to study in detail the thermodynamic functions, in particular their properties in the neighbourhood of the critical temperature. In this model every magnetic moment interacts with every other magnetic moment. Because of its simplicity and because of the correctness of at least of some of its predictions, the CurieWeiss model occupies an important place in the statistical mechanics literature and its application to information theory. It is frequently presented as an introduction to the Ising model or to spin glass models, and usually only general features of the Curie-Weiss model are presented. We discuss here properties of this model in a rather detailed way. We present the exact, approximate and numerical results for this particular model. The exact expression for the limiting magnetic field is derived.
We report on lattice specific heat of bulk hexagonal GaN measured by the heat flow method in the temperature range 20-300 K and by the adiabatic method in the range 5-70 K. We fit the experimental data using two temperatures model. The best fit with the accuracy of 3 % was obtained for the temperature independent Debye's temperature $\theta_{\rm D}=365$ {\rm K} and Einstein's temperature $\theta_{\rm E}=880$ {\rm K}. We relate these temperatures to the function of density of states. Using our results for heat conduction coefficient, we established in temperature range 10-100 K the explicit dependence of the phonon mean free path on temperature $\it{l}_{\rm ph}\propto T^{-2}$. Above 100 K, there is the evidence of contribution of the Umklapp processes which limit phonon free path at high temepratures. For phonons with energy $k_{\rm B}\times 300 $ {\rm K} the mean free path is of the order 100 {\rm nm}Comment: 5 pages, 4 figure
Blackman's diagram of two dimensionless ratios of elastic constants is frequently used to correlate elastic properties of cubic crystals with interatomic bondings. Every's diagram of a different set of two dimensionless variables was used by us for classification of various properties of such crystals. We compare these two ways of characterization of elastic properties of cubic materials and consider the description of various groups of materials, e.g. simple metals, oxides, and alkali halides. With exception of intermediate valent compounds, the correlation coefficients for Every's diagrams of various groups of materials are greater than for Blackaman's diagrams, revealing the existence of a linear relationship between two dimensionless Every's variables. Alignment of elements and compounds along lines of constant Poisson's ratio ν( 100 , m), (m arbitrary perpendicular to 100 ) is observed. Division of the stability region in Blackman's diagram into region of complete auxetics, auxetics and non-auxetics is introduced. Correlations of a scaling and an acoustic anisotropy parameter are considered.
Anisotropies of Young's modulus E, the shear modulus G, and Poisson's ratio ν of all 2D symmetry systems are studied. The shear modulus and Poisson's ratio of 2D crystals have fourfold symmetry. Simple necessary and sufficient conditions on their elastic compliances are derived to identify if any of these crystals is completely auxetic, non-auxetic or auxetic. Examples of all types of auxetic properties of crystals of oblique and rectangular symmetry are presented. Particular attention is paid to 2D crystals of quadratic symmetry. All mechanically stable quadratic crystals are characterized by three parameters belonging to a prism with the stability triangle in the base. Regions in the stability triangle in which quadratic materials are completely auxetic, non-auxetic, and auxetic are established.
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