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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.

Fourth-rank tensors [[V 2 ] 2 ] (Voigt's) type, that embody the elastic properties of crystalline anisotropic substances, were constructed for all 2D crystal systems. Using them we obtained explicit expressions for inverse of Young's modulus E(n), inverse of shear modulus G(m, n) and Poisson's ratio ν(m, n), which depend on components of the elastic compliances tensor S, on direction cosines of vectors n of uniaxial load and the vector m of lateral strain with crystalline symmetry axes. All 2D crystal systems are considered. Such representation yields decomposition

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The electron energy relaxation rate due to an interaction with acoustic phonons has been calculated. Three-dimensional and two-dimensional Fermi electron gases in cubic semiconductors are considered. The anisotropy of the phonon spectrum and relevant phonon polarization states are taken into account. The warping of the phonon spectrum is shown to be of importance at low temperatures.