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Tensor descriptions of material properties can be used to determine the directional dependence of that property. For a monocrystalline material, anisotropy is associated with the crystal symmetry in the sense that more symmetric crystal types have fewer independent coefficients in the tensor description of a given property.
learning the systematics of crystal and glass chemistry. understanding how physical and chemical properties are related to crystal structure and microstructure. studying the engineering significance of these ideas and how they relate to foreign products: past, present, and future. Topics studied are: Chemical bonding, Electronegativity
Additionally, all crystal structures, including the cubic crystal system, are anisotropic with respect to certain properties, and isotropic to others (such as density). [ 4 ] The anisotropy of a crystal’s properties depends on the rank of the tensor used to describe the property, as well as the symmetries present within the crystal.
The net force on each ion is generally calculated explicitly at each numerical step. From this, the stress tensor of the system can be calculated and usually is calculated by the numerical package. By varying the convergence criteria, one can either seek a lowest energy structure or a structure that produces a desired stress tensor.
The Tensorial Anisotropy Index A T [5] extends the Zener ratio for fully anisotropic materials and overcomes the limitation of the AU that is designed for materials exhibiting internal symmetries of elastic crystals, which is not always observed in multi-component composites. It takes into consideration all the 21 coefficients of the fully ...
The symmetry properties of crystal are described by the concept of space groups. [1] All possible symmetric arrangements of particles in three-dimensional space may be described by 230 space groups. The crystal structure and symmetry play a critical role in determining many physical properties, such as cleavage , electronic band structure , and ...
The directional dependence of a crystal's physical property is described by a 3D tensor and depends on the orientation of the crystal. Tensor shapes are more palpable by adding lighting effects (reflection and shadow). 2D sections of interest are selected for display by rotating the tensor interactively around one or more axes.
Moreover, various properties of a crystal, including electrical conductivity, electrical permittivity, and Young's modulus, may be different in different directions in a crystal. For example, graphite crystals consist of a stack of sheets, and although each individual sheet is mechanically very strong, the sheets are rather loosely bound to ...