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A crystal dendrite is a crystal that develops with a typical multi-branching form, resembling a fractal. The name comes from the Ancient Greek word δένδρον ( déndron ), which means "tree" [ citation needed ] , since the crystal's structure resembles that of a tree.
Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media (such as crystals) in which light behaves differently depending on which direction the light is propagating. The index of refraction depends on both composition and crystal structure and can be calculated using the Gladstone–Dale ...
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.
A transversely isotropic material is one with physical properties that are symmetric about an axis that is normal to a plane of isotropy. This transverse plane has infinite planes of symmetry and thus, within this plane, the material properties are the same in all directions. Hence, such materials are also known as "polar anisotropic" materials.
In addition, physical properties are often controlled by crystalline defects. The understanding of crystal structures is an important prerequisite for understanding crystallographic defects. Most materials do not occur as a single crystal, but are poly-crystalline in nature (they exist as an aggregate of small crystals with different orientations).
Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution ("spheroid") but is described by three unequal principle refractive indices n α, n β and n γ. Thus there is no axis around which a rotation leaves the optical properties invariant (as there is with uniaxial crystals whose index ellipsoid is a spheroid).
The elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. [ 1 ] [ 2 ] Other names are elastic modulus tensor and stiffness tensor . Common symbols include C {\displaystyle \mathbf {C} } and Y {\displaystyle \mathbf {Y} } .
Crystals of amethyst quartz Microscopically, a single crystal has atoms in a near-perfect periodic arrangement; a polycrystal is composed of many microscopic crystals (called "crystallites" or "grains"); and an amorphous solid (such as glass) has no periodic arrangement even microscopically.