Why crystalline solids are anisotropic whereas amorphous solids are isotropic?
Is it because in crystalline solids, X, Y and Z dimensions vary, but so does in amorphous.
Please write as simple as possible.
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To qualify as «crystalline», there must be a minimal unique pattern (unit cell) to construct the solid only by applying regular, periodic translations. You may predict the outcome of the translation both in proximity, as well as in far distance reliably. In an amorphous state, there is no such predictability.
For two, anisotropic means that a vectorial property depends on the orientation within the sample. In the case of an amorphous sample (as contrasting to crystalline) like glass there is no orientational difference. As an example, the speed of light in glass is independent on the direction you look at the sample; thus, glass is an isotropic material.
In a crystal, however, the speed of light depends on the relative orientation of the sample, thus crystals generally are anisotropic. Depending on the symmetry of the underlying Bravais lattice, there may be two, or three special directions of observation along those vectorial properties are equal to each other (e.g., uni- and biaxial crystals in birefringence). Then, these directions of observation are isotropic to each other; allong all other directions of observation, however, the crystal's vectorial properties are anisotropic.