A solid state material can be in an ordered or disordered state. An ordered structure is the basis for an ideal crystal, while a disordered state can be either in a glassy or amorphous state. An ideal crystalline state consists of an infinite repetition of the same crystal lattice; this structure itself contains a single atom or group of atoms or molecules.
A lattice is a group of space points arranged periodically. These points are a mathematical representation of the crystal structure. When atoms or molecules, defined as the basis of atoms, are coupled to these periodic space points in a one-to-one correspondence, the crystal structure is defined. The lattice is defined by three translation vectors a 1 , a 2 , and a 3 , and three corresponding arbitrary integers u 1 , u 2 , and u 3 , whereas the smallest unit that defines lattice structure is the lattice-unit cell.
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