Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...

The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).Density (ρ) = (Z × M) / (a × b × c × NA)where:Z is the number of formula units per unit cellM is the molar mass of the substancea, b, and c are the edge lengths of the unit cellNA is Avogadro’s numberFor a simple cubic lattice, atoms are located only at...

A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...

Non-stoichiometric defects refer to a type of defect in the crystal structure of a compound where the ratio of its constituent elements deviates from the ideal stoichiometric ratio. There are two main types of non-stoichiometric defects: metal excess defects and metal deficiency defects.Metal excess defects occur when there is a slight surplus of metal ions than what is required by the stoichiometric ratio of the compound. For example, heating a sodium chloride crystal in sodium vapor results...