Crystalline states short-range order

In contrast to crystalline solids characterized by translational symmetry, the vibrational properties of liquid or amorphous materials are not easily described. There is no firm theoretical interpretation of the heat capacity of liquids and glasses since these non-crystalline states lack a periodic lattice. While this lack of long-range order distinguishes liquids from solids, short-range order, on the other hand, distinguishes a liquid from a gas. Overall, the vibrational density of state of a liquid or a glass is more diffuse, but is still expected to show the main characteristics of the vibrational density of states of a crystalline compound. 

Traditionally, X-ray absorption edge measurements have been used to determine oxidation states of metals in complex materials. The extended X-ray absorption fine structure (EXAFS), on the other hand, provides structural information such as bond distances and coordination numbers even with powdered samples, crystalline or amorphous, the fine structure essentially resulting from short-range order around the absorbing atom. The technique is also useful for studying solid surfaces (SEXAFS). The observation of fine structure beyond the K-absorption edges of materials dates back to... 

Fusion, as an order-disorder transition, is the concept that fusion of a crystalline solid is essentially a change from the almost perfectly ordered solid state to a disordered liquid slate. The vacant spaces in the crystal lattice correspond lo the other component in the binary alloys, which undergo order-disorder transition in the pure form. Evidence from x-ray diffraction measurements indicates that short-range order is retained during fusion but long-range order is lost. 

The transition from the crystalline to the liquid state is accompanied by absorption of heat, a loss of long-range order, and an increase in molecular volume. However, many long chain lipids show only small volume changes (10-20%) during the transition from solid to liquid, which indicates that some short-range order should remain in the liquid state (Small, 1986, pp. 56-57). 

Liquid crystals can be in the smectic, nematic, or isotropic states. In the smectic liquid crystalline state there is a long-range order in the direction of the long axis of the molecules. These molecules may be in single- or bilayer conformation, have molecular axis normal or tilted to the plane of the layer, and frozen or melted chains. In the nematic liquid crystalline state the molecules are aligned side by side but not in specific layers. The isotropic liquid crystalline state is more or less a liquid state, but where clusters with short-range order persist (Small, 1986, pp. 49-51). 

Monocrystalline Quasicrystalline Polycrystalline Semicrystalline Amorphous and glassy state LRO NoncrystaUographic rotational symmetry, no LRO Crystallites separated by grain boundaries Crystalline regions separated by amorphous regions No LRO, no rotational S3fmmetry, does possess short-range order (SRO)... 

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