Ordering is the regularity in which atoms appear in a predictable lattice, as measured from one point. In a highly ordered, perfectly crystalline material, or single crystal, the location of every atom in the structure can be described exactly measuring out from a single origin. Conversely, in a disordered structure such as a liquid or amorphous solid, the location of the first and perhaps second nearest neighbors can be described from an origin (with some degree of uncertainty) and the ability to predict locations decreases rapidly from there out. The distance at which atom locations can be predicted is referred to as the correlation length \xi. A paracrystalline material exhibits correlation somewhere between the fully amorphous and fully crystalline.
The primary, most accessible source of crystallinity information is X-ray diffraction and cryo-electron microscopy, although other techniques may be needed to observe the complex structure of paracrystalline materials, such as fluctuation electron microscopy in combination with Density of states modeling of electronic and vibrational states.
The paracrystalline model is a revision of the Continuous Random Network model first proposed by W. H. Zachariasen in 1932. The paracrystal model is defined as highly strained, microcrystalline grains surrounded by fully amorphous material. This is a higher energy state than the continuous random network model. The important distinction between this model and the microcrystalline phases is the lack of defined grain boundaries and highly strained lattice parameters, which makes calculations of molecular and lattice dynamics difficult. A general theory of paracrystals has been formulated in a basic textbook, and then further developed/refined by various authors.
The paracrystal model has been useful, for example, in describing the state of partially amorphous semiconductor materials after deposition. It has also been successfully applied to synthetic polymers, liquid crystals, biopoloymers, and biomembranes.
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