Paracrystallinity
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In materials science, paracrystalline materials are defined as having short- and medium-range ordering in their lattice (similar to the
liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. T ...
phases) but lacking
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
-like long-range ordering at least in one direction.


Origin and definition

The words "paracrystallinity" and "paracrystal" were coined by the late Friedrich Rinne in the year 1933. Their German equivalents, e.g. "Parakristall", appeared in print one year earlier. A general theory of paracrystals has been formulated in a basic textbook, and then further developed/refined by various authors.
Rolf Hosemann Rolf Hosemann (20 April 1912 in Rostock – 28 September 1994 in Berlin) was a German physicist who laid the mathematical foundations for paracrystallinity. Education and career Hosemann was born in Rostock and studied at the University of Marb ...
's definition of an ideal paracrystal is: "The electron density distribution of any material is equivalent to that of a paracrystal when there is for every building block one ideal point so that the distance statistics to other ideal points are identical for all of these points. The
electron configuration In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon atom ...
of each building block around its ideal point is statistically independent of its counterpart in neighboring building blocks. A building block corresponds then to the material content of a cell of this "blurred" space lattice, which is to be considered a paracrystal."


Theory

''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 In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' ("wit ...
, the location of the nearest 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 In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...
length \xi. A paracrystalline material exhibits a correlation somewhere between the fully amorphous and fully crystalline. The primary, most accessible source of
crystallinity Crystallinity refers to the degree of structural order in a solid. In a crystal, the atoms or molecules are arranged in a regular, periodic manner. The degree of crystallinity has a big influence on hardness, density, Transparency and translucen ...
information is
X-ray diffraction X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
and
cryo-electron microscopy Cryogenic electron microscopy (cryo-EM) is a cryomicroscopy technique applied on samples cooled to cryogenic temperatures. For biological specimens, the structure is preserved by embedding in an environment of vitreous ice. An aqueous sample sol ...
, although other techniques may be needed to observe the complex structure of paracrystalline materials, such as
fluctuation electron microscopy Fluctuation electron microscopy (FEM), originally called Variable Coherence Microscopy before decoherence effects in the sample rendered that naming moot, is a technique in electron microscopy that probes nanometer-scale or "medium-range" order in ...
in combination with density of states modeling of electronic and vibrational states.
Scanning transmission electron microscopy A scanning transmission electron microscope (STEM) is a type of transmission electron microscope (TEM). Pronunciation is tÉ›mor ›sti:i:É›m As with a conventional transmission electron microscope (CTEM), images are formed by electrons passing ...
can provide real-space and reciprocal space characterization of paracrystallinity in nanoscale material, such as
quantum dot Quantum dots (QDs) are semiconductor particles a few nanometres in size, having light, optical and electronics, electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanote ...
solids. The scattering of X-rays, neutrons and electrons on paracrystals is quantitatively described by the theories of the ideal and real paracrystal. Numerical differences in analyses of diffraction experiments on the basis of either of these two theories of paracrystallinity can often be neglected. Just like ideal crystals, ideal paracrystals extend theoretically to infinity. Real paracrystals, on the other hand, follow the empirical α*-law, which restricts their size. That size is also indirectly proportional to the components of the tensor of the paracrystalline distortion. Larger solid state aggregates are then composed of micro-paracrystals.


Applications

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, biopolymers, quantum dot solids, and biomembranes.


See also

*
Amorphous solid In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' ("wit ...
* Crystallite *
Crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...
* DNA * Single crystal * X-ray pattern of a B-DNA paracrystal * X-ray scattering techniques


References

{{reflist Phases of matter