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=====Crystallography===== {{Main|Crystallography}} [[File:Perovskite.jpg|thumb|Crystal structure of a perovskite with a chemical formula ABX<sub>3</sub><ref>{{cite journal |title= Energetics and Crystal Chemical Systematics among Ilmenite, Lithium Niobate, and Perovskite Structures |author= A. Navrotsky |journal= Chem. Mater. |date= 1998 |volume= 10 |issue= 10 |pages= 2787β2793 |doi= 10.1021/cm9801901}}</ref>]] Crystallography is the science that examines the arrangement of atoms in crystalline solids. Crystallography is a useful tool for materials scientists. One of the fundamental concepts regarding the crystal structure of a material includes the [[unit cell]], which is the smallest unit of a crystal lattice (space lattice) that repeats to make up the macroscopic crystal structure. Most common structural materials include [[Parallelepiped|parallelpiped]] and hexagonal lattice types.<ref>Callister, Jr., Rethwisch. "Materials Science and Engineering β An Introduction" (8th ed.) John Wiley and Sons, 2009</ref> In [[single crystal]]s, the effects of the crystalline arrangement of atoms is often easy to see macroscopically, because the natural shapes of crystals reflect the atomic structure. Further, physical properties are often controlled by crystalline defects. The understanding of crystal structures is an important prerequisite for understanding [[crystallographic defect]]s. Examples of crystal defects consist of dislocations including edges, screws, vacancies, self inter-stitials, and more that are linear, planar, and three dimensional types of defects.<ref>Callister, Jr., Rethwisch. "Materials Science and Engineering β An Introduction" (8th ed.). John Wiley and Sons, 2009</ref> New and advanced materials that are being developed include [[nanomaterials]], [[biomaterial]]s.<ref>Callister, Jr., Rethwisch. Materials Science and Engineering β An Introduction (8th ed.)</ref> Mostly, materials do not occur as a single crystal, but in polycrystalline form, as an aggregate of small crystals or grains with different orientations. Because of this, the [[Powder diffraction|powder diffraction method]], which uses diffraction patterns of polycrystalline samples with a large number of crystals, plays an important role in structural determination. Most materials have a crystalline structure, but some important materials do not exhibit regular crystal structure.<ref>{{Cite journal |last=Gavezzotti |first=Angelo |date=1994-10-01 |title=Are Crystal Structures Predictable? |url=http://dx.doi.org/10.1021/ar00046a004 |journal=Accounts of Chemical Research |volume=27 |issue=10 |pages=309β314 |doi=10.1021/ar00046a004 |issn=0001-4842}}</ref> [[Polymer]]s display varying degrees of crystallinity, and many are completely non-crystalline. [[Glass]], some ceramics, and many natural materials are [[Amorphous solid|amorphous]], not possessing any long-range order in their atomic arrangements. The study of polymers combines elements of chemical and statistical thermodynamics to give thermodynamic and mechanical descriptions of physical properties.
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