Editing Crystal structure (section)

== Defects and impurities ==
{{main|Crystallographic defect}}
Real crystals feature defects or irregularities in the ideal arrangements described above and it is these defects that critically determine many of the electrical and mechanical properties of real materials.

=== Impurities ===
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When one atom substitutes for one of the principal atomic components within the crystal structure, alteration in the electrical and thermal properties of the material may ensue.<ref>{{cite book|first=Nikola |last=Kallay |date=2000 |url=https://books.google.com/books?id=ZXsBk20WO1sC |title=Interfacial Dynamics |publisher=CRC Press |isbn=978-0824700065}}</ref> Impurities may also manifest as [[electron spin]] impurities in certain materials. Research on magnetic impurities demonstrates that substantial alteration of certain properties such as specific heat may be affected by small concentrations of an impurity, as for example impurities in semiconducting [[ferromagnetic]] [[alloy]]s may lead to different properties as first predicted in the late 1960s.<ref>{{cite journal|doi = 10.1103/PhysRev.188.870|title = Density of States of an Insulating Ferromagnetic Alloy|year = 1969|author = Hogan, C. M.|journal = Physical Review|volume = 188|issue = 2|pages = 870–874|bibcode = 1969PhRv..188..870H }}</ref><ref>{{cite journal|doi = 10.1103/PhysRevA.32.2530|title = Spin-wave-related period doublings and chaos under transverse pumping|year = 1985|author = Zhang, X. Y.|journal = Physical Review A|volume = 32|pages = 2530–2533|pmid = 9896377|first2 = H|issue = 4|last2 = Suhl|bibcode = 1985PhRvA..32.2530Z }}</ref>

=== Dislocations ===
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{{main|Dislocation}}
Dislocations in a crystal lattice are line defects that are associated with local stress fields. Dislocations allow [[Shear stress|shear]] at lower stress than that needed for a perfect crystal structure.<ref>{{cite book |title= Mechanical Behavior of Materials |last= Courtney |first= Thomas |year= 2000 |publisher= Waveland Press |location= Long Grove, IL |isbn= 978-1-57766-425-3 |pages= 85}}</ref> The local stress fields result in interactions between the dislocations which then result in strain hardening or [[cold working]].

=== Grain boundaries ===
{{Main|Grain boundary}}
Grain boundaries are interfaces where crystals of different orientations meet.<ref name="Physics 1991"/> A grain boundary is a single-phase interface, with crystals on each side of the boundary being identical except in orientation. The term "crystallite boundary" is sometimes, though rarely, used. Grain boundary areas contain those atoms that have been perturbed from their original lattice sites, [[dislocations]], and impurities that have migrated to the lower energy grain boundary.

Treating a grain boundary geometrically as an interface of a [[single crystal]] cut into two parts, one of which is rotated, we see that there are five variables required to define a grain boundary. The first two numbers come from the unit vector that specifies a rotation axis. The third number designates the angle of rotation of the grain. The final two numbers specify the plane of the grain boundary (or a unit vector that is normal to this plane).<ref name="Physics 1994"/>

Grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve strength, as described by the [[Hall–Petch]] relationship. Since grain boundaries are defects in the crystal structure they tend to decrease the [[electrical conductivity|electrical]] and [[thermal conductivity]] of the material. The high interfacial energy and relatively weak bonding in most grain boundaries often makes them preferred sites for the onset of corrosion and for the [[Precipitation (chemistry)|precipitation]] of new phases from the solid. They are also important to many of the mechanisms of [[creep (deformation)|creep]].<ref name="Physics 1994"/>

Grain boundaries are in general only a few nanometers wide. In common materials, crystallites are large enough that grain boundaries account for a small fraction of the material. However, very small grain sizes are achievable. In nanocrystalline solids, grain boundaries become a significant volume fraction of the material, with profound effects on such properties as [[diffusion]] and [[plasticity (physics)|plasticity]]. In the limit of small crystallites, as the volume fraction of grain boundaries approaches 100%, the material ceases to have any crystalline character, and thus becomes an [[amorphous solid]].<ref name="Physics 1994"/>