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A '''lattice constant''' or '''lattice parameter''' is one of the physical dimensions and angles that determine the geometry of the [[unit cell]]s in a [[crystal lattice]], and is proportional to the distance between atoms in the crystal. A [[simple cubic]] crystal has only one lattice constant, the distance between atoms, but in general lattices in three dimensions have six lattice constants: the lengths ''a'', ''b'', and ''c'' of the three cell edges meeting at a vertex, and the angles ''α'', ''β'', and ''γ'' between those edges.
The crystal lattice parameters ''a'', ''b'', and ''c'' have the dimension of length. The three numbers represent the size of the [[unit cell]], that is, the distance from a given atom to an identical atom in the same position and orientation in a neighboring cell (except for very simple crystal structures, this will not necessarily be distance to the nearest neighbor). Their [[SI unit]] is the [[meter]], and they are traditionally specified in [[angstrom]]s (Å); an angstrom being 0.1 [[nanometre|nanometer]] (nm), or 100 [[picometre]]s (pm). Typical values start at a few angstroms. The angles ''α'', ''β'', and ''γ'' are usually specified in [[degree (angle)|degrees]].
==Introduction==
A [[chemical substance]] in the solid state may form [[crystal]]s in which the [[atom]]s, [[molecule]]s, or [[ion]]s are arranged in space according to one of a small finite number of possible [[crystal system]]s (lattice types), each with fairly well defined set of lattice parameters that are characteristic of the substance. These parameters typically depend on the [[temperature]], [[pressure]] (or, more generally, the local state of [[stress (mechanics)|mechanical stress]] within the crystal),<ref name=colm2019>Francisco Colmenero (2019): "Negative area compressibility in oxalic acid dihydrate". ''Materials Letters'', volume 245, pages 25-28. {{doi|10.1016/j.matlet.2019.02.077}}</ref> [[electric field|electric]] and [[magnetic field]]s, and its [[isotope|isotopic]] composition.<ref name=tell1971>Roland Tellgren and Ivar Olovsson (1971): "Hydrogen Bond Studies. XXXXVI. The Crystal Structures of Normal and Deuterated Sodium Hydrogen Oxalate Monohydrate NaHC2O4·H2O and NaDC2O4·D2O". ''Journal of Chemical Physics'', volume 54, issue 1. {{doi|10.1063/1.1674582}}</ref> The lattice is usually distorted near impurities, [[crystal defect]]s, and the crystal's surface. Parameter values quoted in manuals should specify those environment variables, and are usually averages affected by measurement errors.
Depending on the crystal system, some or all of the lengths may be equal, and some of the angles may have fixed values. In those systems, only some of the six parameters need to be specified. For example, in the [[cubic crystal system|cubic system]], all of the lengths are equal and all the angles are 90°, so only the ''a'' length needs to be given. This is the case of [[diamond]], which has {{nowrap|1=''a'' = 3.57 [[angstrom|Å]] = 357 [[picometre|pm]]}} at 300 [[kelvin|K]]. Similarly, in [[hexagonal crystal system|hexagonal system]], the ''a'' and ''b'' constants are equal, and the angles are 60°, 90°, and 90°, so the geometry is determined by the ''a'' and ''c'' constants alone.
The lattice parameters of a crystalline substance can be determined using techniques such as [[X-ray diffraction]] or with an [[atomic force microscope]]. They can be used as a natural length standard of nanometer range.<ref name="automatic1998">{{cite journal|author=R. V. Lapshin|year=1998|title=Automatic lateral calibration of tunneling microscope scanners|journal=Review of Scientific Instruments|volume=69|issue=9|pages=3268–3276|publisher=AIP|___location=USA|issn=0034-6748|doi=10.1063/1.1149091|url=http://www.lapshin.fast-page.org/publications/R.%20V.%20Lapshin,%20Automatic%20lateral%20calibration%20of%20tunneling%20microscope%20scanners.pdf|bibcode=1998RScI...69.3268L}}</ref><ref name="real2019">{{cite journal|author=R. V. Lapshin|year=2019|title=Drift-insensitive distributed calibration of probe microscope scanner in nanometer range: Real mode|journal=Applied Surface Science|volume=470|pages=1122–1129|publisher=Elsevier B. V.|___location=Netherlands|issn=0169-4332|doi=10.1016/j.apsusc.2018.10.149|arxiv=1501.06679|bibcode=2019ApSS..470.1122L|s2cid=119191299 }}</ref> In the [[epitaxy|epitaxial growth]] of a crystal layer over a substrate of different composition, the lattice parameters must be matched in order to reduce strain and crystal defects.
== Volume ==
| [[Caesium iodide|CsI]]||4.567|| Caesium chloride ||
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| [[Aluminium|Al]]||4.046||FCC|| <ref name="Davey">{{cite journal|last1=Davey|first1=Wheeler|title=Precision Measurements of the Lattice Constants of Twelve Common Metals|journal=Physical Review|date=1925|volume=25|issue=6|pages=753–761|doi=10.1103/PhysRev.25.753|bibcode = 1925PhRv...25..753D }}</ref>
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| [[Iron|Fe]]||2.856||BCC||<ref name="Davey" />
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