Lattice constant: Difference between revisions

Revision as of 21:20, 29 January 2020

Latest revision as of 17:59, 2 August 2025

(46 intermediate revisions by 28 users not shown)

Line 1:

{{short description|Physical dimensions of unit cells in a crystal}}

[[Image:UnitCell.png|right|thumb|upright=1.3|Unit cell definition using parallelopiped[[parallelepiped]] with lengths ''a'', ''b'', ''c'' and angles between the sides given by ''α'', ''β'', ''γ''<ref>{{cite web|url=http://www.ccdc.cam.ac.uk/support/documentation/mercury_csd/portable/mercury_portable-4-70.html|title=Unit cell definition using parallelepiped with lengths ''a'', ''b'', ''c'' and angles between the sides given by ''α'', ''β'', ''γ''|archive-url=https://web.archive.org/web/20081004101125/http://www.ccdc.cam.ac.uk/support/documentation/mercury_csd/portable/mercury_portable-4-70.html |archive-date=4 October 2008}}</ref>]]

TheA '''lattice constant''', or '''lattice parameter''', refersis toone of the physical dimensiondimensions and angles that determine the geometry of the [[unit cell]]s in a [[crystal lattice]]., Latticesand inis three dimensions generally have three lattice constants, referredproportional to asthe ''a'',distance ''b'',between and ''c''. However,atoms in the specialcrystal. case ofA [[cubicsimple crystal system|cubic crystal structures]], allcrystal ofhas theonly constantsone arelattice equalconstant, andthe aredistance referredbetween toatoms, asbut, ''a''.in Similarlygeneral, lattices in [[Hexagonalthree crystaldimensions system|hexagonalhave crystalsix structures]],lattice constants: the lengths ''a'' and, ''b'' constants are equal, and we only refer to the ''ac'' andof ''c''the constants.three Acell groupedges ofmeeting latticeat constantsa couldvertex, beand referredthe to asangles ''α'lattice', parameters''β''. However, the full set of lattice parameters consist of the three lattice constants and the''γ'' threebetween angles betweenthose themedges.

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]].

For example,

The lattice constant for [[diamond]] is {{nowrap|1=''a'' = 3.57 [[Ångström|Å]]}} at 300&nbsp;[[Kelvin|K]]. The structure is equilateral although its actual shape cannot be determined from only the lattice constant. Furthermore, in real applications, typically the average lattice constant is given. Near the crystal's surface, lattice constant is affected by the surface reconstruction that results in a deviation from its mean value. This deviation is especially important in nanocrystals since surface-to-nanocrystal core ratio is large.<ref>{{cite journal|first=Mudar A. |last=Abdulsattar |title=Ab initio large unit cell calculations of the electronic structure of diamond nanocrystals |journal=Solid State Sci. |volume=13 |issue=5 |page=843 |date=2011 |access-date=|doi=10.1016/j.solidstatesciences.2011.03.009|bibcode=2011SSSci..13..843A }}</ref> As lattice constants have the dimension of length, their [[SI unit]] is the [[meter]]. Lattice constants are typically on the order of several [[ångström]]s (i.e. tenths of a [[nanometre|nanometer]]). Lattice constants can be determined using techniques such as [[X-ray diffraction]] or with an [[atomic force microscope]]. Lattice constant of a crystal 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|issue=|pages=1122–1129|publisher=Elsevier B. V.|___location=Netherlands|issn=0169-4332|doi=10.1016/j.apsusc.2018.10.149|arxiv=1501.06679}}</ref>

==Introduction==

In [[epitaxy|epitaxial growth]], the lattice constant is a measure of the structural compatibility between different materials.

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.

Lattice constant matching is important for the growth of [[Thin layer chromatography|thin layer]]s of materials on other materials; when the constants differ, strains are introduced into the layer, which prevents epitaxial growth of thicker layers without defects.

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&nbsp;[[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 constant for [[diamond]] is {{nowrap|1=''a'' = 3.57 [[Ångström|Å]]}} at 300&nbsp;[[Kelvin|K]]. The structure is equilateral although its actual shape cannot be determined from only the lattice constant. Furthermore, in real applications, typically the average lattice constant is given. Near the crystal's surface, lattice constant is affected by the surface reconstruction that results in a deviation from its mean value. This deviation is especially important in nanocrystals since surface-to-nanocrystal core ratio is large.<ref>{{cite journal|first=Mudar A. |last=Abdulsattar |title=Ab initio large unit cell calculations of the electronic structure of diamond nanocrystals |journal=Solid State Sci. |volume=13 |issue=5 |page=843 |date=2011 |access-date=|doi=10.1016/j.solidstatesciences.2011.03.009|bibcode=2011SSSci..13..843A }}</ref> As lattice constants have the dimension of length, their [[SI unit]] is the [[meter]]. Lattice constants are typically on the order of several [[ångström]]s (i.e. tenthsparameters of a [[nanometre|nanometer]]).crystalline Lattice constantssubstance can be determined using techniques such as [[X-ray diffraction]] or with an [[atomic force microscope]]. Lattice constant of a crystalThey 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|issue=|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 ==

The volume of the unit cell can be calculated from the lattice constant lengths and angles. If the unit cell sides are represented as vectors, then the volume is the [[dotTriple product]]#Scalar oftriple oneproduct|scalar vector with the [[crosstriple product]] of the other two vectors. The volume is represented by the letter ''V''. For the general unit cell

:<math>V = a b c \sqrt{1+2\cos\alpha\cos\beta\cos\gamma - \cos^2\alpha - \cos^2\beta - \cos^2\gamma}.</math>

For monoclinic lattices with {{nowrap|1=''α'' = 90°}}, {{nowrap|1=''γ'' = 90°}}, this simplifies to

:<math>V = a b c \sin\beta.</math>

For orthorhombic, tetragonal and cubic lattices with {{nowrap|1=''β'' = 90°}} as well, then<ref>{{cite web|author1=Dept. of Crystallography & Struc. Biol. CSIC|title=4. Direct and reciprocal lattices|url=http://www.xtal.iqfr.csic.es/Cristalografia/index-en.html|accessdateaccess-date=9 June 2015|date=4 June 2015}}</ref>

:<math>V = a b c .</math>

Line 35 ⟶ 38:

{| class="wikitable"

|+Lattice constants for various materials at 300&nbsp;K

! Material !! Lattice constant (Å) !! [[Crystal structure]] !! Ref.

|-

| C ([[diamond]])|| 3.567 || [[Diamond cubic|Diamond (FCC)]] || <ref name="APS">{{cite web|title=Lattice Constants|url=http://7id.xray.aps.anl.gov/calculators/crystal_lattice_parameters.html|website=Argon National Labs (Advanced Photon Source)|accessdateaccess-date=19 October 2014}}</ref>

|-

| C ([[graphite]])|| ''a'' = 2.461<br />''c'' = 6.708 || [[Hexagonal crystal family|Hexagonal]]||

|-

| [[Silicon|Si]] || 5.431020511 || Diamond (FCC) || <ref name="Ioffe">{{cite web|title=Semiconductor NSM|url=http://www.ioffe.rssi.ru/SVA/NSM/Semicond/|accessdateaccess-date=19 October 2014|archive-date=24 September 2015|archive-url=https://web.archive.org/web/20150924035757/http://www.ioffe.rssi.ru/SVA/NSM/Semicond/|url-status=dead}}</ref><ref name="nist">{{cite web |title=Fundamental physical constants |url=https://physics.nist.gov/cgi-bin/cuu/Value?asil |website=physics.nist.gov |publisher=NIST |accessdateaccess-date=17 January 2020}}</ref>

|-

| [[Germanium|Ge]] || 5.658 || Diamond (FCC) || <ref name="Ioffe" />

|-

| [[Aluminium arsenide|AlAs]]|| 5.6605 || [[Cubic crystal system#Zincblende structure|Zinc blende (FCC)]] || <ref name="Ioffe" />

|-

| [[Aluminium phosphide|AlP]]|| 5.4510 || Zinc blende (FCC) || <ref name="Ioffe" />

|-

| [[Aluminium antimonide|AlSb]]|| 6.1355 || Zinc blende (FCC) || <ref name="Ioffe" />

|-

| [[Gallium phosphide|GaP]] || 5.4505 || Zinc blende (FCC) || <ref name="Ioffe" />

|-

| [[Gallium arsenide|GaAs]] || 5.653 || Zinc blende (FCC) || <ref name="Ioffe" />

|-

| [[Gallium antimonide|GaSb]] || 6.0959 || Zinc blende (FCC) || <ref name="Ioffe" />

|-

| [[Indium phosphide|InP]] || 5.869 || Zinc blende (FCC) || <ref name="Ioffe" />

|-

| [[Indium arsenide|InAs]] || 6.0583 || Zinc blende (FCC) || <ref name="Ioffe" />

|-

| [[Indium antimonide|InSb]] || 6.479 || Zinc blende (FCC) || <ref name="Ioffe" />

|-

| [[Magnesium oxide|MgO]] || 4.212 || [[Cubic crystal system#Rock-salt structure|Halite]] (FCC) || <ref>{{cite web |title=Substrates |website=Spi Supplies |url=http://www.2spi.com/category/substrates/ |access-date=17 May 2017}}</ref>

|-

| [[Silicon carbide|SiC]] || ''a'' = 3.086<br />''c'' = 10.053 || [[Wurtzite]] || <ref name="Ioffe" />

|-

| [[Cadmium sulfide|CdS]] || 5.8320 || Zinc blende (FCC) ||<ref name="APS"/>

|-

| [[Cadmium selenide|CdSe]]|| 6.050 || Zinc blende (FCC) ||<ref name="APS"/>

|-

| [[Cadmium telluride|CdTe]]|| 6.482 || Zinc blende (FCC) ||<ref name="APS"/>

|-

| [[Zinc oxide|ZnO]]|| ''a'' = 3.25<br />''c'' = 5.2 || Wurtzite (HCP) ||<ref name=Hadis>{{cite book|author= Hadis Morkoç and Ümit Özgur|title=Zinc Oxide: Fundamentals, Materials and Device Technology|date=2009|publisher= WILEY-VCH Verlag GmbH & Co.|___location=Weinheim}}</ref>

|-

| [[Zinc oxide|ZnO]]|| 4.580 || Halite (FCC) ||<ref name="APS"/>

|-

| [[Zinc sulfide|ZnS]]|| 5.420 || Zinc blende (FCC) ||<ref name="APS"/>

|-

| [[Lead(II) sulfide|PbS]]|| 5.9362 || Halite (FCC) ||<ref name="APS"/>

|-

| [[Lead(II) telluride|PbTe]]|| 6.4620 || Halite (FCC) ||<ref name="APS"/>

|-

| [[Boron nitride|BN]]|| 3.6150 || Zinc blende (FCC) ||<ref name="APS"/>

|-

| [[Boron phosphide|BP]]|| 4.5380 || Zinc blende (FCC) ||<ref name="APS"/>

|-

| [[Cadmium sulfide|CdS]]|| ''a'' = 4.160<br />''c'' = 6.756 || Wurtzite||<ref name="APS"/>

|-

| [[Zinc sulfide|ZnS]]|| ''a'' = 3.82<br />''c'' = 6.26 || Wurtzite||<ref name="APS"/>

|-

| [[Aluminium nitride|AlN]]|| ''a'' = 3.112<br />''c'' = 4.982 || Wurtzite||<ref name="Ioffe"/>

|-

| [[Gallium nitride|GaN]]|| ''a'' = 3.189<br />''c'' = 5.185 || Wurtzite ||<ref name="Ioffe"/>

|-

| [[Indium nitride|InN]]|| ''a'' = 3.533<br />''c'' = 5.693 || Wurtzite||<ref name="Ioffe"/>

|-

| [[Lithium fluoride|LiF]]||4.03|| [[Cubic crystal system#Rock-salt structure|Halite]] ||

|-

| [[Lithium chloride|LiCl]]||5.14|| Halite ||

|-

| [[Lithium bromide|LiBr]]||5.50|| Halite ||

|-

| [[Lithium iodide|LiI]]||6.01|| Halite ||

|-

| [[Sodium fluoride|NaF]]||4.63|| Halite ||

|-

| [[Sodium chloride|NaCl]]||5.64|| Halite ||

|-

| [[Sodium bromide|NaBr]]||5.97|| Halite ||

|-

| [[Sodium iodide|NaI]]||6.47|| Halite ||

|-

| [[Potassium fluoride|KF]]||5.34|| Halite ||

|-

| [[Potassium chloride|KCl]]||6.29|| Halite ||

|-

| [[Potassium bromide|KBr]]||6.60|| Halite ||

|-

| [[Potassium iodide|KI]]||7.07|| Halite ||

|-

| [[Rubidium fluoride|RbF]]||5.65|| Halite ||

|-

| [[Rubidium chloride|RbCl]]||6.59|| Halite ||

|-

|RbBr [[Rubidium bromide|RbBr]]||6.89|| Halite ||

|-

| [[Rubidium iodide|RbI]]||7.35|| Halite ||

|-

| [[Caesium fluoride|CsF]]||6.02|| Halite ||

|-

| [[Caesium chloride|CsCl]]||4.123|| [[Cubic crystal system#CesiumCaesium chloride structure|Caesium chloride]] ||

|-

|CsI [[Caesium bromide|CsBr]]||4.567291|| Caesium chloride ||

|-

| [[Caesium iodide|CsI]]||4.567|| Caesium chloride ||

|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>

|-

| [[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>

|Fe||2.856||BCC||<ref name="Davey" />

|-

|Ni [[Iron|Fe]]|3|2.499856||FCCBCC||<ref name="Davey" />

|-

|Cu [[Nickel|Ni]]||3.597499||FCC||<ref name="Davey" />

|-

|Mo [[Copper|Cu]]||3.142597||BCCFCC||<ref name="Davey" />

|-

|Pd [[Molybdenum|Mo]]||3.859142||FCCBCC||<ref name="Davey" />

|-

|Ag [[Palladium|Pd]]|4|3.079859||FCC||<ref name="Davey" />

|-

|W [[Silver|Ag]]|3|4.155079||BCCFCC||<ref name="Davey" />

|-

|Pt [[Tungsten|W]]||3.912155||FCCBCC||<ref name="Davey" />

|-

|Au [[Platinum|Pt]]|4|3.065912||FCC||<ref name="Davey" />

|-

|Pb [[Gold|Au]]||4.920065||FCC||<ref name="Davey" />

|-

|Fe [[Lead|Pb]]|2|4.856920||BCCFCC||<ref name="Davey" />

|TiN||4.249||Halite||

|-

| [[Vanadium|V]]

|ZrN||4.577||Halite||

|3.0399

|BCC

|

|-

| [[Niobium|Nb]]

|HfN||4.392||Halite||

|3.3008

|BCC

|

|-

| [[Tantalum|Ta]]

|VN||4.136||Halite||

|3.3058

|BCC

|

|-

|CrN [[Titanium nitride|TiN]]||4.149249||Halite||

|-

|NbN [[Zirconium nitride|ZrN]]||4.392577||Halite||

|-

| [[Hafnium nitride|HfN]]||4.392||Halite||

|TiC||4.328||Halite||<ref name=Toth>{{cite book|last1=Toth|first1=L.E.|title=Transition Metal Carbides and Nitrides|date=1967|publisher=Academic Press|___location=New York}}</ref>

|-

|ZrC_0.97 [[Vanadium nitride|VN]]||4.698136||Halite||<ref name=Toth />

|-

|HfC_0.99 [[Chromium nitride|CrN]]||4.640149||Halite||<ref name=Toth />

|-

|VC_0.97 [[Niobium nitride|NbN]]||4.166392||Halite||<ref name=Toth />

|-

| [[Titanium carbide|TiC]]||4.328||Halite||<ref name=Toth>{{cite book|last1=Toth|first1=L.E.|title=Transition Metal Carbides and Nitrides|date=1967|publisher=Academic Press|___location=New York}}</ref>

|NC_0.99||4.470||Halite||<ref name=Toth />

|-

|TaC_{0 [[Zirconium carbide|{{chem2|ZrC0.99}97}}]]||4.456698||Halite||<ref name=Toth />

|-

|Cr₃C₂ [[Hafnium carbide|{{chem2|''a'' = 11HfC0.47<br>''b'' = 5.545<br>''c'' = 299}}]]||4.830640||OrthorombicHalite||<ref name=Toth />

|-

|WC||''a'' =[[Vanadium 2carbide|{{chem2|VC0.906<br>''c'' = 297}}]]||4.837166||HexagonalHalite||<ref name=Toth />

|-

|NC_{0 [[Niobium carbide|{{chem2|NbC0.99}}}]]||4.470||Halite||<ref name=Toth />

|ScN||4.52||Halite||<ref name=Saha>{{cite journal|last1=Saha|first1=B.|title=Electronic structure, phonons, and thermal properties of ScN, ZrN, and HfN: A first-principles study|journal=Journal of Applied Physics|date=2010|volume=107|issue=3|pages=033715–033715–8|doi=10.1063/1.3291117|bibcode = 2010JAP...107c3715S |url=http://repository.ias.ac.in/59355/1/18-pub.pdf}}</ref>

|-

| [[Tantalum carbide|{{chem2|TaC0.99}}]]||4.456||Halite||<ref name=Toth />

|LiNbO₃||''a'' = 5.1483<br>''c'' = 13.8631||Hexagonal||<ref name=LB>{{cite web|last1=Goodenough|first1=J. B.|last2=Longo|first2=M.|title=3.1.7 Data: Crystallographic properties of compounds with perovskite or perovskite-related structure, Table 2 Part 1|url=http://www.springermaterials.com/docs/info/10201420_50.html|publisher=SpringerMaterials - The Landolt-Börnstein Database}}</ref>

|-

|CaTiO₃ [[Chromium carbide|{{chem2|Cr3C2}}]]||''a'' = 511.38147<br />''b'' = 5.443545<br />''c'' = 72.645830||[[Orthorhombic perovskitecrystal system|Orthorhombic]]||<ref name=LBToth />

|KTaO₃||3.9885||Cubic perovskite||<ref name=LB />

|-

|BaTiO₃ [[Tungsten carbide|WC]]||''a'' = 32.994906<br />''c'' = 42.034837||Tetragonal perovskiteHexagonal||<ref name=LBToth />

|-

| [[Scandium nitride|ScN]]||4.52||Halite||<ref name=Saha>{{cite journal|last1=Saha|first1=B.|title=Electronic structure, phonons, and thermal properties of ScN, ZrN, and HfN: A first-principles study|journal=Journal of Applied Physics|date=2010|volume=107|issue=3|pages=033715–033715–8|doi=10.1063/1.3291117|bibcode = 2010JAP...107c3715S |url=http://repository.ias.ac.in/59355/1/18-pub.pdf}}</ref>

|SrTiO₃||3.98805||Cubic perovskite||<ref name=LB />

|-

|LiNbO₃ [[Lithium niobate|{{chem2|LiNbO3}}]]||''a'' = 5.1483<br />''c'' = 13.8631||Hexagonal||<ref name=LB>{{cite web|last1=Goodenough|first1=J. B.|last2=Longo|first2=M.|title=3.1.7 Data: Crystallographic properties of compounds with perovskite or perovskite-related structure, Table 2 Part 1|url=http://www.springermaterials.com/docs/info/10201420_50.html|publisher=SpringerMaterials - The Landolt-Börnstein Database}}</ref>

|CaTiO₃||''a'' = 5.381<br>''b'' = 5.443<br>''c'' = 7.645||Orthorhombic perovskite||<ref name=LB />

|-

|PbTiO₃ {{chem2|KTaO3}}||''a'' = 3.904<br>''c'' = 4.1529885||TetragonalCubic perovskite||<ref name=LB />

|-

|EuTiO<sub> [[Barium titanate|{{chem2|BaTiO3}}]]||''a'' = 3.994<br /sub>||7''c'' = 4.810034||Cubic[[Perovskite (structure)|Tetragonal perovskite]]||<ref name=LB />

|-

|SrVO₃ [[Strontium titanate|{{chem2|SrTiO3}}]]||3.83898805||[[Perovskite (structure)|Cubic perovskite]]||<ref name=LB />

|-

|CaVO [[Calcium titanate|{{chem2|CaTiO3}}]]||''a'' = 5.381<subbr />3''b'' = 5.443<br /sub>||3''c'' = 7.767645||Cubic[[Perovskite (structure)|Orthorhombic perovskite]]||<ref name=LB />

|-

|BaMnO₃ [[Lead titanate|{{chem2|PbTiO3}}]]||''a'' = 53.673904<br />''c'' = 4.71152||HexagonalTetragonal perovskite||<ref name=LB />

|-

|CaMnO₃ [[Europium(II) titanate|{{chem2|EuTiO3}}]]||''a'' = 5.27<br>''b'' = 5.275<br>''c'' = 7.464810||OrthorhombicCubic perovskite||<ref name=LB />

|-

|SrRuO₃ {{chem2|SrVO3}}|''a'' = 5.53<br>''b'' = 5.57<br>''c'' = 7|3.85838||OrthorhombicCubic perovskite||<ref name=LB />

|-

|YAlO₃ {{chem2|CaVO3}}|''a'' = 5.179<br>''b'' = 5.329<br>''c'' = 7|3.37767||OrthorhombicCubic perovskite||<ref name=LB />

|-

| {{chem2|BaMnO3}}||''a'' = 5.673<br />''c'' = 4.71||Hexagonal||<ref name=LB />

|-

| {{chem2|CaMnO3}}||''a'' = 5.27<br />''b'' = 5.275<br />''c'' = 7.464||Orthorhombic perovskite||<ref name=LB />

|-

| {{chem2|SrRuO3}}||''a'' = 5.53<br />''b'' = 5.57<br />''c'' = 7.85||Orthorhombic perovskite||<ref name=LB />

|-

| {{chem2|YAlO3}}||''a'' = 5.179<br />''b'' = 5.329<br />''c'' = 7.37||Orthorhombic perovskite||<ref name=LB />

|}

==References==

{{reflist}}

<ref>{{cite book |last1=Rizescu |first1=Costel |last2=Rizescu |first2=Mihaela |title=Structure of Crystalline Solids, Imperfections and Defects in Crystals |date=2018 |publisher=Shutter Waves |___location=Parker, TX |isbn=978-1-947641-17-4 |page=9-15 |pages=77-90 |edition=First |url=https://shutterwaves.com/product/structure-of-crystalline-solids/ |accessdate=29 January 2020}}</ref>

<br />

==External links==

* [https://sciencing.com/lattice-constant-8413525.html How to Find Lattice Constant]

{{Authority control}}

[[Category:Crystals]]

[[Category:Semiconductor properties]]

<references group="15" />