View source for Lithium niobate

{{chembox
| Verifiedfields = changed
| Watchedfields = changed
| verifiedrevid = 476994790
| ImageFile = Lithium niobate crystal.jpg
| ImageFile1 = File:LiNbO3.png
| ImageSize1 = 
| ImageCaption1 = <span style="color:#008000; background-color:#008000;">__</span> [[Lithium|Li]]<sup>+</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style="color:#000080; background-color:#000080;">__</span> [[Niobium|Nb]]<sup>5+</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span style="color:#FF0000;background-color:#FF0000;">__</span> [[Oxygen|O]]<sup>2−</sup>
| ImageFile2 = 
| IUPACName = 
| OtherNames = Lithium niobium oxide, lithium niobium trioxide
|Section1={{Chembox Identifiers
| ChemSpiderID_Ref = {{chemspidercite|correct|chemspider}}
| ChemSpiderID = 10605804
| InChI = 1/Li.Nb.3O/q+1;;;;-1/rLi.NbO3/c;2-1(3)4/q+1;-1
| InChIKey = GQYHUHYESMUTHG-YHKBGIKBAK
| SMILES = [Li+].[O-][Nb](=O)=O
| StdInChI_Ref = {{stdinchicite|correct|chemspider}}
| StdInChI = 1S/Li.Nb.3O/q+1;;;;-1
| StdInChIKey_Ref = {{stdinchicite|correct|chemspider}}
| StdInChIKey = GQYHUHYESMUTHG-UHFFFAOYSA-N
| CASNo = 12031-63-9
| CASNo_Ref = {{cascite|correct|CAS}}
| PubChem = 159404
}}
|Section2={{Chembox Properties
| Formula = LiNbO<sub>3</sub>
| MolarMass = 147.846 g/mol
| Appearance = colorless solid
| Density = 4.30 g/cm<sup>3</sup><ref name=crc>Haynes, p. 4.70</ref>
| MeltingPtC = 1240
| MeltingPt_ref = <ref name=crc/>
| BoilingPt = 
| Solubility = None
| SolubleOther = 
| RefractIndex = n<sub>o</sub> 2.3007, n<sub>e</sub> 2.2116<ref>Haynes, p. 10.250</ref>
| BandGap = 3.77 eV <ref name="Zanatta">{{cite journal |last1=Zanatta |first1=A.R. | title= The optical bandgap of lithium niobate (LiNbO3) and its dependence with temperature |journal=Results Phys. |date=August 2022 |volume=39 |pages=105736–3pp |doi=10.1016/j.rinp.2022.105736 |s2cid=249688492 |doi-access=free }}</ref> 
 }}
|Section3={{Chembox Structure
| Structure_ref=<ref>{{cite journal|doi=10.1063/1.354572|title=The defect structure of congruently melting lithium niobate |year=1993 |last1=Wilkinson |first1=A. P. |last2=Cheetham |first2=A. K. |last3=Jarman |first3=R. H. |journal=Journal of Applied Physics |volume=74 |issue=5 |pages=3080–3083 |bibcode=1993JAP....74.3080W }}</ref>
| CrystalStruct = [[Trigonal]], [[Pearson symbol|hR30]] 
| SpaceGroup = R3c, No. 161 
| PointGroup = 3m (C<sub>3v</sub>)
| LattConst_a = 0.51501 nm
| LattConst_b =  0.51501 nm
| LattConst_c =  0.54952 nm
| LattConst_alpha = 62.057
| LattConst_beta = 62.057
| LattConst_gamma = 60 
| UnitCellFormulas = 6
 }}
|Section4={{Chembox Thermochemistry
| DeltaHf = 
| DeltaHc = 
| Entropy = 
| HeatCapacity = 
 }}
|Section7={{Chembox Hazards
| ExternalSDS = 
| MainHazards =
| NFPA-H = 
| NFPA-F = 
| NFPA-R = 
| NFPA-S = 
| FlashPt =
| LD50 = 8 g/kg (oral, rat)<ref>{{Cite web | url=https://chem.nlm.nih.gov/chemidplus/rn/12031-63-9 | title=ChemIDplus – 12031-63-9 – PSVBHJWAIYBPRO-UHFFFAOYSA-N – Lithium niobate – Similar structures search, synonyms, formulas, resource links, and other chemical information}}</ref>
 }}
|Section8={{Chembox Related
| OtherAnions = 
| OtherCations =
| OtherCompounds = 
 }}
}}

'''Lithium niobate''' ({{chem2|auto=1|LiNbO3}}) is a synthetic [[Salt (chemistry)|salt]] consisting of [[niobium]], [[lithium]], and [[oxygen]]. Its single crystals are an important material for optical waveguides, mobile phones, piezoelectric sensors, optical modulators and various other linear and non-linear optical applications.<ref>{{cite journal |author1=Weis, R. S. |author2=Gaylord, T. K. |title=Lithium Niobate: Summary of Physical Properties and Crystal Structure |journal=Applied Physics A: Materials Science & Processing |volume=37 |issue=4 |pages=191–203 |year=1985 |doi=10.1007/BF00614817 |bibcode=1985ApPhA..37..191W |s2cid=97851423 }}</ref> Lithium niobate is sometimes referred to by the brand name '''linobate'''.<ref>{{cite journal |title=Thermally fixed holograms in LiNbO<sub>3</sub> |first1=D.L. |last1=Staebler |first2=J.J. |last2=Amodei |journal=Ferroelectrics |year=1972 |volume=3 |issue=1 |pages=107–113|doi=10.1080/00150197208235297 |bibcode=1972Fer.....3..107S |s2cid=51674085 }}, seen in {{cite book |title=Landmark Papers On Photorefractive Nonlinear Optics |year=1995 |publisher=World Scientific |page=182 |editor1-first=Pochi |editor1-last=Yeh |editor2-first=Claire |editor2-last=Gu |isbn=9789814502979}}</ref>

==Properties==
Lithium niobate is a colorless solid, and it is insoluble in water. It has a [[trigonal]] [[crystal system]], which lacks [[inversion symmetry]] and displays [[ferroelectricity]], the [[Pockels effect]], the [[piezoelectric]] effect, [[photoelasticity]] and [[nonlinear optics|nonlinear optical]] polarizability. Lithium niobate has negative uniaxial [[birefringence]] which depends slightly on the [[stoichiometry]] of the crystal and on temperature. It is transparent for wavelengths between 350 and 5200 [[nanometer]]s.

Lithium niobate can be [[Dopant|doped]] with [[magnesium oxide]], which increases its [[Laser damage threshold|resistance to optical damage]] (also known as photorefractive damage). Other available dopants are [[iron]], [[zinc]], [[hafnium]], [[copper]], [[gadolinium]], [[erbium]], [[yttrium]], [[manganese]] and [[boron]].

==Growth==
[[File:Lithium Niobate Wafer.jpg|175px|thumb|A Z-cut, single-crystal lithium-niobate wafer|left]]
[[Single crystal]]s of lithium niobate can be grown using the [[Czochralski process]].<ref>{{cite book|title = Lithium Niobate: Defects, Photorefraction and Ferroelectric Switching|first = Tatyana|last = Volk|author2=Wohlecke, Manfred |publisher = Springer|year = 2008|isbn = 978-3-540-70765-3|doi=10.1007/978-3-540-70766-0|pages=1–9}}</ref>

After a crystal is grown, it is sliced into wafers of different orientation. Common orientations are Z-cut, X-cut, Y-cut, and cuts with rotated angles of the previous axes.<ref>{{cite book|last=Wong|first=K. K.|title=Properties of Lithium Niobate|year=2002|publisher=INSPEC|location=London, United Kingdom|isbn=0-85296-799-3|pages=8}}</ref>

=== Thin films ===
Thin-film lithium niobate (e.g. for [[Waveguide (optics)#Two-dimensional waveguides|optical wave guides]]) can be transferred to or grown on sapphire and other substrates, using the [[smart cut]] (ion slicing) process<ref>{{Cite journal |last1=Levy |first1=M. |last2=Osgood |first2=R. M. |last3=Liu |first3=R. |last4=Cross |first4=L. E. |last5=Cargill |first5=G. S. |last6=Kumar |first6=A. |last7=Bakhru |first7=H. |date=1998-10-19 |title=Fabrication of single-crystal lithium niobate films by crystal ion slicing |url=http://aip.scitation.org/doi/10.1063/1.121801 |journal=Applied Physics Letters |language=en |volume=73 |issue=16 |pages=2293–2295 |doi=10.1063/1.121801 |bibcode=1998ApPhL..73.2293L |issn=0003-6951}}</ref><ref>{{Cite journal |title= Enhanced electro-optical lithium niobate photonic crystal wire waveguide on a smart-cut thin film|url=https://opg.optica.org/oe/viewmedia.cfm?uri=oe-20-3-2974&html=true |access-date=2022-07-08 |journal=Optics Express | year=2012 |doi=10.1364/oe.20.002974| pmid=22330535 | last1=Lu | first1=H. | last2=Sadani | first2=B. | last3=Courjal | first3=N. | last4=Ulliac | first4=G. | last5=Smith | first5=N. | last6=Stenger | first6=V. | last7=Collet | first7=M. | last8=Baida | first8=F. I. | last9=Bernal | first9=M. P. | volume=20 | issue=3 | pages=2974–2981 | doi-access=free }}</ref> or [[MOCVD]] process.<ref>{{cite journal|doi=10.1016/0022-0248(95)00570-6|title=Epitaxial growth of lithium niobate thin films by the solid source MOCVD method |year=1996 |last1=Feigelson |first1=R. S. |journal=Journal of Crystal Growth |volume=166 |issue=1–4 |pages=1–16 |bibcode=1996JCrGr.166....1F |doi-access=free }}</ref> The technology is known as lithium niobate on insulator (LNOI).<ref>{{cite book|chapter-url=https://physik.uni-paderborn.de/fileadmin/physik/Alumni/Sohler/2012/SPIE_Photonics_Europe_Hu__LNOI_2012.pdf |doi=10.1117/12.922401 |chapter=Lithium niobate-on-insulator (LNOI): Status and perspectives |title=Silicon Photonics and Photonic Integrated Circuits III |year=2012 |last1=Hu |first1=Hui |last2=Yang |first2=Jin |last3=Gui |first3=Li |last4=Sohler |first4=Wolfgang |volume=8431 |pages=84311D |s2cid=120452519 }}</ref>

==Nanoparticles==
[[Nanoparticle]]s of lithium niobate and [[niobium pentoxide]] can be produced at low temperature.<ref>{{cite journal |author1=Grange, R. |author2=Choi, J.W. |author3=Hsieh, C.L. |author4=Pu, Y. |author5=Magrez, A. |author6=Smajda, R. |author7=Forro, L. |author8=Psaltis, D. |title=Lithium niobate nanowires: synthesis, optical properties and manipulation |journal=Applied Physics Letters |volume=95 |issue=14 |pages=143105 |year=2009 |url=http://link.aip.org/link/?APPLAB/95/143105/1 |doi=10.1063/1.3236777 |bibcode=2009ApPhL..95n3105G |url-status=dead |archive-url=http://arquivo.pt/wayback/20160514132623/http://link.aip.org/link/?APPLAB/95/143105/1 |archive-date=2016-05-14 }}</ref> The complete protocol implies a LiH induced reduction of NbCl<sub>5</sub> followed by ''in situ'' spontaneous oxidation into low-valence niobium nano-oxides. These niobium oxides are exposed to air atmosphere resulting in pure Nb<sub>2</sub>O<sub>5</sub>. Finally, the stable Nb<sub>2</sub>O<sub>5</sub> is converted into lithium niobate LiNbO<sub>3</sub> nanoparticles during the controlled hydrolysis of the LiH excess.<ref>{{cite journal|vauthors=Aufray M, Menuel S, Fort Y, Eschbach J, Rouxel D, Vincent B |title = New Synthesis of Nanosized Niobium Oxides and Lithium Niobate Particles and Their Characterization by XPS Analysis|journal = Journal of Nanoscience and Nanotechnology|volume = 9|issue = 8|pages = 4780–4789|year = 2009|doi = 10.1166/jnn.2009.1087|pmid = 19928149|citeseerx = 10.1.1.465.1919}}</ref> Spherical nanoparticles of lithium niobate with a diameter of approximately 10&nbsp;nm can be prepared by impregnating a mesoporous silica matrix with a mixture of an aqueous solution of LiNO<sub>3</sub> and NH<sub>4</sub>NbO(C<sub>2</sub>O<sub>4</sub>)<sub>2</sub> followed by 10 min heating in an infrared furnace.<ref>{{cite journal|author1=Grigas, A |author2=Kaskel, S |title = Synthesis of LiNbO<sub>3</sub> nanoparticles in a mesoporous matrix |journal = Beilstein Journal of Nanotechnology|volume = 2|pages = 28–33|year = 2011|doi =10.3762/bjnano.2.3|pmid=21977412 |pmc=3045940 }}</ref>

==Applications==
Lithium niobate is used extensively in the telecommunications market, e.g. in [[mobile telephone]]s and [[optical modulator]]s.<ref name=Toney-2015>{{cite book|title = Lithium Niobate Photonics|first = James|last = Toney |publisher = Artech House|year = 2015|isbn = 978-1-60807-923-0}}</ref> Due to its large electro-mechanical coupling, it is the material of choice for [[surface acoustic wave|surface acoustic wave (SAW)]] devices.<ref>{{cite journal |last1=Gruenke |first1=Rachel |last2=Hitchcock |first2=Oliver |year=2024 |title=Surface modification and coherence in lithium niobate SAW resonators |journal=Scientific Reports |volume=14 |page=6663 |doi=10.1038/s41598-024-57168-x}}</ref> For some uses it can be replaced by [[lithium tantalate|lithium tantalate ({{chem2|LiTaO3}})]]. Other uses are in [[laser]] [[second harmonic generation|frequency doubling]], [[nonlinear optics]], [[Pockels effect#Pockels cells|Pockels cell]]s, [[optical parametric oscillator]]s, [[Q-switching]] devices for lasers, other [[acousto-optic effect|acousto-optic]] devices, [[optical switch]]es for gigahertz frequencies, etc. It is an excellent material for manufacture of [[optical waveguide]]s. It's also used in the making of optical spatial low-pass ([[Anti-aliasing filter|anti-aliasing]]) filters. Additionally, it is used in pyroelectric infrared (IR) detectors, where it detects temperature changes by generating electric charges.<ref>{{cite web |url=https://www.samaterials.com/niobium-compounds/66-lithium-niobate-wafers.html |title=CY0066 Lithium Niobate Wafers (LiNbO3 Wafers) |website=Stanford Advanced Materials |access-date=Oct 18, 2024}}</ref>

In the past few years lithium niobate is finding applications as a kind of electrostatic tweezers, an approach known as optoelectronic tweezers as the effect requires light excitation to take place.<ref name="Carrascosa M 2015">{{cite journal | last1=Carrascosa | first1=M. | last2=García-Cabañes | first2=A. | last3=Jubera | first3=M. | last4=Ramiro | first4=J. B. | last5=Agulló-López | first5=F. | title=LiNbO<sub>3</sub>: A photovoltaic substrate for massive parallel manipulation and patterning of nano-objects | journal=Applied Physics Reviews | publisher=AIP Publishing | volume=2 | issue=4 | year=2015 | issn=1931-9401 | doi=10.1063/1.4929374 | page=040605| bibcode=2015ApPRv...2d0605C | hdl=10486/669584 | hdl-access=free }}</ref><ref name="García-Cabañes A 2018">{{cite journal | last1=García-Cabañes | first1=Angel | last2=Blázquez-Castro | first2=Alfonso | last3=Arizmendi | first3=Luis | last4=Agulló-López | first4=Fernando | last5=Carrascosa | first5=Mercedes | title=Recent Achievements on Photovoltaic Optoelectronic Tweezers Based on Lithium Niobate | journal=Crystals | publisher=MDPI AG | volume=8 | issue=2 | date=2018-01-30 | issn=2073-4352 | doi=10.3390/cryst8020065 | page=65| doi-access=free | hdl=10486/681685 | hdl-access=free }}</ref> This effect allows for fine manipulation of micrometer-scale particles with high flexibility since the tweezing action is constrained to the illuminated area. The effect is based on the very high electric fields generated during light exposure (1–100 kV/cm) within the illuminated spot. These intense fields are also finding applications in biophysics and biotechnology, as they can influence living organisms in a variety of ways.<ref name="Blázquez-Castro A 2018">{{cite journal | last1=Blázquez-Castro | first1=A. | last2=García-Cabañes | first2=A. | last3=Carrascosa | first3=M. | title=Biological applications of ferroelectric materials | journal=Applied Physics Reviews | publisher=AIP Publishing | volume=5 | issue=4 | year=2018 | issn=1931-9401 | doi=10.1063/1.5044472 | page=041101| arxiv=2109.00429 | bibcode=2018ApPRv...5d1101B | s2cid=139511670 }}</ref> For example, iron-doped lithium niobate excited with visible light has been shown to produce cell death in tumoral cell cultures.<ref name="Blázquez-Castro A 2011">{{cite journal | last1=Blázquez-Castro | first1=Alfonso | last2=Stockert | first2=Juan C. | last3=López-Arias | first3=Begoña | last4=Juarranz | first4=Angeles | last5=Agulló-López | first5=Fernando | last6=García-Cabañes | first6=Angel | last7=Carrascosa | first7=Mercedes | title=Tumour cell death induced by the bulk photovoltaic effect of LiNbO<sub>3</sub>:Fe under visible light irradiation | journal=Photochemical & Photobiological Sciences | publisher=Springer Science and Business Media LLC | volume=10 | issue=6 | year=2011 | pages=956–963 | issn=1474-905X | doi=10.1039/c0pp00336k | pmid=21336376 | doi-access=free }}</ref>

==Periodically poled lithium niobate (PPLN)==
'''Periodically poled lithium niobate''' ('''PPLN''') is a domain-engineered lithium niobate crystal, used mainly for achieving [[quasi-phase-matching]] in [[nonlinear optics]]. The [[ferroelectric]] domains point alternatively to the ''+c'' and the ''−c'' direction, with a period of typically between 5 and 35&nbsp;[[micrometre|μm]]. The shorter periods of this range are used for [[second-harmonic generation]], while the longer ones for [[Optical parametric oscillator|optical parametric oscillation]]. [[Periodic poling]] can be achieved by electrical poling with periodically structured electrode. Controlled heating of the crystal can be used to fine-tune [[phase matching]] in the medium due to a slight variation of the dispersion with temperature.

Periodic poling uses the largest value of lithium niobate's nonlinear tensor, ''d''<sub>33</sub> = 27&nbsp;pm/V. Quasi-phase-matching gives maximum efficiencies that are 2/π (64%) of the full ''d''<sub>33</sub>, about 17&nbsp;pm/V.<ref>{{cite journal |doi=10.1007/s003400100623 |title=Fabrication of periodically poled lithium tantalate for UV generation with diode lasers |journal=Applied Physics B |volume=73 |issue=2 |pages=111–114 |year=2001 |last1=Meyn |first1=J.-P. |last2=Laue |first2=C. |last3=Knappe |first3=R. |last4=Wallenstein |first4=R.|last5=Fejer |first5=M. M. |bibcode=2001ApPhB..73..111M |s2cid=119763435}}</ref>

Other materials used for [[periodic poling]] are wide-[[band-gap]] inorganic crystals like [[potassium titanyl phosphate|KTP]] (resulting in [[periodically poled KTP]], [[PPKTP]]), [[lithium tantalate]], and some organic materials.

The periodic-poling technique can also be used to form surface [[nanostructure]]s.<ref>{{cite journal |title=Surface nanoscale periodic structures in congruent lithium niobate by domain reversal patterning and differential etching |journal=Applied Physics Letters |volume=87 |issue=23 |pages=233106 |year=2005 |doi=10.1063/1.2137877|bibcode=2005ApPhL..87w3106G |last1=Grilli |first1=Simonetta |last2=Ferraro |first2=Pietro |last3=De Natale |first3=Paolo |last4=Tiribilli |first4=Bruno |last5=Vassalli |first5=Massimo |doi-access=free }}</ref><ref>{{cite journal |title=Modulating the thickness of the resist pattern for controlling size and depth of submicron reversed domains in lithium niobate |journal=Applied Physics Letters |volume=89 |issue=13 |pages=133111 |year=2006 |doi=10.1063/1.2357928| bibcode =2006ApPhL..89m3111F |last1=Ferraro |first1=P. |last2=Grilli |first2=S. }}</ref>

However, due to its low photorefractive damage threshold, PPLN only finds limited applications, namely, at very low power levels. MgO-doped lithium niobate is fabricated by periodically poled method. Periodically poled MgO-doped lithium niobate (PPMgOLN) therefore expands the application to medium power level.

===Sellmeier equations===
The [[Sellmeier equation]]s for the extraordinary index are used to find the poling period and approximate temperature for quasi-phase-matching. Jundt<ref name="Jundt">{{cite journal |author=Jundt, Dieter H. |journal=Optics Letters |volume=22 |title=Temperature-dependent Sellmeier equation for the index of refraction <math>n_e</math> in congruent lithium niobate |year=1997 |pages=1553–1555 |doi=10.1364/OL.22.001553 |pmid=18188296 |issue=20 |bibcode=1997OptL...22.1553J}}</ref> gives

: <math>
  n^2_e \approx 5.35583 + 4.629 \times 10^{-7} f
                + \frac{0.100473 + 3.862 \times 10^{-8} f}{\lambda^2 - (0.20692 - 0.89 \times 10^{-8} f)^2}
                + \frac{100 + 2.657 \times 10^{-5} f}{\lambda^2 - 11.34927^2}
                - 1.5334 \times 10^{-2} \lambda^2,
</math>

valid from 20 to 250&nbsp;°C for wavelengths from 0.4 to 5&nbsp;[[Micrometre|micrometer]]s, whereas for longer wavelengths,<ref name=Deng>{{cite journal |journal=Optics Communications |volume=268 |title=Improvement to Sellmeier equation for periodically poled LiNbO<sub>3</sub> crystal using mid-infrared difference-frequency generation |issue=1 |year=2006 |pages=110–114 |doi=10.1016/j.optcom.2006.06.082 |bibcode=2006OptCo.268..110D |last1=Deng |first1=L. H. |last2=Gao |first2=X. M. |last3=Cao |first3=Z. S. |last4=Chen |first4=W. D. |last5=Yuan |first5=Y.Q. |last6=Zhang |first6=W. J. |last7=Gong |first7=Z. B. }}</ref>

: <math>
  n^2_e \approx 5.39121 + 4.968 \times 10^{-7} f
                + \frac{0.100473 + 3.862 \times 10^{-8} f}{\lambda^2 - (0.20692 - 0.89 \times 10^{-8} f)^2}
                + \frac{100 + 2.657 \times 10^{-5} f}{\lambda^2 - 11.34927^2}
                - (1.544 \times 10^{-2} + 9.62119 \times 10^{-10} \lambda) \lambda^2,
</math>

which is valid for ''T'' = 25 to 180&nbsp;°C, for wavelengths λ between 2.8 and 4.8 micrometers.

In these equations ''f'' = (''T'' − 24.5)(''T'' + 570.82), λ is in micrometers, and ''T'' is in °C.

More generally for ordinary and extraordinary index for MgO-doped {{chem2|LiNbO3}}:

: <math>{
  n^2 \approx a_1 + b_1 f
              + \frac{a_2 + b_2 f}{\lambda^2 - (a_3 + b_3 f)^2}
              + \frac{a_4 + b_4 f}{\lambda^2 - a_5^2}
              - a_6 \lambda^2,
}</math>

with:
{| class="wikitable centre"
|-
! rowspan=2 | Parameters !! colspan="2" | 5% MgO-doped CLN !! 1% MgO-doped SLN
|-
! ''n''<sub>e</sub> !! ''n''<sub>o</sub> !! ''n''<sub>e</sub>
|-
| ''a''<sub>1</sub> || 5.756  || 5.653  || 5.078
|-
| ''a''<sub>2</sub> || 0.0983 || 0.1185 || 0.0964
|-
| ''a''<sub>3</sub> || 0.2020 || 0.2091 || 0.2065
|-
| ''a''<sub>4</sub> || 189.32 || 89.61  || 61.16
|-
| ''a''<sub>5</sub> || 12.52  || 10.85  || 10.55
|-
| ''a''<sub>6</sub> || 1.32×10<sup>−2</sup>  ||  1.97×10<sup>−2</sup>  ||  1.59×10<sup>−2</sup>
|-
| ''b''<sub>1</sub> || 2.860×10<sup>−6</sup> ||  7.941×10<sup>−7</sup> ||  4.677×10<sup>−7</sup>
|-
| ''b''<sub>2</sub> || 4.700×10<sup>−8</sup> ||  3.134×10<sup>−8</sup> ||  7.822×10<sup>−8</sup>
|-
| ''b''<sub>3</sub> || 6.113×10<sup>−8</sup> || −4.641×10<sup>−9</sup> || −2.653×10<sup>−8</sup>
|-
| ''b''<sub>4</sub> || 1.516×10<sup>−4</sup> || −2.188×10<sup>−6</sup> ||  1.096×10<sup>−4</sup>
|}
for congruent {{chem2|LiNbO3}} (CLN) and stochiometric {{chem2|LiNbO3}} (SLN).<ref name=gayer>{{cite journal |journal=Appl. Phys. B |volume=91 |issue=2 |title=Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO<sub>3</sub> |year=2008 |pages=343–348 |doi=10.1007/s00340-008-2998-2 |bibcode=2008ApPhB..91..343G |s2cid=195290628 |last1=Gayer |first1=O. |last2=Sacks |first2=Z. |last3=Galun |first3=E. |last4=Arie |first4=A. }}</ref>

==See also==
<!-- alphabetic order -->
{{div col|colwidth=22em}}
*[[Crystal]]
*[[Crystal structure]]
*[[Crystallite]]
*[[Crystallization]] and [[Crystallization (engineering aspects)|engineering aspects]]
*[[Seed crystal]]
*[[Single crystal]]
*[[Laser-heated pedestal growth]]
*[[Micro-Pulling-Down]]
*[[Nickel niobate]]{{div col end}}

==References==
{{reflist|30em}}

==Cited sources==
*{{cite book |ref=Haynes| editor= Haynes, William M. | date = 2016| title = [[CRC Handbook of Chemistry and Physics]] | edition = 97th | publisher = [[CRC Press]] | isbn = 9781498754293 }}

==External links==
*[https://web.archive.org/web/20040710120217/http://www.inrad.com/pdf/Inrad_datasheet_LNB.pdf Inrad data sheet on lithium niobate]

{{Lithium compounds}}
{{Niobium compounds}}

[[Category:Lithium salts]]
[[Category:Niobates]]
[[Category:Ferroelectric materials]]
[[Category:Nonlinear optical materials]]
[[Category:Crystals]]
[[Category:Second-harmonic generation]]