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Crystaline materials, Notas de estudo de Física

Universidade do Estado do Rio de Janeiro (UERJ)Física

MATERIAIS CRISTALINOS E SUAS PROPRIEDADES DE OPTICA EM INGLES

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Section 1: Crystalline Materials

1.1 Introduction

1.2 Physical Properties

1.3 Optical Properties

1.4 Mechanical Properties

1.5 Thermal Properties

1.6 Magnetooptic Properties

1.7 Electrooptic Properties

1.8 Elastooptic Properties

1.9 Nonlinear Optical Properties

Descubra Notas de estudo de Física Universidade do Estado do Rio de Janeiro (UERJ)

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Section 1: Crystalline Materials

1.1 Introduction

1. 2 Physical Properties

1. 3 Optical Properties

1. 4 Mechanical Properties

1. 5 Thermal Properties

1. 6 Magnetooptic Properties

1.7 Electrooptic Properties

1.8 Elastooptic Properties

1.9 Nonlinear Optical Properties

Section 1: Crystalline Materials 3

Section 1

CRYSTALLINE MATERIALS

1.1 Introduction*

Crystalline materials included in this section are insulators and semiconductors that have a

transparent region within the range from the vacuum ultraviolet (from ~100 nm) to the

infrared (up to 100 μm) portion of the electromagnetic spectrum. Crystals with wide band

gaps are transparent from the ultraviolet through the visible region; crystals with a narrower

band gap may appear opaque but are transparent in the infrared region. Using this broad

transparency definition of optical crystals, virtually all known crystals can be included.

Coverage, however, is limited to those crystals which either occur in nature or are produced

in the laboratory for optical use or with potential for such use. For this reason hydrate or

hydroxide crystals are generally excluded because they are thermally less stable and have

limited tranmission range due to OH absorption. Highly hygroscopic materials are also

excluded because of the obvious difficulty of handling, unless they have already been used,

such as urea, KDP, CD*A, etc. Only pure compounds are considered. Compounds

containing elements having intrinsic absorptions due to incompletely filled d or f shell

electrons are also avoided.

Other critical issues for the use of optical crystals are solid-state phase transitions that occur

as a function of both temperature and pressure and polymorphism. Compounds that have a

very small stability field or serious phase transition problems have limited use as optical

materials. Phase change and decomposition temperatures of crystals are noted in Section 1.

on thermal properties. Generally only the thermodynamically stable structure at room

temperature and pressure are listed in this section. Compounds that have naturally occurring

polymorphic forms are included, however, e.g., CaCO 3 , TiO 2 , and aluminum silicate

Al 2 SiO 5. In other cases, only the stable phase is listed, e.g., quartz (α-SiO 2 ).

Many compounds were considered appropriate as entries of optical crystals in Sections

1.1–1.3 regardless of the amount of information available. As Chai* has noted, merely

showing the existence of a compound with its chemical constituents can help to estimate the

stability of its isomorphs and the structural tolerance of doping or other modifications. Most

of the basic material properties such as optical transparency and refractive indices of an

unstudied compound can be estimated with reasonable accuracy based on its better studied

isomorphs that have measured properties listed in the tables.

Optical crystals in Sections 1.1–1.3 are classified into three categories:

Isotropic crystals include materials through which monochromatic light travels with the

same speed, regardless of the direction of vibration, and the vibration direction of a light ray

is always perpendicular to the ray path. Whereas amorphous materials such as glasses and

plastics are isotropic, only those crystals with cubic symmetry are isotropic.

* This section was adapted from “Optical crystals” by B. H. T. Chai, Handbook of Laser

Science and Technology, Suppl. 2, Optical Materials (CRC Press, Boca Raton, FL, 1995), p.

3 ff (with additions).

Crystallographic Point Groups and Properties

Crystal system

International symbol

Schoenflies symbol

Centro- symmetric

Piezo- electric

Pyro- electric

Cubic m3m O (^) h −43m T (^) d 432 O m3 T (^) h 23 T

Hexagonal 6/mmm D (^) 6h −6m2 D (^) 3h 6mm C (^) 6v 622 D (^6) 6/m C (^) 6h − 6 C (^) 3h 6 C (^6)

Tetragonal 4/mmm D (^) 4h −42m D (^) 2d 4mm C (^) 4v 422 D (^4) 4/m C (^) 4h − 4 S (^4) 4 C (^4)

Trigonal −3m D (^) 3d 3m C (^) 3v 32 D (^3) − 3 S (^6) 3 C (^3)

Orthorhombic mmm D (^) 2h mm2 C (^) 2v 222 D (^2)

Monoclinic 2/m C (^) 2h m C (^) s 2 C (^2)

Triclinic − 1 C (^) i 1 C (^1)

Crystals in the following table are listed alphabetically by chemical name (with mineral

name* and acronym in parentheses) and include the chemical formula, crystal system, and

space group. In the space group notation, a negative number indicates inversion symmetry.

A mineralogy database containing names, physical properties, and an audio pronunciation guide for a very large number of materials is available at www.webmineral.com.

Name, Formula, Crystal System, and Space Group for Optical Crystals

Name Formula

Crystal system (Space group)

Aluminum antimonide AlSb Cubic (F−43m) Aluminum arsenate AlAsO 4 Trigonal (P3 1 2) Aluminum arsenide AlAs Cubic (F−43m) Aluminum borate AlBO 3 Trigonal (R − 3 c) Aluminum borate Al 4 B 2 O 9 Orthorhombic (Pbam) Aluminum fluoride AlF 3 Rhombohedral (R32) Aluminum fluorosilicate (topaz) Al 2 SiO 4 F 2 Orthorhombic (Pbnm) Aluminum gallate AlGaO 3 Hexagonal (P6 3 mmc) Aluminum germanate Al 2 Ge 2 O 7 Monoclinic (C2/c) Aluminum germanate Al 6 Ge 2 O 13 Orthorhombic (Pbnm) Aluminum germanate Al 6 Ge 2 O 13 Orthorhombic (Pbnm) Aluminum hafnium tantalate AlHfTaO 6 Orthorhombic (Pbcn) Aluminum molybdate Al 2 (MoO 4 ) 3 Monoclinic (P2 1 /a) Aluminum niobate AlNbO 4 Monoclinic (C2/m) Aluminum nitride AlN Hexagonal (6 3 mc) Aluminum oxide (corundum, sapphire, alumina) Al 2 O 3 Trigonal (R − 3 c) Aluminum oxynitrate (ALON) Al 23 O 27 N 5 Cubic (F d 3m) Aluminum phosphate (berlinite) AlPO 4 Trigonal (P3 1 2) Aluminum phosphide AlP Hexagonal (6 3 mc) Aluminum silicate (andalusite) Al 2 SiO 5 Orthorhombic (Pmam) Aluminum silicate (kyanite) Al 2 SiO 5 Triclinic (P − 1 ) Aluminum silicate (mullite) Al 6 Si 2 O 13 Orthorhombic (Pbnm) Aluminum silicate (sillimanite) Al 2 SiO 5 Orthorhombic (Pbnm) Aluminum tantalate (alumotantite) AlTaO 4 Orthorhombic (Pc2 1 n) Aluminum titanium tantalate AlTiTaO 6 Tetragonal (P4 2 /mmm) Aluminum tungstate Al 2 (WO 4 ) 3 Orthorhombic (Pcna) Amino carbonyl (urea) (NH 2 ) 2 CO Tetragonal (I−42m) Ammonium aluminum selenate NH 4 Al(SeO 4 ) 2 Trigonal (P321) Ammonium aluminum sulfate NH 4 Al(SO 4 ) 2 Trigonal (P321) Ammonium dihydrogen phosphate (ADP) NH 4 H 2 PO 4 Tetragonal (I−42m) Ammonium gallium selenate NH 4 Ga(SeO 4 ) 2 Trigonal (P321) Ammonium gallium sulfate NH 4 Ga(SO 4 ) 2 Trigonal (P321) Ammonium pentaborate NH 4 B 5 O 8 • 4H 2 O Orthorhombic (Aba2) Antimony niobate (stibiocolumbite) SbNbO 4 Orthorhombic (Pna2 1 ) Antimony oxide (senarmontite) Sb 2 O 3 Cubic (Fd3m)

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Barium magnesium fluoride BaMgF 4 Orthorhombic (A2 1 am) Barium magnesium fluoride Ba 2 MgF 6 Tetragonal (I422) Barium magnesium germanate Ba 2 MgGe 2 O 7 Tetragonal (P42 1 m) Barium magnesium silicate Ba 2 MgSi 2 O 7 Tetragonal (P42 1 m) Barium magnesium tantalate Ba 3 MgTa 2 O 9 Cubic (Fm3m) Barium magnesium vanadate BaMg 2 (VO 4 ) 2 Tetragonal (I4 1 /acd) Barium molybdate BaMoO 4 Tetragonal (I4 1 /a) Barium niobate BaNb 2 O 6 Orthorhombic (Pcan) Barium nitrate (nitrobarite) Ba(NO 3 ) 2 Cubic (P2 1 3) Barium scandate Ba 2 Sc4 O 9 Trigonal(R−3) Barium scandate BaSc 2 O 4 Monoclinic (C2/c) Barium scandate Ba 6 Sc6 O 15 Tetragonal Barium silicate (sabbornite) β-BaSi 2 O 5 Orthorhombic (Pmnb) Barium sodium niobate Ba 2 NaNb 5 O 15 Orthorhombic (Im2a) Barium sodium phosphate Ba 2 Na(PO 5 ) 5 Orthorhombic (P212121)) Barium strontium niobate Ba 3 SrNb 2 O 9 Hexagonal (P63/mmc) Barium strontium tantalate Ba 3 SrTa 2 O 9 Hexagonal (P63/mmc) Barium sulfate (barite) BaSO 4 Orthorhombic (Pbnm) Barium tantalate BaTa 2 O 6 Orthorhombic (Pcan) Barium tantalate BaTa 2 O 6 Orthorhombic (Pcan) Barium tin borate BaSnB 2 O 6 Trigonal(R−3) Barium tin silicate (pabstite) BaSnSi 3 O 9 Hexagonal (P − 6 c2) Barium titanate BaTiO 3 Cubic (Fm3m) Barium titanate BaTiO 3 Tetragonal (Pm3m) Barium titanium aluminate BaTiAl 6 O 12 Orthorhombic (Pnnm) Barium titanium aluminate Ba 3 TiAl 10 O 20 Monoclinic (C2/m) Barium titanium borate BaTiB 2 O 6 Trigonal(R−3) Barium titanium gallate BaTiGa 6 O 12 Orthorhombic (Pnnm) Barium titanium oxide BaTi 4 O 9 Orthorhombic (Pnmm) Barium titanium silicate (benitoite) BaTiSi 3 O 9 Hexagonal (P − 6 c2) Barium titanium silicate (fresnoite) Ba 2 TiSi 2 O 8 Tetragonal (P4bm) Barium tungstate BaWO 4 Tetragonal (I4 1 /a) Barium vanadate Ba 3 (VO 4 ) 2 Rhombohedral (R − 3 m) Barium yttrium borate Ba 3 Lu(BO 3 ) 3 Hexagonal(P6 3 cm) Barium yttrium fluoride BaY 2 F 8 Monoclinic (C2/m) Barium yttrium oxide BaY 2 O 4 Orthorhombic (Pnab) Barium zinc aluminum fluoride Ba 2 ZnAlF 9 Orthorhombic (Pnma) Barium zinc fluoride BaZnF 4 Othorhombic (C222) Barium zinc fluoride Ba 2 Zn 3 F 10 Monoclinic (C2/m) Barium zinc fluoride Ba 2 ZnF 6 Tetragonal (I422) Barium zinc gallium fluoride Ba 2 ZnGaF 9 Monoclinic (P21/n) Barium zinc germanate BaZnGeO 4 Hexagonal (P6 3 ) Barium zinc germanate Ba 2 ZnGe 2 O 7 Tetragonal (P42 1 m)

Section 1: Crystalline Materials 9

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Barium zinc silicate Ba 2 ZnSi 2 O 7 Tetragonal (P42 1 m) Barium zinc silicate BaZnSiO 4 Hexagonal (P6 3 ) Barium zirconium silicate Ba 2 ZrSi 2 O 8 Tetragonal (P4bm) Barium zirconium silicate Ba 2 Zr 2 Si 3 O 12 Cubic (P2 1 3) Barium zirconium silicate (bazirite) BaZrSi 3 O 9 Hexagonal (P6 3 22) Beryllium aluminate BeAl 6 O 10 Orthorhombic (Pca2) Beryllium aluminate (chrysoberyl) BeAl 2 O 4 Orthorhombic (Pnma) Beryllium aluminum silicate (beryl) Be 3 Al2 Si 6 O 18 Hexagonal (P6/mcc) Beryllium fluoroborate (hambergite) Be 2 BO 3 F Monoclinic (C21) Beryllium germanate Be 2 GeO 4 Trigonal(R−3) Beryllium magnesium aluminate (taaffeite) BeMg 3 Al8 O 16 Hexagonal Beryllium oxide (bormellite) BeO Hexagonal (P6 3 /mc) Beryllium scandium silicate (bazzite) Be 3 Sc2 Si 6 O 18 Hexagonal (P6/mcc) Beryllium silicate (phenakite) Be 2 SiO 4 Trigonal(R−3) Bismuth aluminate Bi 2 Al4 O 9 Orthorhombic (Pbam) Bismuth antimonate BiSbO 4 Monoclinic (P2 1 /c) Bismuth borate Bi 4 B 2 O 9 Monoclinic (P2 1 /c) Bismuth germanate Bi 2 Ge 3 O 9 Hexagonal (P6 3 /m) Bismuth germanate Bi 2 GeO 5 Orthorhombic (Cmc2 1 ) Bismuth germanate Bi 12 GeO 20 Cubic (I23) Bismuth germanate (BGO) Bi 4 Ge 3 O 12 Cubic (I43d) Bismuth metaborate BiB 3 O 6 Monoclinic (2/m) Bismuth molybdate Bi 2 Mo 2 O 9 Monoclinic (P2 1 /m) Bismuth molybdate Bi 2 Mo 3 O 12 Monoclinic (P2 1 /m) Bismuth niobate BiNbO 4 Orthorhombic (Pann) Bismuth oxide (bismite) Bi 2 O 3 Monoclinic (P2 1 /c) Bismuth oxymolybdate (koechlinite) γ-Bi 2 MoO 6 Orthorhombic (Pba2) Bismuth oxytungstate (rusellite) Bi 2 WO 6 Orthorhombic (Pba2) Bismuth silicate Bi 2 SiO 5 Orthorhombic (Cmc2 1 ) Bismuth silicate (eulytite) Bi 4 Si 3 O 12 Cubic (I43d) Bismuth silicate (sillenite, BSO) Bi 12 SiO 20 Cubic (I23) Bismuth tantalate BiTaO 4 Orthorhombic (Pnna) Bismuth tin oxide Bi 2 Sn 2 O 7 Hexagonal (P6 3 /m) Bismuth titanate Bi 4 Ti 3 O 12 Orthorhombic (B2cb) Bismuth titanium niobate Bi 3 TiNbO 9 Orthorhombic (A2 1 am) Bismuth titanium oxide Bi 12 TiO 20 Cubic (I23) Bismuth vanadate (clinobisvanite) BiVO 4 Monoclinic (I2/a) Bismuth vanadate (dreyerite) BiVO 4 Tetragonal (I4 1 /amd) Bismuth vanadate (pucherite) BiVO 4 Orthorhombic (Pnca) Boron nitride BN Cubic (F−43m) Boron phosphide BP Cubic (F−43m) Cadmium antimonade Cd 2 Sb 2 O 7 Cubic (Fd3m) Cadmium borate CdB 4 O 7 Orthorhombic (Pbca)

Section 1: Crystalline Materials 11

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Calcium aluminum germanate Ca 2 Al2 GeO 7 Tetragonal (P42 1 m) Calcium aluminum germanate Ca 3 Al2 Ge 3 O 12 Cubic (Ia3d) Calcium aluminum oxyfluoride Ca 2 Al3 O 6 F Hexagonal Calcium aluminum silicate (anorthite) CaAl 2 Si 2 O 8 Triclinic(P−1) Calcium aluminum silicate (gehlenite, CAS) Ca 2 Al2 SiO 7 Tetragonal (P42 1 m) Calcium aluminum silicate (grossularite) Ca 3 Al2 Si 3 O 12 Cubic (Ia3d) Calcium antimonate Ca 2 Sb 2 O 7 Orthorhombic (Imm2) Calcium antimonate Ca 2 Sb 2 O 7 Cubic (Fd3m) Calcium barium carbonate (alstonite) CaBa(CO 3 ) 2 Orthorhombic (Pnam) Calcium beryllium fluorophosphate (herderite) CaBe(PO 4 )F Monoclinic Calcium beryllium phosphate (hurlbutite) CaBe 2 (PO 4 ) 2 Monoclinic (P2 1 /a) Calcium beryllium silicate (gugiaite) Ca 2 BeSi 2 O 7 Tetragonal (P42 1 m) Calcium borate Ca 2 B 2 O 5 Monoclinic (P2 1 /a) Calcium borate Ca 2 B 6 O 11 Monoclinic (P2 1 /b) Calcium borate CaB 4 O 7 Monoclinic (P2 1 /c) Calcium borate Ca 3 B 2 O 6 Rhombohedral (R−3c) Calcium borate (calciborite) CaB 2 O 4 Orthorhombic (Pnca) Calcium boron silicate (danburite) CaB 2 Si 2 O 8 Orthorhombic (Pmam) Calcium carbonate (aragonite) CaCO 3 Orthorhombic (Pnam) Calcium carbonate (calcite) CaCO 3 Rhombohedral (R−3c)) Calcium carbonate (vaterite) CaCO 3 Hexagonal (P6 3 /mmc) Calcium chloroarsenate Ca 2 AsO 4 Cl Orthorhombic (Pbcm) Calcium chloroarsenate Ca 5 (AsO 4 ) 3 Cl Hexagonal(P6 3 /m) Calcium chloroborate Ca 2 BO 3 Cl Monoclinic (P2 1 /c) Calcium chloroborate Ca 2 B 5 O 9 Cl Tetragonal (P4 2 2 1 2) Calcium chlorophosphate Ca 2 PO 4 Cl Orthorhombic (Pbcm) Calcium chlorophosphate (chlorapatite) Ca 5 (PO 4 ) 3 Cl Hexagonal(P6 3 /m) Calcium chlorovanadate Ca 2 VO 4 Cl Orthorhombic (Pbcm) Calcium chlorovanadate Ca 5 (VO 4 ) 3 Cl Hexagonal(P6 3 /m) Calcium fluoride (fluorite, fluorspar, Irtran 3) CaF 2 Cubic (Fm3m) Calcium fluoroarsenate (svabite, CAAP) Ca 5 (AsO 4 ) 3 F Hexagonal(P6 3 /m) Calcium fluoroborate (fabianite) CaB 3 O 5 F Orthorhombic (Pbn2 1 ) Calcium fluorophosphate (apatite, FAP) Ca 5 (PO 4 ) 3 F Hexagonal(P6 3 /m) Calcium fluorophosphate (spodiosite) Ca 2 (PO 4 )F Orthorhombic (Pbcm) Calcium fluorovanadate (VAP) Ca 5 (VO 4 ) 3 F Hexagonal(P6 3 /m) Calcium gadolinium aluminate CaGaAlO 4 Hexagonal (P6 3 /m) Calcium gadolinium double borate Ca 3 Gd 2 (BO 3 ) 4 Orthorhombic (Pc2 1 n) Calcium gadolinium oxysilicate CaGd 4 (SiO 4 ) 3 O Tetragonal (I4/mmm) Calcium gadolinium phosphate Ca 3 Gd(PO 4 ) 3 Cubic (I–43d) Calcium gallate CaGa 2 O 4 Monoclinic (P2 1 /c) Calcium gallate Ca 3 Ga 4 O 9 Orthorhombic (Cmm2) Calcium gallate Ca 5 Ga 6 O 14 Orthorhombic (Cmc2 1 ) Calcium gallium germanate Ca 2 Ga 2 GeO 7 Tetragonal (P42 1 m)

12 Handbook of Optical Materials

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Calcium gallium germanate Ca 3 Ga 2 Ge 4 O 14 Trigonal (P32 1 ) Calcium gallium germanium garnet Ca 3 Ga 2 Ge 3 O 12 Cubic (Ia3d) Calcium gallium silicate (CGS) Ca 2 Ga 2 SiO 7 Tetragonal (P42 1 m) Calcium germanate CaGe 2 O 5 Monoclinic (P2 1 /a) Calcium germanate CaGe 4 O 9 Hexagonal (P –6c2) Calcium hexa-aluminate CaAl 12 O 19 Hexagonal (P63/mmc) Calcium indate CaIn 2 O 4 Orthorhombic (Pbcm) Calcium indium germanate Ca 3 In 2 Ge 3 O 12 Cubic (Ia3d) Calcium indium oxide Ca 3 In 2 O 6 Orthorhombic (Pbam) Calcium iodate (lautarite) Ca(IO 3 ) 2 Monoclinic Calcium lanthanum aluminate CaLaAlO 4 Tetragonal (I4/mmm) Calcium lanthanum borate CaLaBO 4 Hexagonal (P6 3 22) Calcium lanthanum oxyphosphate Ca 4 La(PO 4 ) 3 O Hexagonal (P6 3 /m) Calcium lanthanum oxysilicate CaLa 4 (SiO 4 ) 3 O Hexagonal (P6 3 /m) Calcium lanthanum phosphate Ca 3 La(PO 4 ) 3 Cubic (I –43d) Calcium lanthanum sulfide CaLa 2 S 4 Cubic (I –43d) Calcium lithium magnesium vanadate Ca 2 LiMg 2 V 3 O 12 Cubic (Ia3d) Calcium lithium magnesium vanadate Ca 3 LiMgV3 O 12 Cubic (Ia3d) Calcium lithium zinc vanadate Ca 2 LiZn2 V 3 O 12 Cubic (Ia3d) Calcium lithium zinc vanadate Ca 3 LiZnV 3 O 12 Cubic (Ia3d) Calcium lutetium germanate Ca 3 Lu 2 Ge 3 O 12 Cubic (Ia3d) Calcium magnesium borate (kurchatovite) CaMgB 2 O 5 Orthorhombic Calcium magnesium carbonate (dolomite) CaMg(CO 3 ) 2 Rhombohedral (R−3c) Calcium magnesium carbonate (huntite) CaMg 3 (CO 3 ) 4 Rhombohedral (R32) Calcium magnesium fluoroarsenate (tilasite) CaMgAsO 4 F Orthorhombic Calcium magnesium fluorophosphate (isokite) CaMgPO 4 F Monoclinic (C2/c) Calcium magnesium germanate CaMgGe 2 O 6 Monoclinic (C2/c) Calcium magnesium silicate (akermanite) Ca 2 MgSi 2 O 7 Tetragonal (P42 1 m) Calcium magnesium silicate (diopside) CaMgSi 2 O 6 Monoclinic (C2/c) Calcium magnesium silicate (merwinite) Ca 3 MgSi 2 O 8 Monoclinic (P2 1 /a) Calcium magnesium silicate (monticellite) CaMgSiO 4 Orthorhombic (Pmnb) Calcium magnesium vanadate CaMg 2 (VO 4 ) 2 Tetragonal (I4 1 /acd) Calcium molybdate CaMoO 4 Tetragonal (I4 1 /a) Calcium niobate Ca 2 Nb 2 O 7 Orthorhombic (Pn2 1 a) Calcium niobate (rynersonite) CaNb 2 O 6 Orthorhombic (Pcan) Calcium niobium gallium garnet Ca 3 (Nb,Ga) 2 Ga 3 O 12 Cubic (Ia3d) Calcium oxide (lime) CaO Cubic (Fm3m) Calcium phosphate β-CaP 2 O 7 Hexagonal (P − 6 c2) Calcium phosphate β-CaP 2 O 7 Tetragonal (P4 1 ) Calcium scandate CaSc 2 O 4 Orthorhombic (Pnam) Calcium scandium germanate Ca 3 Sc2 Ge 3 O 12 Cubic (Ia3d) Calcium scandium silicate Ca 3 Sc2 Si 3 O 12 Cubic (Ia3d) Calcium silicate (larnite) b-Ca 2 SiO 4 Monoclionic (P2 1 /n)

14 Handbook of Optical Materials

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Cesium dideuterium arsenate CsD 2 AsO 4 Tetragonal (I−42m) Cesium dideuterium phosphate CsD 2 PO 4 Tetragonal (I−42m) Cesium dihydrogen arsenate CsH 2 AsO 4 Tetragonal (I−42m) Cesium dihydrogen phosphate CsH 2 PO 4 Tetragonal (I−42m) Cesium fluoride CsF Cubic (Fm3m) Cesium gadolinium molybdate CsGd(MoO 4 ) 2 Orthorhombic (Pnma) Cesium gallium sulfate CsGa(SO 4 ) 2 Trigonal (P321) Cesium germanate Ga 2 GeO 5 Orthorhombic (Pnnm) Cesium iodide CsI Cubic (Fm3m) Cesium lanthanum tungstate CsLa(WO 4 ) 2 Tetragonal (P4 2 /nmc) Cesium lithium aluminum fluoride Cs 2 LiAl 3 F 12 Rhombohedral (R–3m) Cesium lithium aluminum fluoride Cs 2 LiAlF 6 Hexagonal (P6 3 /mmc) Cesium lithium beryllium fluoride CsLiBeF 4 Monoclinic (P2 1 /n) Cesium lithium borate (CLBO) CsLiB 6 O 10 Tetragonal (I−42d) Cesium lithium gallium fluoride Cs 2 LiGa 3 F 12 Rhombohedral (R–3m) Cesium lithium gallium fluoride Cs 2 LiGaF 6 Hexagonal (P6 3 /mmc) Cesium lithium sulfate CsLiSO 4 Orthorhombic (Pc2) Cesium magnesium chloride Cs 2 MgCl 4 Orthorhombic (Pnma) Cesium mercury iodide Cs 2 HgI 4 Monoclinic (P2 1 ) Cesium niobium borate (CNB) CsNbB 2 O 6 Orthorhombic (Pn2 1 m) Cesium niobium sulfate CsNbO(SO 4 ) 2 Orthorhombic Cesium potassium aluminum fluoride Cs 2 KAl 3 F 12 Rhombohedral (R–3m) Cesium potassium lanthanum fluoride Cs 2 KLaF 6 Cubic (Fm3m) Cesium scandium molybdate CsSc(MoO 4 ) 2 Trigonal (P−3m1) Cesium scandium tungstate CsSc(WO 4 ) 2 Trigonal (P−3m1) Cesium silver fluoride Cs 2 AgF 4 Tetragonal (I4/mmm) Cesium sodium aluminum fluoride Cs 2 NaAl 3 F 12 Rhombohedral (R–3m) Cesium sodium aluminum fluoride Cs 2 NaAlF 6 Rhombohedral (R–3m) Cesium sodium gallium fluoride Cs 2 NaGaF 6 Rhombohedral (R–3m) Cesium sodium yttrium fluoride Cs 2 NaYF 6 Cubic (Fm3m) Cesium strontium fluoride CsSrF 3 Cubic (Pm3m) Cesium tin germanate Cs 2 SnGe 3 O 9 Hexagonal (P6 3 /m) Cesium titanium germanate Cs 2 TiGe 3 O 9 Hexagonal (P6 3 /m) Cesium titano arsenate (CTA) CsTiOAsO 4 Orthorhombic (P2 1 nb) Cesium zinc aluminum fluoride CsZnAlF 6 Orthorhombic Cesium zinc bromide Cs 2 ZnBr 4 Orthorhombic (Pnma) Cesium zinc chloride Cs 2 ZnCl 4 Orthorhombic (Pnma) Copper bromide (cuprous) CuBr Cubic (Fm3m) Copper chloride (cuprous, nantokite) CuCl Cubic (Fm3m) Copper iodide (cuprous, marshite) CuI Cubic (Fm3m) Cuprous oxide (cuprite) Cu 2 O Cubic (Pm3m) Gadolinium aluminate Gd 4 Al2 O 9 Monoclinic (P2 1 /a) Gadolinium aluminate GdAlO 3 Orthorhombic (Pbnm)

Section 1: Crystalline Materials 15

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Gadolinium aluminum borate GdAl 3 (BO 3 ) 4 Trigonal (R32) Gadolinium aluminum germanate GdAlGe 2 O 7 Monoclinic (P2 1 /c) Gadolinium borate Gd(BO 2 ) 3 Monoclinic (I2/a) Gadolinium borate GdBO 3 Hexagonal (P6 3 /mmc) Gadolinium calcium oxyborate GdCa 4 O(BO 3 ) 3 Monoclinic (Cm) Gadolinium gallium borate GdGa 3 (BO 3 ) 4 Trigonal (R32) Gadolinium gallium garnet (GGG) Gd 3 Ga 5 O 12 Cubic (Ia3d) Gadolinium gallium germanate GdGaGe 2 O 7 Monoclinic (P2 1 /c) Gadolinium germanate Gd 2 GeO 5 Monoclinic (P2 1 /c) Gadolinium germanium beryllate Gd 2 GeBe 2 O 7 Tetragonal (P42 1 m) Gadolinium indate GdInO 3 Hexagonal (P6 3 cm) Gadolinium magnesium borate GdMgB 5 O 10 Monoclinic (P2 1 /c) Gadolinium molybdate Gd 2 (MoO 4 ) 3 Orthorhombic (Pba2) Gadolinium niobate GdNbO 4 Monoclinic (I2/a) Gadolinium niobate Gd 3 NbO 7 Orthorhombic (C222 1 ) Gadolinium orthosilicate Gd 2 SiO 5 Monoclinic (P2 1 /c) Gadolinium oxide Gd 2 O 3 Monoclinic (C2/m) Gadolinium oxymolybdate Gd 2 MoO 6 Monoclinic (I2/c) Gadolinium oxysulfate Gd 2 O 2 SO 4 Orthorhombic Gadolinium oxytungstate Gd 2 WO 6 Monoclinic (I2/c) Gadolinium pentaphosphate GdP 5 O 14 Monoclinic (P21/c) Gadolinium phosphate GdPO 4 Monoclinic (P2 1 /n) Gadolinium scandate GdScO 3 Orthorhombic (Pbnm) Gadolinium scandium aluminum garnet (GSAG) Gd 3 Sc2 Al3 O 12 Cubic (Ia3d) Gadolinium scandium gallium garnet (GSGG) Gd 3 Sc2 Ga 3 O 12 Cubic (Ia3d) Gadolinium strontium borate Gd 2 Sr 3 (BO 3 ) 4 Orthorhombic (P2 1 cn) Gadolinium tantalate Gd 3 TaO 7 Orthorhombic (C222 1 ) Gadolinium titanate Gd 2 Ti 2 O 7 Cubic (Fd3m) Gadolinium tungstate Gd 2 (WO 4 ) 3 Monoclinic (C2/c) Gadolinium vanadate GdVO 4 Tetragonal (I4 1 /amd) Gallium antimonide GaSb Cubic (F−43m) Gallium arsenide GaAs Cubic (F−43m) Gallium germanate α-Ga 4 GeO 8 Monoclinic (C2/m) Gallium molybdate Ga 2 (MoO 4 ) 3 Monoclinic (P2 1 /a) Gallium niobate GaNbO 4 Monoclinic (C2) Gallium nitride - wurtzite α-GaN Hexagonal(P 6 3 m c ) Gallium nitride - zincblende β-GaN Cubic (F−43m) Gallium oxide β-Ga 2 O 3 Monoclinic (A2/m) Gallium phosphate GaPO 4 Trigonal (P3 1 2) Gallium phosphide GaP Cubic (F−43m) Gallium selenide GaSe Hexagonal(P –62m) Gallium sulfide GaS Hexagonal(P –62m) Gallium tungstate Ga 2 (WO 4 ) 3 Orthorhombic (Pcna)

Section 1: Crystalline Materials 17

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Lanthanum germanium beryllate La 2 GeBe 2 O 7 Tetragonal (P42 1 m) Lanthanum indate LaInO 3 Orthorhombic (Pbnm) Lanthanum lutetium gallium garnet (LLGG) La 3 Lu 2 Ga 3 O 12 Cubic (Ia3d) Lanthanum magnesium borate LaMgB 5 O 10 Monoclinic (P2 1 /c) Lanthanum magnesium hexa-aluminate (LMA) LaMgAl 11 O 19 Hexagonal (P6 3 /mmc) Lanthanum metaborate LaB 3 O 6 Monoclinic (I2/a) Lanthanum molbydate La 2 (MoO 4 ) 3 Monoclinic (C2/c) Lanthanum molybdate La 2 (MoO 4 ) 3 Tetragonal (I−42m) Lanthanum niobate LaNbO 4 Monoclinic (I2/a) Lanthanum niobate LaNb 5 O 14 Orthorhombic (Pnam) Lanthanum niobate La 3 NbO 7 Othorhombic (Cmcm) Lanthanum niobogallate La 3 Nb (^) 0.5Ga (^) 5.5O 14 Trigonal (P32 1 ) Lanthanum oxide La 2 O 3 Trigonal (P−3m1) Lanthanum oxybromide LaOBr Tetragonal (P4/nmm) Lanthanum oxymolybdate La 2 MoO 6 Tetragonal (I−42m) Lanthanum oxysulfate La 2 O 2 SO 4 Orthorhombic Lanthanum oxysulfide La 2 O 2 S Trigonal (P−3m) Lanthanum oxytungstate La 2 WO 6 Hexagonal (P6 3 /mmc) Lanthanum pentaphosphate LaP 5 O 14 Orthorhombic (Pcmn) Lanthanum phosphate (monazite) LaPO 4 Monoclinic (P2 1 /n) Lanthanum scandate LaScO 3 Orthorhombic (Pbnm) Lanthanum scandium borate LaSc 3 (BO 3 ) 4 Monoclinic Lanthanum silicate La 2 SiO 5 Monoclinic Lanthanum strontium borate La 2 Sr 3 (BO 3 ) 4 Orthorhombic (P2 1 cn) Lanthanum strontium gallate LaSrGa 3 O 7 Tetragonal (P42 1 m) Lanthanum tantalate La 3 TaO 7 Orthorhombic (Cmcm) Lanthanum tantalogallate La 3 Ta0.5Ga (^) 5.5O 14 Trigonal (P32 1 ) Lanthanum titanate La 2 TiO 5 Orthorhombic (Pnam) Lanthanum titanate La 2 Ti 2 O 7 Monoclinic (P2 1 /c) Lanthanum tungstate La 2 (WO 4 ) 3 Monoclinic (C2/c) Lanthanum yttrium tungstate LaY(WO 4 ) 3 Monoclinic (C2/c) Lathanium vanadate LaVO 4 Monoclinic (P2 1 /c) Lead antimonade Pb 2 Sb 2 O 7 Cubic (Fd3m) Lead bismuth niobate PbBi 2 Nb 2 O 9 Othorhombic (Fmm2) Lead bromide PbBr 2 Othorhombic (Pnma) Lead cadmium niobate Pb 3 CdNb 2 O 9 Orthorhombic Lead calcium chloroarsenate (hedyphane) Pb 3 Ca 2 (AsO 4 ) 3 Cl Hexagonal (P6 3 /m) Lead carbonate (cerussite) PbCO 3 Orthorhombic (Pnam) Lead chloride (cotunnite) PbCl 2 Orthorhombic (Pnam) Lead chloroarsenate (mimetite) Pb 5 (AsO 4 ) 3 Cl Hexagonal (P6 3 /m) Lead chlorophosphate (pyromorphite) Pb 5 (PO 4 ) 3 Cl Hexagonal (P6 3 /m) Lead chlorovanadate (vanadinite) Pb 5 (VO 4 ) 3 Cl Hexagonal (P6 3 /m) Lead fluoride PbF 2 Cubic (Fm3m)

18 Handbook of Optical Materials

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Lead fluoroarsenate Pb 5 (AsO 4 ) 3 F Hexagonal (P6 3 /m) Lead fluorophosphate Pb 5 (PO 4 ) 3 F Hexagonal (P6 3 /m) Lead fluorovanadate Pb 5 (VO 4 ) 3 F Hexagonal (P6 3 /m) Lead germanate PbGeO 3 Monoclinic (P2 1 /a) Lead germanate Pb 3 GeO 5 Monoclinic (P12) Lead germanate Pb 3 Ge 3 O 11 Trigonal (P3) Lead germanate Pb 5 Ge 2 O 7 Hexagonal Lead hafnate PbHfO 3 Orthorhombic (Pbam) Lead hexa-aluminate (magnetoplumbite) PbAl 12 O 19 Hexagonal (P6 3 /mmc) Lead indium niobate Pb 2 InNbO 6 Rhombohedral Lead iodide 2H -PbI 2 Trigonal (P3m1) Lead magnesium niobate Pb 3 MgNb 2 O 9 Orthorhombic Lead molybdate (wulfenite) PbMoO 4 Tetragonal (I4 1 /a) Lead niobate (changbaiite) PbNb 2 O 6 Orthorhombic (Cm2m) Lead nitrate Pb(NO 3 ) 2 Cubic (Pa3) Lead oxide (litharge) PbO Tetragonal (P4/nmm) Lead oxide (massicot) PbO Orthorhombic (Pbcm) Lead phosphate Pb 3 (PO 4 ) 2 Monoclinic (PC2/c) Lead potassium niobate Pb 2 KNb 5 O 15 Orthorhombic (Im2m) Lead scandium niobate Pb 2 ScNbO 6 Rhombohedral Lead selenate (kerstenite) PbSeO 4 Orthorhombic (Pnma) Lead selenide (clausthalite) PbSe Cubic (Fm3m) Lead selenite (molybdomenite) PbSeO 3 Monoclinic Lead silicate (alamosite) PbSiO 3 Monoclinic (Pn) Lead sodium niobate PbNaNb 5 O 15 Orthorhombic (Im2a) Lead sulfate (anglesite) PbSO 4 Orthorhombic (Pnma) Lead sulfide (galena) PbS Cubic (Fm3m) Lead tantalate PbTa 2 O 6 Orthorhombic (Cm2m) Lead telluride (altaite) PbTe Cubic (Fm3m) Lead titanate (macedonite) PbTiO 3 Tetragonal (P4mm) Lead titanium phosphate PbTiP 2 O 8 Orthorhombic Lead tungstate (stolzite) PbWO 4 Tetragonal (I4 1 /a) Lead vanadate Pb 3 (VO 4 ) 2 Monoclinic (P2/c) Lead vanadate (chervetite) Pb 2 V 2 O 7 Monoclinic (P21/a) Lead (^) zinc niobate Pb3ZnNb2O 9 Orthorhombic Lead zinc silica te Pb2ZnSi2O7 Tetragonal (P421m) Lead zinc silicate (larsenite) PbZnSiO4 Orthorhombic (Pnam) Lithium aluminate Li5AlO4 Orthorhombic (Pbca) Lithium aluminate γ-LiAlO 2 Tetragonal (P4 1 2 1 2) Lithium aluminate spinel LiAl 5 O 8 Cubic (P4 1 32) Lithium aluminum borate Li 6 Al2 (BO 3 ) 4 Triclinic(P−1) Lithium aluminum fluorophosphate (amblygonite) LiAl(PO 4 )F Triclinic(P−1) Lithium aluminum germanate LiAlGe 2 O 6 Monoclinic (P21/n)

20 Handbook of Optical Materials

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Lithium germanate Li 2 GeO 3 Orthorhombic (Cmc2 1 ) Lithium indium germanate LiInGe 2 O 6 Orhtorhimbic (Pbca) Lithium indium molybdate LiIn(MoO 4 ) 2 Monoclinic (P2 1 /c) Lithium indium oxide Li 3 InO 3 Trigonal (P−3c1) Lithium indium oxide LiInO 2 Tetragonal(I4 1 /amd) Lithium indium silicate LiInSiO 4 Orthorhombic (Pnma) Lithium indium silicate LiInSi 2 O 6 Monoclinic (C2/c) Lithium indium tungstate LiIn(WO 4 ) 2 Monoclinic (P2/c) Lithium iodate α-LiIO 3 Hexagonal (P6 3 ) Lithium iodide LiI Cubic (Fm3m) Lithium lanthanum borate Li 3 La 2 (BO 3 ) 3 Monoclinic (P2 1 /n) Lithium lanthanum molybdate LiLa(MoO 4 ) 2 Orthorhombic (Pbca) Lithium lanthanum oxide LiLaO 2 Orthorhombic (Pbmm) Lithium lanthanum tetraphosphate LiLaP 4 O 12 Monoclinic (I2/c) Lithium lanthanum tungstate LiLa(WO 4 ) 2 Tetragonal (I4 1 /a) Lithium lutetium borate Li 6 Lu(BO 3 ) 3 Monoclinic (P2 1 /b) Lithium lutetium fluoride LiLuF 4 Tetragonal (I4 1 /a) Lithium lutetium germanate LiLuGeO 4 Orthorhombic (Pbcn) Lithium lutetium oxide LiLuO 2 Tetragonal (I4 1 /amd) Lithium lutetium silicate LiLuSiO 4 Orthorhombic (Pbcn) Lithium lutetium tetraphosphate LiLuP 4 O 12 Monoclinic (I2/c) Lithium lutetium tungstate LiLu(WO 4 ) 2 Monoclinic (P2/c) Lithium magnesium aluminum fluoride LiMgAlF 6 Trigonal (P321) Lithium magnesium borate LiMgBO 3 Monoclinic (C2/c) Lithium magnesium borate Li 2 MgB 2 O 5 Monoclinic Lithium magnesium chloride Li 2 MgCl 4 Cubic (Fd3m) Lithium magnesium gallium fluoride LiMgGaF 6 Tetragonal (P4 2 /mmm) Lithium magnesium germanate Li 2 MgGeO 4 Orthorhombic (Pmn2 1 ) Lithium magnesium indium fluoride LiMgInF 6 Trigonal (P321) Lithium niobate LiNbO 3 Trigonal (R3c) Lithium phosphate (lithiophosphate) Li 3 PO 4 Orthorhombic Lithium scandate LiScO 2 Tetragonal(I4 1 /amd) Lithium scandium germanate LiScGeO 4 Orthorhombic (Pbnm) Lithium scandium germanate LiScGe 2 O 6 Orthorhombic (Pbca) Lithium scandium silicate LiScSiO 4 Orthorhombic (Pbnm) Lithium scandium silicate LiScSi 2 O 6 Monoclinic (C2/c) Lithium scandium tungstate LiSc(WO 4 ) 2 Monoclinic (P2/c) Lithium silicate Li 2 SiO 3 Orthorhombic (Ccm2 1 ) Lithium strontium aluminum fluoride (LiSAF) LiSrAlF 6 Trigonal(P−31c) Lithium strontium gallium fluoride (LiSGF) LiSrGaF 6 Trigonal(P−31c) Lithium tantalate (LT) LiTaO 3 Trigonal (R3c) Lithium tetraborate (diomignite) Li 2 B 4 O 7 Tetragonal (I4 1 cd) Lithium triborate (LBO) LiB 3 O 5 Orthorhombic (Pn2 1 a)

Section 1: Crystalline Materials 21

Name, Formula, Crystal System, and Space Group for Optical Crystals —continued

Name Formula

Crystal system (Space group)

Lithium vanadate LiVO 3 Monoclinic (C2/c) Lithium vanadate Li 3 VO 4 Orthorhombic (Pmn2 1 ) Lithium yttrium borate Li 3 Y 2 (BO 3 ) 3 Monoclinic (P2 1 /n) Lithium yttrium borate Li 6 Y(BO 3 ) 3 Monoclinic (P2 1 /b) Lithium yttrium fluoride (YLF) LiYF 4 Tetragonal (I4 1 /a) Lithium yttrium germanate LiYGeO 4 Orthorhombic (Pbcn) Lithium yttrium oxide LiYO 2 Monoclinic (P2 1 /c) Lithium yttrium silicate LiYSiO 4 Orthorhombic (Pbcn) Lithium yttrium tungstate LiY(WO 4 ) 2 Monoclinic (P2/c) Lithium zinc borate LiZnBO 3 Monoclinic (C2/c) Lithium zinc indium fluoride LiZnInF 6 Trigonal (P321) Lithium zinc niobate LiZnNbO 4 Tetragonal (P4 1 22) Lutetium aluminum borate LuAl 3 (BO 3 ) 3 Trigonal (R32) Lutetium aluminum garnet Lu 3 Al5 O 12 Cubic (Ia3d) Lutetium borate LuBO 3 Rhombohedral (R−3c) Lutetium calcium borate LuCaBO 4 Orthorhombic (Pnam) Lutetium gallium garnet Lu 3 Ga 5 O 12 Cubic (Ia3d) Lutetium molybdate Lu 2 (MoO 4 ) 3 Orthorhombic (Pbcn) Lutetium orthosilicate Lu 2 SiO 5 Monoclinic (C2/c) Lutetium oxide Lu 2 O 3 Cubic (Ia3) Lutetium oxymolybdate Lu 2 MO 6 Monoclinic (I2/c) Lutetium oxysulfate Lu 2 O 2 SO 4 Orthorhombic Lutetium oxytungstate Lu 2 WO 6 Monoclinic (P2/c) Lutetium pentaphosphate LuP 5 O 14 Monoclinic (C2/c) Lutetium phosphate LuPO 4 Tetragonal (I4 1 /amd) Lutetium scandate LuScO 3 Cubic (Ia3) Lutetium scandium aluminum garnet (LSAG) Lu 3 Sc2 Al3 O 12 Cubic (Ia3d) Lutetium tantalate LuTaO 4 Monoclinic (P2/a) Lutetium titanate Lu 2 Ti 2 O 3 Cubic (Fd3m) Lutetium tungstate Lu 2 (WO 4 ) 3 Orthorhombic (Pcna) Lutetium vanadate LuVO 4 Tetragonal (I4 1 /amd) Magnesium aluminate (spinel) MgAl 2 O 4 Cubic (Fd3m) Magnesium aluminum borate (sinhalite) MgAlBO 4 Orthorhombic (Pnma) Magnesium aluminum borosilicate (grandidierite) MgAl 3 BSiO 9 Orthorhombic Magnesium aluminum silicate (cordierite) Mg 2 Al3 (Si 5 Al)O 18 Hexagonal (P6/mcc) Magnesium aluminum silicate (sapphirine) Mg 4 Al8 Si 2 O 20 Monoclinic (P2 1 /a) Magnesium aluminum silicate garnet (pyrope) Mg 3 Al2 Si 3 O 12 Cubic (Ia3d) Magnesium borate (kotoite) Mg 3 B 2 O 6 Orthorhombic (Pnma) Magnesium borate (suanite) Mg 2 B 2 O 5 Monoclinic Magnesium carbonate (magnesite) MgCO 3 Rhombohedral (R−3c) Magnesium chloroborate (boracite) Mg 3 B 7 O 13 Cl Orthorhombic Magnesium fluoride (sellaite, Irtran 1) MgF 2 Tetragonal (P4 2 /mnm) Magnesium fluoroborate Mg 2 BO 3 F Orthorhombic