Metal Chalcogenides: A Rich Source of ... - ACS Publications

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Metal Chalcogenides: A Rich Source of Nonlinear Optical Materials In Chung†,‡ and Mercouri G. Kanatzidis*,† †

Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States Graduate School of Nanoscience and Technology and KAIST Institute for the NanoCentury, KAIST, Daejon 305-701, Republic of Korea

‡

ABSTRACT: Materials chemistry and the pursuit of new compounds through exploratory synthesis are having a strong impact in many technological fields. The field of nonlinear optics is directly impacted by the availability of enabling materials with high performance. Nonlinear optical (NLO) phenomena such as second harmonic and difference frequency generation (SHG and DFG, respectively) are effective at producing a coherent laser beam in difficult to reach frequency regions of the electromagnetic spectrum. Such regions include the infrared (IR), far-infrared, and terahertz frequencies. High performance NLO crystals are critical for applications utilizing these coherent light sources, and new materials are continuously sought for better conversion efficiency and performance. The class of metal chalcogenides is the most promising source of potential NLO materials with desirable properties particularly in the IR region where most classes of materials face various fundamental challenges. We review the recent developments in the discovery of several new high-performing chalcogenide NLO materials for the IR region of the spectrum. Among these, KPSe6, NaAsSe2, and Na2Ge2Se5 have been shown to exhibit some of the highest SHG coefficients (χ(2)) reported, namely, 150, 325, and 290 pm/V, respectively. We focus on their structural characteristics, optical transparency, and nonlinear optical properties. We also discuss a new concept to prepare strong NLO bulk glasses, fibers, and thin films without poling, which would be a promising solution to a main challenge in NLO applications. The impact of cutting-edge theoretical calculations in helping to move this field of materials science and chemistry forward is highlighted. KEYWORDS: synthesis, materials genome, second harmonic generation

1. INTRODUCTION Metal chalcogenides with wide energy gaps are the most promising materials for nonlinear optical (NLO) applications operating in the infrared (IR) region of the electromagnetic spectrum. In the past 20 years, synthesis of new materials in the chalcogenide class has contributed several new compounds with remarkably high NLO response.1−7 This can be regarded as an achievement of synthetic chemistry, which has been enabled by broad-based advances in our understanding and methodology of chalcogenide compound formation and characterization. Developing new coherent light sources with tunable frequencies is of great importance. 8 Although technologies for tunable lasers have been developed over decades, commercially available wavelength ranges with reasonable efficiency are still limited.9 Frequency conversion by an NLO crystal is an effective way of producing coherent light at frequencies where lasers perform poorly or are unavailable. For example, when two incoming intense beams with frequencies ω1 and ω2 are introduced into an NLO medium, they interact nonlinearly to produce four distinct output frequencies: 2ω1 and 2ω2 by second harmonic generation (SHG) together with (ω1 ± ω2) by sum and difference frequency generation (SFG and DFG, respectively).10 As a consequence, laser radiation can be converted from one frequency to another, significantly expanding the range of applications that can be addressed. For example, DFG © 2013 American Chemical Society

is a core process to produce mid-IR light and necessary to facilitate multichannel conversion and all-optical networks.11−13 There have been multiple NLO applications (e.g., affordable blue lasing sources, parametric generation of tunable lights, alloptical photonic and high-capacity communication networks, and optical storage)12 that have been extensively studied over the last two decades using NLO oxides such as BaB2O4 (BBO), LiB3O5 (LBO), LiNbO3 (LNO), KH2PO4 (KDP), and KTiOPO4 (KTP).14,15 Although metal oxide NLO crystals have been developed for the visible and UV regions, strong interest also exists for the IR region to produce light sources that are widely tunable and coherent in the spectral range of 2− 25 μm. This is the so-called fingerprint region for organic and inorganic molecules. Accordingly, it is critical for sensing hazardous and high-risk materials such as chemical warfare agents,16 biohazards,17 explosives,18 pollutants, and trace gases19 for homeland security, environmental monitoring, and industrial process controls. Tunable, narrowband lasers are also necessary for minimal invasive medical surgery20 and direct Special Issue: Celebrating Twenty-Five Years of Chemistry of Materials Received: May 29, 2013 Revised: July 11, 2013 Published: August 9, 2013 849

dx.doi.org/10.1021/cm401737s | Chem. Mater. 2014, 26, 849−869

Chemistry of Materials

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Table 1. New Compounds as IR Nonlinear Optical (NLO) Materialsa compounds Molecular Cs5P5Se1230 [Sb7S8Br2](AlCl4)331 Cs5BiP4Se1232 Ba23Ga8Sb2S3833 K4GeP4Se12 (PC)34 One-Dimensional Cs2CuP3S935 K2P2Se6 (PC, SP)1 CsZrPSe6 (SP)36 γ-NaAsSe2 (SP)35 γ-Li0.2Na0.8AsSe2 (SP)35 β-Li0.2Na0.8AsSe2 (SP)35 LiAsS2 (SP)5,6 A3Ta2AsS11 (A = K, Rb)37 Rb4Ta2S1137 KPSe6 (PC,e SPf)2,3 RbPSe6 (PC, SP)2,3 Sm4GaSbS939 La4InSbS939 Ba2BiInS539 Two-Dimensional {[In(en)3][In5Te9(en)2]·0.5eng}n42 Na2Ge2Se54 Three-Dimensional Na0.5Pb1.75GeS443 β-K2Hg3Ge2S87 [Zn(H2O)4][Zn2Sn3Se9(MeNH2)]44 Li2CdGeS452 Li2CdSnS452 (NH4)5Ga4SbS1045 BaGa4Se748 LiGaGe2Se650 Ba3CsGa5Se10Cl251 Li2In2GeSe653 BaGa2GeS654 BaGa2GeSe654 Benchmark Materials15 ZnGeP2 AgGaSe2 AgGaS2 GaSe Tl3AsSe3

PM/NPMb

relative SHG intensities, χ(2) (pm/V)

unit cell

space group

band gap (eV)

tetragonal orthorhombic orthorhombic orthorhombic orthorhombic

P4̅ P212121 Pmc21 Cmc21 Pca21

2.17 2.03 1.85 2.84 2.0

NPM NPM NPM NPM NPM

1 × LiNbO3 1 × KH2PO4 at 900 nm 2 × AGSec at 1 μm 22 × AGSd at 1.025 μm 30 × AGSe at 730 nm

hexagonal trigonal orthorhombic monoclinic monoclinic monoclinic monoclinic monoclinic orthorhombic orthorhombic orthorhombic orthorhombic orthorhombic orthorhombic

P65 P3121 Pmc21 Pc Pc Cc Cc Cc Pca21 Pca21 Pca21 Aba2 P41212 Cmc21

2.4 2.08 ∼2 1.75 1.72 1.57 1.60 2.21 N/A 2.16 2.18 2.23 2.07 2.38

N/A PM PM NPM NPM NPM NPM NPM N/A PM PM NPM NPM NPM

N/A 53.7 pm/V 15 × AGSe at 820 nm 75 × AGSe at 820 nm 65 × AGSe at 820 nm 55 × AGSe at 820 nm 10 × AGSe at 790 nm 15 × AGSe at 700−900 nm 4 × AGSe 151.3 pm/V 149.4 pm/V 3.8 × AGS at 1.025 μm 1.5 × AGS at 1.025 μm 0.8 × KTiOPO4 at 900 nm

hexagonal orthorhombic

P61 Pna21

2.2 2.38

PM PM

0.5 × AGSe ∼290 pm/V

cubic monoclinic triclinic orthorhombic rhombohedral cubic monoclinic orthorhombic tetragonal monoclinic trigonal trigonal

I-43d C2 P1 Pmn21 Pmn21 P213 Pc Fdd2 I-4 Cc R3 R3

2.08 2.70 2.08 3.10 3.26 2.3 2.64 2.64 2.08 2.30 3.26 2.81

PM PM type I & II PM PM NPM N/A PM PM NPM N/A PM PM

7−8 × LiNbO3 40 pm/V 0.6 × AGSe at 600−1000 nm 70 × α-SiO2 100 × α-SiO2 N/A d11h = 18.2, d13 = −20.6 pm/V d15 = 18.6 pm/V 100 × AGSe at 1.025 μm ∼AgGSe at 1 μm 2.1 × AGS at 1.025 μm 3.5 × AGS at 1.025 μm

tetragonal tetragonal tetragonal hexagonal trigonal

I42̅ d I4̅2d I42̅ d P6̅2m R3m

2.0 1.83 2.73 2.0 1.3

PM PM PM PM PM

150 pm/V 66 pm/V 36 pm/V 108 pm/V 40−60 pm/V

a

Listed are unit cell type, space group, band gap energy, and relative SHG intensities to reference materials. Known second harmonic generation coefficients χ(2) (pm/V) are also indicated. Some isostructural analogues of these compounds are not shown. Relevant benchmark materials are given at the end of the table. bPM = phase-matchability, NPM = nonphase-matchability. These are Type-I otherwise noted. Phase matching depends strongly on the wavelength. cAGSe = AgGaSe2. dAGS = AgGaS2. ePC = Crystal-glass phase-change materials. Their glass counterparts also exhibit significant, intrinsic second-order nonlinear optical response. fSP = Solution-processable. gen = ethylenediamine. hχ(2) = 2d by convention.

phenomena regarding frequency conversion (i.e., SHG, DFG, and SFG).25 Centrosymmetric materials have inversion symmetry and are excluded from this application. Practical NLO materials should possess high second-order nonlinearity, wide optical transparency, phase-matchability, and high thermal stability.26 Oxide NLO materials are generally unsuitable for broad band IR applications because of the presence of IR absorptions in the spectral range of interest. The use of organic/polymer NLO materials is significantly restricted by poor thermal stability and high IR absorption, despite their high optical nonlinearity.27 For this reason, DFG performance is not

imaging of noncentrosymmetric biological structures in tissues, cell metabolism, and disease states.21 Practical advances in the applications mentioned above have been largely limited by the progress in development of available NLO materials. This is mainly a field of optics, but it depends strongly on the availability of complex materials that only chemists can discover and develop. IR NLO materials with excellent performance are relatively rare and show limited structural diversity compared to oxide materials.22−24 Overall, a noncentrosymmetric arrangement of the structural building blocks is a prerequisite for second-order NLO 850



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that do not include chalcogen atoms, for example, K(VO)2O2(IO3)3,55 (Hg6P3)(In2Cl9), and (Hg8As4)(Bi3Cl13),56 are also not covered here. Second, we review efforts to prepare usable forms such as large crystals, optical fibers, and thin films, which can help circumvent bottlenecks in practical NLO applications of these inorganic materials. A main challenge for applications is the costly, lengthy, and labor-intensive processes to prepare large optical quality single crystals, and thus there is interest in using other more accessible forms. In this context, we have proposed a general concept to prepare temporally stable NLO glasses utilizing noncentrosymmetric phase-change materials.1−3,30 Such NLO glasses show significantly strong, intrinsic secondorder NLO responses with no poling. On the basis of the proposed concept, strongly nonlinear optical glass fibers and thin films have been obtained2,32,31,37 and then readily switched to crystalline forms by heating to achieve a large boost in NLO efficiency.2,3 While the importance of synthesis is paramount in identifying and designing new systems, screening and measurements are key to pushing this field forward. Finally, firstprinciples density functional theory (DFT) calculations on the SHG coefficients of NLO materials are scarce. These few pertinent reports will be discussed because they offer new insights in possibly designing high-performing NLO materials.

generally attainable in them. Consequently, NLO materials operating in the broadly defined IR region are highly desirable. Benchmark materials known for several decades are the chalcopyrite compounds such as ZnGeP2 and AgMQ2 (M = Ga, In; Q = S, Se, Te)15,26,28 and the zinc-blende compounds such as GaAs and GaP.29 The former adopt a uniaxial, diamond-like structure due to a slight distortion from the isotropic cubic zinc-blende structure and have good performance. The latter exhibit high second-order nonlinearity and mid-IR transparency; however, they are optically isotropic and as a result nonbirefringent (birefringence is defined as the maximum difference in refractive index within the material; birefringent materials have a refractive index that depends on the polarization and propagation direction of light) and nonphase-matchable in the region of interest.29 For nonphase-matchable NLO materials, through successive layers defined by the coherence length, the second-harmonic waves that are generated have opposite phases resulting in destructive interference thereby canceling each other out. Phase-matchability depends on the region being examined. NLO materials can change from being phase-matchable in one region to being nonphase-matchable in another. Note that chalcogenide compounds are inherently favorable for many IR applications. They feature weaker interatomic bonds than oxides to have redshifted bond stretching frequencies in the near IR region of spectrum resulting in better optical transparency. As a result, chalcogenide compounds are typically more transparent in the mid-IR and IR region than oxides or organic/polymer NLO materials. Generally, sulfides are transparent to ∼11 μm, selenides to ∼15 μm, and tellurides to beyond 20 μm. Chalcogen atoms are also more polarizable than oxygen, which tends to give lower band gaps and higher second-order nonlinearity. In recent years many promising chalcogenide compounds have been discovered with novel compositions and crystal structures that could produce the next generation of NLO materials for the IR region and beyond. This Perspective focuses on the impact exploratory synthesis activities have had in expanding the list of excellent NLO materials, particularly in the broad class of metal chalcogenides. We also discuss the potential of the new materials to meet present challenges in IR NLO applications. First, we summarize recent achievements in synthesizing new chalcogenide IR NLO materials. Examples include molecular compounds of Cs 5 P 5 Se 1 2 , 3 0 [Sb 7 S 8 Br 2 ](AlCl 4 ) 3 , 3 1 Cs5BiP4Se12,32 Ba23Ga8Sb2S38,33 and A4GeP4Se12 (A = K, Rb, Cs);34 one-dimensional compounds of Cs2CuP3S9,35A2P2Se6 (A = K, Rb),1 AZrPQ6 (Q = S, Se),36 AAsQ2 (A = Li, Na; Q = S, Se),5,6 A3Ta2AsS11 (A = K, Rb, Cs),37 APSe6 (A = K, Rb),2,3,38 Ln4GaSbS9 (Ln = Pr, Nd, Sm, Gd−Ho),39 La4InSbS9,40 and Ba2BiInS5;41 two-dimensional compounds of {[In(en)3][In 5 Te 9 (en) 2 ]·0.5en} n (en = ethylenediamine), 42 and Na 2 Ge 2 Se 5 ; 4 and three-dimensional compounds of Na0.5Pb1.75GeS4,43 α- and β-A2Hg3M2S8 (A = K, Rb; M = Ge, Sn),7 [Zn(H2O)4][Zn2Sn3Se9(MeNH2)],44 (NH4)5Ga4SbS10, (NH 4 ) 4 Ga 4 SbS 9 ·H 2 O, (NH 4 ) 5 Ga 4 SbS 10 , 45 BaAl 4 Se 7 , 46 BaGa4Q7 (Q = S,47 Se48,49), LiGaGe2Se6,50 Ba3AGa5Se10Cl2 (A = K, Rb, Cs),51 Li2CdGeS4, Li2CdSnS4,52 Li2In2MQ6 (M = Si, Ge; Q = S, Se),53 and BaGa2GeQ6 (Q = S, Se).54 Their unit cells, space groups, band gaps, phase-matchability, and the estimated/relative SHG intensities are summarized in Table 1. We only cover the noncentrosymmetric compounds for which NLO properties have been reported. New NLO compounds

2. CLASSIC CHALCOGENIDE NLO MATERIALS FOR IR APPLICATIONS The ternary chalcopyrites AgGaS2, AgGaSe2, and ZnGeP2 have been the main IR NLO materials and are commercially available. They belong to the noncentrosymmetric crystal class −42m (Figure 1).15 Their usefulness arises from their high

Figure 1. Crystal structure of chalcopyrite compounds AgGaQ2 (Q = S, Se, Te).

SHG coefficients (χ(2)) of 36, 66, and 150 pm/V, respectively, relatively large birefringence, and advanced crystal growth techniques providing optical quality crystals.28 AgGaS2 and AgGaSe2 are transparent up to 11.4 and 17 μm. Their Li analogues, LiMQ2 (M = Al, Ga, In; Q = S, Se, Te), have also been studied and reported to exhibit promising properties.57−59 Except for LiGaTe2 having a chalcopyrite structure,57 the Li compounds adopt the wurtzite structure of the polar crystal class mm2. GaSe belongs to the crystal class −62m and is one of the best NLO materials for mid-IR generation via DFG (χ(2) = 108 pm/V).15 The layered structure of GaSe is stabilized by 851



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weak van der Waals bonding that gives flaky clay-like character and consequently easily cleaving crystals. Thus, crystals cannot be cut at directions different from the optical axis.58 Ag3AsS3 (3m), HgGa2S4 (−4), Tl3AsSe3 (3m) (Figure 2), and CdSe (6mm) are examples of chalcogenide NLO materials that are rarely used.15

An elaboration on the tetrahedral chalcopyrite family is the quaternary semiconductors Li2CdGeS4 and Li2CdSnS4, which were reported to exhibit NLO properties.52 The compounds crystallize in the Pmn21 space group and have band gaps of 3.10 and 3.26 eV, respectively. Their structure is diamond-like with the tetrahedra pointing in the same direction along the unique c axis. The alignment of the tetrahedra results in the structure lacking an inversion center, a prerequisite for second-harmonic generation (SHG). Li2CdGeS4 displays a type-I phasematchable SHG response of ∼70 × α-quartz, while Li2CdSnS4 exhibits a type-I nonphase-matchable SHG response of ∼100 × α-quartz (Kurtz powder measurement technique62).

3. NEW POLAR CHALCOGENIDES FROM EXPLORATORY SYNTHESIS The widespread adaptation of the alkali metal polychalcogenide fluxes and related salt fluxes63 in discovery synthesis of chalcogenide compounds in the past two decades has contributed a wealth of noncentrosymmetric compounds, many of which have been tested at least in a preliminary sense for NLO activity. As a result, the class of noncentrosymmetric chalcogenides has expanded impressively, and indications are that several of these new generation materials may be in a position to displace existing materials. Our group has focused on a variety of alkali metal polychalcogenide fluxes including polychalcostannate, polychalcophosphate, and polychalcoarsenate fluxes which have proven very productive in leading to new materials. Particularly, the classes of chalcophosphates and chalcoarsenates have proven a fertile source of NLO materials. The building units of [PQ4]3−, [P2Q6]4−, or [AsQ3]3− (Q = S, Se) found in their structures frequently form noncentrosymmetric arrangements by coordination to central metals or polychalcogenide fragments [Qn]2−. Examples include A2P2Se6 (A = K, Rb),1 AZrPQ6 (Q = S, Se),36 AAsQ2 (A = Li, Na; Q = S, Se),5,6 A3Ta2AsS11 (A = K, Rb, Cs),37 and APSe6 (A = K, Rb),2,3,38 For most of the SHG measurements described in this review, unless noted otherwise, the modified Kurtz powder method62,64,65 with a fundamental wavelength (λ) ranging from 1000 to 2000 nm is employed to determine type-I phase-matchability and compare SHG intensities with reference materials. Input light pulses are generated by an optical parametric amplifier driven by a Nd:YAG pulsed laser at 355 nm with a repetition rate of 10 Hz. For phase-matchable samples, the SHG intensity increases with the particle size and it reaches a maximum. For larger particles it stays size-independent because of the existence of a phase-matching direction in the sample.62,64,65 For nonphase-matchable samples, the SHG intensity decreases with the particle size after reaching maximum. Below we present the most significant of these new materials in order of increasing chalcogenide framework dimensionality. We begin with the compounds of the lowest dimensionality (0-D, molecular).

Figure 2. Crystal structure of (a) Ag3AsS3, (b) Tl3AsSe3, and (c) HgGa2S4.

There are no NLO materials that are transparent over the entire spectral range. This limits the availability of operation to a particular spectral region, which is determined by chemical composition, crystal structure, and resulting band gap. In addition, commercially available materials have limitations. For example, AgGaQ2 (Q = S, Se) have negative linear thermal expansion coefficients along the c axis that results in anisotropic thermal expansion (linear thermal expansion coefficient AgGaSe2: α∥c = −0.81 × 10−5/K, α⊥c = 1.98 × 10−5/K, 298− 423 K;60 AgGaS2: α∥c = −1.32 × 10−5/K, α⊥c = 1.27 × 10−5/K, 298−523 K),61 consequently causing thermomechanical stress during crystal growth.

4. NEW IR NLO MATERIALS 4.1. Molecular Chalcogenide NLO Materials. 4.1.1. Cs5P5Se12. Cs5P5Se12 is a molecular salt and crystallizes in the nonpolar space group P4̅ (Figure 3a).30 It features the discrete molecular [P5Se12]5− anion with two types of formal charge, 3+ and 4+, on P. The trivalent formal charge is found on a central P atom coordinated with two ethane-like [P2Se6]4− residues to form a novel octahedral complex. It melts 852



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in the polar Pmc21 space group (Figure 4a). It features octahedral [Bi(P2Se6)2]5− coordination complexes that stack via

Figure 3. Crystal structure of (a) Cs5P5Se12 and (b) [Sb7S8Br2](AlCl4)3. In (b), Sb: blue, S: red, Br: yellow, [AlCl4]− tetrahedron: purple. Reprinted with permission from ref 31. Copyright 2012 American Chemical Society.

congruently at 424 °C and recrystallizes at 243 °C. The electronic absorption spectrum shows a sharp absorption edge at 2.17 eV. The SHG intensity of Cs5P5Se12 is approximately equal to that of LiNbO3 and 25% that of AgGaSe2.66 Cs5P5Se12 is type-I nonphase-matchable in the spectral range examined.62,64 4.1.2. [Sb7S8Br2](AlCl4)3. The compound [Sb7S8Br2](AlCl4)3 is another molecular salt obtained by reacting Sb with S in ionic liquid EMIMBr−AlCl3 as a solvent (EMIM = 1-ethyl-3methylimidazolium) at the low temperature of 165 °C.31 It features a unique cationic chalcogenide cluster [Sb7S8Br2]3+ that results from condensation of two distorted cubic clusters via corner-sharing Sb atoms. Sb and S atoms alternately occupy the other corners of the clusters. Two Sb atoms have terminal Sb−Br bonds pointing out of the cluster. The cationic [Sb7S8Br2]3+ clusters pack in a pseudohexagonal fashion along the a axis. The space between them is occupied by slightly distorted tetrahedral [AlCl4]− anions. The resulting crystal structure adopts the noncentrosymmetric space group P212121 (Figure 3b). The compound exhibits continuously tunable SHG and DFG responses in the spectral range from 550 to 1000 nm that we investigated. The SHG intensity is half at 700 nm and comparable at 900 nm in comparison with that of KDP. It is type-I nonphase-matchable in the spectral range examined. The experimental band gap is 2.03 eV. [Sb7S8Br2](AlCl4)3 was prepared in an ionic liquid: a relatively new synthesis approach that provides new opportunities for discovering novel metal chalcogenides. 4.1.3. Cs5BiP4Se12. Cs5BiP4Se12 shows fascinating growth morphology crystallizing naturally as nanowires and is obtained using a simple synthetic method.32 The compound crystallizes

Figure 4. (a) Crystal structure of Cs5BiP4Se12. (b) A pseudo-1D [Bi(P2Se6)2]5− chain viewed along the [021̅] direction. The green dashed lines depict the short nonbonding interactions [3.478(3) Å] between Se atoms. (c) Representative SEM image of Cs5BiP4Se12 microfibers, demonstrating their flexible nature. (d) Coordination environment of Cs atoms in a polyhedral representation showing the alignment of the macroscopic dipole moment along the c axis. P: gray, Se: red, Cs: blue, Bi: yellow. Reprinted with permission from ref 32. Copyright 2009 American Chemical Society.

weak but selective intermolecular Se···Se interactions to organize in long, flexible fibers and nanowires (Figure 4b). Because of this natural tendency, the Cs5BiP4Se12 nanowires can be obtained pure and in high yield without complex chemical or physical processes (Figure 4c). Although the distorted [BiSe6] octahedra form noncentrosymmetric [Bi(P2Se6)2]5− molecules, the polar structure originates from the acentric packing of the Cs+ ions. The coordination environment of the Cs atoms results in a macroscopic alignment of the dipole moments along the polar c axis (Figure 4d).25 It is consistent with the polar crystal class mm2 of the space group Pmc21. The Cs5BiP4Se12 fibers are widely transparent in the nearand mid-IR, over the range from 0.67 to 18.8 μm, and are found to exhibit a nonlinear optical SHG response at 1 μm that is approximately twice that of the benchmark material AgGaSe2. The material has a nearly direct band gap with a very sharp absorption edge at 1.85 eV and melts congruently at 590 °C. 4.1.4. Ba23Ga8Sb2S38. A common strategy aimed at obtaining noncentrosymmetric compounds is to incorporate asymmetric building blocks into the crystal structure. Examples are secondorder Jahn−Teller distorted d0 metal centers67 such as V5+,68 853



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Zr4+,36,69 Ta5+,70 W6+,71 and Mo6+;72 noncentrosymmetric πorbital systems of (BxOy)n−;23,73,74 and anionic groups with stereochemically active lone pairs such as (IO3) −,74,75 (TeOx)n−,76 [AsS3]3−,5,6,37 [SbS3]3−, and [TeS3]2−.77 Their presence in the structure, however, is insufficient. They must be packed in a noncentrosymmetric fashion. Such an example is Ba23Ga8Sb2S38, or more descriptively Ba23(GaS4)8(SbS3)2.33 The compound adopts the polar space group Cmc21. It consists of the discrete molecular anions: locally nonpolar (when ideal) tetrahedral [GaS4]5− anions and polar pyramidal [SbS3]3− anions with lone pair electrons, isolated by Ba2+ cations (Figure 5).

packing. In contrast, the dipoles of [GaS4]5− anions generated by the 21 symmetry operation are oriented along the c axis, giving the macroscopic polar nature of the compound. Ba23Ga8Sb2S38 is type-I nonphase-matchable though it exhibits ∼22 times stronger SHG response than AgGaS2 (46−74 μm particle size) at 1.025 μm. The experimental band gap is 2.84 eV. 4.1.5. A4GeP4Se12 (A = K, Rb, Cs). The isostructural compounds A4GeP4Se12 crystallize in the polar space group Pca21.34 All compounds feature the discrete molecular anion [GeP4Se12]4− that consists of tetrahedral Ge4+ centers chelated by two bidentate ethane-like [P2Se6] units. The apexes of [GeSe4] tetrahedra are ordered along the c axis at a ∼47° angle dictated by the 21 screw axis along the c axis, resulting in the polar nature of the compounds (Figure 6a). The sulfur analogues also exist but they are packed in a different mode to crystallize in the centrosymmetric C2/c space group. A4GeP4Se12 are stable in air for several weeks, followed by slight decomposition on the surface of the crystals. The compounds are insoluble in methanol and acetonitrile and decompose in N,N-dimethylformamide, N-methylformamide, formamide, and hydrazine. They are water-soluble but are ultimately hydrolyzed in an hour. The compounds melt congruently at 415, 416, and 426 °C for K+, Rb+, and Cs+ salts, respectively. The band gap of A4GeP4Se12 is 2.0 eV for all alkali metal analogues. All three compounds have a meltquenched amorphous phase. The glassy phase undergoes an exothermic glass to crystal phase transition on heating. The measured band gap energies for the glass are 2.1 eV.

Figure 5. Crystal structure of Ba23Ga8Sb2S38. A half of the Sb atoms are shown because of the 50% occupancy. Ba: blue, Ga: purple, Sb: orange, S: yellow, [GaS4]: purple tetrahedra.

The acentric pyramidal [SbS3]3− unit does not contribute to the net polarization because of its overall centrosymmetric

Figure 6. (a) Crystal structure of K4GeP4Se12 viewed down the b axis. The thermal ellipsoids are 90% probability. The polar structural arrangement is seen along the c axis. K: dark blue, Ge: cyan, P: black, Se: red, [GeS4], gray polyhedra. (b) SHG responses of K4GeP4Se12 (■), Rb4GeP4Se12 (●), Cs4GeP4Se12 (▲), and AgGaSe2 (▼) as a function of wavelength from 600−1350 nm. Reprinted with permission from ref 34. Copyright 2012 American Chemical Society. (c) Broadband SHG responses from K4GeP4Se12 (blue peaks) and AgGaSe2 (red peaks) from 0.6−2.0 μm. The colored arrows indicate the band gap of K4GeP4Se12 (0.62 μm) and AgGaSe2 (0.72 μm). A sharp decrease in SHG signal occurs as the SHG frequency approaches their band edges because of the strong absorption of the generated SHG light near the band gap as well as two-photon absorption of the fundamental beam. Similarly, the decrease in SHG intensities in the range of 1.0−1.2 μm can be attributed to higher-order multiphoton absorption effects. Reprinted with permission from ref 78. Copyright 2013 Optical Society of America. 854



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along the c axis, resulting in the chiral space group P65. Note that the 1∞[CuP3S92−] chains are straight and pack in a centrosymmetric fashion (P21/n space group) when crystallizing with the smaller K+ and Rb+ counter cations. The compound is stable in air and water for several weeks and shows a wide band gap at 2.4 eV. Cs2CuP3S9 exhibits SHG activity in preliminary tests, which suggests more detailed studies of the NLO properties should be carried out. 4.2.2. A2P2Se6 (A = K, Rb). The compounds A2P2Se6 (A = K, Rb) crystallize in the chiral space group P3121.1 They feature one-dimensional inorganic polymers consisting of helices of 1 2− + ∞[P2Se6 ] chains separated by A counter cations (Figure 8a,b). Ethane-like [P2Se6] repeat units are condensed with

The wavelength-dependent SHG responses of all three A4GeP4Se12 were examined in the range of 1200−2700 nm (Figure 6b). The compounds are type-I nonphase-matchable in the spectral range investigated. Note that SHG intensity varies with wavelength even though it is within the optical transparency range of A4GeP4Se12. The K analogue exhibits the strongest SHG intensity over the entire spectral range and the experimentally estimated χ(2) values at 1.8 μm are 11.1, 7.1, and 6.1 for K+, Rb+, and Cs+ salts, respectively. At 730 nm, the K+, Rb+, and Cs+ salts show ∼30, 9, and 5 times larger SHG intensities than AgGaSe2, respectively, indicating A4GeP4Se12 compounds are much better SHG materials than the AgGaSe2 in the range of 650−900 nm. Subsequently, AgGaSe 2 outperforms A4GeP4Se12 at 1000 and 1050 nm and then becomes weaker again than A4GeP4Se12 at 1150 and 1200 nm. AgGaSe2 displays stronger SHG than A4GeP4Se12 at 1350 and 1400 nm (Figure 6b). This observation demonstrates the importance of broadband SHG measurements. Recently in the case of K4GeP4Se12 we were able to extend the range of measurements well into the mid-IR, up to 4.0 μm, and we did the same for the benchmark material AgGaSe2 (prepared by a similar method using the same particle sizes).78 The corresponding observed SHG wavelength ranges are from 0.6−2.0 μm, which is much broader than typically performed in these types of studies. The series of blue peaks in Figure 6c represent the measured SHG signals from crystalline K4GeP4Se12 when the laser wavelength is varied by increments of 0.1 μm. It is apparent from these data that although K4GeP4Se12 is a stronger SHG material than AgGaSe2 (red peaks) in the range of 0.6−0.9 μm, it is inferior to AgGaSe2 well into the IR at wavelengths > 1.3 μm. The reversal in NLO performance across the spectrum is striking, and it highlights the importance of specifying the wavelength range when comparisons are being made between materials. 4.2. One-Dimensional NLO Chalcogenide Materials. 4.2.1. Cs2CuP3S9. Cs2CuP3S9 features infinite one-dimensional chains of 1∞[CuP3S92−], running parallel down the c axis, separated by Cs+ cations (Figure 7).35 Cyclic [P3S9]3− units are alternately chelated to Cu+ cations in a tridentate fashion to form [CuP3S10] clusters. The resulting clusters propagate by sharing two S atoms to give inorganic chiral polymeric chains 1 2− 1 2− ∞[CuP3S9 ]. All dipoles in ∞[CuP3S9 ] helices are ordered

Figure 8. (a) Inorganic polymeric chain 1∞[P2Se62−] viewed down the a axis. (b) Structure of K2P2Se6 at 298(2) K looking down the c axis. The thermal ellipsoids with 30% probability are shown. (c) SHG intensities of K2P2Se6 relative to AgGaSe2 over a wide range of wavelengths. Reprinted with permission from ref 1. Copyright 2007 American Chemical Society.

terminal Se−Se linkages to form infinite helices of 1∞[P2Se62−] as if they grew by oxidative polymerization of the [P2Se6]4− anions. The helices are aligned parallel with identical handedness along the crystallographic c axis, preserving chirality in the crystal as expected from the chiral crystal class 321. K2P2Se6 shows wide optical transparency ranging from 0.596 to 19.8 μm. NLO properties of K2P2Se6 are examined as a function of wavelength from 1000 to 2000 nm. The SHG response of crystalline K2P2Se6 is type-I phase-matchable in this spectral range. The SHG intensity of K2P2Se6 reaches a maximum at 789 nm, where it is ∼50 times larger than that of AgGaSe2 (Figure 8c). It is 20-fold stronger than AgGaSe2 at 890 nm. The theoretical χ(2) value is calculated to be 53.7 pm/ V based on highly precise full-potential linearized augmented plane-wave (FLAPW)79 electronic structure calculations at the density functional theory (DFT) level (see Section 6).80

1 Figure 7. Chiral, helix chains of ∞ [CuP3S92−] in polyhedral representation in the unit cell is shown. The Cs atoms are omitted for clarity. [CuS4]7− unit: blue, [P3S9]3− unit: red polyhedron. Adapted and reprinted with permission from ref 35. Copyright 2000 Elsevier B. V.

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trend is observed in solid solutions of K1−xRbxZrPSe6 (x = 0.9, 0.8, 06) and KyCs1−yZrPSe6 (y = 0.8, 0.6). Herein, the species that includes larger and more polarizable alkali metal atoms exhibits stronger SHG responses, presumably because of the larger polarizability of the heavier alkali metal ions. KTiOPO4/ K0.5Rb0.5TiOPO4 and KTiOAsO4/K0.5Cs0.5TiOAsO483 show a similar trend. The AZrPSe6 compounds are type-I phasematchable. Because these compounds are soluble in hydrazine, preparing NLO thin films via solution processing may be feasible.36 The sulfur analogues AZrPS6 crystals are also known and have noncentrosymmetric structures.69 They are quite amenable to solution processing, which is advantageous when considering potential device fabrication. 4.2.4. AAsQ2 (A = Li, Na; Q = S, Se). The ternary family of AAsQ2 (A = Li, Na; Q = S, Se) chalcoarsenates features polymeric 1∞[AsSe2−] single chains that derive from cornersharing pyramidal asymmetric AsQ3 units (Figure 10a,b).5,6 The remarkable conformational flexibility of the chains and the nature of the structure directing alkali metal ions generate an impressive structural diversity in the AAsQ2 system (Figure 10c,d). The relative orientation of one AsQ3 pyramid to its neighbor within the chain is the origin of different chain conformers. For this system, introduction of Na or Se atoms enhances SHG intensities remarkably. LiAsS2 crystallizes in the polar space group Cc.6 The SHG intensity of LiAsS2 is ∼10 times larger than that of AgGaSe2 at 790 nm. Both LiAsS2 and AgGaSe2 show a similar optical transparent region and are type-I nonphase-matchable in the examined spectral region. The noncentrosymmetric structure of LiAsS2 holds up to 40% Na. The resulting Li0.6Na0.4AsS2 is isostructural to LiAsS2 and exhibits 30 times stronger SHG response than AgGaSe2. When the Na substitution is more than 50% centrosymmetric phases of Li0.5Na0.5AsS2, Li0.4Na0.6AsS2 and NaAsS2 form. Variation of the synthetic conditions as well as the alkali metals allows for the stabilization of remarkably diverse chain conformers.5 β-LiAsSe2 (Cc), β-Li0.2Na0.8AsSe2 (Cc), γLi0.2Na0.8AsSe2 (Pc), and γ-NaAsSe2 (Pc) crystallize in polar space groups, whereas α-LiAsSe2 (Fm3̅m) and δ-NaAsSe2 (Pbca) crystallize in centrosymmetric space groups. The compounds β-Li0.2Na0.8AsSe2, γ-Li0.2Na0.8AsSe2, and γ-NaAsSe2 exhibit ∼55, 65, and 75 times stronger SHG signals than that of AgGaSe2, respectively, which is significantly larger than the thioarsenate analogues. These are among the highest SHG responses ever reported. See Section 6 for theoretical calculations of this system. It is very interesting that the AAsQ2 materials are soluble in polar organic solvents, making them available for NLO thin films via solution processing as in the case of APSe6 (see below) and other usable forms of the materials.3 4.2.5. A3Ta2AsS11 (A = K, Rb). The A3Ta2AsS11 (A = K, Rb, Cs) compounds feature parallel 1∞[Ta2AsS113−] chains of low symmetry (Figure 11a).37 The size of the alkali metal has a profound effect on the packing of the chains. The K+ and Rb+ cations favor noncentrosymmetric packing of the 1 3− ∞[Ta2AsS11 ] chains, which adopt the polar space group Cc (Figure 11b), whereas the larger Cs + cation prefers centrosymmetric packing and the P21/n space group (Figure 11c). The noncentrosymmetric packing arises from the inphase alignment of the AsS3 pyramids. The chain consists of bimetallic [Ta2S11]6− units linked with AsS3 pyramids (Figure 12a). Conceptually, the chain derives from the oxidative insertion of As into the S−S units of the [Ta4S22]6− core.84 The

Thermal properties such as thermal expansion and thermal stability of NLO crystals are an important factor for crystal growth and applications under high-power laser irradiation. Such data are rarely obtained, but in this case we determined these properties. Unlike AgGaQ2 (Q = S, Se) exhibiting anisotropic expansion,81 K2P2Se6 single crystal expands isotropically: αa = 1.46 × 10−5/K and αc = 2.41 x10−5/K in the range of 100−400 K. In comparison, the corresponding values of another IR NLO material, ZnGeP2, are α∥c = 1.59 × 10−5/K and α⊥c = 1.75 × 10−5/K in the range of 293−573 K.82 The volumetric thermal expansion coefficient β = 5.35 × 10−5/ K also shows its moderate thermal expansion. Indeed, exposure to abrupt temperature change (200 K/h) and soaking at the high temperature of 500 K for several days does not cause cracking or deformation of single crystals of K2P2Se6. The compound melts congruently at 387 °C, which bodes well for future single crystal growth efforts. 4.2.3. AZrPSe6 (A = K, Rb, Cs). The three quaternary selenophosphate compounds AZrPSe6 (A = K, Rb, Cs) are isostructural and crystallize in the polar space group Pmc21 (Figure 9a).36a The compounds contain Q−Q bonds and are

Figure 9. (a) Crystal structure of AZrPSe6 viewed down the a axis. (b) Polymeric 1∞[ZrPSe6−] chain. Reprinted with permission from ref 36. Copyright 2008 American Chemical Society.

members of a large class of functional materials called polychalcogenides.36b−e They feature parallel inorganic polymeric chains of the infinite 1∞[ZrPSe6−] anions separated by A+ cations (Figure 9b). Zr4+ cations coordinated to Se atoms are stabilized in a distorted bicapped trigonal prismatic geometry. All Zr4+ cations are bonded to three Se atoms from a 1∞[PSe3−] polymeric backbone formed by the condensation of cornersharing tetrahedral PSe4 units. A terminal P−Se bond from the chain projects out perpendicular to the chain direction. The Zr4+ cations are also ligated with η4-bonded Se22− dimers and a terminal Se atom. Unfortunately, the crystal growth habit of this compound is very thin fibrous needles which we supposed will make it very challenging to grow large crystals. The AZrPSe6 compounds have sharp absorption edges at ∼2 eV and show a wide optical transparency range. For example, RbZrPSe6 shows no absorptions through 2−18.5 μm. The SHG responses for all three alkali metal analogues reach a maximum around 820 nm. The intensity of SHG responses follows the polarizability trend Cs > Rb > K. Namely, the Cs and Rb analogues show 15- and 10-fold stronger SHG intensities than AgGaSe2 at 820 nm, respectively, whereas the K analogue exhibits a weaker SHG signal intensity than AgGaSe2. A similar 856



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Figure 11. (a) Single 1∞[Ta2AsS113−] chains, showing the connectivity between AsS3 trigonal pyramids and asymmetric [Ta2S11]6− units. (b) Noncentrosymmetric packing of the 1∞[Ta2AsS113−] chains in K+ and Rb+ salts. The in-phase arrangement of chains is demonstrated by the pale orange arrows. (c) Centrosymmetric packing of the 1 3− + ∞[Ta2AsS11 ] chains in Cs salt resulting in a centrosymmetric phase. Adapted and reprinted with permission from ref 37. Copyright 2009 American Chemical Society. (d) Structure of Rb4Ta2S11.

Figure 10. Different conformers of the single 1∞[AsQ2−] chain derived from the corner-sharing AsQ3 pyramids in LiAsS2 (a) and γ-NaAsSe2 (b). Extended unit cell view of LiAsS2 (c) and γ-NaAsSe2 (d) shows that distinct packing of the chains results in the different noncentrosymmetric structures. Adapted and reprinted with permission from refs 5 and 6. Copyright 2010 American Chemical Society and 2008 John Wiley & Sons Inc., respectively.

In the range of 700−900 nm, the SHG efficiency of A3Ta2AsS11 (A = K, Rb) is ∼15 times stronger than that of AgGaSe2 and comparable to that of CsZrPSe6.36 The compounds are type-I nonphase-matchable at 770 nm. Note that phase-matchability varies with wavelength. For example, AgGaSe2 is phase-matchable only in the range of 3800−12400 nm.15 Accordingly, it is possible that AAsQ2 and A3Ta2AsS11 are phase-matchable at a different wavelength range beyond the examined spectral regions. Unlike the Li1−xNaxAsS2 system, which shows increase of the SHG efficiency with x,6 the efficiencies of K3Ta2AsS11 and Rb3Ta2AsS11 are similar, suggesting negligible contribution from the alkali-metal polarizability. We attempted to see if we can assess the separate contribution of the pyramidal [AsS3]3− and [Ta2S11]6− units toward the total polarizability. We achieved this empirically by studying the NLO properties of Rb4Ta2S11, a noncentrosym-

common dimeric core [Ta2S11]6−85 derives from the trigonal face sharing of two distorted TaS7 pentagonal bipyramids. A3Ta2AsS11 (A = K, Rb) is an example of materials that include two different asymmetric units in a single noncentrosymmetric structure: second-order Jahn−Teller (SOJT)86 distorted d0 metal centers ([TamSn]p−) and anionic groups ([AsS3]3−) with stereochemically active lone pairs. SOJT distorted d0 metal cations in the chalcogenide structures are less common owing to weaker M−S interactions relative to those of M−O, in contrast to abundance in oxides. All three compounds melt incongruently. Apparently, the polysulfide flux enables the formation of the incongruently melting phases in pure form either during the soaking time or on cooling. 857



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produce glassy versions of these materials. These properties will be discussed later in this review. 4.2.7. Ln4GaSbS9 (Ln = Pr, Nd, Sm, Gd−Ho) and Ln4InSbS9 (Ln = La, Pr, Nd). The isostructural compounds Ln4GaSbS9 (Ln = Pr, Nd, Sm, Gd−Ho) adopt the polar space group Aba2.39 A more descriptive formula is (Ln3+)8[(Ga2S6)(Sb2S5)(S2−)7]. The infinite single chains of 1∞[(Ga2S6)(Sb2S5)10−] consist of asymmetric bimetallic [Sb2S5]4− units condensed with dimeric [GaS4]210− residues via corner-sharing S atoms (Figure 13).

Figure 12. Crystal structure, optical transparency, and SHG measurements of KPSe6. (a) The unit cell viewed down the b axis. (b) Far-IR/mid-IR/visible absorption spectra of KPSe6 bulk glass showing wide transparency range. (c) Particle size to SHG intensity diagram of crystalline RbPSe6 indicating type-I phase-matching. (d) Relative SHG intensities of KPSe6 crystal (■) and AgGaS2 (●). Reprinted with permission from ref 2. Copyright 2010 American Chemical Society.

Figure 13.1∞[(Ga2S6)(Sb2S5)10−] chains in Sm4GaSbS9 is represented. The asymmetric and nearly ideal local symmetry of [SbS4]5− and [GaS4]5− units are shown, respectively. The pink arrows indicate the in-phase alignment of dimeric [GaS4]210− tetrahedra and asymmetric bimetallic [Sb2S5]4− units. Adapted and reprinted with permission from ref 39. Copyright 2011 American Chemical Society.

The chains pack in a noncentrosymmetric fashion giving inphase alignment of the dipoles of both the [Sb2S5]4− and [GaS4]210− asymmetric units and are separated by Ln3+ cations and S2− anions. Notable is that the Sb3+ cations are stabilized in four-coordinate seesaw geometry resulting in the asymmetric alignment of the [SbS4]5− building unit of the [Sb2S5]4−. The experimental band gaps for the Sm, Gd, Tb, and Dy compounds are 2.23, 2.41, 2.44, and 2.58 eV, respectively. Sm4GaSbS9 exhibits characteristic sharp absorption peaks at 976, 1115, 1274, 1428, 1574, and 1670 nm, corresponding to f−f transitions of Sm3+ ions. These transitions limit the transparency range to 1.75−25 μm. The Gd and Tb analogues are transparent in the range of 0.75−25 μm and 2.5−25 μm, respectively. The relative SHG intensities of Sm4GaSbS9, Gd4GaSbS9, and Ho4GaSbS9 are ∼3.8, 0.8, and 0.25 times that of AgGaS2 at 1.025 μm, respectively. Tb4GaSbS9 exhibits a very weak SHG response. They are type-I nonphase-matchable at the same wavelength. The Pr, Nd, and Dy compounds do not exhibit noticeable SHG responses. The Ln4InSbS9 (Ln = La, Pr, Nd) compounds crystallize in the chiral space group P41212.40 Their crystal structure differs from Ln4GaSbS9 slightly as the [Sb2S5]4− and [InS4]210− units are arranged around a 2-fold screw axis and neighboring dimers are oriented in the opposite direction. Interestingly, La4InSbS9 shows 1.5 times larger SHG intensity than that of AgGaS2 and is type-I phase-matchable at 1.025 μm.40 In fact, the 422 point group to which the P41212 space group belongs is forbidden from exhibiting second-order NLO activity by Kleinman symmetry because two nonvanishing tensors of the secondorder susceptibilities in this point group are zero.29 The theoretical studies suggest that the origin of the SHG response may be thermal vibrations of the lattice.40 The Pr and Nd compounds do not exhibit SHG response. La4InSbS9 shows an indirect band gap at 2.07 eV and a broad transparency range of 1−25 μm. It shows excellent thermal stability, showing no obvious weight loss up to 765 °C. Similar Kleinman-forbidden

metric compound with the similar polysulfide unit of [Ta2S11]4− but no [AsS3]3− units (Figure 11d), consequently forming discrete molecular structure.85 The SHG response of Rb4Ta2S11 is only ∼4 times that of AgGaSe2, suggesting the pyramidal [AsS3]3− unit may be playing a predominant role on the SHG response of Rb3Ta2AsS11. 4.2.6. APSe6 (A = K, Rb). The isostructural compounds KPSe6 and RbPSe6 crystallize in the polar space group Pca21.2,3,38 They feature one-dimensional inorganic polymeric chains of 1∞[PSe6−] separated by A+ cations (Figure 12a). The chains are formed by condensation of the [PSe4]3− tetrahedral units and Se2 linkages. The polar, noncentrosymmetric chain structure of 1∞[PSe6−] composed of easily polarizable P and Se atoms linked by covalent bonding can produce large optical nonlinearity. KPSe6 and RbPSe6 show optical band gaps of 2.16 and 2.18 eV, respectively. Their optical transparency range is 0.574−19.0 μm for KPSe6 and 0.568−20.2 μm for RbPSe6 (Figure 12b), both of which are similar to that of K2P2Se6. In comparison, the benchmark NLO material for IR applications AgGaSe2 displays a transmission range of 0.76−17.0 μm.15 The compounds melt congruently at 315−320 °C, which is important for NLO crystal growth. APSe6 is type-I phasematchable in the examined wavelength range from 500 to 1000 nm (Figure 12c). The experimental χ(2) of crystalline KPSe6 is 146.4 ± 5.2 pm/ V, which is estimated based on AgGaS2 as a reference (χ(2) = 36 pm/V87) that is also phase-matchable in the spectral range of interest (Figure 12d). The observed value is one of the highest among phase-matchable NLO materials with band gaps larger than 1.0 eV. The experimental value is in good agreement with the theoretical estimate of χ(2) = 151.3 pm/V and 149.4 pm/V for K+ and Rb+ salts, respectively, which is obtained by FLAPW79 electronic structure calculations at the DFT level.80 See Section 6 for more details on theoretical studies. These systems exhibit well-behaved phase-change processes that 858



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SHG response was observed in α-TeO2 exhibiting a secondorder susceptibility d14 of ∼0.36 pm/V at 1.328 μm (generally d = (1/2)χ(2)).88 4.2.8. Ba2BiInS5. Ba2BiInS5 crystallizes in the polar space group Cmc21.41 It is isostructural to antiferromagnetic Ba2BiFeS5.89 The compound consists of 1∞[BiInS54−] anionic polymeric chains, separated by Ba2+ cations (Figure 14). An

Figure 15. Single layer of a chiral 2∞[In5Te9(en)22−] framework with chiral cationic ΔMδλλ−[In(en)3]3+ complexes stabilized in its pores viewed down the c axis. Adapted and reprinted with permission from ref 42. Copyright 2008 American Chemical Society.

intensities are approximately half that of AgGaSe2. Thermogravimetric analysis shows weight loss at 322 K and 520 K, attributed to release of free en and all coordinated amines, respectively. This is expected to limit the ability of the compound to be useful in practical NLO applications. 4.3.2. Na2Ge2Se5. Na2Ge2Se5 crystallizes in the polar space group Pna21.4 Na2Ge2Se5 allows only limited ability to accommodate Sn and Te atoms into its structure. The maximum fractions that could be achieved are Na2Ge1.64Sn0.36Se5 and Na2Ge2Se4.55Te0.45. Na2Ge2Se5 features a layered anionic framework of 2∞[Ge2Se52−] separated by Na+ ions (Figure 16a). The polar structure arises from both the 2 2− + ∞[Ge2Se5 ] anionic layer and the arrangement of Na cations. The main building block of the anionic layer is a [GeSe(μ2− Se3/2)] tetrahedron. These tetrahedra condense via two shared corners to form a helical chain running down the c axis, which is the polar axis of the Pna21 space group (Figure 16b). These helical strands align parallel with identical handedness and link to adjacent chains to form the 2∞[Ge2Se52−] layers via cornersharing Se (Figure 16c). There exist two such layers in the unit cell, and they are related by a 21 screw axis parallel to the c direction. Na2Ge2Se5 melts congruently at 576 °C upon heating. The melt exothermically crystallizes at 509 °C upon cooling. Na2Ge2Se5 exhibits wide optical transparency from 18.2 μm through the mid-IR to the visible spectral region (0.52 μm). Na2Ge2Se5, Na2Ge2Se4.55Te0.45, and Na2Ge1.64Sn0.36Se5 are type-I phase-matchable. Accordingly, their SHG intensities are compared with reference IR NLO materials of AgGaS2 (36 pm/ V)87 and RbPSe6 (149.4 pm/V),90 which are top IR NLO materials and phase-matchable in the examined spectral region. Na2Ge2Se5 exhibits strong SHG responses over a wide range of visible and near IR wavelengths. The SHG intensities of Na2Ge2Se5 are ∼65 and 3.6 times larger than those of AgGaS2 and RbPSe6, respectively, in the optically transparent region (Figure 16d,e). The estimated χ(2) value based on AgGaS2 and RbPSe6 as standards is 290.7 pm/V and 284.3 pm/V, respectively, which are reasonably close. The observed χ(2) value is superior to any other phase-matchable NLO material, for example, ZnGeP2 (150 pm/V), AgGaTe2 (102 pm/V), AgGaSe2 (66 pm/V), and LiNbO3 (12 pm/V), except for CdGeAs2 (Table 1). Note that the band gap of Na2Ge2Se5 at 2.38 eV is much wider than that of ZnGeP2 (2.0 eV), AgGaTe2 (1.36 eV), AgGaSe2 (1.83 eV), and CdGeAs2 (0.57 eV). Table 1 provides representative IR NLO materials and their SHG

Figure 14. Crystal structure of Ba2BiInS5 viewed down the b axis. Adapted and reprinted with permission from ref 41. Copyright 2011 American Chemical Society.

edge-sharing BiS5 tetragonal-pyramid chain and a cornersharing InS4 tetrahedra chain are interconnected with each other via corner-sharing to form the 1∞[BiInS54−] anionic chain. The BiS5 tetragonal pyramids and neighboring InS4 tetrahedra are aligned by cis arrangement through edge-sharing in the chain. As a result, the Bi3+ lone-pair electrons align parallel to give local dipole moments. Finally, the 1∞[BiInS54−] chains are oriented along the c axis, the polar axis of the Cmc21 space group. In contrast, the related compound Ba2BiGaS5 forms in the centrosymmetric Pnma space group due to the Bi3+ lonepair electron alignment in an antiparallel fashion. The IR spectrum does not exhibit obvious optical absorption peaks up to 25 μm. The optical band gap is 2.38 eV. Ba2BiInS5 shows a week SHG efficiency of ∼0.8 times that of KTiOPO4 (KTP) reference and is type-I phase-matchable at 1.025 μm. 4.3. Two-Dimensional Chalcogenide NLO Materials. 4.3.1. {[In(en)3][In5Te9(en)2]·0.5en}n (en = ethylenediamine). {[In(en)3][In5Te9(en)2]·0.5en}n (en = ethylenediamine) was obtained by solvothermal reaction utilizing a novel starting material of the intermetallic Zintl phase with nominal “KIn2” composition.42 It crystallizes in the hexagonal, chiral space group P61. It features chiral anionic layers of [In5Te9(en)2]3− that consist of linking adamantane [In4Te9(en)2]6− clusters coordinated to tetrahedral In3+ centers (Figure 15). Tetrahedral In clusters (T1) and the adamantane-shaped T2 clusters form a supertetrahedral structure. The In−Te framework creates pores that are defined by 18-membered rings made up of nine [InTe4]5− tetrahedra within the layers. Chiral cationic ΔMδλλ− [In(en)3]3+ complexes in octahedral geometry occupy such pores. Consequently, the chirality of the compound arises from both the cationic complexes and anionic layers. The compound shows an absorption edge at ∼2.2 eV. It is type-I phasematching in the range from 600 to 1000 nm. The SHG 859



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orientation of [GeS4]4− anions along the (111) direction (Figure 17a). The compound exhibited 7−8 times greater SHG responses than LiNbO3. It is type-I phase-matchable in the spectral range of interest from 500 nm to 1 μm.92 It reveals sharp optical absorption edge at 2.08 eV.43 4.4.2. α- and β-A2Hg3M2S8 (A = K, Rb; M = Ge, Sn). The αand β-A2Hg3M2S8 (A = K, Rb; M = Ge, Sn) polymorphs crystallize in the polar space groups Aba2 and C2, respectively (Figure 17b).7 They feature a three-dimensional anionic framework of 3∞[Hg3M2S82−] (M = Ge, Sn), isolated by alkali metal cations. Hg atoms are stabilized in two kinds of local coordination geometry: linear [Hg(1)S2]2− and “seesawshaped” highly distorted tetrahedral [Hg(2)S 4]6−. The [MS4]4− anions are condensed with the [Hg(2)S4]6− tetrahedra via corner-sharing to form [Hg2Ge2S8]4− layers. Then, [Hg(1)S2]2− pillars link the latter to build the threedimensional framework. For both the α- and β-phases, all dipoles of the [MS4]4− and the [Hg(2)S4]6− tetrahedra are oriented in-phase along the polar axis of the space groups Aba2 and C2, respectively, providing the highly polar crystal structure (Figure 17b). Both the Ge and Sn analogues are isostructural. The α- and β-polymorphs possess the same type of the [Hg2Ge2S8]4− lamella building block. The subtle difference arises from the different angle at which the linear [S−Hg−S] units bridge the [Hg2Ge2S8]4− layer to a three-dimensional framework. This could explain their relatively facile phase transition and very similar physical properties. Note that one more threedimensional polymorph γ-Rb2Hg3M2S8 (M = Ge, Sn) exists only with Rb+ cation; it crystallizes in the centrosymmetric P21/ c space group.93 When the larger Cs+ cation is used, the [Hg3M2S8]2− building block forms a layered structure and crystallizes in the centrosymmetric P1̅ space group,93 whereas with the smaller K+ and Rb+ cations the same framework prefers a denser three-dimensional structure. This is consistent with the so-called “counterion effect” which for a given charged framework stoichiometry predicts the dimensionality trend as a function of the size of its counterion.94,95 Pure single crystals in a millimeter scale of each phase can be readily obtained by the well-defined growth condition. The compound β-K2Hg3Ge2S8 reveals an optical band gap at 2.70 eV and shows very little light absorption below it, giving a transparent range from ∼500 nm to beyond 10 μm. This is one of the few new generation chalcogenide compounds whose NLO properties were investigated using single crystal samples. The frequency conversion characteristics of β-K2Hg3Ge2S8 were examined on a single crystal microsphere (∼1 mm diameter) using a 3.5 μm idler beam. It is both type-I and typeII phase-matchable. At the optimal propagation directions, the SHG response from both type-I and type-II phase-matching in β-K2Hg3Ge2S8 are approximately a factor of 10 larger than that in LiNbO3, resulting in high χeff(2) values approaching 40 pm/V, as expected from the highly polar crystal structure and extensive covalent bonding between the readily polarizable Hg, Ge, and S atoms. β-K2Hg3Ge2S8 also exhibits good birefringence and high optical damage threshold. The crystals are stable in air and water and show favorable mechanical and thermal characteristics. For example, they do not show cracks or signs of wear when exposed to abrupt changes in temperature. Further studies are needed to better assess the properties of this promising system. 4.4.3. [Zn(H2O)4][Zn2Sn3Se9(MeNH2)]. The open framework polar compound [Zn(H2O)4][Zn2Sn3Se9(MeNH2)] crystallizes

Figure 16. (a) Structure of Na2Ge2Se5 viewed down the b axis. (b) A single strand of the 1∞[Ge2Se52−] helical chain running along the c axis (the polar axis of the Pna21 space group) in a polyhedral presentation. (c) Segment of the 2∞[Ge2Se52−] sheet viewed down the a axis. Na: blue, Sn: yellow, Se: red. (d) Relative SHG intensities of Na2Ge2Se5 crystal (●) and AgGaS2 (▲). (e) Relative SHG intensities of Na2Ge2Se5 crystal (●), RbPSe6 (▼), Na2Ge1.64Sn0.36Se5 (■), and Na2Ge2S4.55Te0.45(◆). Reprinted with permission from ref 4. Copyright 2012 Elsevier B. V.

coefficients χ(2) (pm/V), band gap energy (eV), and transparency range (μm), in comparison to Na2Ge2Se5. Surprisingly, Na2Ge2Se4.55Te0.45 and Na2Ge1.64Sn0.36Se5 exhibit weaker SHG intensities than the parent material despite having bigger congeners of Te and Sn atoms. Their estimated SHG coefficients are 118.0 and 54.1 pm/V, respectively (Figure 16e). The observation is in contrast to the common case. Because of the larger polarizability of Sn and Te than that of Ge and Se, analogous NLO compounds with bigger congeners generally exhibit stronger or at least comparable SHG intensities, as observed in AZrPQ6 (A = K, Rb, Cs; Q = S, Se),36 ATiOPO4 (A = K, Rb),83 AgGaQ2 (Q = S, Se, Te),26 and APSe6 (A = K, Rb).2,3,38 Na2Ge2Se5 nonlinearly mixes optical frequencies effectively to generate continuously tunable visible/ near IR radiation by the DFG process, demonstrating the capability of Na2Ge2Se5 as an efficient nonlinear frequency mixer. Na2Ge2Se5 undergoes phase transition to the molecular salt compound Na4Ge4Se10, which contains the discrete molecular adamantane anion [Ge4Se10]4−.91 This is expected to greatly complicate growth efforts of single crystals.92 4.4. Three-Dimensional Chalcogenide NLO Materials. The main building block of this class is [MQ4]n− (M = group 13 (Al, Ga, In) and/or group 14 (Ge, Sn) elements) tetrahedral units. Their binding modes often favor three-dimensional frameworks. 4.4.1. Na 0.5 Pb 1.75 GeS 4 . The quaternary compound Na0.5Pb1.75GeS4 crystallizes in the noncentrosymmetric cubic space group I4̅3d.43 The structure mainly originates from the 860



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Figure 17. Noncentrosymmetric chalcogenide compounds with three-dimensional framework structure. (a) Na0.5Pb1.75GeS4. Na atoms are omitted for clarity. (b) α- and β-K2Hg3Ge2S8. Space group is represented. Adapted and reprinted with permission from ref 7. Copyright 2003 American Chemical Society. Atoms and building blocks are labeled. (c) [Zn(H2O)4][Zn2Sn3Se9(MeNH2)]. Adapted and reprinted with permission from ref 44. Copyright 2008 Royal Society of Chemistry. (d) (NH4)5Ga4SbS10, (NH4)+ cations are omitted for clarity. (e) Crystal structure of BaGa4Se7. (f) Crystal structure of LiGaGe2Se6 in polyhedral representation.

in the P1 space group.44 The main building blocks are the supertetrahedral (T2) [ZnSn3Se10]6− clusters, which form onedimensional chains via corner-sharing along the a axis. The chains interconnect themselves through Zn2 metal links along the b and c axes to finalize the three-dimensional framework (Figure 17c). Each Zn2 is condensed with three clusters and a terminal methylamine ligand. The charge balancing [Zn(H2O)4]2+ aqua complexes that act as a structure directing agent occupy pores of the framework. The polar nature of the compound arises from the arrangement of [Zn2Sn3Se9(MeNH2)] clusters (Figure 17c). The compound shows remarkable acid stability and proton ion exchange behavior. The band gap of the compound is 2.08 eV. It exhibits SHG efficiency of ∼0.6 times that of AgGaSe2 in the spectral range of 600−1000 nm and is type-I phase-matchable. Again, the presence of organics in the crystal lattice is a disadvantage

raising concerns of long-term stability and laser damage stability. 4.4.4. (NH 4 ) 5 Ga 4 SbS 1 0 , (NH 4 ) 4 Ga 4 SbS 9 ·H 2 O, and (NH4)5Ga4SbS10. The isostructural compounds (NH4)5Ga4SbS10, (NH4)4Ga4SbS9·H2O, and (NH4)5Ga4SbS10 adopt the chiral space group P213.45 The main building block is a supertetrahedral so-called T2 adamantane [Ga4S10]8− cluster that consists of four corner-sharing [GaS4]4− tetrahedra (Figure 17d). Three of the four apexes in the T2 cluster are coordinated to the stereochemically active Sb3+ center, which is stabilized in trigonal pyramidal geometry. Note that the resulting [T2]Sb3 building units form a helix chain propagating along the chiral a axis dictated by the 21 symmetry operation. The chains are then condensed in all dimensions to build up the chiral threedimensional framework. The band gaps of the compounds are 861



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2.3, 2.6, and 2.8 eV, respectively. They exhibit SHG responses in the visible and near IR region. 4.4.5. BaGa4S7 and BaM4Se7 (M = Al, Ga). BaGa4S747 and the isostructural BaM4Se7 (M = Al,46 Ga48) compounds crystallize in the polar space groups Pmn21 and Pc, respectively. They feature the same three-dimensional anionic framework 3 2− 3 2− ∞[Ga4Se7 ] and ∞[M4Se7 ] that is condensed by GaSe4 or MSe4 (M = Al, Ga) tetrahedral units via corner-sharing 3 2− 3 2− ∞[Ga4Se7 ] and ∞[M4Se7 ] anionic framework, respectively (Figure 17e). Their crystal structure is closely related with that of LiGaS2, which is also an NLO material. BaGa4S7, BaAl4Se7, and BaGa4Se7 melt congruently at 1088, 901, and 968 °C, respectively.46,48 Large single crystals can be grown by Bridgman-Stockbarger technique. The BaGa4S7 crystal is hard enough for cutting and polishing with a Mohr’s hardness of ∼5. The thermal expansion coefficient of BaGa4Se7 shows only weak anisotropy: αa = 9.24 × 10−6/K, αb = 1.076 × 10−5/K, and αc = 1.17 x10−5/K.49 Its thermal conductivity coefficients along the crystallographic a, b, and c axis are 0.74(3), 0.64(4), and 0.56(4) W/mK, respectively, lower than those of AgGaS2 (1.5 W/mK) and AgGaSe2 (1.2 W/mK). The band gaps of BaGa4S7, BaAl4Se7, and BaGa4Se7 are 3.54, 3.40, and 2.64 eV, respectively. BaGa4S7 and BaGa4Se7 show a broad transparency range of 0.35−13.7 and 0.47−18.0 μm, respectively, with a strong absorption peak at 15 μm for the latter.49 BaGa4S7 is type-I phase-matchable and exhibits 1.4 times stronger SHG signal than LiGaS2 at 1.025 μm, giving the estimated second-order nonlinear susceptibility d33 of 12.6 pm/ V.47 The laser damage threshold is 1.2 J/cm2 at 1.064 μm with a 15 ns pulse width for BaGa4S7 crystal47 and 557 MW/cm2 at 1.064 μm with a 5 ns pulse width for BaGa4Se749 crystals. The latter value is 3.7 times that of AgGaS2 crystal measured under the same condition. BaAl4Se7 and BaGa4Se7 exhibit 50% and ∼2−3 times larger SHG intensity than AgGaS2 at 532 nm, respectively.46,48 The theoretical calculations yield d15 = 5.2 pm/V and d13 = 4.2 pm/V for BaAl4Se7 and d11 = 18.2 pm/V and d13 = −20.6 pm/V for BaGa4Se7. The calculated birefringence Δn is ∼0.05 for BaAl4Se7 and 0.07 for BaAl4Se7 at wavelengths larger than 1 μm, suggesting they are phasematchable in the IR region. BaAl4Se7 may not be long-term stable in moist air because of the presence of hydrolytically unstable Al−Se bonds. 4.4.6. LiGaGe2Se6. LiGaGe2Se6 crystallizes in the Fdd2 space group.50 LiSe4, GaSe4, and GeS4 tetrahedral units are condensed each other via corner-sharing to form a threedimensional framework. The compound melts congruently at 701 °C and crystallizes at 656 °C (Figure 17f). The bang gap of LiGaGe2Se6 is 2.64 eV. Its SHG intensity is ∼50% that of AgGaSe2 at 1 μm. The calculated birefringence Δn is ∼0.04 at the wavelength larger than 1 μm suggesting SHG of the compound is phase-matchable in the IR region. The major SHG coefficients are calculated to be d15 = 18.6 pm/V, d24 = −9.3 pm/V, and d33 = 12.8 pm/V. 4.4.7. Ba3AGa5Se10Cl2 (A = K, Rb, Cs). The isostructural compounds Ba3AGa5Se10Cl2 (A = K, Rb, Cs) crystallize in the noncentrosymmetric space group I4̅.51 The three-dimensional anionic framework of 3∞[Ga5Se105−] is regarded as a zinc-blende topological structure (Figure 18a). All the Zn and S sites are alternately substituted by the tetrahedral [GaSe4]5− units (T1) and the supertetrahedral [Ga4Se10]8− cluster (T2). Four aligned [GaSe4]5− units form the [Ga4Se10]8− cluster via corner sharing Se atoms. The latter is further condensed with the [GaSe4]5−

Figure 18. Crystal structure of (a) Ba3CsGa5Se10Cl2, (b) Li2In2GeSe6, and (c) BaGa2GeS6. (a) Cs/Ba: blue, Cl: green, T1 tetrahedron [GaSe 4 ] 5− : orange polyhedron, T2 supertetrahedral cluster [Ga4Se10]8−: pink polyhedron. (b) Adapted and reprinted with permission from ref 53. Copyright 2012 American Chemical Society.

unit to give the 3∞[Ga5Se105−] framework, which is interpenetrated by Ba2+ and Cs+ cations and Cl− anions. The overall noncentrosymmetric structure arises from the noncentrosymmetric packing of the T2 cluster. The T1 unit possesses the mirror plane. The compounds Ba3AGa5Se10Cl2 (A = K, Rb, Cs) show optical band gaps at 2.04, 2.05, and 2.08 eV, respectively, and exhibit broad transparent ranges of 0.86−25 μm, 0.65−25 μm, and 0.89−25 μm, respectively. They are type-I nonphasematchable at 1.025 μm in spite of 10, 20, and 100 times larger SHG intensities (from K+ to Cs+ salt) than AgGaS2. These compounds also show broad red emission spectra with maximum peaks at 711−731 nm. 4.4.8. Li2In2MQ6 (M = Si, Ge; Q = S, Se). The isostructural compounds Li2In2MQ6 (M = Si, Ge; Q = S, Se) crystallize in 862



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the Cc space group.53 The tetrahedral building blocks of LiSe4, GaSe4, and GeS4 are condensed via corner-sharing to form a three-dimensional framework (Figure 18b). Li 2 In 2 SiS 6 , Li2In2GeS6, Li2In2SiSe6, and Li2In2GeSe6 melt congruently at 858, 780, 801, and 722 °C and crystallize at 813, 716, 794, and 680 °C, respectively. Their band gaps are measured at 3.61, 3.45, 2.54, and 2.30 eV, respectively. Two of the sulfide compounds exhibit SHG intensity similar to AgGaS2 and two of the selenides close to AgGaSe2 at 1 μm. 4.4.9. BaGa2GeQ6 (Q = S, Se). The presence of two different metals in the chalcogenide framework can help form noncentrosymmetric open framework chalcogenide compounds because of their distinct ionic radius, coordination preferences, and packing characteristics (Figure 18c). Examples are BaGa 2 GeQ 6 (Q = S, Se), 54 [Zn(C 6 N 4 H 18 )(H 2 O)][Zn2Ge3S9(H2O)],96 K6Cd4Sn3Se13,97 K14Cd15Sn12Se46,98 and A6Sn[Zn4Sn4S17] (A = K, Rb, Cs).99 To date the NLO properties of only the first compound have been reported. The compounds BaGa2GeQ6 (Q = S, Se) are isomorphous, crystallizing in the polar, trigonal space group R3.54 [GaQ4]5− and [GeQ4]4− tetrahedral units condense via edge-sharing to form three-dimensional framework structure, isolated by the counter cations Ba2+ (Figure 18c). Ga and Ge atoms are randomly distributed. BaGa2GeS6 shows a relatively large band gap of 3.26 eV with a broad optical transparency range from 0.38 to 13.7 μm. The band gap of BaGa2GeSe6 is 2.81 eV. BaGa2GeS6 and BaGa2GeSe6 exhibit ∼2.1 and 3.5 times larger SHG response than AgGaS2 and are type-I phase-matchable at 1.025 μm. Significant uncertainty on these SHG data might be included because the sieved powder samples and standard were pressed between slide glasses and measured.

significant innate SHG response is observed from the asprepared bulk glassy powders, presumably by virtue of the noncentrosymmetric fragments partially intact in the glassy form of the phase-change materials. The glass of KPSe6 exhibits comparable SHG intensities to AgGaSe2 (Figure 19).

Figure 19. Relative SHG intensities of KPSe6 crystal (■), KPSe6 glass (▲), and AgGaSe2 (◆). Reprinted with permission from ref 2. Copyright 2010 American Chemical Society.

5.2. Strong NLO Glass Fibers. APSe6 (A = K, Rb) optical glassy fibers exhibiting intrinsic SHG response can be drawn from the melt (Figure 20a,b). This of course has to be done under a nitrogen atmosphere because molten chalcogenides react with air. These glass fibers have long length (∼1 m), good mechanical flexibility, high optical transparency, and low optical loss.2 Raman spectroscopy and PDF analyses suggest that the local structural motifs are largely preserved in the glass. The asprepared glass fibers exhibit waveguided SHG and DFG responses over a wide range of wavelengths in the visible and near IR spectral regions (Figure 20c,d). The stoichiometric compounds APSe6 (A = K, Rb) can switch between the crystalline and glassy states without the usual complications that arise in conventional glasses from compositional changes. When KPSe6 glass fibers are annealed at 260 °C for 3 min they crystallize and the measured waveguided SHG response increases by at least 10-fold (Figure 20e). 5.3. Strong NLO Thin Films via Solution Processing. To date, chalcogenide films with high conversion efficiencies for IR applications have been lacking. We recently presented the first example of solution-based deposition process of strong NLO inorganic thin films on silicon, glass, and flexible plastic substrates (Figure 21a).3 The spin-coated films followed by drying at 125 °C on the flexible plastic substrates are intact with no cracks when bent (Figure 21b), lightweight, and shocktolerable. The cross-sectional transmission electron microscopy (TEM) image and corresponding electron diffraction pattern of as-deposited RbPSe6 glass thin film confirms its amorphous nature with no evidence of nanocrystals embedded therein (Figure 21c). We note however that the total absence of nanocrystals is difficult to prove. The strong diffraction peaks detected originate from the Si substrate. The obtained glassy and crystalline films of APSe6 (A = K, Rb; χ(2) ∼ 150 pm/V)2,80 exhibit strong, inherent SHG and DFG in the visible and near IR spectral region at room temperature without the need of poling (Figure 22a,b). Asdeposited glassy APSe6 thin films (∼100 nm thick) rapidly crystallize when heated at 220−250 °C for 5 min, as expected for a phase-change material. The crystallized film generates a new light beam at 766 nm obtained by mixing two distinct light

5. NLO CHALCOGENIDE GLASSES 5.1. Intrinsic Second-Order NLO Responses of Glasses. A main challenge for NLO applications is the costly, lengthy, and labor-intensive process of growing large optical quality single crystals. It is also difficult to fabricate fibers and films of the materials, though many applications require them. Because of their IR transparency and high index of refraction (2.2−3.5),100 chalcogenide glasses are promising contenders for low-loss IR optical fibers or planar waveguides. Can glasses ever have permanent NLO responses? Glasses ordinarily lack a second-order optical nonlinearity because of the presence of inversion symmetry at the macroscopic level. Accordingly, poling techniques using thermal,101 optical,102 and electron beam irradiation103 have been extensively studied104 to artificially induce SHG in glasses. These procedures are complex and expensive; the resulting SHG is too small for practical applications and often nonpermanent. As a result, the application of conventional glassy silica fiber, the backbone of modern telecommunication systems, has to be largely restricted to passive devices, generally requiring the aid of electro-optic systems. Recently, it has been shown that stable chalcogenide glasses prepared from K2P2Se61and KPSe62,3 can be prepared that have strong SHG response. Pair distribution function (PDF) analysis and Raman spectroscopic studies on the crystalline and glass version of K2P2Se6 and KPSe6 reveal that their glassy phases still largely preserve the basic building blocks that define the noncentrosymmetric structure. In contrast to a common glass such as silica, only the long-range crystallographic order is lost but local structure seems intact. In fact, for Cs5P5Se12,30 A4GeP4Se12 (A = K, Rb, Cs),34 K2P2Se61 and KPSe6,2,3 863



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Figure 21. (a) Schematic illustration of APSe6 thin film fabrication procedure. (b) A photograph of RbPSe6 optical glassy thin film on the flexible plastic (ArylLite) substrate. (c) Cross-sectional TEM image of RbPSe6 thin film deposited on a Si substrate. The electron diffraction pattern taken on the corresponding area (inset) shows faint diffuse rings confirming the amorphous nature of the film. Reprinted with permission from ref 3. Copyright 2011 Wiley & Sons Inc.

Figure 20. (a) Representative photograph of an optical fiber showing remarkable flexibility. (b) A representative SEM image of a fiber showing thickness uniformity at 50.0 μm and surface smoothness. (c) The waveguided SHG response transmitted through 10.0 mm long KPSe6 glassy fiber, displaying NLO properties over a wide range of vis/near IR region. (d) The DFG response as a function of λidler, demonstrating wave-mixing capability over a wide range of wavelengths (λidler = 1575.0, 1497.4, 1420.5, 1350.1, and 1282.1 nm; λsignal = 646.4, 675.1, 709.8, 748.8, and 795.6 nm, from left to right). (e) The relative SHG intensities measured from 620 to 805 nm for the pristine glassy and annealed fibers, representing remarkable enhancement of the SHG response after heat treatment at 260 °C for 3 min. Reprinted with permission from ref 2. Copyright 2010 American Chemical Society.

Figure 22. NLO properties of RbPSe6 optically clear amorphous and crystalline thin films over a wide range of vis/near IR region. (a) Illustration of NLO property measurements on thin films. (b) Waveguided SHG response transmitted through 1.25 cm ×1.25 cm × 100 nm size of RbPSe6 glassy thin film. (c) DFG response of RbPSe6 crystalline film, demonstrating wave-mixing capability over a wide range of wavelengths. Tabulated are the wavelengths of two incident beams and those of nonlinearly mixed DFG lights. (d) Photographs of RbPSe6 crystalline film to generate strong visible lights from red to orange to green, by SHG process, representing continuous tunability of light waves. Reprinted with permission from ref 3. Copyright 2011 Wiley & Sons Inc.

waves with wavelengths of 485 and 1323 nm as defined by DFG (|1/λ1 − 1/λ2| = 1/λDFG) (Figure 22c). Because the compounds are optically transparent up to 19−20 μm,2 APSe6 (A = K, Rb) should produce tunable coherent light throughout the mid-IR region, where few suitable NLO materials are available.11 Remarkably, the recrystallized films derived from converting the amorphous films exhibit ∼30 times stronger SHG intensities than the pristine glassy films with continuous 864



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First, K2P2Se6 shows the more dispersed band features near the conduction band minimum (CBM) and consequently gives the smaller and more gradually rising joint density of states (JDOS) near the band gap region in comparison to KPSe6 (Figure 23). To directly reflect the effect of the JDOS on the

tunability from red to green from the incident IR in waveguided mode (Figure 22d). Note that the fabrication cost, time, and simplicity appear superior to any reported methods for NLO thin films. The procedure in principle can be widely applied to many compounds in this class of NLO materials, such as A2P2Se6 (A = K, Rb, Cs)1, AAsQ2 (A = Li, Na; Q = S, Se),5,6 and AM5Q8 (A = K, Rb, Tl; M = Sb, Bi; Q = S, Se).105 It is important to add a caveat here. It is not possible (with the data we have thus far) to unequivocally know where the NLO response originates in the amorphous films and fibers. While a random local structure reminiscent of the parent polar crystal structure is the likely possibility, we cannot absolutely rule out that nanocrystals of the phases are not embedded in the glass matrix giving rise to the response. For practical application this may not be an important question, but it is a fundamental question that is also relevant to the broader field glasses and phase change materials and ultimately needs to be settled. This will require further detailed studies using powerful techniques such as transmission electron microscopy.

Figure 23. Joint density of states for (a) KPSe6 and (b) K2P2Se6. Adapted and reprinted with permission from ref 90. Copyright 2009 American Physical Society.

χ(2) value, the model hypothetical χ(2) are calculated under the condition that all the optical matrix elements are fixed at the same constant value of 0.01. The resulting hypothetical static limits are 48 pm/V for K2P2Se6 and 170 pm/V for KPSe6, similar to the experimentally estimated values. Second, the local density of states (LDOS) also demonstrates the origin of the smaller χ(2) of K2P2Se6 than that of KPSe6. In 1 [P 2Se 62−], P−Se−Se−P covalent polymeric chains of ∞ interactions are weaker than those of the P−Se (terminal) and P−P. Thus, strongly localized characteristics within the [P2Se6] units are more evident rather than one-dimensional characteristics. This results in essentially flat bands and, accordingly, very sharp peaks in the angular momentumresolved LDOS for the lower energy range between −6 and −2.5 eV below valence band maximum (VBM) (Figure 24a,b). Third, the band gap region, especially near the conduction band minimum (CBM) of K2P2Se6, represents relatively more dispersed band features compared to KPSe6. The K atom in K2P2Se6 has more coordinating Se neighbors than that in KPSe6 within 3.5 Å. This difference could cause the delocalization of Se p states near the band gap that may be hybridized with empty K s states. In consequence, K2P2Se6 possesses less onedimensional characteristic than KPSe6, which presumably results in the difference in the χ(2) values. These results demonstrate the importance of crystal and electronic structures such as DOS in determining χ(2). 6.2. Theoretical Calculations on the AAsQ2 System. The importance of theoretical calculations is more clearly evident for the AAsQ2 system. The Se members of the AAsQ2 system possess the same one-dimensional chains of 1∞[AsSe2−]. The experimental SHG response of γ-NaAsSe2 is larger than those of β- and γ-Li0.2Na0.8AsSe2 and LiAsSe2. The observed result is consistent with the trend observed in the Li1−xNaxAsS2 system.6 The result can be naively understood by substitution effect of the more polarizable Na for the Li atom. Firstprinciples DFT calculations of the NLO properties reveals the true origin lies elsewhere.5,90 The one-dimensional structure of γ-NaAsSe2 creates high DOS and consequently large spatial overlap between the optical transition states to give a large static χ(2) value of 324.6 pm/V. For LiAsS2, the presence of the smaller Li cations allows strong interchain interactions that broaden the electronic bands and weaken the one-dimensional characteristic. This results in significantly smaller DOS near the band gap and a much smaller χ(2) value (196.3 pm/V) relative to γ-NaAsSe2 (Figure

6. THEORETICAL CALCULATIONS ON ONE-DIMENSIONAL NLO CHALCOGENIDE MATERIALS There have been extensive experimental studies on NLO properties. However, both an intuitive and theoretical understanding of how a crystal structure affects the value of χ(2) is not highly developed. Generally, first principles theoretical calculations do not address this issue. This is perhaps somewhat surprising since close relationships between many physical properties of materials and their crystal structure are well understood in other fields. To address this, Song et al. employed first principles theoretical calculations to investigate the electronic structures and calculate the frequency-dependent SHG coefficients of selected compounds aiming at finding the key relationships between structure and NLO properties. The electronic structures and their optical matrix elements were calculated using the highly precise full-potential linearized augmented plane wave (FLAPW) method79,106 with the screened exchange local density approximation (sx-LDA) as well as the Hedin-Lundqvist form of the exchange-correlation potential (LDA).107 The sx-LDA method with the FLAPW approach shows great improvements of the excited electronic states over the LDA and yields excellent estimates of the band gaps and band dispersions.108 To understand the SHG response of materials, we carried out first-principles SHG coefficient calculations5,90 using the so-called length-gauge formalism derived by Aversa and Sipe.109 Such calculations were performed on K2P2Se6,1 KPSe6,2,3,38AAsQ2 (A = Li, Na; Q = S, Se),5,6 and (see above) and results demonstrate the promise of theory in guiding the development and selection of NLO materials. 6.1. Theoretical Calculations on KPSe6 and K2P2Se6. K2P2Se6 and KPSe6 consist of the same constituent elements forming similar one-dimensional chains of 1∞[P2Se62−] (Figure 8) and 1∞[PSe6−] (Figure 12), respectively, with similar band gaps (see Table 1). These two compounds also show common density of states (DOS). Therefore it is reasonable that similar SHG coefficient χ(2) values might be expected. However, their calculated χ(2) values are surprisingly different at 53.7 and 151.3 pm/V, respectively. Such a difference results from their distinct electronic structures. 865



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Figure 24. Angular-momentum-resolved local densities of states for (a) KPSe6, (b) K2P2Se6, (c) LiAsS2, and (d) NaAsSe2. The scissor operator is not used in these results. Reprinted with permission from ref 90. Copyright 2009 American Physical Society.

24c,d). This finding provides an enormously valuable insight. The dimensional reduction by introducing the larger Na+ ion accounts for the higher SHG efficiency of the Na-rich systems, rather than the more polarizable nature of Na+ over Li+. As the 1 [AsSe2−] chains are Na+ ions substitute for Li+, the ∞ increasingly pried apart, thereby lowering the dimensionality of the system. Thus, controlling framework dimensionality should be a good strategy in designing better NLO materials.90 Note that dimensionality control and consequent expansion of the similar class of compounds have been well established to develop new materials and improve desirable properties in solid-state chemistry.94,110 Because low dimensionality of the metal chalcogenide network generally gives a higher DOS near the band gap (and by extension higher JDOS), it tends to lead to high NLO response. Therefore, these calculations offer a surprising and useful new insight. Namely, dimensionality of structure not just polarizability is important in dictating the ultimate NLO response. Clearly, the polarizability difference between K2P2Se6 and KPSe6 or between LiAsS2 and NaAsS2 is not very large or large enough to explain the drastically different NLO responses. This insight is very valuable in guiding future experimentation aimed at optimizing NLO behavior. Recently, an ab initio evolutionary algorithm was used to predict the stable and energetically competitive metastable structures of BiInS3.111 The evolutionary algorithm was used to find the global minimum of the energy landscape. Combining geometry optimization with the density functional method and the phonon dispersion calculations, the most stable structure of BiInS3 within several tens of thousands of candidates was suggested. The prediction was that the most stable structure is to be the P21 space group and its SHG coefficient is as large as 59 pm/V. This is a good example of how theory can challenge synthesis to come up with predicted new high performing materials. It would be interesting to see if large crystals of the compound can be grown in this space group.

7. SUMMARY AND PROJECTIONS This review has highlighted the emergence of a new generation of chalcogenide NLO materials that are the fruit of exploratory synthesis. They show rich structural and compositional diversity and excellent IR transparency, and this list continues to expand. In the collection of materials described above there are a few featuring low-dimensional structures which outperform the commercially available IR NLO materials such as AgGaQ2 (Q = S, Se) for SHG intensities at least in the optical region in which they were measured. Crystal dimensions for the materials featured in this review are typically large enough only for single crystal diffraction studies but generally are too small for detailed SHG studies. For the latter, crystal sizes of at least 5 mm on each size are required. Because of this, the comparison of SHG intensity to benchmark NLO materials and determination of phase-matchability is generally accomplished with the Kurtz powder method. Hence, future efforts should be focused on growing much larger, suitable crystals at least for selected materials. The growth of large single crystals will allow in depth NLO studies, for example, determination of type-II phase matchability, laser damage threshold, and assessment for practical use in applications. In addition, the index of refraction and birefringence, which is also wavelength-dependent, may be measured. Previously, NLO properties of samples in powder and single crystal form have been studied using a laser with single or at best a few wavelengths. This gives only a partial answer to the question of how good a material is for NLO applications. Our studies have shown that the SHG intensity of NLO materials varies significantly with wavelength, and the response is not constant even in the spectral region where such materials should be optically transparent. This means that a good NLO material in one region of the spectrum may be inferior in another region. Therefore, NLO studies need to be done over as wide a spectral range as possible. An unanticipated new realization from these recent studies was the realization that stable NLO glasses may be possible 866



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without the need of poling. Because phase-change behavior is common in chalcogenides, the new concept has arisen that exploits noncentrosymmetric phase-change materials to create stable NLO glasses. Systems that behave in this fashion are Cs5P5Se12, A4GeP4Se12 (A = K, Rb, Cs), A2P2Se6 (A = K, Rb), and APSe6. In addition, because of the phase-change properties of many of these materials, NLO glass fibers and thin films can be created which when annealed convert to crystalline counterparts, resulting in a huge boost of their NLO properties while maintaining their shape. These results point to a path that may circumvent some bottlenecks in the practical use of inorganic NLO materials. For example, it may obviate the preparation of large NLO crystals or thin films using physical deposition methods, which may be appropriate for some known applications or even enable new ones. Because of the advantage of mechanical flexibility, uniformity, low processing temperature, formability, and inexpensive fabrication, amorphous NLO films on a flexible plastic may open up new opportunities for NLO and electro-optic applications. Theoretical DFT calculations can provide reliable SHG/ NLO coefficients and birefringence coefficients. Accordingly, it is very useful in combination with the Kurtz powder method to confidently estimate the SHG responses before attempts are made to grow large single crystals. Theoretical electronic structure calculations show that low-dimensionality is a main reason for large second harmonic susceptibilities. These investigations provide a new insight to a valuable design principle for NLO materials and encourage exploratory synthesis of chalcogenide compounds for this purpose. Many structural building blocks are shown to form noncentrosymmetric structures frequently in this review. An interesting topic for theoretical studies would be a combinatorial library of such possible building blocks and structure-directing constituents that can ultimately stabilize noncentrosymmetric arrangements in a crystal. The research opportunities for theorists who are willing to develop code calculating the NLO properties (not only second harmonic but also higher order harmonic generation coefficients) of new materials are significant. Calculations, however, still cannot predict the unpredictable, i.e., the new material that we did not even know is there. Admittedly, the many breakthrough systems in the past were discovered, not predicted. The value of new material synthesis, therefore, cannot be underestimated and underpins virtually all developments in modern day physical science. The continued activities in novel materials discovery in general and chalcogenide chemistry in particular will undoubtedly lead to exciting yet often unanticipated insights that will help push fields of inquiry and technology forward. Finally, we stress that NLO measurements in general have lagged the materials discovery efforts mainly because there is a substantial disconnect between the sample producers and the measurers. The former are solid state and materials chemists with strong interests in synthesis and new structures but with no means to routinely assess NLO properties, and the latter are physicists or engineers with limited access to new materials. Some synthetic chemists have helped to advance the field by building in-house screening measurement facilities. To accelerate developments in this area, however, closer collaborations will need to be established and more joint funded programs will be beneficial.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 847-467-1541. Notes

The authors declare no competing financial interest. Biography Mercouri G. Kanatzidis received his Ph.D. degree in chemistry from the University of Iowa in 1984. He was a postdoctoral research fellow at the University of Michigan and Northwestern University from 1985 to 1987. At Northwestern University he is Charles E. and Emma H. Morrison Professor and also carries a joint appointment as a Senior Scientist at Argonne National Laboratory. He is active in the field of solar energy materials, thermoelectric materials, framework solids, and intermetallics.

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ACKNOWLEDGMENTS We thank our collaborators, Prof. J. B. Ketterson (Physics and Astronomy, Northwestern University) and Prof. J. Jang (Physics, Applied Physics and Astronomy, Binghamton University) for NLO measurements and Dr. J.-H Song (deceased) and Prof. A. J. Freeman (Physics and Astronomy, Northwestern University) for theoretical calculations. Without their creativity, expertise, and strong interest in novel materials, work in our laboratory on this fascinating topic would not have been possible. We thank Ms. Alyssa Haynes and Mr. Jonathan Syrigos for a critical read of the manuscript. Financial support for our synthesis program is provided by the National Science Foundation (Grant DMR-1104965).

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