Designing the syntheses and photophysical simulations of noncentrosymmetric compounds

Abstract

In this paper, we describe the preparations of inorganic noncentrosymmetric (NCS) chalcogenides and their infrared nonlinear optical properties. We present a reasonable synthesis of inorganic NCS compounds by considering the genetic development processes of a living organism. The basic unit having an NCS structure is selected as a chromophore of NCS materials. The NCS compounds are obtained from the NCS chromophore development of normal growth. Chromophore development is an alienation process of growth if the NCS compound is not formed by an NCS chromophore. The normal development of the NCS chromophores (SnS₄) and (Sn₂S₃) affords the NCS crystal of Ba₇Sn₅S₁₅; and the normal development of the NCS chromophores of (BiS₅) and (InS₄) affords a compound of Ba₂BiInS₅ maintaining an NCS structure. In both of them, the Ba²⁺ ions are a charge-compensating agent. The NCS crystals SnGa₄Q₇ (Q = S, Se) were obtained from NCS chromophores of (GaQ₄) and (SnQ₄)_. However, the centrosymmetric (CS) compound of Ba₆Sn₇S₂₀ was obtained because the development of NCS chromophores of the (SnS₄) and (SnS₅) is alienated from the normal process of growth. We give more examples of the NCS chromophore development of normal and alienable processes in this paper. For NCS compounds, we have examined their nonlinear optical (NLO) properties of micro-crystals (powders) and the electronic origin of the NLO response. The intensity of second harmonic generation (SHG), laser-induced damage threshold (LIDT), and infrared transparency were measured, and the conversion efficiency, figure of merit (FOM), and energy band structure were calculated for these NCS compound materials. It is found that the NCS materials of SnGa₄Q₇ (Q = S, Se) possess large conversion efficiencies, high damage threshold and wide transparencies in the mid-infrared region. Moreover, the study of the micro-mechanism elucidates that the stereochemically active lone-pair electrons of Sn²⁺ can significantly improve the polarity of the [SnQ₄] chromophore. Their large NLO responses originate from the covalent interactions of Sn–Q and the cooperative effects of polarities between the chromophores [SnQ₄] and [GaQ₄]. It is also found that the Ba₇Sn₅S₁₅ material has type-I phase- matchability, and that the SHG conversion efficiency and FOM are about twice that of AgGaS₂ at the saturated particle size (particle size of 150–212 μm). The Ba₈Sn₄S₁₅ is not a phase-matching material. The SHG intensity and conversion efficiency of Ba₈Sn₄S₁₅ are separately about 250 times those of α-SiO₂, and the SHG intensity and conversion efficiency are separately about 10 times those of AgGaS₂ at the particle size of 25–45 μm.

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Wen-Dan Cheng

Prof. Wen-Dan Cheng has a tenured position at Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences. He finished his undergraduate study at the Chemical Department of Xiamen University in 1977 and received his M.S. degree from Xiamen University in 1981. He worked as a visiting professor from 08/1998 to 02/1999 at the Department of Physics, Michigan Technological University, as a visiting scholar from 08/1992 to 12/1993 at the Department of Chemistry, Arizona State University and from 08/1987 to 07/1988 at the Department of Chemistry, University of Calgary. His research interests include designing the syntheses of electro-optical, frequency conversion, and thermoelectric materials, and calculations and simulations of their physical properties; modeling of structures and optics for nanoscale materials; simulations of nonlinear optics for fluorescent proteins, and development of calculated simulation methods for physical properties.

Chen-Sheng Lin

Chen-Sheng Lin received his B.S. degree in chemistry from the Xiamen University of China in 1991. He obtained his Ph.D. degree in physical material from City University of Hong Kong in 2006. His research interests focus on the simulation of materials science, including nonlinear optical properties of semiconductors, metal surfaces, molecular electronic structure, and crystal structure prediction using first principles method.

Zhong-Zhen Luo

Zhong-Zhen Luo was born in 1986 in Gansu, China. He received his BS degree in Materials Physics from Lanzhou University in 2009, and obtained his PhD degree in Materials Physics and Chemistry from Fujian Institute of Research on the Structure of Matter (FJIRSM), Chinese Academy of Sciences in 2014. He joined Prof. Wen-Dan Cheng's group as a research assistant professor in July 2014. His research interests focus on the synthesis, structures and physical properties of infrared nonlinear optical materials.

Hao Zhang

Hao Zhang received his B.S. degree in analytical chemistry from the NorthWest University of China in June 1996. He obtained his master's degree in Physics and Chemistry from Fujian Institute of Research on the Structure of Matter (FJIRSM) in 2000. He joined Wen-Dan Cheng's group as a research assistant professor in 2000. His research interests focus on the synthesis, structures and physical properties of infrared and visible nonlinear optical materials.

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Introduction

Noncentrosymmetric (NCS) compounds and their crystals can exhibit a variety of technologically important physical properties, and NCS crystals may become the materials with piezoelectricity, pyroelectricity, ferroelectricity, and second-order nonlinear optical (NLO) response.¹ The structural symmetry of a material affects its properties. There are crystallographic interrelationships between the NCS crystal classes^2,3 and physical properties, and among the 32 crystal point groups,⁴ 20 NCS groups (21 NCS crystal classes excluding point group 432 (O group)) can exhibit the piezoelectric or NLO effect. It has been noted that all pyroelectric materials have NLO behavior, but the converse is not true. An NLO material can be made into an optical frequency conversion device, and it can broaden the wavelength coverage ranges of the laser spectrum. As is well known, one can distinguish between two classes of laser sources.⁵ One class includes sources which generate tunable laser radiation directly from gains in gas discharge, solid-state bulk materials or optical fibers, i.e. direct laser radiation sources. The longest wavelength coverage of a direct solid state laser source is limited to only under 3.5 microns. The other class of laser source is based on the frequency conversion of basic laser sources using NLO crystals. It is for this purpose that many NLO crystals have been developed to broaden the wavelength coverage of the laser spectrum. Scientists and engineers constantly explore new NLO materials to solve the development of optical technology demand and twenty-first century scientific and technological challenges. The main progress has taken place during the last two decades following the advancement in near-infrared solid state laser technology and NLO crystals. The second harmonic generation (SHG) parametric down-conversion and up-conversion processes in NLO crystals as well as their combinations have been widely used to fill in gaps in the laser spectrum in which direct laser radiation does not exist or certain operational regimes are impossible from the vacuum ultraviolet (∼150 nm) to the deep mid-IR (middle infrared) ranges.^6–9 The coherent mid-IR sources have important applications in science and technology, including the detection and quantification of molecular trace gases,¹⁰ medical diagnostics and military systems,^11,12 free space optical communication and deep space exploration, etc.^5,13,14

At present, nonlinear frequency down-conversion is still a powerful method to transform the wavelength of near-IR laser sources to the mid-IR spectral range and generate coherent radiation in all time zones from 3 μm up to 20 μm and above. Non-oxide NLO crystals play a key role, in particular above 5 μm, such as unary, binary, ternary and quaternary arsenides, phosphides, sulfides, selenides or tellurides, and they have been used in such down-conversion devices. During the past ten years, many compounds with large NLO coefficients and wide transparencies in the IR region have been prepared, and they are K₂P₂Se₆,¹⁵ Na₂Ge₂Se₅,¹⁶ K₄GeP₄Se₁₂,¹⁷ Na_0.5Pb_1.75GeS₄,¹⁸ LiGaGe₂Se₆,¹⁹ α- and β-A₂Hg₃M₂S₈ (A = K, Rb; M = Ge, Sn),²⁰ Li₂In₂GeSe₆,²¹ Li₂CdMS₄ (M = Ge, Sn),²² Ba₆Sn₆Se₁₃,²³ [Zn(H₂O)₄][Zn₂Sn₃Se₉(MeNH₂)],²⁴ K₆Cd₄Sn₃Se₁₃,²⁵ K₁₄Cd₁₅Sn₁₂Se₄₆,²⁶ A₆Sn[Zn₄Sn₄S₁₇] (A = K, Rb, Cs),²⁷ BaGa₂GeQ₆ (Q = S, Se),²⁸ Pb₄Ga₄GeQ₁₂ (Q = S, Se),²⁹ Ba₄CuGa₅Q₁₂ (Q = S, Se),³⁰ Ag₂In₂Si(Ge)S₆,³¹ Ag_0.5Pb_1.75Ge(S_1−xSe_x)₄,³² Zn_xBa₂B₂S_5+x (x ≈ 0.2),³³ CsCd₄X^III₅Q₁₂ (X^III = Ga, In; Q = S, Se),³⁴ and Rb₂CdBr₂I₂.³⁵ All of them have their specific advantages but also some drawbacks. The crystals of AgGaS₂, AgGaSe₂, ZnGaP₂, GaSe and CdSe also have some drawbacks, although they can be obtained from the commercial market.³⁶ The crystals of AgGaS₂ and AgGaSe₂ have residual absorption, poor thermal conductivity and anisotropic thermal expansion. The crystals of ZnGaP₂ have limited transparency due to multi-photon and residual absorption. The GaSe crystal has a very low damage threshold, and CdSe has quite modest birefringence and nonlinearity. Accordingly, the development of new, and the improvement of existing nonlinear crystals are critical for advancing a mid-IR coherent source, in particular, with increasing conversion efficiency and output power.

Drs I. Chung and M. G. Kanatzidis considered that the metal chalcogenides are the most promising source of potential NLO materials with desirable properties, particularly in the IR region.³⁷ A general strategy is suggested to employ NCS chromophores as building units in the design of the syntheses of NLO crystals.^38–40 The NCS chromophore includes the distorted polyhedron with a d⁰ cation center resulting from a second-order Jahn–Teller (SOJT) effect,^41–44 polar displacement of a d¹⁰ cation center,⁴⁵ and the stereochemically active lone pair (SCALP) effect of the cation,^46–48 and the distorted triangle and tetrahedron.^49–52a The NLO crystal materials can also be constructed by the multifold NCS chromophore with different coordinate environments.^52b,53 In this paper, we present the reasonable designs of mid-IR NCS crystals by considering the gene development process.

Designs and syntheses of noncentrosymmetric compounds

Optimization of the material chromophore

The NCS chromophore is a fundamental building block (FBB) toward a NCS material. The development of the NCS chromophore will produce an instrumental device, which is through the processes: chromophore → cluster → … → unit cell → single crystal → device. In bio-systems, genetic development is through the processes: gene → genome → … → cell → tissue → organ. There are some common factors between a gene and an NCS chromophore; both are developments from a basic unit toward the purposes of larger dimensions and function. However, their natures are different. A gene is the molecular unit of heredity of a living organism, and it holds the information necessary to build and maintain an organism's cell and pass genetic traits to offspring. The word gene, when applied in non-biological contexts, connotes an FBB toward the purposes of larger dimensions and function.⁵⁴ Here, we must have a clear understanding that the material chromophore is not a life activity and the gene in bio-systems exists in a vital organ. By considering gene development in biosystems, we present reasonable designs of NCS inorganic materials originating from NCS chromophores. An NCS chromophore of a material has different coordinate structures, which are the distorted triangle, pentagon, n-polygon (n is odd number with ≠1), tetrahedron, octahedron, square pyramid, pentagonal pyramid, triangular bipyramid, pentagonal bipyramid, and other NCS structure geometries as shown in Fig. 1.

Fig. 1 Noncentrosymmetric chromophore structures. (a) Non-equilateral triangle (or triangular pyramid), (b) non-equilateral pentagon, (c) tetrahedron, (d) distorted octahedral, (e) square pyramid, (f) pentagonal pyramid, (g) triangular bipyramid, and (h) pentagon bipyramid.

There can be no guarantee of being able to predict a macroscopic NCS material, which is developed from an NCS chromophore. An NCS chromophore will develop gradually with a normal process of growth if the NCS crystal is constructed using an NCS chromophore. The chromophore development will be an alienation process of growth if the NCS structural crystal is not formed by an NCS chromophore. Such cases have been carefully studied by several groups. Dr Poeppelmeier et al.^55–59 synthesized and examined the crystallographically ordered transition-metal oxyfluorides [MO_xF_6−x]ⁿ⁻ (M = d⁰ transition metal, x = 1–3, and n = 2, 3) and determined that the polar or non-polar symmetry originates from the changes in the bond network. Dr Halasyamani et al. studied another series of analogues A₂Ti(IO₃)₆ (A = Li, Na, K, Rb, Cs, Tl) and considered that the polarity results only from the Li and Na phases of cation-size, coordination requirements, and bond valence concept arguments.⁶⁰ Our group synthesized the CS crystal of Ba₂BiGaS₅ and the NCS crystal of Ba₂BiInS₅, and found that they are constructed by the tetrahedral (Ga/InS₄) chromophore and the square-pyramidal (BiS₅) chromophore,⁶¹ and we consider that the different crystal symmetries result from the distorted tetrahedron or the cation size effect in these two compounds.

CS materials of Ba₆Sn₇S₂₀, Ba₂BiGaS₅ and NCS materials of Ba₇Sn₅S₁₅, Ba₂BiInS₅

Compound Ba₇Sn₅S₁₅ was prepared by a solid-state reaction method from stoichiometric amounts of BaS, Sn, and S. It crystallizes in the NCS space group P6₃cm of the hexagonal system, and is constructed by the material chromophores of the tetrahedron (SnS₄) and triangular pyramid (SnS₃).⁶² The Sn–S distances vary from 2.361 to 2.407 Å in the SnS₄ tetrahedron, and the calculated bond valence sums (BVS) of the Sn is 4.27 or 4.14, which is close to the oxidation state +4 of Sn. In the triangular pyramidal (SnS₃), the Sn has a threefold coordination with Sn–S distances ranging from 2.583 to 2.687 Å, and the calculated BVS is 2.30 or 2.25, which is close to the oxidation state of +2. The two triangular pyramids (2SnS₃) are arranged against each other. They share a basal plane and form a triangular bipyramid (Sn₂S₃). The isolated [SnS₄]⁴⁻ tetrahedra and [Sn₂S₃]²⁻ triangular bipyramids are held together by the Ba²⁺ cations.⁶² The NCS chromophores of (SnS₄) and (Sn₂S₃) develop normally into the NCS crystal, and the skeleton frame is plotted in Fig. 2a. Compound Ba₆Sn₇S₂₀ was prepared with the molar ratio of stoichiometric amounts of Ba, Sn, and S. It crystallizes in the CS space group C2/c of the monoclinic system, and is constructed by the material chromophores of the tetrahedron (SnS₄) and triangular bipyramid (SnS₅).⁶² In the triangular bipyramid, the Sn atom is coordinated by five S atoms with Sn–S distances ranging from 3.339 to 3.812 Å, and the calculated BVS of Sn is 4.09 or 3.96, which is close to the oxidation state +4 of Sn. In the SnS₄ tetrahedron, the Sn–S distances vary from 2.327 to 2.481 Å and the calculated BVS of Sn is 3.99 or 4.04, which is also close to the oxidation state +4 of Sn. Three (SnS₄) tetrahedra are connected to each other by corner sharing to form a kind of basic structural unit [Sn₃S₈]⁴⁻, and four (SnS₅) triangular bipyramids are connected to each other by edge sharing to form another basic structural unit [Sn₄S₁₄]¹²⁻. Both of the structural units [Sn₃S₈]⁴⁻ and [Sn₄S₁₄]¹²⁻ are connected to each other by corner sharing to form a three-dimensional framework with the Ba cations in the cavities in the configuration of the Ba₆Sn₇S₂₀.⁶² The development of NCS chromophores of the (SnS₄) and (SnS₅) is alienated from the normal process of growth, and the CS crystal is obtained as shown in Fig. 2b. By the comparisons between these two processes, we consider that the different crystal symmetries between the Ba₆Sn₇S₂₀ and Ba₇Sn₅S₁₅ result from the different oxidation states of Sn ions. We believe that the low oxidation state of Sn ions in the material chromophore (Sn₂S₃) will be favorable for growing NCS crystals.

Fig. 2 The skeleton frame of NCS chromophore development (Ba²⁺ ions are not shown): (a) normal process of chromophores (SnS₅) and (SnS₄) into Ba₇Sn₅S₂₀; (b) alienated process of growth into material Ba₆Sn₇S₂₀ from chromophores (SnS₅) and (SnS₄).

Compound Ba₂BiInS₅ was prepared by a solid-state reaction method from stoichiometric amounts of BaS, Bi, In, and S. It crystallizes in the NCS space group Cmc2 of the orthorhombic system, and is constructed by the NCS chromophores of the tetragonal pyramid (BiS₅) and the tetrahedron (InS₄), and charge-compensating Ba²⁺ ions.⁶¹ The Bi³⁺ ion is coordinated by five S²⁻ ions, and the bond lengths of Bi–S vary from 2.582(5) to 2.959(4) Å, featuring the irregular tetragonal pyramid (BiS₅). In the tetrahedron (InS₄), the In³⁺ ion is coordinated by four S atoms in the tetrahedral arrangement with bond lengths ranging from 2.447(6) to 2.578(6) Å. The edge-shared BiS₅ tetragonal pyramids with parallel arrangements are formed into a chain, and the corner-shared InS₄ tetrahedra are also formed into a chain. These two chains are further interconnected with each other through sharing corners to form the whole ₁^∞[BiInS₅]⁴⁻ anionic chain. The NCS chromophores of (BiS₅) and (InS₄) develop into a compound maintaining an NCS structure, as shown in Fig. 3a. Compound Ba₂BiGaS₅ was prepared by a solid-state reaction method from stoichiometric amounts of BaS, Bi, Ga, and S. It crystallizes in the CS space group Pnma of the orthorhombic system, and is constructed by the NCS chromophores of the tetragonal pyramid (BiS₅) and tetrahedron (GaS₄), and charge-compensating Ba²⁺ ions.⁶¹ The coordinate environments of chromophores (BiS₅) and (GaS₄) in the CS crystal Ba₂BiGaS₅ are the same as those in the NCS crystal Ba₂BiInS₅. In the CS crystal Ba₂BiGaS₅, however, the edge-shared BiS₅ tetragonal pyramids with anti-parallel arrangements are formed into a chain, and the tetrahedral GaS₄ is connected with the tetragonal pyramid BiS₅ by the sharing corner, and the tetrahedra are the alternate arrangements along the chain constructed by the BiS₅. Furthermore, they form an infinite one-dimensional (1D) ₁^∞[BiGaS₅]⁴⁻ anionic chain. The development of the NCS chromophores appears in the alienated process and affords the CS crystal Ba₂BiGaS₅, as shown in Fig. 3b. It is very interesting that the different crystal symmetries between the CS Ba₂BiGaS₅ and NCS Ba₂BiInS₅ are obtained from the same coordinate structure of NCS chromophores of the tetrahedron (GaS₄/InS₄) and tetragonal pyramid (BiS₅). We checked the configurations of these two crystals in detail. A small-sized GaS₄ is connected with the neighboring BiS₅ through edge-sharing. This situation leads to a trans arrangement along the ₁^∞[BiGaS5]⁴⁻ chain with the apexes of BiS₅ pyramids reversed up and down alternately, and results in the CS nonpolar structure of compound Ba₂BiGaS₅. A large-sized InS₄ is connected with the neighboring BiS₅ through corner-sharing, which results in a cis arrangement along the ₁^∞[BiInS₅]⁴⁻ anionic chain with the parallel apexes of BiS₅ pyramids, and affords the NCS polar structure of Ba₂BiInS₅.

Fig. 3 The skeleton frame of NCS chromophore development (Ba²⁺ ions are not shown): (a) normal process of growth from chromophores (BiS₅) and (InS₄) into material Ba₂BiInS₅; (b) alienated process of growth from chromophores (BiS₅) and (GaS₄) into material Ba₂BiGaS₅.

NCS materials of SnGa₄Q₇ (Q = S, Se) and Ba₈Sn₄S₁₅ with Sn–Q covalent interactions

Compounds SnGa₄S₇ and SnGa₄Se₇ were prepared from reactants of Sn, Ga, and S/Se by a solid-state reaction method at high temperature. Both compounds are crystallized in the NCS space group Pc of the monoclinic system, and the remarkable configurations of three-dimensional frameworks are formed by the tetranuclear secondary basic structural unit Ga₄Q₁₁ which is constructed by four GaQ₄ tetrahedra, and the SnQ₄ tetragonal pyramid located in the cavities.⁶³ In other words, the NCS crystals SnGa₄Q₇ (Q = S, Se) are constructed by NCS chromophores of the tetrahedron (GaQ₄) and tetragonal pyramid (SnQ₄), as plotted in Fig. 4. The Sn atom is bonded to four Q atoms at two short and two long distances, forming the SnQ₄ tetragonal pyramid, and the Sn–S bond distances range from 2.654 to 2.992 Å in SnGa₄S₇ and the Sn–Se bonds vary from 2.773 to 3.111 Å in SnGa₄Se₇. All Ga sites are coordinated by four Q atoms to form the tetrahedra GaQ4. The Ga–S bond lengths range from 2.214 to 2.337 Å in SnGa₄S₇ and the Ga–Se bonds vary from 2.346 to 2.463 Å in SnGa₄Se₇. The atomic covalent radii of S, Se, and Sn are individually 1.05(3), 1.20(4), and 1.39(4) Å,⁶⁴ and here, the bond lengths of Sn–S and Sn–Se are a little larger than the sum of the covalent radius due to the crowd coordination environments of SnG₄ (G = S, Se). The calculated ELF (electron localization function) plot shows that there is a charge distribution along the bond axis of Sn–Se (Fig. 5a). This finding indicates the Sn–Se covalent interactions.

Fig. 4 The skeleton frame of NCS chromophore development of the normal process from (SnS₄/Se₄) and (GaS₄/Se₄) into NCS materials of SnGa₄Q₇ (Q = S, Se).

Fig. 5 (a) The electron localization function map of SnGa₄Se₇ at the (001) plane cutting through the Sn and Ga atoms and the electron localization function value ranging from 0 (blue) to 1 (red); (b) the charge distributions of the occupied bands near the Fermi level for Ba₈Sn₄S₁₅ (black, Ba; red, Sn; yellow, S).

Compound Ba₈Sn₄S₁₅was prepared from a stoichiometric mixture of the BaS–SnS–SnS₂ by a solid-state reaction method at high temperature, and it crystallizes in the NCS space group Pca2₁ of the orthorhombic system.⁶⁵ The Ba₈Sn₄S₁₅ crystal is constructed by the NCS chromophores of tetrahedra (SnS₄) and pyramids (SnS₃) with Ba²⁺ cations inserted between them for charge balance. Fig. 6 gives the skeleton frame of the chromophore development of the normal process from NCS chromophores (SnS₃) and (SnS₄). In the tetrahedra SnS₄, the Sn–S distances range from 2.3373 to 2.4124 Å, and the calculated BVS of Sn is 4.20 or 4.09, which is close to the oxidation state +4; in the SnS₃ pyramids, the Sn–S bond lengths range from 2.5336 to 2.6817 Å, and the calculated BVS of Sn is 1.93, which is close to the oxidation state +2.⁶⁵ At the right of Fig. 6, the secondary basic structural unit of Ba₈Sn₄S₁₅ is regarded as a coin-like structure, which forms the two-dimensional (2D) honeycomb structure by an alternate arrangement in parallel. The skeleton of the honeycomb (coin-like configuration) is formed by 6 SnS₃ pyramidal units and 18 Ba atoms in the ordered arrangement on the edge and isolated nine SnS₄ tetrahedral units and eight Ba atoms fill in the cells of the honeycomb. The charge distributions near the Fermi level are the main contributions from the SnS₃ pyramidal units shown in Fig. 5b. This finding also indicates the Sn–S covalent interaction in SnS₃.

Fig. 6 The skeleton frame of NCS chromophore development of the normal process from chromophores (SnS₃) and (SnS₄) into NCS materials of Ba₈Sn₄S₁₅.

Photophysics simulations and micro-mechanisms of infrared NLO materials

Physical properties

The optical conversion efficiency is the most important standard to evaluate the optical properties of NLO materials. While we select an NLO crystal as frequency conversion devices with a certain laser wavelength, the first option is to require high conversion efficiency. For simplicity of representation, we only consider the SHG process of an NLO response. The SHG conversion efficiency is defined as η = I_2ω/I_ω, which is a rate of SHG and incident light intensities. The SHG intensity I_2ω can be written in terms of the intensity of the incident field according to the couple wave theory, and the expression is written as follows:^66a

In the MKS system, we can write the conversion efficiency as

η = CFOMI_ωL²λ_ω⁻²PMF, (2)

in which the PMF is the phase mismatch factor which includes entirely the effect of the wave vector and the constant C = 128π²ε₀⁻¹, and FOM = d_eff² (n_ω⁻²n_ω⁻¹) is defined as a figure of merit. Here, the relationship between the frequency and wavelength of ω = 2πc/λ is employed from formulae (1) to (2). In accordance with formula (2), to maximize SHG efficiency it is essential that the conditions of perfect phase matching are satisfied, i.e. Δk → 0 and PMF = 1, otherwise, there is a dramatic decrease in the SHG efficiency. Under the conditions of PMF = sin² (ΔkL/2)(ΔkL/2)⁻² perfect phase matching, SHG efficiency can be improved by using higher radiation intensity I_ω and shorter radiation wavelength λ_ω, longer interaction length L, and greater figure of merit FOM. The powder SHG conversion efficiency of a new material can be determined by comparisons with the standard material in terms of the measurements of SHG intensity vs. particle size.^63,68

The FOM is determined by the SHG coefficient d and refractive index n of the material, and they can be simulated or calculated by the energy band theory combined with the sum-over-states method⁶⁷ or the classical anharmonic oscillator model.^66b The bulk SHG coefficient, d_eff, can be estimated by the comparisons between the incident optical intensities of the sample and known material.⁶⁸ The optical parameters d and n are related to the space structure, charge distribution and transition energy of the crystal material. The FOM is a primary index for the screening of different NLO materials.

Radiation intensity I_ω is dependent on the incident optical power P at the fundamental frequency and the cross-sectional area A, and it is in accordance with the relationship I_ω = P/A. Accordingly, to obtain the strongest radiation intensity, there must be the largest possible power P and the smallest possible area A if the threshold of the NLO crystal is not a limiting factor. In fact, this situation is not possible, and the threshold is dependent on the optical gap of the material. The latter can be obtained by the calculation of band structures or the measurement of UV–vis diffuse reflectance spectra.⁶⁹

Additionally, the SHG efficiency can be improved if there is a large L/λ_ω ratio. To obtain a large L/λ_ω ratio, it is necessary for light to pass through the crystal as long as possible or through a large size of crystal and provide a shorter incident wavelength. For a thick crystal (a large L), the maximum ratio L/λ_ω for a given wavelength λ_ω is limited by the thermal conductivity of the material (low thermal conduction leads to heat accumulation and the crystal burst within a large size of crystal). For a thin crystal (very small L), obtaining a large L/λ_ω ratio requires the radiation wavelength to be as short as possible. It is limited by the given wavelength of the radiation source and the anti-damage ability of the material. Accordingly, we require a width window of light transparency in NLO materials. This fact allows us to have a wide coverage of the tunable incident wavelength.

The NLO crystal with high quality laser frequency conversion must meet the conditions of strong radiation intensity I_ω, short radiation wavelength λ_ω, long interaction length L, and great figure of merit FOM, which is associated with a high conversion efficiency. Additionally, NLO crystals require: (1) the stability of physical and chemical properties, high hardness, anti-moisture; (2) a good optics uniformity of large-sized crystals; (3) easy processing and low price of crystals, etc. In fact, it is very rare that the NLO crystal is in full compliance with the terms mentioned above. We only select the NLO crystal that meets the most basic conditions according to the application requirement. For example, we require a high conversion efficiency, a large FOM, width infrared transparency including two windows of atmosphere (about 4 and 16 μm), and a large threshold for infrared NLO crystals.

Phase matching requirement. Fig. 7a shows a plot of the SHG intensity vs. particle size for SnGa₄G₇ powders (G = S, Se), and the AgGaS₂ powder was prepared with the same size ranges as the reference.⁶³ The SHG intensities of these powders are essentially proportional to particle sizes, which indicates that they are the type-I phase-matching materials.⁷⁰ The type-I phase matching indicates that the polarizations of both input beans at ω frequencies are parallel to each other, and the polarization of the output bean at 2ω is orthogonal to the input beans. In accordance with formula (2), the phase-matching requirement is essential to maximize the SHG efficiency. Furthermore, we can derive the relative SHG conversion efficiencies η^S/η^R = (I^S_2ω/I_ω)/(I^R_2ω/I_ω) from the relative SHG intensities I^S_2ω/I^R_2ω between the sample and the reference. From Fig. 7a, we can find that the SHG intensities of SnGa₄S₇ and SnGa₄Se₇ are about 1.3 and 3.8 times that of the benchmark AgGaS₂ at the particle size of 150–210 μm, respectively. These findings indicate that the conversion efficiencies of SnGa₄G₇ (G = S, Se) are 1.3 and 3.8 times larger than those of AgGaS₂, separately, under the same experimental conditions and devices. Fig. 7b gives the plots of the SHG intensity of particle-size dependence for Ba₈Sn₅S₁₅ powders. It shows the important feature of the particle size in Fig. 7b, and it is a peak of the intensity when the particle size is close to 95 μm. The intensity increases approximately linearly with the particle size when the particle size is less than 95 μm, and there is an inverse relationship between the intensity and the size when the particle size is larger than 95 μm. Similar features of the particle-size dependence are exhibited by powders of quartz (α-SiO₂) as illustrated in the inset of Fig. 7b, which indicates that Ba₈Sn₄S₁₅ and α-SiO₂ are not phase-matching materials on the basis of SHG measurements in powders.⁷⁰ By the comparisons of the intensity localized at the peak between Ba₈Sn₄S₁₅ and α-SiO₂, we can derive that the SHG intensity and SHG conversion efficiency of Ba₈Sn₄S₁₅ are separately about 250 times those of α-SiO₂, and we also can find that the SHG intensity and SHG conversion efficiency are separately about 10 times those of AgGaS₂ at the particle size of 25–45 μm from Fig. 7b.

Fig. 7 The SHG intensity vs. particle size of powders (a) SnGa₄G₇ (G = S, Se) and AgGS₂; (b) Ba₈Sn₄S₁₅, α-SiO₂ (inset panel), and AgGaS₂.

Figure of merit and nonlinear optical coefficient. In accordance with formula (1), the SHG intensity I_2ω is in direct proportion to the NLO coefficient d_eff² and is inversely proportional to refractive indices (n_ω²n_2ω). And both the refractive index and NLO coefficient are in inverse relationships with the band gaps. The figure of merit (FOM) is a balance indication of contradiction contributions between the refractive index and the NLO coefficient, and well describes the quality of the material-self. The FOM relative value between the sample and the reference can be derived from the plots of SHG intensity vs. particle size, furthermore, the NLO coefficient of the sample can be estimated from the d^S_eff ≈ (I₂^S_ω/I^R_2ω)^1/2d^R_eff from the FOM relative value when omitting the differences of refractive index n between the sample and the reference. The FOMs of SnGa₄G₇ (G = S, Se) are about 1.3 and 3.8 times those of AgGaS₂, and their SHG coefficients d_eff are estimated to be 15.85 and 27.10 pm V⁻¹, with AgGaS₂ (d^R_eff = 13.9 pm V⁻¹ (ref. 71)) as a reference in Fig. 7a.⁶³ The theoretical values of the SHG coefficient d are also obtained by using the velocity-gauge formula derived by Sipe et al.⁶⁷ The space groups of SnGa₄G₇ (G = S, Se) crystals belong to class m, and there are ten non-vanishing tensors (d₁₁, d₁₂, d₁₃, d₁₅, d₂₄, d₂₆, d₃₁, d₃₂, d₃₃, and d₃₅) of second-order susceptibility. Judging from Kleinman's symmetry, only six independent tensor components (d₁₁, d₁₂, d₁₃, d₁₅, d₂₄, and d₃₃) are taken into account in the calculations, and the calculated values are listed in Table 1. The largest and smallest components (d₃₃ and d₁₂) are calculated to be 37.51 and −1.77 pm V⁻¹ for SnGa₄Se₇, and 15.70 and −2.39 pm V⁻¹ for SnGa₄S₇ at a wavelength of 2.05 μm, respectively. The largest components of calculations are of the same order of magnitude as the experimental estimation for SnGa₄G₇ (G = S, Se).

Table 1 Theoretical SHG coefficients d_ij (pm V⁻¹) at a wavelength of 2.05 μm

Compounds	d 11	d 12	d 13	d 15	d 24	d 33
SnGa4S7	−6.82	−2.39	−3.54	9.12	−10.19	15.70
SnGa4Se7	−4.82	−1.77	−5.54	18.84	−13.80	37.51

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The FOM of Ba₈Sn₄S₁₅ is 250 times that of α-SiO₂ and the SHG coefficient d_eff is estimated to be 6.39 pm V⁻¹ in intensity and localized at the peak (i.e. particle size of 95 μm), with α-SiO₂ (d^R_eff = 0.30 pm V⁻¹ (ref. 72)) as a reference in Fig. 7b.⁶⁵ Additionally, the FOM of Ba₈Sn₄S₁₅ is 1.12 times that of AgGaS₂ and the SHG coefficient d_eff is estimated to be 14.71 pm V⁻¹ in intensity at a particle size of 180 μm, with AgGaS₂ (d^R_eff = 13.9 pm V⁻¹(ref. 71)) as a reference in Fig. 7b.⁶⁵ The space group of Ba₈Sn₄S₁₅ belongs to the class mm2, and there are five non-vanishing tensors (d₁₅, d₂₄, d₃₁, d₃₂, and d₃₃) of second-order susceptibility. Under the restriction of Kleinman's symmetry, only three independent SHG tensor components (d₃₁, d₃₂, and d₃₃) are considered. The calculated frequency-dependent SHG coefficients d₃₁, d₃₂, and d₃₃ are plotted in Fig. 8 based on the classical anharmonic oscillator model.^65,66b It is found from Fig. 8 that the theoretical values of d₃₁, d₃₂, and d₃₃ are about 23.97, 21.97, and 23.92 pm V⁻¹ at a wavelength of 2.05 μm (0.60 eV), respectively. Note that the theoretical SHG coefficients d_ij only come from the electronic contributions, not including the contributions from lattice vibrations; and the measured SHG coefficients d_ij of the powder depend on the particle size. Accordingly, the estimated value of d_eff based on the experimental measurement must come from the saturated particle size, i.e. SHG intensity is independent of the variation of particle size.

Fig. 8 The calculated frequency-dependent second harmonic generation tensor components for Ba₈Sn₄S₁₅.

Laser induced damage thresholds. The damage threshold of the material is also an important evaluation condition for a good quality NLO material. The damage threshold value is related to the parameters I_ω and λ_ω written in formula (1). The materials with higher damage threshold can be illuminated by a high intensity of the laser, and this material has a large SHG conversion efficiency. It was reported that the laser damage probability depends on the fluency.^73–75 It was given that the fluence or energy density (J cm⁻²) relates to the electric field (E²₀) and incident wavelength λ.⁷³ Here, a single pulse laser induced damage threshold (LIDT) is employed to evaluate the powder damage threshold.⁷⁶ The same particle size of samples SnGa₄G₇ (G = S, Se), Ba₈Sn₄S₁₅ and reference AgGaS₂ were packaged into the disks with a diameter of 8 mm. The optical microscope was used to observe the changes of the compounds when high-power 1064 nm laser radiation passed with a pulse width τ_p of 8 ns. The power of the laser beam was measured by a Nova II sensor, and the damage spot was measured using a Vernier caliper. Then the recorded laser power and the measured area of the damage spot were used to derive the LIDT values of the samples SnGa₄G₇ (G = S, Se), Ba₈Sn₄S₁₅ and reference AgGaS₂.^63,65 The results of powder LIDTs using single pulse measurement for these samples and reference are summarized in Table 2. The values in brackets correspond to the particle size range (25–45 μm) of Ba₈Sn₄S₁₅ and AgGaS₂, and the other values correspond to the particle size (150–210 μm) of SnGa₄S₇, SnGaSe₇ and AgGaS₂ in Table 2. The comparisons between the sample and the reference were made under the same experimental conditions. Accordingly, we find that the LIDT of Ba₈Sn₄S₁₅ (122.1 MW cm⁻²) is about 26 times that of AgGaS₂ (4.6 MW cm⁻²), and the LIDTs of SnGa₄S₇ (165.1 MW cm⁻²) and SnGa₄Se₇ (40.0 MW cm⁻²) are about 19 and 4.6 times that of AgGaS₂ (8.6 MW cm⁻²), respectively. The high LIDTs imply that these materials are promising for high-power NLO application in the IR region.

Table 2 Results of powder LIDT measurements for compounds

Compound	Damage energy (mJ)	Spot diameter (mm)	Damage threshold (MW cm^−2)
SnGa4S7	49.83	3.1	165.1
SnGa4Se7	34.00	5.2	40.0
Ba8Sn4S15	55.37	3.8	122.1
AgGaS2	12.13 (10.05)	6.7 (8.3)	8.6 (4.6)

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Micro mechanism of NLO response for infrared materials

Band structures and density of states. The structures of energy bands are used to determine the optical gap and transparent zone, and the transport properties of the material. The densities of states near the Fermi level are employed to determine the atomic or group charge distribution, and to analyze the process of charge transfers and the electronic origin of the NLO response. The calculated band structures along the special k-point in the first Brillouin zone (BZ) and the partial density of states (PDOS) and total density of states (TDOS) are plotted in Fig. 9 for the Ba₂BiInS₅ compound.⁶¹ It is found from Fig. 9a that the valence band maximum (VBM) is located at the middle of the Γ–S line, while the conduction band minimum (CBM) is located at the Γ point, indicating an indirect band gap of 1.61 eV for the Ba₂BiInS₅ compound. It is found from Fig. 9b that the highest occupied states ranging from −4.0 to 0.0 eV (Fermi level) mainly contain S-3p states with small mixtures of Bi-6s6p and In-5s5p states; the lowest unoccupied states from 1.6 eV to 4.5 eV strongly involve unoccupied Bi-6p states and less unoccupied In-5s5p states. Thus, the charge transfers from occupied S-3p states to unoccupied Bi-6p states and to the hybridized In-5s5p states are believed to make the main contributions to the optical absorption. We can see from PDOS that the dominant contribution to the Bi-6s state is found at the lower energy range of −8.0 to −9.4 eV, and that the indirect mixing between Bi-6s and Bi-6p states is mediated by hybridization with S-3p states at the top of the valence band for the Ba₂BiInS₅ compound. Although the hybridized states of Bi-6s with S-3p close to the Fermi level account for only a small fraction of the total Bi-6s states, they play an important and crucial role in the formation of the Bi-6s stereochemically active lone-pair electrons. These results show that the formation of the Bi³⁺ 6s² lone pair depends on the S²⁻ anion, and this dependence on the electronic states of the anion is evidence of the stereochemically active lone pair. Further evidence of the stereochemically active lone-pair electron can also be found based on the partial electron density (PED) of Fig. 10.⁶¹ The PEDs of the states from −2.5 to 0.0 eV (Fermi level) were calculated for the Ba₂BiInS₅ compound, and plotted in Fig. 10. Two-dimensional electron density slices containing Bi and S atoms are shown through the (001) plane. An almost spherical electron distribution can be seen around the S atoms, and an asymmetric density distribution is clearly present around each Bi atom which is directed away from their nearest-neighboring S atom. This finding indicates that there are stereochemically active Bi³⁺ lone pairs. The stereochemically active Bi³⁺ lone pairs manifest in parallel local dipole alignment fashions and the cooperative effects of all local dipoles lead to the enhancement of macroscopic dipole moments. This is a micro origin leading to a large SHG response of the Ba₂BiInS₅ compound. Fig. 11 gives the plots of the calculated band structures and densities of states of the Ba₇Sn₅S₁₅.⁶² It is found from Fig. 11a that this compound is an indirect band-gap material with a gap of 2.14 eV. From Fig. 11b, we find that the band just above the Fermi level is predominantly derived from Sn-5p states in group [Sn₂S₃]²⁻, and is also a small contribution from Sn-5s and S-3p states in group [SnS₄]⁴⁻. However, the band just below the Fermi level is mostly composed of S-3p states in [Sn₂S₃]²⁻ and [SnS₄]⁴⁻ groups. Accordingly, the charge transfers across the band-gap edge originate from the (Sn₂S₃) and (SnS₄) polyhedra.

Fig. 9 (a) The band structures and (b) total and partial density of states for Ba₂BiInS₅ using the norm-conserving pseudopotential method. The Fermi level is set at 0.0 eV.

Fig. 10 The partial electron density maps for compound Ba₂BiInS₅, and the electron density is represented from blue (0.0 e Å⁻³) to red (0.11 e Å⁻³). The above DFT calculations were performed using the PAW potential method.

Fig. 11 (a) The band structures and (b) density of states for the Ba₇Sn₅S₁₅ compound.

Local dipole moment. The local dipole moments of [Sn₂S₃]²⁻ and [SnS₄]⁴⁻ are 2.1287 and 0.9547 Debye, respectively, in a Ba₇Sn₅S₁₅ compound based on the electronic structural calculations of isolate groups.⁶² These results show that the polarization is much larger for the isolate trigonal–bipyramidal [Sn₂S₃]²⁻ than for the isolate tetrahedral [SnS₄]⁴⁻ in the Ba₇Sn₅S₁₅ material. Accordingly, we consider that the group (Sn₂S₄) makes the most contribution to the NLO response of the Ba₇Sn₅S₁₅ material. Fig. 12a gives the top view of the electron density contour surface for isolate [Sn₂S₃]²⁻, and indicates the charge transfers from S²⁻ to Sn²⁺ ions. Fig. 12b shows the plots of group [Sn₂S₃]²⁻ arrangements in the Ba₇Sn₅S₁₅ crystal, and it is found that the dipole origins of [Sn₂S₃]²⁻ along the z direction are parallel to each other. The polarity superposition of the [Sn₂S₃]²⁻ groups will strengthen the crystal polarity and lead to a large SHG response of a crystal material Ba₇Sn₅S₁₅. Table 3 lists the local dipole moments of the [SnS₃]⁴⁻ and [SnS₄]⁴⁻ anionic groups within the Ba₈Sn₄S₁₅ compound based on the calculations of an ab initio method with the Gaussian03 package.⁶⁵ The obtained results show that the polarization of the isolate pyramidal [SnS₃]⁴⁻ is much larger than that of the isolate tetrahedral [SnS₄]⁴⁻. The average dipole moments of the [SnS₄]⁴⁻ and total dipole moments of 6 [SnS₄]⁴⁻ groups in the unit cell are 1.8305 and 10.9832 Debye, respectively, and the average dipole moments of [SnS₃]⁴⁻ and total dipole moments of 2 [SnS₃]⁴⁻anions are 11.7229 and 23.4459 Debye, respectively, in the unit cell of the Ba₈Sn₄S₁₅ compound. A large dipole moment of [SnS₃]⁴⁻anions is attributed to its pyramidal geometry, which has the lone pair electrons of stereochemical activity. Thus, the [SnS₃]⁴⁻ anions can make more contribution than the [SnS₄]⁴⁻ anions to the NLO response of Ba₈Sn₄S₁₅.

Fig. 12 (a) The top view of the electron density contour surface and the dipole moment for isolate [Sn₂S₃]²⁻. (b) The arrangement of [Sn₂S₃]²⁻ in a 2 × 2 unit cell for the Ba₇Sn₅S₁₅ crystal, the [SnS₄]²⁻ group was not shown for clarity. Atom color: S: yellow, Sn: gray, Ba: green.

Table 3 Calculative dipole moments of [SnS₄]⁴⁻ and [SnS₃]⁴⁻ anions

Anion group	Dipole moment (Debye)
[Sn(1)S4]^4−	1.2359
[Sn(2)S4]^4−	3.0696
[Sn(3)S4]^4−	1.8126
[Sn(4)S4]^4−	1.5062
[Sn(5)S4]^4−	2.0640
[Sn(6)S4]^4−	1.2949
[Sn(7)S3]^4−	11.8679
[Sn(8)S3]^4−	11.5780

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Summary and prospect

We describe the optimization of NCS chromophores of materials, and present a way of designing the syntheses of inorganic NCS compounds based on the normal processes of development of NCS chromophores. We introduce the alienation process of NCS chromophore development when the NCS compound is not formed by NCS chromophores. We illustrate these concepts by taking actual examples. The NCS chromophores of (SnS₄) and (Sn₂S₃) were normally developed to obtain the NCS crystal of Ba₇Sn₅S₁₅. The NCS chromophores of (BiS₅) and (InS₄) were developed into a compound of Ba₂BiInS₅ maintaining an NCS structure. The NCS crystals SnGa₄Q₇ (Q = S, Se) were obtained by NCS chromophores of (GaQ₄) and (SnQ₄). In contrast, the CS compound of Ba₆Sn₇S₂₀ was obtained because the development of NCS chromophores of the (SnS₄) and (SnS₅) is alienated from the normal process of growth. We give more examples of NCS chromophore development, which is the normal or alienable process of chromophore growth, in this paper. Here, we only describe the inorganic NCS chalcogenides which are constructed by two chromophores. Moreover, they are constructed by three or multiple NCS chromophores which would be obtained based on the present method.

For NCS compounds, we investigate their NLO properties of micro-crystals (powders) and the electronic origin of the NLO response in view of the calculations and simulations. The SHG intensity, laser-induced damage threshold, and infrared transparency were measured. Furthermore, the relative conversion efficiency and figure of merit are derived based on SHG intensity measurements. The calculated charge distributions and local dipole are employed to evaluate the micromechanism of NCS materials. It is found that the NCS materials of SnGa₄Q₇ (Q = S, Se) possess large conversion efficiencies, high damage threshold and wide transparencies in the mid-infrared region. Also, the study of the micro-mechanism was done to elucidate that the stereochemically active lone-pair electrons of Sn²⁺ can significantly improve the polarity of the [SnQ₄] chromophore. Their large NLO responses originate from the covalent interactions of Sn–Q and the cooperative effects of polarities between the [SnQ₄] and [GaQ₄] chromophores. It is also found that the Ba₇Sn₅S₁₅ material has type-I phase-matchability, and that the SHG conversion efficiency and figure of merit are about twice those of AgGaS₂ at the saturated particle size (particle size of 150–212 μm). The Ba₈Sn₄S₁₅ is not a phase-matching material. The SHG intensity and conversion efficiency of Ba₈Sn₄S₁₅ are separately about 250 times those of α-SiO₂, and the SHG intensity and conversion efficiency are separately about 10 times those of AgGaS₂ at the particle size of 25–45 μm.

Based upon the requirements of high quality NLO crystals, we believe that the NLO crystals of SnGa₄Q₇ (Q = S, Se) are in full compliance with the mentioned requisites, and they are good candidates to be applied in laser frequency conversion of the mid-infrared zone. In the future, the key work will be to grow single crystals with sizes larger than 10 mm on the one hand, and on the other hand, to try to prepare transparent films with an NLO response.

Acknowledgements

This investigation was based on work supported by the National Basic Research Program of China (grant no. 2014CB845605) and the National Natural Science Foundation of China (21173225, 91222204 and 21101156).

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