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Article

K2CdGe3S8: A New Infrared Nonlinear Optical Sulfide

by
Zi-Xuan Wu
1,2,
Wen-Fa Chen
1,2,
Bin-Wen Liu
1,
Xiao-Ming Jiang
1,* and
Guo-Cong Guo
1,*
1
State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, China
2
University of Chinese Academy of Sciences, Beijing 100190, China
*
Authors to whom correspondence should be addressed.
Symmetry 2023, 15(1), 236; https://doi.org/10.3390/sym15010236
Submission received: 10 November 2022 / Revised: 29 December 2022 / Accepted: 4 January 2023 / Published: 15 January 2023
(This article belongs to the Special Issue Advances in Nonlinear Optics and Symmetry)
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Abstract

:
A quaternary metal chalcogenide, namely K2CdGe3S8 (I), is obtained through a high-temperature solid-state approach. Compound I crystallizes with the non-centrosymmetric space group P212121. It features a 2D layer structure with [CdGe3S8] layers consisting of tetrahedral GeS4 and CdS4 units, and counter K+ embedded between the layers. The compound exhibits a powder second-harmonic generation (SHG) response of ~0.1 times that of KH2PO4 (KDP) with phase-matchable character at the laser wavelength of 1064 nm. Remarkably, it has a wide band gap (3.20 eV), which corresponds to a favorable high laser-induced damage threshold of 6.7 times that of AgGaS2. In addition, the calculated birefringence (Δn) is 0.039 at the wavelength of 1064 nm, which satisfies the Δn criteria for a promising infrared NLO material.

1. Introduction

Nonlinear optical (NLO) materials play a crucial role in laser technology due to the frequency conversion effect and have wide applications in science and industrial fields, such as medical treatment, radar, and remote sensing [1,2,3,4,5,6,7,8,9,10,11]. For practical laser uses, a promising NLO crystal must meet the following technical requirements [12,13,14], namely, broad transparent region, large second-harmonic generation (SHG) coefficient, wide band gap for improved laser-induced damage threshold (LIDT), moderate birefringence Δn (~0.03–0.10), low dn/dT as material requirements, good crystal growth habit, and good chemical stability. Typical crystals including LiB3O5, β-BaB2O4, KH2PO4, and KTiPO4 are mostly used in the deep ultraviolet, ultraviolet, and visible-near infrared (IR) regions, while they are seriously limited in the mid- and far-IR regions due to their strong chemical absorptions. During the past decades, a series of excellent IR NLO crystals have been successfully synthesized and commercialized in the chalcogenide and pnictide systems, including AgGaS2 (AGS) [15], AgGaSe2 (AGSe) [16], and ZnGeP2 [17], which demonstrate the merits of a broad IR transparency and large NLO coefficients. However, all these crystals have serious drawbacks such as a low laser-induced damage threshold (LIDT), and strong two and multiphoton absorptions, thus considerably restricting their high-power applications. Therefore, exploring new high-performance IR NLO materials is of great importance, but comes with a big challenge.
The family of non-centrosymmetric metal chalcogenides is one of the best candidates to achieve excellent IR NLO properties due to their structural diversity and functional flexibility. Chalcogenides of group 14 elements have a strong tendency to exist with tetrahedral coordination, including MQ4 (M = Si, Ge, and Sn; Q = S, Se) [18] tetrahedra, the corner-sharing M2Q7 [19] unit, edge-sharing M2Q6 dimer [17], isolated M3Q9 ring [20] and adamantane M4Q10 unit [21,22]. These MmQn units can be further assembled into 1D chains, 2D layers and 3D networks, which can be modulated by the template role of counter cations. The architectures that are constructed of acentric MQ4 tetrahedra tend to form non-centrosymmetric structures, which is a prerequisite and challenging condition for NLO materials [23,24,25,26,27,28,29,30]. Moreover, most metals in chalcogenides, especially transition d10 metals, are usually tetra-coordinated to form distorted tetrahedral units; this fact increases the chance of SHG generation. Moreover, to expand the optical energy gap, a good molecular design strategy would be the introduction of alkali and alkaline earth metal cations (Li+, Na+, Mg2+, and so on), which are beneficial to high LIDTs. Under the guidance of these ideas, the I-IIB-IVA-VI compounds would be promising IR NLO candidates with a non-centrosymmetric structure for the SHG effect, wide band gap, and high LIDT. For example, in the structure of Na2ZnGe2S6 [31], each [GeS4] tetrahedron is corner-shared to form [GeS3]n chains, which further connect with discrete [ZnS4] tetrahedra to build a 3D framework. Na2ZnGe2S6 has been reported to possess optimal comprehensive performances with a wide band gap of 3.25 eV for a high LIDT (7 × AgGaS2), and a remarkable phase matchable SHG intensity (~0.9 × AgGaS2). Similarly, AZn4Ga5Se12 (A = K, Rb, or Cs) [32] in the non-centrosymmetric space group R3 feature 3D diamond-like frameworks and exhibit strong SHG responses (2.8–3.7 × AgGaS2) and high LIDTs (19.2–23.4 × AgGaS2) as well as moderate band gaps (2.41–2.49 eV). It has been evident that these examples are good candidates for IR NLO materials; however, the I-IIB-IVA-VI system is far from fully exploited.
Herein, the simultaneous introduction of the tetrahedral CdS4 and GeS4 units affords a new quaternary IR NLO chalcogenide, namely, K2CdGe3S8 (I). We will report its synthesis, crystal structure, linear and nonlinear optical properties, theoretical calculation of electronic structure band, and optical properties of I.

2. Experiment Section

2.1. Synthesis

For the preparation of I, reactants of CdCl2 powder (0.10 mmol, Aladdin, 99%), Ge metal (1.03 mmol, Alfa, 99.99%), S powder (2.59 mmol, Sinopharm, 99.9%), Li metal (1.05 mmol, Sinopharm, 99%), and KCl powder (1.55 mmol, Aladdin, 99%) were weighed in an argon-filled glovebox. All reagents were loaded into a quartz tube with a carbon crucible inside and sealed under a vacuum with 10−3 Torr; the tube was then put into a furnace with the following temperature curves. First heating to 400 °C for 5 h and holding there for 5 h, then heating to 700 °C for 5 h and keeping at that temperature for 100 h; subsequently, cooling it down to 400 °C for 96 h at a rate of 3 °C/h before turning down the furnace. Single crystals of I were finally obtained and were separated manually after washing the products with alcohol and deionized water.

2.2. Single-Crystal X-ray Diffraction (XRD) Analysis

A transparent crystal of 0.12 × 0.12 × 0.02 mm3 was choosen for single-crystal XRD analysis. Generally, the growth of bulk crystal is difficult; some methods can be used for sulfides, such as Bridgman, chemical vapor deposition and horizontal gradient freeze. A diffraction dataset was collected by using a Rigaku FR-X Microfocus diffractometer, which was equipped with Mo-Kα radiation (λ = 0.71073 Å) and operated at 45 kV and 66 mA at 297 K. The CrysAlisPro software [33] was used to reduce the dataset. The structure of I was solved based on the direct method, and F2 full matrix least squares method was used to perform the structural refinement. The structure of I was analyzed using the crystal software SHELXL 97 package [34]. The PLATON program [35] was adopted to check the symmetry of the final structure, and no higher symmetry was found. Details of data collection, structure refinements, and crystal parameters are given in Table 1. Detailed asymmetric atomic parameters and selected bond lengths are presented in Table 2 and Table 3, respectively.

2.3. Powder XRD Analysis

The purity of sample I was checked by powder XRD analysis using a Rigaku Flex600 X-ray diffractometer equipped with Cu Kα (λ = 1.54057 Å) radiation in the 2θ range of 5° to 65° with the scan step size of 0.02° at 293 K. The experimental and simulated powder XRD patterns of I are shown in Figure 1; the experimental XRD pattern is consistent with the simulation one, indicating that the powder sample of compound I is a pure phase (Figure 1a).

2.4. Energy-Dispersive X-ray Spectroscopy (EDS) Analysis

Element analysis of the title compound was performed using a Hitachi S-3500 SEM spectrometer equipped with an EDS. The result demonstrates that the concentration of each element in I, K:Cd:Ge:S = 2.3:1:3.7:9.6, is consistent with the experimental formula of I determined from single-crystal XRD measurement (Figure 1b).

2.5. IR and UV-Vis-NIR Diffuse-Reflectance Spectroscopy

The Fourier transform IR spectrum (Figure 2b) of I with the wavelength from 4000 to 400 cm−1 was recorded on a Nicolet Magana 750 FT-IR spectrophotometer. The UV-Vis-NIR diffuse reflectance spectrum (Figure 2a) of I was collected on the Perkin-Elmer Lambda 950 UV-Vis-NIR spectrophotometer with the wavelength ranging from 200 to 2500 nm, and BaSO4 as a reference. The Kubelka–Munk formula [36] was applied to transform the reflection spectra into the absorption spectra: α/S = (1 − R)2/2 R, where α represents the absorption coefficient, S represents the scattering coefficient, and R represents the reflectance.

2.6. Powder SHG and LIDT Measurements

Powder SHG of I was characterized by the Kurtz–Perry method [37] under the polarized laser irradiation of 2 mJ and 1064 nm with transmission mode at room temperature. Manually selected crystals and benchmark KDP were screened into five particle size ranges, namely, 30–50, 50–75, 75–100, 100–150, and 150–200 μm, for phase matching measurements. The frequency-doubling signals (532 nm) were detected by an Andor’s DU420A-BR-DD CCD. The powder LIDT of compound I and the reference AGS were assessed by the single-pulse powder LIDT method with the same particle size range [38]. The samples were irradiated with a 1064 nm (pulse width τp is 10 ns) laser beam until damage occurred on the surface of the sample. Then, the apparent color change was observed by an optical microscope. The LIDT was computed by the equation LIDT = E/πr2τp, where E, r, and τp are the energy of a single pulse, the spot radius, and the pulse width, respectively.

2.7. Computational Methods

Based on density functional theory (DFT) [39,40,41,42], the electronic band structure, density of states (DOS), and optical properties of compound I were calculated by the ABINIT software package. The orbital electrons of S-3s23p4, K-3s23p64s1, Ge-3d104s24p2, and Cd-4d105s2 were set as valence electrons. Exchange and correlation effects were addressed by generalized gradient approximation (GGA). The plane-wave cutoff energy was set to 18 Hartree, and a 5 × 3 × 2 Monkhorst–Pack k-point grid was adopted. Four hundred empty bands were used for optical calculations. Linear optical properties were described by the complex dielectric function ε i j = ε i j , r e ( ω ) + ε i j , i m ( ω ) , where the imaginary part ε i j , i m ( ω ) generated other optical constants by Kramers–Kroning transformation.
The frequency dependence of SHG tensors χ i j k ( − 2 ω , ω , ω ) were theoretically calculated by the “sum over states” and density functional perturbation method. SHG susceptibility is mainly from three parts: (1) the intra-band transition term χ i n t r a ( − 2 ω , ω , ω ) ; (2) the pure inter-band transition term χ i n t e r ( − 2 ω , ω , ω ) ; and (3) the modulation term χ m o d ( − 2 ω , ω , ω ) of intra-band contribution by the inter-band motion-related polarization energy [43].

3. Results and Discussion

3.1. Crystal Structure

Compound I was synthesized by the high-temperature solid-state method with a yield of 40% based on Ge, the compound was stable in the atmosphere for more than half a year. Phase I crystallizes in the orthorhombic space group of P212121 (No. 19, Table 1), and there are two independent K, one Cd, three Ge, and eight S atoms in the asymmetric unit. The Cd–S and Ge–S bond distances fell in the ranges of 2.503(4)–2.529(4) Å and 2.143(7)–2.262(4) Å, respectively, which are close to those in a series of chalcogenides, such as Na2CdGe2S6 (2.510–2.534 Å) [44], BaCdGeS4 (2.451–2.613 Å) [45], K2ZnGe3S8 (2.148–2.285 Å) [46], KLaGeS4 (2.175–2.220 Å) [47], KBiGeS4 (2.181–2.239 Å) [48] and Na5AgGe2S7 (2.189–2.247 Å) [49]. Meanwhile, the ∠S–Cd–S bond angles in I range from 98.62° to 118.50°, which differ significantly from the bond angle of 109.5° in the regular tetrahedral coordination, indicating that the [CdS4] tetrahedra in I are distorted. This phenomenon is caused by the second-order Jahn–Teller distortion of Cd2+ in a tetrahedral coordination environment. As illustrated in Figure 3a, compound I features a 2D layer structure. All Cd and Ge atoms are tetrahedrally coordinated to form CdS4 and GeS4 units, respectively. Each three GeS4 and one CdS4 tetrahedra share corners with each other to form a [CdGe3S11] cluster, all of which further share edges of GeS4 tetrahedra along the c direction and sulfur corners of GeS4 and CdS4 tetrahedra along the a direction, establishing the [CdGe3S8] layers (Figure 3b). All potassium cations in I are surrounded by six sulfur atoms with K–S distances of 3.239–3.725 Å (Table 3), which benefits the structural stabilization of I.

3.2. Optical Properties

As depicted in Figure 2a, the absorption spectrum of I transformed from UV-Vis-NIR diffuse reflectance indicates that compound I has an optical band gap of 3.20 eV, which is larger than that of commercial IR NLO crystals AgGaS2 (2.73 eV) [26], and comparable to those of the newly reported Cs2ZnGe3S8 (3.32 eV) [17], Cs2CdGe3S8 (3.38 eV) [17], K2ZnGe3S8 (3.36 eV) [42], K2MnGe3S8 (2.95 eV) [50] and Rb2CdGe3S8 (3.16 eV) [51]. It can be seen from the IR spectrum (Figure 3b) that compound I possesses a characteristic absorption at 6.25 μm, which can be attributed to the absorption arising from the stretching vibration in H2O. Therefore, compound I is transparent in the wide infrared range of 0.78–12 μm, where 0.78 μm corresponds to one-half of the band gap. The infrared transparent range covers the two most important atmosphere transparency windows at 3–5 and 8–12 μm.

3.3. SHG and LIDT Properties

To further evaluate the SHG property of I, the Kurtz and Perry method was used to measure the frequency doubling signal of powdery samples under the irradiation of a fundamental frequency 1064 nm laser. Crystalline KDP is selected as the reference for SHG comparison. As shown in Figure 4a, the measured SHG intensity of I was positively correlated with the particle size, indicating that the title compound is phase matchable. For the sample with the particle range of 75–100 µm, the SHG intensity of I is about 0.1 times that of benchmark KDP at 1064 nm (Figure 4b).
In addition, the well-known one single pulse method was adopted to measure the powder LIDT of compound I and AGS at 1064 nm. As presented in Table 4, compound I exhibits a LIDT of 268.05 mJ/cm2, approximately 6.7 times that of AGS powder (42.32 mJ/cm2). The positive correlation between LIDT and optical band gap has been widely accepted. Although the wide band gap can avoid two-photon and three-photon absorptions, the thermal expansion characteristic of NLO crystal also has a great influence on the LIDT. Therefore, the temperature dependence of cell lengths of compound I were characterized to investigate the thermal-expansion coefficient (TEC) by single crystal X-ray diffraction at 100–340 K with a step of 20 K. As displayed in Figure 5 the corresponding TEC values of I along the a-, b- and c-axes were 1.55 × 10−5, 4.86 × 10−5, and 2.05 × 10−5, respectively. The thermal-expansion anisotropy (TEA, δ; defined as δ = max{(αi − αj)/αi(i,j = a,b,c)}) of I is 2.12, which is remarkably lower than that of the AGS (2.95) [24,52], indicating that compound I has superior LIDT than that of AGS.

3.4. Electronic Structure and NLO Coefficient Calculations

To further investigate the intrinsic relationships between structure and the second-order NLO properties of I, first-principles calculations of electronic structure and NLO coefficients with the single crystal structure were performed. As can be seen from the calculated band structure (Figure 6a), compound I is an indirect band gap material with a theoretical band gap of 2.51 eV, which is smaller than the experimental result (3.20 eV). This phenomenon is reasonable because of the limitations of DFT calculations. The partial density of states (PDOS) of the title compound (Figure 6b) show that the top of the valence band is mainly constituted by S–3p states, and S–3p and Ge–4s states contribute mostly to the conduction band bottom. Therefore, GeS4 units are mainly responsible for the band gap absorptions.
Due to the point group of 222, only one independent nonzero SHG tensor, namely d123, is left for compound I, under the restriction of Kleinman symmetry. As shown in Figure 6c, the calculated d123 of I is −0.067 pm·V−1 at a wavelength of 1064 nm. In addition, the effective NLO coefficient at 1064 nm is 0.057 pm·V−1 (Figure 6c), which is in agreement with the experimental results. The refractive indexes nx, ny and nz along x, y and z directions at 1064 nm are 1.729, 1.747 and 1.769, respectively, among which nz and nx are the largest and smallest of all the refractive indices along different directions, respectively. As shown in Figure 6d, the calculated Δn is 0.039 at 1064 nm, supporting the phase-matching behavior, while in the region of 2–5 μm, compound I is non-phase-matchable.

4. Conclusions

A new quaternary chalcogenide K2CdGe3S8 has been synthesized by utilizing the high-temperature solid-state method. The compound features a 2D layer structure, in which the [CdGe3S8] layers are comprised of tetrahedral GeS4 and CdS4 units. The counter K+ cations are embedded between the layers. Particle size-dependent powder SHG studies reveal that compound I exhibits a phase-matchable SHG response of ~0.1 times that of KH2PO4 (KDP) at 1064 nm. The compound presents a favorable laser-induced damage threshold of 6.7 times that of AgGaS2, which is consistent with its relatively wide band gap of 3.2 eV and low thermal-expansion anisotropy. DFT calculations reveal that the valence band top and conduction band bottom of I are dominated by the states of GeS4 units, which are mainly responsible for the band gap absorptions. The theoretical birefringence index (Δn) of I is 0.039 at 1064 μm, which satisfies the Δn criteria for a promising IR NLO material.

Author Contributions

Conceptualization, Z.-X.W. and B.-W.L.; methodology, Z.-X.W.; theoretical calculation, W.-F.C.; writing—original draft preparation, Z.-X.W.; writing—review and editing, B.-W.L. and X.-M.J.; supervision, G.-C.G. All authors have read and agreed to the published version of the manuscript.

Funding

This work was funded by the National Natural Science Foundation of China (21827813, 21921001, 22175172, 22075283, 92161125), the Youth Innovation Promotion Association of Chinese Academy of Sciences (2020303, 2021300).

Data Availability Statement

CCDC 2215394 contains the crystallographic data for this paper. These data can be obtained free of charge via https://www.ccdc.cam.ac.uk/Community/Depositastructure/CSDCommunications/ (accessed on 3 January 2023).

Conflicts of Interest

The authors declare no conflict of interest.

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Symmetry 15 00236 g001 550
Figure 1. Simulated and experimental powder XRD patterns (a) and EDS (b) of compound I.
Figure 1. Simulated and experimental powder XRD patterns (a) and EDS (b) of compound I.
Symmetry 15 00236 g001
Symmetry 15 00236 g002 550
Figure 2. (a) Absorption spectrum of I transformed from UV-Vis-NIR diffuse reflectance; (b) IR spectrum of I.
Figure 2. (a) Absorption spectrum of I transformed from UV-Vis-NIR diffuse reflectance; (b) IR spectrum of I.
Symmetry 15 00236 g002
Symmetry 15 00236 g003 550
Figure 3. (a) Ball and stick representation of the layered structure of I as viewed down the a-axis. (b) A [CdGe3S8] layer, dark green and purple tetrahedral present GeS4 and CdS4 units, respectively. The [CdGe3S11] cluster is identified using dotted ellipse.
Figure 3. (a) Ball and stick representation of the layered structure of I as viewed down the a-axis. (b) A [CdGe3S8] layer, dark green and purple tetrahedral present GeS4 and CdS4 units, respectively. The [CdGe3S11] cluster is identified using dotted ellipse.
Symmetry 15 00236 g003
Symmetry 15 00236 g004 550
Figure 4. (a) Particle size dependence of SHG intensities of I and KDP under 1064 nm laser irradiation. (b) SHG signals of I and KDP in the size range of 75–100 µm.
Figure 4. (a) Particle size dependence of SHG intensities of I and KDP under 1064 nm laser irradiation. (b) SHG signals of I and KDP in the size range of 75–100 µm.
Symmetry 15 00236 g004
Symmetry 15 00236 g005 550
Figure 5. Temperature variation of the lattice parameters of I along the a, b, and c directions.
Figure 5. Temperature variation of the lattice parameters of I along the a, b, and c directions.
Symmetry 15 00236 g005
Symmetry 15 00236 g006 550
Figure 6. Calculated electronic band structure (a), partial densities of states (PDOS) (b), SHG coefficient tensor d123 and effective SHG coefficient deff (c), and the energy-dependent birefringence (d) of I.
Figure 6. Calculated electronic band structure (a), partial densities of states (PDOS) (b), SHG coefficient tensor d123 and effective SHG coefficient deff (c), and the energy-dependent birefringence (d) of I.
Symmetry 15 00236 g006
Table
Table 1. Crystal data and structure refinements for I.
Table 1. Crystal data and structure refinements for I.
Empirical formulaK2Ge3CdS8
CCDC2,215,394
Formula weight664.85
Temperature/K293(2)
Crystal systemorthorhombic
Space groupP212121
a/Å7.3758(3)
b/Å12.1051(5)
c/Å16.8658(6)
Volume/Å31505.86(10)
Z4
ρcalc (g/cm3)2.933
μ/mm−18.945
F(000)1240.0
Crystal size/mm30.12 × 0.12 × 0.02
RadiationMo Kα (λ = 0.71073)
2θ range for data collection/°4.83 to 51
Index ranges−8 ≤ h ≤ 6, −14 ≤ k ≤ 14, −16 ≤ l ≤ 20
Reflections collected8972
Independent reflections2792 [Rint = 0.0236, Rsigma = 0.0262]
Data/restraints/parameters2792/0/133
Goodness-of-fit on F20.717
Final R indexes [I > = 2σ (I)]R1 = 0.0327, wR2 = 0.0835
Final R indexes [all data]R1 = 0.0367, wR2 = 0.0872
Largest diff. peak/hole/e Å−31.84/−1.32
Flack parameter−0.01(3)
aR = Σ||Fo| − |Fc||/Σ|Fo|, bwR = Σ(w(Fo2 − Fc2)2)/Σ(w(Fo2)2))1/2.
Table
Table 2. Fractional atomic coordinates (×104) and equivalent isotropic displacement parameters (Å2 × 103) for I.
Table 2. Fractional atomic coordinates (×104) and equivalent isotropic displacement parameters (Å2 × 103) for I.
AtomXYzU(eq)
K112,537(8)3585(4)4448(3)65.1(13)
K27684(12)1998(7)1683(5)115(2)
Cd14694.9(14)4981.9(10)542.7(8)32.0(3)
Ge19689.7(19)5293.1(12)1540.8(10)24.1(4)
Ge27686(3)5666.3(13)4867.9(9)29.3(4)
Ge37374(2)4561.0(13)3275.4(8)26.2(4)
S17314(5)6326(3)1580(2)27.7(7)
S27807(7)3886(3)4507(2)36.2(10)
S37192(8)6341(3)3650(2)38.1(10)
S49962(6)4246(4)2649(3)39.4(10)
S54971(7)3817(4)2776(3)49.8(14)
S69766(10)3997(6)582(3)78(2)
S72106(6)6311(4)1442(3)46.0(12)
S8
S8B		10,430(40)
9840(60)		6120(30)
6460(30)		5266(19)
5470(16)		37(6)
50(8)
Ueq is defined as 1/3 of the trace of the orthogonalized Uij tensor.
Table
Table 3. Selected bond distances (Å) in I.
Table 3. Selected bond distances (Å) in I.
BondDistance/ÅBondDistance/ÅBondDistance/Å
Ge(1)-S(1)2.154(4)Ge(3)-S(4)2.215(5)K(1)-S(5)#53.355(7)
Ge(1)-S(4)2.267(4)Ge(3)-S(5)2.160(5)K(1)-S(7)#63.376(7)
Ge(1)-S(6)2.254(5)Cd(1)-S(1)2.526(4)K(2)-S(3)#73.725(10)
Ge(1)-S(7)#52.173(4)Cd(1)-S(5)2.521(5)K(2)-S(4)3.590(10)
Ge(2)-S(2)2.241(4)Cd(1)-S(7)2.502(4)K(2)-S(5)3.500(11)
Ge(2)-S(3)2.241(4)Cd(1)-S(8)#82.510(8)K(2)-S(6)3.415(12)
Ge(2)-S(6)#62.211(6)K(1)-S(1)#43.239(6)K(2)-S(7)#73.274(10)
Ge(2)-S(8)2.211(6)K(1)-S(2)#13.477(6)K(2)-S(8)#83.681(12)
Ge(3)-S(2)2.255(4)K(1)-S(3)3.509(8)K(1)-K(1)#14.896(7)
Ge(3)-S(3)2.250(4)K(1)-S(4)3.667(7)K(1)-K(2)#34.553(10)
Symmetry transformation used to generate equivalent atoms: (#1) 1/2 + X, 1/2-Y, 1-Z; (#3) 2-X, 1/2 + Y, 1/2-Z; (#4) 2-X, −1/2 + Y, 1/2-Z; (#5) 1 + X, +Y, +Z; (#6) 3/2-X, 1-Y, 1/2 + Z; (#7) 1-X, −1/2 + Y, 1/2-Z; (#8) 3/2-X, 1-Y, −1/2 + Z; (#9) 1-X, 1/2 + Y, 1/2-Z; (#10) −1 + X, +Y, +Z.
Table
Table 4. LIDT Comparison of I and AGS.
Table 4. LIDT Comparison of I and AGS.
CompoundsLIDT
(mJ/cm2)		Band Gap
(eV)		TEC (×10−5)TEA
abc
I268.053.201.564.882.092.12
AGS42.322.622.092.09−1.072.95
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Wu, Z.-X.; Chen, W.-F.; Liu, B.-W.; Jiang, X.-M.; Guo, G.-C. K2CdGe3S8: A New Infrared Nonlinear Optical Sulfide. Symmetry 2023, 15, 236. https://doi.org/10.3390/sym15010236

AMA Style

Wu Z-X, Chen W-F, Liu B-W, Jiang X-M, Guo G-C. K2CdGe3S8: A New Infrared Nonlinear Optical Sulfide. Symmetry. 2023; 15(1):236. https://doi.org/10.3390/sym15010236

Chicago/Turabian Style

Wu, Zi-Xuan, Wen-Fa Chen, Bin-Wen Liu, Xiao-Ming Jiang, and Guo-Cong Guo. 2023. "K2CdGe3S8: A New Infrared Nonlinear Optical Sulfide" Symmetry 15, no. 1: 236. https://doi.org/10.3390/sym15010236

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