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Prediction and Characterization of NaGaS2, A High Thermal Conductivity Mid-Infrared Nonlinear Optical Material for HighPower Laser Frequency Conversion Dianwei Hou,† Arun S Nissimagoudar,‡ Qiang Bian,† Kui Wu,† Shilie Pan,*,† Wu Li,*,‡ and Zhihua Yang*,†

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CAS Key Laboratory of Functional Materials and Devices for Special Environments, Xinjiang Technical Institute of Physics & Chemistry, CAS; Xinjiang Key Laboratory of Electronic Information Materials and Devices, 40-1 South Beijing Road, Urumqi 830011, China ‡ Institute for Advanced Study, Shenzhen University, Shenzhen 518060, People’s Republic of China S Supporting Information *

ABSTRACT: Infrared nonlinear optical (IR NLO) crystals are the major materials to widen the output range of solid-state lasers to mid- or far-infrared regions. The IR NLO crystals used in the middle IR region are still inadequate for high-power laser applications because of deleterious thermal effects (lensing and expansion), low laser-induced damage threshold, and two-photon absorption. Herein, the unbiased global minimum search method was used for the first time to search for IR NLO optical materials and ultimately found a new IR NLO material NaGaS2. It meets the stringent demands for IR NLO materials pumped by highpower laser with the highest thermal conductivity among common IR NLO materials able to avoid two-photon absorption, a classic nonlinear coefficient, and wide infrared transparency.

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INTRODUCTION

Accordingly, because of the urgent need in civil and military applications, such as atmospheric monitoring, laser radar, and laser guidance, considerable efforts have been made to investigate promising IR NLO materials. Several IR NLO crystals (e.g., chalcopyrite-type AgGaS2, AgGaSe2, and ZnGeP2) have been commercially available since the 1970s.6 Nevertheless, their properties severely restrict their wider applications.2 AgGaS2 and AgGaSe2 have not only low LIDT, resulting from TPA due to a narrow band gap, but also poor thermal conductivity and anisotropic thermal expansion. Another common commercially available material, ZnGeP2, has excellent nonlinear coefficient (5.9 × AgGaS2) but shows low LIDT and strong TPA when using conventional 1 μm (Nd:YAG) or 1.55 μm (Yb:YAG) laser-pumping sources.7 Until now, hundreds of halides,8−11 phosphides,12−14 and chalcogenides15−17 have been synthesized, yet their applications in the mid-infrared region are limited due to inherent deficiencies, such as thermal effects, small nonlinear coefficients, or low LIDT. The reason for the narrow band gap of AgGaS2, a famous IR NLO material, originates from the d-orbital, which elevates the energy position of the valence band (VB) relative to the conduction band (CB),18 thereby narrowing the band gap. The analysis of reported crystal compositions and structures shows that materials with small alkali metals, such as Li, have more

Infrared nonlinear optical (IR NLO) materials are essential for the development of all-solid-state laser sources (2−20 μm) by frequency conversion technology. However, the IR NLO materials used in the middle IR region are still inadequate for high-power laser applications because of deleterious thermal effects (lensing and expansion), low laser-induced damage threshold (LIDT), and two-photon absorption (TPA). Indeed, most NLO materials designed thus far have excellent nonlinear coefficients, but their thermal properties and LIDT, which are key indices to characterize the performance of mid-infrared NLO materials, are inadequate.1 Previous studies have shown that electron absorption causes thermal and electronic effects, thereby leading to laser damage.2 A wide band gap (wider than 3.0 eV)3 usually corresponds to high LIDT and low TPA in an IR NLO crystal. However, a wide band gap often hinders significant second harmonic generation (SHG) responses. Hence, an ideal IR NLO material should achieve a balance between the band gap Eg (>3.0 eV) and the nonlinear coefficient dij (>3.9 pm/V).4 In addition to the band gap, thermal conductivity also plays a key role in LIDT. Laserinduced damage is generally categorized into two primary fundamental mechanisms: thermal and field-induced processes. Continuous wave lasers damage materials, because thermal absorption causes melting or vaporization.5 Therefore, materials with high thermal conductivity, which disperse the heat quickly and indirectly enhance LIDT, should be designed to overcome this problem. © XXXX American Chemical Society

Received: April 29, 2018

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DOI: 10.1021/acs.inorgchem.8b01174 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

interaction range were used to obtain third-order IFCs. The ShengBTE package was used to obtain third-order IFCs and solve the phonon Boltzmann transport equation iteratively to get thermal conductivity values of compound NaGaS2 and reference compounds.

benefits, because they widen the band gap of several compounds,6 for example, AgGaTe2 (1.32 eV) compared to LiGaTe2 (2.30 eV) and AgInTe2 (0.91 eV) compared to LiInTe2 (2.14 eV). Furthermore, the inclusion of small alkali metals in NLO materials also increases the frequencies of the crystal lattice vibrations and Debye temperature, thereby increasing the thermal conductivity.19 The thermal conductivity of LiGaS2 is ∼5 times higher than that of AgGaS2 and 4−8 times higher than that of BaGa4S7(Se).20 However, the nonlinear coefficient of LiGaS2 (d31 = 5.8 pm/V) is lower than that of AgGaS2 (d36 = 12.5 pm/V), presumably because of the small polarization of the Li ion.21 While replacing Li by Na can significantly improve the nonlinear optical effect,22 we used Na instead of Li, because Na is expected to maintain a wide band gap while providing a strong SHG response. Moreover, chalcogenides are the most promising materials for NLO applications operating in the IR region, because they have high nonlinear coefficients and wide optical transparency ranges.15 In particular, tetrahedral [GaS4] is the structural building block and the polarity unit of several famous IR NLO materials, such as AgGaS2, LiGaS2, and BaGa4S7. Therefore, we aimed to combine the Na ion with the [GaS4] tetrahedron to form a new NLO material. Thus far, compounds LiGaS2, KGaS2,23 RbGaS2,24 and CsGaS225 have all been synthesized and studied in detail. However, to our best knowledge, no report of the structure of NaGaS2 has been published due to its challenging synthesis.26 In this article, the unbiased global minimum search method was used to determine the structure of NaGaS2 and to study its optical and thermal properties.

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RESULTS AND DISCUSSION The energetically favored structures NaGaS2 and Na4Ga4S8 crystallize in the tetragonal crystal system with a noncentrosymmetric space group I4̅2d and P41212, respectively. The energy of compound Na4Ga4S8 is ∼0.026 eV/atom higher than that of NaGaS2. The structure of NaGaS2 compared to that of Na4Ga4S8 is shown in Figure 1a,b. Although both

Figure 1. Crystal structure of (a) NaGaS2 and (b) Na4Ga4S8; (c) alignment of tetrahedra in NaGaS2; crystal structure of Na4Ga4S8 viewed from a (d), b (e), and c (f) directions.

COMPUTATIONAL METHODS

Crystal structure prediction27 enables to analyze the crystal structure of materials before they are synthesized, which significantly accelerates the discovery of new materials. Crystal structure analysis by particle swarm optimization (CALYPSO)28,29 was used to search for the structure that has successfully predicted a series of new structures knowing only the chemical composition and stoichiometry.30−32 The energy landscape of the Na−Ga−S ternary system with a 1:1:2 molar ratio and a cell size ranging from 1 to 6 was searched at ambient pressure. A population of structures belonging to certain space group symmetries in the first generation are produced randomly. For subsequent calculations, each generation contained 30 structures, in which 60% of the lower enthalpy structures were utilized to create the structures in the next generation by artificial bee colony algorithm with symmetry, with the remaining 40% of structures generated randomly. The structure search for each cell size was stopped after 30 generations iteratively. Structural optimization and enthalpy calculations were performed at ambient pressure using the plane-wave pseudopotential method, as implemented in the VASP code.33 The phonon spectrum of the stable compound was calculated using the supercell method,34 as implemented in the Phonopy code.35 Electronic, linear optical, and nonlinear optical properties were calculated with the CASTEP package36 for the global minimum structure, NaGaS2. Phonon properties, containing frequencies, velocities, and scattering rates, are mainly determined by interatomic force constants (IFCs). Solving the phonon Boltzmann transport equation (BTE) with first principles is one of the noteworthy approaches to study phonon transport in solids. The second- and third-order force constants are generated by Phonopy and thirdorder.py,37,38 respectively. The quantities such as second and third IFCs involved in the calculation of lattice thermal conductivity are obtained from density functional theory as implemented in the VASP package. The second-order IFCs were obtained using finite displacement method implemented in Phonopy package with 2 × 3 × 2 supercell of the conventional cell, whereas a 2 × 2 × 2 supercell of the conventional cell and a cutoff 0.5 nm for the

structures consist of [NaS4] and [GaS4] tetrahedra, they have different arrangements. In the compound NaGaS2, the tetrahedral [NaS4] and [GaS4] connect to each other via corner-sharing S atoms to generate a three-dimensional, diamond-like framework, and they are all in alignment (Figure 1c). In Na4Ga4S8, [NaS3] and [GaS3] groups are connected to each other by sharing S atoms to form an infinite layer (Figure 1e). As shown in Figure 1d,f, the layers are connected by Na−S and Ga−S bonds to form a three-dimensional (3D) structure. Na4Ga4S8 has two types of channels with radii of 1.6 and 1.2 Å, respectively. The lattice parameters of NaGaS2 and Na4Ga4S8 are listed in Table S1. To assess the thermodynamic stability of the NaGaS2 and Na4Ga4S8 structures, we calculated the enthalpy of formation per atom using the following formula: ΔHf (NaGaS2 ) = [2H(NaGaS2 ) − H(Na 2S) − H(Ga 2S3)] /(2 × 4)

where ΔHf is the enthalpy of formation per atom, and H is the calculated enthalpy per chemical unit for each compound at ambient pressure. Here, Na2S and Ga2S3 are chosen as an example of possible decomposition compounds. According to our computations, the H value of NaGaS2, Na2S, and Ga2S3 are −16.292, −10.354, and −21.486 eV/unit, respectively. Therefore, the ΔHf of NaGaS2 is −0.093 eV/atom. Other possible decomposition paths are listed in Table S2. NaGaS2 and Na4Ga4S8 are thus deemed thermodynamically stable, because their enthalpy of formation from either elements or any other possible compounds are negative. Phonon dispersion curves of B

DOI: 10.1021/acs.inorgchem.8b01174 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry NaGaS2 and NaGa4S8 are shown in Figure 2a and Figure S1, respectively. The kinetic stability of the predicted structure is

Table 1. Experimental and Calculated Band Gaps, Birefringence Values (Δn), and Nonlinear Coefficients of Several IR NLO Crystals compounds Ega (eV) NaGaS2 AgGaS2 AgGaSe2 ZnGeP2 LiGaS2 BaGa4S7 a

2.7241 1.8342 2.0043 3.6244 3.5445

sX-LDA (eV)

Δn

dij × AgGaS2

3.12 2.30 1.69 1.68 3.58 3.53

0.048 (calculation) 0.053 0.021 0.046 0.040 0.063

1.1 1.0 2.5 5.5 0.45 1.0

Experimental measurement of the band gap.

Figure 2. Calculated phonon dispersion curves of NaGaS2 (a) and AgGaS2 (c). (b) Phonon density of states (PhDOS) projected on Na, Ga, and S atoms of NaGaS2. (d) Experimental and calculated band gap and birefringence (Δn) of several IR NLO crystals (AGSe (AgGaSe2), ZGP (ZnGeP2), AGS (AgGaS2), NGS (NaGaS2), BGS (BaGa4S7), and LGS (LiGaS2)).

confirmed, because no imaginary phonon was found. The thermodynamic and kinetic stability confirm that NaGaS2 could be synthesized in experience. Although it is hard to be obtained at the stoichiometric ratio, it may be helpful to synthesize NaGaS2 by adjusting the molar ratios or changing the temperature program.39 The topmost phonon dispersion curves provide information on the cutoff edge of the infrared absorption.40 The largest frequencies of NaGaS2 and AgGaS2 (Figure 2a,c) are ∼11.5 and 11.4 THz, respectively, which shows that the infrared light is transparent in a similar range, especially in two atmospheric transparent windows, 3−5 and 8−14 μm. As shown in Figure 2b, the motion of the S atoms mainly dominates the vibrational states in the high-frequency regimes (7.6−11.5 THz), while the coupling of the Ga−S and Na−S pairs in the lattices contributes to the low frequency regimes (1.6−4.2 THz) and (4.5−6.4 THz), respectively. The band gaps of NaGaS2 and Na4Ga4S8 calculated with the Perdew−Burke−Ernzerhof (PBE) functional are 2.46 and 2.77 eV, respectively. As the electronic band structure shown in Figures S2 and S3, both NaGaS2 and Na4Ga4S8 are the direct band gap compounds. The exchange-correlation functional of PBE usually underestimates the band gap due to exchangecorrelation energy discontinuity. The screened exchange local density approximation sX-LDA functional was used to estimate the band gap of NaGaS2 and Na4Ga4S8 obtaining wider band gaps of 3.12 and 3.47 eV, respectively. To confirm the accuracy of the sX-LDA method, several benchmark crystals were calculated, and the results are shown in Figure 2d and Table 1, which is in a good agreement between theoretical and experimental data. According to the partial density of states (Figure 3a), the band gap of NaGaS2 is determined by the Ga and S atoms, because the top of VB is dominated by S 3p orbitals, and the bottom of CB is contributed by unoccupied Ga 3s orbitals. The proximity of electronic state transitions to the band gap has a strong effect on the optical properties of the compound. For compound NaGaS2, its optical properties is

Figure 3. (a) Partial density of states (upper three panels) and the spectral decomposition of d36 (bottommost panel) for NaGaS2. (b) Virtual electron occupied (Veocc) process. (c) Virtual electron unoccupied (Veunocc) process.

determined by Ga and S elements. To calculate the optical properties, a scissor operator (0.66 eV) was set as the difference of the calculated sX-LDA and PBE band gap value. The refractive index results demonstrate that NaGaS2 is a negative, uniaxial crystal with 0.048 birefringence at 1064 nm (Figure S4). This number is between the birefringence value of ZnGeP2 (Δn = 0.046 at 1064) and AgGaS2 (Δn = 0.053 at 1064), which is adopted for phase matching in the SHG process. Materials that may have NLO behavior must crystallize in the non-centrosymmetric space group.46 However, because of Kleinman symmetry47 relations, even though compound Na4Ga4S8 crystallizes in the non-centrosymmetric space group, no SHG effects are observed. The study of nonlinear optical properties only focuses on NaGaS2. Nonlinear coefficient plays a key role in the applications of NLO crystals. Therefore, the nonlinear coefficient of NaGaS2 was calculated using an expression originally proposed by Rashkeev et al. and developed by Zhang et al.:48 χijk(2) = χijk(2) (VE) + χijk(2) (VH) (2) where χ(2) ijk (VE) and χijk (VH) represent the contribution of virtual electron (VE) processes and virtual hole (VH) processes, respectively.49 In practice, the tensor din is used instead of the tensor χ(2) ijk , and the two tensors are correlated (2) using the equation χ(2) ijk = χin = 2din (n = jk). The calculated nonlinear coefficient of NaGaS2 is d36 = 13.24 pm/V, which is

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because it reduces thermal stress and fracture ratio during crystal growth processes.20

1.1 times that of AgGaS2 (d36 = 12.5 pm/V) and more than two times that of LiGaS2 (d31 = 5.8 pm/V). Furthermore, the band-resolved method was used to investigate the origin of the strong NLO effect of the compound NaGaS2 from the electronic structure standpoint. In light of the spectral decomposition of d36 (an effective SHG direction, Figure 3a), the range that makes the main contribution is in the upper part of the VB from −3.44 to 0 eV and in the bottom of the CB (from 3.12 to 12.12 eV). The SHG density method is used to identify the spatial distribution of electronic states contributing to the nonlinear coefficient in real space. On the basis of the results of the band-resolved calculations, the contribution of the VE and VH processes to the effective SHG tensor d36 are 97.71% and 2.29%, respectively. Therefore, only the VE process is analyzed. The nonlinear coefficient of the tensor d36 for NaGaS2 is shown in Figure 3b,c, which clearly shows that the orbital of sulfur is the main contributor to the nonlinear optical effect. Considering that a high thermal conductivity can disperse heat quickly reducing thermal lensing and expansion effects and enhancing LIDT, we calculated the thermal conductivity of compound NaGaS2 and reference compounds. The results shown in Figure 4a (for thermal conductivity of directions x, y,

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CONCLUSION In summary, the design of materials that can be used in frequency conversion devices pumped by high-power laser and have high LIDT is unpredictable and uncontrollable. Notwithstanding, in this article, the structure of a new IR NLO material, NaGaS2, has been determined using the global minimum search method combined with density functional theory calculations. NaGaS2 achieves a fine balance between a high nonlinear coefficient and a wide band gap, which ensures that NaGaS2 can be used as a frequency conversion material pumped by high-power lasers. Most importantly, NaGaS2 has the highest thermal conductivity among common IR NLO materials that can avoid TPA, which ensures its high LIDT. High LIDT further ensures that NaGaS2 can be pumped by high-power laser. The high thermal conductivity, classic nonlinear coefficient (13.24 pm/V), wide infrared transparency, adequate band gap (3.12 eV), and moderate optical birefringence (0.048) of NaGaS2 demonstrate that NaGaS2 meets critical demands for promising IR NLO candidates.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b01174. Computational details, structure parameters, formation enthalpies of reaction pathway, calculated phonon dispersion curves, calculated band gap, calculated refractive of crystal, calculated thermal conductivity (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (S.P.) *E-mail: [email protected]. (W.L.) *E-mail: [email protected]. (Z.Y.) ORCID Figure 4. Thermal conductivity (a) and phonon lifetimes (b) of four IR NLO crystals.

Shilie Pan: 0000-0003-4521-4507 Zhihua Yang: 0000-0001-9214-3612 Notes

The authors declare no competing financial interest.

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and z, see Figure S5) show that the thermal conductivity of NaGaS2 is higher than that of LiGaS2 and considerably higher than those of AgGaS2 and AgGaSe2, clearly facilitating heat dissipation. The thermal conductivity can also be characterized in terms of Debye temperature ΘD. ΘD can be extracted from the PhDOS. At low-frequency limit, the PhDOS per unit cell can be well-described by αω2, where α is related to ΘD using the equation α = (9sℏ3)/(kBΘD)3, where s is the number of atoms in the unit cell.50 The Debye temperature calculated for NaGaS2, LiGaS2, AgGaS2, and AgGaSe2 are 90, 81, 56, and 47 K, respectively. Higher Debye temperature suggest higher sound speeds and longer phonon lifetimes, as shown in Figure 4b that NaGaS2 has the longest phonon lifetimes and, consequently, highest thermal conductivity. Thus confirming the ShengBTE results demonstrate that NaGaS2 has the highest thermal conductivity among the common IR NLO compounds able to avoid TPA.9 High thermal conductivity is also conducive to growing higher-quality large-size crystals,

ACKNOWLEDGMENTS This work is supported by the Shanghai Cooperation Organization Science and Technology Partnership Program (Grant No. 2017E01013), the National Basic Research Program of China (Grant No. 2014CB648400), the National Natural Science Foundation of China (Grant Nos. 11774414 and 11474353).

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DOI: 10.1021/acs.inorgchem.8b01174 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b01174 Inorg. Chem. XXXX, XXX, XXX−XXX