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Strongest SHG in Polar R3MTQ7 Family: Atomic Distribution Induced Nonlinear Optical Cooperation Yong-Fang Shi, Yu-Kun Chen, Mei-Chun Chen, Li-Ming Wu, Hua Lin, Liu-Jiang Zhou, and Ling Chen Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.5b00177 • Publication Date (Web): 16 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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Chemistry of Materials

Strongest SHG in Polar R3MTQ7 Family: Atomic Distribution Induced Nonlinear Optical Cooperation Yong-Fang Shi, Yu-kun Chen, Mei-Chun Chen, Li-Ming Wu*, Hua Lin, Liu-Jiang Zhou, Ling Chen* Key Laboratory of Optoelectronic Materials Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, People’s Republic of China, To

whom

correspondence

should

be

addressed.

E-mail:

[email protected],

Tel:

(011)86-591-6317-3131; [email protected]. Tel: (011)86-591-6317-3211. Abstract: The well-known polar R3MTQ7 is a large family of noncentrosymmetric chalcogenides, despite of adopting the same crystal structure type, its members show distinctively different nonlinear optical (NLO) properties, and this is quite unusual. Yet, the intrinsic reason remains unknown. Herein, we report the discovery of six new members, La3Ga0.5(Ge0.5/Ga0.5)S7 (1), La3In0.5(Ge0.5/In0.5)S7 (2), Sm3Ga0.5(Ge0.5/Ga0.5)S7 (3), La3In0.33GeS7 (4), Sm3In0.33GeS7 (5) and Gd3In0.33GeS7 (6). Remarkably, polycrystalline 1 and 2 show the strongest second harmonic generation (SHG) of this family, 4.8 and 1.8 times that of the benchmark AgGaS2 at 2.05 µm in the same particle size of 74–106 µm. For the first time we reveal that for R3MTQ7 family, the atomic distribution mainly determines the NLO property, and members showing strong SHG must have a formula of R3M0.5TQ7. Furthermore, we illustrate whether the building unit MS6 octahedron is half occupied (1–3) or one third occupied (4–6) is total energy driven and charge balance controlled. Keywords: chalcogenide material, solid state chemistry, polar noncentrosymmetric compound, IR nonlinear optical chalcogenide

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Introduction Chalcogenides are used as nonlinear optical (NLO) materials in the IR region to create tunable mid-IR laser sources that are important in telecommunications, atmospheric sensing, medical applications and biological imaging, etc.1 The second-order nonlinear response is constrained by the space group of the material — that is, the second-order polarization can occur only in noncentrosymmetric crystals. For a material that is centrosymmetry, the second-order nonlinear susceptibility tensor χ(2) must vanish identically.2 From the point of view of structural chemistry, the second-order nonlinear response is determined by the crystal packing pattern and the alignment of the structure building units. Because the second-order generation is a cooperative interaction of the induced polarizations of each individual asymmetric building unit that instantaneously responds to the applied optical field. For example, in many NLO compounds, the MQ4 tetrahedron building units are oriented along one direction,3 such as in AgGaS2,4 BaGa4S7,5 La3CuGeS76, Li2Ga2GeS6,7 Li2CdSnS4,8 CsMn4In5Se12,9 and Pb4Ga4GeS12.10 Conventionally, solid state chemists classify materials according to their structure types. Materials belonging to the same structure type shall have the same space group and with the same set of Wycokkof sites occupied. For example, both AgGaS24 and AgGaSe211 belong to the chalcopyrite (CuFeS2) structure type with space group of I 42d (No. 122) and show similar second-order susceptibilities of d36 (10.6 µm) = 11 and 33 pm/V, respectively.3c And CsCd4Ga5S1212 and CsCd4In5Se129 adopting the same trigonal structure type with R3 (No. 146) space group, show d33 (2.05 µm) = 26.4 and 81.6 pm/V.9,

12

Usually, if the difference resulted from the identity of

component is excluded, materials belonging to the same structure type have similar NLO properties. R3MTQ7, represents a large well-known chiral polar family of chalcogenides, where M can be occupied by various metal ions with different valence state, such as monovalent Na+, Cu+, Ag+ (with full occupancy); or bivalent Mg2+, Co2+, Ni2+, Zn2+, Cd2+ (with half occupancy); or occasionally trivalent Al3+, In3+ (with fractional occupancy); and T is usually known as tetravalent Si4+, Ge4+, Sn4+; and Q is S, Se.13 The local coordination of M sitting at the 2a Wyckoff site is either an MQ3 trigonal 2


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or an MQ6 octahedral/trigonal antiprismatic sphere; and the T locating at the 2b Wyckoff site has a TQ4 tetrahedral coordination.13 However, compounds of this family show significantly different NLO properties, e.g., some show very weak SHG responses, e.g. La3CuGeSe7, 0.3 × SiO2;6 Sm3Al0.33SiS7, 0.3 × KTP;13l but some show quite strong SHG, e.g. ZnY6Si2S14, 2 × KTP.13l The intrinsic reason is not yet known. Herein, six new members of this family are discovered, La3Ga0.5(Ge0.5/Ga0.5)S7 (1), La3In0.5(Ge0.5/In0.5)S7 (2), Sm3Ga0.5(Ge0.5/Ga0.5)S7 (3), La3In0.33GeS7 (4), Sm3In0.33GeS7 (5) and Gd3In0.33GeS7 (6). Polycrystalline 1 and 2 show the strongest SHG of this family, 4.8 and 1.8 times that of the benchmark AgGaS2 at 2.05 µm in the same particle size of 74–106 µm, respectively. For the first time, we demonstrate that whether the building unit MS6 octahedron is half occupied (1–3) or one third occupied (4–6) is intrinsically driven by the requirements of both total energy and charge balance. More importantly, the atomic distribution mainly determines the NLO property; members showing strong SHG should have a general formula of R3M0.5TQ7. Syntheses, crystal structures, electronic structures and theoretical discussions are reported. Experiment Section Syntheses. All acquired elements were stored inside an Ar-filled glovebox (moisture and oxygen levels less than 0.1 ppm), and all manipulations were carried out in the glovebox or under vacuum. La, Sm and Gd (99.5% or higher) were purchased from Huhhot Jinrui Rare Earth Co. Ltd. Ga shot, Ge powders and S powders (99.999%) were purchased from Sinopharm Chemical Reagent Co., Ltd. The reactants were loaded with corresponding ratios into a silica crucible, which was then put inside a longer silica jacket. This assembly was then flame-sealed under high vacuum of 10–3 Pa. Yellow single crystals of 1–6 were synthesized from solid state reactions of the mixture of RE, Ge, In/Ga, and S. The heating profiles are listed as following: The mixture was heated to 950°C in 35 hours or 980°C in 60 hours and annealed at that temperature for 120 hours or 100 hours, then subsequently cooled at a rate of 5 °C/h to 300 °C, before switching off the furnace.

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35h 120h 120h 30°C  → 950°C → 950°C → 300°C for 1, 2, 4–6 60h 100h 120h 30°C  → 980°C → 980°C → 300° C for 3 All these compounds are stable in the air for more than six months. Semi-quantitative energy dispersive analysis (EDS) using a scanning electron microscope on several yellow crystals indicated that the presence of RE, Ga/In, Ge, and S elements (Figure S1 in the Supporting Information). After the establishment of the formula by the single crystal diffraction data refinement, compounds 1–3 and 5 could be synthesized as pure phase from the stoichiometric element mixtures at 950°C (Figure 1). However, 4 and 6 were always mixed with small amounts of an unknown phase (Figure 1, as the red arrow indicated). The high yield of the stoichiometric syntheses of the title compounds substantiated that the crystal structures were correctly solved. Some selected occupancy and synthetic conditions for compounds 1 – 6 are summarized in Table 1. Single Crystal Structure Determinations. All data were collected on a Rigaku Saturn724 CCD, Mercury CCD or SCXMini diffractometer equipped with graphite-monochromated Mo Kα radiation (λ = 0.71073 Å) at 293 K. The data were corrected by Lorentz and polarization factors. Absorption corrections were performed by the multiscan method.14 All structure were solved by the direct methods and refined by the full-matrix least-squares fitting on F2 by SHELX-97.15The ADDSYM algorithm from the program PLATON was utilized to verify the structures.16 The assignments of Ln, Ga/In, Ge and S were determined on the basis of interatomic distance, relative equivalent isotropic displacement parameter and valence balance requirement. Refinements of Ln3M0.5(Ge0.5/M0.5)S7 (Ln = La, Sm; M = Ga, In). In these structures, Ga2 or In2 atom occupied the Wyckoff 2a site, denoted as octahedral coordinated site (O). And Ge1 and Ga1 (or In1) jointly shared the Wyckoff 2b site, denoted as tetrahedral coordinated site (T). There were two ways, namely models A and B, to solve the structures 1 and 3 as listed in Table 2. Took La3Ga0.5(Ge0.5/Ga0.5)S7 (1) as an example to describe in details. In model A: the O site (2a) was first treated as fully occupied by Ge atom. The subsequent 4


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refinement generated a large temperature factor of 0.095 Å2. Then, free refinement generated occupancy of 48.06 % Ge on the O site with a temperature factor of 0.026 Å2. While Ga atoms fully occupied the 2b sites (T) with reasonable atomic displacement parameter, 0.010 Å2. Subsequently, the occupancy of Ge on the 2a site was fixed as 0.5, and the refinement generated R values of R1 = 0.0233, wR2 = 0.0514 and a charge-balanced formula of (La3+)3(Ge4+)0.5(Ga3+)1(S2–)7. Based on model A, the structure optimization utilizing first principles calculations generated lattice parameters of a = 10.241 Å, b = 10.241 Å, and c = 6.084 Å, which were comparable with the experimental data (Table 3). However, the calculated band gap, 1.0 eV, was considerably smaller than the experimental band gap (2.54 eV). (Table 2) Alternatively, compound 1 could be solved in model B, in which the O site (2a) was half occupied by Ga2 atom with occupancy of 49.08 % and a temperature factor of 0.025 Å2. Because of the charge balance requirement, the T site (2b) had to be shared by Ge4+ and Ga3+. The refinement results in occupancies of 59.66 % Ge1 and 40.34% Ga1, respectively. Thereby, the T site was assigned to be disordered by 0.5 Ga and 0.5 Ge, and the subsequent refinements yielded R1 = 0.0232 and wR2 = 0.0504, with a charge-balanced formula of (La3+)3(Ga3+)0.5(Ge4+/Ga3+)0.5(S2–)7. The residual peaks were of 0.694 and -0.800 e/Å3 in the final Fourier difference map. A similar treatment was utilized in AlxDy3(SiyAl1–y)S7.13l The first principles calculations of model B generated a band gap of 1.86 eV. This value was 0.86 eV wider than that of model A, and was in better agreement with the experimental value (2.54 eV). More importantly, the total energy of model B is 0.485 eV lower than that of model A. The detailed comparison between models A and B was listed in Table 2. Consequently, 1 and 3 was refined in model B. Besides, the stoichiometric syntheses, EDX results (as summarized in Table 1) indicated these formulas of Ln3M0.5(Ge0.5/M0.5)S7 were corrected. For compound 2, model A generated an unreasonably low temperature factor of 0.02 Å2 for Ge on the O site (2a site) and a tendency of inversion twinning. Therefore, 2 was then successfully refined in model B with R1 = 0.0251 and wR2 = 0.0694, and residual peaks of 1.024 and –1.805 e/Å3 in the final Fourier difference map (Table 3). 5



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Refinements of Ln3In0.33GeS7 (Ln = La, Sm, Gd). Compounds 4–6 also adopted the La6ZnSi2S14 structure type13. As summarized in Table 1, in structures of 4–6, the T site (2b) was fully occupied by Ge atom. Take 5 as an example, the O site (2a) was occupied by In atoms with an occupancy of 35.2 % and a temperature factor of 0.013 Å2, otherwise, the atomic displacement parameters would be unacceptably high, 0.107 Å2. In order to satisfy the charge balance, in the final refinement, the In occupancy on the 2a site was fixed to be 1/3, all atoms were refined with anisotropic displacement parameters, the resulted R values were R1 = 0.0323 and wR2 = 0.0619. The maximum and minimum peaks in the final Fourier difference map were 1.510 and –1.075 e/Å3 (Table 3). Recall that Ga and Ge could not be crystallographically distinguished owing to their very similar X-ray scattering factors, thus, the valence bond sums (VBS)17 were calculated according to the bond valence (sij), sij = exp[(Rij–dij)/0.37], where the dij was bond length between two nearest neighboring atoms i–j, Rij was the bond-valence parameter as tabulated in the literature, the total atom valence Vi = ∑sij.17 (Table S2) The calculated VBS suggest normal oxidation states of In3+ and Ge4+ in 2, 5 and 6, but some deviations in 1, 3 and 4. In brief, as listed in Table 1, the formulas of 1–3 should be written as La3Ga0.5(Ge0.5/Ga0.5)S7 (aka La3GaGe0.5S7), La3In0.5(Ge0.5/In0.5)S7, Sm3Ga0.5(Ge0.5/Ga0.5)S7, respectively. For 4–6: the formulas are Ln3In0.33GeS7 (Ln = La, Sm, Gd). Crystallographic data and structural refinement details were summarized in Table 3, the positional coordinates and isotropic equivalent thermal parameters were given in Table S1 (Supporting Information), and bond distances and angles in Tables S3.1–6. Powder X-ray Diffraction. The XRD patterns were collected on a PANalytical X’Pert Pro diffractometer at 40 kV and 40 mA using Cu Kα radiation (λ = 1.5406Å) at ambient temperature (2θmax = 80º). Elemental Analysis. The elemental analyses of La, Sm, Gd, Ga, In, Ge, S have been examined with the aid of a field emission scanning electron microscope (FESEM, JSM6700F) equipped with an energy dispersive X-ray spectroscope (EDX, Oxford INCA), as shown in Figure S1 in the SI. 6


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Magnetic Susceptibility. The direct current magnetic susceptibility of 3 was measured on a Quantum Design MPMS-XL magnetometer in the temperature range of 2–300 K. The pure phased polycrystalline samples were ground and loaded into gelatin capsules. The data were corrected for the susceptibility of the containers and for the diamagnetic contributions from the ion core. UV–Vis–Near IR and IR Spectroscopies. The optical diffuse reflectance spectra of polycrystalline samples were measured at room temperature using a Perkin-Elmer Lambda 900 UV–Vis spectrophotometer equipped with an integrating sphere attachment and BaSO4 as a reference in the range of 0.19–2.5 µm. The absorption spectrum was calculated from the reflection spectrum via the Kubelka-Munk function: α/S = (1–R)2/2R, in which α is the absorption coefficient, S is the scattering coefficient, and R is the reflectance.18 The IR data were measured by a Perkin-Elmer Spectrum one FT-IR spectrophotometer in the range of 2.5–25 µm. Polycrystalline samples were ground with KBr and pressed into transparent pellets for spectra measurement. Second Harmonic Generation (SHG) Measurements. Powder SHG measurements were performed on a modified Kurtz-NLO system using 2.05 µm laser radiation19. The output signals were detected by a photomultiplier. Compounds 1 and 2 were carefully ground and sieved with particle size of 30–46, 46–74, 74–106, 106–150 and 150–210 µm, respectively. Powdered AgGaS2 sieved in the same particle size ranges was used as a reference. Computational Sections: Electronic Structure Calculations. The calculation models of 1 and 2 were built in P3 (143) instead of P63 (173) according to the single crystal structure. Half of Ga2 or In2 atoms at 1a sites (0, 0, z) (corresponding to the 2a site in P63) were removed, and the 1b site was assigned as Ga1 or In1 and the 1c site was assigned as Ge (1b and 1c correspond to the 2b site in P63). For 5, with 1/3 occupancy on the 2a site, a 1 × 1 × 3 super cell in P63 was thus build, in which only the fully occupied In atoms with z = 0 and 1.5 were remained. The structure optimized lattice parameters, a = 10.297 Å, b = 10.297 Å, and c = 5.954 Å for 1; a = 10.376 Å, b = 10.376 Å, and c = 6.019 Å for 2; and a = 10.122 Å, b = 10.122 Å, and c = 7



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17.374 Å for 5, were comparable to single crystal diffraction data (Table 3). Band structures and densities of states (DOS) for 1, 2 and 5 were calculated by the Vienna ab initio simulation package VASP.20The generalized gradient approximation (GGA)21 was chosen as the exchange-correlation functional and a plane wave basis with the projector augmented wave (PAW) potentials was used.22 And spin was not considered. The plane-wave cutoff energy of 400 eV, and the threshold of 10–5 eV were set for the self-consistent-field convergence of the total electronic energy. Pseudo atomic calculations were performed for La, 5d16s2; Sm, 6s2 with all f electrons considered as inner core elelctrons; Ag, 4d105s1; Ge, 3d104s24p2; Ga, 3d104s24p1; In, 3d105s2dp1 and S, 3s23p4. The k integration over the Brillouin zone was performed by the tetrahedron method23 using Γ-centered k-points grids with 0.015 Å-1 spacing for 1, 2, 5 and AgGaS2, and the Fermi level (Ef = 0 eV) was selected as the reference of the energy. The optical property calculation for 1, 2, 5 and AgGaS2 used more than 300 empty bands. The linear optical property was calculated in terms of the dielectric function ε(ω) = ε1(ω) + iε2(ω). The scissors operators of 0.69, 0.58, 0.56 and 1.79 eV were applied in these calculations for 1 (a.k.a. 1B), 2, 5 and AgGaS2, respectively. The imaginary part ε2(ω) can be obtained from the momentum matrix elements between the occupied and unoccupied wave functions,24 and the real part ε1(ω) by the Kramer-Kronig relationship. We assumed if the orientation of the crystal surface is parallel to the optical axis, the reflectivity R (ω ) can be deduced directly from the Fresnel’s formula:

R (ω ) =

ε (ω ) − 1 ε (ω ) + 1

2

.... (1)

And the refractive index n(ω ) and the absorption coefficient α (ω ) follow the formulas: defined as (2) and (3) followed.

n(ω ) =

1 1 [ ε12 (ω ) + ε 22 (ω ) + ε1 (ω )]2 …. (2) 2

2 1

2 2

1 2

α (ω ) = 2ω[ ε (ω ) + ε (ω ) − ε1 (ω )] …. (3) Calculations of SHG Coefficients. Using the so-called length-gauge formalism derived by 8


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Aversa and Sipe25,

26

at a zero-frequency limit, the second-order nonlinear susceptibility

χ abc ( −2ω , ω , ω ) could be written as: χ abc (−2ω , ω , ω ) =

a rnm {rmlb rlnc } e3 [ωn f ml + ωm f ln + ωl f nm ] + ∑ h 2 Ω nml ,k ωnmωmlωln

f nm a b i e3 c b a c c a b [rnm (rmn;c + rmn ∑ ;b ) + rnm ( rmn ;c + rmn ;a ) + rnm ( rmn ;b + rmn ; a )] …. (4) 2 2 4 h Ω nm ,k ωmn b rmn ,a =

a b a rnm ∆bmn + rnm ∆ mn

ωnm

+

i

ωnm

∑ (ω

a b lm nl lm

r r − ωnl rnlb rlma ) …. (5)

l

When the frequency of incident light changed, the second-order nonlinear susceptibility

χ abc ( −2ω , ω , ω ) could be written by equation (6): χ abc (−2ω , ω , ω ) =

a rnm {rmlb rlnc } 2 f mn f ln f ml e3 [ + + ]+ ∑ 2 h Ω nml ,k ω ln − ωml ωmn − 2ω ωln − ω ωml − ω

i e3 2 1 a b c a b a c f nm [ rnm (rnm (rnm ∑ ;c + rmn ;b ) + ;c rmn + rnm;b rmn ) + 2 2 h Ω nm,k ωmn (ωmn − 2ω ) ωmn (ωmn − ω ) 1

ω

2 mn

(

1 4 1 a b c b c c b − ) rnm ( rmn ∆ cmn + rmn ∆ bmn ) − × ( rnm ; a rmn + rnm ; a rmn )] …. (6) ωmn − ω ωmn − 2ω 2ωmn (ωmn − ω )

Where r was the position operator, hω nm = hω n − hω m was the energy difference between bands m and n,

f nm = f n − f m was the difference of the Fermi distribution functions, subscripts or

a a superscripts a, b, and c were Cartesian indices, Ω was the unit cell volume, ∆ amn = ( pnn − pmm )/m

b was the difference between the electronic velocities at the bands n and m, and rmn , a was the

so-called generalized derivative of the coordinate operator in the k space.

Results and Discussion Crystal Structure. Ln3M0.5(Ge0.5/M0.5)S7 (Ln = La, Sm; M = Ga, In) and Ln3In0.33GeS7 (Ln = La, Sm, Gd). Compounds 1–6 are isostructural to the well-known Ln6ZnSi2S1413 and crystallize in the polar hexagonal space group P63. And 1–3 are the first Ga-members in this family. Their structures feature chains of face-sharing GaS6 (or InS6) octahedra that are surrounded by both discrete Ln3+ cations and 9



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isolated TS4 tetrahedra. The center of each TS4 tetrahedron is disordered by Ge14+/Ga13+ (or Ge14+/In13+) in the cases of 1–3, but solely occupied by Ge4+ in 4–6 (Figure 2). Figure 3 shows the extending of the chains of GaS6 (or InS6) octahedra and the arrangements of the discrete TS4 tetrahedra along the c-direction. The chains of GaS6 octahedra are running parallel to the 63 axis, and the isolated TS4 tetrahedra are operated by the 3-fold rotation axis. The distortion of the TS4 tetrahedron is seen by the T–S bond difference of 0.04–0.07 Å for 1–6 (Tables S3.1–6). In comparison, GaS6 or InS6 octahedra are less distorted. The Ga–S bond difference is of 0.04 Å in 1 and the Ga–S or In–S bond difference is within 0.01 Å in 2–5. The Ln atom is coordinated to eight S atoms in a distorted bicapped trigonal prism, with normal Ln–S distances.13 Previous crystallographic studies show that the octahedral 2a site (O) prefers not only monovalent cations, such as Na+, Cu+, Ag+ (with which the formula is written as Ln3XIXVIQ7), but also divalent cations, such as Mg2+, Co2+, Ni2+, Zn2+ and Cd2+, occasionally trivalent Al3+ and In3+; however, the tetrahedral 2b site (T) favors tetravalent cations, such as Si4+, Ge4+, Sn4+.6,13a–l Differently, 1, 2 and 3 show that trivalent Ga3+ or In3+ occupies both O and T sites. As listed in Table 1, 1–6 illustrate that T site favors tetravalent Ge4+. The intrinsic reason is that with Ge4+ occupying the T site, the structure is more energetic stable as discussed below. (Table 2) Table 1 also tells that if the Ge source is sufficient (judging from the loading ratios of Ga : Ge or In : Ge), the T site preferentially take Ge4+ until the 100% occupancy is reached, in a manner similar to cases 4–6. Otherwise, the T site also takes Ga3+ atom until the sum occupancy of Ge4+ and Ga3+ reaches 100%, and the remaining Ga3+ occupies the O site as in the cases of 1–3. And the O site occupancy of Ga3+ or In3+ is limited by the charge balance requirement.

Magnetic and Optical Properties. The inverse magnetic susceptibility of 3 does not follow the Curie-Weiss law (Figure S2), and it is typical for Sm3+-containing compounds, where spin-orbit coupling splits the 6H ground term for Sm3+ resulting in a temperature dependence of the effective moment of 4f electrons. Similar phenomenon are found in Ln4GaSbS9,29 RE6Zn1+xSb14,27 and CsLnCdTe3.28 10


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The experimental band gap (Figure S3) and IR transparency (Figure S4) of 1–3, 5 and benchmark AgGaS2 are measured and some are listed in Table 5. Compounds 1–3, 5 exhibit band gap about 2.5 eV and are transparent from about 0.7 to 22 µm, which are comparable with those of commercial AgGaS2 (2.56 eV; 0.60–23 µm) and other reported compounds, Y6ZnSi2S14 (2.38 eV; 2.5–14.3 µm)13l. The band gaps and IR transparencies of 4 and 6 were not measured because their pure phases were not obtained under the current experimental condition. Subsequently, the powder SHG response of 1 and 2 at room temperature were measured under 2.05 µm laser radiation. Polycrystalline 1 and 2 show SHG intensities about 4.8 and 1.8 times that of AgGaS2 in the same particle size of 74–106 µm (Figure 4b), which are the strongest in this family. On the contrary, polycrystalline 4, 5, and 6 only show very weak SHG responses. This is very striking because usually materials belonging to the same structure type should have similar NLO properties. Why the NLO properties of 1–6 are so different? We consider this is determined by the structure feature. As shown in Figure 3, the chain of octahedra propagates along the c axis. Note that there is a certain angle between the orientations long the c direction of adjacent octahedra. Therefore, when the 2a site is fully occupied, the polarization along the c direction of each octahedron is almost completely canceled, making the SHG weak. Similarly, different degree of cancellation happens in the cases of fractional occupancy such as, 0.33, 0.66; except for the case of 0.5 occupancy, in which, all the filled octahedra are in-phase aligned, giving rise to the strongest SHG in this family. Roughly, as the occupancy of 2a site decrease from 1 to 0, the SHG intensity (SHGoccpancy) varies in a trend: SHG1.0 < SHG0.67 < SHG0.5 > SHG0.44 > SHG0.38 > SHG0.33 > SHG0. In order to confirm our thought, we have summarized all the reported members in R3MTQ7 family. As tabulated in Table 4, the SHG intensity of all the members of this family is apparently correlated with the occupancy of the 2a site. For example, compounds with fully occupied 2a site show very weak or null SHG intensities, such as La3CuGeSe7 (about 30% that of quartz, very weak), and La3CuGeS7 does not exhibit NLO property.6 Compounds with 0.5 occupancy on 2a site show strong SHG intensities, such as Y6ZnSi2S14 (~2 × KTP, medium).13l And compounds with 0.38 or 11



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0.33 occupancies show very weak SHG intensities, such as Sm3Al0.33SiS7 (0.3 × KTP, very weak).13l Nicely, all experimental observations fit in the SHGocc variation trend we proposed. Therefore, we predict that the future exploration on the promising NLO materials in this family should focus on the formula of R3M0.5TQ7.

Theoretical Studies. The electronic band structures of 1, 2 and 5 are studied as shown in Figure 5. Compounds 1 and 2 have indirect band gaps of 1.85 and 2.03 eV, and compound 5 has a direct band gap of 1.8 eV. These are comparable with the experimental ones (1: 2.54 eV; 2: 2.61 eV; 5: 2.36 eV; Table 5 and Figure S3 in the SI). The total and partial densities of states of 1，2 and 5 reveal the significant contributions from S-3p states to the valence band (VB) top (Figure 6). The bottom of the conduction band (CB) of 1 originates from S-3p (~33%), La-5d (~26%), Ga-4s (~21%) and Ge-4s (~13%) states; and that of 2 is mostly formed by La-5d (~40%), S-3p (~27%), In-5s (19%) and Ge-4s (~7%) states. The bottom of CB of 5 (1.8–3.0 eV) mainly consists of Sm-5d (~53%), S-3p (~24%), Ge-4s (~10%) and In-5s (5%) states. Therefore, the optical absorptions of 1 and 2 can be primarily ascribed to the transition processes from the fully-occupied S-3p states to the unoccupied La-5d, Ga-4s/In-5s and Ge-4s states, whereas that of 5 is from S-3p states to Sm-5d and Ge-4s states. In details, in the case of 1, the VB-3 region below the Fermi level contains mainly the S-3s (~93%) states. The VB-2 region is primarily derived from S-3p (~67%) with a small amount of Ga-4p (7%) and Ge-4p (5%) states. The VB-1 region is mostly S-3p states (~88%) with a small amount of La-5d (~8%) states. Above the Fermi level, the main components of each region are described as follows: CB-1, La-5d (~57%) and S-3p (~24%) Ga 4s (~7%) and Ge-4s (4%) states; CB-2, La-5d (~72%), and S-3p (~15%), Ga-4p (3%) and Ge-4p (3%) states; CB-3, La-5d (~43%), S-3p (~30%), Ga-4p (~12%) and Ge-4p (~3%) states. In the case of 2, the VB-2 region is primarily derived from S-3p (~72%) with a small amount of In-5p (6%) and Ge-4p (6%) states. The VB-1 region is mostly S-3p states (~88%) with a small amount of La-5d (~5%) states. Above the Fermi level, the main components of each region are described as follows: CB-1, La-5d (~53%), S-3p (~25%), In 5s (~9%) and Ge-4s (5%) states; CB-2, 12


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La-5d (~72%), S-3p (~16%), In-5p (2%) and Ge-4p (4%) states; CB-3, La-5d (~44%), S-3p (~31%), In-5p (~10%) and Ge-4p (~3%) states. As shown in Table 5 and Figure S8, in principle, the calculated absorption edges of 1, 2 and 5 are consistent with the experimental observations. As shown in Figure S7, the static birefringence of 1, 2 and 5 are calculated to be 0.023, 0.007 and 0.008, respectively. The static birefringence 1 is comparable to that of AgGaS2 (0.039). Yet, those of 2 and 5 are about one order of magnitude smaller than that of AgGaS2, indicating a nonphase matchable behavior. Point group 6 only has two independent components of the second-order nonlinear optical susceptibility tensor, namely, χ113 and χ333 components under the restriction of Kleinman’s symmetry. To simplify the notation by introducing a contracted matrix dil, these are χ 113 = 2d15 and

χ

333

= 2d 33 respectively. Considering the partial occupancy of the title compounds, models of 1 and

2 are built in P3 (class 3), which shows 6 non-vanishing second-order susceptibility tensors ( χ 11,

χ 14, χ 15, χ 22, χ 31, χ 33). Four of these are independent SHG tensors ( χ 11, χ 15, χ 22, χ 33) under the restriction of Kleinman’s symmetry. The calculated SHG coefficients and linear optical parameters of 1 and AgGaS2 are listed in Table 5 and Figures S5–S9. The calculated SHG coefficients of the selected title compounds are comparable with that of AgGaS2. The cutoff-energy-dependent SHG coefficient (d33) has been studied to understand the origin of the SHG of 1 and 2. As shown in Figure 7, the VB-1 and CB-3 regions contribute mainly to the SHG response because of the dramatic increase of d33. In comparison, the d33 variations in VB-2, VB-3 and CB-1, CB-2 are insignificant. Recall those revealed in Figure 6, VB-1 is mainly composed of filled S-3p (~88%) and La-5d (~8%), and CB-3 is mostly La-5d (~43%) and S-3p (~30%) with small contributions of Ga-4p (~12%) and Ge-4p (~3%) states. Although the magnitude of integrated partial DOS (IPDOS) of Ge-4p states is small, IPDOS per atom of Ge-4p states is much higher with respect to those of La-5d, S-3p, etc.. Thus, the SHG response should originate from the transition processes from S-3p, La-5d states to La-5d, S-3p, Ge-4p, Ga-4p/In-5p states.

Conclusion 13



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In summary, six new asymmetric polar members of La6ZnSi2S14 family, La3Ga0.5(Ge0.5/Ga0.5)S7 (1), La3In0.5(Ge0.5/In0.5)S7 (2), Sm3Ga0.5(Ge0.5/Ga0.5)S7 (3), La3In0.33GeS7 (4), Sm3In0.33GeS7 (5) and Gd3In0.33GeS7 (6), were synthesized and characterized. Polycrystalline 1 and 2 exhibit the strongest second harmonic generation (SHG) responses of this family, ~4.8 and 1.8 times that of the benchmark AgGaS2 at the particle size of 74–106 µm, at 2.05 µm, in non phase matchable behaviors. For the first time, we explain that the unique atomic distribution of this family over the octahedral 2a and tetrahedral 2b sites is a result of the requirements of both the total energy and the charge balance. More interestingly, we uncover that for R3MTQ7 family, the atomic distribution mainly determines the nonlinear optical property; and members showing strong SHG should have a formula of R3M0.5TQ7. These insights will shed useful light on the design and development of promising NLO materials.

ASSOCIATED CONTENT Supporting Information The cif files, additional tables and figures. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected], Tel: (011)86-591-63173131 *[email protected], Tel: (011)86-591-63173211.

Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China under Projects (21225104, 21233009, 21171168, 21301175 and 91422303).

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Figure 1. The experimental X-ray powder diffraction patterns of La3Ga0.5(Ge0.5/Ga0.5)S7 (1), La3In0.5(Ge0.5/In0.5)S7 (2), Sm3Ga0.5(Ge0.5/Ga0.5)S7 (3), La3In0.33GeS7 (4), Sm3In0.33GeS7(5) and Gd3In0.33GeS7 (6). Red arrow: unknown phase.

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Figure 2. Structure of La3Ga0.5(Ge0.5/Ga0.5)S7 (1) viewed down the c axis. The La–S bonds were omitted for the sake of clarity. Rose: La; yellow: S; Pink octahedron: GaS6; Aqua tetrahedron: TS4 (T = disordered Ga/Ge).

16


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Figure 3. View of chain of face-sharing GaS6 octahedra in La3Ga0.5(Ge0.5/Ga0.5)S7 (1) along the c axis. And the arrangement of (Ga/Ge)S4 tetrahedra with the 3-fold rotation axis passing through.

17



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Figure 4. (a) Phase-matching curves, ie., particle size vs SHG intensity , for La3Ga0.5(Ge0.5/Ga0.5)S7 (1) and La3In0.5(Ge0.5/In0.5)S7 (2). (b) Oscilloscope traces of the second harmonic generated signals AgGaS2, 1 and 2.

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Figure 5. Calculated band structure of (a) La3Ga0.5(Ge0.5/Ga0.5)S7 (1), (b) La3In0.5(Ge0.5/In0.5)S7 (2) and (c) Sm3In0.33GeS7 (5). Г (0, 0, 0); A (0, 0, 0.5); H (–1/3, 2/3, 0.5); K (–1/3, 2/3, 0); M (0, 0.5, 0) and L (0, 0.5, 0). The Fermi levels (blue dotted line) are set to 0. The valence band maximum (VBM) and conduction band minimum (CBM) are indicated by pink arrow lines.

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Figure 6. Total and partial DOS for (a) La3Ga0.5(Ge0.5/Ga0.5)S7 (1), (b) La3In0.5(Ge0.5/In0.5)S7 (2) and (c) Sm3In0.33GeS7 (5) Dash line: Ef; Dotted line: different regions in VB and CB.

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Figure 7. The cutoff-energy-depending static SHG coefficients for (a) La3Ga0.5(Ge0.5/Ga0.5)S7 (1) and (b) La3In0.5(Ge0.5/In0.5)S7 (2). Solid line: Ef; short dash line: different regions in VB and CB.

21



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Table 1. Selected occupancy and synthetic conditions for compounds 1 – 6 Formula Octahedral 1 site (2a) Tetrahedra l site (2b) Loading ratio2 Product phase analysis

Occupancy

1 La3(Ga0.5)O(Ge0.5/Ga0.5)TS

2 La3(In0.5)O(Ge0.5/In0.5)TS

3 Sm3(Ga0.5)O(Ge0.5/Ga0.5)TS

4 La3(In0.33)O(Ge)TS

5 Sm3(In0.33)O(Ge)TS

6 Gd3(In0.33)O(Ge)TS

7

7

7

7

7

7

0.5Ga2

0.5In2

0.5Ga2

1/3In

1/3In

1/3In

0.5Ge1+0.5Ga1

0.5Ge1+0.5In1

0.5Ge1+0.5Ga1

1Ge

1Ge

1Ge

6:2:1:14 1

6:2:1:14 2

6:2:1:14 3

6:0.67:2:14 4 + 5 % unknown

6:0.67:2:14 5

6:0.67:2:14 6 + 5 % unknown

1

: Atomic coordinations and occupancies of each of Compounds 1–6 are listed in Table S1 in the supporting information

2

: loading ratio of Ln: Ga : Ge : S or Ln: In : Ge : S

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Table 2. Comparison between model A and B of compound 1 model A model B Octahedral 0.5Ge 0.5Ga2 site (2a) Tetrahedral Ga 0.5Ge1+0.5Ga1 site (2b) 4+ 3+ La3(Ge )0.5(Ga )1S7 La3(Ga3+)0.5(Ga3+0.5/Ge4+0.5)S7 Resulting formula single crystal refinement 0.0233/0.0514 0.0232/0.0504 R1/wR2 1.0 1.86 Eg(cal.) (eV) 0 -0.485 Relative total energy (eV) Occupancy

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Table 3. Crystallographic Data and Structure Refinements for compounds 1–6a 1 La3(Ga0.5) (Ge0.5/Ga0.5)TS

2 La3(In0.5) (Ge0.5/In0.5)TS

3 Sm3(Ga0.5) (Ge0.5/Ga0.5)TS

4 La3(In0.33)O(Ge)TS

5 Sm3(In0.33)O(Ge)TS

6 Gd3(In0.33)O(Ge)TS

7

7

7

7

7

7

1494.33

1584.53

1562.97

1504.41

1573.05

1614.45

yellow

yellow

yellow

yellow

yellow

yellow

O

Formula

O

O

Fw Crystal color Space group a (Å)

10.2560(6)

10.279(3)

9.887(3)

10.3608(7)

10.029(2)

9.938(3)

c (Å)

5.9148(5)

5.930(2)

5.881(3)

5.8371(7)

5.770(2)

5.747(2)

3

V (Å ) Dc (g cm-3) µ (mm-1) GOOF on F2 R1, wR2 (I > 2σ(I)) a

538.80(6)

542.6(2)

497.9(3)

542.64(8)

502.6(2)

491.6(3)

4.605

4.849

5.213

4.604

5.197

5.453

16.783

16.309

22.984

16.287

22.358

25.178

1.037

1.183

1.027

1.232

1.165

1.177

0.0232 0.0504

0.0251 0.0694

0.0464 0.0874

0.0207 0.0480

0.0323 0.0619

0.0122 0.0275

R1, wR2 (all data)

0.0246 0.0511

0.0255 0.0697

0.0521 0.0908

0.0213 0.0482

0.0337 0.0627

0.0126 0.0312

largest diff. Peak / hole (e Å-3)

0.694/-0.8

1.024/-1.805

1.826/-1.787

0.665/-1.375

1.510/-1.075

0.652/-1.046

P63 (No.173)

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Flack paramete 0.03(3) 0.03(5) r a R1 = Σ||Fo| - |Fc||/Σ|Fo|, wR2 = [Σw(Fo2 - Fc2)2/Σw(Fo2)2]1/2

–0.03(6)

0.05(2)

0.02(3)

0.05(2)

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Table 4 Structure-NLO property relationship in R3MTQ7 family and the SHG prediction 2a site occ. 1

comp. La3CuGeSe7

ref 6

La3CuGeS7 Ce3CuSnSe7 Y3NaSiS7 Y3CuSiS7 Y3CuSiSe7 La3CuSiS7 Y3CuGeS7 Y3CuGeSe7 Dy3CuGeSe7 La3AgSiSe7 R3CuSnS7

13i 13g 13j and reference therein

experimental SHG 1064 nm; 0.3 × SiO2 (vw)* (n) N/V N/V N/V

SHG prediction

(w) or (n)

R3CuSnSe7 0.67 0.5

Ce3Ag0.63SiS6.63Cl0.37 La3Ga0.5(Ge0.5/Ga0.5)S7 1 La3In0.5(Ge0.5/In0.5)S7

13k this work

N/V 2.05 µm; 4.8 × AgGaS2 (s)

2

2.05 µm; 1.8 × AgGaS2 (s)

Sm3Ga0.5(Ge0.5/Ga0.5)S7 3

(w) might because poor crystalline 2.1 µm; 2 × KTP (m) 2.1 µm; 2 × KTP (m) N/V

0.44 0.38 0.33

Y3Zn0.5SiS7 Dy3Al0.5Si0.5Al0.5S7 R3Mg0.5GeS7 open to be explored La3Al0.44Si0.93S7 Dy3Al0.38Si0.85Al0.15S7 Sm3Al0.33SiS7

0

Ln3In0.33Ge2S7 4–6 Sm3S2ClSiS4

13l 13j 13f 13l 13l this work

N/V 2.1 µm; 1 × KTP (w) 2.1 µm; 0.3 × KTP (vw) (vw)

13k

N/A

(m)

(s) or (m) (s) or (m) (m)

(vw) or (n)

* w: weak SHG; m: medium SHG; s: strong SHG; n: Null SHG; N/A: not available. SiO2:1 d33 (1.064 µm) = 0.3 pm/V; KTP (KTiOPO4):1 d15 (1.313 µm) = 1.4 pm/V; d24 (1.313 µm) = 2.6 pm/V; d33 (1.313 µm) = 11.1 pm/V; AgGaS2:1 d36 (1.054 µm) = 23.6 pm/V; d36 (2.06 µm) = 18.2 pm/V; d33 (10.6 µm) = 12.5 pm/V.

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Table 5. Optical properties of 1 compared with those of benchmark AgGaS2. 1

AGS

d33=18.56 SHG coefficient (pm/V) at 2.05 µm ¶

d15 =12.33

d36= 18.21

d11 = 4.76 d22 = 3.20 0.70(obs)b

0.60(obs)a

0.49(cal)¶

0.46(cal)¶

0.70–22.4

0.60–23a

2.54(obs)b

2.56(obs)a

1.85(cal)¶

2.703c

Static birefringence¶

0.023

0.039

Average refractive index at 2.05 µm ¶

2.801

2.489

Average static dielectric cons.¶

8.571

6.149

absorption edge (µm) trans. range (µm) band gap (eV)

a: measured on ground single crystals. b: measured on polycrystalline products. ¶

: calculated. More details are in Supporting Information.

27



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Reference 1. Nikogosyan, D. N. Nonlinear optical crystals: a complete survey; Springer-Science: New York, 2005. 2. Boyd, R. W. Nonlinear Optics; Academic Press, 3 edition, 2008. 3. (a) Sheldrick, W. S.; Wachhold, M. Coord. Chem. Rev. 1998, 176, 211. (b) Mitchell, K.; Ibers, J. A. Chem. Rev. 2002, 102, 1929. (c) Dmitriev, V. G.; Gurzadyan, G. G.; Nikogosyan, D. N. Handbook of Nonlinear optical crystals, Springer: New York, 1999. 4. (a) Harasaki, A.; Kato, K. Jpn. J. Appl. Phys. 1997, 36, 700. (b) Atuchin, V. V.; Kidyarov, B. I.; Peryukhina, N. V. Comput. Mater. Sci. 2006, 37, 507. (c) Jayaraman, A.; Narayanamurti, V.; Kasper, H. M.; Chin, M. A.; Maines, R. G.. Phys. Rev. B 1976, 14, 3516. 5. Lin, X.S.; Zhang, G.; Ye, N. Cryst. Growth Des. 2009, 9, 1186. 6. Poduska, K. M.; DiSalvo, F. J.; Min, K.; Halasyamani, P. S. J. Alloys Compd. 2002, 335, L5. 7. Kim, Y.; Seo, I. S.; Martin, S. W.; Baek, J.; Halasyamani, P. S.; Arumugam, N.; Steinfink, H. Chem. Mater. 2008, 20, 6048. 8. Lekse, J. W.; Moreau, M. A.; McNerny, K. L.; Yeon, J.; Halasyamani, P. S.; Aitken, J. A. Inorg. Chem. 2009, 48, 7516. 9. Lin, H; Chen, L; Zhou, L. J; Wu, L.M. J. Am. Chem. Soc. 2013, 135, 12914. 10. Chen, Y, K; Chen M, C; Zhou, L, J; Chen, L; Wu, L. M. Inorg. Chem. 2013, 52, 8334. 11. Hahn,H.; Frank,G.; Klingler, W., Meyer,A. D.; Störger, G. Z. Anorg. Allg. Chem.1953, 271, 153 . 12. Lin, H; Zhou, L. J; Chen, L. Chem. Mater. 2012, 24, 3406. 13. (a) Guittard, M.; Julienpo, M. Bull. Soc. Chim. Fr. 1970, 7, 2467. (b) Collin, G.; Etienne, J.; Laruelle, P. Bull. Soc. Fr. Mineral. Cr. 1973, 96, 12. (c) Hwu, S. J.; Bucher, C. K.; Carpenter, J. D.; Taylor, S. P. Inorg. Chem. 1995, 34, 1979. (d) Gitzendanner, R. L.; Spencer, C. M.; DiSalvo, F. J.; Pell, M. A.; Ibers, J. A. J. Solid State Chem. 1997, 131, 399. (e) Huang, F. Q.; Ibers, J. A. Acta Cryst. C 1999, 55, 1210. (f) Yang, Y. T.; Ibers, J. A. J. Solid State Chem. 2000, 155, 433. (g) Hartenbach, I.; Schleid, T. J. Solid State Chem. 2003, 171, 382. (h) Wu, L. B.; Huang, F. Q. Z. Kris-New Cryst. St. 2005, 220, 305. (i) Gulay, L. D.; Kaczorowski, D.; Pietraszko, A. J. Alloys Compd. 2005, 403, 49. (j) Huch, M. R.; Gulay, L. D.; Ekseyuk, I. 28


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