Article pubs.acs.org/cm
Sulfides with Strong Nonlinear Optical Activity and Thermochromism: ACd4Ga5S12 (A = K, Rb, Cs) Hua Lin,†,‡ Liu-Jiang Zhou,†,‡ and 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, ‡ Graduate University of Chinese Academy of Sciences, Beijing 100039, People’s Republic of China S Supporting Information *
ABSTRACT: Noncentrosymmetric quaternary sulfides, ACd4Ga5S12 (A = K, Rb, Cs) have been synthesized by a modified reactive flux method with high yields. Single-crystal X-ray diffraction analyses revealed they adopted a known KCd4Ga5S12-structure type in the trigonal space group R3 (No. 146) with cell parameters of a = 13.7905(5)−13.8639(5) Å, c = 9.3304(6)−9.3974(6) Å and Z = 3. Each asymmetric MS4 tetrahedral building unit (centered by disordered Cd and Ga) is aligned in the same direction along the c axis and connected via vertexes forming a chiral 3D framework, inside which the cuboctahedral S12 cavities accommodate A cations. These compounds have been discovered to exhibit the second largest powder second harmonic generation (SHG) intensities among sulfides to date, about 12, 11, and 10 times commercial AgGaS2 in the particle size of 46−74 at 2.05 μm incident laser with comparable wide transparency ranges (0.42−25 μm). Besides, their intense luminescence emissions around 590 nm shift to about 520 nm from 298 to 10K indicating thermochromism properties. The Vienna ab initio theoretical studies have aided the understanding of electronic structures and linear and nonlinear optical properties. KEYWORDS: quaternary sulfides, ACd4Ga5S12, second harmonic generation (SHG), nonlinear optical activity, thermochromism
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red emission at room temperature,22 and CdGa2Se4 exhibiting strong thermochromism from 582 to 715 nm between 285 and 9 K.23 In 1993, Schwer and co-workers had dissolved ternary CdGa2S4 in bromides and iodides and discovered KCd4Ga5S12 and RbCd4Ga5S12; they had also targeted on “CsCd4Ga5S12”, but failed, and consequently concluded that chlorides did not work as a flux in such systems.24 In this paper, we developed a new simple approach using ACl (A = K, Rb, Cs) chlorides as reactive fluxes to synthesize these compounds and find the then-unknown Cs-member, ACd4Ga5S12 (A = K, Rb, Cs) from the mixture of elements. More interestingly, for the first time, these compounds are discovered as multiple functional materials that exhibit both IR NLO properties and thermochromism. Their powder SHG intensities at 2.05 μm are the second strongest to date among sulfides, that are about 12, 11, 10 times that of commercial AgGaS2 for K-, Rb-, Csmember, respectively. And their intense emissions around 590 nm shift to about 520 nm when temperature decreases from 298 to 10K. The electronic structures and linear and nonlinear optical properties are understood with the aid of the Vienna ab initio theoretical studies.
INTRODUCTION Infrared nonlinear optical (NLO) crystals can effectively widen the IR laser wavelength range and are crucial in laser frequency conversion techniques in many fields, such as long-distance laser communication. The crystalline solid IR NLO materials have special advantage in the production of all solid state IR laser devices, which are stable and portable in practical applications.1 The number of commercial IR NLO crystals is limited, a few examples are I1−III1−VI2 semiconductors, such as AgGaS22,3 and AgGaSe2,4 but each of them unfortunately has its own drawbacks. It is therefore of broad scientific and technological importance to develop new IR NLO crystals. On the other hand, II1 −III2−VI4 semiconductors are also interesting,5 for instance, CdGa2S4 has low birefringence and large nonlinear coefficients;6 CdGa2Se4 is a promising photoconductor;7 and ZnGa2Se48 a wide bandgap material with high photosensitivity and strong luminescence. Both I1−III1−VI2 and II1−III2−VI4 are constructed by tetrahedron building units. Note that similar tetrahedral building units are found in many other NLO compounds, for example, LiGaQ2,9 BaGa4S7,10 BaGa 4 Se 7 , 1 1 Sm 4 GaSbS 9 , 1 2 (K 3 I)[SmB 1 2 (GaS 4 ) 3 ], 1 3 Li2CdGeS4,14 Li2CdSnS4,14 Li2Ga2GeS6,15 K2Hg3Ge2S8,16 AgGaGe 3 Se 8 , 1 7 Ba 3 CsGa 5 Se 1 0 Cl 2 , 1 8 BaGa 2 GeS 6 , 1 9 and Ba23Ga8Sb2S38.20 Meanwhile, chalcogenides containing d10 metals are usually luminescent, such as CdS and CdSe with strong and tunable luminescence,21 K2Cd3S4 displaying strong © 2012 American Chemical Society
Received: May 19, 2012 Revised: August 11, 2012 Published: August 18, 2012 3406
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Figure 1. Property of CsCd4Ga5S12: (a) experimental (black) and simulated (red) powder XRD patterns; (b) TG (blue) and DSC (black) diagrams; (c) UV−vis diffuse-reflectance spectrum; (d) reflection (inset) and FT-IR spectra.
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phased quaternary products after simple washing. We consider the slightly excess of the flux and the slow annealing process are the two major reasons for the clean formation of the quaternary compounds. Crystal Structure Determinations. All data collections were performed on a Rigaku Saturn70 CCD or Mercury CCD diffractometer equipped with graphite-monochromated Mo Kα radiation (λ = 0.71073 Å) at 293 K. The data were corrected for Lorentz and polarization factors. Absorption corrections were performed by the multiscan method.25 Structures were solved by the direct methods and refined by the full-matrix least-squares fitting on F2 by SHELX-97.26 The atomic coordinates before the last refinement cycles were standardized using STRUCTURE TIDY. 27 Take CsCd4Ga5S12 as an example, all observed reflections (4040 reflections) were used in the refinement, R3̅ (No. 148, centrosymmetric) and R3 (No. 146, chiral) were the only two candidate space groups. The mean |E2-1| = 0.788, suggested a chiral space group, therefore, R3 was selected. The initial structure refinement generated one Cs, four S, and three “Cd” atoms with R values of R1 = 7.40% and wR2 = 14.54%. According to the EDX result, the compound should also consist Ga atoms as well; subsequently, Ga and Cd were constrained to share the same crystallographic site and freely refined their occupancies by using “exyz” and “eadp” commands in SHELX. Such a treatment generated a Cd:Ga ratio of 4:5, which agreed well with the EDX results. Finally, the structure converged to much better R values of R1 = 2.17%, wR2 = 4.38% with all atoms refined anisotropically and generated a formula of CsCd4.0(3)Ga5.0(3)S12 (hereafter denoted as CsCd4Ga5S12) and a Flack parameter of 0.02(3). This refinement agreed with the previous report of KCd4Ga5S12.24 Moreover, the strong SHG effect of CsCd4Ga5S12 substantiated that the noncentrosymmetric of this compound. The
EXPERIMENTAL SECTION
Syntheses. Reactants were stored in an Ar-filled glovebox with controlled oxygen and moisture levels below 0.1 ppm. Elements with purities higher than 99.99% were purchased from Sinopharm Chemical Reagent. The title compounds were obtained from a mixture of Cd, Ga, and S in a molar ratio of 4: 5: 12 with slightly excess 1.1 mol ACl as reactive fluxes. The reactants were loaded in a fused-silica tube under vacuum and then heated to 473 K in 10 h, kept at this temperature for 1 day, and then heated to 1273 K in 150 h, followed by a dwell period of 7 days, subsequently cooled to 473 at 2 K/h before switching off the furnace. The products were washed first with distilled water to remove the excess ACl and chloride byproducts, and then dried with ethanol. After such a treatment, pure phases were obtained according to powder X-ray diffraction patterns shown in Figure 1a and Figure S1 in the Supporting Information. Semiquantitative energy-dispersive X-ray spectroscope (EDX) analyses carried out on several single crystals revealed the presence of A, Cd, Ga and S in a ratio CsCd4.0(2)Ga4.9(3)S12.2(2), which was close to ACd4.0(3)Ga5.0(3)S12 established by single-crystal diffraction data (see Figure S2 in the Supporting Information). No other element was detected. These compounds are stable in air for several months. Although the two lighter ACd4Ga5S12 (A = K, Rb) has been previously prepared by Schwer and co-workers24 via solving ternary CdGa2S4 in KBr or RbBr flux with 1:9 molar ratio at 1173 K for 1 day, of which the yields are not reported, and the products were not always single phase and often contained binary sulfides, ternary CdGa2S4, even in some cases, sphalerite solid solution of CdS and Ga2S3. The major improvement of our method lies in the ability of producing pure 3407
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quantum efficiency were recorded on a FLS920 fluorescence spectrophotometer equipped (Edinburgh Instruments Ltd.) with a continuous Xe-900 xenon lamp and a μF900 microsecond flash lamp. For low-temperature measurements, microcrystalline samples were mounted on a closed cycle helium cryostat. The excitation slit width is 3 mm and emission slit width is 0.25 mm. F number of the monochromator: 300 mm and detector: R928p (from Hamamatsu). The single photon counting mode is employed in data acquisition. Time-resolved luminescence spectra were obtained by ps LD at room temperature (measurements on the device LifeSpec-ps, Edinburgh Instruments Ltd.).
crystallographic data were listed in Table 1 and Tables S2−S4 in the Supporting Information.
Table 1. Crystallographic Data and Refinement Details for CsCd4Ga5S12 formula fw cryst syst crystal color space group a (Å) c (Å) V (Å3) Z Dc (g/cm3) μ (mm−1) GOOF on F2 R1, wR2 (I > 2σ(I))a R1, wR2 (all data) obsvd/constraint*/param largest diff. peak and hole (e/Å3) absolute structure param extinction coefficient
CsCd4Ga5S12b 1315.83 trigonal light-yellow R3 (No. 146) 13.8639(5) 9.3974(6) 1564.3(2) 3 4.190 14.007 1.010 0.0217, 0.0438 0.0227, 0.0441 1580/2/71 0.997, −1.140 0.02(3) 0.0103(2)
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COMPUTATIONAL SECTION
Electronic Structure Calculations. According to the singlecrystal structure refinement results, Cd and Ga atoms share each of the three 9b Wyckoff sites with Cd occupancies of about 1/2, 1/2 and 1/3, respectively; we had thus designed some possible configurations to probe the site preference of Cd. The calculation model was built in the P1 symmetry with 12 Cd and 15 Ga atoms distributed in the most energetic favorable mannerbut accounting for the individual occupancy factors in the R3 structureon the 27 corresponding positions in the unit cell as shown in Figure S14 in the Supporting Information. The geometrical optimization, band structures and density of states (DOS) CsCd4Ga5S12 were calculated by the Vienna ab initio simulation package VASP30a The generalized gradient approximation (GGA)30b was chosen as the exchange-correlation functional and a plane wave basis with the projector augmented wave (PAW) potentials was used.30c,d The valence electrons of the elements included Cs: 6s1, Cd: 4d105s2, Ga: 4s24p1 and S: 3s23p4. In the geometrical optimization, an energy cutoff of 370 eV and a 2 × 2 × 2 Monkhorst-Pack k-point grid were employed. The atoms are allowed to relax until forces on atoms are less than 0.02 eV/Å. In the static selfconsistent-field calculation, the plane-wave cutoff energy of 283 eV, and the threshold of 10−5 eV were set. The k integration over the Brillouin zone was performed by the tetrahedron method30e using a Monkhorst-Pack grid, 3 × 3 × 5 for CsCd4Ga5S12, and 17 × 17 × 17 for AgGaS2. The Fermi level (Ef = 0 eV) was selected as the reference of the energy. Optical Properties Calculations. More than 700 empty bands were used in the optical property calculations for CsCd4Ga5S12, and 74 empty bands for AgGaS2. The scissors operators of 1.20 and 1.79 were utilized, respectively. The k-point grids were set as the same as those for the electronic structure calculations. In the linear optical property calculations, the dielectric function was defined as ε(ω) = ε1(ω) + iε2(ω). The imaginary part ε2(ω) obtained from the momentum matrix elements between the occupied and unoccupied wave functions. And the real part ε1(ω), the adsorption coefficient α(ω), reflectance coefficient R(ω), and refractive index n(ω) were obtained from the imaginary part of the dielectric function ε2(ω) via the KramersKroning transform.31 The static and dynamic second-order nonlinear susceptibility χabc(−2ω,ω,ω) of CsCd4Ga5S12 were calculated based on the electronic structure via the so-called length-gauge formalism by Aversa and Sipe.32
R1 = Σ∥Fo| − |Fc∥/Σ|Fo|, wR2 = [Σw(Fo2 − Fc2)2/Σw(Fo2)2]1/2. bThe Crystallographic Data and Refinement Details for ACd4Ga5S12 (A = K, Rb) are listed in the Supporting Information, Table S2. *The two constraints are “exyz” and “eadp” commands. a
X-ray Powder Diffraction. The XRD patterns were taken at room temperature on a Rigaku DMAX 2500 powder X-ray diffractometer by using Cu Kα radiation (λ = 1.5406 Å) at room temperature in the range of 2θ = 10−70° with a scan step width of 0.05°. Elemental Analysis. Spectra were collected on a field emission scanning electron microscope (FESEM, JSM6700F) equipped with an energy-dispersive X-ray spectroscope (EDX, Oxford INCA) on clean single crystal surfaces. Differential Thermal Analysis. Differential thermal analysis (DTA) scans were measured on a NETZSCH STA 449C simultaneous analyzer. Reference (Al2O3) and crystal samples (cal.10 mg) were enclosed in Al2O3 crucibles and heated from room temperature to 1000 °C at a rate of 10 °C/min under a constant flow of nitrogen gas. UV−Vis−Near IR and IR Spectroscopies. The optical diffuse reflectance spectra of polycrystalline powder 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.28 The IR data were measured by a Nicolet Magana 750 FT-IR spectrophotometer in the range of 2.5−25 μm. Polycrystalline samples were ground with KBr and pressed into transparent pellets for the IR spectra measurement. Second Harmonic Generation (SHG) Measurements. The SHG response was measured on polycrystalline powder samples by using the Kurtz and Perry method with 2.05 μm Q-switch laser.29 Sample was ground and sieved into a series of distinct particle size ranges of 30−46, 46−74, 74−106, 106−150, 150−210 μm, respectively, which were pressed into a disk with diameter of 8 mm that was put between glass microscope slides and secured with tape in a 1 mm thick aluminum holder, and AgGaS2 crystals were crushed, ground and sieved into the same size range and were used as the reference. Photoluminescence Measurement. The solid-state luminescence emission spectra, excitation spectra, and powder sample
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RESULTS AND DISCUSSION Synthesis. Although K-, Rb-members of the title compounds had been synthesized by Schwer in 1993,24 route 1, we have established a modified method, route 2, to produce the target compounds with cheaper chlorides as reactive fluxes. All compounds were obtained as single phase after simply washed by water to remove the soluble byproducts. (Figure 1a and Figure S1 in the Supporting Information) The major differences between these two methods lie in the different flux ratio and the different heating profile. For instance, different amount, extremely excess vs nearly stoichiometric (36 vs 1.1 mol flux per reaction) flux is utilized; and different annealing time, 24 h vs 752 h, is used. The reported method often suffered from either a sphalerite solid solution or a 3408
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These data are consistent with those observed in CdGa2S4,33 KCd4Ga5S12,24 and AgCd2GaS4.34 The Cs atom resides at 3a site within the S-sublattice, (Figure 2) and centers the S12 cuboctahedron (Figure 3). The
mixture of binary or ternary sulfides in the product, which we consider as a rapid annealing method did not benefit the formation of the desired quaternary products. Differently, our modified method generates target quaternary compounds together with minor soluble byproducts, and is promising to be scaled up. 1173 K, 1 day
CdGa 2S4 + ABr ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ ACd4 Ga5S12 + CdS + Ga 2S3 + CdGa 2S4 + ABr + XBrx loading ratio 4: 36 (XBrx indicates the unknown bromide) (route 1) 1273 K, 4 weeks
Cd + Ga + S + ACl ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ ACd4 Ga5S12 + XCl x Figure 3. View of (a) the Cs-centered S12 cuboctahedron and (b) the anisotropic thermal elipsoids of Cs atom with Cs−S distances marked.
loading ratio 4: 5: 12: 1.1 (XClx indicates the unknown halide)
Cs−S distances range from 3.719(2) to 3.759(3) Å with an average of 3.742 Å. These Cs−S distances are in agreement with expected. For instance, the sum of the Shannon ionic radii35 is about 3.72 Å, (rCs+ = 1.88 Å for CN 12, rS2− = 1.84 Å for CN 6). These data are consistent with those observed in CsGa3S5 (3.572−3.810 Å),36 Cs2CdBi2S5 (3.532−3.861 Å).37 On going from Cs+ to K+, the thermal vibration parameters (Ueq) of A increase considerably from 0.025 to 0.066, because the S12 cuboctahedron is obviously larger for the smaller K+ cation. This is reflected by the similar unit cell parameters of the title compounds. For example, the ionic radii (CN = 12) increase about 14.6% from K+ to Cs+ (1.64, 1.72 Å, and 1.88 Å, respectively),35 the unit-cell volumes only increase 1.8%. (Table 1 and Table S3 in the Supporting Information) Besides, the identity of the alkali metal on going from K+ to Rb+ to Cs+ does not significantly affect the occupancies of the three tetrahedral interstice sites (9b sites, see Table S3 in the Supporting Information). Nevertheless, the ionic nature of the alkali metal cations does affect the overall polarity of the title compounds. And the increase trend of the ionic nature of the A+ cation is in direct proportion with the increase in the NLO property of the title compounds. Optical Properties. The powder NLO properties of the title compounds have been studied for the first time. Figure 4 shows the curves of the particle size versus the SHG intensity indicating a non type-I phase-matchable nature38 of the title compounds at 2.05 μm. These compounds realize their SHG intensity maxima at the particle size of 46−74 μm (Figure 4, Table 2) that are roughly 12×, 11× or 10 × AgGaS2. These values are the second largest among sulfides to date, some other examples are Ba23Ga8Sb2S38, 22×;18 Sm4GaSbS9, 3.8×;20 La4InSbS4, 1.5×;39 Eu2Ga2GeS7, 1.6 × AgGaS2.40 On going from Cs+ to K+, the SHG intensities of the compounds increase as the ionic radii of the cations decrease. Similar trend has been seen in ACaCO3F (A = K, Rb, Cs).41 The title compounds are light yellow in color and have band gaps of 2.98−3.09 eV, these are similar to those reported: AgGaS 2 (2.56 eV, see Figure S5a in the Supporting Information), BaGa4S7 (3.54 eV),18 CdGa2S4 (3.45 eV),42 and ZnGa2S4 (3.22 eV).43 The title compounds show transparent ranges roughly from 0.42 to 25 μm that are similar to that of AgGaS2 (0.6−23 μm, see Figure S5b in the Supporting Information). Thermal Stabilities. CsCd4Ga5S12 has excellent thermal stability and shows no obvious weight loss up to 744 °C (Figure 1b). To check the thermal stability, we designed a
(route 2)
Crystal Structure. ACd 4 Ga 5 S 12 (A = K, Rb, Cs). CsCd4Ga5S12 has been obtained for the first time, which crystallizes in trigonal R3 space group with a = 13.8639(5), c = 9.3974(6) adopting a chalcopyrite-related structure known for K- and Rb-members.24 (Table 1 and Tables S2−S4 in the Supporting Information) Figure 2 shows the structure of CsCd4Ga5S12, in which S atoms are nearly cubic close packed, and the three 9b sites are
Figure 2. (a) Structure and (b) tetrahedron packing of CsCd4Ga5S12 viewed down the b-direction with the unit cell marked. Purple, Cs, cyan, M (M = Cd/Ga), yellow, S; tetrahedron, MS4.
partially filled by Cd and Ga with Cd/Ga occupancies of 0.51(4)/0.49(4), 0.48(2)/0.52(2), and 0.34(2)/0.66(2), respectively (see Table S2 in the Supporting Information). Each distorted MS4 (M = Cd/Ga) tetrahedron is centered by a 9b site and aligned in the same direction along the c axis as shown in Figure 2b. The M−S bond ranging from 2.351(4) to 2.416(4) Å and the S−M−S angle deviates from 103.98(2) to 115.51(7)° (see Table S4 in the Supporting Information). 3409
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Figure 4. (a) Phase-matching curves, i.e., particle size versus SHG response, for KCd4Ga5S12, RbCd4Ga5S12, CsCd4Ga5S12, and AgGaS2 (reference). (b) Oscilloscope traces of SHG signals of KCd4Ga5S12, RbCd4Ga5S12, CsCd4Ga5S12, and AgGaS2 (reference) in the particle size of 46−74 μm.
respectively. After such a treatment, samples heated at 700 and 800 °C were still single-phased CsCd4Ga5S12; the 850 and 900 °C amples contained minor binary CdS and Ga2S3 as impurities (see Figure S6 in the Supporting Information). These data are in principle consistent with the TG analysis. Photoluminescence Properties. The title compounds ACd4Ga5S12 display at room temperature (RT) intense emission bands centered at 584−595 nm with excitation maximum at 376−395 nm (Figure 5 and S7). These emissions are similar to the 577 nm emission of CdGa2S444 and 440−500 nm emissions of Ga/S supertetrahedra frameworks.45 The quantum yields at room temperature were 1.97, 2.12, and 2.53% for K-, Rb-, and Cs-compounds, respectively. And the
Table 2. Measured Optical Properties for ACd4Ga5S12 (A = K, Rb, Cs)
a b
ACd4Ga5S12
SHG intensitya
trans. region (μm)b
Eg (eV)
A=K A = Rb A = Cs
12.2 11.1 9.8
0.45−25 0.43−25 0.42−25
2.98 3.02 3.09
Relative to commercial AgGaS2 (46−74 μm) with λincident = 2.05 μm. Measured on polycrystalline sample.
series of experiments as following. Four samples of pure CsCd4Ga5S12 powder were put into silica tubes under vacuum, and annealed for 12 h at 700, 800, 850, and 900 °C,
Figure 5. (a) Normalized solid-state emission (solid line) and excitation (dotted line) spectra of CsCd4Ga5S12 collected at (a) room temperature and (b) 10 K, respectively. (c) CIE-1931 chromaticity diagram showing the near yellow and green fluorescence of CsCd4Ga5S12 at RT and 10 K. The CIE coordinates for the emission are (0.49, 0.48) at RT and (0.27, 0.44) at 10 K. CIE coordinates are calculated using the software GoCIE obtained from http://www.geocities.com/krjustin/gocie.html. 3410
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Supporting Information) As the temperature decreases to 10 K, CsCd4Ga5S12 emits at 504 nm (Figure 5b) and the quantum yield increases to 27.53%. The emission blue shift is clearly visualized by the CIE-1931 chromaticity diagram coordinates, from (0.49, 0.48) at RT to (0.27, 0.44) at 10 K. The related ternary compound CdGa2 Se4 shows similar but more significant shift, from 715 nm at 298 K to 582 nm at 9 K.23 Similarly, the 580 nm emission of {[Cd3(TTHA)(dps)(H2O)3]2}H2O at 298K shifts to 538 nm at 10 K.46 The temperature-dependent emission spectra in Figure 6 and Figure S8 in the Supporting Information show that emissions of ACd4Ga5S12 blue shift linearly with enhanced intensities. Thus, compound ACd4Ga5S12 will be potential candidates for applications in temperature-sensing devices.47 Obviously, ACd4Ga5S12 compounds are examples that exclude the influence of any organic guest molecule and lanthanide ion center. 48 According to the luminescent mechanism of CdGa2Se4,23,49 we consider that the strong photoluminescence of the title compounds may be related to the presence of the point defects. Band Structure and Linear and Nonlinear Optical Property Studies. The band structure and density of state (DOS) of CsCd4Ga5S12 are plotted in Figure 7. The top of valence band (VB) and the bottom of conduction band (CB) are located at the same k-point (Γ), describing the direct band gap of 1.89 eV for CsCd4Ga5S12, which is smaller than the experimental 3.09 eV. Such a discrepancy is due to the discontinuity of the exchange-correlation potential that underestimates the band gap in semiconductors and insulators.50 The total and partial DOSs for CsCd4Ga5S12 are shown in Figure 7b. Below the Fermi level in the region of VB-1, the S-3p state has the largest contribution and mixes with minor contributions from Cd-5s, Cd-4p, Cd-4d, and Ga-4p states. The VB-2 region is primarily derived from Cd-4d, Ga-4s and S-3p states with small contributions of Cs-5p and neglectable S-3s states. Above the Fermi level, CB-1 region is derived mainly from S-3p and Ga-4s states mixing with small amounts of Cd-5s and Ga-4p states; CB-2 region is predominately S-3p, Cd-5s,
solid-state lifetime are 15−21 ms (Table 3) suggesting a fluorescent character. The low temperature (10 K) emission Table 3. Photoluminescence Data for ACd4Ga5S12 (A = K, Rb, Cs) λex (nm)
λem (nm)
ACd4Ga5S12
rt
10 K
rt
10 K
rt
Φf (%) 10 K
τ (ms) (rt)
A=K A = Rb A = Cs
395 387 376
375 370 362
595 590 584
532 515 504
1.97 2.12 2.53
26.59 31.82 43.01
15.31 17.09 21.13
spectra of ACd 4 Ga 5 S 12 show interesting luminescence thermochromism. (Table 3, Figure 6 and Figure S8 in the
Figure 6. Relative emission spectra of compound CsCd4Ga5S12 collected with the same excitation in the solid state at different temperature.
Figure 7. (a) Calculated band structure of CsCd4Ga5S12 (Γ (0, 0, 0); F (0, 1/2, 0); Q (0, 1/2, 1/2), and Z (0, 0, 1/2)), the Fermi level is set at 0.0 eV. (b) Total and partial densities of states of CsCd4Ga5S12. 3411
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eV), is larger than that of AgGaS2 (d36 (2.05 μm) = 18.2 pm/ V). (for comparison, the previous reported value for AgGaS2 is (d36 (10.6 μm) = 12 pm/V.2) Our calculation results are in accordance with the experimental observations. The calculated linear and nonlinear optical parameters for CsCd4Ga5S12 and AgGaS2 are summarized in Table 4 (see
and Ga-4p states; CB-3 are mainly S-3p and Ga-4p states. Therefore, the optical absorptions of CsCd4Ga5S12 are mainly ascribed to the charge transitions from S-3p states to Ga-4s, Ga4p and Cd-5s states. The frequency-dependent dielectric functions of CsCd4Ga5S12, including calculated imaginary ε2(ω) and real ε1(ω), are shown in the Supporting Information, Figure S9. The main peaks of imaginary part ε2(ω) are located around 6.8, which can be mainly regarded as electronic interband transitions from the S-3p to Cd-5s and Ga-4p states. The average value of the polarized zero-frequency dielectric constants is 5.864, which is calculated from the equation ε1(0) = [ε1xx(0) + ε1yy(0)+ ε1zz(0)]/3 (see thr Supporting Information, Table S5). The refractive index n, birefringence (Δn), absorption coefficient α and reflectivity R were also calculated (see Figures S10−S13 in the Supporting Information). The function n appears its peak value around 4.8 eV and rapidly decreases in the region from 5.0 to 10.0 eV, corresponding mainly to the higher values for R in this range. The absorption coefficient α is very large (about 1 × 105 cm−1) because of the free carrier adsorptions in semiconductors.51 The static birefringence of CsCd4Ga5S12 is only 0.003 and obviously smaller than the static birefringence of AgGaS2 (0.039). The highest Δn values is 0.17 and locating around 7.91 eV. The relatively small Δn values in the IR region (
