Theoretical Design of Layered AlGaS3 as a New Nonlinear Optical

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Theoretical Design of Layered AlGaS3 as a New Nonlinear Optical Material with Strong Second Harmonic Generation Response Jing Lin, Jiajia Huang, Xu Cai, Zhenxing Fang, Shuping Huang, Yi Li, Kaining Ding, and Yongfan Zhang Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b01523 • Publication Date (Web): 01 Feb 2019 Downloaded from http://pubs.acs.org on February 3, 2019

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Crystal Growth & Design

Theoretical Design of Layered AlGaS3 as a New Nonlinear Optical Material with Strong Second Harmonic Generation Response Jing Lin,a Jiajia Huang,a Xu Cai,a Zhenxing Fang,b,* Shuping Huang,a Yi Li,a,c Kaining Ding,a Yongfan Zhang a,c,* a

State Key Laboratory of Photocatalysis on Energy and Environment, College of Chemistry, Fuzhou University, Fuzhou, Fujian, 350116, China b Department of Physics, Zunyi Normal University, Zunyi, Guizhou, 563006, China c Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen, Fujian, 361005, China

Abstract Using the evolutionary algorithm combined with the first-principles calculations, the stoichiometry and the structure of a new family of Al-Ga-S ternary sulfides are explored, and a layered configuration with the R3m space group is predicted as the most stable structure of AlGaS3. The second order nonlinear optical (NLO) properties of AlGaS3-R3m phase are further calculated, and our results reveal that it is a promising candidate for the mid-infrared NLO material. Besides the high laser damage threshold and the good phase match ability in the transmission range 0.4 - 24 μm that covers most of the mid-IR windows, the second harmonic generation (SHG) of AlGaS3-R3m is about four times stronger than that of the commercial AgGaS2 crystal. The strong SHG activity of AlGaS3-R3m phase can be attributed to a special layered arrangement of the structure, namely two kinds of coordination polyhedra (i.e., [AlS6]9- octahedra and [GaS4]5- tetrahedra) are distributed in the opposite sides of the single AlGaS3 layer, which helps to strengthen the polarity of the material. Additionally, with respect to the layered structures, other phases of AlGaS3 crystallized in condensed bulk structures that only contain tetrahedral motifs ([AlS4]5- and [GaS4]5-) show relatively weak SHG responses. The present study suggests that the constructing of two-dimensional layered structure can provide an effective way to find new NLO material with strong SHG effect.

Keywords: Second-order nonlinear optical responses; second harmonic generation; density functional theory; evolutionary algorithm.

Corresponding authors. E-mail addresses: [email protected]; [email protected] *

1

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Crystal Growth & Design 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1. Introduction Nonlinear optical (NLO) crystals have important applications in many fields including optoelectronic device, tele-communication, information storage, and medical apparatuses etc., due to their advantages in the laser frequency conversion.1 However, up to date, only few crystals can satisfy the requirements in the mid-infrared (IR) and far-IR regions. The current commercial NLO materials (such as AgGaS2) used in IR region unfortunately suffer some drawbacks, including low laser damage threshold, phase mismatch in the work transmission range, and easily creating defects during single crystal growth.2 Thus, extensive works have been performed to explore new IR NLO materials in recent years.3-6 In order to improve the strength of the second harmonic generation (SHG), the combination of Jahn-Teller ions (such as transition metal ions with d0 electronic configurations or cations containing lone-pair electrons) with other SHG motifs, and the stacking of multiform active SHG units in the same orientation have been proved to be effective to enhance the polarity of the NLO crystals.7-9 Nevertheless, due to the intrinsic contradiction between the second harmonic susceptibility and the laser damage threshold, namely, the strong SHG susceptibility requires a small band gap but the small band gap will result in the low laser damage threshold, it is still a challenging work to balance these two parameters.10-13 It is interesting that in a recent work, we have found that when the configuration of In2Se3 crystal varies from 3D bulk to 2D nanosheet, the band gap is only changed slightly, however the NLO activity can be increased significantly, in which the magnitude of the SHG coefficient of 2D system can be several times larger than that of bulk structure.14 Such distinct enhancement of the SHG strength is strongly correlated with a special arrangement of two different In-Se polyhedra, namely [InSe6]9- octahedra and [InSe4]5- tetrahedra, in the opposite sides of In2Se3 monolayer. Similar findings have also been reported in other 2D compounds including MoS2 and GaSe.15-17 2


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Actually, it is obvious that with respect to the bulk material with complicated structure, it is more easily to arrange the different SHG building blocks in the same orientation within a nanosheet, which results in the remarkable enhancement of the dipole moment of the system. Therefore, the constructing of low-dimensional structure can provide a promising way to design new NLO material with strong SHG effect. Considering the silver thiogallate, the most representative commercial NLO crystal used in the IR region, in this work, we select AgGaS2 as a starting point to construct a new layered-2D material by replacing silver with aluminum. It is noted that the replacements of Ag atom with main group metal elements including Li, Na and Mg have been realized in experiments.18-21 After performing extensively global structural searches based on the first-principles calculations,22-24 some thermodynamic stable AlGaS3 compounds are identified and especially among them a layered configuration with a space group of R3m is energetically most favorable. In this structure, two different tetrahedral units of [AlS6]9- and [GaS4]5- are distributed in the opposite sides of AlGaS3 layer, and its SHG susceptibility is about four times stronger than that of AgGaS2, meanwhile, the improvement of laser damage threshold (about 2 - 3 times) can be expected. The present work can provide a new approach to design the NLO materials with outstanding performances.

2. Computational Details We performed the global structure searches of Al-Ga-S systems by employing the evolutionary algorithm combined with the first-principles calculations through the Vienna ab initio simulation package (VASP).25 The projected augmented wave26,27 (PAW) potentials were used to describe the core

electrons.

The

generalized

gradient

approximation

Perdew-Burke-Ernzerhof

(PBE)

exchange-correlation functional28 was used in the structural optimization, and the Heyd-Scuseria3



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Ernzerhof (HSE06) screened hybrid functional29 was adopted in the band structure calculations. The influences of van der Waals interactions were also taken into account by using the dispersion corrected vdW-DF2 functional due to the layered structure was involved.30 In the calculations, the cut-off energy for the plane-wave basis was set to 500 eV, and the energy convergence tolerance for self-consistency was set to 10-6 eV and the force criterion was set to 0.001 eV/Å. In the global structure searches, we firstly determined the stoichiometry of Al-Ga-S system with variable component calculations implemented in the USPEX (Universal Structure Predictor: Evolutionary Xtallography) code,31 and the results shown in Figure 1 indicate that the composition with AlGaS3 formula is located at the convex hull of the potential energy. Then the geometries of AlGaS3 were explored by considering that there are 5, 10, 15, 20 and 30 atoms contained in the unit cells with different sizes. The cohesive energies of AlGaS3 compounds were calculated by using the following formula, which has been used to evaluate the stabilities of the predicted materials,32 Ecoh= EAlGaS3 – (EAl + EGa + 3ES)

(1)

where EAl, EGa, and ES are the energies of a single Al, Ga, and S atom in their most stable bulks, respectively, and EAlGaS3 is the total energy of AlGaS3 compound. Furthermore, to check the dynamic stability of the predicted structures, the phonon dispersion curves were calculated, and the molecular dynamic (MD) simulations were also carried out to confirm the thermodynamic stability of AlGaS3 compounds. During the MD simulation the supercells with different sizes were employed,

namely,



(3 × 3 × 1) for R3m structure, (2 × 2 × 4) for Bm, ( 3 × 3 × 2) for P 3 m, (4 × 4 × 1) for Cmc21 structure, (3 × 4 × 3) for Pm, (1 × 4 × 3) for Cm, and (3 × 1 × 2) for Cc phase, respectively. The

4


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simulation lengths were 10 ps with a time step of 1 fs and the Nośe heat bath method was used to control the temperatures at 300 and 1000 K. In the present work, we used the length-gauge formalism derived by Aversa and Sipe33,34 to calculate the SHG coefficients of AlGaS3, and at the zero-frequency limit the second-order nonlinear abc susceptibility  (2 ,  ,  ) can be expressed as,

 abc (2 ,  ,  ) 

1 V

i 4V

a rnm {rmlb rlnc }



nml , k

mlln

f nm



nm , k

[n f ml  m f ln  l f nm ] 

nm

2 mn

a b c b a c c a b [rnm (rmn ;c  rmn ;b )  rnm ( rmn ;c  rmn ; a )  rnm ( rmn ;b  rmn ; a )]

(2)

where superscripts (a, b, and c) indicate Cartesians components; n and m represent the energy bands; a is the matrix element of the position operator; f nm  f n  f m is the difference of the Fermi rnm

distribution functions;  mn   m   n is the frequency difference for the energy bands m and n at b the same k point; V is the volume of the unit cell; rmn is the generalized derivative of the ;a

coordinate operator in the k space,

b mn ;a

r



a b rnm bmn  rnm amn

 nm



i

 nm

 (

r r   nl rnlb rlma )

a b lm nl lm

(3)

l

a a where amn  ( p nn  p mm ) / m is the difference between the electronic velocities at the energy bands

n and m. In the calculations of the optical properties of AlGaS3, after carefully examining the convergences of the optical properties as functions of the size of k-point mesh and the number of empty bands, a dense k-mesh was adopted, and the energy cutoff of empty bands involved in the calculations was taken to be at least 32 eV above the valence-band maximum. In addition, the scissor operation was adopted in the optical properties calculation because of the insufficient cancellation of 5



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the self-interaction correction inherent in the pure DFT method.35 The band gap obtained by HSE06 functional was used to determine the scissor parameter. In the following sections, the d-tensor defined as dij 

 abc 2

was used to represent second-order nonlinear optical susceptibility, in which

Voigt notation indices were introduced to simplify second rank tensors.

3. Results and Discussion 3.1 Structures of AlGaS3 Using the global evolutionary algorithm, the formula AlGaS3 has firstly been predicted due to it has the lowest enthalpy by variable component calculations. Then as shown in Figure 2, we have searched the stable structures of AlGaS3 with different cell formula units (Z = 1, 2, 3, 4 and 6). Besides the Ga2S3-similiar structure (the Cc-like structure below the article), we also find some new structures of Al-Ga-S ternary systems. After examining more than 40000 structures, four typical layered structures with Bm, R3m, 

Cmc21 and P 3 m space groups, and four bulk structures crystallized in Pm, Cm, and Cc space groups have been identified. The optimized cell parameters of eight structures are listed in Table 1 and the corresponding structures are shown in Figure 3. Since there are two 3D structures with Cc space group (Figures 3g and 3h), in the following sections, we denote two structures as Cc and Cc-like, and the structure of Cc-like is similar to Ga2S3 compound observed in the experiment. As shown in Figure 3a-3d, in all layered configurations the aluminum atoms are sixfold-coordinated while the gallium atoms are fourfold-coordinate. It is noted that the [AlS6]9octahedra and [GaS4]5- tetrahedra are distributed in the opposite sides within a single sheet. For the R3m, Bm and Cmc21 phases, although the cell shapes are different (hexagonal vs. monoclinic), the arrangements of two kinds of polyhedra are similar, in which AlGaS3 nanosheets consist of five 6


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atomic layers stacked in the same sequence of S-Al-S-Ga-S. The thickness of AlGaS3 single layer is about 5.9 Å, and the space between two adjacent layers is in the range from 3.5 to 3.9 Å. We will see that the optical properties of these three layered configurations are also quite similar. On the other 

hand, in the P 3 m structure, the stacking sequences of adjacent nanosheets are reversed, consequently it belongs to the configuration with inversion centre and will not exhibit SHG activity. For the rest four AlGaS3 bulk crystals with 3D structure (Figures 3e-3h), except that Al atoms are five-fold coordinated in the Pm phase, both Al and Ga atoms are four-fold coordinated. Therefore, above results indicate that the coordination environment of Al atom is more flexible than that of Ga atom. According to the calculated cohesive energies of different AlGaS3 compounds listed in Table 1, it is clear that the AlGaS3 with R3m space group is most energetically stable among eight structures. Thus, we will focus this structure in the following sections. As shown in Figure 3a, the R3m phase is formed by stacking AlGaS3 monolayer in ABCABC sequence, namely, there are three layers in the unit cell. The calculated cell parameters are a = 3.60 Å and c = 28.69 Å, and the average lengths of Al-S and Ga-S bonds are 2.44 and 2.28 Å, respectively, which are close to the lengths of normal Al-S and Ga-S bonds measured experimentally for Al2S3-P61 (about 2.34 Å)36 and Ga2S3-Cc crystals (about 2.32 Å).37 Additionally, the cohesive energy of R3m phase (-4.337 eV/formula) also falls in between the results of Al2S3-P61 (-5.349 eV/formula) and Ga2S3-Cc (-3.614 eV/formula). Thus, it seems that AlGaS3 with layered configuration can be synthesized experimentally. Furthermore, to quantify the possibility of the formation of AlGaS3 monolayer through the exfoliation procedure, the binding energy is also determined. The corresponding value is about 35 meV/atom, which is smaller than the binding energies of graphite (~ 50 meV/atom)38 and transition-metal dichalcogenides (~ 60 meV/atom).39 This result means that 7



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adjacent layers are weakly coupled to each other and the isolated AlGaS3 monolayer can be obtained from R3m phase. To check the dynamic stability of R3m structure, phonon dispersion curve is calculated (the phonon curves of other phases are provided in the Figure S1 in the Supporting Information), and as shown in Figure 4a, no imaginary frequency is observed, implying that the predicted structure is dynamically stable. Furthermore, the MD calculations are performed to examine the thermal stability of R3m at the temperatures of 300 K and 1000 K. Several snap shots for the MD simulation at times of 0, 0.5, 1.0, 1.5, 2.0 and 2.5 ps are shown in Figure S2, and although the variations of the framework of are observed, the original layered structure is still preserved even at 1000 K, which demonstrates the outstanding thermal stability of AlGaS3-R3m structure. 3.2 Electronic structures The band structures of different AlGaS3 compounds are calculated by using HSE06 hybrid functional, and the corresponding band gaps are summarized in Table 1. Figure 4b displays the band structure of R3m phase obtained by HSE06 method. It shows that AlGaS3-R3m is a semiconductor with a direct band gap at the  point. The corresponding band gap (3.1 eV) is larger than that of AgGaS2 (2.64 eV)40 and is close to those of LiGaS2 (3.76 eV),41 LiGaSe2 (3.13 eV)42 and MgGa2S4 (3.4 eV)43 crystals. So a higher laser damage threshold may be expected for AlGaS3-R3m.44 Since the top of valance band presents an obvious platform around the  point and the bottom of conductor band has a shape of parabola, we can expect that such band structure favors the nonlinear response of the NLO crystals according to the similar situation in the thermoelectric materials. Some partial density of states (DOSs) of R3m phase are shown in Figure 4c. It is clear that the valence band maximum (VBM) is dominated by the S-3p orbitals, while the hybridizations of S-3p and Ga-4s 8


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states show main contributions to the conduction band minimum (CBM). According to the position (3.2 eV) of the edge of absorption spectrum and the DOSs of VBM and CBM, it shows that the electron transition between VBM and CBM followed the selection rule.45 The calculated band gap indicates that the transmission range of AlGaS3-R3m (0.4 - 24 μm) can cover most part of atmospheric windows and some of terahertz (THz) ranges.46 3.3 The SHG susceptibility of AlGaS3-R3m In this section, we focus on the SHG response of the R3m structure. There are night nonvanishing independent SHG coefficients for R3m space group, and based on the Kleinman symmetry, besides the d33 tensor, the relationships of other tenses at static limit are d24 = d15, d31 = d32, and d22 = -d16 = -d21. As listed in Table 2, the static SHG coefficient with the highest magnitude is d33, and the corresponding value is 69.5 pm/V. Therefore, with respect to the commercial AgGaS2 crystal (17.6 pm/V),47 the AlGaS3-R3m exhibits a stronger SHG response (about four times) than AgGaS2. The frequency-dependent variation of the d33 tensor is plotted in Figure 4d. The first peak with a magnitude of 762.2 pm/V appears at about 2.4 eV, and the strongest SHG response may be observed at 4.0 eV. Moreover, the birefringence curve of AlGaS3-R3m is shown in the insert of Figure 4d, it can be seen that the birefringence is about 0.09 in the IR region (< 1.6 eV), suggesting AlGaS3-R3m has an excellent ability of phase match for SHG response and can realizes the high-performance frequency transformation in the IR region. To deeply understand the relationship between electronic structure and the SHG activity of AlGaS3-R3m, the variation of static d33 coefficient as a function of the cutoff energy is given in Figure 5a. It is clear that the d33 coefficient shows obvious changes in the energy windows of -1.0 – 0 eV and 2.0 – 3.5 eV. Based on the associated partial charge density maps and the projected DOSs 9



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shown in Figure 5, the dominant components in the energy from -1.0 eV to 0 eV are the 3p states of the S atoms which bond with Al atoms. On the other hand, for those empty states located in the energy region of 2.0 – 3.5 eV, they are mainly originated from the states of Ga and the surrounding S atoms. Therefore, it seems that the strong SHG response of AlGaS3-R3m can be attributed to the transitions from the occupied bands derived from the octahedral [AlS6]9- unit in one side to the unoccupied bands belonged to the tetrahedral [GaS4]5- unit in another side of AlGaS3 monolayer. The calculated static SHG coefficients of other AlGaS3 with layered arrangements, namely Bm, and Cmc21 phases are listed in Table 2, and the corresponding frequency-dependent variations of the SHG coefficients are given in Figure S3. Similar magnitudes of static d33 coefficient (around 69 pm/V) are obtained, indicating other AlGaS3 compounds with layered structure also exhibit strong SHG susceptibility. In contrast, for those AlGaS3 with bulk structure (see Table 2), the relatively weak SHG responses and small magnitudes of birefringence are predicted. These results also demonstrate that the 2D-layered structure has obvious advantages in the field of NLO compared to the 3D bulk structure.

4. Conclusions In this work, the geometries, electronic properties and optical properties of AlGaS3 compounds have been systematically studied on the basis of quantum mechanical calculations. Layered AlGaS3 in the R3m space group is predicted to be a superior mid-infrared nonlinear optical crystal. Besides the high laser damage threshold and the good phase match ability in the transmission range 0.4-24 μm, which covers most of mid-IR window, it owns about 4 times of magnitude of the second harmonic susceptibility larger than that of the commercial AgGaS2 crystal. The excellent properties of AlGaS3-R3m attributes to the layered configuration and the electron transition of the [AlS6]9- and 10


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[GaS4]5- motifs. Other AlGaS3 compounds, which only contain the tetrahedral motifs ([AlS4]5- and [GaS4]5-) with the triangular prism vacancies, have also been proved as a candidate of NLO crystals, which have about two times of second harmonic respond than AgGaS2. Present work gives an idea to find the new balance NLO crystal and enriches two-dimensional layered crystal families.

Supporting Information The phonon dispersion curves of AlGaS3 compounds with different space groups; snap shots for the MD simulation results of R3m phase in 300 and 1000 K at t = 0, 0.5, 1.0, 1.5, 2.0, and 2.5 ps; and the frequency-dependent SHG coefficient and the birefringence of different AlGaS3 compounds.

Acknowledgements This work was supported by National Natural Science Foundation of China (grant nos. 21773030, 11847085, 21373048, 21203027, and 51574090), the Independent Research Project of State Key Laboratory of Photocatalysis on Energy and Environment (2014A02), and Natural Science Foundation of Fujian Province (2017J01409). The calculations were performed on the supercomputing center of Fujian Province installed at the Fuzhou University.

Competing interests The authors declare that there are no competing interests.

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Figure Captions Figure 1 The convex hulls of Al-Ga-S compounds with variable component calculations. Two figures are obtained by the same calculation settings, except that the number of atoms is doubled in figure (b). The results show that the stoichiometry of AlGaS3 is preferred for this ternary system. Figure 2 The enthalpies of AlGaS3 with different cell formula units (Z=1, 2, 3, 4 and 6). For clarify, the space groups of the typical structures found in each Z value are provided. Since the global evolutionary algorithm is executed several times for the same Z value, the corresponding results are denoted by different colors. Figure 3 Structures of AlGaS3 crystallized in different space groups found by global evolutionary algorithm. In the figures, the Al, Ga, and S atoms are denoted by pink, cyan, and yellow spheres, respectively. Figure 4 (a) Phonon dispersion, (b) band structure, (c) density of states (DOSs), and (d) frequency-dependent d33 coefficient of AlGaS3-R3m phase. In Figure (d), the birefringence curve is shown in the insert. Figure 5 (a) The variation of static d33 coefficient as a function of the cutoff energy, and (b) total and projected density of states of AlGaS3-R3m phase. The partial charge density maps are drawn at the isosurface level 0.015 e/Å3 by considering states in the energy regions from -1.0 eV to VBM and from 2.0 to 3.5 eV, respectively.

12


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Figure 1

(a)

(b)

13



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Figure 2

14


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Figure 3



(a) R3m

(b) Bm

(c) P 3 m

(d) Cmc21

(e) Pm

(f) Cm

(g) Cc

(h) Cc-like

15



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Figure 4

(a)

(b)

(c)

(d)

16


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Figure 5

(a)

(b)

17



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Table 1 The optimized cell parameters, the thickness (h) and the interlayer distance (d) for the layered structures, the cohesive energies and the bandgap (Eg) calculated by HSE06 functional of different AlGaS3 compounds Cohesive energy

Structure

a(Å)

b (Å)

c (Å)

α

β

γ

h/d(Å)

R3m

3.60

3.60

28.69

90.0

90.0

120.0

5.9/3.7

-4.337

3.13

Bm

6.24

9.70

3.60

90.0

90.0

102.4

5.9/3.6

-4.313

3.16

Cmc21

3.62

6.20

19.47

90.0

90.0

90.0

5.9/3.9

-4.293

3.25

P3m

3.61

3.61

18.87

90.0

90.0

120.0

5.9/3.5

-4.251

2.75

Pm

6.00

3.52

5.83

90.0

63.2

90.0

–

-4.289

3.87

Cm

12.49

3.70

5.45

90.0

115.8

90.0

–

-4.290

2.91

Cc

6.60

11.23

7.39

90.0

124.2

90.0

–

-4.292

2.90

Cc-like

11.43

6.54

9.84

90.0

142.0

90.0

–

-4.314

3.40



(eV/formula)

Eg (eV)

18


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Table 2 The static birefringence (Δn) and the magnitudes of static SHG coefficients of AlGaS3 compounds in different phases dij (pm/V) a

Systems

Δn

AlGaS3-R3m

0.09

d15 = 8.70

d22 = 14.65

d33 = 69.50

AlGaS3-Bm

0.09

d11 = 14.79

d12 = 14.80

d13 = 0.01

d15 = 8.43

d24 = 8.42

d33 = 69.10

AlGaS3-Cmc21

0.09

d15 = 9.57

d24 = 11.38

d33 = 69.38

AlGaS3-Pm

0.06

d11 = 4.50

d12 = 0.14

d13 = 27.64

d15 = 37.12

d24 = 20.80

d33 = 15.17

d11 = 2.64

d12 = 2.91

d13 = 4.69

d15 = 27.71

d24 = 14.78

d33 = 6.36

d11 = 7.73

d12 = 30.53

d13 = 15.48

d15 = 0.44

d24 = 0.24

d33 = 0.34

d11 = 0.53

d12 = 9.61

d13 = 8.51

d15 = 10.50

d24 = 5.99

d33 = 1.94

AlGaS3-Cm

AlGaS3-Cc

AlGaS3-Cc-like

0.05

0.05

0.03

a. The SHG coefficients of AlGaS3 crystallized in different space groups have the features of that for the Pm, Bm, Cm, Cc phases d26=d12, d35=d13, d31=d15, d32=d24, and for Cmc21, d31=d15, d32=d24.

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For Table of Contents Use Only

Theoretical Design of Layered AlGaS3 as a New Nonlinear Optical Material with Strong Second Harmonic Generation Response Jing Lin, Jiajia Huang, Xu Cai, Zhenxing Fang, Shuping Huang, Yi Li, Kaining Ding, Yongfan Zhang

When the silver atoms in AgGaS2 crystal are replaced by aluminum, a new layered-2D material, AlGaS3 with the R3m space group is predicted as the most stable structure, which exhibits a stronger second harmonic susceptibility.

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Theoretical Design of Layered AlGaS3 as a New Nonlinear Optical

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