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A module-guided design scheme for deepultraviolet nonlinear optical materials Bing-Hua Lei, Zhihua Yang, Hongwei Yu, Chao Cao, Zhi Li, Cong Hu, Kenneth R. Poeppelmeier, and Shilie Pan J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b03057 • Publication Date (Web): 27 Jul 2018 Downloaded from http://pubs.acs.org on July 27, 2018

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Journal of the American Chemical Society

A Module-Guided Design Scheme for Deep-Ultraviolet Nonlinear Optical Materials Bing-Hua Lei,1,2 Zhihua Yang,1* Hongwei Yu,1 Chao Cao,3 Zhi Li,1 Cong Hu,1,2 Kenneth R. Poeppelmeier,4* Shilie Pan1* 1

CAS Key Laboratory of Functional Materials and Devices for Special Environments, Xinjiang Technical Institute of Physics & Chemistry, CAS; Xinjiang Key Laboratory of Electronic Information Materials and Devices, 40-1 South Beijing Road, Urumqi 830011, China; 2

University of Chinese Academy of Sciences, Beijing 100049, China;

3

Condensed Matter Group, Department of Physics, Hangzhou Normal University, Hangzhou 310036, China;

4

Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, United States. ABSTRACT: Design of functional materials with targeted properties is a challenge because of the diversity of their potential structures. The functional performances of materials are mainly determined by the chemistry and electronic structure of modules consisting of local atomic groups with special arrangement. Tetrahedral modules are excellent modules for designing deep-ultraviolet/ultraviolet (UV) nonlinear optical (NLO) materials, but they are rarely favored due to their unpredictable optical anisotropy and second harmonic generation (SHG) response. In this work, we have developed a module-guided ab initio approach for evaluating the optical anisotropy of tetrahedral modules. The application of this method indicates that the tetrahedral modules with specific arrangement will enhance the optical anisotropy of materials. With the functional modules consisting of tetrahedral modules and rare-earth cations, new high-performance rare-earth phosphates were assembled. These materials are promising deep-UV NLO materials because of their appropriate birefringences, large band gap, moderate SHG response and easy to obtain a large size crystal.

INTRODUCTION The rapid increase in computational power of current supercomputer architectures and great advances in firstprinciples calculations enable scientists to discover materials with desirable properties in enormous data repositories by high-throughput computational materials design15 , creating novel compounds with required characteristics by crystal structure prediction6 or learning from data directly7. During the process of screening or prediction, whether in organic or inorganic compounds, finding the structural units that determine a compound’s properties, named functional modules, is the key to success8-11. With good understanding of FMs, novel materials can be designed, predicted and synthesized efficiently. Nonlinear optical (NLO) materials12 for generating infrared (IR)13-20 or ultraviolet (UV)/ deep-UV coherent light are in great demand and attract much attention21-27 attributable to their potential applications in laser micromachining, material-processing, photolithography, optical measurements and manipulating entangled photons28. However, the criteria are very rigorous for a deep-UV NLO material: a wide transparency window (absorption edge < 180 nm), a moderate SHG response (comparable to KH2PO4 (KDP)), an appropriate birefringence (0.11 > ∆n > 0.07 at 1064 nm) and ease in obtaining large single crystals. As a

result of the unremitting efforts of researchers, triangle planar modules BO3, B3O6 and CO3 with parallel arrangement were validated as the FMs which control second harmonic generation (SHG) effect in UV/deep-UV NLO materials29-40. Subsequently, many excellent NLO materials containing CO3, BO3 or B3O6 have been discovered37-38, 41-43 and even commercialized44-48. At present, there are only a few materials that can meet these conditions including β-BaB2O4 (β-BBO)44 and the KBBF family49-51 consisting of KBe2BO3F2 (KBBF), RbBe2BO3F2 (RBBF), Na2BeB2O5 (NBBO). Unfortunately, the last three are not environmentally friendly because of toxic BeO required in the synthesis. Additionally, KBBF and RBBF have a layer habit that severely hinders the growth of large single crystals52. For β-BBO, its large birefringence beyond the appropriate region results in a photorefractive phenomenon which reduces the output power of harmonic light53. Therefore, finding an optimal composition that satisfies the NLO criteria is still a serious challenge for the discoveries of materials. Tetrahedral groups, such as BO4 or PO4 are excellent modules because it will effectively avoid layer habit and their large energy gap is beneficial to the deep UV transmission54-64. Traditionally, they are used to enrich the diversity of crystal structure31-32 and rarely employed to

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design or synthesize deep-UV NLO materials owing to the habitually weak optical anisotropy. Birefringence determined by optical anisotropy is one of the indispensable properties for UV/deep-UV materials because it is required in phase matching (PM) and determines coherent UV laser output, i.e. the shortest SHG PM wavelength. In general, a large birefringence between 0.07 and 0.11 is desired to allow for PM while avoiding spatial walk-off. 53, 65. To date, the shortest SHG PM wavelength in phosphates is only 258 nm, observed in KDP66 which has a small birefringence of 0.034. Providentially, some centrosymmetric (CS) phosphates with large birefringences were reported, such as LnPO4, Ln = (Sc, Y, Tb, Dy, Ho, Er, Tm, Yb, and Lu)67. Inspired by these compounds, there may be an FM which enhances the birefringence in phosphates and can be transplanted into non-centrosymmetric (NCS) compounds. Accordingly, we proposed a quantitative method

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based on chemical characteristics to evaluate the birefringence of crystals and discovered that the ‘zipper’ arrangement of the PO4 tetrahedra with large angle deviation would enhance the birefringence of phosphates. Rare-earth cations without influence on bandgap were introduced to induce angle deviation of PO4 groups and break inversion symmetry while the ‘zipper’ arrangement of PO4 tetrahedra is preserved. Consequently, fifteen intriguing NCS compounds were designed in a new system Y-Sc-Lu-P-O, four of which have excellent NLO properties. To the best of our knowledge, the birefringences of all these new NCS materials are much larger than that of reported deep-UV NCS phosphates and facilitate one of compounds α-YSc(PO4)2 having the shortest PM deep-UV wavelength in existing phosphates. These results demonstrate that our approach is available for designing deepUV NLO materials with tetrahedral modules.

Figure 1. Assembling optical materials with modules and fillers. (a) Typical modules in borates, carbonates and phosphates used in deep-UV region. Fillers (gray modules) are usually alkaline and alkaline earth metals. (b) A schematic outlining the relationship between the arrangement of modules and properties of corresponding materials. For functional materials, besides the chemistry and electronic structure, the arrangement of modules is the other vital factor influencing overall performance of materials. For planar modules, concurrent-parallel arrangement is the optimum in NLO materials while, for linear optical materials, parallel arrangement is sufficient. (c) A modular description of KBBF family. Planar BO3 and BeO3F tetrahedral modules compose parallel Be-B-O-F layers which guarantee the appropriate birefringence and moderate SHG effect. (d) A modular description of BBO. The planar B3O6¬ modules polymerized by BO3 modules are nearly concurrent-parallel in crystal structures, which empower it strong optical anisotropy and large SHG response owing to synergistic effect of BO3 modules. (e) A modular description of CS material CaCO3. Parallel arrangement of planar CO3 modules guarantees large birefringence of CaCO3. (f) and (g) Tetrahedral modules in BPO4 and ScPO4. From the crystal structure, there is no obvious distinction but the birefringences have an extremely large difference.


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RESULTS AND DISCUSSION Module-Guided Dismantling Materials. According to the relationship between local atom groups and properties, many functional materials can be dismantled with modules and fillers. Modules may determine the corresponding properties of materials by their chemistry and electronic structures and fillers maintain the dynamic or chemical balance in a unit cell. Most of existing optical functional materials can be described in this way. As illustrated in Figure 1, deep-UV optical materials are concentrated in borates, carbonates and phosphates. Based on insights into the structure-property relationship, BO3, CO3, B3O6, BeO3F, BO4 and PO4 groups can be regarded as modules because of their large influence on material performances (Figure 1a). In BO3, CO3 and B3O6 modules, the sp2 hybridization facilitates the planar configuration which is beneficial to optical anisotropy and SHG response. The lopsided coordination in BeO3F modules causes the asymmetric polarizability in an external electric field. The compounds constructed from BO4 or PO4 usually have large bandgaps owing to the strong interaction of σ bonds in groups. Besides local properties of modules, the arrangement of modules is the other essential factor to overall performance of materials. Theoretically and as exhibited in experiments, there are infinite arrangements for modules in crystal structures, but some modules with specific arrangements will maximize performances and be regarded as FMs, such as the concurrent parallel arrangement of planar modules in linear and NLO materials as illustrated in Figure 1b. Figures 1c and 1d show the modular description of typical NLO materials. For the KBBF family, the parallel BO3 modules in the BeB-O-F layers guarantee appropriate birefringence and moderate SHG response. Fillers are potassium, rubidium, cesium atoms and beryllium. In the β-BBO crystal structure, because of polymerization from three BO3 modules, the parallel-arrangement B3O6 modules have an enhancement to optical properties compared with BO3 modules and give β-BBO strong optical anisotropy and large SHG susceptibility. For linear optical materials, unlike NLO materials which require concurrent parallel arrangement to guarantee NCS, only parallel arrangement is enough, like the parallel arrangement of planar CO3 modules (Figure 1e) in the birefringent crystal CaCO3. However, tetrahedral modules, unlike planar modules, are extremely complex in optical response and spatial distribution. In general, in materials with large bandgaps, such as deep-UV NLO materials, the optical anisotropy and SHG response of tetrahedral modules are relatively weak. On the other hand, determining the optical spatial arrangements of tetrahedra is also thorny. Although some deepUV NLO materials assembled with tetrahedral modules have short deep-UV cutoff edge and moderate SHG response, extremely small birefringences are the common and disastrous imperfection. To the best of our knowledge, there is no deep-UV NLO material assembled with tetrahedral modules whose birefringence is larger than 0.04. BPO4 has a remarkable deep-UV cutoff edge of

134 nm, large SHG effect two times as that of KDP but near optical isotropy prevents this material’s application in the deep-UV region54. Curiously, not all compounds containing tetrahedral modules with deep-UV cutoff edge are almost optically isotropic. YPO4 has an impressive large birefringence and deep-UV cutoff edge. As shown in Figure 1f and 1g, the geometry and arrangement of tetrahedral modules have no obvious distinction from that in BPO4 crystal structure. Therefore, a new approach should be proposed to analyze the chemistry and electronic structure of tetrahedral modules and characterize the corresponding arrangement in crystal structures. Approach. To detect birefringence controlled by the FMs, REDA (response electron distribution anisotropy) method was employed to characterize optical anisotropy and evaluate the birefringences of materials68. The formula can be expressed as, ℜ ∆n =

∑[N Z c

a ∆ρ

g

b

]g

.

(1)

2 n1 E o

Where, ℜ is the correction coefficient, Nc is the coordination number of the nearest neighbor cations to the central anion, Za is the formal chemical valence of the anion and b b b b Eo is the optical bandgap ∆ρ = ρ max − ρ min , ρ max and b are the maximum and minimum of the covalent ρ min electron density of the covalent bond on the optical principal axes of a crystal, and n1 is the minimum refractive index. In Figure 2a, the experimental birefringences of some typical NLO or birefringence materials are compared with their calculated values by using Equation (1). With the REDA method, our calculated values (Table S1) are consistent with the experimental ones.

Figure 2. Structure-property relationship analysis with the REDA method. (a) Comparison of birefringences calculated



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by the REDA method and from experiments for some typical NLO and birefringent materials. For each point, the abscissa is the experiment value and the ordinate is the calculated birefringence. (b) The PO4 (purple) or BO4 (navy) module arrangements and optical anisotropy distribution (black and blue arrows indicate the maximal and minimal polarization directions) in BPO4 (up) and ScPO4 (down). Although they are both assembled with tetrahedral modules, the optical anisotropy has obvious distinction. (c) The function of the anisotropy index ΔI of PO4 module in ScPO4 with a rotation matrix. ΔI reaches maximum at θ = 0, which indicates the zipper arrangement of tetrahedra in ScPO4 is the optimum.

and the results calculated by REDA method, Iz = I2, Ix = Iy = I1 (I2＞I1, I2=1.98, I1=1.50 for PO4 in ScPO4). We introduce an Euler angles S (θ , ϕ ) for the tetrahedra and ϕ ,θ are

Besides the evaluation of birefringences, we also considered the identify of FMs that dominate the birefringences in the compounds constructed from tetrahedral modules. For ScPO4, the calculated birefringence of ScPO4 is 0.106 that agrees well with the value of 0.112 from the firstprinciples calculation (Figure S1). The REDA index ζ = N c Z a ∆ ρ b n1 E o of the PO4 tetrahedron is 0.307 compared to 0.115 of the ScO8 polyhedron, indicating that the contribution of the PO4 tetrahedra for the birefringence is over 70%, which is also verified by first-principles calculations of the hypothetical Sc-free ScPO4 (Figure S1). It is worth noting that scandium is not a colorless filler anymore. According to the bonding orbitals (shown in Figure S2) of scandium and oxygen and the projected density of states (PDOS) (Figure S3), there is covalent bonding between Sc-3d and O-2p orbitals. In addition, the bond overlap population of ScPO4 shown in Table S2 confirms the certain covalent interaction between scandium and oxygen. According to the REDA method, the Sc-O bond should be taken into account. In addition, reviewing the calculation process, the outstanding contribution to birefringence results from the large angle deviation (deviation to the angle of regular tetrahedron 109°28’) of PO4 groups (Figure S4), which is caused by the covalent interaction of scandium-oxygen. Figure 2 shows the distribution directions of the maximal (black arrows) and minimal (blue arrows) response electron of PO4 (BO4) in BPO4 (Figure 2b up) and ScPO4 (Figure 2b down) based on the REDA method. In ScPO4, the PO4 tetrahedra take a zipper arrangement which aligns the maximal and minimal covalent electron distribution directions of the PO4 tetrahedra and enhances the optical anisotropy. Whereas in BPO4, the irregular arrangement of the PO4 (BO4) groups results in an extremely small birefringence. In PO4 modules, because of the same bond length of P-O, according to

(4)

the bond valence thoery, the bond valence V b of four P-O bonds are equal. According to REDA method, the electron distribution anisotropy determined by bond valence index I of along principal optic axises are I i =| I i |, i = x, y, z, I i =

∑V

b ij

.

(2)

j

Here, Vijb is a component of V b along i axis from j bond. For PO4 modules in ScPO4, according to the symmetry

between 0~ π 2 . Then, '

I i = S (θ , ϕ ) I i , i = x, y, z ,

(3)

Where,

 cosϕ cosθ  S (θ , ϕ ) =  sin ϕ cosθ  − sin θ 

− sin ϕ cosϕ sin θ   cosϕ sin ϕ sin θ  . 0 cosθ 

Therefore, the anisotropy index ∆I of the PO4 modules is ∆I = I 2' − I 1' = I 2 cos 2 θ + I 1 sin 2 θ − I 2 cos 2 ϕ sin 2 θ − I 1 (cos 2 ϕ cos 2 θ + sin 2 ϕ )

.

(5)

Figure 2c shows change of the anisotropy index between z and x (y) axis as rotating angle. From the Figure, the contribution of optical anisotropy of materials has the maximum when θ = 0 , which indicates that PO4 modules arrangement in ScPO4 is the optimum. Design Scheme. Since the FMs, the zipper-like arrangement of PO4 tetrahedra and rare-earth cations, are beneficial to generating a large birefringence, it is expected to combine YPO4, ScPO4, LuPO4 into one compound to get some interesting phosphates with large birefringence, just like combining LiB3O5 and CsB3O5 to form CsLiB6O1045. Additionally, as demonstrated above, rare-earth cations become modules other than fillers because of covalent interaction with oxygen and therefore have a possibility to enhance SHG response69. As illustrated in Figure 3, PO4, YO8, ScO8, LuO8 were chosen as the modules (Figure 3a). Following the outline in Figure 3b, during the design, the FMs were maintained and meanwhile, we controlled the position of rare-earth cations by filling rest Wyckoff positions in crystal structures under non-centrosymmetry ( 4 , mm2) from the parent group (4/mmm) which the FMs belong to and regulating the symmetry in order to form NCS compounds with moderate SHG response as shown in Figure S5. Inspired by this idea, finally, we found a series of NCS compounds AmBnCl(PO4)m+n+l (A, B, C = Y, Sc, Lu; 0 ≤ m, n, l ≤ 3: m+n+l = 4) as listed in Table 1. By combining YPO4 and ScPO4 to α-YSc(PO4)2 as a demonstration, as shown in Figure 3c, the zipper-like arrangement is maintained in α-YSc(PO4)2, which is expected to guarantee the optical anisotropy. On the other hand, we allocate yttrium and scandium randomly to the position of cation attempting to break the inversion symmetry. Consequently, in this system, fifteen NCS and three CS structures were obtained.


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Table 1. Evaluation of stability and the NLO properties of AmBnCl(PO4)m+n+l. The bandgap values (Eg) come from the results of hybrid functional PBE0 calculation. Compounds

Space group

Eg (eV)

Cut-off edge (nm)

Δn@1064nm

dij (pm/V)

ΔE (meV/atom)

Shortest SHG PM wavelength (nm)

β-ScLu(PO4)2

Pmmn

6.96

178

0.118

-----------------------

16.10

----

α-ScLu(PO4)2

I4

6.94

179

0.120

d15=0.34, d24=-0.34

14.99

212

α-YSc2Lu(PO4)4

Pmm2

6.98

178

0.126

d15=0.03, d24=-0.05

12.09

203

Lu3Sc(PO4)4

P4

6.78

183

0.104

d15=0.17, d24=-0.17

11.65

217

β-YSc2Lu(PO4)4

P4

6.98

178

0.126

d15=-0.29, d24=0.29

11.51

207

Sc3Lu(PO4)4

P4

7.08

175

0.136

d15=0.17, d24=-0.17

11.40

206

α-YScLu2(PO4)4

Pmm2

6.82

182

0.107

d15=-0.15, d24=0.12

10.14

207

β-YSc(PO4)2

Pmmn

7.03

176

0.101

----------------------

10.05

----

α-YSc(PO4)2

I4

7.02

177

0.102

d15=0.38, d24=-0.38

9.98

200

β-YScLu2(PO4)4

P4

6.84

181

0.108

d15=0.21, d24=-0.21

9.52

211

YSc3(PO4)4

P4

6.78

183

0.115

d15=0.11, d24=-0.11

8.02

230

β-Y2ScLu(PO4)4

P4

6.85

181

0.114

d15=-0.09, d24=0.09

7.89

205

α-Y2ScLu(PO4)4

Pmm2

6.87

180

0.113

d15=-0.15, d24=0.18

7.38

206

Y3Sc(PO4)4

P4

6.8

182

0.122

d15=-0.09, d24=0.09

7.11

201

YLu3(PO4)4

P4

7.05

176

0.088

d15=0.03, d24=-0.03

0.41

216

β-YLu(PO4)2

Pmmn

7.42

167

0.093

------------------------

0.16

----

α-YLu(PO4)2

I4

7.45

166

0.095

d15=0.06, d24=-0.06

-0.02

209

Y3Lu(PO4)4

P4

7.88

157

0.098

d15=0.03, d24=-0.03

-0.92

199

*KDP

Im2d

7.04

176

0.034

d36=0.39

-----

258

*BPO4

I4

9.25

134

0.007

d36=0.76, d15≈0.00

-----

>532

*Ba3(ZnB5O10)PO4

Pmn21

6.89

180

0.033

≈ 4×KDP (powder)

-----

355

*The data all come from experiment Figure 3. Module-guided design of NLO materials in rareearth phosphates. (a) Selected modules for design. Because of the covalent interaction between rare-earth cations and oxygen, rare-earth cations become modules other than fillers anymore. (b) Outlining the design scheme of NLO materials. During the design, the zipper arrangement is maintained to guarantee the optical anisotropy of new materials and rareearth cations are employed to modulate the symmetry of crystal structures. (c) Crystal structure of α-YSc(PO4)2 and its PM curve based on calculated refractive indices. The large birefringence, to the best of our knowledge, is the largest one in NCS phosphate and gives α-YSc(PO4)2 the shortest PM wavelength in phosphates.

Thermodynamic Stability. The thermodynamic stability of the predicted phosphates was determined by the grand canonical linear programming70-71. In this process, the total energy change (ΔE) for a chemical reaction involving reactants that are known to be thermodynamically stable and a product, which is the ground state structure for our predicted compounds should be calculated. Compounds with negative ΔE are identified to be thermodynamically



stable and, commonly, it is suggested that the composition could be potentially synthesized under appropriate experimental conditions when ΔE < +25 meV per atom70. The total energy change ΔE (meV/atom) calculated by CASTEP72 for these new compounds are listed in Table 1. These eighteen compounds in Table 1 have negative ΔE or ΔE < +25 meV/atom and therefore, they are all promising for synthesizing. Combination Optical Properties. The bandgap and optical properties calculated with hybrid functional PBE0 and length-gauge formalism derived by Aversa and Sipe73 are listed in Table 1. As we expected, owing to the arrangement of the PO4 group, the birefringences (Δn@1064 nm) of these compounds are between 0.09~0.13. Comparatively, α-YSc(PO4)2, Sc3Lu(PO4)4, α-YScLu2(PO4)4 and βYScLu2(PO4)4 have more appropriate birefringence (0.102, 0.103, 0.105 and 0.106) for NLO materials. With regard to NLO properties, α-YSc(PO4)2 and α-ScLu(PO4)2 have SHG effects as large as that of KDP66 (0.39 pm/V) and Sc3Lu(PO4)4, Lu3Sc(PO4)4, α-Y2ScLu(PO4)4, βYSc2Lu(PO4)4, α-YScLu2(PO4)4, β-YScLu2(PO4)4 also have acceptable values of ≥1/3 KDP. According to previous research69, the relatively strong covalent interaction between scandium and oxygen will enhance the SHG effect. The bond-overlap population of α-YSc(PO4)2, Sc3Lu(PO4)4, α-YScLu2(PO4)4 and β-YScLu2(PO4)4 are shown in Table S2. Large overlap implies strong covalent interaction74. Obviously, the Lu-O bonds have much less overlap than the Sc-O and Y-O bonds, which indicates that lutetium has a relatively weak covalent interaction with oxygen than scandium and yttrium. In addition, the SHG-density method75 show that Y and Sc also have direct contribution to the SHG effect as shown in Figure S6. Therefore, the introduction of lutetium in Sc3Lu(PO4)4, αYScLu2(PO4)4 and β-YScLu2(PO4)4 will weaken the response of SHG response. In the combination of optical properties, Sc3Lu(PO4)4, α-YScLu2(PO4)4 and βYScLu2(PO4)4 have good deep-UV NLO performances with acceptable SHG effect values of ≥1/3 KDP, appropriate birefringence and α-YSc(PO4)2 meets the criteria of deep-UV NLO materials. Figure 3c illustrates the direct shortest type I PM SHG wavelength is about 200 nm for α-YSc(PO4)2, which is 58 nm shorter than that of KDP66. As a result, we have demonstrated an effective strategy where holding the zipper-like arrangement of PO4 groups gives large birefringence while the acentric coordination environment of the rare earth cation is responsible for the SHG behavior. In order to check the stability of α-YSc(PO4)2, the newly developed Artificial Bee Colony (ABC) algorithm as implemented in the CALYPSO code76-77 were employed to search global minimum in YSc(PO4)2. The last eight phases in the YSc(PO4)2 system in order of energy are shown in Figure 4a. Judging from the energy, α-YSc(PO4)2 is thermodynamically stable with a minimal energy. In terms of the mechanical stability, the elastic constants for α-YSc(PO4)2 (as a representative) were calculated and

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listed in Table S2. The calculation coincides the mechanical stability criterion for the tetragonal system at corresponding pressures78, demonstrating its mechanically stable. In addition, only a single minimum is found in the wide range of volume modification from the total energy as a function of volume per atom (Figure 4b) and none of the imaginary phonon modes exists in phonon spectra (Figure 4c), which further confirms the dynamic stability of α-YSc(PO4)2 79. Furthermore, because of the similarity in chemical and physical characteristics of yttrium and scandium, in experiment, YSc(PO4)2 may become solid solution with atoms disorder. The disorder model is shown in Figure S7. Figure 4d lists the energy of compounds and solid solutions, which indicates, in YSc(PO4)2 system, compounds are more stable compared with solid solution.

Figure 4. Global minimum searching in the Y-Sc-P-O system and mechanical stability studies of α-YSc(PO4)2. (a) The results of global minimum searching. Eight phases with low energies and the one with lowest energies in these phases were listed in the Figure. Judging from energy, α-YSc(PO4)2 is thermodynamically stable. (b) and (c) are the total energy as a function of volume per atom and phonon spectra of αYSc(PO4)2, respectively. Only a single minimum observed and no imaginary phonon modes emerged in figures demonstrates its dynamic stability. (d) Energies comparison of ordered and disordered YSc(PO4)2. The ratio refers to the molar ratio of yttrium and scandium in a unit cell. In terms of energies, compounds are more stable than solid solution.

CONCLUSION In summary, we investigated the birefringence of phosphates by using the REDA approximation and find that the zipper arrangement of the PO4 groups with large angle deviation caused by rare-earth cation are the FMs of optical properties in phosphates. The FMs can enhance the optical anisotropy of materials and exhibit moderate SHG response. Following the module-guided design scheme, a series of NCS rare-earth phosphates combining with ‘zipper’ arrangement of the PO4 groups and rareearth cations were designed based on first-principles calculations. These NCS rare-earth phosphates, AmBnCl(PO4)m+n+l (A, B, C = Y, Sc, Lu; 0 ≤ m, n, l ≤ 3:


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m+n+l = 4), to the best of our knowledge, possess largest birefringences in NCS phosphates with deep-UV cutoff edge. Among these compounds, α-YSc(PO4)2, Sc3Lu(PO4)4, α-YScLu2(PO4)4 and β-YScLu2(PO4)4 have good deep-UV NLO performances. α-YSc(PO4)2 has a PM wavelength of 58 nm shorter than that of KDP. Considering the possibility of synthesis, we also checked the stability of these structures. Therefore, according to the results above, there is a possibility for discovering an excellent deep-UV NLO material in rare-earth phosphates. The design strategy may accelerate the exploration of NLO materials in phosphates and can be used to design other materials with desirable properties.

COMPUTATIONAL DETAILS First-Principles Calculation Methods. First-principles calculations based on density functional theory (DFT) with local density approximation (LDA) were performed by a plane72 wave pseudopotential calculation package CASTEP . For the geometry optimization, the convergence is achieved if the −4 residual force on each atom is less than 5×10 Å, and the −6 energy change is less than 5.0×10 eV/atom. The 4s 4p 4d 5s, 3s 3p 3d 4s, 3s 3p, and 2s 2p orbitals of Y, Sc, P, and O are chosen to be valence orbitals in the pseudopotentials, respectively. The cut-off energy for the plane-wave basis was 380 eV and the Brillouin zone was sampled by 4 × 4 × 4 Monkhorst-1 Pack k-point with a separation less than 0.05 Å . For phonon spectra, the q-mesh in Brillouin zone is 8 × 8 × 8. We kept the default values of the CASTEP code on the aspect of the other calculation parameters and convergence criteria. Calculated Methods for Optical Properties and Accurate Band Gap. The linear optical properties can be obtained by the real part of dielectric function. The so-called length-gauge for73 malism derived by Aversa and Sipe was adopted to calculate NLO properties. At a zero frequency, the static second-order nonlinear susceptibilities can be described to virtual elec80-81 trons (VE) and virtual hole (VH) processes . 2） 2） 2） χ（αβγ = χ（αβγ (VE) + χ（αβγ (VH ) . (2)

(6)

(2)

Where χαβγ (VE) and χαβγ (VH) are computed with the formulas as follows:

χαβγ ( 2 ) (VE ) =

e3 2

2h m (

χαβγ ( 2 ) (VH ) =

∑ ∫ 4π 3 P(αβγ ) Im[Pvcα Pccβ'Pcγ'v ], vcc '

1 3 2 ωcv ωvc '

e3 2h 2 m 3 (

+

2 4 ωvc ωc ' v

d 3k

∑ ∫ 4π

3

1 3 2 ωcv ω v 'c

+

2

ASSOCIATED CONTENT Supporting Information Interaction orbital and partial density states of ScPO4. Bond angles of PO4 in ScPO4 and BPO4. Birefringences we calculated based on DFT for α-YSc(PO4)2, YSc3(PO4)4, Y3Sc(PO4)4 YPO4, and ScPO4. Birefringences of some compounds calculated by REDA comparing with experimental values. Bond overlap population of α-YSc(PO4)2, Sc3Lu(PO4)4, αYScLu2(PO4)4 and β-YScLu2(PO4)4. Independent elastic constants Cij, bulk, and shear moduli (B, G and E all in GPa), G/B of α-YSc(PO4)2,YSc3(PO4)4 and Y3Sc(PO4)4. This material is available free of charge via the Internet at http://pubs.acs.org.

Corresponding Author *[email protected] (Z. Yang) *[email protected] (K. R. Poeppelmeier) *[email protected] (S. Pan).

[

P (αβγ ) Im Pvvα ' Pcvβ ' Pcvγ

ωvc4 ωcv '

(7)

)

]

Notes The authors declare no competing financial interest. .

vv 'c

Global Minimum Searching in YSc(PO4)2. Our artificial bee colony (ABC) structural searching approach is based on a global minimization of free energy surfaces merging ab initio 76-77 total-energy calculations with CALYPSO methodology as implemented in the CALYPSO code and is originally at84 tributed to Karaboga et al. , with symmetry constraint is implemented into CALYPSO software to keep the structural symmetry during structure evolution. This method is designed to predict the stable structures of given compounds with only the knowledge of chemical compositions at given condition, such as pressure. The structures of stoichiometry YSc(PO4)2 were searched twice with simulation cell sizes of 13 formula units at ambient pressure. The first generation was produced randomly, each generation contained 50-60 struc85-86 tures. Local optimizations using the VASP code and stopped when Gibbs free energy changes became smaller -5 than 1 × 10 eV per cell. In the next CALYPSO runs, 60% of lowest-enthalpy structures were utilized to produce the structures in the next generation by ABC algorithm, and the rest 40% structures were generated randomly. The structural searching simulation for each run was stopped after 20003600 structures (40-60 generations) were obtained.

AUTHOR INFORMATION

d 3k

3

late the optical properties more accurately, scissors 82-83 was employed. In this work, we use the band operator gap calculated by PBE0 hybrid functional as the experimental band gap. The converged criteria are as same as that in ab initio calculation except a smaller Monkhorst-Pack K-grid of -1 3×3×3 with a separation less than 0.07 Å .

(8)

ACKNOWLEDGMENT

)

Here, α, β, γ are Cartesian components, and v/v', c/c' denote valence bands (VBs) and conduction bands (CBs). And P(αβγ), hωij and Pijα refer to full permutation, the band energy difference and momentum matrix elements, respectively. As we all know, the DFT calculation with the LDA exchangecorrelation usually underestimates the band gap. To calcu-

This work is supported by the National Basic Research Program of China (Grant No. 2014CB648400), the National Key Research Project (Grant Nos. 2016YFB1102302, 2016YFB0402104), National Natural Science Foundation of China (Grant Nos. 11474353, 51425206, U1129301, 91622107), the Recruitment Program of Global Experts (1000 Talent Plan, Xinjiang Special Program), K.R.P. acknowledges sup-



port from the National Science Foundation (Solid State Chemistry Award No. DMR-1307698, 1608218).

ABBREVIATIONS NLO, nonlinear optical; UV, ultraviolet; SHG, second harmonic; IR, infrared; PM, phase matching; FMs, functional modules; CS, centrosymmetric; NCS, non-centrosymmetric; VE, virtual electron; VH, virtual hole; VBs: valence bands; CBs; conduction bands; ABC, artificial bee colony.

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