M4Mg4(P2O7)3 (M = K, Rb): Structural Engineering of

Jan 30, 2017 - On the basis of their short ultraviolet (UV) absorption edges, phosphates are ideal candidates for deep-UV nonlinear optical (NLO) appl...
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M4Mg4(P2O7)3 (M = K, Rb): Structural Engineering of Pyrophosphates for Nonlinear Optical Applications Hongwei Yu,† Joshua Young,‡,∥ Hongping Wu,†,§ Weiguo Zhang,† James M. Rondinelli,*,‡ and P. Shiv Halasyamani*,† †

Department of Chemistry, University of Houston, 112 Fleming Building, Houston, Texas 77204-5003, United States Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, Illinois 60208-3108, United States § Xinjiang Technical Institute of Physics & Chemistry, Chinese Academy of Sciences, 40-1 Beijing Road, Urumqi, Xinjiang 830011, China ‡

S Supporting Information *

ABSTRACT: On the basis of their short ultraviolet (UV) absorption edges, phosphates are ideal candidates for deep-UV nonlinear optical (NLO) applications. However, their often-weak second-harmonic generating (SHG) responses reduce their NLO applications. It has been demonstrated that the SHG response in polyphosphates or orthophosphates could be enhanced by highly polymerized P−O groups or aligned nonbonding O-2p orbitals of isolated PO4 units. Herein, we report on the design and synthesis of two pyrophosphates, K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3, with potential NLO applications. Both materials exhibit relatively large SHG responses with 1064 nm radiation, 1.3× and 1.4× KH2PO4 (KDP) for K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3, respectively. In addition, absorption edges below 200 nm were observed for both materials. For K4Mg4(P2O7)3, single crystal vacuum-UV transmission measurements revealed an absorption edge of 170 nm. First-principles electronic structure calculations identify that the NLO responses arise from the presence of the corner-connected [Mg4P6O21] double layers. We also investigated these compounds using hybrid density functionals, which are found to produce much better agreement with the experimental optical results. Finally, we detail the structural distortions giving rise to the NLO responses. Our results indicate that phosphates with low polymerized P−O groups, such as pyrophosphates, may exhibit large SHG responses if their structures are properly designed.

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INTRODUCTION Deep-ultraviolet (UV) nonlinear optical (NLO) materials capable of producing coherent light of wavelengths below 200 nm play a crucial role in semiconductor manufacturing, photolithography, laser systems, atto-second pulse generation, and advanced instrument development.1−3 However, designing and synthesizing new deep-UV NLO materials present challenges owing to their strict structural and physical property requirements.4−6 Structurally, the materials must crystallize in one of 20 of the 21 noncentrosymmetric (NCS) crystal classes (crystal class 432 lacks a center of symmetry, but the secondharmonic generating (SHG) tensors are of equal and opposite magnitude resulting in a null SHG response).7 With respect to properties, the materials need to possess a wide band gap (Eg > 6.2 eV), large SHG coefficients (dij > 0.39 pm/V), moderate birefringence (Δn ∼ 0.07), chemical stability with a large laser damage threshold (LDT > 5 GW/cm2), and easy growth of large (centimeter size) high quality single crystals.8,9 On the basis of the above requirements, borates and phosphates may be considered ideal candidates for deep-UV NLO applications attributable to the variety of NCS structures, wide UV transmission window, and the growth of large single © 2017 American Chemical Society

crystals. During the past 30 years, owing to the success of anionic group theory,10 the exploration of deep-UV NLO materials has mainly focused on borate materials.11−33 Specifically, the beryllium borates,20−25 such as KBe2BO3F2 (KBBF),24 Na2Be4B4O11,17 and Na2CsBe6B5O15,20 and the beryllium-free borates, such as K3B6O10Cl,19 Ba4B11O20F,28 Cs2B4SiO10,16 and Li4Sr(BO3)2,27 exhibit attractive NLO properties. Another class of materials with potential deep-UV NLO applications, phosphates, went relatively unexplored until recently when the first nonboron-containing deep-UV NLO phosphates, Ba3P3O10X (X = Cl, Br), were discovered.34 In Ba3P3O10X (X = Cl, Br), the asymmetric Cl−P3O10 groups are thought to be the origin of their attractive NLO properties, i.e., SHG efficiencies of 0.6× and 0.5× KDP, respectively, and a deep-UV absorption edge of 180 nm.34 Unlike borates, in NLO active phosphates, the coordination of the P atoms is strictly tetrahedral. It is widely thought that the tetrahedral configuration is helpful for facilitating a short UV absorption Received: January 13, 2017 Revised: January 28, 2017 Published: January 30, 2017 1845

DOI: 10.1021/acs.chemmater.7b00167 Chem. Mater. 2017, 29, 1845−1855

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Chemistry of Materials Table 1. Crystal Data and Structure Refinement for K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 empirical formula temperature wavelength formula weight crystal system space group unit cell dimensions (Å)

Z volume (Å3) calculated density (Mg/m3) absorption coefficient (mm−1) reflections collected/unique completeness to theta (27.48°) goodness-of-fit on F2 final R indices [I > 2sigma(I)]a R indices (all data) flack factor extinction coefficient largest diff. peak and hole (e·Å−3) a

K4Mg4(P2O7)3 296(2) K 0.71073 Å 775.46 monoclinic Pc a = 5.2162(2) b = 20.8820(9) c = 9.5137(4) β = 90.3390(10)° 2 1036.26(7) 2.485 1.544 6100/4116 [R(int) = 0.0154] 99.2% 1.049 R1 = 0.0204, wR2 = 0.0474 R1 = 0.0213, wR2 = 0.0478 0.03(3) 0.0047(3) 0.302 and −0.292

Rb4Mg4(P2O7)3

960.94 orthorhombic Amm2 a = 5.2878(3) b = 21.1901(12) c = 9.6973(5) 2 1086.57(10) 2.937 9.609 3351/988 [R(int) = 0.0198] 100.0% 1.103 R1 = 0.0173, wR2 = 0.0394 R1 = 0.0178, wR2 = 0.0395 0.053(12) 0.00059(19) 0.725 and −0.612

R1 = Σ||Fo| − |Fc||/Σ|Fo| and wR2 = [Σw(Fo2 − Fc2)2/Σw Fo4]1/2 for Fo2 > 2σ(Fo2).

edge.35 Therefore, from a coordination polyhedra perspective, phosphates are an attractive choice for deep-UV NLO materials.34,36−48 Nonetheless, phosphates often suffer from a weak SHG response. It has been shown that the microscopic second-order nonlinear susceptibility of the PO4 units is 1 order of magnitude smaller than that of the BO3 and B3O6 groups.10 In order to obtain SHG-response-enhanced phosphates, we have previously introduced borate groups and other NLOactive structural units, e.g., d0 transition metal cations susceptible to second-order Jahn−Teller distortions, cations with stereoactive lone pairs, and d10 cations that undergo offcenter displacements, into phosphates. In doing so, we synthesized a variety of enhanced SHG efficient and deep-UV or UV transparent materials such as Ba3(ZnB5O10)PO4 and A3B3CD2O14 (A = Sr, Ba, or Pb; B = Mg or Zn; C = Te or W; D = P or V).38,45,49 Despite this progress, it remains rare for phosphates without other NLO-active structural units to exhibit a large SHG response. Recent research has demonstrated that the SHG response of phosphates can be enhanced by connecting the P−O groups or aligning the nonbonding O-2p orbitals of isolated PO4 units in the crystal structure.36,41,46,50 With these different strategies, Li et al.36,41 and Zhao et al.46 synthesized deep-UV NLO phosphates with large SHG responses, >1× KDP, LiCs2PO4, and RbBa(PO3)5, respectively. Notably, these two strategies are suitable for orthophosphates or highly polymerized phosphates. For phosphates with relatively low P−O polymerization such as pyrophosphate and triphosphate, large SHG responses are not anticipated.34,42,46,51 Since many NCS phosphates exhibit low P−O polymerization,34,42,44,46,51 the challenge is whether these types of materials can be judiciously designed to exhibit large SHG responses. There has been a recent report of a pyrophosphate with a large SHG response (1.5× KDP): CsLiCdP2O7.39 This material, however, contains d10 Cd2+ cations and involves the use of toxic CdO in the synthesis.

With this challenge in mind, we successfully designed and synthesized two new NLO active pyrophosphates, K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3. Here, we report on the syntheses, crystal growth, functional properties, and electronic structures of both materials. We find that both materials exhibit an SHG response larger than KDP. Equally as important, both materials have deep-UV absorption edges; this suggests that K4Mg4P6O21 and Rb4Mg4P6O21 have potential NLO applications below 200 nm. By performing density functional theory calculations and a detailed structural analysis, we show that the formation of the P2O7−MgO4−MgO5 network is responsible for both the presence of the NLO activity (by lifting inversion symmetry) and the magnitude of the response. Furthermore, we show that advanced exchange-correlation functionals that include exact Fock exchange greatly improve the accuracy of the computed band gaps. Our experimental results and theoretical calculations demonstrate that low-polymerized phosphates such as pyrophosphates are viable candidates for NLO applications if their structures are judiciously designed.

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EXPERIMENTAL SECTION

Synthesis. Polycrystalline K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 were synthesized by conventional solid-state methods. Stoichiometric amounts of K2CO3 (Rb2CO3 for Rb4Mg4(P2O7)3; Alfa Aesar, 98%), MgO (Alfa Aesar, 99%), and NH4H2PO4 (Alfa Aesar, 98%) were ground thoroughly and pressed into pellets, respectively. The pellets were placed on a platinum plate and heated to 400 °C for 20 h to decompose carbonates and NH4H2PO4, and then, the temperature was raised to 700 °C, held for 5 days, with several intermittent grindings. Laboratory powder X-ray diffraction indicated pure K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 were obtained (see Figure S1). Crystal Growth. The single crystals of K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 were grown from the high temperature solution with K2O−P2O5 and Rb2O−P2O5 as the flux system, respectively. The polycrystalline powders of K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 were mixed thoroughly with K2CO3/Rb2CO3 and NH4H2PO4 at molar ratios of K 4 Mg 4 (P 2 O 7 ) 3 /K 2 CO 3 /NH 4 H 2 PO 4 = 1:1:1.5 for K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3/Rb2CO3/NH4H2PO4 = 1:1:2 for Rb4Mg4(P2O7)3. The mixture was heated to 850 °C in a platinum 1846

DOI: 10.1021/acs.chemmater.7b00167 Chem. Mater. 2017, 29, 1845−1855

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Figure 1. A ball-and-stick representation of K4Mg4(P2O7)3 is given. The P2O7 groups connect with three MgO4/MgO5 polyhedra to form a [(Mg2P2O6)O5] layer. The two [(Mg2P2O6)O5] layers are connected to form [Mg4P6O21] double layers. The [Mg4P6O21] double layers stack along the b axis and are connected by sharing O atoms to form a three-dimensional (3D) framework with K+ cations residing in the cavities. symmetries were found.54 Crystal data and structure refinement information for K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 are listed in Table 1. The final refined atomic positions and isotropic thermal parameters and selected bond lengths and angles are listed in Tables S1 and S2, respectively. Infrared Spectroscopy. The Fourier transform infrared spectroscopy (FTIR) spectra in the 400−4000 cm−1 range were recorded on a Bruker Tensor 37 FTIR (see Figure S3). Thermal Analysis. The thermal properties were measured on an EXSTAR TG/DTA 6300 instrument under flowing nitrogen gas, heated from room temperature to 1250 °C at a rate of 10 °C min−1 in a Al2O3 crucible (see Figure S4). (Vacuum) UV−vis-NIR Diffuse Reflectance Spectra. The UV− vis-NIR diffuse reflectance spectrum was measured at room temperature with a Cary 5000 UV−vis-NIR spectrophotometer in the 200− 2500 nm wavelength range (see Figure 4). Vacuum UV transmission spectra were collected on a 7 × 5 × 0.5 mm3 single crystal of K4Mg4(P2O7)3 on a VUVas2000 (McPherson Corporation) from 120 to 220 nm. SHG Measurement. Powder SHG were measured by using the Kurtz-Perry method with Q-switched Nd:YAG lasers at the wavelength of 1064 nm.55 Polycrystalline samples of K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 and KH2PO4 (KDP) were ground and sieved into distinct particle size ranges (125 μm). Sieved KDP powder was used as a reference. The intensity of the frequency-doubled output emitted from the sample was measured using a photomultiplier tube. Refractive Index Measurements. A (010) wafer of K4Mg4(P2O7)3 with size of 5 × 5 × 1 mm3 was polished using a Unipol-300 grinding/polishing machine (MTI Co.) for the refractive index measurements. The measurements were carried out using a Metricon Model 2010/M prism coupler (Metricon Co.) at 450.2, 532, 636.5, 829.3, and 1062.6 nm. Laser Damage Threshold Measurement. A well-polished (010) crystal wafer of K4Mg4(P2O7)3 was used for the measurement of laser damage threshold. The measurement was carried out on an Nd:YAG nanosecond laser (Model: Minilite II, Continuum Eletro-Optics, Inc.) at a wavelength of 1064 nm. The laser pulse duration was set at 6 ns, and the frequency was fixed at 15 Hz. The laser beam was focused with a convex lens, resulting in a beam diameter of 0.36 mm. Computational Methods. All calculations were performed using density functional theory56 as implemented in the Vienna Ab Initio Simulation Package (VASP).57,58 The internal atomic positions of both the ground state polar structures and the high symmetry reference phases were fully relaxed using a 7 × 3 × 5 Monkhorst−Pack k-point

crucible and kept this temperature for 24 h in order for a clear and homogeneous melt. A platinum wire was then dipped into the melt. The temperature was decreased to 750 °C (772 °C for Rb4Mg4(P2O7)3) at a rate of 2 °C h−1. Some small crystals were observed to nucleate on the platinum wire. Then, the platinum wire was pulled out of the solution and allowed to cool to room temperature at a rate of 10 °C h−1. Colorless crystals of K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 were obtained for structure determinations. For K4Mg4(P2O7)3, a centimeter-size crystal was also grown (see Figure S2). Some small K4Mg4(P2O7)3 crystals obtained by the above method were used as seed crystals. With these seeds, a saturation temperature of 743 °C was determined by observing the growth or dissolution of the seed crystals when soaking in the melt composition as given above. A high quality K4Mg4(P2O7)3 seed was dipped into the surface of the melt at 748 °C (5 °C higher than the saturation temperature). This was followed by decreasing the temperature to 743 °C (the saturation point) over 30 min. From this temperature, the solution was cooled at a rate of 0.2 °C per day until the desired crystal size was obtained. The K4Mg4(P2O7)3 crystal was pulled out of the solution and cooled to room temperature at a rate of 10 °C/h. Powder X-ray Diffraction. Powder X-ray diffraction analyses of K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 were carried out at room temperature on a PANalytical X’Pert PRO diffractometer equipped with Cu Kα radiation (λ = 1.5418 Å). Data were collected in the angular range of 2θ = 10−70° with a scan step width of 0.008° and a scan time of 0.5 s. The experimental powder X-ray diffraction patterns are in agreement with those calculated on the basis of the single-crystal crystallographic data (see Figure S1). Structural Characterization. Single crystals for K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 with dimensions 0.093 × 0.121 × 0.153 mm3 and 0.116 × 0.089 × 0.06 mm3 were selected for their structure determinations. Data were collected on a Bruker SMART APEX2 diffractometer equipped with a 4K CCD area detector using graphitemonochromated Mo Kα radiation (λ = 0.71073 Å). The data were integrated using the Bruker SAINT program,52 with the intensities corrected for Lorentz factor, polarization, air absorption, and absorption attributable to the variation in the path length through the detector faceplate. Absorption corrections based on the multiscan technique were applied. The structures were solved by direct methods using SHELXS-97.53 All atoms were refined using full matrix leastsquares techniques; final least-squares refinement is on Fo2 with data having Fo2 ≥ 2σ (Fo2). The final difference Fourier synthesis map showed the maximum and minimum peaks at 0.302 and −0.292 e·Å−3 for K4Mg4(P2O7)3 and at 0.662 and −0.685 e·Å−3 for Rb4Mg4(P2O7)3. The structures were checked with PLATON, and no higher 1847

DOI: 10.1021/acs.chemmater.7b00167 Chem. Mater. 2017, 29, 1845−1855

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Figure 2. A ball-and-stick representation of Rb4Mg4(P2O7)3 is given. The P2O7 groups connect with three MgO4/MgO5 polyhedra to form a [(Mg2P2O6)O5] layer. The two [(Mg2P2O6)O5] layers are connected to form [Mg4P6O21] double layers. The [Mg4P6O21] double layers stack along the b axis and are connected by sharing O atoms to form a three-dimensional (3D) framework with Rb+ cations residing in the cavities.

Figure 3. A structural comparison of (a) K4Mg4(P2O7)3 and (b) Rb4Mg4(P2O7)3. K4Mg4(P2O7)3 contains two different orientations of the [Mg4P6O21] double-layer with the bent P2O7 group connecting the double-layers, whereas Rb4Mg4(P2O7)3 contains a single orientation of the [Mg4P6O21] double-layer with the stretched P2O7 group connecting the double-layers.

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mesh,59 a 600 eV plane wave cutoff, and projector augmented-wave (PAW) pseudopotentials60 with the PBEsol functional.61 The high symmetry reference phases were identified with the help of the PSEUDO tool of the Bilbao Crystallographic Server,62 while the mode decompositions were performed using the ISODISTORT tool of the ISOTROPY suite.63 The density of states at the PBEsol level was computed using an increased 9 × 5 × 7 k-point mesh. We also computed the density of states using the HSE0664 and PBE065 hybrid functionals with 25% Hartree-Fock exact exchange included. HSE06 uses a screened form of the Coulomb potential unlike PBE0. Owing to the increase in computational cost, we used a reduced 400 eV plane wave cutoff and 4 × 4 × 4 Γ-centered k-point mesh.

RESULTS AND DISCUSSION

Crystal Structures. The crystal structures of K4Mg4(P2O7)3 and Rb 4Mg 4(P 2O 7) 3 were determined by single X-ray diffraction. Although K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 have the same stoichiometric ratio, they are not isostructural. K4Mg4(P2O7)3 crystallizes in the monoclinic space group Pc, whereas Rb4Mg4(P2O7)3 crystallizes in the orthorhombic space group Amm2. The structure of K4Mg4(P2O7)3 is shown in Figure 1. The basic building units for K4Mg4(P2O7)3 are the P2O7, MgO4, and MgO5 groups (Figure 1a). In the structure, three oxygen atoms on one end of the P2O7 group connect with three MgO4/MgO5 1848

DOI: 10.1021/acs.chemmater.7b00167 Chem. Mater. 2017, 29, 1845−1855

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Table 2. Sellmeier Coefficients for K4Mg4(P2O7)3 Derived from Their Measured Refractive Indices ni

A

B

C

D

nx ny nz

2.17155 2.19961 2.20411

0.00782 0.01079 0.01001

0.03608 −0.00449 0.00285

0.00407 0.0056 0.00612

K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 are not isostructural despite exhibiting the same stoichiometric ratio and similar frameworks (see Figures 1 and 2). Although both materials exhibit [Mg4P6O21] double-layers, the orientation of these layers is different, attributable to the different alkali metal cation, K+ and Rb+. Two different orientations of the [Mg4P6O21] double-layer, labeled A and A′, are observed in K4Mg4(P2O7)3 (Figure 3a). The cavities in the A and A′ layers are filled by 10-coordinate K(1) and 7-coordinate K(4) cations, respectively. A single orientation of the [Mg4P6O21] doublelayer is observed in Rb4Mg4(P2O7)3 (Figure 3b). The cavities in this layer are filled with 9-coordinate Rb(1). The K−O bond distances for K(1) and K(4) range from 2.662(2) to 3.348(2) Å, with an average bond length of 2.940(6) Å, whereas the Rb− O bond lengths for Rb(1) range from 2.796(3) to 3.284(3) Å with an average bond length of 3.081(6) Å. The larger K−O bond length range compared with Rb−O, i.e., 0.686 Å versus 0.488 Å, and smaller size of the K+ cation, results in a buckling of the [Mg4P6O21] double-layer that creates the two different layer orientations, A and A′. Another consequence of this buckling is the orientation of the P2O7 groups that connect the double-layers (see Figure 3a,b). In K4Mg4(P2O7)3, the P2O7 group is bent with a P−P distance of 2.917(3) Å, whereas in Rb4Mg4(P2O7)3, the same group is “stretched”, i.e., more “linear” (P−O−P angle is ∼144°) and exhibits a longer P−P distance of 2.956(6) Å. The bent versus stretched orientations may also be understood through the sizes of the K+ and Rb+ cations. The smaller K+ cations, K(2) and K(3), between the layers result in the [Mg4P6O21] layers being closer together, whereas the larger Rb(2) and Rb(3) cations push the same layers apart. As such, for K4Mg4(P2O7)3, the interlayer P2O7 group is bent, whereas in Rb4Mg4(P2O7)3 the P2O7 group is stretched. In both K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3, the P atoms are bonded to four O atoms with P−O bond lengths ranging from

Figure 4. Diffuse reflection spectrum shows that the reflectance for K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 is nearly 70% at 200 nm. The VUV transmission spectrum for a single crystal of K4Mg4(P2O7)3 is shown in the inset and indicates an absorption edge of 170 nm.

groups to form a [(Mg2P2O6)O5] layer (Figure 1b). The two [(Mg2P2O6)O5] layers are further connected by the other end of the P2O7 group to form [Mg4P6O21] double layers. The [Mg4P6O21] double layers are stacked along the b axis and connect with each other through the bridging oxygen atoms of another P2O7 group to form a three-dimensional (3D) framework with K+ cations residing in the space of the framework (Figure 1c,d). In connectivity terms, the structure may be described as {2[MgO4/2]2− 2[MgO5/2]3− 6[PO4/2]+}4− with the charge balanced by the four K+ cations. Rb 4 Mg 4 (P 2 O 7 ) 3 exhibits a similar framework to K4Mg4(P2O7)3 (Figure 2). The basic units for Rb4Mg4(P2O7)3 are also the P2O7, MgO4, and MgO5 groups (Figure 2a). In the structure, the P2O7, MgO4, and MgO5 groups connect to form [Mg4P6O21] double layers that stack along the b axis and are scaffolded into a 3D framework. The Rb+ cations fill the spaces of the framework (Figure 2b−d). In connectivity terms, the structure may be described as {2[MgO4/2]2− 2[MgO5/2]3− 6[PO4/2]+}4− with the charge balanced by the four Rb+ cations. It should be noted that the P2O7 groups that connect the double-layers exhibit two orientations and these two orientations are statically disordered (see inset in Figure 2d).

Figure 5. (a) The phase matching curves for K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3. The solid curve is a guide to the eye, not a fit to the data. The inset is a photo of the K4Mg4(P2O7)3 crystal under 1064 nm radiation. (b) Oscilloscope traces showing SHG intensities for K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 with KDP as a reference. 1849

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Figure 6. (a) Refractive-index data and dispersion curves for K4Mg4(P2O7)3. The curves are the Sellmeier equation fits. A birefringence of 0.0108 is determined at 1064 nm. (b) The Type I phase-matching region from 988 to 2368 nm (494 to 1184 nm) is observed for the fundamental (second harmonic) wavelength, i.e., between the two vertical blue lines.

powder XRD pattern of the solidified melts revealed that K4Mg4(P2O7)3 decomposed into K2MgP2O7 (PDF #52-1084) and Mg2P2O7 (PDF #32-0626) (see Figure S6a) and Rb4Mg4(P2O7)3 decomposed into unknown phases (see Figure S6b); this suggests suitable fluxes are necessary for their crystal growth. (Vacuum)UV-vis Diffuse Reflectance Spectrum. The UV−vis diffuse reflectance spectra were collected (see Figure 4). K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 have large transmission ranges, >90%, from 300 to 2500 nm with a short UV cutoff edge below 200 nm. Vacuum (V) UV−vis data were collected on a 7 × 5 × 0.5 mm3 crystal of K4Mg4(P2O7)3. The VUV data indicates that K4Mg4(P2O7)3 has an absorption edge of 170 nm (Figure 4 inset). Further, the IR transparent spectrum of K4Mg4(P2O7)3 was also measured (Figure S7). These show that the transparent region of K4Mg4(P2O7)3 is 170−4210 nm, which is comparable with other phosphate NLO crystals, such as BPO4 (134−4230 nm),68 KH2PO4 (176−1550 nm),69 and KTiOPO4 (350−4500 nm).70 Second-Harmonic Generation Properties. Both K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 crystallize in noncentrosymmetric space groups, Pc for K4Mg4(P2O7)3 and Amm2 for Rb4Mg4(P2O7)3. Powder SHG measurements show that K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 are type 1 phase-matchable at 1064 nm (see Figure 5). The SHG efficiencies of K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 are ∼1.3× and ∼1.4× KDP in the 90 to 120 μm particle range, respectively. Refractive Index Data and Birefringence. The refractive index of single crystal K4Mg4(P2O7)3 was measured by the prism coupling method.71 A 5 × 5 × 1 mm3 crystal was used. The measured refractive indices along x, y, and z axes at different wavelengths, 450.2, 532, 636.5, 829.3, and 1062.6 nm, are listed in Table S3. On the basis of the measurement, the refractive indices, ni(λ), of K4Mg4(P2O7)3 as a function of wavelength λ were fitted by the least-squares method to the Sellmeier equation:70

Table 3. Band Gap of K4Mg4(P2O7)3 and Rb4Mg4(P2O7)3 Computed Using Density Functional Theory with the PBE, HSE06, and PBE0 Functionals As Compared to the Experimental Measurements K4Mg4(P2O7)3 Rb4Mg4(P2O7)3

PBE

HSE06

PBE0

experiment

4.85 eV (255 nm) 4.15 eV (299 nm)

6.43 eV (192 nm) 5.68 eV (218 nm)

7.25 eV (171 nm) 6.48 eV (191 nm)

7.29 eV (170 nm) >6.20 eV (