LiNa5Mo9O30: Crystal Growth, Linear, and Nonlinear Optical

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LiNa5Mo9O30: Crystal Growth, Linear and Nonlinear Optical Properties Weiguo Zhang, Hongwei Yu, Jacqueline Cantwell, Hongping Wu, Kenneth R. Poeppelmeier, and P. Shiv Halasyamani Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b01756 • Publication Date (Web): 09 Jun 2016 Downloaded from http://pubs.acs.org on June 13, 2016

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Chemistry of Materials

LiNa5Mo9O30: Crystal Growth, Linear and Nonlinear Optical Properties Weiguo Zhang1, Hongwei Yu,1 Jacqueline Cantwell,2 Hongping Wu,1 Kenneth R. Poeppelmeier,2 P. Shiv Halasyamani*1

1. Department of Chemistry, University of Houston, 112 Fleming Building, Houston, TX 77204-5003

2. Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3133

CORRESPONDING AUTHOR EMAIL ADDRESS: [email protected]

Abstract: We report on the crystal growth, linear and nonlinear optical properties of LiNa5Mo9O30. The refractive indices were measured, and a very large birefringence of 0.2545 at 450.2 nm was determined. In addition, calculated phase-matching curves indicate that LiNa5Mo9O30 can achieve non-critical type I and type II phase-matching (NCPM) for incident 1064nm radiation. Maker-fringe measurements, to determine individual non-linear optical coefficients, were also performed on the crystals in d31 = 1.4 pm/V, d32 = 4.3 pm/V, and d33 = 1.1 pm/V. The laser damage threshold (LDT) is around 1.2 GW/cm2 at 1064 nm using a 6 ns Nd:YAG laser operating at 5 The quality of the crystals were measured by high resolution x-ray diffraction rocking curve measurements that revealed a full width at half maximum (FWHM) of 59'' from the (001) reflection. The absorption edge was determined to be 357 nm, with transmission up to 5.26 µm. Our results indicate that single crystal LiNa5Mo9O30 is an 1

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excellent polarizer as well as second-order nonlinear optical material.

Introduction Nonlinear optical materials have efficiently expanded laser wavelengths from the UV-vis to the IR by cascaded frequency conversion.1-7 These materials are indispensable

for

semiconductor

lithography

and

a

variety

of

scientific

instrumentation. In addition to exhibiting structural non-centrosymmetry, i.e. lack of an inversion center, viable NLO materials must also possess moderate birefringence, 0.06 – 0.08, for phase-matching, a large laser damage threshold, relative ease of crystal growth, and NLO coefficients where dij > d36 KH2PO4 (KDP) 0.39 pm/V.8-10 Through intense research a variety of NLO materials such as β-BaB2O4, LiB3O5, CsLiB6O10, CsB3O5, LiNbO3, KTiOPO4, AgGaQ2 (Q = S, Se), and ZnGeP2 have been discovered.11-19 The usefulness of these materials is predicated on the growth and characterization of large, high quality single crystals. In growing these crystals investigators have been to measure a variety of physical properties crucial to assess if the material will have any technological NLO applications.

In this paper we report on the high quality and large crystal growth (centimeter size crystals) of LiNa5Mo9O30 and its associated optical - linear and non-linear properties. LiNa5Mo9O30 was first reported by Hamza et al. during their attempt to replace one Na+ with Li+ in Na6Mo11O36.20 In the Hamza et al. work, the main focus was on solving and refining the crystal structure that had a racemic twin issue. Other than the crystal structure, no physical properties were reported. We also describe for the first time Maker fringe measurements on LiNa5Mo9O30 that enable us to determine specific NLO coefficients. In addition refractive index and laser damage threshold (LDT) measurements were performed. These measurements allow us to determine the birefringence of the material, as well as its stability under intense laser radiation. We demonstrate that growing high quality and large single crystals of a NLO material is critical to fully assess any potential technological applications.

2


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Experimental Section LiNa5Mo9O30 Synthesis. Polycrystalline LiNa5Mo9O30 was synthesized by solid-state reaction techniques. Stoichiometric amounts of Na2CO3 (Alfa Aesar, 99.5%), Li2MoO4 (Alfa, 98.5%) and MoO3 (Alfa Aesar, 99.95%) were ground, placed into a platinum crucible, and heated in air to 450 °C for 24 h and 500 °C for 48 h with intermittent re-grindings. Powder X-ray Diffraction. Powder X-ray diffraction measurements were carried out on a PANalytical X’Pert PRO diffractometer equipped with Cu Kα radiation (λ = 1.54056 Å) in the 2θ range from 10° to 70°. Single Crystal Growth of LiNa5Mo9O30. Polycrystalline LiNa5Mo9O30 was placed in a platinum crucible, and heated to 650 oC for 24 h in order to form a homogenous melt. Heating Na2CO3, Li2MoO4 and MoO3 with a molar ratio 5:1:17, slowly (50 o

C/h) to 650 oC and holding for 24 h will also form a homogenous melt. Either may be

used for the crystal growth. Crystals of LiNa5Mo9O30 were first grown by spontaneous crystallization, i.e. crystals formed on a platinum wire dipped into the melt. Seed crystals were selected from these spontaneously grown crystals. A crystallization temperature of 561oC was determined by observing the growth or dissolution of the seed crystals when dipped into the melt. A [001] oriented seed was introduced into the melt at a rotation rate of 10 rpm at 2 oC higher than the crystallization temperature of 561oC in order to reduce surface defects. The temperature was decreased to the crystallization temperature at a cooling rate of 0.4 o

C/min. From the crystallization temperature, the melt was cooled at a rate of 0.1 oC

per hour to 560 oC. Simultaneously, the seed was pulled at a rate of 2 mm/h. When the crystal growth process was done, i.e. by observing the gap between the growing crystal and the crucible wall (when the crystal edge is very close to the crucible wall the crystal growth is considered completed), the crystal is pulled from the melt and cooled (20 oC/h) to room temperature. Single-Crystal X-ray Diffraction. A colorless transparent block-shaped crystal (0.144 × 0.089 × 0.067 mm3) cut from a large single crystal of LiNa5Mo9O30 was used for single-crystal data collection. Data were collected using a Siemens SMART 3



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diffractometer equipped with a 1 K CCD area detector using graphite– monochromated Mo Kα radiation. A hemisphere of data was collected suing a narrow-frame method with scan widths of 0.30 o in ω and an exposure time of 35 s per frame. The data were integrated using the Siemens SAINT program,21 with the intensities corrected for Lorentz polarization, air absorption, and absorption attributable to the variation in the path length through the detector faceplate. Multi-scan was used for the absorption correction on the hemisphere of data. The data were solved by direct method using SHELXS-97 and refined using SHELXL-97.22,23 All of the atoms were refined with anisotropic thermal parameters and converged for I > 2σ(I). All calculations were performed using the WinGX-98 crystallographic software package.24 High-Resolution X-ray Diffraction. High-resolution X-ray diffraction (HRXRD) was performed on a Rigaku High Resolution ATXG diffractometer equipped with a 4-bounce Ge-220 monochromator set for Cu-Kα radiation (λ = 1.54056 Å). The scan range and speed were 0.2° and 0.001° s-1 respectively.

(001) oriented wafers of

LiNa5Mo9O30 with and without pulling were mechanically polished on both sides and used for the HRXRD measurements. Thermal properties analysis. Thermogravimetric (TG) analysis and differential thermal analyses (DTA) were performed on an EXSTAR TG/DTA 6300 thermal analysis system (SII Nano Technology Inc.). Polycrystalline LiNa5Mo9O30 was placed in a platinum pan and heated/cooled in air at the rate of 10 oC/min between 20 oC and 700 oC. Laser Damage Threshold Measurement. The laser damage threshold (LDT) of LiNa5Mo9O30 was measured using 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 5 Hz. The laser beam was focused with a convex lens, resulting in a beam diameter of 0.36 mm. A well-polished (001) LiNa5Mo9O30 crystal wafer was placed in the beam diameter. The power of the laser was gradually increased until damage was apparent on the crystal surface, i.e., a gray track was observed on the crystal surface. 4


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Powder Second Harmonic Generation Measurement. Powder SHG measurements were performed on a modified Kurtz-NLO system25 using a pulse Nd:YAG laser (Quantel Laser, Ultra 50) with a wavelength of 1064 nm. A detailed description of the equipment and methodology has been published elsewhere.26 As the powder SHG efficiency has been shown to depend strongly on particle size,25 polycrystalline LiNa5Mo9O30 was ground and sieved into distinct particle size ranges (< 20, 20 – 45, 45 – 63, 63 – 75, 75 – 90,

90 – 125, 125 – 150 µm) to investigate its phase-matching

behavior. Polycrystalline KH2PO4 (KDP) was also sieved into similar particle sizes for SHG efficiency comparison. Optical

Spectra

Measurement.

UV-visible-Near

infrared

(UV-vis-NIR)

transmission data were collected on a Varian Cary 5000 scan UV-vis-NIR spectrophotometer over the 200-2500 nm spectral range at room temperature. A piece of (010) crystal wafer with a thickness of 1 mm was used to perform the measurement. Infrared transmission spectra were recorded on a Thermo Nicolet Nexus 470 FTIR spectrometer in the 400-4000 cm-1 range. Refractive Index Measurements. A (010) wafer was polished using the Unipol-300 grinding/polishing machine (MTI Co.). One of the optical axes, z-axis, is coincident to the crystallographic b-axis. The other two optical axes, x and y, were determined by using a polarized microscope (Olympus BX41, Leeds Instruments, Inc.) and are in the crystallographic ac-plane. The refractive indices were measured using a Metricon Model 2010/M prism coupler (Metricon Co.) at five different wavelengths: 450.2, 532, 636.5, 829.3, and 1062.6 nm. Maker Fringe Measurements. Maker fringe measurements27,28 were performed on two crystal wafers cut perpendicular to the a- and b- crystallographic axes in order to measure d31, d32 and d33 nonlinear optical coefficients. The crystals were cut plane parallel and polished to optical quality using a Unipol-300 grinding/polishing machine (MTI Co.). A Q-switched Nd:YAG laser (Quantel Laser, Ultra 50) with a pulse width of 7 ns and repetition frequency of 20 Hz was employed as the fundamental light source (1064 nm). The second harmonic signal generated from the sample wafer was detected by a side window photomultiplier tube (PMT) (Zolix Instruments, 5



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PMTH-S1-CR131), averaged by a fast-gated integrator and boxcar average (Stanford Research Systems), and then automatically recorded by a computer. A KH2PO4 (KDP) (110) wafer (Crystrong Photoelectric Tech. Co., Ltd. China) was used as a reference. Results and Discussion Polycrystalline LiNa5Mo9O30 was synthesized through standard solid-state techniques (see Experimental Section). The powder XRD pattern of the polycrystalline material is in good agreement with the calculated pattern from the single crystal data (see Figure S1). TG/DTA measurements were performed in air to determine the stability and melting or decomposition temperature of the material. As seen in Figure S2, during heating there is one sharp endothermic peak around 522 oC, and during cooling there is one sharp exothermic pear around 437 oC. Both transitions occur without any weight loss indicating LiNa5Mo9O30 melts congruently.

Crystal Growth and Laser Damage Threshold Measurements. As LiNa5Mo9O30 melts congruently, we were able to grow high quality single crystals from the stoichiometric melt using [100]- and [001]-oriented seeds. Figure 1 shows the grown crystals (Figures 1a-c) and simulated morphologies (Figure 1d) with indexed (hkl) planes based on Bravais-Friedel-Donnay-Harker (BFDH) theory.29-31 The crystals shown in Figures 1a and 1b were grown under the same conditions - growth time, temperature, rotation and pulling rate (see Experimental Section) - but with different seed orientations. The crystal grown with a [100]-oriented seeds exhibits (040), (022), (111), and (242) faces and has a size of 9 × 8 × 7 mm3, whereas the crystal grown a [001]-oriented seed exhibits (040), (004), (022), and (111) faces and has a size of 17 × 13 × 11 mm3. Clearly the crystal grown with the [001]-oriented seed grows faster exhibits larger regular faces compared with the crystal grown from the [100]-oriented seed. In Figure 1c, the crystal was grown with a [001]-oriented seed with a pulling of 2mm hr-1. The green dash in Figure 1c depicts the melt surface level, i.e. the part of the crystal above the green dashed line was pulled out of the melt, whereas the part below the green dashed line remained submerged in the melt, i.e 'unpulled'. From 6


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inspection, it is clear that the part of the crystal above the melt reveals growth steps, whereas the part below melt exhibits a very smooth surface. In order to quantify the crystal growth quality with and without pulling, rocking curve measurements were performed.

It is clear from Figure 2 that the crystal grown without pulling is of

quality compared with pulling, i.e. FWHM of 59" vs 98". Laser damage threshold (LDT) measurements were performed using a pulsed nanosecond laser (1064 nm, 6 5 Hz). A well-polished high-quality (001) wafer of LiNa5Mo9O30 has a LDT of ~ 1.2 GW/cm2 which is comparable with other well-known NLO crystals (see Table 1).

Figure 1. Photos (a – c) and simulated morphology (d) of as-grown LiNa5Mo9O30 single crystals along [100] (a) and [001] (b and c) orientations.

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Figure 2. High-resolution X-ray diffraction (HRXRD) Rocking Curves for (001) LiNa5Mo9O30 wafer.

Table 1. Laser Damage Threshold, Birefringence (Δn), and NLO coefficients (dij) of single crystal LiNa5Mo9O30 and other well-known NLO crystals. Crystal

LDT (GW/cm2)

Birefringence ∆n (nmax-nmin)

dij (pm/V) at 1064 nm

LiNa5Mo9O30

1.2

0.2545 – 0.1935

d31 = 1.4

(this work)

(1064 nm, 6 ns, 5 Hz)

(450.2 – 1062.6 nm)

d32 = 4.3

0.84

0.1064 – 0.0752

d22 = 2.1

(1064 nm, 7 ns)

(420 – 1600 nm)

d31 = -4.35

LiNbO3 (LN)15,32-34

d33 = 1.1

d33 = -27.2 KTiOPO4 (KTP)35,36

15

0.1277 – 0.0921

d31 = 2.2

(1064 nm, 1 ns)

(435.8 – 1064 nm)

d32 = 3.7 d33 = 14.6

8


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KBe2BO3F2 (KBBF)37-39

>5

0.077

(1064 nm, 8 ns)

(404.7 nm)

β-BaB2O4

4.5

0.1247 – 0.1128

d15 = 0.03

(β- BBO)40-42

(1064 nm, 10 ns, 10Hz)

(404.7 – 1014 nm)

d22 = 2.2

11.2

0.0457 – 0.0399

d31 = 0.67

(1064 nm, 7.5 ns)

(253.7 – 1064.2 nm)

d32 = 0.85

LiB3O5 (LBO)33,43,44

d11 = 0.49

d33 = 0.04

d33 = 0.04 CsB3O5 (CBO)45,46 CsLiB6O10 (CLBO)47-49

4.5

0.0646 – 0.0587

(1064 nm, 5 ns)

(354.7 – 1064 nm)

29

0.0541 – 0.0498

(1064 nm, 1.1 ns)

(420 – 1064 nm)

d14 = 1.08

d36 = 0.74

Crystal Structure and Dipole Moment Calculations. The crystal structure of LiNa5Mo9O30 was reported as a racemic twin.20 We collected single crystal data on a small piece of one of our grown crystals and did not observe any racemic twinning. The crystallographic data and structural refinements for LiNa5Mo9O30 are given in Table 2. Selected bond lengths and angles for LiNa5Mo9O30 crystal structure have deposited in supporting information (Table S1). A ball-and-stick and polyhedral representation of LiNa5Mo9O30 is shown in Figure 3. LiNa5Mo9O30 contains five unique Mo6+ cations that are coordinated to six oxygen atoms in an octahedral manner. There is a relatively long bond, ~ 2.547(7) Å, between Mo(2) and O(13) (see Table S1). In the Hamza et al. work, Mo(i) – O bonds longer than 2.5 Å were neglected, and the structure of LiNa5Mo9O30 was described containing MoO6 octahedra and MoO5 pyramids.20 Bond valence sums (BVS)50,51 of the cations were calculated and are listed in Table S2. Note that the BVS of Mo(2) is 6.04 and 5.86 with and without including the relatively long Mo(2) – O(13) (~ 2.547(7) Å) bond respectively. Clearly, the BVS of Mo(2) including the Mo(2) – O(13) bond length is

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much closer to the oxidation state of Mo6+. Thus all the Mo6+ cations are considered six-coordinate and the structure of LiNa5Mo9O30 may be described as a three-dimensional MoO6 framework. In connectivity terms the structure may be written

as

{2[Mo(1)O2O3/2O1/3]5/3- 2[Mo(2)O1O3/2O2/3]1/3- 2[Mo(3)O1O2/2O3/3]0

2[Mo(4)O1O3/2O2/3]1/3- [Mo(5)O2O2/2O2/3]4/3-}6- with charge balance retained by the one Li+ and five Na+ cations. Each Mo6+ is displaced from the center of its oxide octahedron attributable to second-order Jahn-Teller effects.52-58 As such each MoO6 octahedron exhibits a local dipole moment, or polarization. As described earlier,59,60 the direction of this local polarization may occur along the edge (local C2 direction), face (local C3 direction), corner (local C4 direction), or in between one of these directions. With respect to LiNa5Mo9O30, all of these local polarization directions are observed. A face-type, C3, distortion is observed for Mo(1) and Mo(4), whereas a corner-type, C4, distortion exhibited by Mo(2) and Mo(3). Finally, an edge-type, C2, distortion is seen for Mo(5). The magnitudes of the polarizations were calculated as described earlier,61,62 and are given in Table S2. As LiNa5Mo9O30 crystallizes in a polar space group, Fdd2 (crystal class mm2), a macroscopic polarization is observed. If the individual polarizations of the Mo6+ octahedra are summed, a macroscopic polarization is observed along the negative c-axis - consistent with the polar direction of crystal class mm2.63 Table 2. Crystallographic data and structural refinements for LiNa5Mo9O30. Empirical formula Formula weight T (K) Wavelength (Å) Crystal system Space group a (Å) b (Å) c (Å) V ( Å3 ) Z ρ calcd (g/cm3) µ (mm-1)

LiNa5Mo9O30 1465.35 296(2) 0.71073 Orthorhombic Fdd2 (No. 43) 7.2265(2) 37.1575(11) 17.9398(5) 4817.2(2) 4 4.041 4.743

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F(000) Crystal size (mm3) Theta range (deg) Limiting indices Reflections collected/unique Completeness Absorption correction Refinement method Data/restraints/parameters GOF (F2) Final R indices [I>2sigma(I)] R indices (all data) Flack parameter Extinction coefficient

5408 0.144 × 0.089 × 0.067 2.19 – 27.45 -8 ≤ h ≤9, -48 ≤ k ≤42, -22 ≤ l ≤23 7010 / 2645 [R(int) = 0.0264] 99.9% Semi-empirical from equivalents Full-matrix least-squares on F2 2645 / 1 / 207 1.128 R1 = 0.0145, wR2 = 0.0322 R1 = 0.0146, wR2 = 0.0323 0.00(4) -0.001005(15)

Figure 3. Ball-and-stick and polyhedral representation of LiNa5Mo9O30 in the bc-plane. The local dipole moments on the individual MoO6 octahedra are shown in blue, with the macroscopic moment shown in red. Note that the macroscopic dipole moment is toward the -c axis.

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Powder SHG Measurements. Powder SHG efficiency versus particle size (20 – 150 um) (see Figure S3) revealed that LiNa5Mo9O30 has an SHG efficiency approximately 2 x KDP. The measurements also indicate LiNa5Mo9O30 is type-I phase-matchable, and falls in the class A category of SHG materials.25 The powder data is consistent with our phase-matching calculations from the refractive index data (see below).

UV-Vis-NIR and Infrared Transmission Measurements. The UV-vis-NIR transmission spectra of a (010) wafer of LiNa5Mo9O30 indicate the UV absorption edge for is around 357 nm (see Figure S4). In Figure S5, the infrared transmission spectra of the same wafer indicate that the IR transmission cut-off edge is 5.26 µm. Thus LiNa5Mo9O30 exhibits a very broad transmission range from 357 nm - 5.26 µm.

Refractive Index Measurements. A Metricon Model 2010/M prism coupler was used to measure the refractive indices, n(λ), as a function of wavelength (λ) for LiNa5Mo9O30. The estimated accuracy is 2 × 10-4, and Table 3 gives the measured refractive indices at different wavelengths along the x, y, and z axes. A least-squares method was used to fit the dispersion parameters of the refractive indices, ni, using the Sellmeier equation:64

ni2 = A +

B − Dλ 2 λ −C , 2

In this equation A, B, C, and D are the Sellmeier parameters, whereas λ is the wavelength in µm. Table 4 list the four Sellmeier coefficients for each refractive index. The differences between the measured data and calculated values were estimated, and as can be seen in Figure 4 there is an excellent fit between these two parameters. As seen in Table 3, LiNa5Mo9O30 is an optically negative biaxial crystal33 as (nz - ny) < (ny - nx). The maximum birefringence ∆n (nz-nx) range from 0.2545 (at 450.2 nm) to 0.1935 (at 1062.6 nm) that is much larger than that of other well-known nonlinear optical materials such as LiNbO3 (LN), KTiOPO4 (KTP), KBe2BO3F2 (KBBF), β-BaB2O4 (β- BBO), LiB3O5 (LBO), CsB3O5 (CBO), and CsLiB6O10 12


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(CLBO) (see Table 1). Solely considering the birefringence, LiNa5Mo9O30 is comparable with commonly used polarizers such as YVO4 (∆n = 0.209 at 1064 nm),65 TiO2 (∆n = 0.333 – 0.252 at 454 - 1330 nm),66 and α-BaB2O4(α-BBO) (∆n = 0.116 at 1064 nm)67. However, it is hard to grow high quality crystals of YVO4, and TiO2, due to their high melting temperature and growth habit,68,69 whereas α-BBO67 has a phase transition and large anisotropic thermal expansion, which may cause cracking during its crystal growth. Therefore, based on an overall consideration of birefringence, transmission range, and growth habit and facility, LiNa5Mo9O30 has overwhelming predomination as a novel polarizer. Meanwhile, based on measured refractive indices and fitted Sellmeier equations, type I and II second-order NLO phase-matching curves of LiNa5Mo9O30 were calculated with a fundamental wavelength of 1064 nm. As seen in Figure 5, LiNa5Mo9O30 is type-I phase-matchable from θ = 90o (φ = 26.7o) to θ = 51.3o (φ = 1.2o) and type-II phase-matchable from θ = 90o (φ = 42.9o) to θ = 37.2o (φ = 1.7o). As θ = 90o for both type I and II phase-matching, LiNa5Mo9O30 may be non-critical phase-matched (NCPM) at 1064nm. NCPM permits large angular acceptance and eliminates walk-off between the fundamental and harmonic radiation that produces the highest SHG efficiency.70,71 Table 3. Measured refractive index along x, y, and z axes at different wavelengths for single crystal LiNa5Mo9O30. Wavelength (µm) 0.4502 0.532 0.6365 0.8293 1.0626

nx

ny

nz

∆n (nz-nx)

1.8756 1.8455 1.8266 1.8103 1.8009

2.0776 2.0382 2.0123 1.9893 1.9764

2.1301 2.0774 2.0414 2.0115 1.9944

0.2545 0.2319 0.2148 0.2012 0.1935

Table 4. Sellmeier coefficients derived from the measured refractive indices of single crystal LiNa5Mo9O30. Sellmeier coefficients A

nx 3.22232

ny 3.86068

nz 3.90232 13



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B C D

0.04077 0.06618 0.01546

0.06855 0.05333 0.01622

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0.09576 0.05249 0.01178

Figure 4. Measured refractive indices along x, y, and z optical axes (symbols) and calculated fit curves from the Sellmeier coefficients for single crystal LiNa5Mo9O30.

Figure 5. Second harmonic phase-matching conditions at a fundamental wavelength of 1064 nm for single crystal LiNa5Mo9O30.

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Maker Fringe Measurements. In order to determine individual NLO coefficients, Maker fringe measurements were performed. A schematic of the Maker fringe measurements system is shown in Figure 6. LiNa5Mo9O30 crystalizes in the noncentrosymmetric space group Fdd2 that belongs to crystal class mm2. Crystal class mm2 has three nonzero independent second-order NLO coefficients, d31, d32, and d33 after Kleinman symmetry is considered.72,73 In order to measure the three independent NLO coefficients, two LiNa5Mo9O30 crystal wafers with the (100) and (010) faces perpendicular to the laser beam were used. The crystal wafer placement for measuring each NLO coefficient are shown in the insets of Figures 7a, b, and c. The measured and calculated Maker fringes are shown in Figures 7a, b, and c for the d31, d32, and d33 NLO coefficients respectively. The Maker fringes for measuring the d36 NLO coefficient of KH2PO4 (KDP) were also collected and used as a reference (see Figure S6). According to Maker fringe theory, the generated second harmonic power, P2ω, may be expressed as followed:27,28

P2ω (θ ) =

512π 2 d 2 Pω2tω4T2ω R(θ ) p 2 (θ )β (θ )sin 2 Ψ , cw2 (nω2 − n22ω )2

where

Ψ=

2π L

λ

(nω cos θω − n2ω cos θ 2ω ) ,

In these equations, c is the speed of light in air, w is the radius of light beam, nω and n2ω are the refractive indices at the fundamental and harmonic wavelength, respectively, d is the NLO coefficient, Pω is the fundamental beam power, tω and T2ω are the transmission coefficients of the fundamental wave and the harmonic wave, respectively; R(θ) is the incident multiple-reflection correction, p(θ) is the projection factor, β(θ) is the beam size correction, L is the sample thickness, and λ is the wavelength of the fundamental beam in air, respectively. If

1 tω4T2ω R(θ ) p 2 (θ )β (θ ) (nω − n22ω )2 2

is taken as f(n,θ) that is only a function of refractive indices (n) and incident angle (θ), 15



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P2ω can be simplified to

P2ω (θ ) =

512π 2 d 2 pω2 cw

2

f (n,θ )sin 2 Ψ .

The f(n,θ) part depicts the envelope of the Maker fringe, and sin2Ψ determines the minima oscillating position. By fitting the calculated and measured Maker fringes, a constant, C = 512π2d2pω2/(cw2), can be obtained. The magnitude of the second-order NLO coefficient of a LiNa5Mo9O30 crystal can be determined relative to d36 of KDP crystal, and the coefficient equation can be expressed as

d sample =

Csample CKDP

× d36 ( KDP)

Based on the measurements and calculations, the NLO coefficients of LiNa5Mo9O30 crystal relative to d36(KDP) have been determined, and are d31 = 3.6 × d36(KDP), d32 = 11 × d36(KDP), and d33 = 2.9 × d36(KDP) respectively. As the d36 coefficient of KDP is 0.39 pm/V,33 the absolute NLO coefficients of LiNa5Mo9O30 crystal are d31 = 1.4 pm/V, d32 = 4.3 pm/V, and d33 = 1.1 pm/V. These values compare well to other well-known NLO materials (see Table 1). Recently, there are some other kinds of nonlinear optical molybdates, e.g. BaTeMo2O9 (α and β phase),74,75 Na2Te3Mo3O16,76 ZnTeMoO6,77 MgTeMoO6,78 CdTeMoO6,79 Cs2TeMo3O12,80 and Zn2TeMoO7,81 which have been grown into single crystals. So far only the NLO coefficients of BaTeMo2O9 (d14 = -3.13 pm/V, d31 = 9.88 pm/V, d32 = -2.26 pm/V, d33 = 4.57 pm/V)82 and Cs2TeMo3O12 (d32 = 6.8 pm/V, d33 = 6.5 pm/V)83 have been fully investigated based on single crystals. Lack of sufficient size of high quality crystals may prevent the investigation of specific NLO coefficients of other aforementioned molybdate crystals. For instance, the high viscosity of the high temperature solution challenged large size and high quality Na2Te3Mo3O16 crystals,76 whereas the layered 16


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growth tendency prevents large size in three-dimension of ZnTeMoO6,77 MgTeMoO6,78 and CdTeMoO679 crystals. Besides, all these kind of molybdate crystals were grown by top-seeded solution growth (TSSG) method which involves flux system. Choosing proper flux system would cost a lot of effort and the crystal growth period may take weeks or longer by TSSG method. Taking growth facility into account, LiNa5Mo9O30 is also a strong competitor for SHG application to the recently developed molybdate crystals even though its NLO coefficients are slightly weaker than that of BaTeMo2O9 and Cs2TeMo3O12.

Figure 6. Schematic of the Maker fringe measurement system.

17



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Figure 7. Measured and calculated Maker Fringe Data and fitted envelope for (a) d31, (b) d32, and (c) d33 for LiNa5Mo9O30.

Conclusions Large, centimeter size, crystals of LiNa5Mo9O30 have been grown through the stoichiometric melt. Linear optical measurements revealed a maximum birefringence of 0.2545 (at 450.2 nm) to 0.1935 (at 1062.6 nm), with a transmission range from 357nm to 5.26 µm. The quality of the crystals were investigated by x-ray diffraction rocking curves and revealed a FWHM of 59'' for the (001) reflection. In addition, crystals of LiNa5Mo9O30 can achieve both type I and II non-critical phase-matching. Maker fringe measurements revealed NLO coefficients of d31 = 1.4 pm/V, d32 = 4.3 pm/V, and d33 = 1.1 pm/V. Given that large and high quality crystals of LiNa5Mo9O30 can easily be grown, the material is attractive for NLO as well as birefringent applications.

Supporting Information

The cif for LiNa5Mo9O30, selected bond lengths and angles, bond valence sum (BVS) and dipole moment calculations, powder XRD, TG/DTA data, transmission spectra, 18


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powder SHG, and Maker fringe data for KDP. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENT. WZ, HY, HW, and PSH thank the Welch Foundation (Grant E-1457), the National Science Foundation (DMR-1503573), and the Texas Center for Superconductivity for support. JC and KRP thank the National Science Foundation (DMR-1307698). We thank Prof. Jerry Yang and Dr. Xing He for the laser damage threshold measurements. This work also made use of the J.B. Cohen X-Ray Diffraction Facility supported by the MRSEC program of the National Science Foundation (DMR-1121262) at the Materials Research Center of Northwestern University.

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Table of Contents

LiNa5Mo9O30: Crystal Growth, Linear and Nonlinear Optical Properties Weiguo Zhang1, Hongwei Yu,1 Jacqueline Cantwell,2 Hongping Wu,1 Kenneth R. Poeppelmeier,2 P. Shiv Halasyamani*1 1. Department of Chemistry, University of Houston, 112 Fleming Building, Houston, TX 77204-5003

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2. Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3133

CORRESPONDING AUTHOR EMAIL ADDRESS: [email protected] Large, centimeter size, single crystals of LiNa5Mo9O30 were successfully grown and their linear and nonlinear optical properties were investigated. Refractive index measurements and calculations indicated LiNa5Mo9O30 can achieve non-critical type I and type II phase-matching (NCPM) for incident 1064 nm radiation. Nonlinear optical coefficients of d31 = 1.4 pm/V, d32 = 4.3 pm/V, and d33 = 1.1 pm/V at 1064 nm were determined through Maker fringe measurements. Our results indicate that single crystal LiNa5Mo9O30 is an excellent NLO material at 1064 nm.

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LiNa5Mo9O30: Crystal Growth, Linear, and Nonlinear Optical

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