Rb₂Na(NO₃)₃: A Congruently Melting UV-NLO Crystal with a Very Strong Second-Harmonic Generation Response

Abstract

Crystals of congruently melting noncentrosymmetric (NCS) mixed alkali metal nitrate, Rb₂Na(NO₃)₃, have been grown through solid state reactions. The material possesses layers with NaO₈ hexagonal bipyramids and NO₃ triangular units. Rb⁺ cations are residing in the interlayer space. Each NaO₈ hexagonal bipyramid shares its corners and edges with two and three NO₃ units, respectively, in order to fulfill a highly dense stacking in the unit cell. The NaO₈ groups share their six oxygen atoms in equatorial positions with three different NO₃ groups to generate a NaO₆-NO₃ layer with a parallel alignment. The optimized arrangement of the NO₃ groups and their high density in the structure together produce a strong second-harmonic generation (SHG) response. Powder SHG measurements indicate that Rb₂Na(NO₃)₃ has a strong SHG efficiency of five times that of KH₂PO₄ (KDP) and is type I phase-matchable. The calculated average nonlinear optical (NLO) susceptibility of Rb₂Na(NO₃)₃ turns out to be the largest value among the NLO materials composed of only [NO₃]⁻ anion. In addition, Rb₂Na(NO₃)₃ exhibits a wide transparency region ranging from UV to near IR, which suggests that the compound is a promising NLO material.

1. Introduction

Nonlinear optical (NLO) crystals, especially those producing coherent ultraviolet (UV) light, are continuously attracting enormous attention, attributed to their auspicious applications in laser science and technology [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. To be a useful UV-NLO material, however, it should exhibit a high NLO coefficient and a wide UV transmittance. Recently, many borate-based UV-NLO crystals [15,16,17,18,19,20,21,22] revealing a variety of structural possibilities and considerably large microscopic second-order susceptibility with moderate birefringence based on the anionic group theory have been reported [23,24,25]. A few representative materials include β-BaB₂O₄ (BBO) [16], LiB₃O₅ (LBO) [17], CsB₃O₅ (CBO) [18], CsLiB₆O₁₀ (CLBO) [19,20], KBe₂BO₃F₂ (KBBF) [21], and Sr₂Be₂B₂O₇ (SBBO) [22]. The unique advantage of the [BO₃]³⁻ group has motivated many chemists’ interests further in finding new NLO materials with other functional groups, such as nitrates and carbonates. Specifically, [NO₃]⁻ and [CO₃]²⁻ groups possess the similar π-conjugated molecular orbitals in trigonal planar structures. Recently, materials containing carbonates have been widely studied, and a series of relevant materials exhibiting excellent NLO characteristics have been uncovered [26,27,28,29,30,31,32,33]. Systematic examinations of [NO₃]⁻-containing materials with proper NLO properties, however, have rarely been achieved in contrast to the successful investigations of carbonates and borates [34,35,36,37]. In fact, there is no known nitrate compound that can be used as a practical NLO material up to now. On the basis of Li’s calculations, the microscopic second-order susceptibility, β⁽²⁾, of the [NO₃]⁻ group is expected to be larger than that of the [BO₃]³⁻ or [CO₃]²⁻ group [38]. Therefore, we have chosen the [NO₃]⁻ anionic group as a basic building unit to develop novel UV-NLO crystals with high NLO coefficients. In order to obtain NLO materials exhibiting strong second-harmonic generation (SHG) effects, a number of methods have been discussed. Combining asymmetric building units, such as distorted octahedra with a d⁰ transition metal cation [39,40,41], polyhedra with a d¹⁰ metal cation revealing a polar displacement [42,43], and metal ions with ns² lone pair electrons [44] in the frameworks of new materials is a common approach to increase the incidence of many good NLO materials [45,46]. Incorporation of the above mentioned acentric building units into a nitrates system may also enlarge the SHG efficiency of materials. However, a critical issue found from all these design strategies is that the absorption edge is red-shifted with the building blocks. To warrant high transmission in the UV region, counter cations that do not exhibit d–d or f–f transitions, such as alkali metals and alkaline earth metals, should be incorporated. Based on the relationships between the structures and overall NLO properties, there are two approaches to produce large NLO effects: (i) choosing favorable structural units and having them aligned in a parallel manner, and (ii) increasing the density of the NLO structural units. In this article, we report phase pure synthesis, structure determination, characterization, and calculations of a promising UV-NLO material, Rb₂Na(NO₃)₃. To the best of our knowledge, the reported material reveals the largest average NLO susceptibility among the NLO materials containing only [NO₃]⁻ anion.

2. Results and Discussion

2.1. Crystal Structure Description

The structure of Rb₂Na(NO₃)₃ has been recently reported using a crystal obtained from the study of the NaNO_3–RbNO₃ phase diagram [47]. However, we redetermined the crystal structure of the material in order to better understand the details of the NLO properties. In this study, high quality single crystals of Rb₂Na(NO₃)₃ have been easily grown using NH₄NO₃ as flux. Rb₂Na(NO₃)₃ crystallizes in an orthorhombic polar noncentrosymmetric (NCS) space group, Pmc2₁ (No. 26). Rb₂Na(NO₃)₃ exhibits a layered structure that consists of NaO₈ hexagonal bipyramids and NO₃ trigonal plane units. Rb⁺ cations reside in the interlayer space and make an overall charge balance. Within the layer, the N is coordinated to three O atoms to generate an NO₃ trigonal plane unit with the N–O bond lengths of 1.228(3)–1.265(4) Å and O–N–O bond angles of 117.6(2)–124.7(4)°. The Na is coordinated to six equatorial O atoms and two apical O atoms to create NaO₈ hexagonal bipyramids (see Figure 1a). The Na–O bond lengths in the NaO₈ polyhedra range from 2.332(3) to 2.685(3) Å. Each NaO₈ hexagonal bipyramid shares its corners through oxygen atoms and forms a 1D chain structure along the a-direction (see Figure 1b). Then the 1D chains are further connected by NO₃ groups and a layer parallel to the bc-plane is obtained (see Figure 1c). As seen in Figure 1c,d, NO₃ groups serve as both intra- and inter-chain linkers. In connectivity terms, the material may be described as an anionic layer of {[Na(1)O_6/2O_2/3]^6.333−·[N(1)O_1/2O_2/1]⁰·[N(2)O_1/3O_2/2]^2.333+·[N(3)O_3/2]²⁺}²⁻, with the charge balance maintained by two Rb+ cations. Each NaO₈ hexagonal bipyramid shares its corners and edges with two and three NO₃ triangles, respectively. While the oxygen atoms in N(2)O₃ and N(3)O₃ groups are connected to Na, the two oxygen atoms in N(1)O₃ are not linked further and are dangling. The NaO₈ polyhedra share their six equatorial oxygen atoms with three separate NO₃ groups to generate a flat NaO₆–NO₃ layer. Owing to its special coordination, the NaO₆ moiety in the flat layer pushes its three adjacent NO₃ groups to array into a perfect parallel alignment and result in maximum contribution to the SHG effect. The other two NO₃ groups are inclined to the NaO₆–NO₃ layer, giving additional contributions to the SHG effect.

The bond valence sums for Rb₂Na(NO₃)₃ are calculated using the following formula

$$V_i={\displaystyle \sum _j{S}_{ij}}={\displaystyle \sum _j\text{exp}\left\{\left(r_0-r_{ij}\right)/B\right\}}$$

where S_ij is the bond valence associated with bond length, and r_ij, r₀, and B (usually 0.37) are empirically determined parameters [48,49]. The calculated bond valences for Rb⁺, Na⁺, N⁵⁺, and O²⁻ atoms in Rb₂Na(NO₃)₃ are 1.14–1.22, 1.13, 4.94–5.04, and 1.97–2.13, respectively.

2.2. Thermal Properties

The thermal behavior of Rb₂Na(NO₃)₃ was investigated using thermogravimetric/differential thermal analysis (TG/DTA). As seen in Figure 2a, the DTA curve for Rb₂Na(NO₃)₃ exhibits only one endothermic peak at 182 °C, along with a negligible weight loss observed in the TGA curve, possibly due to the volatility upon melting. In addition, analysis of the powder XRD patterns for Rb₂Na(NO₃)₃ before and after melting strongly suggests that Rb₂Na(NO₃)₃ does not change the phase all the time, and melts congruently (see Figure 2b). Therefore, we believe that large crystals of Rb₂Na(NO₃)₃ could be easily grown in air.

2.3. Optical Properties

UV-vis diffuse reflectance spectral data for Rb₂Na(NO₃)₃ were collected (see Figure 3a). Absorption data (K/S) were worked out from the following Kubelka–Munk function [50,51]:

$$F(R)=\frac{{(1-R)}^2}{2R}=\frac{K}{S}$$

In which K is the absorption, R is the reflectance, and S is the scattering. Extrapolating the linear part of the sloping upward curve to zero in the (K/S)-versus-E plot yields the appearance of absorption. No absorption from 0.27 to 2.5 µm in the UV-Vis-IR of Rb₂Na(NO₃)₃ indicates that the compound has wide transparent regions that range from near-UV to mid-IR. The optical band gap of Rb₂Na(NO₃)₃ is 4.74 eV. The relatively smaller optical band gap may be attributed to the two dangling oxygen atoms in N(1)O₃. It has been shown in borates that the terminal oxygen atoms red-shift the absorption edge, making it difficult to reach the deep-UV.

As seen in Figure 3b, the IR spectrum of Rb₂Na(NO₃)₃ reveals peaks at 1384 and 840 cm⁻¹, which can be assigned to the stretching and bending vibrations of [NO₃]⁻ groups, respectively. Bands occurring at 1018 and 690 cm⁻¹ are attributed to the asymmetric and symmetric stretches of [NO₃]⁻ groups. The assignments are consistent with previously reported data [34,35,36,37].

2.4. NLO Properties

The curve of the SHG signal vs. particle size acquired from the measurements made on ground crystals of Rb₂Na(NO₃)₃ is shown in Figure 4a. The result is consistent with a type I phase-matching behavior according to the rule proposed by Kurtz and Perry [52]. Rb₂Na(NO₃)₃ exhibited a very large SHG response which was five times that of KH₂PO₄ (KDP) (see Figure 4b). Because the reported d₃₆ coefficient for KDP is 0.39 pm/V [53], the derived d_eff coefficients for Rb₂Na(NO₃)₃ is 1.9 pm/V. It should be noted that the intensity is the largest reported to date among the NLO materials consisting of only [NO₃]⁻ anion.

The dipole transition from the cations (Rb⁺ and Na⁺ in this case) to the anionic groups ([NO₃]⁻ in this case) is the off-site transition, according to the anionic group theory [22,23,24]. Its value is about one order smaller than the dipole transition of the intra-atomic transitions within anionic groups. Therefore, the main contribution to the SHG coefficients in Rb₂Na(NO₃)₃ is from the anionic [NO₃]⁻ groups. In other words, the transition within nitrate anions is much larger than that of the charge transfer between the p-originated states of anions and the s-states of cations. Therefore, the macroscopic second-order susceptibility χ⁽²⁾ could be demonstrated by Equation (1) based on the anionic group theory,

$${\mathsf{\chi }}_{ijk}^{(2)}=\frac{F}{V}{\displaystyle \sum _P}{\displaystyle \sum _{i^{\prime }{j}^{\prime }{k}^{\prime }}}{\mathsf{\alpha }}_{i{i}^{\prime }}{\mathsf{\alpha }}_{j{j}^{\prime }}{\mathsf{\alpha }}_{k{k}^{\prime }}{\mathsf{\beta }}_{i^{\prime }{j}^{\prime }{k}^{\prime }}^{(2)}(P) \mathrm{P}={[{\mathrm{NO}}_3]}^{-}$$

(1)

where F is the correction factor of the local field, V is the volume of the unit cell, α_iiʹ, α_jjʹ, and α_kkʹ are the direction cosines between the macroscopic coordinates of the crystal and the microscopic coordinates of [NO₃]⁻ groups, and ${\mathsf{\beta }}_{i^{\prime }{j}^{\prime }{k}^{\prime }}^{(2)}$ is the microscopic second-order susceptibility tensors of an individual group. Owing to the fact that [NO₃]⁻ is a planar group in point group D_3h, there are only two non-vanishing second-order susceptibilities, ${\mathsf{\beta }}_{111}^{(2)}$ = ${\mathsf{\beta }}_{222}^{(2)}$. Since the geometrical factor, g, can be extracted from Equation (1),

$${\mathsf{\chi }}_{ijk}^{(2)}=\frac{F}{V}{g}_{ijk}{\mathsf{\beta }}_{111}^{(2)}([\mathrm{N}{\mathrm{O}}_3])$$

(2)

In the case of unspontaneous polarization, the structural criterion C is defined as:

$$C=\frac{g}{n}$$

(3)

Equation (2) may be simplified according to the deduction process shown in reference [54]:

$${\mathsf{\chi }}_{ijk}^{(2)}=F\times (\frac{n}{V})\times C\times {\mathsf{\beta }}_{111}([\mathrm{N}{\mathrm{O}}_3])$$

(4)

where n is the number of anionic groups in a unit cell. Therefore, the NLO coefficient ${\mathsf{\chi }}_{ijk}^{(2)}$ is proportional to the structural criterion (C) and the density of the [NO₃]⁻ group (n/V). In the crystal structure of Rb₂Na(NO₃)₃, each NaO₈ trigonal bipyramid connects with five NO₃ groups (see Figure 1a). One NaO₈ polyhedron shares its six equatorial oxygen atoms with three of the five separate NO₃ groups to form a flat NaO₆–NO₃ layer. The three neighboring NO₃ groups put in order into a perfect parallel alignment to provide a major contribution to the C factor. The other two NO₃ groups are inclined to the NaO₆–NO₃ layer, giving additional contributions to the C factor. Following the computing method used previously [27,29], the calculated C factor for Rb₂Na(NO₃)₃ is to be 82%.

To obtain further understanding of the SHG effects as directed by the density of NLO-active groups and the arrangement of the NLO-active groups, the calculated coefficient of NLO effect for Rb₂Na(NO₃)₃ was compared with those for other nitrates NLO materials (see

Table 1. Nonlinear optical (NLO) effects of Rb₂Na(NO₃)₃, [Pb₄(OH)₄](NO₃)₄ [35], [LaPb₈O(OH)₁₀(H₂O)](NO₃)₇ [36], LaPb₈O(OH)₁₀(H₂O)](NO₃)₇ 2H₂O [36], Sr₂(OH)₃NO₃ [37], and K₂La(NO₃)₅ 2H₂O [55].

Crystals	SHG Coefficient (Visible) (× KDP)	Structural Criterion C	Density of [NO3] (n/V) (Å−3)	(n/V) × C (Å−3)
Rb2Na(NO3)3	5	0.82	0.0128	0.0105
[Pb4(OH)4](NO3)4	0.7	0.17	0.0109	0.0018
[LaPb8O(OH)10(H2O)](NO3)7	1.3	0.32	0.0087	0.0028
[LaPb8O(OH)10(H2O)](NO3)7 2H2O	1.1	0.31	0.0081	0.0025
Sr2(OH)3NO3	3.6	1.00	0.0075	0.0075
K2La(NO3)5 2H2O	2.4	0.36	0.0135	0.0049

). Although the density of [NO₃]⁻ and the structural criterion C for Rb₂Na(NO₃)₃ are not the largest in these six NCS nitrates, the SHG coefficient of Rb₂Na(NO₃)₃ is the largest. Although the structural criterion C for Rb₂Na(NO₃)₃ is lower than that of Sr₂(OH)₃NO₃ (100%) [37], the SHG coefficient of Rb₂Na(NO₃)₃ is larger than that of Sr₂(OH)₃NO₃. On the other hand, Rb₂Na(NO₃)₃ has a much higher density of [NO₃]⁻ groups compared to Sr₂(OH)₃NO₃. Though K₂La(NO₃)₅ 2H₂O has the highest density of [NO₃]⁻ groups, a small structural criterion C arising from its unfavorable arrangement of the [NO₃]⁻ groups in the structure lead to a moderate SHG coefficient (see Figure S1). Thus, balancing the density of NLO-active groups and the structural criterion C is very important to the SHG coefficient. A relatively high density of [NO₃]⁻ groups and a relatively large structural criterion values of C factors produce the strong NLO effect of Rb₂Na(NO₃)₃.

2.5. Theoretical Calculations

Band structure calculations reveal that Rb₂Na(NO₃)₃ has an indirect band gap of 3.24 eV (see Figure S2), which is smaller than the experimental value of 4.74 eV. The tendency for electronic band structure calculations with the DFT method to underestimate the band gap has been well documented [56,57,58]. Thus, the scissor value of 1.5 eV for Rb₂Na(NO₃)₃ is applied to the subsequent SHG calculations based on the Perdew–Burke–Ernzerhof (PBE) functional.

The total and partial densities of states (DOS and PDOS) for Rb₂Na(NO₃)₃ are presented in Figure 5. The valence bands (VB) spanning over −30.0 to −15.0 eV originate predominately from Rb 5s, Na 2p, O 2s, N 2s, and N 2p states as well as, to a lesser extent, from O 2p and Rb 4p states. VBs ranging from −10.0 to −5.0 eV are mostly formed by Rb 4p, N 2p, O 2p, and O 2s states hybridized with small amounts of Na 2p and N 2s states. VBs from −5.0 eV to the Fermi level (EF) are mostly from the contributions of O 2p states. O 2p and N 2p states make up the conduction bands (CB) between EF and 5.0 eV. CBs ranging from 5.0 to 10.0 eV mainly consist of Rb 5s and Rb 4p states with a small portion of Na 2p, O 2p, and N 2s states. Because linear and nonlinear optical properties are mainly determined by the states close to the forbidden band that largely consists of the p orbital of the [NO₃]⁻ groups, the electron transition is provided by inside excitation of the [NO₃]⁻ group, indicating a great contribution from the NO₃ polyhedra to the SHG coefficients.

Considering the spatial symmetry and the Kleinman’s full permutation symmetry condition for a lossless nonlinear medium, crystal class with mm2 point group has only three independent nonvanishing elements, i.e., d₃₁ (=d₁₅), d₃₂ (=d₂₄), and d₃₃. The calculated nonlinear coefficients are shown in Figure 6. At the pumping wavelength of 1064 nm, the calculated d_ij (Einstein shortened notation of the NLO coefficient ${\mathsf{\chi }}_{ijk}^{(2)}$) coefficient values of PBE are as follows: d₁₅ = d₃₁ = 3.48 pm/V, d₂₄ = d₃₂ = 0.83 pm/V, and d₃₃ = 2.64 pm/V. The discrepancy between calculated and experimental d_ij coefficient may arise from both the theoretical method and the experimental measurement. At the theoretical side, it’s found that conventional density functional method like B3LYP overestimations of χ⁽¹⁾ [59], which straightforward overestimate the χ⁽²⁾ according to Equation (6). Although we have applied the scissor-operation to modify the underestimated band gap given by the PBE exchange-correlation functional, it may still overestimate χ⁽¹⁾. We also try the hybrid functional HSE06 and obtain the d_ij components: d₃₁ = 1.85 pm/V, d₃₂ = 0.88 pm/V, and d₃₃ = 1.35 pm/V. It is a great improvement compared to the PBE functional, but is somewhat over-rectified. Furthermore, the anharmonic oscillator (AHO) model uses the atomic resonance frequency to estimate the local field factor, which could not offer the accurate in-crystal polarizing field effect. At the experiment side, our measurement is performed on powder samples while the theoretical models are built on the hypothesis of a perfect single crystal. Higher level theoretical methods, like explicitly calculating the d_ij by using electron correlation [60] and more accurate determination of the nonlinear coefficient on a single crystal will be the focus of future research.

3. Materials and Methods

3.1. Materials and Synthesis

Single crystals of Rb₂Na(NO₃)₃ were grown through solid state reactions. A mixture of RbNO₃ (Alfa Aesar, 99%), (Alfa Aesar, Seoul, Korea), NaNO₃ (Alfa Aesar, 99%), and NH₄NO₃ (Alfa Aesar, 99%) in a molar ratio of 4:2:1 was thoroughly ground in a mortar and pestle and transferred into a platinum crucible. The reaction mixture was heated at 300 °C for one day until a transparent melt was formed. The melt was allowed to cool slowly at a rate of 3 °C/h to the final crystallization temperature, 150 °C. After that the obtained product mixture was quenched to room temperature. Colorless transparent crystals shown in Figure S3 in the Supplementary Materials were obtained. Pure polycrystalline samples of Rb₂Na(NO₃)₃ were synthesized through the solid state reactions from the stoichiometric mixture of RbNO₃ and NaNO₃ at 150 °C for 2 days. Synthesized Rb₂Na(NO₃)₃ has been deposited to the Noncentrosymmetric Materials Bank http://ncsmb.knrrc.or.kr.

3.2. Single Crystal Structure Determination

Single crystal X-ray diffraction data of Rb₂Na(NO₃)₃ were collected at room temperature on a Bruker SMART BREEZE diffractometer (Bruker, Karlsruhe, Germany) equipped with a 1K CCD area detector using graphite monochromated Mo Kα radiation. The structure was solved by the direct method and refined by full-matrix least-squares fitting on F² using SHELX-97 [61]. The refined structure was verified using the ADDSYM algorithm from the program PLATON [62], and no higher symmetries were found. CCDC 1449459 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/conts/retrieving.html (or from the CCDC, 12 Union Road, Cambridge CB2 1EZ, UK; Fax: +44-1223-336033; E-mail: [email protected]). Relevant crystallographic data and details of the experimental conditions for Rb₂Na(NO₃)₃ are summarized in

Table 2. Crystallographic Data for Rb₂Na(NO₃)₃.

CCDC NO	1449459
formula	Rb2Na(NO3)3
fw	379.96
crystal system	Orthorhombic
space group	Pmc21 (No. 26)
a (Å)	5.313(2)
b (Å)	9.077(4)
c (Å)	9.700(4)
V (Å3)	467.8(4)
Z	2
ρcalcd (g/cm3)	2.697
T (K)	298.0(2)
λ (Å)	0.71073
R(F) a	0.029
Rw(Fo2) b	0.069
Flack parameter	0.017(16)

^a R(F) = Σ||F_o| − |F_c||/Σ|F_o|. ^b R_w(F_o²) = [Σw(F_o² − F_c²)²/Σw(F_o²)²]^1/2.

. Atomic coordinates and isotropic displacement parameters are listed in

Table 3. Atomic Coordinates, Isotropic Displacement Parameters, and Bond Valence Sums for Rb₂Na(NO₃)₃.

	x	y	z	Ueq a	BVS
Rb(1)	0.5	0.08284 (7)	0.53258 (6)	0.0278 (2)	1.22
Rb(2)	0.5	−0.37843 (7)	0.70652 (6)	0.0290 (2)	1.14
Na(1)	1	0.2987 (3)	0.7520 (3)	0.0312 (6)	1.13
N(1)	1	−0.0531 (6)	0.7396 (6)	0.0238 (11)	5.04
N(2)	0.5	−0.2517 (6)	0.3837 (6)	0.0249 (11)	4.94
N(3)	1	0.4120 (6)	0.4519 (6)	0.0234 (12)	5.03
O(1)	1	0.0592 (6)	0.6636 (6)	0.0365 (12)	2.11
O(2)	0.7910 (10)	−0.1055 (5)	0.7734 (6)	0.0557 (12)	2.08
O(3)	0.2975 (7)	−0.2289 (4)	0.4447 (4)	0.0394 (9)	2.01
O(4)	0.5	−0.2987 (6)	0.2620 (5)	0.0343 (11)	2.09
O(5)	1	0.5419 (6)	0.8311 (6)	0.0340 (11)	2.13
O(6)	0.7977 (10)	0.3903 (5)	0.5120 (6)	0.0573 (12)	1.97

^a U_eq is defined as one third of the trace of the orthogonalized U_ij tensor.

. Selected bond lengths and angles for Rb₂Na(NO₃)₃ are listed in Table S1 in the Supplementary Materials.

3.3. Powder X-Ray Diffraction (PXRD)

The PXRD data were obtained on a Bruker D8-Advance diffractometer (Bruker, Karlsruhe, Germany) using Cu Kα radiation at room temperature with 40 kV and 40 mA in the 2θ range of 5–70° with a scan step width of 0.05° and a fixed time of 0.2 s. The PXRD pattern for Rb₂Na(NO₃)₃ showed a very good agreement with the calculated data from the single-crystal model.

3.4. Thermal Analysis

The thermogravimetric/differential thermal analysis (TG/DTA) scans were performed on a NETZSCH STA 449C simultaneous analyzer (NETZSCH, Bavaria, Germany). The reference (Al₂O₃) and polycrystalline Rb₂Na(NO₃)₃ were enclosed in separate alumina crucibles and heated from room temperature to 500 °C at a rate of 10 °C/min under a constant flow of nitrogen gas. The TG residues were visually inspected and then analyzed by powder X-ray diffraction (Bruker, Karlsruhe, Germany) after heating.

3.5. Infrared (IR) Spectroscopy

IR spectrum of the sample was recorded on a Thermo Scientific Nicolet 6700 FT-IR spectrometer (Thermo Electron Corporation, Waltham, MA, USA) in the 400–4000 cm⁻¹ range, with the sample embedded in a KBr matrix.

3.6. UV-Vis Diffuse Reflectance Spectroscopy

UV-Vis diffuse reflectance spectral data were obtained on a Varian Cary 500 scan UV-Vis-NIR spectrophotometer (Varian, Palo Alto, CA, USA) over the spectral range 200–2500 nm at room temperature. The reflectance spectrum was transformed into the absorbance data using the Kubelka–Munk function [50,51].

3.7. Scanning Electron Microscope (SEM)/Energy-Dispersive Analysis by X-ray (EDX)

SEM/EDX analyses have been performed using a Hitachi S-3400N/Horiba Energy EX-250 instruments (Hitachi, Tokyo, Japan). EDX for Rb₂Na(NO₃)₃ reveals an approximate Rb:Na ratio of 2.1:1.0.

3.8. Second-Harmonic Generation (SHG) Measurements

Powder SHG measurements were performed using a modified Kurtz and Perry NLO measurement system (Jinsung, Daejeon, Korea) with 1064 nm radiation [52]. A more detailed explanation of the methods and the apparatus utilized has been published previously [2].

3.9. Computational Details

The density functional theory (DFT) calculations for the experimental crystal structure of Rb₂Na(NO₃)₃ were carried out using the CASTEP code [63]. The generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) [64] and the hybrid functional HSE06 [65] were chosen. The converge criteria of energy was 10⁻⁵ eV/atom. The cutoff energy for the plane wave basis was set to be 850 eV. The k-points sampling in the Brilliouin zone was placed to be 3 × 3 × 4 according to the Monkhorst–Pack scheme [66]. The valences of composed atoms were as follows: Rb 4s² 4p⁶ 5s¹; Na 2s² 2p⁶ 3s¹; N 2s² 2p³; O 2s² 2p⁴. The calculated second-order susceptibilities are indicated in terms of the first-order susceptibilities as follows:

$${\mathsf{\chi }}_{ijk}^{(2)}(-{\mathsf{\omega }}_3;{\mathsf{\omega }}_1,{\mathsf{\omega }}_2)=F^{(2)}{\mathsf{\chi }}_{ii}^{(1)}({\mathsf{\omega }}_3){\mathsf{\chi }}_{jj}^{(1)}({\mathsf{\omega }}_1){\mathsf{\chi }}_{kk}^{(1)}({\mathsf{\omega }}_2)$$

(5)

This was obtained from a classical anharmonic oscillator (AHO) model [67], in which F⁽²⁾ is local field correction and is defined as:

$$F^{(2)}=\frac{m{\mathsf{\epsilon }}_0^2{\mathsf{\varpi }}_0^2}{N^2{e}^{3}d}$$

(6)

where d is the lattice constant, e is the electron charge, N is the atomic density, ${\mathsf{\varpi }}_0$ is the atomic resonance frequency, ε₀ is the permittivity of free space, and m is the electron mass. The first-order susceptibility at the low-frequency region is given by χ_ii⁽¹⁾(ω) = [ε(ω)_i − 1]/4π, and the dielectric function ε(ω)_i are obtained from the optical properties calculation of CASTEP.

4. Conclusions

A NCS mixed alkali metal nitrate NLO material, Rb₂Na(NO₃)₃, has been synthesized through conventional solid state reactions. The material features an anionic layered structure. Powder SHG measurements reveal that Rb₂Na(NO₃)₃ is phase-matchable (type I) with a very large SHG response of approximately five times that of KDP. The strong SHG efficiency of the material is attributed to the high density and the optimized arrangement of the NLO-active NO₃ groups in the structure, which is in good agreement with the results obtained from the theoretical calculations. In addition, Rb₂Na(NO₃)₃ exhibits a wide transparent region ranging from UV to near IR and melts congruently. On the basis of these arguments, this compound is a potential candidate for applications in novel UV-NLO materials. Our future research efforts will be devoted to growing large crystals of Rb₂Na(NO₃)₃ to further study their optical properties, such as refractive indices, the Sellmeier equations, second-order NLO coefficients, and laser damage threshold.