Novel Non-Centrosymmetric NdSr 4 O(BO 3 ) 3 Borate and Nd(Ca 1 − x Sr x ) 4 O(BO 3 ) 3 Solid Solutions: Preparation, Crystal Structures, Thermal Expansion and Optical Properties

: A novel non-centrosymmetric NdSr 4 O(BO 3 ) 3 borate and solid solutions of Nd(Ca 1 − x Sr x ) 4 O (BO 3 ) 3 ( x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 1.0) were synthesized by solid-state reactions as well as crystallization from a melt. The crystal structures of the Nd(Ca 1 − x Sr x ) 4 O(BO 3 ) 3 solid solutions with x = 0.2, 0.5 and 1.0 were determined from single crystal X-ray diffraction data and reﬁned in the monoclinic space group Cm to R obs = 0.028, 0.034 and 0.028, respectively. The thermal expansion of the samples with x = 0, 0.2 and 0.5 was investigated using powder high-temperature X-ray diffraction in the temperature range of 25–1000 ◦ C. A similarity of the thermal and compositional (Ca-Sr substitution) deformations of Nd(Ca 1 − x Sr x ) 4 O(BO 3 ) 3 solid solutions is revealed: Heating of Nd(Ca 0.5 Sr 0.5 ) 4 O(BO 3 ) 3 by 1 ◦ C leads to the same deformations of the crystal structure as increasing the amount of Sr atoms in Nd(Ca 0.5 Sr 0.5 ) 4 O(BO 3 ) 3 by 0.26 at% Sr. The SHG signal of the series of Nd(Ca 1 − x Sr x ) 4 O(BO 3 ) 3 solid solutions has a maximum at approximately x = 0.2.

The crystal structure of LnCa 4 O(BO 3 ) 3 consists of M1-M3 octahedra (M = Ca 2+ , Ln 3+ ) and BO 3 trigonal planar groups [1,2,20]; the M3 polyhedra can be described as eightfold polyhedra [13,21].Ions occupied these positions partially orderly: rare earths elements filled mainly the M1 positions, calcium-M2 and M3.Currently, there are studies of structures in which Ca 2+ ions are replaced by other metal ones, mainly Sr 2+ ; the effect of these Crystals 2023, 13, 1395 2 of 18 substitutions on various properties has been studied [22][23][24].According to Liu et al. [22], the NLO properties of GdCa 4 O(BO 3 ) 3 crystals can be significantly improved by doping with 4% Sr 2+ .The SHG efficiency achieved with Sr-doped and undoped GdCa 4 O(BO 3 ) 3 was 37 and 28%, respectively.It was shown in [24] that 35% of Sr ions can be incorporated instead of Ca into Gd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions.Moreover, by adjusting the Sr content in La(Ca 1−x Sr x ) 4 O(BO 3 ) 3 crystals (x = 0-0.4), the optical birefringence can be controlled and the blue light can be obtained in the range of 495-473 nm through type-I NCPM SHG of the corresponding fundamental wavelengths [23].Wide ranges of Ca → Sr substitution are due to the closeness of the ionic radii of Ca 2+ and Sr 2+ (1.14 Å and 1.32 Å, respectively, for coordination number 6 [25]) and this maintains the congruent melting property, enabling the production of high-quality crystals.At the same time, the combination of coupled substitution with Na and REE is very limited, and the combination of Ca with Sr, Na and Gd could not be synthesized [24].
Some studies on LnCa 4 O(BO 3 ) 3 have focused on a variety of properties: melting points [2,21,26], thermal expansion [27], photoluminescence [28][29][30][31], thermal conductivity [27], dielectric, elastic and piezoelectric behavior [26,32,33] and magnetism [20,34].However, thermal expansion of the LnCa 4 O(BO 3 ) 3 family is poorly studied; there are only thermal expansion coefficients along the crystallographic axes for GdCa 4 O(BO 3 ) 3 [27], which is insufficient to characterize an anisotropy of thermal expansion for a monoclinic crystal.In the case of oblique crystals, it is necessary to calculate the principal values of the thermal expansion tensor in order to study the expansion anisotropy.In addition, LnCOB has shown itself to be a promising material for efficient non-linear frequency conversion through non-critical phase matching (NCPM), and ongoing research is exploring its potential applications in optical technology [23].The family of rare earth calcium oxoborates, LnCOB, contains promising candidates for pyro-and piezoelectric applications; their use is not limited to phase transitions [24].Due to its congruent melting and absence of phase transitions, it can be grown from the melt directly and used in pyro-and piezoelectrics.
Here, in order to investigate the influence of cation substitutions on NLO properties and to expand the RCOB (R = REE) family, we report the results of synthesis and complex investigations of new NLO Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions and a new NdSr 4 O(BO 3 ) 3 compound.In the series of NdCa 4 O(BO 3 ) 3 compounds, it was possible to almost double the Ca → Sr substitution limits for Nd (x is approximately 0.7) in comparison to Gd (x = 0.35) and La (x = 0.4) [24].In addition, a new non-centrosymmetric NdSr 4 O(BO 3 ) 3 compound obtained in the present studies can be considered as the prototype of a new REESr 4 O(BO 3 ) 3 series, where doped additives can be introduced into the position of a rare earth element to study the luminescent properties of these multifunctional materials.

Synthesis
Polycrystalline samples of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 (x = 0; 0.1; 0.2; 0.3; 0.4; 0.5; 0.7; 0.8; 0.9; 1) were synthesized by multi-step solid-state reactions from CaCO 3 , SrCO 3 , Nd 2 O 3 and H 3 BO 3 (99.90%purity).Boric acid was added with an excess of 3% as noted in [24].To remove the adsorption moisture, the reagents were pre-calcined: strontium and calcium carbonate at 600 • C/6 h, neodymium oxide at 800 • C/3 h.After homogeneous grinding and mixing in an agate mortar for 1 h, tablets were pressed from the powder using a hydraulic press at a pressure of 80 kg/cm 2 , after the tablet was heated at 900 • C for 9 h.The polycrystalline products with the common formula Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 were synthesized by a three-step sintering process.The first step was heating tablets in a platinum crucible at 1200 • C and exposing them for 30 h with slow cooling in the Nabertherm HTC furnace.In the second step, heating was carried out to 1300 • C for 60 h, followed by slow cooling in the furnace by switching off the furnace.The last step was heating at 1350 • C with exposure for half an hour.All powder samples were examined by means of X-ray powder diffraction (XRD).To obtain small single crystals, the samples were heated in platinum crucibles above melting temperature of 1430 • C for half an hour, after which they were slowly cooled in the furnace.

Powder X-ray Diffraction
Powder diffraction data of the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 samples after three heat treatments were collected using a Rigaku MiniFlex II diffractometer (CuKα, 2θ = 10-70 • , step 0.02 • ).The phase composition was determined using PDXL-integrated X-ray powder diffraction software and PDF-2 2016 (ICDD) database [35].Quantitative phase analysis of the samples and unit cell parameters of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions were refined by Rietveld method in the RTT program software [36].X-ray powder diffraction patterns of the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 samples after heat treatment at 1300 • C are given in Figure S1.

Single Crystal X-ray Diffraction
Single crystals of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 , x = 0.2, 0.5 were selected in polarized light using an optical microscope and attached to a glass fiber using epoxy glue.The experimental data were collected on a Bruker Apex II diffractometer utilizing MoKα radiation.Lorentz and polarization corrections were applied.The absorption correction based on a crystal shape was performed.The structures were solved using a charge-flipping method [37] implemented in JANA2006 [38].The structures could be refined to R obs = 0.028, 0.034 and 0.28 for x = 0.2, 0.5 and 1.0, respectively.Details of data collection and structure refinement are summarized in Table 1.Atomic coordinates, occupancies and atomic anisotropic displacement parameters are given in Tables S1-S6, selected bond lengths are in Table S7.Further details of the crystal structure investigations can be obtained from the Cambridge Structural Database by quoting the depository numbers CSD 2286252 (NdCa 3.2 Sr 0.8 O(BO 3 ) 3 ), 2286231 (NdCa 2 Sr 2 O(BO 3 ) 3 ) and 2286250 (NdSr 4 O(BO 3 ) 3 ).Data visualization was performed with the Vesta 3 [39] software.

High-Temperature Single-Crystal X-ray Diffraction
The temperature-dependent structural behavior of Nd(Ca 0.8 Sr 0.2 ) 4 O(BO 3 ) 3 solid solution (x = 0.2) under heating in the air was studied in situ by high-temperature single-crystal X-ray diffraction using a XtaLAB Synergy-S diffractometer (Rigaku Oxford Diffraction, Japan) operated with monochromated MoKα radiation (λ[MoKα] = 0.71073 Å) at 50 kV and 40 mA and equipped with an HyPix-6000HE detector with a unique high-temperature FMB Oxford system.The sample heating is performed using a gas blower up to 1000 (±1) • C, which consists of a hot air generator controlled by a Eurotherm regulator and gas flow controller.For this experiment, the single crystal with an approximate size of 30 µm × 20 µm × 40 µm was mounted on the glass fiber, which was placed into the quartz capillary.Diffraction data were collected at different temperatures without changing the orientation of the crystal in the range of 27-1000 • C with a temperature step of 100 • C. The crystal structures were refined at 11 temperatures, including room temperature after heating.Crystal data and experimental details for 6 are given in Table S8, selected bond lengths are in Table S9.Anisotropic displacement parameters were refined for all atoms.

High-Temperature Powder X-ray Diffraction
Homogeneous solid solutions of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 , x = 0, 0.2, 0.5, were investigated by X-ray powder diffraction at high temperatures using the Rigaku Ultima IV diffractometer (CuKα 1+2 , 40 kV/30 mA, 25−1000 • C, temperature step of 20 • C, Rigaku R-300 high-temperature attachment).A Pt-Pt/Rh thermocouple was used to control the temperature.As an example, a 2D-top view of HTXRD pattern of the sample Nd(Ca 0.5 Sr 0.5 ) 4 O(BO 3 ) 3 is presented in Figure S2.Multi-stage processing of experimental data was carried out using the RietveldToTensor 2.0 software [37].The first step included the refinement of the unit cell parameters and quantitative phase composition at different temperatures by the Rietveld method using the room-temperature crystallographic information file (CIF) obtained in this work from single-crystal XRD data as a model for Rietveld refinement.Then temperature dependences of unit-cell parameters and volume were approximated by polynomial functions for all samples (Table S10), the components of the tensor (α ij ) of thermal expansion were determined in a Cartesian crystal-physical coordinate system using the coefficients of approximation and finally drawing figures of thermal expansion coefficients (α) were performed in the RietveldToTensor software.A detailed description of the data processing and calculation of eigenvalues of thermal expansion tensor is given in [36].Standard orientation of the crystallographic axes (set II for monoclinic systems) with respect to the crystal-physical axes has been used.The eigenvalues of the tensors of thermal expansion and TECs along crystallographic axes were calculated (see Table 3), and the latter are compared to the results obtained in [27].

Thermal Analysis
The high-temperature behavior was studied by differential scanning calorimetry (DSC) and thermogravimetry (TG) on a NETZSCH STA 429 thermal analyzer.Measurements were performed on tablets containing approximately 20-50 mg placed in a Pt-Rh crucible.The heating and cooling rate was 20 • C/min in the heating range of 20-1450 • C and then cooled at 900 • C. For example, microphotographs of the tablet of NdCa 4 O(BO 3 ) 3 in the Pt crucible before (left) and after (right) heating to 1445 • C are given in Figure S3.The temperatures of the thermal effects were estimated as the first derivative onset temperatures, when possible, and as maximum temperatures in the case of multiple peaks overlapping.According to the TG data, very small mass losses gradually occurred during heating, apparently due to the high heating rate.

Spectroscopy
UV-Vis absorption spectra were measured using a PerkinElmer Lambda 1050 spectrophotometer equipped with a 150-mm integrated sphere.Barium sulfate (BaSO 4 ) sample was used as a blank.Raman spectra were collected with a Horiba LabRam HR800spectrometer at 632.8 nm excitation.

Second Harmonic Generation (SHG) Measurements
SHG measurements were made using the Kurtz−Perry method against polycrystalline α-quartz (grain size of 0.07−0.5 µm).A 31-A femtosecond Ti:Sapphire amplifier with a pulse energy of 1 mJ, pulse duration of 35 fs and repetition rate of 1 kHz as a source of radiation at λω = 800 nm was used.The SHG signal was registered in reflection mode and measured by a spectrometer based on a single monochromator M266 and multichannel CCD detector UC-12T3.

Powder X-ray Diffraction Studies
After heat treatment at 1200 • C, the samples of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 were homogeneous in the range of x Sr compositional parameter x = 0-0.3,and peaks corresponded to the XRD patterns of LnCa 4 O(BO 3 ) 3 borate in accordance with the data (PDF-2 ICDD).The samples with x = 0.4 and 0.5 contained a few additional peaks of Sr 3 B 2 O 6 .After heat treatment at 1300 • C, the samples of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 were homogeneous up to x = 0.5 and the sample with x = 0.7 contained approximately 7 wt % of Sr 3 B 2 O 6 as an impurity (Figure S1).The substitution of Ca by Sr shows that Sr can be incorporated up to an amount of 70 at.% and homogeneous solid solutions were found for x Sr = 0-0.7.With further increasing content, the peaks of Sr 3 B 2 O 6 and NdBO 3 could appear in the PXRD patterns: in the sample with x Sr = 0.8, the content of the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solution (x ~0.7) decreased to approximately 65 wt % respectively, while the Sr 3 B 2 O 6 content increased to approximately 25 wt % and additional peaks of unidentified phase were observed (Figure S1).In the PXRD pattern of the sample with x = 0.9, the content of the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solution (x ~0.7) decreased gradually to 50 wt %, Sr 3 B 2 O 6 and NdBO 3 appeared at approximately 25 and 25 wt %.After heat treatment at 1350 • C, the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions were homogeneous in the same region as the compositional parameter (x = 0.5); the sample with x = 0.7 also contained a solid solution and approximately 7% of Sr 3 B 2 O 6 borate.Multi-phase samples (x = 0.8, 0.9) melted and contained at least three phases: the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions (x ~0.7), Sr 3 B 2 O 6 and NdBO 3 .Thus, the miscibility range can be estimated to be x Sr ~0-0.7.This is almost twice the Ca → Sr substitutions in the Gd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 series [24].The PXRD pattern of novel NdCa 4 O(BO 3 ) 3 borate (x = 1) contained also the Sr 3 B 2 O 6 admixture in an amount of approximately 8 wt %.
The unit cell parameters of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions after heat treatment at 1300 • C increase almost linearly with the gradual growth of Sr 2+ content to x = 0.7 (Figure 1) according to the larger ionic radii of Sr 2+ ([6] 1.32 Å) ions in comparison to Ca 2+ ([6] 1.14 Å) ones [25].The parameter c increases most strongly, while a and b change insignificantly, and the monoclinic angle increases by 0.4 • .With a further increase in the content of strontium ions (x > 0.7), a multi-phase region appears in which the parameters remain practically unchanged to x = 1 (Figure 1

Crystal Structures of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 Solid Solutions
There are three M1-M3 sites for Nd and Ca and Sr cations, B1 and B2 and O1-O6 sites in asymmetric units in the series of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions (Tables S1-S6).The cations are distributed over the three sites (Tables 2 and S1-S3): in the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions (x = 0.2, 0.5) Nd 3+ ions are situated at the M1 (2a) and M3 (4b) crystallographic sites; the Sr 2+ ions occupy the two M2 (4b) and M3 (4b) sites, while Ca 2+ occupy all three sites; in the new NdSr 4 O(BO 3 ) 3 compound cations are ordered, Nd 3+ ions occupy only the M1 (2a) site, Sr-M2 (4b) and M3(4b) ones.This distribution of the cations over the three sites agrees with the bond valence sum (BVS) of the sites (Table 2).For instance, in the case of solid solutions, the BVS (M1) is less than 3, since, in addition to Nd 3+ , the position is partially filled with Ca 2+ , while in the NdSr 4 O(BO 3 ) 3 borate, the BVS (M1) is closer to 3 due to ordering cation distribution.
The crystal structures of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 borates consist of four groups: M1, M2, M3 polyhedra and two independent isolated [BO 3 ] − groups (Figure 2a).In all structures, M1 and M2 are both six-coordinated polyhedra and M3 is an eightfold-coordinated one.While two of the eight M3-O bond lengths are significantly longer than the other six (Table S7), the M3 site may be treated as eight-coordinated.In the compounds, the 'long' M3-O bond lengths are all greater than 2.90 Å whereas the other bonds range 2.35-2.65 for x = 0.2 and 2.39-2.71Å for x = 0.5 (Table S7).The M1-M3 polyhedra are either edge or corner-connected.There are three edge-linked polyhedral chains along the c axis: M1 octahedra are connected via O1-O6 edges to form single chains; M2 and M3 polyhedra-via O2-O3 and O4-O5 edges to form double chains (Figure 2a, bottom), Crystals 2023, 13, 1395 7 of 18 respectively.These chains are connected by the vertices of the polyhedra to form a cationic framework.The M3O 8 polyhedra share edges with trigonal planar [BO 3 ] − groups, which are tilted at different angles relative to the ab-plane.The crystal structures of Nd(Ca1−xSrx)4O(BO3)3 borates consist of four groups: M1, M2, M3 polyhedra and two independent isolated [BO3] − groups (Figure 2a).In all structures, M1 and M2 are both six-coordinated polyhedra and M3 is an eightfold-coordinated one.While two of the eight M3-O bond lengths are significantly longer than the other six (Table S7), the M3 site may be treated as eight-coordinated.In the compounds, the 'long' M3-O bond lengths are all greater than 2.90 Å whereas the other bonds range 2.35-2.65 for х = 0.2 and 2.39-2.71Å for х = 0.5 (Table S7).The M1-M3 polyhedra are either edge or corner-connected.There are three edge-linked polyhedral chains along the c axis: М1 octahedra are connected via О1-О6 edges to form single chains; M2 and M3 polyhedravia O2-O3 and O4-O5 edges to form double chains (Figure 2a, bottom), respectively.These chains are connected by the vertices of the polyhedra to form a cationic framework.The M3O8 polyhedra share edges with trigonal planar [BO3] − groups, which are tilted at different angles relative to the ab-plane.Upon the Ca → Sr substitutions, the average bond length in the M1O6 octahedra is practically constant.It increases by 0.03 Å, while the average bond lengths in M2O6 and in M3O8 polyhedra increase by 0.08 Å and 0.09 Å, i.e., approximately three times more (Tables 2 and S7).The <M2-O> average bond length increases from 2.354 Å [20] to 2.435 Å, <M3-O>-from 2.556 Å to 2.65 Å, while the <M1-O> bond length in M1O6 polyhedra-from 2.40 to 2.42 Å (Figure 3 bottom left, Tables 2 and S7).Individual bond lengths change more sharply a few of them are even reduced, such as d(M1-O4) Upon the Ca → Sr substitutions, the average bond length in the M1O 6 octahedra is practically constant.It increases by 0.03 Å, while the average bond lengths in M2O 6 and in M3O 8 polyhedra increase by 0.08 Å and 0.09 Å, i.e., approximately three times more (Tables 2 and S7).The <M2-O> average bond length increases from 2.354 Å [20] to 2.435 Å, <M3-O>-from 2.556 Å to 2.65 Å, while the <M1-O> bond length in M1O 6 polyhedrafrom 2.40 to 2.42 Å (Figure 3 bottom left, Tables 2 and S7).Individual bond lengths change more sharply a few of them are even reduced, such as d(M1-O4) decreased by −0.03 Å.The bonds located close to the c axis and connecting the polyhedra in chains, for example, the M1-O6 bonds by 0.12 Å, M2-O1 by 0.08 Å, and the M3-O5 by 0.06 Å, are more elongated.This correlates with the maximum γ 33 axis of the compositional deformation tensor, which is also located close to the c axis (see § 3.3.2).While the contracting bonds are located near the perpendicular direction, the chains, expanding in a direction close to the c axis, have to contract in the framework slightly.
Сa 2+ by Sr 2+ ions in the M1-M3 positions.Since the M1 position is predominantly occupied by Nd 3+ ions, the substitution does not strongly affect the average bond length in the M1O6 polyhedron.As Ca 2+ ions are replaced by Sr 2+ ones, the latter are gradually distributed over the M2 and M3 positions approximately equally (Figure 3 top left), although among M1-M3 polyhedra it is the M3O8 polyhedron that is the largest and most distorted, i.e., it could be expected that it would be mainly filled with strontium.Note that in NdCa4O(BO3)3 M2O6 is the smallest and least distorted octahedron; however, it becomes larger than the M1O6 octahedron (Figure 3 bottom left), as Ca 2+ ions are replaced by Sr 2+ ones due to the larger size of Sr 2+ ions.In the case of solid solutions, the Ca, Sr and Nd cations are more randomly distributed over the M1-M3 sites than in the new NdSr4O(BO3)3 borate, in which they are completely ordered.In the RCOB family, REE and Ca cations are completely ordered in the case of large REE ions, such as La [40] (ICSD #93152); [41] (ICSD #180596), and they are disordered as the radii of REE decrease [20].For instance, for LuCa4O(BO3)3 [3] (ICSD #39718), the cationic distribution is the following: Occ M1 0.64, Ca 0.36; M2: Ca 0.82, Lu 0.18: M3 Ca 1.
Both [BO3] − triangles are tilted at different angles from the ab-plane.The tiltings of each of these borate groups are 12.66° and 34.59° for х = 0.2, 13.53° and 34.78° for х = 0.5, and 13.23 and 34.32 for x = 1.0.Some studies [34,42] found that the tilting of these borate groups changed regularly as the size of the lanthanide ions varied.There are O1 oxygen atoms not linked with boron.Hence, this crystal structure can be described in terms of oxy-centered polyhedra (Figure 1b).Additional oxygen atoms have [O(1)M(1)2M( 2)2] tetrahedral coordination and form corner-shared chains along the c axis.Compared to an increase in average bond lengths in M1-M3 polyhedra, the average The reason for structural changes is obvious in the partially ordered substitution of Ca 2+ by Sr 2+ ions in the M1-M3 positions.Since the M1 position is predominantly occupied by Nd 3+ ions, the substitution does not strongly affect the average bond length in the M1O 6 polyhedron.As Ca 2+ ions are replaced by Sr 2+ ones, the latter are gradually distributed over the M2 and M3 positions approximately equally (Figure 3 top left), although among M1-M3 polyhedra it is the M3O 8 polyhedron that is the largest and most distorted, i.e., it could be expected that it would be mainly filled with strontium.Note that in NdCa 4 O(BO 3 ) 3 M2O 6 is the smallest and least distorted octahedron; however, it becomes larger than the M1O 6 octahedron (Figure 3 bottom left), as Ca 2+ ions are replaced by Sr 2+ ones due to the larger size of Sr 2+ ions.In the case of solid solutions, the Ca, Sr and Nd cations are more randomly distributed over the M1-M3 sites than in the new NdSr 4 O(BO 3 ) 3 borate, in which they are completely ordered.In the RCOB family, REE and Ca cations are completely ordered in the case of large REE ions, such as La [40] (ICSD #93152); [41] (ICSD #180596), and they are disordered as the radii of REE decrease [20].For instance, for LuCa 4 O(BO 3 ) 3 [3] (ICSD #39718), the cationic distribution is the following: Occ M1 0.64, Ca 0.36; M2: Ca 0.82, Lu 0.18: M3 Ca 1.
Crystals 2023, 13, 1395 9 of 18 Both [BO 3 ] − triangles are tilted at different angles from the ab-plane.The tiltings of each of these borate groups are 12.66 • and 34.59 • for x = 0.2, 13.53 • and 34.78 • for x = 0.5, and 13.23 and 34.32 for x = 1.0.Some studies [34,42] found that the tilting of these borate groups changed regularly as the size of the lanthanide ions varied.
There are O1 oxygen atoms not linked with boron.Hence, this crystal structure can be described in terms of oxy-centered polyhedra (Figure 1b).Additional oxygen atoms have [O(1)M(1) 2 M(2) 2 ] tetrahedral coordination and form corner-shared chains along the c axis.Compared to an increase in average bond lengths in M1-M3 polyhedra, the average bond length in OM 4 tetrahedra increases weaker (Figure 3 bottom left) hence, an oxy-centered OM 4 tetrahedron could be considered as the rigid structural unit.A weak increase of the tetrahedron is caused by the substitution of smaller Ca atoms with larger Sr ones in the M2 position, which leads to the elongation of O1-M2 bonds and an increasing c parameter.
The major contribution to the optical non-linearity originates from the [BO 3 ] − groups that form delocalized π-type bonds perpendicular to the [BO 3 ] plane.The CaO 6 octahedra share corners with the [BO 3 ] group.The Sr-O-B bonding angles will be more stretched compared to the Ca-O-B bonding since the radius of the Sr 2+ ion is larger than that of the Ca 2+ ion, resulting in a more distorted p-type electron cloud in the BO 3 group.The M1-O4-B2 angles are equal to 109.8 • , 111.9 • and 113.4 • ; M3-O5-B2-121.8• , 123.1 • and 121.6 • for x = 0.2, 0.5 and 1, respectively.The other bond angles vary within the error.It is possible that these changes in angles affect the π-bonds of borate triangles and, accordingly, their non-linear optical properties.

Compositional versus Thermal Properties in Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 Solid Solutions
It is well known [43][44][45][46][47] that in compounds with a mainly ionic character, the replacement of a smaller cation by a bigger one changes the crystal structure in a similar way to heating.The coefficient of the thermal expansion α a = (1/a)(da/dt) is analogous to the coefficient of the compositional deformation γ a = (1/a)(da/dx), where x, the compositional parameter, is a characteristic of the chemical composition [46].Thus, we can calculate the compositional equivalents of the thermal expansion [46].

Thermal Expansion
The thermal behavior of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions with x = 0, 0.2 and 0.5 was investigated within a temperature range of 25-1000 • C from powder HTXRD data.Within this range, only the diffraction peaks of the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions were observed for x = 0 and 0.2, while for x = 0.5, with further heating above 900 • C, weak additional reflections marked as stars in Figure S2 appeared in the HTXRD patterns at approximately 900 • C. Apparently, this solid solution starts to decompose.By the way, anomalies in the HTXRD patterns at approximately 900 • C were noted in [27].
The unit cell parameters increase in heating from 25 • C to 1000 • C for all phases (Figure 4).For x = 0.5, a distinctive convex bend was found in the range of 400-600 • C in the temperature dependence of the monoclinic β angle.The deviation from the "linear" growth of the parameters can probably be caused by the redistribution of Nd 3+ , Ca 2+ and Sr 2+ cations over the M1-M3 sites with temperature.Temperature dependencies of the monoclinic unit-cell parameters and the volume of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 , x = 0.0, 0.2 and 0.5, were approximated independently using quadratic polynomials in the temperature range 25-800 • C, in which no phase transformations occur (Table S10).Thermal expansion coefficients along principal axes of the tensor and its orientation in the monoclinic plane defined by µ 1a angle equal to the angle between α 11 and a axis, as well as coefficients along crystallographic axes and volume for Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 (x = 0, 0.2, 0.5) solid solutions, are given in Table 3.The structures expand to their maximum along the α33 axis of the thermal expansion tensor, which is close to the c axis, where edge-shared chains of M1-M3 polyhedra extend in parallel in the cationic framework of the structure.Almost perpendicular to the c axis, the planes of the BO3 triangles are also located, which may be the reason for the greater expansion of the structure perpendicular to the planes of the triangles in accordance with the principles of high-temperature crystallochemistry of borates [48].The structures expand to their maximum along the α 33 axis of the thermal expansion tensor, which is close to the c axis, where edge-shared chains of M1-M3 polyhedra extend in parallel in the cationic framework of the structure.Almost perpendicular to the c axis, the planes of the BO 3 triangles are also located, which may be the reason for the greater expansion of the structure perpendicular to the planes of the triangles in accordance with the principles of high-temperature crystallochemistry of borates [48].

Formula Coefficient Tensor Region
Main parameters of the thermal expansion tensor α (×10  For quantitative comparison, one can use the compositional equivalent of the thermal expansion, α/γ (0.01 at% Sr/ • C) [46].The average compositional equivalent of the thermal expansion of the Nd(Ca 0.5 Sr 0.5 ) 4 O(BO 3 ) 3 structure is calculated to be 0.00026 at% Sr/ • C (Table 4, (α/γ) aver = α V ).This means that heating Nd(Ca 0.5 Sr 0.5 ) 4 O(BO 3 ) 3 by 1 • C leads to the same deformations as increasing the Sr 2+ ion content in the compounds by 0.26 at%.The closeness of (α/γ) 11 , (α/γ) 22 and (α/γ) 33 (0.28, 0.21 and 0.29 at%/ • C) to the average value (0.26 at%/ • C) indicates a high degree of similarity of the deformations occurring with changes in temperature and chemical composition.The thermal expansion of unit-cell parameters of the solid solution is discussed in Section 3.3.2and here we present data on the thermal expansion of bonds in the Nd(Ca 0.8 Sr 0.2 ) 4 O(BO 3 ) 3 solid solution.Individual and average bond lengths increase with temperature (Figure S4, Table S9).Changes in individual bond lengths vary from 0.012 Å to 0.072 Å.As a rule, stronger increases offer enough long bond lengths; for example, in an M1O 6 octahedron (M1-O6) bond, the length equal to 2.515 Å at room temperature increases by 0.072 Å, for others see Table S9.In spite of the difference in oxygen atoms surrounding the M1-M3 positions (C.N. range from six to eight), the change in the average <M-O> distances with temperature is almost the same for all of the polyhedra (approximately 0.003 Å between 300 K and 1273 K) (Figure 3, right, Table S9).The coefficients of thermal expansion calculated for average distances of the M-O bond lengths are <α In the oxy-centered tetrahedra, O1M 4 bond lengths weakly increase with temperature increasing (Figure 3, right, Table S9).Thermal expansion calculated for an average distance of the O1-M bond length is <α M1-O > = 9 × 10 −6 • C −1 that is one and a half times less than the <α M-O > in M1-M3 polyhedra.This indicates more significant rigidity in this group.
Individual B-O bond lengths within [BO 3 ] triangular groups practically do not change with temperature, and even most of them decrease slightly (Table S9).The average B-O bond lengths are also almost constant with temperature: the changes in the <B-O> lengths are −0.002 and −0.007 Å (Figure 3, right, Table S9).This contraction of bond lengths seems to be an artifact of the X-ray diffraction method.The effect of thermal motion on the estimation of bond lengths from a diffraction experiment is well known and described in detail [47,48,50,51].The B-O bonds seem to be a very rigid group, as the whole vibrates as a rigid body motion that leads to a slight decrease of the boron-oxygen distances with a temperature increase from XRD data.The refinement of the anisotropic parameters of thermal vibrations for the O atoms demonstrates that the vibration amplitudes increase approximately twice (1.9-2.5).Groups are located in a preferred orientation that dictates the anisotropy of thermal expansion in the direction perpendicular to plane triangles (Figure 3, right).
3.4.Melting Processes of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 Solid Solutions from DCS Data DSC curves on heating of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 samples demonstrate strong thermal endothermic effects corresponding to melting processes (Figure 5): onset temperatures for homogeneous solid solutions melting (x = 0-0.5)decreased from 1389 • C to 1246 • C (1389, 1356, 1299, 1267, 1266, 1246 • C for x = 0, 0.1, 0.2, 0.3, 0.4 and 0.5, respectively) as well as the temperature of maximum endothermic effects from 1455 • C to 1316 • C (1455, 1427, 1386, 1363, 1336 and 1316 • C) as Ca is replaced by Sr.This is due to the fact that the strength of the Ca-O bonds is shorter and therefore weaker than the Sr-O bond strength; therefore, with an increase in the content of Sr ions, a decrease in the temperature of solid solutions can be expected.The peaks corresponding to the melting of solid solutions are broadened, especially for x = 0.2 and 0.3 (Figure 5), due to melting processes occurring in a two-phase region-here recrystallization in the presence of a liquid phase takes place.Overlapping peaks can be split, as in samples with x = 0.1 and 0.2, where the first weak peaks (1396 and 1344 • C for x = 0.1 and 0.2) might be attributed to solidus temperature while the strong peaks are to liquidus temperature.It is noteworthy that the difference in liquidus and solidus temperatures decreases to x = 0.5.Multiphase samples melt by eutectic reaction.In the case of insignificant second phase amounts, peaks appeared before strong peaks, such as in the sample with x = 1, where there are two peaks, a small one at 1209 • C according to the eutectic point and a strong one at 1291 • C-liquidus point-in the binary eutectic NdSr 4 O(BO 3 ) 3 -Sr 3 B 2 O 6 system.In the case of three phases existence, first, apparently a small ternary eutectic mix melts at 1181 • C, then the endothermic effect at 1281 • C corresponds to liquius temperature in the ternary system, and the endothermic effect at 1281 • C could be interpreted as liquius temperature in the binary system (Figure 5).apparently a small ternary eutectic mix melts at 1181 °C, then the endothermic effect at 1281 °C corresponds to liquius temperature in the ternary system, and the endothermic effect at 1281 °C could be interpreted as liquius temperature in the binary system (Figure 5).On the cooling curves, crystallization occurs at a lower temperature due to hysteresis in the melting and crystallization temperatures.It is noteworthy that the hysteresis reaches a maximum in solid solutions up to 70-80 °C for x = 0.2, 0.3 and decreases in single chemical compounds and multiphase samples to 20-40 °C.

Raman Spectra
Raman spectra of the Nd(Ca1−xSrx)4O(BO3)3 samples are presented in Figure 6a.Peaks below 500 cm −1 associated with libration modes of the (BO3) matrix units.The wide peak around 600 cm −1 corresponds to the bending vibrations of (BO3) triangles.The most intensive peak in the region of 925 cm −1 is associated with symmetric stretching vibrations νs(BO3) [52].This peak consists of two bands, the position of the maxima of which shifts to the low-frequency region with an increase in the concentration of strontium in the samples (Figure 6b).The presence of two bands is probably due to two symmetrically independent boron atoms, as was shown in the structural part.In this case, with an increase in the Sr concentration, the position of both maxima shifts linearly towards low frequencies (Figure 6c).According to one of the theoretical models, the shift of the phonon band towards low frequencies can be associated with an increase in mass upon isovalent substitution in a solid solution [53].For example, this shift is observed in Ca3(BO3)2 and Sr3(BO3)2 crystalline samples [54].

Raman Spectra
Raman spectra of the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 samples are presented in Figure 6a.Peaks below 500 cm −1 associated with libration modes of the (BO 3 ) matrix units.The wide peak around 600 cm −1 corresponds to the bending vibrations of (BO 3 ) triangles.The most intensive peak in the region of 925 cm −1 is associated with symmetric stretching vibrations ν s (BO 3 ) [52].This peak consists of two bands, the position of the maxima of which shifts to the low-frequency region with an increase in the concentration of strontium in the samples (Figure 6b).The presence of two bands is probably due to two symmetrically independent boron atoms, as was shown in the structural part.In this case, with an increase in the Sr concentration, the position of both maxima shifts linearly towards low frequencies (Figure 6c).According to one of the theoretical models, the shift of the phonon band towards low frequencies can be associated with an increase in mass upon isovalent substitution in a solid solution [53].For example, this shift is observed in Ca 3 (BO 3 ) 2 and Sr 3 (BO 3 ) 2 crystalline samples [54].

Optical Bandgap
The absorption spectra show a set of bands that all correspond to neodymium transitions (Figure 7a).It should be noted that the concentration of Nd 3+ ions in the samples is so high that no luminescence is observed due to concentration quenching.In the spectral region below 250 nm, a blue edge of the transparency window is observed, which is associated with fundamental absorption.The position of the fundamental edge of optical absorption was used to determine the optical band gap using the Tauc plot graphics.It was found that there is a decrease in the optical band gap when calcium is substituted by strontium ions (Figure 7a).This is consistent with the theory of the influence of the mass of substituting ions on the band gap [53].

Second Harmonic Generation
SHG signal was recorded for the Nd(Ca1−xSrx)4O(BO3)3 samples under otherwise equal conditions, which makes it possible to qualitatively estimate the efficiency of light conversion into the second harmonic of the investigated solid solutions (Figure 8a).The obtained experimental results show that the optical nonlinearity of the Nd(Ca1−xSrx)4O(BO3)3 crystals can be improved with partial substitution of Sr 2+ ions for Ca 2+ ions in the crystal up to x = 0.2.To determine the SHG efficiency, the obtained results were compared with the results of crystalline quartz with the same particle size distribution (Figure 8b).Obviously, the synthesized solid solutions demonstrate an order of magnitude better ability to generate the second harmonic compared to crystalline quartz, although the SHG response shown in Figure 8b is indeed not typical.This is most likely due to the peculiarities of the polycrystalline samples, where microparticles are agglomerates of smaller particles.Probably, in the samples with different sizes of granules, not all agglomerates were separated into individual particles, which led to the dependence of SHG response.

Optical Bandgap
The absorption spectra show a set of bands that all correspond to neodymium transitions (Figure 7a).It should be noted that the concentration of Nd 3+ ions in the samples is so high that no luminescence is observed due to concentration quenching.In the spectral region below 250 nm, a blue edge of the transparency window is observed, which is associated with fundamental absorption.The position of the fundamental edge of optical absorption was used to determine the optical band gap using the Tauc plot graphics.It was found that there is a decrease in the optical band gap when calcium is substituted by strontium ions (Figure 7a).This is consistent with the theory of the influence of the mass of substituting ions on the band gap [53].

Optical Bandgap
The absorption spectra show a set of bands that all correspond to neodymium transitions (Figure 7a).It should be noted that the concentration of Nd 3+ ions in the samples is so high that no luminescence is observed due to concentration quenching.In the spectral region below 250 nm, a blue edge of the transparency window is observed, which is associated with fundamental absorption.The position of the fundamental edge of optical absorption was used to determine the optical band gap using the Tauc plot graphics.It was found that there is a decrease in the optical band gap when calcium is substituted by strontium ions (Figure 7a).This is consistent with the theory of the influence of the mass of substituting ions on the band gap [53].

Second Harmonic Generation
SHG signal was recorded for the Nd(Ca1−xSrx)4O(BO3)3 samples under otherwise equal conditions, which makes it possible to qualitatively estimate the efficiency of light conversion into the second harmonic of the investigated solid solutions (Figure 8a).The obtained experimental results show that the optical nonlinearity of the Nd(Ca1−xSrx)4O(BO3)3 crystals can be improved with partial substitution of Sr 2+ ions for Ca 2+ ions in the crystal up to x = 0.2.To determine the SHG efficiency, the obtained results were compared with the results of crystalline quartz with the same particle size distribution (Figure 8b).Obviously, the synthesized solid solutions demonstrate an order of magnitude better ability to generate the second harmonic compared to crystalline quartz, although the SHG response shown in Figure 8b is indeed not typical.This is most likely due to the peculiarities of the polycrystalline samples, where microparticles are agglomerates of smaller particles.Probably, in the samples with different sizes of granules, not all agglomerates were separated into individual particles, which led to the dependence of SHG response.

Second Harmonic Generation
SHG signal was recorded for the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 samples under otherwise equal conditions, which makes it possible to qualitatively estimate the efficiency of light conversion into the second harmonic of the investigated solid solutions (Figure 8a).The obtained experimental results show that the optical nonlinearity of the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 crystals can be improved with partial substitution of Sr 2+ ions for Ca 2+ ions in the crystal up to x = 0.2.To determine the SHG efficiency, the obtained results were compared with the results of crystalline quartz with the same particle size distribution (Figure 8b).Obviously, the synthesized solid solutions demonstrate an order of magnitude better ability to generate the second harmonic compared to crystalline quartz, although the SHG response shown in Figure 8b is indeed not typical.This is most likely due to the peculiarities of the polycrystalline samples, where microparticles are agglomerates of smaller particles.Probably, in the samples with different sizes of granules, not all agglomerates were separated into individual particles, which led to the dependence of SHG response.Finally, consider the features of the structure that may affect the optical nonlinearity.In addition to the already reported factors improving the optical nonlinearity in this borate family, such as a partial substitution of Yb for Y in YCa4O(BO3)3 [19] or doping of Sr for Ca in GdCa4O(BO3)3 [22], we believe that, in accordance with the anion group theory [55][56][57][58], the significant contribution to the NLO properties originates also from the BO3 groups that form delocalized π-type bonds perpendicular to the BO3 plane.Accordingly, special attention is therefore paid in borates to the orientation of the triangular groups [48, [58][59][60].In this family [BO3], triangular groups are located at a small angle to each other (see Figure 3).Another relatively new crystal chemistry factor that can affect the optical non-linearity is the additional oxygen atom, which is not bonded to the B atom.Its role in influencing the optical nonlinearity is not quite clear; however, its influence in [61] has already been noted, apparently for the first time.It is coordinated by metal atoms and forms a rigid O1M4 tetrahedron, which leads to distortion of cationic M polyhedra.This situation is described in detail in the case of Ca-Sr substitution in GdCOB, similar to Ca-Sr substitution in NdCOB (see Section 3.2).

Conclusions
Novel non-centrosymmetric Nd(Ca1−xSrx)4O(BO3)3 solid solutions and a new NdSr4O(BO3)3 compound with large second harmonic generation responses were synthesized by solid-state reactions and characterized by powder and single crystal X-ray diffraction in the wide range of temperatures.It turned out that Ca ions can be replaced by Sr ones up to approximately 70% which exceeds practically twice similar substitutions in the REE(Ca1−xSrx)4O(BO3)3 solid solution seria (x = 0.35 for Gd and 0.4 for La).Moreover, a new non-centrosymmetric NdSr4O(BO3)3 borate has been obtained and structurally characterized from single-crystal XRD data, which can be a prototype of a new LnSr4O(BO3)3 series that may exhibit important properties for practical applications due to the features of the crystal structure.
The anisotropy of thermal expansion of Nd(Ca1−xSrx)4O(BO3)3 solid solutions with x = 0, 0.2, 0.5 is not very sharp (αmax/αmin < 2), it is apparently caused by thermal vibrations of rigid BO3 groups perpendicular to the plane of groups in accordance with the principles of high-temperature crystal chemistry of borates.Anisotropy of thermal expansion of Nd(Ca1−xSrx)4O(BO3)3 solid solutions (x = 0, 0.2, 0.5) is similar to compositional deformations that occur during Ca-Sr substitutions, a compositional equivalent of the thermal expansion, α/γ (0.01 at% Sr/°C) was applied.
The experimental results showed that the optical nonlinearity of the Nd(Ca1−xSrx)4O(BO3)3 crystals can be improved by the partial substitution of Sr 2+ ions for Ca 2+ ions up to x = 0.2 in the structure.Crystal chemistry basis may contribute to this: Finally, consider the features of the structure that may affect the optical nonlinearity.In addition to the already reported factors improving the optical nonlinearity in this borate family, such as a partial substitution of Yb for Y in YCa 4 O(BO 3 ) 3 [19] or doping of Sr for Ca in GdCa 4 O(BO 3 ) 3 [22], we believe that, in accordance with the anion group theory [55][56][57][58], the significant contribution to the NLO properties originates also from the BO 3 groups that form delocalized π-type bonds perpendicular to the BO 3 plane.Accordingly, special attention is therefore paid in borates to the orientation of the triangular groups [48, [58][59][60].In this family [BO 3 ], triangular groups are located at a small angle to each other (see Figure 3).Another relatively new crystal chemistry factor that can affect the optical nonlinearity is the additional oxygen atom, which is not bonded to the B atom.Its role in influencing the optical nonlinearity is not quite clear; however, its influence in [61] has already been noted, apparently for the first time.It is coordinated by metal atoms and forms a rigid O1M 4 tetrahedron, which leads to distortion of cationic M polyhedra.This situation is described in detail in the case of Ca-Sr substitution in GdCOB, similar to Ca-Sr substitution in NdCOB (see Section 3.2).

Conclusions
Novel non-centrosymmetric Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions and a new NdSr 4 O(BO 3 ) 3 compound with large second harmonic generation responses were synthesized by solid-state reactions and characterized by powder and single crystal X-ray diffraction in the wide range of temperatures.It turned out that Ca ions can be replaced by Sr ones up to approximately 70% which exceeds practically twice similar substitutions in the REE(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solution seria (x = 0.35 for Gd and 0.4 for La).Moreover, a new non-centrosymmetric NdSr 4 O(BO 3 ) 3 borate has been obtained and structurally characterized from single-crystal XRD data, which can be a prototype of a new LnSr 4 O(BO 3 ) 3 series that may exhibit important properties for practical applications due to the features of the crystal structure.
The anisotropy of thermal expansion of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions with x = 0, 0.2, 0.5 is not very sharp (α max /α min < 2), it is apparently caused by thermal vibrations of rigid BO 3 groups perpendicular to the plane of groups in accordance with the principles of high-temperature crystal chemistry of borates.Anisotropy of thermal expansion of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solutions (x = 0, 0.2, 0.5) is similar to compositional deformations that occur during Ca-Sr substitutions, a compositional equivalent of the thermal expansion, α/γ (0.01 at% Sr/ • C) was applied.
The experimental results showed that the optical nonlinearity of the Nd(Ca 1−x Sr x ) 4 O (BO 3 ) 3 crystals can be improved by the partial substitution of Sr 2+ ions for Ca 2+ ions up to x = 0.2 in the structure.Crystal chemistry basis may contribute to this: location of plain BO 3 ), which may indicate the stability of the new NdSr 4 O(BO 3 ) 3 phase.The parameters determined from powder and single-crystal XRD data (Figure 1, open and filled circles) are in good agreement.Crystals 2023, 13, x FOR PEER REVIEW 6 of 18 NdSr4O(BO3)3 phase.The parameters determined from powder and single-crystal XRD data (Figure 1, open and filled circles) are in good agreement.

Figure 1 .
Figure 1.The unit-cell parameters and the volume versus Sr-content in the Nd(Ca1−xSrx)4O(BO3)3 solid solution.Values obtained from powder and single-crystal XRD data are shown with open and filled circles.

Figure 1 .
Figure 1.The unit-cell parameters and the volume versus Sr-content in the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 solid solution.Values obtained from powder and single-crystal XRD data are shown with open and filled circles.

Figure 2 .
Figure 2. View of the Nd(Ca0.5Sr0.5)4O(BO3)3crystal structure in terms of cation-centered polyhedral along the c axis (a, top left), chains of M1-M3 edge-shared polyhedra extended along the c axis (a, bottom left), the Nd(Ca0.5Sr0.5)4O(BO3)3structure in the ac-plane in terms of oxy-centered polyhedra (b) and the figures of thermal expansion tensor of this solid solution.

Figure 2 .
Figure 2. View of the Nd(Ca 0.5 Sr 0.5 ) 4 O(BO 3 ) 3 crystal structure in terms of cation-centered polyhedral along the c axis (a, top left), chains of M1-M3 edge-shared polyhedra extended along the c axis (a, bottom left), the Nd(Ca 0.5 Sr 0.5 ) 4 O(BO 3 ) 3 structure in the ac-plane in terms of oxy-centered polyhedra (b) and the figures of thermal expansion tensor of this solid solution.

Figure 3 .
Figure 3. Distribution of cations over M1-M3 positions (top left), changes of average bond lengths in the cationic M1-M3 polyhedra and oxy-centered OM4 tetrahedra versus chemical composition (bottom left) and temperature (right).

Figure 3 .
Figure 3. Distribution of cations over M1-M3 positions (top left), changes of average bond lengths in the cationic M1-M3 polyhedra and oxy-centered OM 4 tetrahedra versus chemical composition (bottom left) and temperature (right).

Figure 4 .
Figure 4. Dependencies of unit-cell parameters of the Nd(Ca1−xSrx)4O(BO3)3 versus chemical composition (left) and temperature (right).E.s.d. for the cell parameters is comparable with the size of the data points.

Figure 4 .
Figure 4. Dependencies of unit-cell parameters of the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 versus chemical composition (left) and temperature (right).E.s.d. for the cell parameters is comparable with the size of the data points.

3. 3 . 3 .
Temperature-Dependent Structural Evolution of Nd(Ca 0.8 Sr 0.2 ) 4 O(BO 3 ) 3 Solid Solution from Single-Crystal XRD DataTo expand our knowledge of the structure response to increasing temperature, we investigated the temperature-dependent structural behavior of Nd(Ca 0.8 Sr 0.2 ) 4 O(BO 3 ) 3 solid solution in the range of 300-1273 K. First, we examine the thermal redistribution of Nd, Ca and Sr cations over M1-M3 positions.It turned out that the redistribution of cations does not exceed 5-10%.

Figure 5 .
Figure 5. DCS heating curves of Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 samples after heat-treatment at 1300 • C. On the cooling curves, crystallization occurs at a lower temperature due to hysteresis in the melting and crystallization temperatures.It is noteworthy that the hysteresis reaches a maximum in solid solutions up to 70-80 • C for x = 0.2, 0.3 and decreases in single chemical compounds and multiphase samples to 20-40 • C.

Figure 7 .
Figure 7. Absorption spectra of the Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 samples (a); dependence of optical bandgap on the Sr concentration (b).

Figure 8 .
Figure 8. SHG signal dependence on Sr concentration for Nd(Ca 1−x Sr x ) 4 O(BO 3 ) 3 samples (a); SHG signal dependencies as a function of particle size for Nd(Ca 0.8 Sr 0.2 ) 4 O(BO 3 ) 3 and SiO 2 polycrystals as the reference (b).