Crystal Structure of Gd(Ca3.319Sr0.681)O[BO3]3 and Gd(Ca2.592Sr1.408)O[BO3]3

The structure family of the rare‐earth calcium oxoborates RX2Z2$RX_{2}{Z}_{2}$ O[BO3]3 (RCOB) has been investigated mainly with regard to their optical characteristics. Due to their monoclinic‐domatic structure they exhibit pyro‐ and piezoelectric properties, which is not dependent on the numerous possible substitutions of the rare‐earth cation site R. The rare‐earth cations are known to show partial disorder with the earth alkaline cation positions X and Z. To study whether a stabilization of the cation occupation is possible without disorder, calcium oxoborates are chemically modified using the Ca substitutes, Sr, Na, Y, Gd on the X and Z positions. No oxoborate phases can be synthesized by coupled substitution of Ca with Sr, Na, and a rare‐earth element. Only with single substitution of Sr the oxoborate phases can be synthesized. It is found that up to 35% Sr can be incorporated into the structure. From the synthesized Gd(Ca 4−x$_{4-{{x}}}$ Srx)O[BO3]3 precursor material, single crystals have been grown and used for the refinement of the first structure model. The structures have been refined in space group C1m1$C1m1$ . A replacing only of Ca with Sr, mainly on the X position, has been observed. The stoichiometry resulting from the refinement is Gd(Ca3.319Sr0.681)O[BO3]3 and Gd(Ca2.592Sr1.408)O[BO3]3.


Introduction
Synthetic materials play an important role in many technological processes. For piezoelectric applications, PZT ceramic (lead zirconate titanate) is one of the most important materials and widely used. However, PZT ceramic does not exist as DOI: 10.1002/crat.202200255 homogeneous single crystal. Such single crystals with well-defined chemical composition are of growing interest, because their properties are highly reproducible. But only a few materials can be synthesized as single crystals. Hydrothermally grown quartz is the most prominent single crystal material, especially for piezoelectric applications as crystal oscillator due to its well-known and well-defined electromechanical properties and structure. PZT and quartz are limited in their use as high temperature piezoelectric materials due to phase transitions. Quartz can be used up to 350 • C. [1] Materials like LiNbO 3 or Langasite are limited to temperatures below 1000 • C as well. The family of the rare earth calcium oxoborates RX 2 Z 2 O[BO 3 ] 3 (RCOB, space group C1m1) contains promising candidates to overcome this limit. [2] RCOB was discovered in 1974 by Kindermann [3] and was first described by Khamaganova et al. [4] as a non-centrosymmetric monoclinic material. Due to its congruent or almost congruent melting it can be grown from the melt directly. RCOBs crystallize in the structure type Ca 5 F[BO 3 ] 3 , where only structures are known, which have either Cd or Ca on the X and Z positions, respectively, partially mixing with R. Comparing the ionic radii [5] in sixfold coordination, both elements and Ag have similar size (deviation about 6%). Based on this selection criterion, substitution elements such as Mn (17% smaller ionic radius) and Sr (18% larger ionic radius) can be shortlisted. However, Sr will be investigated preferentially due to its chemical similarity as an alkaline earth element to Ca.
A manifold chemical variability of RCOBs is enabled by the numerous possible substitutions regarding the differently coordinated cations as well as anions, which is highly relevant for structure-property relations. For example literature reports the unexceptional substitution of R (R = Y, La, Pr, Nd, Sm, Gd, Tb, Er, Tm) among each other. [6][7][8][9][10][11][12][13][14] The extent to which the alkaline earth element Ca can be exchanged at positions X and Z remains uncertain. Even more, the question arises whether these positions allow deviations in the oxidation state. In addition, an exchange within the anion complex is possible, too, e.g. Ca 5 F[BO 3 ] 3 . [15] Hence, the exchange of both the rare earth and the oxoanion position is possible, leading probably to changes in properties, e.g. Whereas the substitution of rare earth elements is well investigated, [1,16] including series of mixed crystals, [17] the potential to replace alkaline earth elements has not yet been fully investigated. Ideally, Ca is incorporated in the crystal structure occupying the X and Z positions, but an intrinsic cation disorder of both positions with R is observed depending on annealing temperature [18] and the rare earth used. [19] The present work aims to expand the oxoborate structure family by modification of the synthesis route using different Ca substituents on the X and Z positions. It is to be clarified, whether a stabilization of the cation occupation is possible without a disorder. In this study, element substitutions were carried out on GdCa 4 O[BO 3 ] 3 , [10] because this oxoborate is particularly easy to grow, and on LaCa 4 O[BO 3 ] 3 . [6] In addition, a medium rare earth, such as Gd, is better suited to answer the question of disorder in comparison to other rare earths, because only the R and Z positions disorder at room temperature and the melting behavior is congruent. [18]

Synthesis
Single crystal rare earth calcium oxoborates can be grown by the Czochralski method. [6][7][8][9][10][11][12][13][14] The polycrystalline precursor materials are synthesized by means of a solid-state reaction after the following equation: A stoichiometric mixture of CaCO 3 , B 2 O 3 , and R 2 O 3 with an additional amount of ≈3 wt.-% of B 2 O 3 , to compensate absorbed water, [6,10] was sintered. The more complex compounds follow the subsequent reaction (exemplary for the most complex case of a coupled substitution, Na and the additional R substitute Ca on Z site): where the rare earth R is either Gd or La as well as Y in the same ratio. Depending on the desired stoichiometry of the synthesis product, Na 2 CO 3 can be fully replaced by SrCO 3 . In the case of a Ca free synthesis product, CaCO 3 needs to be replaced by SrCO 3 or Na 2 CO 3 , as well. All substances were synthesized by a two-step sintering process. The first sintering involves drying the raw materials, decarbonating and initiating a conversion to an immediate precursor of the oxoborates. Appropriate temperature levels were selected at 120 • C (water release of B 2 O 3 ), 450 • C (melting of B 2 O 3 ), 850 • C (decarbonation), and 1000 • C. Subsequently grinding and pressing again reduces the pore volume, increases the reactivity between grains and ensures almost complete conversion to the synthesis product. For each material system the final temperature in the second sintering step of 10 h is differently set for and can be found in Table 1. The syntheses for the explorative substitution of the cation sites X, Z, and R were carried out with different compositions (see Table 1). Attempts were made to replace Ca 2+ either with Sr 2+ or coupled with Na + and Gd 3+ . In addition, investigations were made to modify the material system LaSrCaO[BO 3 ] 3 [20] by replacing Ca with a combination of Na and Y. Here, La and Y were primarily chosen, because La is rather found on X and R positions as compared to Y, which is more likely incorporated on R and Z positions. [21] Thus, a stable compound with a marginal disorder should be obtained.

Phase Formation
All synthesized powders were examined by means of X-ray powder diffraction and then subjected to a quantitative phase-analysis using the Rietveld program TOPAS V6 by Bruker [22] (see Figure 1). A selection of the appropriate phases was made with the help of the program Match! by Crystal Impact, [23] taking into account the chemical composition. Table 2 shows the results for the different substitutions. The structure models for the phase analysis were taken from the Inorganic Crystal Structure Database (ICSD) and refined with respect to lattice parameters, crystallite size, and where necessary for strain. It becomes clear that the expansion of the oxoborate structure family is only possible with a single substitution of Sr. With a coupled substitution of two elements no new oxoborate phase could be synthesized (see Table 2). In all cases, pure oxoborate phases were not achieved-at least one secondary phase was detected in every synthesis.
The explorative substitution of Ca by Sr in the compound GdCa 4 O[BO 3 ] 3 shows that Sr can be incorporated up to an amount of 50 at.-% (nominal, expected amount), which can be illustrated by a shift in the lattice parameters with increasing Sr content (see Figure 3). An extension of the lattice parameters is plausible with regard to the ionic radii r Sr > r Ca . [5] 3 employed the structure models and site occupancy factors from single-crystal X-ray diffraction (see below). Considering the deviations from the nominal stoichiometry found there and the absence of Gd containing impurity phases in the powder X-ray diffraction, we cross-checked this result with cation-ratios of Gd, Ca, and Sr obtained from X-ray fluorescence  (XRF) results. Given the moderate yields for the nominal compositional parameter x nom = 2, the compounds for x nom = 3, 4 were not synthesized. A final conclusion about the synthesizability or the stability of the two compounds can therefore not be drawn. The coupled substitution of Ca with Na and Gd or even in combination with Sr on the X and Z positions leads to only moderate or no conversion rates. In the case of synthesizing GdCa 2 NaGdO[BO 3 ] 3 the main phase is GdCa 4 O[BO 3 ] 3 . However, only 46.1 wt.-% of this main phase were determined using Rietveld analysis. The R wp value was also comparatively poor. In addition, many secondary phases were identified, which are almost entirely sodium borates. The reason for this is the reactivity of Na with boric acid. This leads to the conclusion that Na is hardly incorporated into the oxoborate structure, or only to a small extent. The Rietveld analysis also showed that Na is more likely to be found on the R position than on X and Z. This is remarkable since the ionic radii of Na and Ca are more similar than that of Gd and Ca. A possible explanation could be that the alkali metal ions with smaller ionic radii, e.g. Na, tend to assume less coordination [40] and therefore rather occupy the sixfold coordinated R position.
The Rietveld analysis of the powder for the synthesis of GdSr 2 NaGdO[BO 3 ] 3 does not include an oxoborate phase. In contrast, a Sr-containing orthoborate Sr 3 Gd 2 [BO 3 ] 4 was obtained with a weight fraction of 68.7%. This finding fits the fact that Ca cannot completely be substituted by Sr in GdCa 4 O[BO 3 ] 3 . Instead, Sr borates are formed in the presence of B 2 O 3 . Na behaves similarly and reacts mainly to different sodium borates. It is therefore not surprising that the inert Gd 2 O 3 appears unchanged as the main secondary phase.
The powder of the compound LaCa 2 NaYO[BO 3 ] 3 reveals an oxoborate as the main phase (72.6 wt.-%), with a mixed occupancy of La and Y on the R and with Ca and Y on the X positions. It is consistent that Na is not in the oxoborate structure on X and Z, but can be incorporated to a small extent on the R position. Due to the small number of secondary phases and a GoF of 1.9, the oxoborate can be verified to be stable. The most common secondary phase is a La-containing sodium borate. The reaction product of the synthesis is therefore again determined by the reactivity of sodium with boric acid.
Regarding all investigated phases Gd(Ca 4−x Sr x )O[BO 3 ] 3 with x nom = 1, 2 are the most promising candidates for synthesis and possible crystal growth. Since, no oxoborate phases were formed with a coupled substitution using different ions, we did not investigate these materials further.

Crystal Structure Solution
Melting experiments were carried out on Gd(Ca 4−x Sr x )O[BO 3 ] 3 with x nom = 1, 2 in order to obtain small crystals for single-crystal X-ray diffraction (SC-XRD). The melts were produced in a platinum crucible and cooled with 1 K min −1 . The product was extracted mechanically and single-crystal fragments were obtained by sizing. Finally, single crystals with an average size of about 100 µm were measured.
Crystal structure solutions have been deposited in the Cambridge Suctural database (CSD) and are visualized in More details on the SC-XRD experiment, the structure refinement, structural parameters, and bond lengths are found in the Supporting Information. Both substances still crystallize in monoclinic crystal metrics (see Figure 2) exhibiting space group C1m1 like all members of the rare earth calcium oxoborate Gd(Ca 4−x Sr x )O[BO 3 ] 3 structure family. [3] An increasing Sr content leads to an increase of the lattice parameters and the monoclinic angle (see Figure 3).
To refine the occupancy disorder between the cations, a split position for each element of the R, X, and Z sites was defined and restricted to the same atomic positions as well as anisotropic atomic displacement parameters. Furthermore, the overall sum of the occupancy for each Wyckoff site was constrained to 1. The first refinement step resulted in no occupancy of Sr on the R site and Gd on the X site, which is why these refinements were subsequently excluded. Additionally, to be comparable with structure   [41] were used.
solutions of other rare earth calcium oxoborates, [21,42] the ideal stoichiometry for the final refinement was set to the sum stoichiometry, with r = 2 ⋅ z2 (r being the occupancy of the R site, x the occupancy of the X site and z1 as well as z2 the occupancy of the Z site). Regarding Figure 4, the site occupation factors clearly indicate that Sr is preferably incorporated into the structure on the eightfold coordinated X position. Because Sr has the largest ionic radius of the cations [5] in Gd(Ca 4−x Sr x )O[BO 3 ] 3 , this can be explained by the dimensions of the coordination polyhedra, since the cation at the X position surrounds a polyhedron that is 60% larger compared to the octahedra that coordinate the cations at the R and Z positions. In addition, Sr is found to a small extent on the Z position, but does not occupy the R position. It is supposed that the large difference of ≈24 pm in the ionic radius between sixfold coordinated Sr and Gd in combination with the variation in the oxidation state causes this effect. However, the structure allows the incorporation of Sr for Ca at the Z position in spite of the relatively large difference in the ion radius of 14 pm, in favor of the crystal-chemical similarity of the two alkaline earth ions. The cation disorder on the R position between Gd and Ca, which is already present in GdCa 4 O[BO 3 ] 3 with ≈7%, can also be demonstrated for the Sr-doped compounds in the same order of magnitude. Obviously, these two ions can be replaced, in spite of their different charge, because they have more similar ionic radii and the two coordination octahedra only show a volume difference of 4%. From the crystal structure data it can be deduced that the incorporation of Sr does not enhance the degree of ordering concerning the occupation of the cation positions in Gd(Ca 4−x Sr x )O[BO 3 ] 3 .

Conclusion
In conclusion, the synthesis of stable oxoborates, which are isostructural to the RCOB family, is partially possible. While Ca can be replaced by Sr up to 35%, a coupled substitution with Na and a rare earth ion is very limited. Oxoborate phases can be synthesized, but are accompanied by a lot of secondary phases. The complete substitution of Ca by Sr, Na and Gd could not be realized neither. A reason can be found in the reactivity of Na and Sr toward B 2 O 3 , which leads to the formation of borates with different stoichiometries. If a small proportion of Na is incorporated into the oxoborate structure at all, Na does not occupy an X or Z position as expected, but disorders with the rare earth ion on the R position.
The structural characterization of Gd(Ca 4−x Sr x )O[BO 3 ] 3 with x = 0.681, 1.408 (resulting from structure refinement) shows a clear cation disorder of all positions. Therefore, a higher degree of ordering was not achieved by the substitution. The extent to which substitutions with other elements can be successful remains an open question. The present investigations have shown that this is probably a major challenge. Further investigations have to clarify, whether the experimental results can be transferred to large and small rare-earths.

Experimental Section
X-Ray Powder Diffraction: GdCa 4−x Sr x O[BO 3 ] 3 powders with x nom = 1, 2 were measured in reflective parallel beam geometry with a Ni-filtered Cu source on a D8 Discover diffractometer (Bruker AXS, Karlsruhe). The parallel beam was achieved by a Göbel mirror, collimated vertically to 0.05 mm and axially to 2.5°. The secondary beam path was left open to take advantage of the 1D strip detector (LynxEye), with discrimination levels adapted for optimal signal-to-noise-ratio, that means suppression of the Gd-fluorescence radiation. Scans were conducted in the 2 range from 10°to 70°with an oversampled step width of Δ2 = 0.005°and 6 s or 7 s exposure time. GdSr 2 NaGdO[BO 3 ] 3 and LaCa 2 NaYO[BO 3 ] 3 powders were measured in Bragg-Brentano geometry with a Fe-filtered Co-source on a URD6 − 2 diffractometer (Seifert Analytical X-Ray/XRD Eigenmann GmbH, Schnaittach) with 220 mm radius, variable aperture, and anti-scatter slits, a semiconductor point detector (Meteor 0D), and without further monochromatization. Scans were conducted in the 2 range from 10°to 60°at a step width of 0.02 • and 10 s exposure time per point.
Single Crystal X-Ray Diffraction: GdCa 4−x Sr x O[BO 3 ] 3 with x nom = 1, 2 single crystals had been measured with a D8 Quest diffractometer (Bruker AXS, Karlsruhe) equipped with an Mo source ( = 0.71073 Å), Triumph monochromator and Photon100 area detector. More experimental details can be found in the Supporting Information. Structure solution and refinement were performed using SHELX, [43] and disorder refinement was performed using Jana2006. [44]

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.