Structural Instability in Single-Crystal Rare-Earth Scandium Borates

Article Cite This: Cryst. Growth Des. 2018, 18, 1571−1580

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Structural Instability in Single-Crystal Rare-Earth Scandium Borates RESc3(BO3)4 Galina M. Kuz’micheva,† Irina A. Kaurova,*,† Victor B. Rybakov,‡ Vadim V. Podbel’sky,§ and Nikolay K. Chuykin§ †

Institute of Fine Chemical Technologies, Moscow Technological University, Vernadskogo pr. 86, Moscow 119571 Russia Lomonosov State University, Vorobyovy Gory, Moscow 119992, Russia § Higher School of Economics, National Research University, Myasnitskaya str. 20, Moscow 101000 Russia Downloaded via UNIV OF SUNDERLAND on November 7, 2018 at 09:17:17 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: An influence of the type of rare-earth (RE) cation and composition of initial charge on the symmetry, structural features, and real composition of the single-crystal huntite family rare-earth scandium borates RESc3(BO3)4 (RE = Ce, Pr, Nd), grown by the Czochralski method, has been studied by single crystal and powder X-ray diffraction. A crystallization of scandium borates in the space groups C2/c (RE = Ce) and P321 (RE = Pr, Nd) has been found. Disordering in the structures with the space group P321, which has been first determined for the huntite family compounds, is due to the RE and Sc redistribution over two trigonal-prismatic sites to maintain the stability of crystal structure. The crystals grown from the initial charges NdSc3(BO3)4 and Nd1.25Sc2.75(BO3)4 are characterized by the greatest disordering, and they are isotypic, rather than isostructural, to the crystals obtained from the charges Pr1.1Sc2.9(BO3)4 and Pr1.25Sc2.75(BO3)4. A change in the unit cell parameters and interatomic distances depending on the RE radius and composition of the initial charge is found and explained. Analysis of our and literary data for RESc3(BO3)4 with the RE = La, Ce, Pr, Nd, Sm, Eu allowed to reveal a morphotropic series for scandium borates based on the size factor (the RE3+ radius), suggest methods for evaluating the specific crystal symmetry depending on the type of RE cation, and propose factors affecting its realization. The comparison of huntite family REM3(BO3)4 (M = Al, Ga, Sc) single crystals allowed to establish basic differences between their crystal structures, mainly due to the different sizes of RE and M ions. medium temperature phase β-LaSc3(BO3)4 with the space group R32 (huntite structure), and a low-temperature phase γLaSc3(BO3)4 with the space group Cc. The temperature of the phase transition from γ-LaSc3(BO3)4 to β-LaSc3(BO3)4 is 1050 °C, whereas from β-LaSc3(BO3)4 to α-LaSc3(BO3)4 is 1200 °C.4 All the modifications were grown by flux and Czochralski methods from stoichiometric melts or by solid state synthesis. An X-ray diffraction study of powdered LSB single crystals obtained by a solid state synthesis and heat-treated at temperatures from 1000 to 1350 °C showed that the α- and γ-phases of LaSc3(BO3)4 are identical and belong to the space group C2/c.5 In addition, Fedorova et al.,5 Li et al.,6 and Ye et al.7 failed to obtain a stable β-phase by a solid state reaction, suggesting that this phase is metastable or stable in a narrow temperature range. According to refs 8−10, in the structures of trigonal R32 and monoclinic C2/c modifications, the La atom is located at the center of a distorted trigonal prism with similar interatomic distances (CNLa = 6, CN is a coordination number) and with

1. INTRODUCTION Rare-earth scandium borate crystals and solid solutions with the corresponding general compositions RESc 3 (BO 3 ) 4 and (RE,RE′)Sc3(BO3)4 (RE, RE′ are rare earth elements) belonging to the huntite family (huntite CaMg3(CO3)4, the space group R32) are related to promising optical materials used in photonics, in particular, to create diode-pumped highefficiency compact lasers covering various spectral regions.1−3 These media are characterized by a high absorption efficiency for the pump radiation, which greatly contributes to achieving a maximum pump power density in an active element.2 Physical and chemical properties of rare-earth scandium borates, described in detail,1−3 are due to their crystal structure. These crystals demonstrate an anomalously low luminescence concentration quenching, which is caused by a large distance between the nearest RE ions (∼6 Å). Due to the noncentrosymmetric structure, scandium borate crystals possess nonlinear optical properties, which ensure a self-doubling of laser generation frequency.2 RESc3(BO3) crystals may have different symmetry depending on the type of RE cation. LaSc3(BO3)4, LSB. Three modifications are known: a hightemperature phase α-LaSc3(BO3)4 with the space group C2/c, a © 2018 American Chemical Society

Received: November 2, 2017 Revised: January 31, 2018 Published: February 12, 2018 1571

DOI: 10.1021/acs.cgd.7b01534 Cryst. Growth Des. 2018, 18, 1571−1580

Crystal Growth & Design

Article

Figure 1. Combination of coordination polyhedra in LaSc3(BO3)4 (space group Cc) (a),4 CeSc3(BO3)4 (CSB-1.0, space group C2/c) (b), LaSc3(BO3)4 (space group R32) (c),8,9 and PrSc3(BO3)4 (PSB-1.1, space group P321) (d).

three different ones (CNLa = 2 + 2 + 2), respectively, whereas in the monoclinic Cc structure, the La atom occupies a distorted octahedron with all different La−O distances (according to ref 4). In the LSB crystal structures with the space groups Cc, C2/c, and R32, the Sc atoms occupy three (Sc1, Sc2, Sc3, all the interatomic distances are different), two (CNSc1 = 2 + 2 + 2; Sc2, all the distances are different), and one (CNSc = 2 + 2 + 2) crystallographic sites, respectively, forming distorted octahedra. The B1 and B2 atoms are surrounded by the O atoms forming regular and isosceles (the space group R32) or scalene (the space group C2/c) triangles. In turn, in the structure with the space group Cc, the B atoms occupy four different scalene triangles.4 The LSB crystal structures were solved within the framework of the space groups Cc,4 R32,8,9 and C2/c10 without any refinement of site occupancies, i.e., the real compositions were considered to be stoichiometric. Figure 1 shows the combination of coordination polyhedra in all the structures. A comparison of the combination of coordination polyhedra in the structures with the space groups Cc and R32 shows that a transition from the low-symmetry γ- to the high-symmetry βmodification is logically accompanied by a decrease in the

number of different structural fragments for cations: one (Sc) and two (B1 and B2) structural fragments (space group R32) are formed from three Sc (Sc1, Sc2, Sc3) and four B (B1, B2, B3, B4) ones (space group Cc), respectively. CeSc3(BO3)4, CSB. According to refs 11 and 12, the CSB can possess trigonal (space group R32) or monoclinic (space group C2/c) symmetry depending on a synthesis method. Coordinates of atoms, thermal parameters, interatomic distances, and bond angles in the CSB crystals obtained by the flux method were refined within the framework of the space group R32;11 however, the precise real composition was not determined. The CSB crystals grown by the Czochralski technique were found to be crystallized in the space group C2/c, but no refinement of the crystal structure was performed. PrSc3(BO3)4, PSB. When refining the crystal structure of PSB crystal grown by the Czochralski method from the initial charge with composition Pr1.1Sc2.9(BO3)4, the extinction laws for an overwhelming number of diffraction reflections witness crystallization of this compound in the space group C2/c or Cc. However, a small number of additional reflections with I ≥ 3σ(I) was revealed, which are characteristic for the space group C2/m, C2, or Cm (h + k = 2n for hkl; h = 2n, l = 2n for h0l; h = 1572



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Table 1. Main Crystallographic Data and the Refined Compositions of CSB-1.0 (space group C2/c) as well as PSB and NSB (space group P321) According to the XRD Data crystals

CSB-1.0

PSB-1.1

PSB-1.25

NSB-1.0

NSB-1.25

initial composition system, space group, Z a, Å b, Å c, Å β (γ), deg refined compositions

CeSc3(BO3)4 monoclinic, C2/c, 4 7.7297(3) 9.8556(3) 12.0532(5) 105.405(3) CeSc3(BO3)4

Pr1.1Sc2.9(BO3)4 trigonal, P321, 3 9.7758(20) 9.7758(20) 7.9395(16) 120.0 [(Pr0.419Sc0.081(4))(1) Pr0.500(4)(2)]Sc3(BO3)4 (Pr0.919Sc0.081(4))Sc3(BO3)4

Pr1.25Sc2.75(BO3)4 trigonal, P321, 3 9.7781(44) 9.7781(44) 7.9391(25) 120.0 [(Pr0.424Sc0.076(4))(1) Pr0.500(4)(2)]Sc3(BO3)4 (Pr0.924Sc0.076(4))Sc3(BO3)4

NdSc3(BO3)4 trigonal, P321, 3 9.7816(13) 9.7816(13) 7.9461(16) 120.0 [(Nd0.500(4))(1) Nd0.500(2)]Sc3(BO3)4 NdSc3(BO3)4

Nd1.25Sc2.75(BO3)4 trigonal, P321, 3 9.7633(18) 9.7633(18) 7.9247(20) 120.0 [(Nd0.500(1) Nd0.410Sc0.090(20)(2)] Sc3(BO3)4 (Nd0.910Sc0.090(20)) Sc3(BO3)4

2n for h00).2,12 For these crystals, a nonsynchronous second harmonic generation was observed that indicates a noncentrosymmetric structure, which, most likely, crystallizes in the space group C2 as a subgroup of the C2/c known for huntite family compounds. Due to a small number of additional reflections (∼5%), coordinates of atoms, thermal parameters, interatomic distances, and bond angles of PSB crystal structure were refined in the space group C2/c.12 In addition, the structure of the crystals with the charge composition PrSc3(BO3)4 was solved in the space group R32.13,14 In all the cases, site occupancies were not refined.2,12−14 NdSc3(BO3)4, NSB. The structure of NSB crystals grown from the initial charge with the composition NdSc3(BO3)4 was refined within the framework of the space group R32.13,14 The unit cell parameters of crystal with the initial charge composition Nd1.25Sc2.75(BO3)4, determined by the autoindexing of 21 reflections (h0h̅0, 000l) in the range of interplanar distances d = 2.01−8.14 Å, correspond to the primitive trigonal cell (a = 9.74, c = 15.83 Å) with the double c parameter compared with the huntite structure (the space group R32).15 In the range of d = 3.96−4.00 Å, several broad reflections with a width of 1.23−1.4° were detected (the remaining reflections of approximately the same intensity had a width of 1.05°). As a result, a primitive trigonal cell with the double parameters a = 19.526(3) and c = 15.838(2) Å was found. The presence of such diffraction reflections indicates a disordering in the crystal structure. The structure of the crystal with the charge composition Nd1.25Sc2.75(BO3)4 was refined in the space groups R32, P321, and P3 (P321 and P3 are the most probable) with the unit cell parameters a = 9.763(3), c = 7.919(2) Å.15 In all the cases, anomalous (negative) thermal parameters for the O and B atoms were observed, which indicates problems in the X-ray diffraction analysis of NSB. The Nd and Sc site occupancies were only refined by the Rietveld method for powdered single crystals with the charge composition Nd1.25Sc2.75(BO3)4 (space group R32).15 As a result, the crystal composition was found to be stoichiometric, i.e., NdSc3(BO3)4. RESc3(BO3)4 (RE = Sm, Eu). The structures of Czochralskigrown crystals with the charge compositions RESc3(BO3)4 with RE = Sm, Eu were refined in the space group R32.14 However, the precise real composition was not determined, i.e., any refinement of site occupancies was not performed. Thereby, there are only several works devoted to the investigation of RESc3(BO3)4 crystal structure, their results being incomplete, contradictory, and, in some cases, questionable. Up to this time, there is no unified opinion on a

symmetry and structure of these compounds. In addition, any correlations between structure, precise real crystal composition (in the majority of cases, it was not determined or determined for powdered crystals only), and synthesis conditions, in particular, initial charge composition, were not revealed. It is known that a real composition of compounds, taking into account a deficiency of all crystallographic sites, may differ from a composition of initial charge and, hence, correlations between composition and functional properties will be changed.16,17 A correct determination of symmetry and structure of huntite family rare-earth scandium borates becomes very important since a possible structural transition from one space group to another can be accompanied by a loss (or acquisition) of the center of symmetry and results in a loss (or acquisition) of nonlinear optical properties in a laser crystal. It was found that the introduction of 5 at. % Nd3+ ions (the corresponding concentration was determined to be 2.3 × 1020 cm−3) into LaSc3(BO3)4 results in a transition from the space group C2/c (LSB) to C2 (LSB:Nd), i.e., a transition from a centrosymmetric to a noncentrosymmetric structure; it is accompanied by a fundamental change in the properties.18 All these structural aspects are not given much attention in modern materials science. The aim of this work is to establish dynamics and causes for structural transitions in the huntite family RESc3(BO3)4 compounds depending on the type of rare-earth (RE) cation.

2. MATERIALS AND METHODS The RESc3(BO3)4 (RE = Ce, Pr, Nd) single crystals were grown by the Czochralski technique in iridium crucibles of 40 mm in diameter in a “Kristall-3” unit. The pulling rate was 1−2 mm/h, and the seed was rotated at 8−10 rpm. The seed was oriented so that its optical axis coincided with the pulling axis (within a few degrees). The growth time was 60−70 h. The average diameter of the grown crystals was 15−20 mm, and the average length was 10−15 cm. The conditions used to grow crystals are described in detail in ref 19. The objects of investigation are given in Table 1. The X-ray powder diffraction (XRPD) data for samples ground to a powder were collected in a reflection mode at room temperature on a HZG-4 (flat graphite monochromator) X-ray powder diffractometer using CuKα radiation and a diffracted beam (step-scan mode; the count time was 15 s and the step size was 0.02°) in the 2θ angle range of 10−80°. The qualitative phase analysis of the samples, which was performed with the PCPDFWIN automatic search software for reading the PDF-2 database, showed that all the samples were single phase. The unit cell parameters were refined by the FullProf-2007 program.20 The X-ray diffraction (XRD) analysis of microcrystals ∼0.1 × 0.1 × 0.1 mm3 in size was carried out on a Enraf-Nonius CAD-4 single1573



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Figure 2. Projections of the regular (a) and distorted (b) trigonal prism, and the regular (c) and distorted (d) octahedron (the ⟨111⟩ direction).

Figure 3. Relationship between the a (a), b (b), and c (c) unit cell parameters and the RE radius for the RESc3(BO3)4 single crystals (RE = Pr, Ce, La) (space group C2/c). crystal diffractometer at room temperature (MoKα or AgKα, graphite monochromator, ω/2θ scan mode) (Table S1, Supporting Information). To reduce an error associated with the absorption, the XRD data were collected over the entire Ewald sphere. The preliminary XRD data processing was carried out using the WinGX pack21 with a correction for absorption (MULTISCAN). The crystal structures of the compounds are solved by the Paterson method and direct (statistical) methods.22 The atomic coordinates, anisotropic displacements parameters for all the atoms, and occupancies of cation and oxygen sites were refined using the SHELXL2013 software package,22 taking into account the atomic scattering curves for neutral atoms. The structural parameters were refined in several steps. Initially, the coordinates of “heavy” (RE, Sc) and “light” (O and B) atoms were refined with fixed thermal

parameters. Then the refinement of the thermal parameters in isotropic and anisotropic approximations was performed in the same order with fixed positional parameters. Finally, the occupancies of RE, Sc, and O sites were refined step by step. The electroneutrality of the system, the number and grade of atom location, crystallochemically acceptable interatomic distances, real thermal parameters, and the lowest values of the R-factors served as criteria for the accuracy and correctness of the refinement performed. Crystallographic data have been deposited with the Cambridge Crystallographic Data Centre, CCDC codes 1575235−1575236. The results of the refinement of atomic coordinates, thermal parameters, site occupancies, and interatomic distances in space groups P321 (RE = Pr, Nd) and C2/c (RE = Ce) are given in Tables S1−S4, Supporting Information. 1574



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The “Program for investigation the dynamics of changes in the structural parameters of compounds with different symmetry” has been developed to visualize the general crystal structure, combination of coordination polyhedra, and individual polyhedra, to calculate structural parameters (interatomic distances and bond and distortion angles), and to build correlations between structural parameters and a size of ions for the huntite family compounds having different symmetry. The basic characteristics: CPU, Intel Core i5 6600k; RAM, at least 8 GB; Programming language, C#; OS, Windows 10 with the Microsoft.NET Framework 4.0 or higher; size, 17 756 KB.

for the low-temperature modification with the space group Cc, in which the coordination polyhedron for RE is a distorted octahedron.4 At the same time, two crystallochemically different Tb atoms (possibly together with the Sc atoms) occupy the centers of distorted octahedra. It should be noted that the polyhedra derived from the regular trigonal prism (Figure 2a) and regular octahedron (Figure 2c) differ in a rotation angle between the upper and lower triangular faces (φ): φ = 0° for a trigonal prism and φ = 60° for an octahedron. It can be conditionally assumed that the ranges 0° < φ ≪ ∼30° and ∼30° ≪ φ < 60° correspond to a distorted trigonal prism (Figure 2b) and a distorted octahedron (Figure 2d), respectively. From that standpoint, in the LSB structures, φ = 14° (space group Cc), φ = 8° (space group C2/ c), and φ = 9.6° (space group R32) were found for the RE polyhedron (a distorted trigonal prism), and φ ≈ 54−58° (Sc1, Sc2, Sc3), φ ≈ 53° (Sc1) and 58° (Sc2), and φ ≈ 54° were found for the Sc one (a distorted octahedron), respectively. It follows that in the γ-LaSc3(BO3)4 structure (space group Cc) the La atom is located in a distorted trigonal prism rather than a distorted octahedron, as was earlier mentioned by Wang et al.4 However, a decrease in the size of trigonal prism with decreasing RE radius should facilitate its transition to an octahedron since the lower limit of stability is greater for a trigonal prism (rRE/RO = 0.528; R is an anionic radius) rather than octahedron (rRE/RO = 0.414). It should be noted that a distortion of polyhedron contributes to an increase in its lower limit of stability.25 3.1. XRD Investigations of CSB. Figure 3 shows our (Table 1) and literature10,12 unit cell parameters for RESc3(BO3)4 (RE = La, Ce, Pr) single crystals crystallized in the space group C2/c depending on the RE radius. It can be seen that the parameters of CeSc3(BO3)4 (CSB-1.0, present work) are sharply increased (Table 1) if compared with those found for the RE = La, Ce, Pr (according to the published data). It may indicate a difference in a composition or symmetry between the CeSc3(BO3)4 and RESc3(BO3)4 (RE = La, Pr) crystals. The refinement of site occupancies in the CSB-1.0 structure did not reveal any deficiency (within the calculation error) (Table 1), i.e., the compositions of initial charge and grown crystal are similar and equal to CeSc3(BO3)4 (Table 1, Figure 1b).

3. RESULTS AND DISCUSSION According to refs 12 and 23, the compounds with the composition RESc3(BO3)4 form a morphotropic series, which

Figure 4. Relationship between the average RE−O interatomic distance in trigonal prism and the RE ionic radius for the RESc3(BO3)4 compounds (RE = Pr, Ce, La) (space group C2/c).

can be conventionally divided into huntite (RE = La - Eu with rREVI = 0.95−1.02 Å,24 r is a cationic radius) and nonhuntite family compounds, e.g., the compound with the RE = Tb (rTbVI = 0.92 Å) crystallizes in the superstructure to ScBO3 (space group R3̅). Hence, the reason for the formation of a morphotropic series is the size factor. In the huntite-type structure, the RE atoms are located in trigonal prisms, except

Figure 5. Relationship between the a (a) and c (b) unit cell parameters and the RE radius for the RESc3(BO3)4 compounds (RE = Eu, Sm, Nd, Pr, Ce, La) (space groups R32 and P321). 1575



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Figure 6. Relationship between the RE1−O interatomic distance in the RE1O6 polyhedron (a) or the average RE2−O interatomic distance in the RE2O6 polyhedron (b) and the weighted average cation radius (r*) in the trigonal-pyramidal site in the huntite family RESc3(BO3)4 structures (RE = Pr, Nd) (space group P321).

Figure 7. Relationship between the rotation angle (φ) of the upper face with respect to the lower one in the RE1O6 (a) and RE2O6 (b) trigonal prisms and the corresponding RE1−O and the average RE2−O interatomic distances in the same polyhedra in the huntite family RESc3(BO3)4 structures (RE = Pr, Nd) (space group P321).

The relationship between the average RE−O interatomic distance and the RE radius is almost rectilinear (Figure 4). However, the specific Ce−O (2.447−2.466 Å) and Pr−O (2.434−2.456 Å)12 interatomic distances with Δ ≈ 0.02 Å are in the narrower range than the La−O distances (2.444−2.485 Å)10 with Δ ≈ 0.04 Å. Thus, the occupancies of all the cation (except for B) and O sites as well as positional and thermal parameters, interatomic distances, and bond angles have been first refined in the space group C2/c for single-crystals having initial charge composition CeSc3(BO3)4. 3.2. XRD Investigations of PSB and NSB. When refining the structures of crystals grown from the charges with initial compositions Pr1.1Sc2.9(BO3)4 (PSB-1.1), Pr1.25Sc2.75(BO3)4 (PSB-1.25), NdSc3(BO3)4 (NSB-1.0), and Nd1.25Sc2.75(BO3)4 (NSB-1.25), the extinction laws for general diffraction reflections indicate the space group R32. However, 60% of the additional reflections with I ≥ 3σ(I) are typical for the space group P321 (h + k = 3n, l = 2n + 1 for hkl). It should be noted that the noncentrosymmetric monoclinic crystals (space group C2) were obtained from the charge with the composition Pr1.1Sc2.9(BO3)4,12 which is probably due to a type of seed (composition, symmetry, or orientation). The PSB crystals crystallized in the space group P321 were obtained and structurally described here for the first time.

In the crystal structure with the space group P321 (Figure 1d), the RE and Sc crystallographic sites, typical for the space group R32, are split into two, RE1 and RE2, sites with a distorted trigonal-prismatic oxygen environment and two, Sc1 and Sc2, sites with a distorted octahedral oxygen environment, respectively. In addition, the number of B and O sites is also increased in the structure with the space group P321 (Figure 1d) compared with the R32 one (Figure 1c). Figure 5 shows the relationship between the unit cell parameters and the RE radius for the huntite-family RESc3(BO3)4 compounds crystallized in the space groups R32 (for RE = La, Ce, Sm, Eu, Nd, Pr, according to the literature data) and P321 (for RE = Pr, Nd with different compositions of the initial charge, according to our data) (Table 1). It should be noted that the unit cell parameters, atomic coordinates, thermal parameters, and interatomic distances of NSB-1.25, determined by our team, differ from those given in refs 2 and 15, whereas the NSB-1.0 structure was solved for the first time. A decrease in the unit cell parameters with decreasing RE size is observed in Figure 5. The composition of initial charge for the PSB-1.1 and PSB-1.25 crystals does not influence their unit cell parameters significantly (taking into account the standard deviations) (Table 1, Figure 5), which may indicate only a slight difference between the real compositions of these crystals obtained from different initial charges. This was confirmed by 1576



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An analysis of the interatomic distances in the structures crystallized in the space group P321 and their comparison with each other shows that the RE1−O distance is smaller than the average RE2−O distance in the PSB-1.1, PSB-1.25, and NSB1.0 structures (Figure 6). However, in the RE2O6 polyhedron, the ratio of interatomic distances is different: dPr2−O1 > dPr2−O4 for the PSB-1.1 and PSB-1.25 structures and dNd2−O1 < dNd2−O4 for the NSB-1.0 structure (Figure 6). Another situation is observed for the interatomic distances in the NSB-1.25 structure: the Nd1−O distance in the Nd1O6 polyhedron is longer than the average Nd2−O distance in the Nd2O6 polyhedron, but comparable to one of the Pr2−O1 distances in the PSB-1.1 and PSB-1.25 structures and the Nd2−O4 distance in the NSB-1.0 structure (Figure 6). Moreover, the average Nb2−O interatomic distance in the NSB-1.25 structure is significantly shorter than all the RE−O distances in the PSB1.1, PSB-1.25, and NSB-1.0 structures that confirm the highest Sc content found in this site (Table 1). At the same time, the average RE−O interatomic distances (RE = Pr, Nd) in all the structures studied are almost the same (∼2.435 Å). The B−O interatomic distances in the PSB and NSB structures under investigation are mainly within the region 1.33−1.41 Å, found for the rare-earth scandium borates.2,12,14,15 However, the B1−O5 distance in the PSB-1.1 (1.460 Å) and PSB-1.25 (1.450 Å) structures and the B2−O7 distance in the PSB-1.1 (1.299 Å), PSB-1.25 (1.276 Å), and NSB-1.0 (1.240 Å) structures go beyond the above-mentioned intervals. It may indicate a symmetry decrease to the space group P3, which was assumed by Rybakov et al.15 It should be noted that the refinement of NSB-1.0 structure (for example) within the framework of the space group R32 with the same unit cell parameters (Table 1) but without taking into account weak reflections (about 60%), responsible for the space group P321, leads to the B−O interatomic distances 1.380(15) Å and 1.367(18) Å in two B polyhedra. The rotation angle φ in the RE1O6 trigonal prism increases with increasing RE1−O interatomic distance (Figure 7a) and remains practically unchanged with increasing average RE2−O interatomic distance (Figure 7b) in the PSB-1.1, PSB-1.25, and NSB-1.0 structures. The rotation angle φ in the NSB-1.25 structure is essentially small and large in the Nd1O6 and Nd2O6 polyhedra, respectively (Figure 7), i.e., the RE1O6 and RE2O6 trigonal prisms are unequal in the NSB structures, especially in the NSB-1.25, compared to the PSB structures. An analysis of Figures 6 and 7 shows that the NSB-1.0 and NSB-1.25 crystals (space group P321) are characterized by the greatest structure disordering and not isostructural but isotypic23 to the crystals with the nominal composition PrSc3(BO3)4 (space group P321). This is evidenced by a different location of the Nd ions (or Nd ions together with the Sc ions) in trigonal prisms, leading to another character of the changes in the interatomic distances in these polyhedra (Figure 8). The NSB structure is represented by right (NSB-1.0) and left (NSB-1.25) forms (Figure 8c,d). 3.3. XRPD Investigations of PSB and NSB. Figure 9 shows the powder diffraction patterns of the PSB-1.1, NSB-1.0, and NSB-1.25 samples with the refined unit cell parameters a = 9.7890(8), 9.7923(7), 9.7762(8) Å and c = 7.9471(6), 7.9538(5), 7.9336(5) Å, respectively, i.e., the character of variation of the unit cell parameters for powdered samples is the same as that found for microcrystals (Table 1). The diffraction patterns are almost identical except for the NSB-1.25 sample; it shows the splitting of the first diffraction reflection,

Figure 8. Combination of coordination polyhedra in Pr1.1Sc2.9(BO3)4 (PSB-1.1) (a), Pr1.25Sc2.75(BO3)4 (PSB-1.25) (b), NdSc3(BO3)4 (NSB1.0) (c), Nd1.25Sc2.75(BO3)4 (NSB-1.25) (d) (space group P321), and RESB (space group R32) (e). The RE and Sc polyhedra are colored by green and blue, respectively.

the compositions refined for the first time, which can be written as [(Pr0.419Sc0.081(4))(1)]Pr0.5(2)Sc3(BO3)4 or (Pr0.919Sc0.081(4))Sc3(BO3)4 for the PSB-1.1 and [(Pr0.424Sc0.076(4))(1)]Pr0.5(2)Sc3(BO3)4 or (Pr0.924Sc0.076(4))Sc3(BO3)4 for the PSB-1.25 (Table 1). At the same time, based on the different unit cell parameters found for the NSB-1.0 and NSB-1.25 crystals (Table 1, Figure 5), their real compositions should be significantly different. Indeed, the refined compositions are as follows: NdSc3(BO3)4 for the NSB-1.0 and (Nd0.500(1)[Nd0.410Sc0.090(20)(2)]Sc3(BO3)4 or (Nd0.910Sc0.090(20))Sc3(BO3)4 for the NSB-1.25. The interatomic distances in the REO6 polyhedra correlate with their compositions (Table 1). 1577



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Figure 9. Powder diffraction patterns of Pr1.1Sc2.9(BO3)4 (PSB-1.1), NdSc3(BO3)4 (NSB-1.0), and Nd1.25Sc2.75(BO3)4 (NSB-1.25) samples.

necessary to perform a single-crystal XRD experiment with a careful analysis of diffraction reflections. 3.4. Main Results and Comparative Analysis of RareEarth Scandium Borates. The results presented in this study and data available in the literature suggest several conclusions: (1) Stoichiometric RESc3(BO3)4 crystals (RE = La, Ce, Pr, Nd) form the morphotropic series of the huntite family structures: LaSc3(BO3)4 (space group C2/c),10 CeSc3(BO3)4 (space group C2/c), PrSc3(BO3)4 (space group C2),12 and NdSc3(BO3)4 (space group P321); the reason is the size factor (the RE radius). (2) Crystal structures of huntite family rare-earth aluminum and gallium borates REM3(BO3)4 (M = Al, Ga) differ from those of scandium borates: (i) the aluminum and gallium borates (M = Al, Ga) are crystallized in the space group R32,2 and the scandium borates (M = Sc), in the space group P321; (ii) antisite defects (redistribution of cations over crystallo-

probably caused by the sample decomposition into two isostructural solid solutions with different unit cell parameters. The same was observed, for example, for the langasite family La3Ga4(Ga,Si)O14 crystals: the splitting of the first diffraction reflection is due to the phase compositions in the trigonalpyramidal site, different primarily in the Ga/Si ratio.26 In the crystals with the initial charge composition Nd1.25Sc2.75(BO3)4, the presence of solid solutions with different Sc distribution over trigonal-prismatic sites is possible. It indicates the formation of order−disorder (OD) structures. All the diffraction reflections of the samples are indexed within the framework of the space group R32, i.e., any additional reflections, detected by the XRD analysis, were not revealed in the diffraction patterns of powdered samples. Therefore, to determine a proper symmetry and reveal structural features for huntite family rare-earth scandium borate crystals, it is 1578



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+ 0.75b R32 2 ) 1/2 , b C2/c = b R32 , c C2/c = 0.666(4c R32 2 + 0.75bR322)1/2.29 (7) For the RESc3(BO3)4 (RE = Sm, Eu) compounds with a small difference between the cation radii (rSmVI = 0.96 Å, rEuVI = 0.95 Å, rScVI = 0.745 Å), a crystallization in the ordered highsymmetry structure with the space group R32, as shown in ref 14, is highly doubtful.

4. CONCLUSIONS The X-ray diffraction study of the huntite family rare-earth scandium borates RESc3(BO3)4 with RE = Ce, Pr, Nd, grown by the Czochralski method using the initial charge of different compositions, allowed to first solve (RE = Pr, Nd; space group P321) and refine (RE = Ce, space group C2/c; RE = Pr, Nd, space group P321) their crystal structures, as well as to determine the precise real compositions and reveal a distribution of RE and Sc ions over two trigonal-prismatic sites (space group P321). The crystals grown from the initial charges with compositions NdSc3(BO3)4 and Nd1.25Sc2.75(BO3)4 are characterized by the greatest disordering, in contrast to the crystals with the initial charge compositions Pr1.1Sc2.9(BO3)4 and Pr1.25Sc2.75(BO3)4. The results obtained allowed to reveal a morphotropic series for scandium borates based on the size factor.

Figure 10. RE content in the initial charge and grown crystal for RESc3(BO3)4 (RE = Pr, Nd).

graphic sites) are absent in the structures REM3(BO3)4 (M = Al, Ga) due to different sizes of the RE and Al(Ga) ions, in contrast to scandium borates (rAlVI < rGaVI < rScVI); (iii) noncentrosymmetric structures with monoclinic symmetry are different for aluminum2 and scandium12 borates. (3) Disordering in the structures of scandium borates with the nominal compositions RESc3(BO3)4 (RE = Pr, Nd), crystallized in the space group P321, is due to the redistribution of Sc (rScVI = 0.745 Å) and RE (Pr, rPrVI = 0.99 Å; Nd, rNdVI = 0.98 Å) ions over two trigonal-prismatic sites with different Sc/ RE ratios to maintain a stability of structure, rather than in one site, which is typical for huntite family aluminum (rAlVI = 0.535 Å) and gallium (rGaVI = 0.620 Å) borates, crystallized in the space group R32. (4) The crystals grown from the charges with compositions NdSc3(BO3)4 and Nd1.25Sc2.75(BO3)4 are characterized by the greatest disordering (especially NSB-1.25) and isotypic to the crystals grown from the charges Pr 1.1 Sc 2.9 (BO 3 ) 4 and Pr1.25Sc2.75(BO3)4, as evidenced by differences between these structures, characteristic of isostructural compounds.23 (5) Real compositions of crystals are affected by initial charge compositions, which, in general, differ from compositions of grown crystals (except for congruent-melting compounds): the compositions of the initial charge and grown crystals are different for the PSB-1.1, PSB-1.25, and NSB-1.25 samples (Table 1, Figure 10). (6) A symmetry of grown crystals is affected by technique and conditions for crystal growth (in particular, composition, symmetry, and orientation of a seed), type and concentration of dopants (impurity atoms), temperature (polymorphic transitions), and packing defects, which are described for rare-earth aluminum borates27 and possible for scandium borates. This conclusion is based on certain effects observed in the diffraction patterns, which are characteristic of the OD structures:28 (i) a presence of diffuse areas along with the point ones; (ii) a presence of diffraction reflections of a high symmetry; (iii) a difficulty in determining a real space group; (iv) similar a and b unit cell parameters and a multiple c parameter (for classical polytypes), wherein, for the huntite family compounds, the b parameters are the same, and the a and c parameters can be represented as a linear combination of vectors. For example, the unit cell parameters of the huntite family structures with the space groups R32 and C2/c are correlated as aC2/c = 0.666(cR322

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.7b01534. Crystallographic data, experimental details, and refined structure parameters of CeSc3(BO3)4 (CSB-1.0) (sp. gr. C2/c) as well as Pr 1 . 1 Sc 2. 9 (BO 3 ) 4 (PSB-1.1), Pr1.25Sc2.75(BO3)4 (PSB-1.25), NdSc3(BO3)4 (NSB-1.0), and Nd1.25Sc2.75(BO3)4 (NSB-1.25) (sp. gr. P321) according to the X-ray diffraction data (PDF) Accession Codes

CCDC 1575235−1575236 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +7 495 246 05 55 (434). Fax: +7 495 434 87 11. E-mail: [email protected]. ORCID

Irina A. Kaurova: 0000-0003-0340-1638 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The reported study was supported by the RFBR [research project No. 16-33-00497]. REFERENCES

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Structural Instability in Single-Crystal Rare-Earth Scandium Borates

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