Complex Structural Behavior of BiMn7O12 Quadruple Perovskite

Sep 26, 2017 - Below T2 = 460 K, BiMn7O12 is likely to exhibit a transition to space group Im. Finally, below about T3 = 290 K, a triclinic distortion...
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Complex Structural Behavior of BiMn7O12 Quadruple Perovskite Alexei A. Belik,*,† Yoshitaka Matsushita,‡ Yu Kumagai,§ Yoshio Katsuya,∥ Masahiko Tanaka,∥ Sergey Yu. Stefanovich,⊥ Bogdan I. Lazoryak,⊥ Fumiyasu Oba,# and Kazunari Yamaura†,& †

Research Center for Functional Materials, National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305−0044, Japan ‡ Material Analysis Station, National Institute for Materials Science (NIMS), Sengen 1-2-1, Tsukuba, Ibaraki 305-0047, Japan § Materials Research Center for Element Strategy, Tokyo Institute of Technology, Yokohama 226-8503, Japan ∥ Synchrotron X-ray Station at SPring-8, NIMS, Kouto 1-1-1, Sayo-cho, Hyogo 679-5148, Japan ⊥ Department of Chemistry, Moscow State University, 119991, Moscow, Russia # Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8503, Japan & Graduate School of Chemical Sciences and Engineering, Hokkaido University, North 10 West 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan S Supporting Information *

ABSTRACT: Structural properties of a quadruple perovskite BiMn7O12 were investigated by laboratory and synchrotron Xray powder diffraction between 10 and 650 K, single-crystal Xray diffraction at room temperature, differential scanning calorimetry (DSC), second-harmonic generation, and firstprinciples calculations. Three structural transitions were found. Above T1 = 608 K, BiMn7O12 crystallizes in a parent cubic structure with space group Im3̅. Between 460 and 608 K, BiMn7O12 adopts a monoclinic symmetry with pseudoorthorhombic metrics (denoted as I2/m(o)), and orbital order appears below T1. Below T2 = 460 K, BiMn7O12 is likely to exhibit a transition to space group Im. Finally, below about T3 = 290 K, a triclinic distortion takes place to space group P1. Structural analyses of BiMn7O12 are very challenging because of severe twinning in single crystals and anisotropic broadening and diffuse scattering in powder. First-principles calculations confirm that noncentrosymmetric structures are more stable than centrosymmetric ones. The energy difference between the Im and P1 models is very small, and this fact can explain why the Im to P1 transition is very gradual, and there are no DSC anomalies associated with this transition. The structural behavior of BiMn7O12 is in striking contrast with that of LaMn7O12 and could be caused by effects of the Bi3+ lone electron pair.

1. INTRODUCTION A-site ordered quadruple perovskites, AA′3B4O12, show many interesting physical and chemical properties:1,2 for example, reentrant structural transitions,3 intersite charge transfer and disproportionation,2 giant dielectric constant,4 multiferroic properties,5 and high catalytic activity.6 AA′3B4O12 has a 12fold-coordinated A site and a square-planar-coordinated A′ site, while B sites have the usual octahedral coordination for perovskites. The A′ site is typically occupied by Jahn−Teller cations (such as Cu2+ and Mn3+, in most cases) or other cations which allow a square-planar coordination (Mn2+, Fe2+, Co2+, and Pd2+). A and B sites can be occupied by a large variety of different elements as in classical ABO3 perovskites (with A = Na+, Mn2+, Cd2+, Ca2+, Sr2+, R3+ (R = rare earths), Bi3+ and B = Mn3+/4+, Fe3+, Cr3+, Al3+, Ti4+, V4+, Ge4+, Sn4+, Ru4+, Ir4+, Ta5+, Nb5+, Sb5+, and others).1 Therefore, the AA′3B4O12 subfamily of the perovskite family has also numerous representatives. © 2017 American Chemical Society

The simplest chemical compositions are realized with A′ = B, and this happens only for manganese. With high enough pressure (of 18−22 GPa), the AA′3B4O12-type structure was even synthesized for A = Mn: that is, in Mn2O3.7 AA′3B4O12type manganites were discovered in the 1970s by Marezio et al.,8,9 and their composition can be written as AMn7O12 in brief. These manganites can have spin, orbital, and charge degrees of freedom depending on the oxidation state of the A cation.1,3,5,8−11 NaMn7O12 with the average oxidation state of manganese at the B site of +3.5 shows a commensurate chargeorder transition at 176 K from a parent cubic Im3̅ structure,10 which is common for all AMn7O12, to a complex superstructure with space group C2/m.11 This 1:1 charge-order transition is accompanied by the appearance of sole Mn3+ sites and orbital Received: July 6, 2017 Published: September 26, 2017 12272

DOI: 10.1021/acs.inorgchem.7b01723 Inorg. Chem. 2017, 56, 12272−12281

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Inorganic Chemistry

Figure 1. Differential scanning calorimetry (DSC) curves of BiMn7O12 between 300 and 650 K on (a) heating and (b) cooling (three runs were performed to check the reproducibility) with 10 K/min. The insets show details.

order. Spin order transitions occur at TN1 = 92 K and TN2 = 125 K in NaMn7O12.10,11 AMn7O12 (A = Cd, Ca, Sr, Pb)5,12−18 with the average oxidation state of manganese at the B site of +3.25 shows a 1:3 charge-order transition at 462 K (A = Ca)14 from the parent cubic Im3̅ structure to an R3̅ structure, and this transition is accompanied by the appearance of a sole Mn3+ site with a compressed MnO6 octahedron.12 This unusual Jahn− Teller distortion is probably a reason for an incommensurate structural modulation transition at 258 K (A = Ca) from R3̅ to R3̅(0,0,γ)0, which is often referred to as an orbital modulation transition.13 CdMn7O12 exhibits a commensurate structural modulation transition at 254 K from R3̅ to P3.̅ 15 AMn7O12 (A = Cd, Ca, Sr) shows two spin-order transitions5,13,14 and PbMn7O12 has three (with TN = 43, 77, 83 K).17 Spin-induced multiferroic properties were found in AMn7O12 (A = Cd, Ca, Sr, Pb) at one Néel temperature.5,17,18 AMn7O12 (A = rare earths and Bi)19−30 with an average oxidation state of manganese at the B site of +3 exhibits an orbital-order transition from the Im3̅ structure to an I2/m structure at 653 K (A = La),19 and two spin-order transitions (TN1 = 21 K and TN2 = 78 K for A = La20 and TN1 = 28 K and TN2 = 59 K for A = Bi).22 Dielectric anomalies are found at the Néel temperatures of BiMn7O12;22,23 however, the origin of these dielectric anomalies is still an open question (whether

they are caused by spin-induced ferroelectric or antiferroelectric transitions or other reasons). The crystal symmetry of BiMn7O12 at room temperature was suggested to be noncentrosymmetric with the Im space group from single-crystal data.23 However, in other works, the structure was refined in centrosymmetric space group I2/m from powder diffraction data.25,26,29 Very recently a triclinic structural distortion was found in BiMn7O12 below about 295 K, and the structure was refined in space group P1.30 High-temperature (HT) structural properties of BiMn7O12 have not yet been investigated. Therefore, the structural and physical properties of BiMn7O12 are not fully investigated and understood. In this work, we addressed the problem of structural properties of BiMn 7 O 12 . We found three structural transitions and investigated them by laboratory and synchrotron X-ray powder diffraction between 10 and 650 K, single crystal X-ray diffraction at room temperature, differential scanning calorimetry (DSC), and first-principles calculations.

2. EXPERIMENTAL SECTION BiMn7O12 was prepared from a stoichiometric mixture of Mn2O3 and Bi 2 O 3 (99.9999%). Single-phase Mn 2 O 3 was prepared from commercial MnO2 (99.99%) by heating in air at 923 K for 24 h. The mixtures were placed in Au capsules and treated at 6 GPa and about 1370 K for 2 h (heating time to the desired temperature was 10 12273

DOI: 10.1021/acs.inorgchem.7b01723 Inorg. Chem. 2017, 56, 12272−12281

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Figure 2. (left) Fragments of low-temperature laboratory X-ray powder diffraction patterns of BiMn7O12. The 242 monoclinic reflection is marked by an asterisk. This reflection visibly shows triclinic splitting below about 250 K. (right) Fragments of high-temperature synchrotron X-ray powder diffraction patterns of BiMn7O12. Indexes of some reflections are given; the splitting of these reflections determines the difference between the a and c monoclinic lattice parameters. min) in a belt-type high-pressure apparatus. After the heat treatments, the samples were quenched to room temperature (RT) and the pressure was slowly released. All of the samples obtained were black pellets. The temperature of our high-pressure apparatus is controlled by the heating power with a calibrated relationship between power and temperature. X-ray powder diffraction (XRPD) data were collected at RT on a RIGAKU MiniFlex600 diffractometer using Cu Kα radiation (2θ range of 10−80°, a step width of 0.02°, and a scan speed of 1°/min). BiMn7O12 contained trace amounts of Mn2O3 and Bi2O2CO3 impurities (Figure S1). Low-temperature (LT) XRPD data from 10 to 300 K and high-temperature (HT) XRPD data from 298 to 650 K were measured on a Rigaku SmartLab instrument using Cu Kα1 radiation (45 kV, 200 mA; 2θ range of 5−120°, step width of 0.02°, and scan speed of 4°/min) using a cryostat system and a furnace attachment. XRPD patterns were analyzed, and lattice parameters were obtained by the Rietveld method using RIETAN-2000.31

Synchrotron X-ray powder diffraction (SXRPD) data were measured between 100 and 650 K on a large Debye−Scherrer camera at the BL15XU beamline of SPring-8.32,33 The intensity data were collected between 3 and 59.34° at 0.003° intervals in 2θ; the incident beam was monochromated at λ = 0.65298 Å. The samples were packed into Lindemann glass capillaries (inner diameter 0.1 mm), which were rotated during the measurement. The absorption coefficients were also measured, and Rietveld analysis was applied using the RIETAN-2000 program.31 We note that we used data between 14.8 and 59.34° in the Rietveld refinements (below 600 K, that is, except for the cubic phase) because the use of all data resulted in a model with significantly suppressed Jahn−Teller distortions at the B sites already at 380 K. X-ray intensity measurements for the crystal structure analysis of a BiMn7O12 single crystal (0.055 × 0.042 × 0.037 mm in size) were carried out using a Rigaku Saturn CCD diffractometer equipped with a VariMax confocal optics for Mo Kα radiation (λ = 0.71073 Å) at 293(2) K. Cell refinement and data reduction were carried out using 12274

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Inorganic Chemistry the program d*trek package in the CrystalClear software suite.34 A preliminary structure was solved using SHELXT35 and refined by fullmatrix least squares on F2 using the SHELXL-2014/736 in WinGX program package.37 Differential scanning calorimetry (DSC) curves were recorded on a Mettler Toledo DSC1 STARe system at a heating/cooling rate of 10 K/min under N2 flow between 140 and 673 K in Al capsules. Several DSC runs were performed to check the reproducibility. Second-harmonic generation (SHG) responses of powder and pellet samples were measured in a reflection mode. A Q-switch pulsed Nd:YAG Minilite-I laser operating at λω = 1064 nm was used as the radiation source (repetition frequency 15 Hz, pulse duration 3 ns). The power of the laser beam on the samples was adjusted by an attenuator to avoid optical damage that occurred above 1 MW/cm2. Doubled frequency optical signals from samples were selected with a set of filters, measured with a photomultiplier, and calibrated relative to a signal from a quartz powder standard (I2ω/I2ω(SiO2)). First-principles calculations were performed (at T = 0 K) using the projector augmented-wave (PAW) method38 as implemented in the VASP code.39 PAW data sets with radial cutoffs of 1.59, 1.48, 1.22, and 0.80 Å for Bi, La, Mn, and O, respectively, were employed. The exchange−correlation interactions between electrons were treated using the Perdew−Burke−Ernzerhof generalized gradient approximation parametrized for solids40 with Hubbard U correction.41 The effective U value on the Mn 3d orbitals was set to 5 eV, and only the ferromagnetic configurations were considered. All structural transitions observed in this study occur near or above RT, and Néel temperatures of BiMn7O12 are much lower. Therefore, magnetism should not significantly influence the structural properties. Lattice constants and internal positions were fully relaxed until the stress and forces acting on all atoms converged to less than 0.7 GPa and 0.05 eV/Å, respectively. The cutoff energy was set to 550 eV, and a Γ-centered 6 × 6 × 6 k-point sampling for the reciprocal space integration was employed.

3. RESULTS AND DISCUSSION 3.1. Differential Scanning Calorimetry of BiMn7O12. DSC measurements (Figure 1) showed two HT anomalies with maxima at T2 = 460 K and T1 = 608 K (on heating). The first heating DSC curve is noticeably different from the next heating curves, and it exhibits more complex behavior (this observation is reproducible on other samples as well (Figure S2 in the Supporting Information)). This fact could be caused by annealing effects of the quenched metastable BiMn7O12 phase. All cooling curves matched each other very well (with maxima at 455 and 600 K). After the first heating, we observed good reproducibility on the DSC curves, indicating that both HT phase transitions are reversible. Both DSC anomalies showed noticeable shoulders from the LT side indicating that the phase transitions are gradual. No detectable DSC anomalies were observed between 140 and 370 K (Figure S3 in the Supporting Information). This fact shows that the phase transition at T3 = 290 K (see below) is highly smeared and gradual. 3.2. Lattice Parameters of BiMn7O12. Figure 2 (left) shows laboratory XRPD data between 10 and 300 K emphasizing the evolution of the (242) monoclinic reflection. This reflection is visibly split below about 250 K. The splitting of this reflection can only be described by a triclinic distortion, which was recently detected in BiMn7O12.30 Figure 2 (right) shows SXRPD data between 355 and 478 K emphasizing the evolution of the 206 and 602 monoclinic reflections as an example. The splitting of these reflections is determined by the difference between the a and c lattice parameters. These reflections are gradually merged on heating, and above about 460 K, they merge completely, meaning that

Figure 3. Temperature dependence of the lattice parameters, angles, and unit cell volumes of BiMn7O12: T, triclinic; M, monoclinic; C, cubic. The inset shows details of the temperature dependence of the β angle.

Table 1. Structure Parameters of BiMn7O12 at 293 K from Single-Crystal X-ray Diffraction Data Refined in Space Group Ima site

x

y

z

Ueq (Å2)

Bi Mn1 Mn2 Mn3 Mn4 Mn5 O1 O2 O3 O4 O5 O6 O7 O8

0.00042(14) 0.26294(9) 0.27302(10) 0.52334(16) 0.51567(15) 0.0214(2) 0.3342(9) 0.7198(8) 0.2068(9) 0.3416(6) 0.3452(8) 0.0058(6) 0.1887(6) 0.0332(6)

0 0.24190(9) 0.25158(10) 0 0 0 0 0 0.5 0.1886(6) 0 0.1803(6) 0.3108(6) 0.1734(5)

0.21748(14) 0.49183(8) 0.00005(11) 0.24305(14) 0.74595(18) 0.75248(16) 0.4109(8) 0.0772(7) 0.9260(8) 0.7291(6) 0.0579(8) 0.5729(6) 0.2626(6) 0.9437(5)

0.01988(10) 0.00506(11) 0.00569(12) 0.00816(19) 0.0085(2) 0.0097(2) 0.0090(8) 0.0068(7) 0.0089(8) 0.0090(6) 0.0085(8) 0.0101(6) 0.0085(6) 0.0075(5)

a

Crystal data: space group Im (No. 8, unique axis b, cell choice 3), Z = 2; a = 7.5168(10) Å, b = 7.3707(6) Å, c = 7.5254(6) Å, β = 91.293(2)°, and V = 416.83(7) Å3; R1(all) = 3.84%, wR2(all) = 8.80%, and goodness of fit 1.203; ρcal = 6.259 g/cm3.

the a parameter is metrically equal to the c parameter. A monoclinic cell with a = c can always be transformed to a cell 12275

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Table 2. Structure Parameters of BiMn7O12 at 293, 380, and 480 K Refined from Synchrotron X-ray Powder Diffraction Data in Space Group I2/ma T (K) a (Å) b (Å) c (Å) β (deg) V (Å3) x(Bi) y(Bi) z(Bi) B(Bi) (Å2) B(Mn1) (Å2) B(Mn2) (Å2) B(Mn3) (Å2) B(Mn4) (Å2) B(Mn5) (Å2) x(O1) y(O1) z(O1) B(O1) (Å2) x(O2) z(O2) B(O2) (Å2) x(O3) z(O3) B(O3) (Å2) x(O4) y(O4) z(O4) B(O4) (Å2) Rwp (%) Rp (%)

Figure 4. Fragments (15−40°) of experimental (black crosses), calculated (red line), and difference (blue line) synchrotron XRPD patterns of BiMn7O12 at T = 293 K obtained (a) in the Im model with fixed structural parameters at the single-crystal values (Table 1) and (b) in the I2/m model with all refined structural parameters (Table 2). The tick marks show possible Bragg reflection positions. The insets show details between 31 and 33°.

with metric characteristics identical with those of orthorhombic crystals (aO = aM + cM, bO = bM, and cO = aM − cM); however, the parent Im3̅ structure does not have orthorhombic subgroups with two axes along the diagonals of the original cubic phase.9 For this reason, the real symmetry should remain monoclinic, and such a monoclinic phase is referred as I2/ m(o), where “o” stands for pseudo-orthorhombic. The pseudoorthorhombic metric means that the XRPD data can be well fitted in space group Fmmm. The fitting can even be performed by the Rietveld method (with a = 10.50563(11) Å, b = 7.40782(8) Å, c = 10.72483(11) Å for synchrotron XRPD at 480 K; see Figure S4 and Table S1 in the Supporting Information), but the structural model used has unrealistic disordering of the oxygen sublattice. Unrealistic disordering means that, by the Fmmm symmetry, the oxygen atoms are split in such a way that the same MnO6 octahedron has completely different orientations. Almost the same R values for the I2/m and Fmmm models could be explained by the fact that synchrotron XRPD is not very sensitive to oxygen atoms (in the presence of heavy atoms). Figure 3 depicts temperature dependence of the lattice parameters obtained from the laboratory XRPD data. The Rietveld refinements were performed in space group P1 between 10 and 290 K (using the structural parameters from ref 30), and the lattice parameters obtained were transformed to space group I1 to plot them on the same figure (aI1 = bP1 + cP1, bI1 = aP1 + cP1, and cI1 = aP1 + bP1). The Rietveld refinements were performed in space group I2/m between 250 and 600 K. The monoclinic I2/m lattice parameters and triclinic I1 lattice parameters merge very well between 250 and 290 K. The triclinic γ angle deviates from 90° in the

293

380

480

7.51369(3) 7.36913(3) 7.52185(3) 91.2110(3) 416.387(3) 0.0111(5) 0.0207(3) −0.0125(4) 0.68(3) 2.29(12) 2.51(13) 1.67(8) 0.80(4) 2.37(5) 0.0116(13) 0.1793(13) 0.6803(13) 3.0(2) 0.6908(18) 0.8346(20) 4.7(3) 0.3326(18) 0.8177(19) 3.6(3) 0.1788(11) 0.6851(11) 0.0145(10) 1.6(2) 3.87 2.61

7.50917(3) 7.38829(3) 7.51595(3) 91.2290(3) 416.888(3) 0.0109(5) 0.0200(3) −0.0155(6) 1.42(4) 2.36(14) 1.51(12) 1.10(7) 0.59(4) 1.69(5) 0.0158(11) 0.1746(11) 0.6845(10) 1.06(18) 0.6993(14) 0.8348(15) 2.3(3) 0.3323(15) 0.8184(16) 2.0(2) 0.1760(11) 0.6849(10) 0.0129(10) 1.03(18) 3.91 2.43

7.50582(9) 7.40780(6) 7.50700(9) 91.1831(4) 417.312(8) 0.0106(10) 0.0249(5) −0.0183(15) 2.25(9) 2.5(3) 1.03(19) 0.76(9) 0.73(6) 1.27(6) 0.0169(15) 0.1672(15) 0.6875(13) 0.6(3) 0.7089(17) 0.8321(19) 1.8(3) 0.3313(20) 0.8206(20) 1.0(2) 0.1739(14) 0.6874(13) 0.0130(12) 0.2(2) 3.98 2.40

a

Crystal data: space group I2/m (No. 12, unique axis b, cell choice 3), Z = 2; Bi cations occupy the 8j site (x, y, z) close to the ideal 2a site (0, 0, 0), Mn1-2c site (1/2, 0, 0), Mn2-2d site (1/2,1/2, 0), Mn3-2b site (0, 1/2, 0), Mn4-4e site (0.75, 0.25, 0.75), Mn5-4f site (0.25, 0.25, 0.75), O2 and O3-4i site (x, 0, z), and O1 and O4-8j site (x, y, z). g(Bi) = 0.25 and g(Mn1) = g(Mn2) = g(Mn3) = g(Mn4) = g(Mn5) = g(O1) = g(O2) = g(O3) = g(O4) = 1, where g is the occupation factor.

temperature range of 10−290 K, while the triclinic α angle starts to deviate from 90° below about 250 K, where reflection splitting is visibly detectable (Figure 2). Because of the absence of DSC anomalies during the monoclinic to triclinic transition, the phase transition temperature can be determined from the deviation of the triclinic γ angle from 90° as T3 = 290 K. There are no anomalies on the temperature dependence of a, b, c, and β at T3 (note that tiny jumps at 300 K are artifacts because LT and HT data obtained on different attachments are combined at 300 K). On the other hand, the temperature dependence of a, b, c, and β shows clear anomalies and kinks at T2. Above T1 = 608 K, all observed reflections can be indexed in a cubic system and space group Im3̅. The aC cubic lattice parameter increases with increasing temperature. Temperature dependence of the (normalized) unit cell volume shows no anomalies at T3, a small kink at T2, and a small drop at T1 on heating (Figure 3). The temperature dependence of the lattice parameters is anisotropic in both BiMn7O12 (between 10 and 600 K) and LaMn7O12 (at least between 300 and 650 K):19 the a and c 12276

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Figure 5. Fragments (15−40°) of experimental (black crosses), calculated (red line), and difference (blue line) synchrotron XRPD patterns of BiMn7O12 at T = 480 K obtained in the I2/m model with all refined structural parameters (Table 2). The tick marks show possible Bragg reflection positions. The inset shows details between 31 and 33°.

and RF = 6.41%). Note that large RI and RF values are results of anisotropic broadening and diffuse scattering. The refinement of all structural parameters in the Im model just slightly improved the R values (Rwp = 3.69%, Rp = 2.42%, RI = 8.48%, and RF = 4.55%) in comparison with the fixed-parameter model. However, some of the resultant Mn−O bond lengths strongly deviated from reasonable values after the refinements in the Im model using SXRPD data. This fact prevented us from a reliable comparison of structural parameters below and above T2. On the other hand, the I2/m model gave reasonable Mn−O bond lengths. Therefore, only the I2/m symmetry was used when dealing with SXRPD data. We note that the BiMn7O12 structure was not reported in the Im model at RT even using neutron powder diffraction data, which are more sensitive to locations of oxygen atoms.29 Structural parameters of BiMn7O12 at 293 K refined in space group I2/m from SXRPD data are summarized in Table 2, and fitting results are shown in Figure 4b. The RT structural features we obtained agree very well with the previous results:25,26 we found very large thermal parameters for oxygen atoms and some manganese atoms. However, at 380 K, when the same modification is still stable, we observed that many thermal parameters are noticeably reduced (in contrast to the expected trend from enhanced thermal fluctuations), and they can be considered as normal and acceptable. Therefore, very large thermal parameters at RT either could be artifacts from the monoclinic to triclinic phase transition or could be caused by a larger deviation of the structure from the centrosymmetric I2/m model toward the noncentrosymmetric Im model. Note that, at 380 K, both the Im and I2/m models already gave the same R values (Rwp ≈ 3.92% and Rp ≈ 2.42%). Attempts to split Bi atoms (at all temperatures) were successful in the sense that the resulting standard deviations of fractional coordinates were much smaller than the coordinates themselves, and the Bi thermal parameter was reduced after splitting. Structural parameters of BiMn7O12 at 480 K (above T2) were also refined in space group I2/m (Table 2), and fitting results are shown in Figure 5. Bond lengths, bond valence sums (BVS),43 and distortion parameters of MnO6 octahedra are summarized in Table 3. It seems that diffuse scattering is enhanced at high temperatures (Figure 5 and Figure S5 in the Supporting Information), suggesting that the domain size is

parameters decrease, while the b parameter strongly increases with increasing temperature. Almost no detectable anomalies were observed at TN1 = 55 K and TN2 = 23 K of BiMn7O12 on the temperature dependence of the lattice parameters, except for a very tiny kink in the triclinic β angle (the inset of Figure 3). 3.3. Crystal Structures of BiMn7O12. Structural analyses of BiMn7O12 turned out to be very challenging. Single crystals of BiMn7O12 are severely twinned in most cases, and the monoclinic to triclinic phase transition at RT can produce some artifacts. Among more than 50 crystals we could select one crystal suitable for the RT single-crystal structural analysis. The crystal structure could be solved and refined in space group Im (Table 1 and Table S2 in the Supporting Information) similar to the case for ref 23. Unfortunately, the size of the suitable crystal was too small for HT single-crystal experiments on available equipment, and attempts to cool the crystal to study a low-temperature structure failed because the crystal became severely twinned. Because only RT structural parameters were available from single-crystal data, it was difficult to unambiguously conclude whether the Im symmetry is real or an artifact of the monoclinic to triclinic phase transition that occurs exactly at RT. On the other hand, SXRPD data suffer from strong anisotropic hkl-dependent peak broadening30 and the presence of diffuse scattering between strong Bragg reflections. These features, which could not be fully taken into account in our refinements, prevented us from unambiguously distinguishing between Im and I2/m symmetries similarly to previous work.29 The same features found in SXRPD patterns of BiMn7O12 were observed on SXRPD patterns of a BiCrO3 perovskite (crystallizing in centrosymmetric space group C2/c) and attributed to the formation of nano domains with a size of about 10 nm.42 Twinning domains with the size of a few tens of nanometers were also observed in BiMn7O12,23 and they could be a reason for anisotropic broadening and diffuse scattering. We could obtain a very good fit of the SXRPD data at RT in the Im symmetry (Figure 4a) with structural parameters fixed at our RT single-crystal values. The resultant R values (Rwp = 3.74%, Rp = 2.42%, RI = 8.49%, and RF = 4.74%) were smaller than those obtained in the I2/m symmetry with all refined structural parameters (Rwp = 3.87%, Rp = 2.61%, RI = 9.87%, 12277

DOI: 10.1021/acs.inorgchem.7b01723 Inorg. Chem. 2017, 56, 12272−12281

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Inorganic Chemistry Table 3. Bond Lengths, Bond Valence Sums (BVS), and Distortion Parameters of MnO6 (Δ) in BiMn7O12 at 293, 380, and 480 K Obtained in the I2/m Model

Table 4. Structure Parameters, Bond Lengths, and Bond Valence Sums (BVS) of BiMn7O12 at 630 Ka Structure Parameters

T (K) Bi−O4 (Å) Bi−O2 (Å) Bi−O1 (Å) Bi−O4 (Å) Bi−O2 (Å) Bi−O1 (Å) Bi−O3 (Å) Bi−O1 (Å) Bi−O4 (Å) Bi−O4 (Å) Bi−O1 (Å) Bi−O3 (Å) BVS(Bi)a Mn1−O3 (Å) Mn1−O2 (Å) Mn1−O1 (Å) BVS(Mn1) Mn2−O1 (Å) Mn2−O4 (Å) BVS(Mn2) Mn3−O4 (Å) Mn3−O3 (Å) Mn3−O2 (Å) BVS(Mn3) Mn4−O4 (Å) Mn4−O2 (Å) Mn4−O1 (Å) BVS(Mn4) Δ(Mn4)b Mn5−O1 (Å) Mn5−O3 (Å) Mn5−O4 (Å) BVS(Mn5) Δ(Mn5)

×2 ×2 ×4 ×4 ×4 ×4 ×2 ×2 ×2 ×2 ×2

×2 ×2 ×2

293

380

480

2.513(8) 2.589(15) 2.590(11) 2.595(8) 2.650(15) 2.741(10) 2.760(14) 2.767(10) 2.781(8) 2.855(8) 2.909(10) 3.000(14) +2.28 1.841(14) 1.918(13) 2.725(10) +3.21 1.894(9) 2.776(8) +3.04 1.916(8) 2.724(14) 2.870(16) +2.87 1.901(8) 2.002(5) 2.111(10) +3.18 18.3 × 10−4 1.928(10) 2.006(5) 2.126(8) +3.04 16.3 × 10−4

2.515(8) 2.544(12) 2.529(9) 2.593(8) 2.579(12) 2.675(8) 2.745(13) 2.749(8) 2.775(8) 2.846(8) 2.884(9) 3.004(13) +2.47 1.837(10) 1.965(10) 2.777(8) +3.03 1.895(8) 2.794(8) +3.02 1.902(8) 2.728(13) 2.900(11) +2.96 1.917(7) 1.993(4) 2.140(8) +3.09 21.1 × 10−4 1.900(8) 2.011(4) 2.119(8) +3.14 19.8 × 10−4

2.468(12) 2.510(16) 2.449(13) 2.542(12) 2.513(20) 2.629(12) 2.723(19) 2.709(14) 2.792(12) 2.859(11) 2.873(15) 2.996(18) +2.76 1.829(11) 2.032(11) 2.841(10) +2.83 1.877(11) 2.818(11) +3.14 1.906(9) 2.743(18) 2.917(15) +2.92 1.914(9) 1.978(4) 2.156(11) +3.11 25.7 × 10−4 1.904(11) 2.017(4) 2.118(10) +3.11 18.9 × 10−4

WP

Bi Mn1 Mn2 O

16f 0.0223(9) 6b 0 8c 0.25 24g 0 Bond Lengths and

Bi−O × 3 Bi−O × 3 Bi−O × 3 Bi−O × 3 BVS(Bi) Bi−Bi Bi−Bi

2.446(10) 2.617(3) 2.746(5) 2.899(10) +2.71 0.334(14) 0.47(2)

z

B (Å2)

x 0.5 0.25 0.1730(4) Sums

1.6(2) 2.08(5) 0.87(3) 2.10(10)

y x 0.5 0.25 0.3115(4) Bond Valence

Mn1−O × 4 Mn1−O × 4 BVS(Mn1) Mn2−O × 6 BVS(Mn2)

1.915(3) 2.825(3) +2.75 2.0110(11) +3.04

a

g(Bi) = 0.125, g(Mn1) = 1, g(Mn2) = 1, and g(O) = 1, where g is the occupation factor. Crystal data: space group Im3̅ (No. 204); Z = 2; a = 7.48358(2) Å and V = 419.1095(17) Å3; Rwp = 3.87% and Rp = 2.12%; ρcal = 6.225 g/cm3. WP = Wyckoff position.

Figure 6. Experimental (black crosses), calculated (red line), and difference (blue line) synchrotron XRPD patterns of BiMn7O12 at 630 K in the cubic Im3̅ structure. The tick marks show possible Bragg reflection positions.

N

BVS = ∑i = 1 νi , where νi = exp[(R0 − li)/B], N is the coordination number, B = 0.37, R0(Bi3+) = 2.09, and R0(Mn3+) = 1.76.43 bΔ = (1/ N N N)∑i = 1[(li − lav)/lav]2, where lav = (1/N)∑i = 1 li is the average Mn−O distance and N is the coordination number. a

x

site

reduced. Detailed electron microscopy studies are needed to understand this behavior. We also note that the driving force for the pseudo-orthorhombic metrics between T2 and T1 remains unclear. At RT, Mn−O bond lengths reasonably agree with the previous results obtained from neutron powder diffraction29 and SXRPD data (Table S3 in the Supporting Information).25,26 The MnO6 octahedra at RT exhibit noticeable Jahn− Teller distortions expected for Mn3+ cations. No significant changes in Jahn−Teller distortions are found below and above T2. This fact shows that this monoclinic to monoclinic transition in BiMn7O12 is not related to orbital ordering in comparison with BiMnO3.44 BiMnO3 exhibits an isosymmetric monoclinic to monoclinic transition (from C2/c to C2/c) at 474 K, and the transition was associated with the (partial) orbital disorder on the basis of the resultant Mn−O bond

Figure 7. Crystal structures of BiMn7O12: (left) At 630 K in the cubic Im3̅ structure (without Bi splitting); (right) At 293 K in the monoclinic Im structure (viewed along the monoclinic b axis). Elongated Mn−O bond lengths due to the Jahn−Teller distortions in MnO6 octahedra are marked by black lines. Note that distortions in the P1, I2/m, and I2/m(o) models cannot be distinguished from that of the Im model by eye.

lenghts.44 A transition to a parent Pnma structure occurs at a much higher temperature of 770 K in BiMnO3. 12278

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Figure 8. Calculated relative energies of different structures for (a) BiMn7O12 and (b) LaMn7O12.

as “background”, and it could originate from local symmetry breaking near defects and surfaces. For white or transparent materials, SHG signals of about 0.05−0.1 usually confirm that the symmetry of materials is centrosymmetric (with tiny signals assigned to local symmetry breaking). However, BiMn7O12 is black, and it could significantly absorb the generated SHG green light. Therefore, SHG studies did not allow us to unambiguously determine the presence or absence of a center of symmetry. 3.5. First-Principles Calculations on BiMn7O12 and LaMn7O12. Because experimental methods could not allow us to unambiguously distinguish between the Im and I2/m models, we turned to first-principles calculations. The calculations confirmed that noncentrosymmetric structures of BiMn7O12 are more stable than centrosymmetric structures (Figure 8a). Note that the P1̅ model results in higher energy than the I2/m model. This could be due to the following two reasons. The first reason is an energy barrier between subgroup and supergroup structures. We obtained the initial structures from the X-ray diffraction data. If the space group assumed for fitting the data is not correct, the initial structure could deviate significantly from the true one, and it could have an energy barrier on the way to the supergroup structure. The second reason is an insufficient number of atoms in the unit cell of the subgroup structure: the unit cell volume of P1̅ is half of that of I2/m. Such cell reduction may prohibit lone pair electrons of Bi3+ from pointing to free space. Similar calculations performed for LaMn7O12 as a reference showed that the I2/m structure is the most stable (Figure 8b) in agreement with experimental findings,20 and noncentrosymmetric initial models converge to centrosymmetric models (the smaller unit cells of the P1̅ and P1 models can explain why their energies are higher than those of the I2/m and Im models, respectively). We also calculated energies of the Im3̅m model (with a ≈ 7.5 Å); however, the energy of this structure was much higher than that of the Im3̅ model, as expected. Energies of the BiMn7O12 structures change as P1 < Im ≪ I2/m < P1̅ (Figure 8a). Therefore, on the basis of these findings, we can assign the transition at T1 to the Im3̅ to I2/ m(o) transition, the transition at T2 to I2/m(o) to Im, and the transition at T3 to Im to P1. Our first-principles calculations also indicate that the Im structure should be a correct structure between T2 and T3 despite some ambiguity during the refinements and the presence of the RT monoclinic to triclinic phase transition. A very small energy difference between the Im and P1 models can explain why the monoclinic to triclinic

Structural parameters at 630 K refined in space group Im3̅ in a parent structure of BiMn7O12 are summarized in Table 4, and fitting results are shown in Figure 6. Bi atoms could be split similar to the Bi splitting in the cubic structures of BiMn7O12+δ and Bi0.94Mn7O12 (in these cases, the cubic structure was observed at RT).26,27 Without the Bi splitting, the Bi thermal parameter was 3.97(4) Å2. All Mn−O bond lengths in the MnO6 octahedron are the same (by the symmetry) and, therefore, there are no Jahn−Teller distortions. Therefore, the transition at T1 (from Im3̅ to I2/m(o)) should correspond to the orbital ordering transition. During this transition, two opposite O atoms shift closer to Mn atoms, two opposite O atoms shift away from Mn, and the two remaining opposite O atoms stay at almost the same distance (Figure 7). This is the generally observed so-called Q2 mode of the Jahn−Teller distortions. The same behavior is found in LaMn7O12, which shows just one structural transition from Im3̅ to I2/m below 650 K, and on the basis of the temperature dependence of Mn−O bond lengths in LaMn7O12, this transition corresponds to an orbital-order transition.19 No other structural phase transitions were detected in LaMn7O12 in comparison with BiMn7O12. Therefore, the structural properties of BiMn7O12 are strikingly different from those of the related LaMn7O12, and they should be attributed to the presence of a lone electron pair of Bi3+. The BVS values for Bi3+ are significantly lower than +3 when the structural parameters are obtained in the I2/m model at RT: BVS(Bi)= +2.47 (from neutron data),29 +2.36 and +2.22 (from previous SXRPD),25,26 and +2.28 (our present SXRPD). With increasing temperature, the BVS values of Bi3+ obtained in the I2/m model increase (Table 3), and at 480 K, the BVS(Bi) value of +2.76 is reasonable. In other words, the I2/m symmetry provides a reasonable crystal structure description above T2. On the other hand, our single-crystal RT results in the Im model give BVS(Bi) = +2.77 (BVS(Bi) = +2.62 for the previous single crystal RT results).23 These features give indirect evidence that the symmetry could be I2/m above T2 and Im below T2. 3.4. Second-Harmonic Generation Studies of BiMn7O12. At RT, we observed SHG signals of about 0.05 (for BiMn7O12 powder) and 0.1 (for a BiMn7O12 pellet) in comparison to that of quartz. The SHG signals gradually decreased on heating and approached 0.02−0.03 that of quartz at 670 K without any clear anomalies at T1 and T2; the SHG signals returned to 0.05−0.1 at RT after cooling. The SHG signal of 0.02−0.03 in the cubic Im3̅ phase could be considered 12279

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phase transition is very gradual, and there are no DSC anomalies associated with this transition. The behavior of BiMn7O12 is different from that of BiMnO3, where firstprinciples calculations showed that the C2/c structure is the most stable and noncentrosymmetric initial models converged into the centrosymmetric C2/c structure.45

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01723. Laboratory and synchrotron XRPD patterns, additional DSC curves, and structural information (PDF) Accession Codes

CCDC 1561806 contains 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 data_ [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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REFERENCES

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4. CONCLUSION We found that the quadruple perovskite BiMn7O12 exhibits three structural transitions on cooling: Im3̅ to I2/m(o) at T1 = 608 K, I2/m(o) to Im at T2 = 460 K, and Im to P1 at T3 = 290 K, and this behavior is in a striking contrast with that of a related quadruple perovskite LaMn7O12. First-principles calculations clearly demonstrated that noncentrosymmetric structures of BiMn7O12 are more stable than centrosymmetric structures even though the experimental structural analysis of BiMn7O12 is very challenging because of severe twinning in single crystals and anisotropic broadening and diffuse scattering in powder. We emphasize that a noncentrosymmetric structure does not necessarily equal ferroelectricity, and dielectric anomalies observed at the Néel temperatures of BiMn7O12 are not related to high-temperature structural phase transitions reported here. The nature of dielectric anomalies at Néel temperatures is determined by the symmetry of magnetic spin structures.

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail for A.A.B.: [email protected]. ORCID

Alexei A. Belik: 0000-0001-9031-2355 Yoshitaka Matsushita: 0000-0002-4968-8905 Bogdan I. Lazoryak: 0000-0003-1952-5555 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Japan Society for the Promotion of Science (JSPS) through Grants-in-Aid for Scientific Research (15K14133, 16H04501, and 26410081) and JSPS Bilateral Open Partnership Joint Research Projects. The synchrotron radiation experiments were performed at the NIMS synchrotron X-ray station at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (Proposal Nos. 2016B4504 and 2017A4503). 12280

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