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Acta Cryst. (2007). E63, i151    [ doi:10.1107/S1600536807026098 ]

The [gamma]-phase of SrTeO3 at 583 K

V. E. Zavodnik, S. A. Ivanov and A. I. Stash

Abstract top

As a part of current systematic investigations of strontium tellurite, SrTeO3, with particular emphasis on crystal chemistry and phase transitions, the structure of the [gamma] phase has been determined at 583 K using a single-crystal analysis. Both structural and nonlinear optical measurements indicate a [beta]-[gamma] first-order phase transition temperature that is close to 563 K. The structure of the [gamma] phase is monoclinic (C2) and does not differ essentially from the [alpha] phase (C2). Comparison of the [alpha] and [gamma] structures shows that the main atomic shifts and tiltings are connected with Te4, Te5 and Te6 pyramids.

Comment top

Although ferroelectric STO has been under intensive investigation for a long time (Yamada & Iwasaki,1972,1973; Simon et al.,1979; Libertz & Sadovskaya, 1980, Antonenko et al., 1982; Kudzin et al.,1988) there is still no a complete understanding of its rich polymorphism. Recently, in the two first papers of the present series the structures of α and β phases of STO were published (Zavodnik et al., 2007a, 2007b). The purpose of this communication is to report on the structure of γ-phase. There is a number of experimental studies of physical properties near the reversible first order β-γ phase transition (Libertz & Sadovskaya, 1980; Kudzin et al.,1982,1988, Sadovskaya, 1984). All the measured constants exhibit abrupt changes, a small thermal hysteresis and a remarkably discontinuous volume change were found (Ismailzade et al., 1979, Simon et al.,1979, Dityatiev et al., 2006). At 563 K the second harmonic generation (SHG) signal appeared, reflecting a transition to the noncentrosymmetric structure. The value of the spontaneous polarization along [010] polar axis was estimated as 0.037 c/m2 at 585 K (Yamada & Iwasaki, 1972,1973). It was determined (Sadovskaya, 1984, Kudzin et al., 1988) that β-γ phase transition is connected with the formation and motion interfaces which are formed by crystallographic planes with indices (0 0 1) and (2 0 3). The peculiarities of the interface motion are the same as during the martensite transformation. No success was obtained in attempts to determine the γ-phase structure using X-ray and neutron powder diffraction (Simon et al.,1979; Ismailzade et al., 1979, Dityatiev et al., 2006). Last investigator (Dityatiev et al., 2006) believed that γ-STO at to be monoclinic C2/c. The polyhedral representation of γ-STO structure is presented on Figure 1. The current research indicates that γ-phase structure is supposed to be the same in many respects to α-phase structure. The Te—O bond lengths for Te3 and Te6 cations are located at distances greater than 2.7 Å and do not contribute to the first coordination sphere of Te4+. Figure 2 illustrates a comparison of α and γ-STO structures. The main atomic shifts and tiltings are connected with Te4, Te5 and Te6 pyramids while the maximum these values were observed for Te5 (O52α-O52γ 0.93 Å, O52α-Te5—O52γ 28.4°). It is not unreasonable to ask why the α and γ-phases separated by β-phase are structurally same. Full determination of the absolute configuration of γ-phase awaits the additional measurements and provides the means for tackling this important question. The relationship between the structures of the different phases will be describe later.

Related literature top

Single crystals of SrTeO3 (STO) were prepared by Sadovskaya (1984). Structural phase transitions of STO have been studied by X-ray powder diffraction by Ismailzade et al. (1979) and Simon et al. (1979), by neutron powder diffraction by Dityatiev et al. (2006), and by second harmonic generation by Libertz & Sadovskaya (1980). The temperature dependence of physical properties of STO was analysed by Yamada & Iwasaki (1972, 1973), Yamada (1975) and Kudzin et al. (1988). For related literature, see: Antonenko et al. (1982); Avramenko et al.(1984); Kudzin et al. (1982); Zavodnik et al. (2007a,b).

Experimental top

The single crystals of STO were grown by Czochralski technique as described earlier (Libertz & Sadovskaya, 1980; Avramenko et al., 1984). The products were characterized in a scanning electron microscope (Jeol 820) with an energy-dispersive spectrometer (LINK AN10000), confirming the presence and stoichiometry of Sr and Te. SHG measurements showed that there is no a symmetry centre in γ-phase which is stable between 563 K and 633 K with small thermal hysteresis (near 5 K). This conclusion is in a full agreement with the results of Libertz & Sadovskaya (1980). A special Enraf–Nonius mini-heater based on a goniometer head was used. The tested single-crystal was maintained by a special high-temperature silicate-based glue. The temperature interval of existence of the γ-phase was controlled by well calibrated thermocouple and with help of an appearance (or vanishing) of superstructural reflections (for example, (021) diffraction peak).

Refinement top

The structure of STO was solved by the direct method in space group C2 where the atomic coordinates of all Sr and Te cations were found. The O atoms were localized by difference Fourier maps. The selection of space group C2 for description of crystal structure of γ-phase STO was based on the experimental data of second harmonic generation (SHG) obtained on tested single crystals. The temperature dependence of SHG signal confirms that the structure of γ-phase STO is noncentrosymmetric with the polar axis along (010) direction. The choice of the portion of reciprocal space (k >0), used in our experiments results from the constructional features of high-temperature equipment. Secondly, the data collection of two equivalent sets of reflections was used for a performance evaluation of empirical absorption correction because the HABITUS of tested single-crystal was very far from a proper polyhedral shape. Absorption coefficient for used crystal is very high (µ=12.3 mm−1 for Ag-radiation and µ=22.8 mm−1 for Mo-radiation). We were unable to rely on the possibility to fix the effect of anomalous scattering using Ag-radiation because the maximum value Δf' for Te cations is equal to −1.212 (only 2.3%). Several additional experiments at 583 K on Mo-radiation were performed (as a supplementary to our experiment on Ag-radiation) using the identical single crystals with a significantly less size because of very strong absorbtion·In this case the maximum value of Δ f' for Sr cations is equal to −1.657 (4.5%). The absolute configuration of this phase was determined making use of anomalous scattering. For these additional data collections, the special modifications of Enraf–Nonius mini-heater were made in order to determine the intensities of Friedel pairs (hkl) and (-h-k-l). For the experiment with best accuracy the following results were obtained: 1857 non-zero reflections including the Friedel pairs, the agreement factors- 0.041 and 0.045, Flack parameters- 0.11 (3) and 0.72 (4) for absolute and inverted structures, correspondingly. Precise X-ray diffraction study of single crystals at high temperatures is a challenging task because there is usually only a small number of measured X-ray reflections in the data and they cover a rather limited range of sinθ/λ. The thermal vibration parameters for oxygen anions were very high and strongly anisotropic. It was difficult to use an anisotropic approximation in these high-temperature refinements because the ratio of statistically reliable reflections to a number of refined parameters was very far from an optimal value. A positive definite refinements with anisotropic atomic displacement parameters were impossible for O atoms at 583 K. It was a main reason why the oxygen atoms were refined isotropically. A special attention must be given to the accuracy of interatomic distances of Te—O which are not rather similar as in the case of room temperature experiment for α-phase (Zavodnik et al.,2007a). But all these Te—O bond lengths can be found acceptable if we take into account the standard deviation. For polar space group C2 the origin was fixed along the polar b axis in least square refinements. The highest residual electron density peak is located 0.92Å from atom Te6 and the deepest hole is located 0.74 Å from atom O22. Several atoms (Te4,Te5, Sr6, O12, O42 and O52) have increased isotropic atomic displacement parameters. These atoms are located inside significant voids which are larger than the voids for the rest of the atoms. The same peculiarity was also observed for the α- and β-STO structures. At the heating of γ-phase there is structural phase transition C2->C2/m and at 583 K some indicators on the mirror plane m are remarkable.

Computing details top

Data collection: CAD-4-PC (Enraf–Nonius, 1993); cell refinement: CAD-4-PC; data reduction: CAD-4-PC; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND (Brandenburg, 2005); software used to prepare material for publication: SHELXL97.

Figures top
[Figure 1] Fig. 1. The crystal structure of γ-SrTeO3 at 583 K. The sequence of Sr polyhedra are presented, Te cations occupy two different kinds of voids in a three-dimensional lattice.
[Figure 2] Fig. 2. A comapison of crystal structure of α and γ phases of STO. The TeO3 units are shown. The Sr positions have been omitted for clarity.
strontium tellurite top
Crystal data top
SrTeO3F000 = 2736
Mr = 263.22Dx = 4.789 Mg m−3
Monoclinic, C2Ag Kα radiation
λ = 0.56086 Å
Hall symbol: C 2yCell parameters from 24 reflections
a = 28.262 (6) Åθ = 12.3–14.5º
b = 5.935 (1) ŵ = 12.04 mm−1
c = 15.434 (3) ÅT = 583 (2) K
β = 122.21 (3)ºPrism, colourless
V = 2190.4 (8) Å30.24 × 0.22 × 0.09 mm
Z = 24
Data collection top
Enraf–Nonius CAD-4 with high-temperature device
diffractometer		Rint = 0.079
Radiation source: fine-focus sealed tubeθmax = 20.0º
Monochromator: β-filterθmin = 2.1º
T = 583(2) Kh = −30→34
ω/2θ scansk = −7→0
Absorption correction: analytical
(Alcock, 1970)		l = −15→18
Tmin = 0.141, Tmax = 0.3893 standard reflections
2335 measured reflections every 60 min
2285 independent reflections intensity decay: none
1156 reflections with I > 2σ(I)
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.042  w = 1/[σ2(Fo2) + (0.0585P)2]
wR(F2) = 0.103(Δ/σ)max < 0.001
S = 0.94Δρmax = 2.51 e Å−3
2285 reflectionsΔρmin = −2.18 e Å−3
183 parametersExtinction correction: SHELXL97, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
1 restraintExtinction coefficient: 0.00036 (5)
Crystal data top
SrTeO3V = 2190.4 (8) Å3
Mr = 263.22Z = 24
Monoclinic, C2Ag Kα
a = 28.262 (6) ŵ = 12.04 mm−1
b = 5.935 (1) ÅT = 583 (2) K
c = 15.434 (3) Å0.24 × 0.22 × 0.09 mm
β = 122.21 (3)º
Data collection top
Enraf–Nonius CAD-4 with high-temperature device
diffractometer		1156 reflections with I > 2σ(I)
Absorption correction: analytical
(Alcock, 1970)		Rint = 0.079
Tmin = 0.141, Tmax = 0.3893 standard reflections
2335 measured reflections every 60 min
2285 independent reflections intensity decay: none
Refinement top
R[F2 > 2σ(F2)] = 0.042Δρmax = 2.51 e Å−3
wR(F2) = 0.103Δρmin = −2.18 e Å−3
S = 0.94Absolute structure: ?
2285 reflectionsFlack parameter: ?
183 parametersRogers parameter: ?
1 restraint
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Te1−0.01952 (6)0.4326 (9)0.14806 (10)0.0371 (4)
Te20.49454 (5)0.4367 (8)0.65532 (10)0.0286 (4)
Te30.11356 (5)−0.0611 (7)0.27897 (10)0.0267 (4)
Te40.35558 (6)−0.0645 (9)0.22906 (13)0.0434 (5)
Te50.14933 (6)0.9420 (9)−0.00044 (10)0.0406 (4)
Te60.26226 (5)0.4413 (7)0.41764 (9)0.0236 (3)
Sr10.12299 (7)0.4497 (9)0.42053 (14)0.0296 (5)
Sr20.24724 (8)0.4533 (9)0.11004 (15)0.0295 (5)
Sr30.24269 (9)−0.0454 (11)0.27598 (14)0.0370 (6)
Sr40.37712 (8)0.4159 (8)0.39581 (16)0.0282 (8)
Sr50.12480 (7)0.4440 (12)0.15394 (14)0.0356 (6)
Sr60.0000−0.079 (2)0.00000.0601 (16)
Sr70.50000.9165 (19)0.50000.0445 (15)
O110.0545 (8)0.508 (4)0.2171 (13)0.048 (5)*
O12−0.0152 (16)0.145 (7)0.108 (3)0.133 (14)*
O13−0.0485 (10)0.573 (5)0.0288 (17)0.067 (7)*
O210.4447 (10)0.656 (4)0.5752 (18)0.048 (7)*
O220.5460 (8)0.527 (4)0.6244 (14)0.046 (5)*
O230.4556 (13)0.202 (5)0.564 (2)0.065 (9)*
O310.1610 (9)0.183 (4)0.3309 (15)0.037 (5)*
O320.0979 (7)−0.011 (4)0.1455 (11)0.040 (5)*
O330.1708 (14)−0.268 (6)0.315 (2)0.084 (10)*
O410.3210 (12)−0.307 (5)0.249 (2)0.051 (8)*
O420.4061 (12)0.010 (6)0.363 (2)0.103 (10)*
O430.3094 (11)0.151 (5)0.231 (2)0.050 (8)*
O510.1802 (9)0.719 (4)0.1100 (16)0.039 (5)*
O520.2047 (13)1.015 (6)−0.024 (2)0.105 (11)*
O530.1681 (11)1.195 (5)0.0773 (19)0.061 (8)*
O610.2331 (5)0.418 (5)0.2787 (9)0.028 (3)*
O620.3166 (10)0.657 (4)0.4485 (18)0.034 (6)*
O630.3064 (9)0.190 (3)0.4327 (16)0.023 (5)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Te10.0249 (6)0.0491 (13)0.0340 (7)−0.001 (3)0.0136 (6)0.002 (3)
Te20.0245 (7)0.0286 (10)0.0334 (6)−0.003 (2)0.0160 (5)0.001 (2)
Te30.0261 (7)0.0251 (9)0.0321 (6)0.008 (2)0.0176 (5)0.012 (2)
Te40.0353 (8)0.0342 (11)0.0720 (11)−0.003 (3)0.0361 (8)−0.002 (3)
Te50.0302 (7)0.0469 (11)0.0319 (7)0.003 (3)0.0079 (6)0.005 (2)
Te60.0187 (5)0.0240 (8)0.0278 (6)−0.004 (2)0.0122 (5)−0.004 (2)
Sr10.0267 (9)0.0209 (13)0.0326 (9)−0.008 (2)0.0099 (7)−0.002 (2)
Sr20.0266 (9)0.0217 (14)0.0423 (10)0.005 (2)0.0197 (8)0.002 (2)
Sr30.0384 (10)0.0375 (17)0.0323 (9)0.001 (3)0.0169 (8)−0.002 (3)
Sr40.0218 (8)0.024 (2)0.0374 (9)−0.0008 (14)0.0151 (8)0.0041 (15)
Sr50.0261 (9)0.0453 (16)0.0329 (9)0.011 (3)0.0141 (8)0.010 (3)
Sr60.0311 (15)0.077 (5)0.0444 (17)0.0000.0016 (13)0.000
Sr70.0217 (13)0.062 (4)0.0467 (16)0.0000.0161 (12)0.000
Geometric parameters (Å, °) top
Te1—O131.77 (2)Sr4—O432.72 (3)
Te1—O111.827 (19)Sr4—O212.78 (2)
Te1—O121.84 (4)Sr5—O53v2.58 (3)
Te2—O211.83 (2)Sr5—O512.59 (2)
Te2—O221.84 (2)Sr5—O13vii2.59 (2)
Te2—O231.86 (3)Sr5—O612.611 (12)
Te3—O311.84 (2)Sr5—O112.66 (2)
Te3—O331.86 (4)Sr5—O33iii2.71 (3)
Te3—O321.886 (16)Sr5—O322.79 (2)
Te4—O421.84 (3)Sr5—O312.82 (2)
Te4—O431.84 (3)Sr5—O32iii3.31 (2)
Te4—O411.85 (3)Sr6—O122.34 (4)
Te5—O531.81 (3)Sr6—O12vii2.34 (4)
Te5—O521.84 (3)Sr6—O322.496 (16)
Te5—O511.96 (2)Sr6—O32vii2.496 (16)
Te6—O611.848 (12)Sr6—O13viii2.65 (3)
Te6—O621.85 (2)Sr6—O13v2.65 (3)
Te6—O631.88 (2)Sr7—O42ix2.42 (3)
Sr1—O63i2.52 (2)Sr7—O42iii2.42 (3)
Sr1—O62ii2.52 (2)Sr7—O23ix2.60 (3)
Sr1—O21ii2.61 (3)Sr7—O23iii2.60 (3)
Sr1—O312.68 (2)Sr7—O22vi2.84 (2)
Sr1—O112.692 (18)Sr7—O222.84 (2)
Sr1—O23i2.79 (3)Sr7—O212.85 (3)
Sr1—O33iii3.10 (4)Sr7—O21vi2.85 (3)
Sr2—O52iv2.37 (3)O13—Sr5vii2.59 (2)
Sr2—O512.47 (2)O13—Sr6iii2.65 (3)
Sr2—O41iii2.49 (3)O21—Sr1i2.61 (3)
Sr2—O432.51 (3)O22—Sr4vi2.44 (2)
Sr2—O53v2.53 (3)O23—Sr7v2.60 (3)
Sr2—O612.844 (13)O23—Sr1ii2.79 (3)
Sr2—O52v3.14 (3)O32—Sr5v3.31 (2)
Sr3—O632.53 (2)O33—Sr5v2.71 (3)
Sr3—O432.61 (3)O33—Sr1v3.10 (4)
Sr3—O51v2.61 (2)O41—Sr2v2.49 (3)
Sr3—O332.75 (4)O41—Sr4v2.55 (3)
Sr3—O612.77 (3)O42—Sr7v2.42 (3)
Sr3—O412.91 (3)O51—Sr3iii2.61 (2)
Sr3—O62v2.94 (2)O52—Sr2x2.37 (3)
Sr3—O53v3.00 (3)O52—Sr2iii3.14 (3)
Sr3—O313.16 (2)O53—Sr2iii2.53 (3)
Sr3—O61v3.20 (3)O53—Sr5iii2.58 (3)
Sr4—O22vi2.44 (2)O53—Sr3iii3.00 (3)
Sr4—O41iii2.55 (3)O61—Sr3iii3.20 (3)
Sr4—O622.67 (3)O62—Sr1i2.52 (2)
Sr4—O232.67 (3)O62—Sr3iii2.94 (2)
Sr4—O422.68 (4)O63—Sr1ii2.52 (2)
Sr4—O632.71 (2)
O13—Te1—O11104.0 (10)O22vi—Sr4—O62130.8 (7)
O13—Te1—O1299.3 (15)O41iii—Sr4—O6274.3 (9)
O11—Te1—O1299.4 (14)O22vi—Sr4—O2385.3 (8)
O21—Te2—O2292.8 (11)O41iii—Sr4—O23165.8 (9)
O21—Te2—O2395.1 (9)O62—Sr4—O23107.0 (8)
O22—Te2—O23104.6 (12)O22vi—Sr4—O4280.6 (9)
O31—Te3—O3394.2 (12)O41iii—Sr4—O42121.4 (9)
O31—Te3—O3292.5 (9)O62—Sr4—O42148.2 (9)
O33—Te3—O3295.2 (12)O23—Sr4—O4265.0 (9)
O42—Te4—O4386.8 (14)O22vi—Sr4—O63165.1 (7)
O42—Te4—O4199.3 (13)O41iii—Sr4—O63109.1 (8)
O43—Te4—O4195.5 (10)O62—Sr4—O6362.3 (5)
O53—Te5—O5287.6 (14)O23—Sr4—O6383.3 (8)
O53—Te5—O5198.4 (11)O42—Sr4—O6385.9 (8)
O52—Te5—O51107.6 (12)O22vi—Sr4—O43105.5 (8)
O61—Te6—O6298.4 (10)O41iii—Sr4—O4375.5 (6)
O61—Te6—O6386.5 (10)O62—Sr4—O43110.3 (8)
O62—Te6—O6396.4 (8)O23—Sr4—O43116.1 (9)
O63i—Sr1—O62ii78.2 (6)O42—Sr4—O4355.8 (8)
O63i—Sr1—O21ii126.5 (8)O63—Sr4—O4371.3 (8)
O62ii—Sr1—O21ii73.2 (8)O22vi—Sr4—O2178.7 (7)
O63i—Sr1—O31117.1 (7)O41iii—Sr4—O21109.0 (8)
O62ii—Sr1—O3173.7 (7)O62—Sr4—O2168.4 (8)
O21ii—Sr1—O3196.9 (8)O23—Sr4—O2160.0 (6)
O63i—Sr1—O11135.2 (7)O42—Sr4—O21122.2 (8)
O62ii—Sr1—O11141.5 (8)O63—Sr4—O21103.7 (8)
O21ii—Sr1—O1192.0 (7)O43—Sr4—O21174.4 (8)
O31—Sr1—O1173.2 (6)O53v—Sr5—O5174.9 (7)
O63i—Sr1—O23i84.5 (8)O53v—Sr5—O13vii89.6 (8)
O62ii—Sr1—O23i122.2 (9)O51—Sr5—O13vii78.3 (7)
O21ii—Sr1—O23i74.4 (8)O53v—Sr5—O6169.3 (7)
O31—Sr1—O23i156.7 (7)O51—Sr5—O6166.2 (7)
O11—Sr1—O23i85.4 (7)O13vii—Sr5—O61142.1 (7)
O63i—Sr1—O33iii78.9 (8)O53v—Sr5—O11151.6 (8)
O62ii—Sr1—O33iii119.7 (9)O51—Sr5—O11132.7 (7)
O21ii—Sr1—O33iii154.4 (8)O13vii—Sr5—O1190.3 (7)
O31—Sr1—O33iii68.9 (6)O61—Sr5—O11123.2 (5)
O11—Sr1—O33iii64.0 (7)O53v—Sr5—O33iii132.1 (10)
O23i—Sr1—O33iii110.1 (10)O51—Sr5—O33iii77.3 (9)
O52iv—Sr2—O51124.7 (10)O13vii—Sr5—O33iii121.8 (10)
O52iv—Sr2—O41iii85.8 (11)O61—Sr5—O33iii63.9 (9)
O51—Sr2—O41iii85.7 (9)O11—Sr5—O33iii70.2 (9)
O52iv—Sr2—O4398.3 (11)O53v—Sr5—O3266.9 (7)
O51—Sr2—O43133.6 (9)O51—Sr5—O32141.8 (6)
O41iii—Sr2—O4380.4 (8)O13vii—Sr5—O32100.7 (7)
O52iv—Sr2—O53v133.5 (10)O61—Sr5—O3299.2 (7)
O51—Sr2—O53v77.9 (7)O11—Sr5—O3285.3 (6)
O41iii—Sr2—O53v139.7 (9)O33iii—Sr5—O32129.7 (8)
O43—Sr2—O53v84.8 (9)O53v—Sr5—O3196.5 (8)
O52iv—Sr2—O61157.2 (8)O51—Sr5—O31130.0 (6)
O51—Sr2—O6164.2 (7)O13vii—Sr5—O31151.6 (7)
O41iii—Sr2—O6173.5 (8)O61—Sr5—O3164.8 (6)
O43—Sr2—O6169.4 (8)O11—Sr5—O3171.4 (6)
O53v—Sr2—O6166.3 (7)O33iii—Sr5—O3173.0 (8)
O52iv—Sr2—O52v83.7 (8)O32—Sr5—O3157.5 (5)
O51—Sr2—O52v120.4 (8)O53v—Sr5—O32iii134.3 (7)
O41iii—Sr2—O52v153.1 (9)O51—Sr5—O32iii62.1 (6)
O43—Sr2—O52v76.7 (9)O13vii—Sr5—O32iii68.2 (7)
O53v—Sr2—O52v51.7 (9)O61—Sr5—O32iii104.0 (7)
O61—Sr2—O52v110.6 (8)O11—Sr5—O32iii71.0 (6)
O63—Sr3—O4376.0 (8)O33iii—Sr5—O32iii53.7 (8)
O63—Sr3—O51v176.9 (7)O32—Sr5—O32iii153.2 (6)
O43—Sr3—O51v100.8 (8)O31—Sr5—O32iii122.2 (6)
O63—Sr3—O33106.8 (9)O12—Sr6—O12vii111 (2)
O43—Sr3—O33177.1 (10)O12—Sr6—O3278.8 (11)
O51v—Sr3—O3376.4 (8)O12vii—Sr6—O3290.8 (11)
O63—Sr3—O6157.4 (5)O12—Sr6—O32vii90.8 (11)
O43—Sr3—O6169.4 (7)O12vii—Sr6—O32vii78.8 (11)
O51v—Sr3—O61121.8 (6)O32—Sr6—O32vii161.6 (12)
O33—Sr3—O61112.7 (8)O12—Sr6—O13viii150.5 (10)
O63—Sr3—O41102.9 (7)O12vii—Sr6—O13viii90.9 (12)
O43—Sr3—O4159.2 (6)O32—Sr6—O13viii81.5 (7)
O51v—Sr3—O4175.1 (7)O32vii—Sr6—O13viii113.5 (7)
O33—Sr3—O41118.9 (10)O12—Sr6—O13v90.9 (12)
O61—Sr3—O41128.3 (6)O12vii—Sr6—O13v150.5 (10)
O63—Sr3—O62v70.5 (4)O32—Sr6—O13v113.5 (7)
O43—Sr3—O62v104.1 (8)O32vii—Sr6—O13v81.5 (7)
O51v—Sr3—O62v110.4 (7)O13viii—Sr6—O13v77.1 (12)
O33—Sr3—O62v76.3 (9)O42ix—Sr7—O42iii153.4 (18)
O61—Sr3—O62v127.8 (5)O42ix—Sr7—O23ix69.8 (10)
O41—Sr3—O62v65.2 (7)O42iii—Sr7—O23ix92.6 (11)
O63—Sr3—O53v118.0 (7)O42ix—Sr7—O23iii92.6 (11)
O43—Sr3—O53v74.3 (8)O42iii—Sr7—O23iii69.8 (10)
O51v—Sr3—O53v60.8 (6)O23ix—Sr7—O23iii98.5 (14)
O33—Sr3—O53v104.7 (9)O42ix—Sr7—O22vi132.3 (10)
O61—Sr3—O53v61.4 (6)O42iii—Sr7—O22vi72.7 (10)
O41—Sr3—O53v106.3 (8)O23ix—Sr7—O22vi114.5 (7)
O62v—Sr3—O53v170.0 (7)O23iii—Sr7—O22vi130.4 (8)
O63—Sr3—O3175.8 (6)O42ix—Sr7—O2272.7 (10)
O43—Sr3—O31127.9 (8)O42iii—Sr7—O22132.3 (10)
O51v—Sr3—O31106.5 (6)O23ix—Sr7—O22130.4 (8)
O33—Sr3—O3154.2 (7)O23iii—Sr7—O22114.5 (7)
O61—Sr3—O3158.5 (5)O22vi—Sr7—O2270.9 (8)
O41—Sr3—O31171.2 (7)O42ix—Sr7—O21110.7 (9)
O62v—Sr3—O31106.5 (6)O42iii—Sr7—O2184.0 (9)
O53v—Sr3—O3181.6 (7)O23ix—Sr7—O21172.1 (11)
O63—Sr3—O61v124.0 (5)O23iii—Sr7—O2173.6 (7)
O43—Sr3—O61v121.9 (7)O22vi—Sr7—O2171.4 (7)
O51v—Sr3—O61v57.4 (6)O22—Sr7—O2155.7 (7)
O33—Sr3—O61v56.0 (8)O42ix—Sr7—O21vi84.0 (9)
O61—Sr3—O61v168.6 (5)O42iii—Sr7—O21vi110.7 (9)
O41—Sr3—O61v63.1 (6)O23ix—Sr7—O21vi73.6 (7)
O62v—Sr3—O61v54.1 (5)O23iii—Sr7—O21vi172.1 (11)
O53v—Sr3—O61v118.0 (6)O22vi—Sr7—O21vi55.7 (7)
O31—Sr3—O61v110.2 (5)O22—Sr7—O21vi71.4 (7)
O22vi—Sr4—O41iii83.5 (8)O21—Sr7—O21vi114.3 (11)
Symmetry codes: (i) −x+1/2, y+1/2, −z+1; (ii) −x+1/2, y−1/2, −z+1; (iii) x, y+1, z; (iv) −x+1/2, y−1/2, −z; (v) x, y−1, z; (vi) −x+1, y, −z+1; (vii) −x, y, −z; (viii) −x, y−1, −z; (ix) −x+1, y+1, −z+1; (x) −x+1/2, y+1/2, −z.
Acknowledgements top

The authors thank Dr L. Ya. Sadovskaya for single-crystal preparation and Dr S. Yu. Stefanovich for the second harmonic generation measurements. This research was supported by the Russian Foundation for Basic Research (grant 06–03–32449).

references
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