Crystal structure of SrGeO₃ in the high-pressure perovskite-type phase

Single crystals of the SrGeO₃ (strontium germanium trioxide) high-pressure phase have been synthesized successfully at 6 GPa and 1223 K. The compound crystallizes with the ideal cubic perovskite-type structure (space group Pm-3m), which consists of a network of corner-linked regular GeO₆ octa­hedra (point-group symmetry m-3m), with the larger Sr atoms located at the centers of cavities in the form of SrO₁₂ cubocta­hedra (point-group symmetry m-3m) in the network. The degrees of covalencies included in the Sr—O and the Ge—O bonds calculated from bond valences are 20.4 and 48.9%, respectively. Thus, the Ge—O bond of the GeO₆ octa­hedron in the SrGeO₃ perovskite has a strong covalency, comparable to those of the Si—O bonds of the SiO₄ tetra­hedra in silicates with about 50% covalency. The thermal vibrations of the O atoms in the title compound are remarkably suppressed in the directions of the Ge—O bonds. This anisotropy ranks among the largest observed in stoichiometric cubic perovskites.

1. Chemical context

The phase transitions of the perovskite-type compounds ABO₃ have long attracted much attention for various industrial applications, as represented in ferroelectric substances such as BaTiO₃. The strontium germanate SrGeO₃ undergoes a sequence of phase transitions at high pressures and high temperatures of pyroxenoid (pseudowollastonite) type → walstromite type → perovskite type (Shimizu et al., 1970; Akaogi et al., 2005). In a recent study (Mizoguchi et al., 2011), it was reported that the high-pressure perovskite-type phase of SrGeO₃ is a promising transparent electronic conductor. A detailed structural study of this perovskite-type phase is important to elucidate the origin of the conduction mechanism. Despite such importance, the high-pressure perovskite-type phase has been studied so far only on the basis of polycrystalline samples and its powder X-ray diffraction pattern has only suggested that it adopts the ideal cubic perovskite structure. Perovskite-type compounds are well-known to have various symmetries owing to a slight tilting of the BO₆ octa­hedra (Glazer, 1972, 1975). However, it is often difficult to determine their actual symmetries from powder X-ray diffraction techniques. Thus, more precise data based on single crystal X-ray diffraction are indispensable for the determination of the crystal structure of the SrGeO₃ high-pressure perovskite-type phase. We recently succeeded in the growth of SrGeO₃ perovskite-type single crystals at high pressure and high temperature. The crystal structure refined from single-crystal X-ray diffraction data is reported here.

2. Structural commentary

The high-pressure phase of SrGeO₃ crystallizes with the cubic perovskite-type structure (space group Pmm). The crystal structure consists of a network of corner-linked regular GeO₆ octa­hedra with the larger Sr atoms located at the centers of cavities in the network, forming SrO₁₂ cubocta­hedra (Fig. 1). As a result of the ideal symmetry, tilts and distortions of the GeO₆ octa­hedra are not present. The Sr, Ge and O atoms occupy Wyckoff positions 1a (0, 0, 0), 1b (0.5, 0.5, 0.5) and 3c (0, 0.5, 0.5), respectively, without any freedom of atomic positions. The corresponding site symmetries are mm, mm and 4/mm.m, respectively. The observed Sr—O distance in the SrO₁₂ cubocta­hedron and the Ge—O distance in the GeO₆ octa­hedron are 2.6855 (1) Å and 1.8989 (1) Å, respectively, which are much shorter than the distances expected from the effective ionic radii (Sr—O = 2.84 Å, Ge—O = 1.93 Å; Shannon, 1976). The ratios of covalency included in the bonds calculated from f′_c/s (= as^M-1) are 20.4% for the Sr—O bond and 48.9% for the Ge—O bond, where f′_c, given by as^M (Brown & Shannon, 1973), is the covalence in bonds; s is the bond valence; a and M are parameters relating covalence to bond valence. This value of the present Ge—O bond ranks among the largest in B—O bonds of BO₆ octa­hedra in A²⁺B⁴⁺O₃-type cubic perovskites (A = twelvefold-coordinated cations, B = sixfold-coordinated cations) [cf. 39.8% for the Ti—O bond in SrTiO₃ (Abramov et al., 1995) and 37.8% for the Zr—O bond in BaZrO₃ (Levin et al., 2003)]. It is noteworthy, thus, that the Ge—O bond of the GeO₆ octa­hedron in the present crystal has a strong covalency comparable to those of the Si—O bonds of the SiO₄ tetra­hedra in silicates with about 50% covalency.

Figure 1 Representation of the SrGeO3 perovskite-type structure showing corner-linked GeO6 octa­hedra.

The site-symmetry constraints require that the displacement ellipsoids of the Sr and Ge atoms are always spherical and that of the O atom is an uniaxial ellipsoid with one determinable ellipsoid-axis in the direction of the Ge—O bond and two undeterminable ones in the directions perpendicular to it. The mean-square displacement (MSD) of the O atom is the smallest [〈u_S²〉 = 0.0011 (8) Ų] in the former direction and the largest [〈u_L²〉 = 0.0077 (7) Ų] in the latter directions. The 〈u_S²〉/〈u_L²〉 ratio of 0.14 calculated for the present crystal indicates that the displacement ellipsoid of the O atom is remarkably compressed in the former directions, as shown in Fig. 2. Such remarkable anisotropy is commonly observed in cubic perovskites with stoichiometric compositions, and the present 〈u_S²〉/〈u_L²〉 ratio ranks among the smallest observed [cf. 〈u_S²〉/〈u_L²〉 = 0.14 for LaAlO₃ (Nakatsuka et al., 2005), 0.43 for SrTiO₃ (Abramov et al., 1995), 0.38 for KTaO₃ (Zhurova et al., 2000), 0.50 for SrFeO₃ (Hodges et al., 2000) and 0.29 for BaZrO₃ (Levin et al., 2003)]. The remarkable anisotropy of the MSD of the O atom in the SrGeO₃ perovskite-type structure might be related to the strong covalency of the Ge—O bond.

Figure 2 The unit cell of the cubic SrGeO3 perovskite with displacement ellipsoids drawn at the 80% probability level.

3. Synthesis and crystallization

A polycrystalline sample of SrGeO₃ pseudowollastonite as the starting material was prepared by solid-state reaction of special grade reagents SrCO₃ and GeO₂. The resulting SrGeO₃ pseudowollastonite material was charged in a gold capsule and then put into a BN sample chamber. As shown in Fig. 3, the sample chamber was put between a pair of LaCrO₃ disc heaters and encased in a cubic-shaped pressure-transmitting medium made of boron-ep­oxy resin. This cell assembly was compressed with a 700 ton cubic anvil-type press. After being kept at 6 GPa and 1223 K for 1 h, the product was quenched by shutting off the electric power supply. The pressure was then released slowly and the product was recovered at ambient conditions. Single crystals of SrGeO₃ perovskite were found in the recovered sample, together with an unknown single-crystal phase.

Figure 3 Cell assembly used in the synthetic experiment at high pressure.

4. Refinement

The unit-cell parameters of the crystal under investigation assuming a triclinic cell only exhibit a minute deviation from a cubic unit cell [a = 3.7979 (2), b = 3.7978 (3), c = 3.7972 (3) Å, α = 89.984 (6), β = 89.997 (6), γ = 89.988 (5)°]. Systematic absences of reflections also agreed with space group Pmm. Indeed, the present crystal was satisfactorily refined in the ideal cubic perovskite structure as judged from the excellent reliability indices (Table 1).

Table 1
Experimental details

Crystal data
Chemical formula	SrGeO3
Mr	208.23
Crystal system, space group	Cubic, Pmm
Temperature (K)	296
a (Å)	3.7978 (2)
V (Å^3)	54.78 (1)
Z	1
Radiation type	Mo Kα
μ (mm^−1)	37.73
Crystal size (mm)	0.10 × 0.08 × 0.08
Data collection
Diffractometer	Rigaku AFC-7R
Absorption correction	ψ scan (North et al., 1968)
Tmin, Tmax	0.037, 0.049
No. of measured, independent and observed [F > 3σ(F)] reflections	521, 116, 66
Rint	0.023
(sin θ/λ)max (Å^−1)	1.219
Refinement
R[F > 3σ(F)], wR(F), S	0.011, 0.010, 1.95
No. of reflections	64
No. of parameters	6
Δρmax, Δρmin (e Å^−3)	1.04, −1.38
Computer programs: WinAFC (Rigaku, 1999), RADY (Sasaki, 1987), ATOMS for Windows (Dowty, 2000) and publCIF (Westrip, 2010).

Intensity data were averaged in Laue symmetry mm to give 116 independent reflections. Of these, independent reflections with F_o 3σ(F_o) were omitted for refinement. Even if independent reflections had intensities of F_o > 3σ(F_o) after averaging, those averaged from a data set of equivalent reflections including reflection(s) with F_o 3σ(F_o) were also discarded since these reflections were potentially affected by multiple diffraction. Moreover, independent reflections with (sin θ)/λ < 0.220 Å⁻¹ were eliminated to reduce secondary extinction effects and to avoid dependence on atomic charge as far as possible in the choice of atomic scattering factors. Finally, 64 independent reflections were used in the present refinement. Several correction models for the secondary extinction effects were attempted during the refinement, and the isotropic correction of Type I (Becker & Coppens, 1974a,b) with a Gaussian mosaic spread distribution model yielded the best fits. Crystal data, data collection and structure refinement details are summarized in Table 1.

Supporting information

Computing details

Data collection: WinAFC (Rigaku, 1999); cell refinement: WinAFC (Rigaku, 1999); data reduction: RADY (Sasaki, 1987); program(s) used to refine structure: RADY (Sasaki, 1987); molecular graphics: ATOMS for Windows (Dowty, 2000); software used to prepare material for publication: publCIF (Westrip, 2010).

Strontium germanium trioxide

Crystal data

SrGeO3	Dx = 6.315 Mg m^−3
Mr = 208.23	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 25 reflections
Hall symbol: -P 4 2 3	θ = 21.5–25.0°
a = 3.7978 (2) Å	µ = 37.73 mm^−1
V = 54.78 (1) Å^3	T = 296 K
Z = 1	Fragment, colorless
F(000) = 94	0.10 × 0.08 × 0.08 mm

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.023
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North et al., 1968)	h = 0→9
Tmin = 0.037, Tmax = 0.049	k = 0→9
521 measured reflections	l = 0→9
116 independent reflections	3 standard reflections every 150 reflections
66 reflections with F > 3.0σ(F)	intensity decay: none

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
R[F^2 > 2σ(F^2)] = 0.019	(Δ/σ)max < 0.001
wR(F^2) = 0.020	Δρmax = 1.04 e Å^−3
S = 1.95	Δρmin = −1.38 e Å^−3
64 reflections	Extinction correction: isotropic Type I (Becker & Coppens, 1974a,b)
6 parameters	Extinction coefficient: 0.40 (1)E3

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Sr	0.0000	0.0000	0.0000	0.00300 (9)
Ge	0.5000	0.5000	0.5000	0.00182 (9)
O	0.0000	0.5000	0.5000	0.0055 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sr	0.0030 (2)	0.0030	0.0030	0.0000	0.0000	0.0000
Ge	0.0018 (2)	0.0018	0.0018	0.0000	0.0000	0.0000
O	0.0011 (8)	0.0077 (7)	0.0077	0.0000	0.0000	0.0000

Geometric parameters (Å, º)

Sr—O	2.6855 (1)	Ge—O^i	1.8989 (1)
Sr—O^i	2.6855 (1)	Ge—O^ii	1.8989 (1)
Sr—O^ii	2.6855 (1)	Ge—O^xii	1.8989 (1)
Sr—O^iii	2.6855 (1)	Ge—O^xiii	1.8989 (1)
Sr—O^iv	2.6855 (1)	Ge—O^xiv	1.8989 (1)
Sr—O^v	2.6855 (1)	O—O^i	2.6855 (1)
Sr—O^vi	2.6855 (1)	O—O^ii	2.6855 (1)
Sr—O^vii	2.6855 (1)	O—O^v	2.6855 (1)
Sr—O^viii	2.6855 (1)	O—O^vi	2.6855 (1)
Sr—O^ix	2.6855 (1)	O—O^xv	2.6855 (1)
Sr—O^x	2.6855 (1)	O—O^xvi	2.6855 (1)
Sr—O^xi	2.6855 (1)	O—O^xii	2.6855 (1)
Ge—O	1.8989 (1)	O—O^xiii	2.6855 (1)
O—Sr—O^i	60.00	Sr—O—O^vi	60.00
O—Sr—O^ii	60.00	Sr—O—O^xv	120.00
O—Sr—O^iii	120.00	Sr—O—O^xvi	120.00
O—Sr—O^iv	120.00	Sr—O—O^xii	120.00
O—Sr—O^v	60.00	Sr—O—O^xiii	120.00
O—Sr—O^vi	60.00	Ge—O—Ge^xx	180.00
O—Sr—O^vii	180.00	Ge—O—O^i	45.00
O—Sr—O^viii	90.00	Ge—O—O^ii	45.00
O—Sr—O^ix	120.00	Ge—O—O^v	135.00
O—Sr—O^x	90.00	Ge—O—O^vi	135.00
O—Sr—O^xi	120.00	Ge—O—O^xv	135.00
O—Sr^i—O^ii	60.00	Ge—O—O^xvi	135.00
O—Sr^i—O^iii	120.00	Ge—O—O^xii	45.00
O—Sr^ii—O^iv	120.00	Ge—O—O^xiii	45.00
O—Ge—O^i	90.00	Ge—O^xx—O^v	45.00
O—Ge—O^ii	90.00	Ge—O^xx—O^vi	45.00
O—Ge—O^xii	90.00	Ge—O^xx—O^xv	45.00
O—Ge—O^xiii	90.00	Ge—O^xx—O^xvi	45.00
O—Ge—O^xiv	180.00	O—O^i—O^ii	60.00
O—Ge^i—O^ii	90.00	O—O^i—O^xvi	180.00
O—Ge^i—O^xii	90.00	O—O^i—O^xii	60.00
O—Ge^ii—O^xiii	90.00	O—O^ii—O^xv	180.00
Sr—O—Sr^xvii	90.00	O—O^ii—O^xiii	60.00
Sr—O—Sr^xviii	90.00	O—O^v—O^vi	60.00
Sr—O—Sr^xix	180.00	O—O^v—O^xv	60.00
Sr—O—Ge	90.00	O—O^v—O^xiii	180.00
Sr—O—Ge^xx	90.00	O—O^vi—O^xvi	60.00
Sr—O—O^i	60.00	O—O^vi—O^xii	180.00
Sr—O—O^ii	60.00	O—O^xv—O^xvi	60.00
Sr—O—O^v	60.00	O—O^xii—O^xiii	60.00

Symmetry codes: (i) z, x, y; (ii) y, z, x; (iii) y−1, z−1, x; (iv) z−1, x, y−1; (v) z−1, x, y; (vi) y−1, z, x; (vii) x, y−1, z−1; (viii) x, y−1, z; (ix) y, z−1, x; (x) x, y, z−1; (xi) z, x, y−1; (xii) y, z, x+1; (xiii) z, x+1, y; (xiv) x+1, y, z; (xv) y−1, z, x+1; (xvi) z−1, x+1, y; (xvii) x, y, z+1; (xviii) x, y+1, z; (xix) x, y+1, z+1; (xx) x−1, y, z.