Barium chromium oxide, Ba₃Cr₂O₈, as grown by the traveling solvent floating-zone technique

Large single crystals of the incongruently melting compound tribarium dichromium octa­oxide, Ba₃Cr₂O₈, were grown by the traveling solvent floating-zone technique for the first time and characterized by X-ray diffraction at room temperature. The structure is composed of CrO₄^3- tetra­hedra and Ba²⁺ ions. The chromium ions are found in the rare +5 valence state and form double-layered triangular lattices, which are stacked along the c axis with threefold periodicity. All atoms lie on special positions. One Ba, one O and the Cr atoms have site symmetry 3m, the other Ba atom has site symmetry m, and the other O atom has site symmetry m. Magnetic measurements suggest that this material is a spin dimer system with a spin-singlet ground state.

Key indicators

• Single-crystal X-ray study
• T = 296 K
• Mean [sigma](r-O) = 0.001 Å
• R factor = 0.021
• wR factor = 0.051
• Data-to-parameter ratio = 48.8

checkCIF/PLATON results

No syntax errors found



Alert level C
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ ....          ?
PLAT731_ALERT_1_C Bond    Calc   2.9267(5), Rep   2.9268(2) ......       2.50 su-Ra
              BA2  -O1      1.555   7.454
PLAT731_ALERT_1_C Bond    Calc   2.9267(5), Rep   2.9268(2) ......       2.50 su-Ra
              BA2  -O1      1.555   7.344
PLAT731_ALERT_1_C Bond    Calc   2.9267(6), Rep   2.9268(2) ......       3.00 su-Ra
              BA2  -O1      1.555   9.564
PLAT731_ALERT_1_C Bond    Calc   2.9267(7), Rep   2.9268(2) ......       3.50 su-Ra
              BA2  -O1      1.555   8.544
PLAT731_ALERT_1_C Bond    Calc   2.9267(7), Rep   2.9268(2) ......       3.50 su-Ra
              BA2  -O1      1.555   8.444
PLAT731_ALERT_1_C Bond    Calc   2.9267(6), Rep   2.9268(2) ......       3.00 su-Ra
              BA2  -O1      1.555   9.554
PLAT731_ALERT_1_C Bond    Calc   2.9267(5), Rep   2.9268(2) ......       2.50 su-Ra
              O1   -BA2     1.555  13.545
PLAT731_ALERT_1_C Bond    Calc   2.9267(5), Rep   2.9268(2) ......       2.50 su-Ra
              O1   -BA2     1.555  13.655

Alert level G
PLAT794_ALERT_5_G Check Predicted Bond Valency for Cr1         (5)       4.66

   0 ALERT level A = In general: serious problem
   0 ALERT level B = Potentially serious problem
   9 ALERT level C = Check and explain
   1 ALERT level G = General alerts; check

   9 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   0 ALERT type 2 Indicator that the structure model may be wrong or deficient
   0 ALERT type 3 Indicator that the structure quality may be low
   0 ALERT type 4 Improvement, methodology, query or suggestion
   1 ALERT type 5 Informative message, check

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S1. Comment

The system Ba₃Cr₂O₈ was recently synthesized in polycrystalline form to study its magnetic properties (Nakajima et al., 2006). Susceptibility and high-field magnetization measurements have provided evidence that this material is a new spin dimer system. The interesting magnetic properties observed motivated our growth of large single crystals up to 6 mm x 4 mm x 1 mm in size. Fig.1 shows the structure of Ba₃Cr₂O₈, which consists of a series of CrO4^3- tetrahedra and Ba²⁺ ions.

Smaller single crystals of Ba₃Cr₂O₈ (suitable for X-ray work) were previously grown using a flux method (Mattausch and Muller-Buschbaum, 1972), but the magnetic properties of these crystals were never investigated. The authors did solve the crystallographic structure, but the reported R values were quite high (> 0.08) and both the isotropic and anisotropic displacement parameters were not presented. It follows that the purpose of this work is to present a more accurate and complete solution of the crystallographic structure of this system. This work also proves that single crystals of materials containing the difficult-to-stabilize Cr⁵⁺ ion can be grown by the traveling solvent floating zone technique.

Related literature

For details of the first single-crystal growth of Ba₃Cr₂O₈ (X-ray size crystals), see Mattausch & Muller-Buschbaum (1972). For a more recent synthesis of Ba₃Cr₂O₈ and some measurements of magnetic properties, see Nakajima et al. (2006). Additional details describing the growth of large single crystals by the traveling solvent floating-zone method and subsequent magnetic characterization measurements, see Aczel et al. (2007).

S2. Experimental

Large single crystals of the title compound were grown by the traveling solvent floating zone method in an Ar enviroment, using BaCO₃ and Cr₂O₃ as starting materials. The growth rate was fast (both 27 mm/h and 18 mm/h were applied), which was necessary to maintain zone stability. The feed and seed rods were rotating in opposite directions at 20 rpm throughout the growth, and a 3 cm boule of the desired Ba₃Cr₂O₈ phase was obtained on the seed rod. Due to the very fast growth, the as-obtained boule consisted of many well oriented crystalline grains.

Computing details

Data collection: APEX2 (Bruker, 2006); cell refinement: APEX2 (Bruker, 2006); data reduction: APEX2 (Bruker, 2006); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997a); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997a); molecular graphics: GRETEP (Laugier & Bochu, 2003); software used to prepare material for publication: SHELXTL (Sheldrick, 1997b).

Figures

Fig. 1. 50% displacement ellipsoid plot of the unit cell. Ba ions are shown in dark blue, Cr ions are shown in blue, and O ions are shown in red.

tribarium dichromium octaoxide

Crystal data

Ba3Cr2O8	Dx = 5.248 Mg m^−3
Mr = 644.02	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3m	Cell parameters from 2788 reflections
Hall symbol: -R 3 2"	θ = 2.9–42.1°
a = 5.7450 (2) Å	µ = 16.87 mm^−1
c = 21.3883 (10) Å	T = 296 K
V = 611.35 (4) Å^3	Rod, blue
Z = 3	0.30 × 0.05 × 0.02 mm
F(000) = 840

Data collection

Bruker APEXII CCD area-detector diffractometer	928 independent reflections
Radiation source: fine-focus sealed tube	779 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.034
ϕ and ω scans	θmax = 52.2°, θmin = 2.9°
Absorption correction: numerical (face correction; APEX2; Bruker, 2006)	h = −8→12
Tmin = 0.38, Tmax = 0.77	k = −12→10
9434 measured reflections	l = −47→46

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.021	w = 1/[σ^2(Fo^2) + (0.0269P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.051	(Δ/σ)max = 0.001
S = 1.07	Δρmax = 1.98 e Å^−3
928 reflections	Δρmin = −2.01 e Å^−3
19 parameters	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0065 (3)

Special details

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 > 2σ(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 (Ų)

	x	y	z	Uiso*/Ueq
Ba1	0.0000	0.0000	0.0000	0.01420 (5)
Ba2	0.0000	0.0000	0.205924 (6)	0.00918 (5)
Cr1	0.0000	0.0000	0.407042 (18)	0.00721 (6)
O1	0.82832 (9)	0.17168 (9)	0.89871 (5)	0.01272 (17)
O2	0.0000	0.0000	0.32872 (9)	0.0273 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.01762 (7)	0.01762 (7)	0.00736 (7)	0.00881 (3)	0.000	0.000
Ba2	0.00956 (5)	0.00956 (5)	0.00841 (6)	0.00478 (3)	0.000	0.000
Cr1	0.00723 (8)	0.00723 (8)	0.00718 (11)	0.00361 (4)	0.000	0.000
O1	0.0143 (3)	0.0143 (3)	0.0137 (4)	0.0102 (3)	0.00047 (14)	−0.00047 (14)
O2	0.0366 (8)	0.0366 (8)	0.0085 (7)	0.0183 (4)	0.000	0.000

Geometric parameters (Å, º)

Ba1—O1^i	2.7589 (10)	Ba2—Cr1^xix	3.5101 (2)
Ba1—O1^ii	2.7589 (10)	Ba2—Cr1^xx	3.5101 (2)
Ba1—O1^iii	2.7589 (10)	Cr1—O2	1.675 (2)
Ba1—O1^iv	2.7589 (10)	Cr1—O1^xxi	1.7133 (9)
Ba1—O1^v	2.7589 (10)	Cr1—O1^xxii	1.7133 (9)
Ba1—O1^vi	2.7589 (10)	Cr1—O1^xxiii	1.7134 (9)
Ba1—O2^vii	3.3183 (1)	Cr1—Ba2^xx	3.5101 (2)
Ba1—O2^viii	3.3183 (1)	Cr1—Ba2^xxiv	3.5101 (2)
Ba1—O2^ix	3.3183 (1)	Cr1—Ba2^xix	3.5101 (2)
Ba1—O2^x	3.3183 (1)	Cr1—Ba1^xxv	3.6724 (2)
Ba1—O2^xi	3.3184 (1)	Cr1—Ba1^xxvi	3.6724 (2)
Ba1—O2^xii	3.3184 (1)	Cr1—Ba1^xxvii	3.6725 (2)
Ba2—O2	2.626 (2)	Cr1—Cr1^xxiv	4.5764 (6)
Ba2—O1^i	2.8155 (10)	Cr1—Cr1^xx	4.5764 (6)
Ba2—O1^v	2.8155 (10)	O2—Ba1^xxvi	3.3183 (1)
Ba2—O1^iii	2.8155 (10)	O2—Ba1^xxv	3.3183 (1)
Ba2—O1^xiii	2.9268 (2)	O2—Ba1^xxvii	3.3184 (1)
Ba2—O1^xiv	2.9268 (2)	O1—Cr1^xxiii	1.7133 (9)
Ba2—O1^xv	2.9268 (2)	O1—Ba1^xxviii	2.7589 (10)
Ba2—O1^xvi	2.9268 (2)	O1—Ba2^i	2.8155 (10)
Ba2—O1^xvii	2.9268 (2)	O1—Ba2^xxix	2.9268 (2)
Ba2—O1^xviii	2.9268 (2)	O1—Ba2^xxx	2.9268 (2)
O1^i—Ba1—O1^ii	180.00 (3)	O1^xvi—Ba2—O1^xviii	56.85 (4)
O1^i—Ba1—O1^iii	64.86 (3)	O1^xvii—Ba2—O1^xviii	116.445 (13)
O1^ii—Ba1—O1^iii	115.14 (3)	O2—Ba2—Cr1^xix	70.902 (7)
O1^i—Ba1—O1^iv	115.14 (3)	O1^i—Ba2—Cr1^xix	71.74 (2)
O1^ii—Ba1—O1^iv	64.86 (3)	O1^v—Ba2—Cr1^xix	123.145 (7)
O1^iii—Ba1—O1^iv	180.00 (3)	O1^iii—Ba2—Cr1^xix	123.145 (7)
O1^i—Ba1—O1^v	64.86 (3)	O1^xiii—Ba2—Cr1^xix	87.343 (18)
O1^ii—Ba1—O1^v	115.14 (3)	O1^xiv—Ba2—Cr1^xix	87.343 (18)
O1^iii—Ba1—O1^v	64.86 (3)	O1^xv—Ba2—Cr1^xix	137.11 (2)
O1^iv—Ba1—O1^v	115.14 (3)	O1^xvi—Ba2—Cr1^xix	29.108 (18)
O1^i—Ba1—O1^vi	115.14 (3)	O1^xvii—Ba2—Cr1^xix	137.11 (2)
O1^ii—Ba1—O1^vi	64.86 (3)	O1^xviii—Ba2—Cr1^xix	29.109 (18)
O1^iii—Ba1—O1^vi	115.14 (3)	O2—Ba2—Cr1^xx	70.900 (7)
O1^iv—Ba1—O1^vi	64.86 (3)	O1^i—Ba2—Cr1^xx	123.146 (7)
O1^v—Ba1—O1^vi	180.00 (3)	O1^v—Ba2—Cr1^xx	123.146 (7)
O1^i—Ba1—O2^vii	70.56 (3)	O1^iii—Ba2—Cr1^xx	71.74 (2)
O1^ii—Ba1—O2^vii	109.44 (3)	O1^xiii—Ba2—Cr1^xx	29.109 (18)
O1^iii—Ba1—O2^vii	70.56 (3)	O1^xiv—Ba2—Cr1^xx	137.11 (2)
O1^iv—Ba1—O2^vii	109.44 (3)	O1^xv—Ba2—Cr1^xx	29.109 (18)
O1^v—Ba1—O2^vii	126.55 (4)	O1^xvi—Ba2—Cr1^xx	87.343 (18)
O1^vi—Ba1—O2^vii	53.45 (4)	O1^xvii—Ba2—Cr1^xx	87.343 (18)
O1^i—Ba1—O2^viii	70.56 (3)	O1^xviii—Ba2—Cr1^xx	137.11 (2)
O1^ii—Ba1—O2^viii	109.44 (3)	Cr1^xix—Ba2—Cr1^xx	109.841 (7)
O1^iii—Ba1—O2^viii	126.55 (4)	O2—Cr1—O1^xxi	110.14 (4)
O1^iv—Ba1—O2^viii	53.45 (4)	O2—Cr1—O1^xxii	110.14 (4)
O1^v—Ba1—O2^viii	70.56 (3)	O1^xxi—Cr1—O1^xxii	108.80 (4)
O1^vi—Ba1—O2^viii	109.44 (3)	O2—Cr1—O1^xxiii	110.14 (4)
O2^vii—Ba1—O2^viii	119.913 (4)	O1^xxi—Cr1—O1^xxiii	108.79 (4)
O1^i—Ba1—O2^ix	109.44 (3)	O1^xxii—Cr1—O1^xxiii	108.79 (4)
O1^ii—Ba1—O2^ix	70.56 (3)	O2—Cr1—Ba2^xx	109.099 (7)
O1^iii—Ba1—O2^ix	53.45 (4)	O1^xxi—Cr1—Ba2^xx	56.202 (7)
O1^iv—Ba1—O2^ix	126.55 (4)	O1^xxii—Cr1—Ba2^xx	140.76 (4)
O1^v—Ba1—O2^ix	109.44 (3)	O1^xxiii—Cr1—Ba2^xx	56.204 (7)
O1^vi—Ba1—O2^ix	70.56 (3)	O2—Cr1—Ba2^xxiv	109.099 (7)
O2^vii—Ba1—O2^ix	60.087 (4)	O1^xxi—Cr1—Ba2^xxiv	140.76 (4)
O2^viii—Ba1—O2^ix	180.00 (7)	O1^xxii—Cr1—Ba2^xxiv	56.202 (7)
O1^i—Ba1—O2^x	109.44 (3)	O1^xxiii—Cr1—Ba2^xxiv	56.204 (7)
O1^ii—Ba1—O2^x	70.56 (3)	Ba2^xx—Cr1—Ba2^xxiv	109.842 (7)
O1^iii—Ba1—O2^x	109.44 (3)	O2—Cr1—Ba2^xix	109.098 (7)
O1^iv—Ba1—O2^x	70.56 (3)	O1^xxi—Cr1—Ba2^xix	56.205 (7)
O1^v—Ba1—O2^x	53.45 (4)	O1^xxii—Cr1—Ba2^xix	56.205 (7)
O1^vi—Ba1—O2^x	126.55 (4)	O1^xxiii—Cr1—Ba2^xix	140.76 (4)
O2^vii—Ba1—O2^x	180.00 (7)	Ba2^xx—Cr1—Ba2^xix	109.841 (7)
O2^viii—Ba1—O2^x	60.087 (4)	Ba2^xxiv—Cr1—Ba2^xix	109.841 (7)
O2^ix—Ba1—O2^x	119.913 (4)	O2—Cr1—Ba1^xxv	64.579 (6)
O1^i—Ba1—O2^xi	126.55 (4)	O1^xxi—Cr1—Ba1^xxv	124.876 (11)
O1^ii—Ba1—O2^xi	53.45 (4)	O1^xxii—Cr1—Ba1^xxv	45.56 (4)
O1^iii—Ba1—O2^xi	70.56 (3)	O1^xxiii—Cr1—Ba1^xxv	124.874 (11)
O1^iv—Ba1—O2^xi	109.44 (3)	Ba2^xx—Cr1—Ba1^xxv	173.677 (12)
O1^v—Ba1—O2^xi	70.56 (3)	Ba2^xxiv—Cr1—Ba1^xxv	73.364 (2)
O1^vi—Ba1—O2^xi	109.44 (3)	Ba2^xix—Cr1—Ba1^xxv	73.365 (2)
O2^vii—Ba1—O2^xi	119.912 (4)	O2—Cr1—Ba1^xxvi	64.579 (6)
O2^viii—Ba1—O2^xi	119.912 (4)	O1^xxi—Cr1—Ba1^xxvi	45.56 (4)
O2^ix—Ba1—O2^xi	60.088 (4)	O1^xxii—Cr1—Ba1^xxvi	124.876 (11)
O2^x—Ba1—O2^xi	60.088 (4)	O1^xxiii—Cr1—Ba1^xxvi	124.874 (11)
O1^i—Ba1—O2^xii	53.45 (4)	Ba2^xx—Cr1—Ba1^xxvi	73.364 (2)
O1^ii—Ba1—O2^xii	126.55 (4)	Ba2^xxiv—Cr1—Ba1^xxvi	173.677 (12)
O1^iii—Ba1—O2^xii	109.44 (3)	Ba2^xix—Cr1—Ba1^xxvi	73.365 (2)
O1^iv—Ba1—O2^xii	70.56 (3)	Ba1^xxv—Cr1—Ba1^xxvi	102.921 (7)
O1^v—Ba1—O2^xii	109.44 (3)	O2—Cr1—Ba1^xxvii	64.579 (6)
O1^vi—Ba1—O2^xii	70.56 (3)	O1^xxi—Cr1—Ba1^xxvii	124.873 (11)
O2^vii—Ba1—O2^xii	60.088 (4)	O1^xxii—Cr1—Ba1^xxvii	124.873 (11)
O2^viii—Ba1—O2^xii	60.088 (4)	O1^xxiii—Cr1—Ba1^xxvii	45.56 (4)
O2^ix—Ba1—O2^xii	119.912 (4)	Ba2^xx—Cr1—Ba1^xxvii	73.365 (2)
O2^x—Ba1—O2^xii	119.912 (4)	Ba2^xxiv—Cr1—Ba1^xxvii	73.365 (2)
O2^xi—Ba1—O2^xii	180.00 (7)	Ba2^xix—Cr1—Ba1^xxvii	173.678 (12)
O2—Ba2—O1^i	142.65 (2)	Ba1^xxv—Cr1—Ba1^xxvii	102.920 (7)
O2—Ba2—O1^v	142.64 (2)	Ba1^xxvi—Cr1—Ba1^xxvii	102.920 (7)
O1^i—Ba2—O1^v	63.40 (3)	O2—Cr1—Cr1^xxiv	46.451 (7)
O2—Ba2—O1^iii	142.64 (2)	O1^xxi—Cr1—Cr1^xxiv	156.59 (4)
O1^i—Ba2—O1^iii	63.40 (3)	O1^xxii—Cr1—Cr1^xxiv	84.09 (3)
O1^v—Ba2—O1^iii	63.40 (3)	O1^xxiii—Cr1—Cr1^xxiv	84.09 (3)
O2—Ba2—O1^xiii	78.99 (2)	Ba2^xx—Cr1—Cr1^xxiv	124.602 (5)
O1^i—Ba2—O1^xiii	99.33 (2)	Ba2^xxiv—Cr1—Cr1^xxiv	62.648 (3)
O1^v—Ba2—O1^xiii	131.476 (10)	Ba2^xix—Cr1—Cr1^xxiv	124.602 (5)
O1^iii—Ba2—O1^xiii	68.34 (4)	Ba1^xxv—Cr1—Cr1^xxiv	51.460 (3)
O2—Ba2—O1^xiv	78.99 (2)	Ba1^xxvi—Cr1—Cr1^xxiv	111.030 (13)
O1^i—Ba2—O1^xiv	99.33 (2)	Ba1^xxvii—Cr1—Cr1^xxiv	51.460 (3)
O1^v—Ba2—O1^xiv	68.34 (4)	O2—Cr1—Cr1^xx	46.451 (7)
O1^iii—Ba2—O1^xiv	131.476 (10)	O1^xxi—Cr1—Cr1^xx	84.09 (3)
O1^xiii—Ba2—O1^xiv	157.90 (4)	O1^xxii—Cr1—Cr1^xx	156.59 (4)
O2—Ba2—O1^xv	78.99 (2)	O1^xxiii—Cr1—Cr1^xx	84.09 (3)
O1^i—Ba2—O1^xv	131.476 (10)	Ba2^xx—Cr1—Cr1^xx	62.648 (3)
O1^v—Ba2—O1^xv	99.33 (2)	Ba2^xxiv—Cr1—Cr1^xx	124.602 (5)
O1^iii—Ba2—O1^xv	68.34 (4)	Ba2^xix—Cr1—Cr1^xx	124.602 (5)
O1^xiii—Ba2—O1^xv	56.85 (4)	Ba1^xxv—Cr1—Cr1^xx	111.030 (13)
O1^xiv—Ba2—O1^xv	116.445 (13)	Ba1^xxvi—Cr1—Cr1^xx	51.460 (3)
O2—Ba2—O1^xvi	78.99 (2)	Ba1^xxvii—Cr1—Cr1^xx	51.460 (4)
O1^i—Ba2—O1^xvi	68.34 (4)	Cr1^xxiv—Cr1—Cr1^xx	77.758 (11)
O1^v—Ba2—O1^xvi	131.476 (10)	Cr1—O2—Ba2	180.0
O1^iii—Ba2—O1^xvi	99.33 (2)	Cr1—O2—Ba1^xxvi	88.29 (4)
O1^xiii—Ba2—O1^xvi	60.73 (4)	Ba2—O2—Ba1^xxvi	91.71 (4)
O1^xiv—Ba2—O1^xvi	116.445 (13)	Cr1—O2—Ba1^xxv	88.29 (4)
O1^xv—Ba2—O1^xvi	116.445 (13)	Ba2—O2—Ba1^xxv	91.71 (4)
O2—Ba2—O1^xvii	78.99 (2)	Ba1^xxvi—O2—Ba1^xxv	119.913 (4)
O1^i—Ba2—O1^xvii	131.475 (10)	Cr1—O2—Ba1^xxvii	88.29 (4)
O1^v—Ba2—O1^xvii	68.34 (4)	Ba2—O2—Ba1^xxvii	91.71 (4)
O1^iii—Ba2—O1^xvii	99.33 (2)	Ba1^xxvi—O2—Ba1^xxvii	119.912 (4)
O1^xiii—Ba2—O1^xvii	116.445 (13)	Ba1^xxv—O2—Ba1^xxvii	119.912 (4)
O1^xiv—Ba2—O1^xvii	56.85 (4)	Cr1^xxiii—O1—Ba1^xxviii	108.12 (5)
O1^xv—Ba2—O1^xvii	60.73 (4)	Cr1^xxiii—O1—Ba2^i	147.49 (5)
O1^xvi—Ba2—O1^xvii	157.90 (4)	Ba1^xxviii—O1—Ba2^i	104.39 (3)
O2—Ba2—O1^xviii	78.99 (2)	Cr1^xxiii—O1—Ba2^xxix	94.688 (19)
O1^i—Ba2—O1^xviii	68.34 (4)	Ba1^xxviii—O1—Ba2^xxix	98.010 (19)
O1^v—Ba2—O1^xviii	99.33 (2)	Ba2^i—O1—Ba2^xxix	80.67 (2)
O1^iii—Ba2—O1^xviii	131.476 (10)	Cr1^xxiii—O1—Ba2^xxx	94.688 (19)
O1^xiii—Ba2—O1^xviii	116.445 (13)	Ba1^xxviii—O1—Ba2^xxx	98.009 (19)
O1^xiv—Ba2—O1^xviii	60.73 (4)	Ba2^i—O1—Ba2^xxx	80.67 (2)
O1^xv—Ba2—O1^xviii	157.90 (4)	Ba2^xxix—O1—Ba2^xxx	157.90 (4)

Symmetry codes: (i) −x+1, −y, −z+1; (ii) x−1, y, z−1; (iii) y, −x+y+1, −z+1; (iv) −y, x−y−1, z−1; (v) x−y−1, x−1, −z+1; (vi) −x+y+1, −x+1, z−1; (vii) −x+2/3, −y+1/3, −z+1/3; (viii) −x−1/3, −y−2/3, −z+1/3; (ix) x+1/3, y+2/3, z−1/3; (x) x−2/3, y−1/3, z−1/3; (xi) −x−1/3, −y+1/3, −z+1/3; (xii) x+1/3, y−1/3, z−1/3; (xiii) x−1/3, y+1/3, z−2/3; (xiv) x−4/3, y−2/3, z−2/3; (xv) −x+y+2/3, −x+4/3, z−2/3; (xvi) −y+2/3, x−y−2/3, z−2/3; (xvii) −y−1/3, x−y−2/3, z−2/3; (xviii) −x+y+2/3, −x+1/3, z−2/3; (xix) −x+1/3, −y−1/3, −z+2/3; (xx) −x+1/3, −y+2/3, −z+2/3; (xxi) x−y−1/3, x−2/3, −z+4/3; (xxii) y−1/3, −x+y+1/3, −z+4/3; (xxiii) −x+2/3, −y+1/3, −z+4/3; (xxiv) −x−2/3, −y−1/3, −z+2/3; (xxv) x−1/3, y−2/3, z+1/3; (xxvi) x+2/3, y+1/3, z+1/3; (xxvii) x−1/3, y+1/3, z+1/3; (xxviii) x+1, y, z+1; (xxix) x+1/3, y−1/3, z+2/3; (xxx) x+4/3, y+2/3, z+2/3.