Description of Ba1 + xNixRh1 − xO3 with x = 0.1170 (5) in superspace: modulated composite versus modulated-layer structure

Schönleber, A.; Zúñiga, F.J.; Perez-Mato, J.M.; Darriet, J.; zur Loye, H.-C.

doi:10.1107/S0108768105039212

Description of Ba_1 + xNi_xRh_1 - xO₃ with x = 0.1170 (5) in superspace: modulated composite versus modulated-layer structure

A. Schönleber, F. J. Zúñiga, J. M. Perez-Mato, J. Darriet and H.-C. zur Loye

The structure of the compound Ba_1 + xNi_xRh_1 - xO3 [x = 0.1170 (5)] has been analyzed at room temperature within the (3 + 1)-dimensional superspace approach using single-crystal X-ray diffraction data. Two different models are presented, the compound is refined as modulated composite as well as modulated-layer structure. In both models discontinuous atomic domains are applied to describe the structural modulations. While the first approach stresses the pseudo-one-dimensional constitution, the latter highlights the layered character of these structures.

Keywords: perovskite-related compounds; discontinuous atomic domains; superspace formalism.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768105039212/ck5013sup1.cif Contains datablocks publication, modulated_composite, modulated_layer
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768105039212/ck5013modulated_compositesup2.hkl Contains datablock modulated_composite
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768105039212/ck5013modulated_layersup3.hkl Contains datablock modulated_layer

Computing details top

For both compounds, program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

Figures top

(modulated_composite) top

Crystal data top

Ba_1.117Ni_0.117O₃Rh_0.883	Z = 3
M_r = 299.1	F(000) = 389
Trigonal, R3m(00γ)0s†	D_x = 6.575 Mg m⁻³
q = 0.55850c*‡	Mo Kα radiation, λ = 0.71069 Å
a = 10.0576 (8) Å	µ = 19.78 mm⁻¹
c = 2.5862 (8) Å	T = 293 K
V = 226.56 (7) Å³	× × mm

;

Data collection top

1955 independent reflections	k = ?→?
1127 reflections with I > 3σ(I)	l = ?→?
h = ?→?

Refinement top

Refinement on F	53 parameters
R[F² > 2σ(F²)] = 0.038	Weighting scheme based on measured s.u.'s w = 1/(σ²(F) + 0.000625F²)
wR(F²) = 0.048	(Δ/σ)_max = 0.0002
S = 1.26	Δρ_max = 2.01 e Å⁻³
1127 reflections	Δρ_min = −2.54 e Å⁻³

Crystal data top

Ba_1.117Ni_0.117O₃Rh_0.883	V = 226.56 (7) Å³
M_r = 299.1	Z = 3
Trigonal, R3m(00γ)0s†	Mo Kα radiation
q = 0.55850c*‡	µ = 19.78 mm⁻¹
a = 10.0576 (8) Å	T = 293 K
c = 2.5862 (8) Å	× × mm

;

Data collection top

1955 independent reflections

1127 reflections with I > 3σ(I)

Refinement top

R[F² > 2σ(F²)] = 0.038	53 parameters
wR(F²) = 0.048	Δρ_max = 2.01 e Å⁻³
S = 1.26	Δρ_min = −2.54 e Å⁻³
1127 reflections

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
O	0.1513 (5)	0	0.5	0.039 (3)
Rh	0	0	0	0.0145 (4)
Ni	0	0	0	0.034 (2)
Ba1	0.6483 (4)	0	0.25	0.0104 (4)
Ba2	0.6721 (2)	0	0.25	0.0169 (5)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O	0.037 (3)	0.064 (6)	0.024 (2)	0.032 (3)	0.0070 (15)	0.014 (3)
Rh	0.0066 (2)	0.0066 (2)	0.0304 (10)	0.00331 (12)	0	0
Ni	0.024 (2)	0.024 (2)	0.053 (5)	0.0122 (10)	0	0
Ba1	0.0072 (4)	0.0081 (5)	0.0160 (9)	0.0041 (3)	−0.0005 (2)	−0.0010 (4)
Ba2	0.0111 (9)	0.0186 (5)	0.0236 (7)	0.0093 (3)	0.00620 (14)	0.0124 (3)

Bond lengths (Å) top

	Average	Minimum	Maximum
O—Oⁱ	3.07 (2)	3.065 (19)	3.07 (2)
O—Oⁱⁱ	3.07 (2)	3.065 (19)	3.07 (2)
O—Oⁱⁱⁱ	2.64 (6)	2.20 (4)	2.77 (6)
O—O^iv	3.23 (6)	3.09 (6)	3.45 (5)
O—O^v	3.49 (6)	3.46 (6)	3.53 (5)
O—O^vi	2.96 (3)	2.87 (2)	3.00 (3)
O—O^vii	2.96 (3)	2.89 (3)	3.00 (3)
O—O^viii	2.64 (6)	2.20 (3)	2.77 (5)
O—O^ix	3.49 (5)	3.46 (5)	3.55 (6)
O—O^x	3.22 (6)	3.09 (6)	3.43 (4)
O—O^xi	2.96 (3)	2.87 (3)	3.00 (4)
O—O^xii	2.96 (3)	2.88 (3)	3.00 (4)
O—Rh	1.99 (3)	1.71 (2)	2.07 (4)
O—Rh^xiii	2.00 (3)	1.74 (2)	2.07 (4)
O—Ni^xiv	2.05 (2)	1.99 (2)	2.12 (3)
O—Ni^xv	2.04 (2)	1.957 (19)	2.12 (3)
O—Ba1^xvi	17.48 (13)	2.911 (14)	2.92 (3)
O—Ba1^xvii	17.48 (13)	2.911 (14)	2.92 (3)
O—Ba1^xviii	29.3 (3)	2.66 (3)	2.67 (2)
O—Ba1^xix	16.61 (12)	2.756 (14)	2.78 (3)
O—Ba1^xx	16.68 (16)	2.72 (3)	2.84 (3)
O—Ba1^xxi	19.85 (17)	3.20 (3)	3.42 (3)
O—Ba1^x	16.61 (13)	2.756 (15)	2.78 (3)
O—Ba1^xxii	19.81 (18)	3.20 (3)	3.42 (3)
O—Ba1^xxiii	11.04 (11)	2.73 (3)	2.80 (3)
O—Ba1^xxiv	8.45 (8)	2.80 (3)	2.84 (3)
O—Ba2^xxv	65.1 (4)	2.92 (3)	4.884 (18)
O—Ba2^xxvi	63.5 (4)	2.92 (3)	4.879 (19)
O—Ba2^xxvii	30.4 (3)	2.93 (3)	3.24 (3)
O—Ba2^xviii	11.73 (13)	2.93 (3)	2.94 (3)
O—Ba2^xxviii	39.2 (4)	2.93 (3)	3.25 (3)
O—Ba2^xxix	11.54 (10)	2.83 (3)	2.94 (2)
O—Ba2^xxx	28.5 (3)	2.79 (4)	2.97 (2)
O—Ba2^v	63.4 (6)	2.87 (3)	4.92 (2)
O—Ba2^xxxi	98.3 (4)	3.49 (3)	6.75 (2)
O—Ba2^xx	34.4 (5)	2.52 (3)	2.72 (3)
O—Ba2^xxxii	11.61 (10)	2.84 (3)	2.97 (2)
O—Ba2^xxxiii	28.4 (3)	2.79 (4)	2.95 (2)
O—Ba2^xxxiv	65.3 (6)	2.88 (4)	4.92 (2)
O—Ba2^xxiii	34.4 (5)	2.51 (4)	2.72 (3)
Rh—Rh^xxxv	2.548 (11)	2.4663 (17)	2.652 (14)
Rh—Rh^xiii	2.548 (11)	2.4663 (17)	2.652 (14)
Rh—Niⁱ	2.703 (10)	2.633 (9)	2.769 (11)
Rh—Ni^xv	2.703 (10)	2.633 (9)	2.769 (11)
Rh—Ba1^xvi	20.442 (13)	3.384 (3)	3.4295 (18)
Rh—Ba1^xxxvi	20.442 (13)	3.384 (3)	3.4295 (18)
Rh—Ba1^xxxvii	20.442 (13)	3.384 (3)	3.4295 (18)
Rh—Ba1^xx	20.442 (13)	3.384 (3)	3.4295 (18)
Rh—Ba1^x	20.44 (3)	3.384 (5)	3.430 (4)
Rh—Ba1^xxxviii	20.44 (3)	3.384 (5)	3.430 (4)
Rh—Ba2^xxxix	14.08 (11)	3.47 (3)	3.57 (2)
Rh—Ba2^xl	35.2 (3)	3.45 (4)	3.70 (2)
Rh—Ba2^xxvi	44.6 (2)	3.346 (12)	3.47 (2)
Rh—Ba2^xxvii	35.2 (3)	3.45 (4)	3.70 (2)
Rh—Ba2^xviii	14.08 (11)	3.47 (3)	3.57 (2)
Rh—Ba2^xli	44.6 (2)	3.346 (12)	3.47 (2)
Rh—Ba2^xxix	14.08 (11)	3.47 (3)	3.57 (2)
Rh—Ba2^xxx	35.2 (3)	3.45 (4)	3.70 (2)
Rh—Ba2^v	44.6 (2)	3.346 (12)	3.47 (2)
Rh—Ba2^xlii	35.2 (3)	3.45 (4)	3.70 (2)
Rh—Ba2^xliii	14.08 (11)	3.47 (3)	3.57 (2)
Rh—Ba2^xliv	44.6 (2)	3.346 (12)	3.47 (2)
Rh—Ba2^xxxii	14.08 (8)	3.47 (2)	3.574 (17)
Rh—Ba2^xxxiii	35.2 (2)	3.45 (3)	3.697 (16)
Rh—Ba2^xlv	44.6 (5)	3.35 (3)	3.47 (5)
Rh—Ba2^xlvi	35.2 (2)	3.45 (3)	3.697 (16)
Rh—Ba2^xlvii	14.08 (8)	3.47 (2)	3.574 (17)
Rh—Ba2^xxiii	44.6 (5)	3.35 (3)	3.47 (5)

Symmetry codes: (i) x₁, x₂, x₃−1, x₄; (ii) x₁, x₂, x₃+1, x₄; (iii) −x₂, x₁−x₂, x₃, x₄; (iv) −x₂+2/3, x₁−x₂−2/3, x₃−2/3, x₄; (v) −x₂+2/3, x₁−x₂−2/3, x₃+1/3, x₄; (vi) x₂, −x₁+x₂, −x₃, −x₄; (vii) x₂, −x₁+x₂, −x₃+2, −x₄; (viii) −x₁+x₂, −x₁, x₃, x₄; (ix) −x₁+x₂+1/3, −x₁+2/3, x₃−1/3, x₄; (x) −x₁+x₂+1/3, −x₁+2/3, x₃+2/3, x₄; (xi) x₁−x₂, x₁, −x₃, −x₄; (xii) x₁−x₂, x₁, −x₃+2, −x₄; (xiii) −x₂, −x₁, x₃+1, x₁/2; (xiv) −x₁, −x₂, −x₃, −x₄; (xv) −x₁, −x₂, −x₃+1, −x₄; (xvi) x₁−2/3, x₂+2/3, x₃+2/3, x₄; (xvii) x₁−1/3, x₂−2/3, x₃+4/3, x₄; (xviii) −x₁+1, −x₂, −x₃+1, −x₄; (xix) −x₂+2/3, x₁−x₂−2/3, x₃+4/3, x₄; (xx) x₂+2/3, −x₁+x₂+1/3, −x₃+4/3, −x₄; (xxi) x₂+2/3, −x₁+x₂+1/3, −x₃+7/3, −x₄; (xxii) x₁−x₂−2/3, x₁−1/3, −x₃+2/3, −x₄; (xxiii) x₁−x₂−2/3, x₁−1/3, −x₃+5/3, −x₄; (xxiv) x₁−x₂−2/3, x₁−1/3, −x₃+8/3, −x₄; (xxv) x₁−2/3, x₂+2/3, x₃+5/3, x₄; (xxvi) x₁−1/3, x₂−2/3, x₃+1/3, x₄; (xxvii) −x₁+1, −x₂, −x₃, −x₄; (xxviii) −x₁+1, −x₂, −x₃+2, −x₄; (xxix) −x₂, x₁−x₂−1, x₃, x₄; (xxx) −x₂, x₁−x₂−1, x₃+1, x₄; (xxxi) x₂+2/3, −x₁+x₂+1/3, −x₃+1/3, −x₄; (xxxii) −x₁+x₂+1, −x₁+1, x₃, x₄; (xxxiii) −x₁+x₂+1, −x₁+1, x₃+1, x₄; (xxxiv) −x₁+x₂+1/3, −x₁+2/3, x₃+5/3, x₄; (xxxv) −x₂, −x₁, x₃−1, x₁/2; (xxxvi) −x₁+2/3, −x₂−2/3, −x₃+4/3, −x₄; (xxxvii) −x₂−2/3, x₁−x₂−1/3, x₃+2/3, x₄; (xxxviii) x₁−x₂−1/3, x₁−2/3, −x₃+4/3, −x₄; (xxxix) x₁−1, x₂, x₃, x₄; (xl) x₁−1, x₂, x₃+1, x₄; (xli) −x₁+1/3, −x₂+2/3, −x₃+5/3, −x₄; (xlii) x₂, −x₁+x₂+1, −x₃, −x₄; (xliii) x₂, −x₁+x₂+1, −x₃+1, −x₄; (xliv) x₂−2/3, −x₁+x₂+2/3, −x₃+5/3, −x₄; (xlv) −x₁+x₂+2/3, −x₁+1/3, x₃+1/3, x₄; (xlvi) x₁−x₂−1, x₁−1, −x₃, −x₄; (xlvii) x₁−x₂−1, x₁−1, −x₃+1, −x₄.

(modulated_layer) top

Crystal data top

BaNi_0.105O_2.686Rh_0.791	Z = 6
M_r = 267.9	F(000) = 696
Trigonal, X3c1(00γ)000†	D_x = 6.577 Mg m⁻³
q = 0.20950c*	Mo Kα radiation, λ = 0.71069 Å
a = 10.0576 (8) Å	µ = 19.78 mm⁻¹
c = 4.6306 (7) Å	T = 293 K
V = 405.65 (8) Å³	× × mm

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₂, x₁−x₂, x₃, x₄; (3) −x₂, −x₁, 1/2+x₃, x₄; (4) −x₁+x₂, −x₁, x₃, x₄; (5) x₁, x₁−x₂, 1/2+x₃, x₄; (6) −x₁+x₂, x₂, 1/2+x₃, x₄; (7) −x₁, −x₂, −x₃, −x₄; (8) x₂, −x₁+x₂, −x₃, −x₄; (9) x₂, x₁, 1/2−x₃, −x₄; (10) x₁−x₂, x₁, −x₃, −x₄; (11) −x₁, −x₁+x₂, 1/2−x₃, −x₄; (12) x₁−x₂, −x₂, 1/2−x₃, −x₄; (13) 1/3+x₁, 2/3+x₂, x₃, 1/3+x₄; (14) 1/3−x₂, 2/3+x₁−x₂, x₃, 1/3+x₄; (15) 1/3−x₂, 2/3−x₁, 1/2+x₃, 1/3+x₄; (16) 1/3−x₁+x₂, 2/3−x₁, x₃, 1/3+x₄; (17) 1/3+x₁, 2/3+x₁−x₂, 1/2+x₃, 1/3+x₄; (18) 1/3−x₁+x₂, 2/3+x₂, 1/2+x₃, 1/3+x₄; (19) 1/3−x₁, 2/3−x₂, −x₃, 1/3−x₄; (20) 1/3+x₂, 2/3−x₁+x₂, −x₃, 1/3−x₄; (21) 1/3+x₂, 2/3+x₁, 1/2−x₃, 1/3−x₄; (22) 1/3+x₁−x₂, 2/3+x₁, −x₃, 1/3−x₄; (23) 1/3−x₁, 2/3−x₁+x₂, 1/2−x₃, 1/3−x₄; (24) 1/3+x₁−x₂, 2/3−x₂, 1/2−x₃, 1/3−x₄; (25) 2/3+x₁, 1/3+x₂, x₃, 2/3+x₄; (26) 2/3−x₂, 1/3+x₁−x₂, x₃, 2/3+x₄; (27) 2/3−x₂, 1/3−x₁, 1/2+x₃, 2/3+x₄; (28) 2/3−x₁+x₂, 1/3−x₁, x₃, 2/3+x₄; (29) 2/3+x₁, 1/3+x₁−x₂, 1/2+x₃, 2/3+x₄; (30) 2/3−x₁+x₂, 1/3+x₂, 1/2+x₃, 2/3+x₄; (31) 2/3−x₁, 1/3−x₂, −x₃, 2/3−x₄; (32) 2/3+x₂, 1/3−x₁+x₂, −x₃, 2/3−x₄; (33) 2/3+x₂, 1/3+x₁, 1/2−x₃, 2/3−x₄; (34) 2/3+x₁−x₂, 1/3+x₁, −x₃, 2/3−x₄; (35) 2/3−x₁, 1/3−x₁+x₂, 1/2−x₃, 2/3−x₄; (36) 2/3+x₁−x₂, 1/3−x₂, 1/2−x₃, 2/3−x₄.

Data collection top

2495 independent reflections	k = ?→?
1195 reflections with I > 3σ(I)	l = ?→?
h = ?→?

Refinement top

Refinement on F	53 parameters
R[F² > 2σ(F²)] = 0.038	Weighting scheme based on measured s.u.'s w = 1/(σ²(F) + 0.000625F²)
wR(F²) = 0.050	(Δ/σ)_max = 0.0003
S = 1.31	Δρ_max = 1.85 e Å⁻³
1195 reflections	Δρ_min = −2.38 e Å⁻³

Crystal data top

BaNi_0.105O_2.686Rh_0.791	V = 405.65 (8) Å³
M_r = 267.9	Z = 6
Trigonal, X3c1(00γ)000†	Mo Kα radiation
q = 0.20950c*	µ = 19.78 mm⁻¹
a = 10.0576 (8) Å	T = 293 K
c = 4.6306 (7) Å	× × mm

Data collection top

2495 independent reflections

1195 reflections with I > 3σ(I)

Refinement top

R[F² > 2σ(F²)] = 0.038	53 parameters
wR(F²) = 0.050	Δρ_max = 1.85 e Å⁻³
S = 1.31	Δρ_min = −2.38 e Å⁻³
1195 reflections

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
O	0.1521 (5)	0	0.25	0.037 (3)
Rh	0	0	0	0.0166 (4)
Ni	0	0	0.25	0.032 (4)
Ba1	0.6467 (8)	0	0.25	0.0083 (6)
Ba2	0.67341 (18)	0	0.25	0.0171 (8)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O	0.032 (2)	0.059 (5)	0.028 (3)	0.030 (2)	0.0056 (14)	0.011 (3)
Rh	0.0091 (4)	0.0091 (4)	0.0317 (9)	0.0046 (2)	0	0
Ni	0.002 (4)	0.002 (4)	0.091 (10)	0.0010 (18)	0	0
Ba1	0.0060 (8)	0.0068 (7)	0.0125 (9)	0.0034 (4)	−0.0017 (3)	−0.0033 (5)
Ba2	0.0124 (9)	0.0159 (14)	0.0241 (7)	0.0079 (7)	0.00579 (14)	0.0116 (3)

Experimental details

	(modulated_composite)	(modulated_layer)
Crystal data
Chemical formula	Ba_1.117Ni_0.117O₃Rh_0.883	BaNi_0.105O_2.686Rh_0.791
M_r	299.1	267.9
Crystal system, space group	Trigonal, R3m(00γ)0s†	Trigonal, X3c1(00γ)000‡
Temperature (K)	293	293
Wave vectors	q = 0.55850c*§	q = 0.20950c*
a, c (Å)	10.0576 (8), 2.5862 (8)	10.0576 (8), 4.6306 (7)
V (Å³)	226.56 (7)	405.65 (8)
Z	3	6
Radiation type	Mo Kα	Mo Kα
µ (mm⁻¹)	19.78	19.78
Crystal size (mm)	× ×	× ×

Data collection
Diffractometer	?	?
Absorption correction	–	–
No. of measured, independent and observed [I > 3σ(I)] reflections	?, 1955, 1127	?, 2495, 1195
R_int	?	?

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.038, 0.048, 1.26	0.038, 0.050, 1.31
No. of reflections	1127	1195
No. of parameters	53	53
No. of restraints	?	?
Δρ_max, Δρ_min (e Å⁻³)	2.01, −2.54	1.85, −2.38

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₂, x₁−x₂, x₃, x₄; (3) −x₂, −x₁, x₃, 1/2+x₄; (4) −x₁+x₂, −x₁, x₃, x₄; (5) x₁, x₁−x₂, x₃, 1/2+x₄; (6) −x₁+x₂, x₂, x₃, 1/2+x₄; (7) −x₁, −x₂, −x₃, −x₄; (8) x₂, −x₁+x₂, −x₃, −x₄; (9) x₂, x₁, −x₃, 1/2−x₄; (10) x₁−x₂, x₁, −x₃, −x₄; (11) −x₁, −x₁+x₂, −x₃, 1/2−x₄; (12) x₁−x₂, −x₂, −x₃, 1/2−x₄; (13) 1/3+x₁, 2/3+x₂, 2/3+x₃, x₄; (14) 1/3−x₂, 2/3+x₁−x₂, 2/3+x₃, x₄; (15) 1/3−x₂, 2/3−x₁, 2/3+x₃, 1/2+x₄; (16) 1/3−x₁+x₂, 2/3−x₁, 2/3+x₃, x₄; (17) 1/3+x₁, 2/3+x₁−x₂, 2/3+x₃, 1/2+x₄; (18) 1/3−x₁+x₂, 2/3+x₂, 2/3+x₃, 1/2+x₄; (19) 1/3−x₁, 2/3−x₂, 2/3−x₃, −x₄; (20) 1/3+x₂, 2/3−x₁+x₂, 2/3−x₃, −x₄; (21) 1/3+x₂, 2/3+x₁, 2/3−x₃, 1/2−x₄; (22) 1/3+x₁−x₂, 2/3+x₁, 2/3−x₃, −x₄; (23) 1/3−x₁, 2/3−x₁+x₂, 2/3−x₃, 1/2−x₄; (24) 1/3+x₁−x₂, 2/3−x₂, 2/3−x₃, 1/2−x₄; (25) 2/3+x₁, 1/3+x₂, 1/3+x₃, x₄; (26) 2/3−x₂, 1/3+x₁−x₂, 1/3+x₃, x₄; (27) 2/3−x₂, 1/3−x₁, 1/3+x₃, 1/2+x₄; (28) 2/3−x₁+x₂, 1/3−x₁, 1/3+x₃, x₄; (29) 2/3+x₁, 1/3+x₁−x₂, 1/3+x₃, 1/2+x₄; (30) 2/3−x₁+x₂, 1/3+x₂, 1/3+x₃, 1/2+x₄; (31) 2/3−x₁, 1/3−x₂, 1/3−x₃, −x₄; (32) 2/3+x₂, 1/3−x₁+x₂, 1/3−x₃, −x₄; (33) 2/3+x₂, 1/3+x₁, 1/3−x₃, 1/2−x₄; (34) 2/3+x₁−x₂, 1/3+x₁, 1/3−x₃, −x₄; (35) 2/3−x₁, 1/3−x₁+x₂, 1/3−x₃, 1/2−x₄; (36) 2/3+x₁−x₂, 1/3−x₂, 1/3−x₃, 1/2−x₄.

‡ Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₂, x₁−x₂, x₃, x₄; (3) −x₂, −x₁, 1/2+x₃, x₄; (4) −x₁+x₂, −x₁, x₃, x₄; (5) x₁, x₁−x₂, 1/2+x₃, x₄; (6) −x₁+x₂, x₂, 1/2+x₃, x₄; (7) −x₁, −x₂, −x₃, −x₄; (8) x₂, −x₁+x₂, −x₃, −x₄; (9) x₂, x₁, 1/2−x₃, −x₄; (10) x₁−x₂, x₁, −x₃, −x₄; (11) −x₁, −x₁+x₂, 1/2−x₃, −x₄; (12) x₁−x₂, −x₂, 1/2−x₃, −x₄; (13) 1/3+x₁, 2/3+x₂, x₃, 1/3+x₄; (14) 1/3−x₂, 2/3+x₁−x₂, x₃, 1/3+x₄; (15) 1/3−x₂, 2/3−x₁, 1/2+x₃, 1/3+x₄; (16) 1/3−x₁+x₂, 2/3−x₁, x₃, 1/3+x₄; (17) 1/3+x₁, 2/3+x₁−x₂, 1/2+x₃, 1/3+x₄; (18) 1/3−x₁+x₂, 2/3+x₂, 1/2+x₃, 1/3+x₄; (19) 1/3−x₁, 2/3−x₂, −x₃, 1/3−x₄; (20) 1/3+x₂, 2/3−x₁+x₂, −x₃, 1/3−x₄; (21) 1/3+x₂, 2/3+x₁, 1/2−x₃, 1/3−x₄; (22) 1/3+x₁−x₂, 2/3+x₁, −x₃, 1/3−x₄; (23) 1/3−x₁, 2/3−x₁+x₂, 1/2−x₃, 1/3−x₄; (24) 1/3+x₁−x₂, 2/3−x₂, 1/2−x₃, 1/3−x₄; (25) 2/3+x₁, 1/3+x₂, x₃, 2/3+x₄; (26) 2/3−x₂, 1/3+x₁−x₂, x₃, 2/3+x₄; (27) 2/3−x₂, 1/3−x₁, 1/2+x₃, 2/3+x₄; (28) 2/3−x₁+x₂, 1/3−x₁, x₃, 2/3+x₄; (29) 2/3+x₁, 1/3+x₁−x₂, 1/2+x₃, 2/3+x₄; (30) 2/3−x₁+x₂, 1/3+x₂, 1/2+x₃, 2/3+x₄; (31) 2/3−x₁, 1/3−x₂, −x₃, 2/3−x₄; (32) 2/3+x₂, 1/3−x₁+x₂, −x₃, 2/3−x₄; (33) 2/3+x₂, 1/3+x₁, 1/2−x₃, 2/3−x₄; (34) 2/3+x₁−x₂, 1/3+x₁, −x₃, 2/3−x₄; (35) 2/3−x₁, 1/3−x₁+x₂, 1/2−x₃, 2/3−x₄; (36) 2/3+x₁−x₂, 1/3−x₂, 1/2−x₃, 2/3−x₄.

§ ;

Computer programs: (Jana2000; Petricek and Dusek, 2000).

Selected bond lengths (Å) for (modulated_composite) top

	Average	Minimum	Maximum
O—Oⁱ	3.07 (2)	3.065 (19)	3.07 (2)
O—Oⁱⁱ	3.07 (2)	3.065 (19)	3.07 (2)
O—Oⁱⁱⁱ	2.64 (6)	2.20 (4)	2.77 (6)
O—O^iv	3.23 (6)	3.09 (6)	3.45 (5)
O—O^v	3.49 (6)	3.46 (6)	3.53 (5)
O—O^vi	2.96 (3)	2.87 (2)	3.00 (3)
O—O^vii	2.96 (3)	2.89 (3)	3.00 (3)
O—O^viii	2.64 (6)	2.20 (3)	2.77 (5)
O—O^ix	3.49 (5)	3.46 (5)	3.55 (6)
O—O^x	3.22 (6)	3.09 (6)	3.43 (4)
O—O^xi	2.96 (3)	2.87 (3)	3.00 (4)
O—O^xii	2.96 (3)	2.88 (3)	3.00 (4)
O—Rh	1.99 (3)	1.71 (2)	2.07 (4)
O—Rh^xiii	2.00 (3)	1.74 (2)	2.07 (4)
O—Ni^xiv	2.05 (2)	1.99 (2)	2.12 (3)
O—Ni^xv	2.04 (2)	1.957 (19)	2.12 (3)
O—Ba1^xvi	17.48 (13)	2.911 (14)	2.92 (3)
O—Ba1^xvii	17.48 (13)	2.911 (14)	2.92 (3)
O—Ba1^xviii	29.3 (3)	2.66 (3)	2.67 (2)
O—Ba1^xix	16.61 (12)	2.756 (14)	2.78 (3)
O—Ba1^xx	16.68 (16)	2.72 (3)	2.84 (3)
O—Ba1^xxi	19.85 (17)	3.20 (3)	3.42 (3)
O—Ba1^x	16.61 (13)	2.756 (15)	2.78 (3)
O—Ba1^xxii	19.81 (18)	3.20 (3)	3.42 (3)
O—Ba1^xxiii	11.04 (11)	2.73 (3)	2.80 (3)
O—Ba1^xxiv	8.45 (8)	2.80 (3)	2.84 (3)
O—Ba2^xxv	65.1 (4)	2.92 (3)	4.884 (18)
O—Ba2^xxvi	63.5 (4)	2.92 (3)	4.879 (19)
O—Ba2^xxvii	30.4 (3)	2.93 (3)	3.24 (3)
O—Ba2^xviii	11.73 (13)	2.93 (3)	2.94 (3)
O—Ba2^xxviii	39.2 (4)	2.93 (3)	3.25 (3)
O—Ba2^xxix	11.54 (10)	2.83 (3)	2.94 (2)
O—Ba2^xxx	28.5 (3)	2.79 (4)	2.97 (2)
O—Ba2^v	63.4 (6)	2.87 (3)	4.92 (2)
O—Ba2^xxxi	98.3 (4)	3.49 (3)	6.75 (2)
O—Ba2^xx	34.4 (5)	2.52 (3)	2.72 (3)
O—Ba2^xxxii	11.61 (10)	2.84 (3)	2.97 (2)
O—Ba2^xxxiii	28.4 (3)	2.79 (4)	2.95 (2)
O—Ba2^xxxiv	65.3 (6)	2.88 (4)	4.92 (2)
O—Ba2^xxiii	34.4 (5)	2.51 (4)	2.72 (3)
Rh—Rh^xxxv	2.548 (11)	2.4663 (17)	2.652 (14)
Rh—Rh^xiii	2.548 (11)	2.4663 (17)	2.652 (14)
Rh—Niⁱ	2.703 (10)	2.633 (9)	2.769 (11)
Rh—Ni^xv	2.703 (10)	2.633 (9)	2.769 (11)
Rh—Ba1^xvi	20.442 (13)	3.384 (3)	3.4295 (18)
Rh—Ba1^xxxvi	20.442 (13)	3.384 (3)	3.4295 (18)
Rh—Ba1^xxxvii	20.442 (13)	3.384 (3)	3.4295 (18)
Rh—Ba1^xx	20.442 (13)	3.384 (3)	3.4295 (18)
Rh—Ba1^x	20.44 (3)	3.384 (5)	3.430 (4)
Rh—Ba1^xxxviii	20.44 (3)	3.384 (5)	3.430 (4)
Rh—Ba2^xxxix	14.08 (11)	3.47 (3)	3.57 (2)
Rh—Ba2^xl	35.2 (3)	3.45 (4)	3.70 (2)
Rh—Ba2^xxvi	44.6 (2)	3.346 (12)	3.47 (2)
Rh—Ba2^xxvii	35.2 (3)	3.45 (4)	3.70 (2)
Rh—Ba2^xviii	14.08 (11)	3.47 (3)	3.57 (2)
Rh—Ba2^xli	44.6 (2)	3.346 (12)	3.47 (2)
Rh—Ba2^xxix	14.08 (11)	3.47 (3)	3.57 (2)
Rh—Ba2^xxx	35.2 (3)	3.45 (4)	3.70 (2)
Rh—Ba2^v	44.6 (2)	3.346 (12)	3.47 (2)
Rh—Ba2^xlii	35.2 (3)	3.45 (4)	3.70 (2)
Rh—Ba2^xliii	14.08 (11)	3.47 (3)	3.57 (2)
Rh—Ba2^xliv	44.6 (2)	3.346 (12)	3.47 (2)
Rh—Ba2^xxxii	14.08 (8)	3.47 (2)	3.574 (17)
Rh—Ba2^xxxiii	35.2 (2)	3.45 (3)	3.697 (16)
Rh—Ba2^xlv	44.6 (5)	3.35 (3)	3.47 (5)
Rh—Ba2^xlvi	35.2 (2)	3.45 (3)	3.697 (16)
Rh—Ba2^xlvii	14.08 (8)	3.47 (2)	3.574 (17)
Rh—Ba2^xxiii	44.6 (5)	3.35 (3)	3.47 (5)

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Description of Ba1 + xNixRh1 - xO3 with x = 0.1170 (5) in superspace: modulated composite versus modulated-layer structure

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Description of Ba_1 + xNi_xRh_1 - xO₃ with x = 0.1170 (5) in superspace: modulated composite versus modulated-layer structure