Contribution of powder diffraction for structure refinements of aperiodic misfit cobalt oxides

Two families of misfit cobalt oxides have been reinvestigated using neutron and synchrotron powder diffraction data and Rietveld structure refinements in the four-dimensional formalism for aperiodic structures. In the first system [Ca₂CoO₃][CoO₂]_1.62, the structure-specific features of two complex polytypic phases previously described from single-crystal diffraction data have been confirmed for the main term of the series and are described with the C2/m(1,δ,0)s0 superspace symmetry (R_p = 0.026, R_wp = 0.031, R_B = 0.014). The high-resolution synchrotron diffraction experiments have been interpreted with a triclinic distortion of the structure, probably related to an intrinsic modulation of the [Ca₂CoO₃] sublattice in relation with Co and O split atomic sites. In the second system Ca_0.82(Cu_0.65Co_0.35O₂), a new occupation modulation of the metallic site is shown with the Fmmm(α11)0ss superspace symmetry (R_p = 0.031, R_wp = 0.039, R_B = 0.027) and is interpreted in relation with the modulated interatomic distances of the square coordination of the cationic site. In both cases, recently developed tools for structure refinements of aperiodic systems using powder diffraction data (in the JANA2000 package) have proved their efficiency, in particular as specific complements to previous single-crystal structure refinements.

Computing details

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

Figures

(I)

Crystal data

Ca0.816Co0.28Cu0.72O2	V = 186.94 Å^3
Mr = 127	Z = 4
Orthorhombic, Xmmm(α00)0ss†	F(000) = 243
q = 0.81577a*‡	Dx = 4.510 Mg m^−3
a = 2.7954 Å	Neutron radiation, λ = 1.2251 Å
b = 6.3078 Å	?, ? × ? × ? mm
c = 10.6017 Å

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

‡ ;

Data collection

2θmin = 6°, 2θmax = 125.7°, 2θstep = −1°

Refinement

Rp = 0.031	Profile function: Pseudo-Voigt
Rwp = 0.039	41 parameters
Rexp = 0.021	Weighting scheme based on measured s.u.'s
R(F) = 0.029	(Δ/σ)max = 0.046
χ^2 = NOT FOUND	Background function: 10 Legendre polynoms
2156 data points	Preferred orientation correction: none

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Cu1	0	0	0	0.0073 (3)
Co1a	0	0	0	0.0073 (3)	0.503 (11)
Cu2	0	0	0	0.0073 (3)
Co2a	0	0	0	0.0073 (3)	0.503 (11)
O1	0.5	0	−0.12013 (6)	0.0078 (3)
Ca	0	0.25	0.25	0.0107 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cu1	0.0063 (5)	0.0105 (6)	0.0051 (6)	0	0	−0.0023 (11)
Co1a	0.0063 (5)	0.0105 (6)	0.0051 (6)	0	0	−0.0023 (11)
Cu2	0.0063 (5)	0.0105 (6)	0.0051 (6)	0	0	−0.0023 (11)
Co2a	0.0063 (5)	0.0105 (6)	0.0051 (6)	0	0	−0.0023 (11)
O1	0.0052 (4)	0.0130 (5)	0.0052 (4)	0	0	0
Ca	0.0191 (11)	0.0042 (7)	0.0087 (8)	0	0	0

Geometric parameters (Å, º)

	Average	Minimum	Maximum
Cu1—O1^i	1.969 (3)	1.920 (4)	1.9965 (11)
Cu1—O1	1.969 (3)	1.920 (4)	1.9965 (11)
Cu1—O1^ii	1.969 (3)	1.920 (4)	1.9965 (11)
Cu1—O1^iii	1.969 (3)	1.920 (4)	1.9965 (11)
Co1a—O1^i	1.851 (2)	1.837 (3)	1.864 (2)
Co1a—O1	1.853 (2)	1.840 (3)	1.867 (2)
Co1a—O1^ii	1.851 (2)	1.837 (3)	1.864 (2)
Co1a—O1^iii	1.853 (2)	1.840 (3)	1.867 (2)
Cu2—O1^i	1.960 (2)	1.923 (2)	1.9965 (11)
Cu2—O1	1.960 (2)	1.923 (2)	1.9965 (11)
Cu2—O1^ii	1.960 (2)	1.923 (2)	1.9965 (11)
Cu2—O1^iii	1.960 (2)	1.923 (2)	1.9965 (11)
Co2a—O1^i	1.853 (2)	1.840 (3)	1.867 (2)
Co2a—O1	1.851 (2)	1.837 (3)	1.864 (2)
Co2a—O1^ii	1.853 (2)	1.840 (3)	1.867 (2)
Co2a—O1^iii	1.851 (2)	1.837 (3)	1.864 (2)
Ca—O1^iv	28.938 (16)	2.2997 (13)	3.6370 (9)
Ca—O1^v	28.938 (16)	2.2997 (13)	3.6370 (9)
Ca—O1^vi	38.751 (18)	2.3485 (12)	4.6941 (6)
Ca—O1^vii	25.805 (13)	2.2997 (13)	2.4245 (15)
Ca—O1^viii	38.751 (18)	2.3485 (12)	4.6941 (6)
Ca—O1^ii	38.751 (18)	2.3485 (12)	4.6941 (6)
Ca—O1^iii	25.805 (13)	2.2997 (13)	2.4245 (15)
Ca—O1^ix	38.751 (18)	2.3485 (12)	4.6941 (6)
Ca—O1^x	28.938 (16)	2.2997 (13)	3.6370 (9)
Ca—O1^xi	28.938 (16)	2.2997 (13)	3.6370 (9)
O1^i—Cu1—O1	95.39 (5)	94.96 (5)	95.82 (4)
O1^i—Cu1—O1^xii	67.54 (3)	64.91 (4)	71.59 (3)
O1^i—Cu1—O1^xiii	82.84 (5)	77.51 (6)	86.81 (7)
O1^i—Cu1—O1^ii	84.87 (13)	82.0 (2)	89.2 (2)
O1^i—Cu1—O1^iii	175.72 (4)	171.43 (9)	180
O1^i—Cu1—O1^xiv	97.12 (6)	95.26 (8)	100.26 (10)
O1^i—Cu1—O1^x	112.46 (7)	106.52 (10)	116.98 (12)
O1—Cu1—O1^i	95.39 (5)	94.96 (5)	95.82 (4)
O1—Cu1—O1^xii	67.54 (3)	64.91 (4)	71.59 (3)
O1—Cu1—O1^xiii	82.84 (5)	77.51 (6)	86.81 (7)
O1—Cu1—O1^ii	175.72 (4)	171.43 (9)	180
O1—Cu1—O1^iii	84.87 (13)	82.0 (2)	89.2 (2)
O1—Cu1—O1^xiv	97.12 (6)	95.26 (8)	100.26 (10)
O1—Cu1—O1^x	112.46 (7)	106.52 (10)	116.98 (12)
O1^ii—Cu1—O1^i	84.87 (13)	82.0 (2)	89.2 (2)
O1^ii—Cu1—O1	175.72 (4)	171.43 (9)	180
O1^ii—Cu1—O1^xii	112.46 (7)	106.52 (10)	116.98 (12)
O1^ii—Cu1—O1^xiii	97.12 (6)	95.26 (8)	100.26 (10)
O1^ii—Cu1—O1^iii	95.39 (5)	94.96 (5)	95.82 (4)
O1^ii—Cu1—O1^xiv	82.84 (5)	77.51 (6)	86.81 (7)
O1^ii—Cu1—O1^x	67.54 (3)	64.91 (4)	71.59 (3)
O1^iii—Cu1—O1^i	175.72 (4)	171.43 (9)	180
O1^iii—Cu1—O1	84.87 (13)	82.0 (2)	89.2 (2)
O1^iii—Cu1—O1^xii	112.46 (7)	106.52 (10)	116.98 (12)
O1^iii—Cu1—O1^xiii	97.12 (6)	95.26 (8)	100.26 (10)
O1^iii—Cu1—O1^ii	95.39 (5)	94.96 (5)	95.82 (4)
O1^iii—Cu1—O1^xiv	82.84 (5)	77.51 (6)	86.81 (7)
O1^iii—Cu1—O1^x	67.54 (3)	64.91 (4)	71.59 (3)
O1^i—Co1a—O1	93.55 (5)	93.55 (5)	93.55 (5)
O1^i—Co1a—O1^xii	82.15 (4)	78.95 (3)	85.34 (4)
O1^i—Co1a—O1^xiii	68.48 (3)	66.09 (3)	70.87 (3)
O1^i—Co1a—O1^ii	88.25 (14)	85.83 (14)	90.67 (14)
O1^i—Co1a—O1^iii	165.73 (3)	165.71 (3)	165.74 (2)
O1^i—Co1a—O1^xiv	111.52 (7)	107.83 (7)	115.21 (7)
O1^i—Co1a—O1^x	97.91 (5)	95.94 (5)	99.89 (5)
O1—Co1a—O1^i	93.55 (5)	93.55 (5)	93.55 (5)
O1—Co1a—O1^xii	68.46 (3)	66.08 (3)	70.85 (3)
O1—Co1a—O1^xiii	82.11 (4)	78.92 (3)	85.31 (4)
O1—Co1a—O1^ii	165.73 (3)	165.71 (3)	165.74 (3)
O1—Co1a—O1^iii	88.08 (14)	85.67 (14)	90.50 (14)
O1—Co1a—O1^xiv	97.86 (5)	95.88 (5)	99.83 (5)
O1—Co1a—O1^x	111.44 (7)	107.75 (7)	115.13 (7)
O1^ii—Co1a—O1^i	88.25 (14)	85.83 (14)	90.67 (14)
O1^ii—Co1a—O1	165.73 (3)	165.71 (3)	165.74 (2)
O1^ii—Co1a—O1^xii	97.91 (5)	95.94 (5)	99.89 (5)
O1^ii—Co1a—O1^xiii	111.52 (7)	107.83 (7)	115.21 (7)
O1^ii—Co1a—O1^iii	93.55 (5)	93.55 (5)	93.55 (5)
O1^ii—Co1a—O1^xiv	68.48 (3)	66.09 (3)	70.87 (3)
O1^ii—Co1a—O1^x	82.15 (4)	78.95 (3)	85.34 (4)
O1^iii—Co1a—O1^i	165.73 (3)	165.71 (3)	165.74 (3)
O1^iii—Co1a—O1	88.08 (14)	85.67 (14)	90.50 (14)
O1^iii—Co1a—O1^xii	111.44 (7)	107.75 (7)	115.13 (7)
O1^iii—Co1a—O1^xiii	97.86 (5)	95.88 (5)	99.83 (5)
O1^iii—Co1a—O1^ii	93.55 (5)	93.55 (5)	93.55 (5)
O1^iii—Co1a—O1^xiv	82.11 (4)	78.92 (3)	85.31 (4)
O1^iii—Co1a—O1^x	68.46 (3)	66.08 (3)	70.85 (3)
O1^i—Cu2—O1	95.24 (5)	94.96 (5)	95.82 (4)
O1^i—Cu2—O1^xii	82.61 (4)	77.47 (4)	86.86 (5)
O1^i—Cu2—O1^xiii	67.77 (3)	64.92 (4)	71.57 (3)
O1^i—Cu2—O1^ii	85.11 (10)	81.82 (12)	89.33 (13)
O1^i—Cu2—O1^iii	174.24 (4)	171.36 (6)	180
O1^i—Cu2—O1^xiv	112.23 (5)	106.44 (6)	117.07 (7)
O1^i—Cu2—O1^x	97.33 (5)	95.32 (6)	100.18 (6)
O1—Cu2—O1^i	95.24 (5)	94.96 (5)	95.82 (4)
O1—Cu2—O1^xii	82.61 (4)	77.47 (4)	86.86 (5)
O1—Cu2—O1^xiii	67.77 (3)	64.92 (4)	71.57 (3)
O1—Cu2—O1^ii	174.24 (4)	171.36 (5)	180
O1—Cu2—O1^iii	85.11 (10)	81.82 (12)	89.33 (13)
O1—Cu2—O1^xiv	112.23 (5)	106.44 (6)	117.07 (7)
O1—Cu2—O1^x	97.33 (5)	95.32 (6)	100.18 (6)
O1^ii—Cu2—O1^i	85.11 (10)	81.82 (12)	89.33 (13)
O1^ii—Cu2—O1	174.24 (4)	171.36 (5)	180
O1^ii—Cu2—O1^xii	97.33 (5)	95.32 (6)	100.18 (6)
O1^ii—Cu2—O1^xiii	112.23 (5)	106.44 (6)	117.07 (7)
O1^ii—Cu2—O1^iii	95.24 (5)	94.96 (5)	95.82 (4)
O1^ii—Cu2—O1^xiv	67.77 (3)	64.92 (4)	71.57 (3)
O1^ii—Cu2—O1^x	82.61 (4)	77.47 (4)	86.86 (5)
O1^iii—Cu2—O1^i	174.24 (4)	171.36 (6)	180
O1^iii—Cu2—O1	85.11 (10)	81.82 (12)	89.33 (13)
O1^iii—Cu2—O1^xii	97.33 (5)	95.32 (6)	100.18 (6)
O1^iii—Cu2—O1^xiii	112.23 (5)	106.44 (6)	117.07 (7)
O1^iii—Cu2—O1^ii	95.24 (5)	94.96 (5)	95.82 (4)
O1^iii—Cu2—O1^xiv	67.77 (3)	64.92 (4)	71.57 (3)
O1^iii—Cu2—O1^x	82.61 (4)	77.47 (4)	86.86 (5)
O1^i—Co2a—O1	93.55 (5)	93.55 (5)	93.55 (5)
O1^i—Co2a—O1^xii	68.46 (3)	66.08 (3)	70.85 (3)
O1^i—Co2a—O1^xiii	82.11 (4)	78.92 (3)	85.31 (4)
O1^i—Co2a—O1^ii	88.08 (14)	85.67 (14)	90.50 (14)
O1^i—Co2a—O1^iii	165.73 (3)	165.71 (3)	165.74 (3)
O1^i—Co2a—O1^xiv	97.86 (5)	95.88 (5)	99.83 (5)
O1^i—Co2a—O1^x	111.44 (7)	107.75 (7)	115.13 (7)
O1—Co2a—O1^i	93.55 (5)	93.55 (5)	93.55 (5)
O1—Co2a—O1^xii	82.15 (4)	78.95 (3)	85.34 (4)
O1—Co2a—O1^xiii	68.48 (3)	66.09 (3)	70.87 (3)
O1—Co2a—O1^ii	165.73 (3)	165.71 (3)	165.74 (2)
O1—Co2a—O1^iii	88.25 (14)	85.83 (14)	90.67 (14)
O1—Co2a—O1^xiv	111.52 (7)	107.83 (7)	115.21 (7)
O1—Co2a—O1^x	97.91 (5)	95.94 (5)	99.89 (5)
O1^ii—Co2a—O1^i	88.08 (14)	85.67 (14)	90.50 (14)
O1^ii—Co2a—O1	165.73 (3)	165.71 (3)	165.74 (3)
O1^ii—Co2a—O1^xii	111.44 (7)	107.75 (7)	115.13 (7)
O1^ii—Co2a—O1^xiii	97.86 (5)	95.88 (5)	99.83 (5)
O1^ii—Co2a—O1^iii	93.55 (5)	93.55 (5)	93.55 (5)
O1^ii—Co2a—O1^xiv	82.11 (4)	78.92 (3)	85.31 (4)
O1^ii—Co2a—O1^x	68.46 (3)	66.08 (3)	70.85 (3)
O1^iii—Co2a—O1^i	165.73 (3)	165.71 (3)	165.74 (2)
O1^iii—Co2a—O1	88.25 (14)	85.83 (14)	90.67 (14)
O1^iii—Co2a—O1^xii	97.91 (5)	95.94 (5)	99.89 (5)
O1^iii—Co2a—O1^xiii	111.52 (7)	107.83 (7)	115.21 (7)
O1^iii—Co2a—O1^ii	93.55 (5)	93.55 (5)	93.55 (5)
O1^iii—Co2a—O1^xiv	68.48 (3)	66.09 (3)	70.87 (3)
O1^iii—Co2a—O1^x	82.15 (4)	78.95 (3)	85.34 (4)

Symmetry codes: (i) x₁−1, x₂, x₃, x₄; (ii) −x₁, −x₂, −x₃, −x₄; (iii) −x₁+1, −x₂, −x₃, −x₄; (iv) x₁−1/2, x₂, x₃+1/2, x₁/2; (v) x₁+1/2, x₂, x₃+1/2, x₁/2; (vi) x₁−1, x₂+1/2, x₃+1/2, x₄; (vii) x₁, x₂+1/2, x₃+1/2, x₄; (viii) x₁+1, x₂+1/2, x₃+1/2, x₄; (ix) −x₁+2, −x₂, −x₃, −x₄; (x) −x₁+1/2, −x₂+1/2, −x₃, −x₁/2; (xi) −x₁+3/2, −x₂+1/2, −x₃, −x₁/2; (xii) x₁−1/2, x₂−1/2, x₃, x₁/2; (xiii) x₁−1/2, x₂+1/2, x₃, x₁/2; (xiv) −x₁+1/2, −x₂−1/2, −x₃, −x₁/2.