Structures of incommensurate and commensurate composite crystals Na_xCuO₂ (x = 1.58, 1.6, 1.62)

Na_xCuO₂ (x ≃ 1.6) has been synthesized for different compositions x, resulting in both commensurate and incommensurate composite crystals. The crystal structures are reported for two incommensurate compounds (x = 1.58 and 1.62) determined by Rietveld refinements against X-ray powder diffraction data. The incommensurate compounds and commensurate Na₈Cu₅O₁₀ (x = 1.6) are found to possess similar structures, with valence fluctuations of Cu²⁺/Cu³⁺ as the origin of the modulations of the CuO₂ subsystems; the displacive modulations of Na being defined by the closest Na—O contacts between the subsystems. A comparison of the structure models obtained from single-crystal X-ray diffraction, synchrotron-radiation X-ray powder diffraction and X-ray powder diffraction with Cu Kα₁ radiation indicates that single-crystal X-ray diffraction is by far the most accurate method, while powder diffraction with radiation from an X-ray tube provides the least accurate structure model.

Computing details

Cell refinement: (Jana2000; Petricek and Dusek, 2000) for (I). Program(s) used to solve structure: (Jana2000; Petricek and Dusek, 2000) for (I). For all compounds, program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000). Molecular graphics: (Diamond 3, Brandenburg, 2004) for (I). For all compounds, software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

Figures

(I) sodium copper oxide

Crystal data

CuNa1.57664O2	V = 121.73 (1) Å^3
Mr = 661.6	Z = 2
Monoclinic, C2/m(0β0)s0†	F(000) = 125
q = 0.78832b*‡	Dx = 9.023 Mg m^−3
a = 8.24153 (4) Å	Synchrotron radiation, λ = 0.65046 Å
b = 2.78589 (2) Å	T = 293 K
c = 5.71687 (3) Å	?, ? × ? × ? mm
β = 111.9698 (5)°

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, x₂, −x₃, 1/2+x₄; (3) −x₁, −x₂, −x₃, −x₄; (4) x₁, −x₂, x₃, 1/2−x₄; (5) 1/2+x₁, 1/2+x₂, x₃, x₄; (6) 1/2−x₁, 1/2+x₂, −x₃, 1/2+x₄; (7) 1/2−x₁, 1/2−x₂, −x₃, −x₄; (8) 1/2+x₁, 1/2−x₂, x₃, 1/2−x₄.

‡ ;

Data collection

Radiation source: NSLS, Brookhaven National Laboratory

2θmin = 5°, 2θmax = 43.404°, 2θstep = 0.004°

Refinement

Rp = 0.075	36 parameters
Rwp = 0.101	0 restraints
Rexp = 0.050	Weighting scheme based on measured s.u.'s
R(F) = 0.048	(Δ/σ)max = 0.295
χ^2 = NOT FOUND	Background function: 4 Legendre polynoms
9602 data points	Preferred orientation correction: none
Profile function: Pseudo-Voigt

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

	x	y	z	Uiso*/Ueq
Cu1	0	0.5	0	0.0038 (2)*
O1	0.0493 (3)	0	0.2416 (3)	0.0091 (7)*
Na1	−0.1512 (3)	0.25	0.3832 (4)	0.0141 (6)*

Bond lengths (Å)

	Average	Minimum	Maximum
Cu1—Cu1^i	2.790 (2)	2.763 (4)	2.816 (4)
Cu1—Cu1^ii	2.790 (2)	2.764 (4)	2.816 (4)
Cu1—Cu1^iii	4.3546 (15)	4.217 (2)	4.494 (2)
Cu1—Cu1^iv	4.3543 (15)	4.217 (2)	4.494 (2)
Cu1—Cu1^v	4.3551 (15)	4.217 (2)	4.494 (2)
Cu1—Cu1^vi	4.3554 (15)	4.217 (2)	4.494 (2)
Cu1—O1^i	4.376 (8)	4.314 (6)	4.490 (11)
Cu1—O1^vii	4.714 (9)	4.599 (10)	4.791 (5)
Cu1—O1	1.899 (8)	1.841 (7)	1.961 (8)
Cu1—O1^viii	4.715 (9)	4.599 (9)	4.791 (5)
Cu1—O1^ii	1.898 (8)	1.841 (7)	1.962 (8)
Cu1—O1^ix	4.376 (8)	4.314 (6)	4.490 (11)
Cu1—O1^x	4.532 (6)	4.271 (12)	4.878 (12)
Cu1—O1^iv	4.427 (9)	4.392 (18)	4.476 (18)
Cu1—O1^v	5.050 (8)	4.908 (7)	5.260 (7)
Cu1—O1^vi	4.214 (8)	3.989 (16)	4.391 (15)
Cu1—O1^xi	5.051 (8)	4.908 (7)	5.260 (7)
Cu1—O1^xii	4.376 (8)	4.314 (6)	4.490 (11)
Cu1—O1^xiii	1.899 (8)	1.841 (7)	1.961 (8)
Cu1—O1^xiv	4.715 (9)	4.599 (10)	4.791 (5)
Cu1—O1^xv	1.898 (8)	1.841 (7)	1.962 (8)
Cu1—O1^xvi	4.714 (9)	4.599 (9)	4.791 (5)
Cu1—O1^xvii	4.377 (8)	4.314 (6)	4.490 (11)
Cu1—O1^xviii	5.049 (8)	4.908 (7)	5.260 (7)
Cu1—O1^xix	4.213 (8)	3.989 (16)	4.391 (15)
Cu1—O1^xx	5.049 (8)	4.908 (7)	5.260 (7)
Cu1—O1^xxi	4.427 (9)	4.392 (18)	4.476 (18)
Cu1—O1^xxii	4.534 (6)	4.271 (12)	4.878 (12)
Cu1—Na1^vii	816.4 (11)	3.084 (4)	5.162 (6)
Cu1—Na1^viii	734.9 (11)	3.075 (3)	4.248 (8)
Cu1—Na1^xxiii	1159.5 (10)	4.232 (5)	6.972 (6)
Cu1—Na1^i	1317.8 (11)	4.952 (7)	8.515 (5)
Cu1—Na1	755.7 (13)	2.902 (5)	4.952 (7)
Cu1—Na1^ii	670.3 (14)	2.899 (5)	4.058 (5)
Cu1—Na1^ix	1120.9 (11)	4.058 (5)	6.861 (6)
Cu1—Na1^vi	770.7 (10)	3.127 (4)	5.181 (5)
Cu1—Na1^xi	648.8 (10)	2.641 (9)	4.233 (5)
Cu1—Na1^xxiv	1146.2 (9)	4.233 (5)	7.515 (6)
Cu1—Na1^xiii	1011.4 (11)	3.834 (5)	6.324 (5)
Cu1—Na1^xv	630.0 (13)	2.899 (5)	3.834 (5)
Cu1—Na1^xvii	863.0 (13)	3.201 (10)	5.922 (5)
Cu1—Na1^xiv	1055.5 (10)	4.172 (5)	6.565 (5)
Cu1—Na1^xvi	697.5 (11)	3.075 (3)	4.172 (5)
Cu1—Na1^xxv	919.1 (11)	3.738 (8)	6.149 (5)
Cu1—Na1^xix	995.9 (9)	3.365 (4)	6.564 (5)
Cu1—Na1^xx	632.8 (10)	2.641 (9)	3.374 (6)
Cu1—Na1^xxvi	854.5 (10)	3.183 (9)	5.329 (5)
O1—O1^i	2.789 (11)	2.668 (14)	3.008 (15)
O1—O1^ii	2.789 (11)	2.668 (14)	3.008 (15)
O1—O1^iii	4.355 (13)	4.267 (11)	4.484 (16)
O1—O1^iv	4.354 (13)	4.267 (11)	4.484 (16)
O1—O1^v	4.355 (13)	4.267 (11)	4.484 (16)
O1—O1^vi	4.355 (13)	4.267 (11)	4.484 (16)
O1—O1^xii	3.795 (11)	3.729 (13)	3.862 (12)
O1—O1^xxvii	4.354 (13)	4.116 (11)	4.474 (15)
O1—O1^xiii	2.575 (11)	2.50 (2)	2.654 (14)
O1—O1^xiv	3.346 (13)	3.301 (17)	3.39 (2)
O1—O1^xv	3.795 (11)	3.729 (13)	3.862 (12)
O1—O1^xvi	4.353 (13)	4.116 (11)	4.474 (15)
O1—O1^xviii	4.871 (11)	4.633 (13)	5.051 (13)
O1—O1^xix	4.871 (11)	4.633 (13)	5.051 (13)
O1—O1^xxviii	3.783 (10)	3.640 (8)	4.067 (12)
O1—O1^xxii	3.784 (10)	3.640 (8)	4.067 (12)
O1—Na1^vii	952.7 (19)	4.578 (14)	5.444 (11)
O1—Na1^viii	1076 (2)	4.578 (14)	6.169 (9)
O1—Na1^i	998 (2)	3.507 (11)	6.988 (7)
O1—Na1	495 (2)	2.230 (11)	3.507 (11)
O1—Na1^ii	695 (2)	2.257 (12)	4.620 (8)
O1—Na1^ix	1300.7 (18)	4.620 (8)	7.808 (8)
O1—Na1^v	1003.5 (19)	3.709 (9)	6.400 (7)
O1—Na1^vi	542 (2)	2.189 (7)	3.709 (9)
O1—Na1^xi	706.7 (19)	2.189 (7)	4.981 (8)
O1—Na1^xxiv	1344.1 (18)	4.981 (8)	8.486 (8)
O1—Na1^xiii	980 (2)	4.193 (12)	5.889 (10)
O1—Na1^xv	841 (2)	3.93 (2)	4.693 (14)
O1—Na1^xvii	1208 (2)	4.693 (14)	7.635 (9)
O1—Na1^xxvii	1293.3 (17)	4.749 (8)	7.933 (8)
O1—Na1^xiv	680.0 (19)	2.250 (10)	4.749 (8)
O1—Na1^xvi	481.1 (19)	2.220 (9)	3.246 (9)
O1—Na1^xxv	989.6 (18)	3.246 (9)	6.769 (7)
O1—Na1^xix	941.6 (17)	3.799 (7)	5.978 (8)
O1—Na1^xx	826.8 (17)	3.756 (15)	4.811 (7)
O1—Na1^xxvi	1184.5 (18)	4.781 (10)	7.023 (8)
O1—Na1^xxix	1062 (2)	4.480 (8)	6.457 (10)
O1—Na1^xxx	960 (2)	4.480 (8)	5.339 (14)
O1—Na1^xxii	1091 (2)	4.625 (10)	6.823 (9)
O1—Na1^xxxi	962.3 (19)	4.446 (6)	5.236 (11)
Na1—Na1^i	3.553 (7)	3.059 (10)	4.233 (10)
Na1—Na1^ii	3.549 (7)	3.059 (10)	4.233 (10)
Na1—Na1^iii	5.444 (9)	4.811 (11)	5.758 (7)
Na1—Na1^iv	4.163 (9)	3.639 (18)	4.617 (17)
Na1—Na1^xxxii	5.444 (9)	4.811 (11)	5.758 (7)
Na1—Na1^v	5.444 (9)	4.811 (11)	5.758 (7)
Na1—Na1^vi	4.161 (9)	3.639 (18)	4.617 (17)
Na1—Na1^xi	5.440 (9)	4.811 (11)	5.758 (7)
Na1—Na1^xiv	2.982 (8)	2.550 (6)	3.197 (9)
Na1—Na1^xvi	2.980 (8)	2.550 (6)	3.197 (9)
Na1—Na1^xix	4.453 (8)	4.347 (9)	4.534 (7)
Na1—Na1^xxix	3.064 (10)	3.029 (9)	3.088 (9)
Na1—Na1^xx	4.453 (8)	4.347 (9)	4.534 (7)
Na1—Na1^xxx	3.064 (10)	3.029 (9)	3.088 (9)

Symmetry codes: (i) x₁, x₂−1, x₃, x₄; (ii) x₁, x₂+1, x₃, x₄; (iii) x₁−1/2, x₂−1/2, x₃, x₄; (iv) x₁−1/2, x₂+1/2, x₃, x₄; (v) x₁+1/2, x₂−1/2, x₃, x₄; (vi) x₁+1/2, x₂+1/2, x₃, x₄; (vii) x₁, x₂, x₃−1, x₄; (viii) x₁, x₂+1, x₃−1, x₄; (ix) x₁, x₂+2, x₃, x₄; (x) x₁−1/2, x₂+1/2, x₃−1, x₄; (xi) x₁+1/2, x₂+3/2, x₃, x₄; (xii) −x₁, −x₂−1, −x₃, −x₄; (xiii) −x₁, −x₂, −x₃, −x₄; (xiv) −x₁, −x₂, −x₃+1, −x₄; (xv) −x₁, −x₂+1, −x₃, −x₄; (xvi) −x₁, −x₂+1, −x₃+1, −x₄; (xvii) −x₁, −x₂+2, −x₃, −x₄; (xviii) −x₁−1/2, −x₂−1/2, −x₃, −x₄; (xix) −x₁−1/2, −x₂+1/2, −x₃, −x₄; (xx) −x₁−1/2, −x₂+3/2, −x₃, −x₄; (xxi) −x₁+1/2, −x₂+1/2, −x₃, −x₄; (xxii) −x₁+1/2, −x₂+1/2, −x₃+1, −x₄; (xxiii) x₁, x₂+2, x₃−1, x₄; (xxiv) x₁+1/2, x₂+5/2, x₃, x₄; (xxv) −x₁, −x₂+2, −x₃+1, −x₄; (xxvi) −x₁−1/2, −x₂+5/2, −x₃, −x₄; (xxvii) −x₁, −x₂−1, −x₃+1, −x₄; (xxviii) −x₁+1/2, −x₂−1/2, −x₃+1, −x₄; (xxix) −x₁−1/2, −x₂+1/2, −x₃+1, −x₄; (xxx) −x₁−1/2, −x₂+3/2, −x₃+1, −x₄; (xxxi) −x₁+1/2, −x₂+3/2, −x₃+1, −x₄; (xxxii) x₁−1/2, x₂+3/2, x₃, x₄.

(II)

Crystal data

Cu5Na8O10	V = 121.73 Å^3
Mr = 661.6	Z = 1
Monoclinic, C2/m(0β0)s0†	F(000) = 125
q = 0.80000b*‡	Dx = 9.023 Mg m^−3
a = 8.2417 Å	X-ray radiation, λ = 0.70926 Å
b = 2.7859 Å	µ = 22.32 mm^−1
c = 5.7167 Å	T = 293 K
β = 111.9709°	× × mm

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, x₂, −x₃, 1/2+x₄; (3) −x₁, −x₂, −x₃, −x₄; (4) x₁, −x₂, x₃, 1/2−x₄; (5) 1/2+x₁, 1/2+x₂, x₃, x₄; (6) 1/2−x₁, 1/2+x₂, −x₃, 1/2+x₄; (7) 1/2−x₁, 1/2−x₂, −x₃, −x₄; (8) 1/2+x₁, 1/2−x₂, x₃, 1/2−x₄.

‡ ;

Data collection

5656 independent reflections	k = ?→?
4523 reflections with I > 3σ(I)	l = ?→?
h = ?→?

Refinement

Refinement on F	5656 reflections
R[F^2 > 2σ(F^2)] = 0.035	107 parameters
wR(F^2) = 0.033	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
S = 2.95	(Δ/σ)max = 0.002

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

	x	y	z	Uiso*/Ueq
Cu1	0	0.5	0	0.0107
O1	0.05204	0	0.242277	0.0161
Na1	−0.154182	0.25	0.377855	0.0268

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cu1	0.012659	0.010929	0.008165	0	0.003339	0
O1	0.023003	0.014862	0.009429	0	0.004993	0
Na1	0.021659	0.042864	0.016004	0	0.007236	0

Bond lengths (Å)

	Average	Minimum	Maximum
Cu1—Cu1^i	2.7895	2.7577	2.8181
Cu1—Cu1^ii	2.7895	2.7577	2.8181
Cu1—O1	1.8991	1.8579	1.9298
Cu1—O1^ii	1.8991	1.8579	1.9298
Cu1—Na1^iii	17.5745	3.0599	4.1968
Cu1—Na1	20.3621	3.2115	5.1372
Cu1—Na1^ii	15.7315	2.8961	3.776
Cu1—Na1^iv	20.5305	3.2528	5.1985
Cu1—Na1^v	15.6325	2.738	3.3056
Cu1—O11	1.9004	1.8332	1.9504
Cu1—O11^ii	1.9004	1.8332	1.9504
Cu1—Na11^ii	16.2516	2.8958	3.8568
Cu1—Na11^vi	19.3148	3.0749	4.7487
Cu1—Na11^vii	18.0009	3.1054	4.1987
Cu1—Na11^viii	15.6102	2.8067	3.4583
Cu1—Na11^ix	19.4405	3.2627	5.1377
O1—O1^i	2.7886	2.709	2.8845
O1—O1^ii	2.7886	2.709	2.8845
O1—Na1	13.4019	2.2948	3.6968
O1—Na1^ii	15.5059	2.3242	4.3988
O1—Na1^iv	14.3695	2.2962	3.7564
O1—Na1^v	15.8104	2.2962	3.8109
O1—O11	2.5776	2.5176	2.654
O1—O11^x	3.3653	3.3482	3.3886
O1—Na11^x	18.6881	2.3551	4.8118
O1—Na11^vii	11.6155	2.2979	2.3551
O1—Na11^xi	21.7372	3.0006	5.4042
Na1—Na1^i	3.4932	3.0793	3.9071
Na1—Na1^ii	3.4932	3.0793	3.9071
Na1—O11^x	9.3842	2.2772	2.4236
Na1—O11^vii	10.7287	2.3301	3.6216
Na1—Na11^x	2.9994	2.7945	3.1618
Na1—Na11^vii	2.9994	2.7945	3.1618
Na1—Na11^xii	3.0505	2.9911	3.1095
Na1—Na11^xiii	3.0505	2.9911	3.1095
O11—O11^i	2.792	2.6948	3
O11—O11^ii	2.792	2.6948	3
O11—Na11	19.025	2.5664	4.7373
O11—Na11^ii	11.9068	2.3115	2.5664
O11—Na11^vi	22.0161	3.1755	5.5575
O11—Na11^xiv	19.4868	2.7714	5.1699
O11—Na11^viii	12.0532	2.2831	2.7714
Na11—Na11^i	3.4961	3.0733	3.8669
Na11—Na11^ii	3.4961	3.0733	3.8669

Symmetry codes: (i) x₁, x₂−1, x₃, x₄; (ii) x₁, x₂+1, x₃, x₄; (iii) x₁, x₂+1, x₃−1, x₄; (iv) x₁+1/2, x₂+1/2, x₃, x₄; (v) x₁+1/2, x₂+3/2, x₃, x₄; (vi) x₁, x₂+2, x₃, x₄; (vii) x₁, x₂+1, x₃+1, x₄; (viii) x₁−1/2, x₂+3/2, x₃, x₄; (ix) x₁−1/2, x₂+5/2, x₃, x₄; (x) x₁, x₂, x₃+1, x₄; (xi) x₁, x₂+2, x₃+1, x₄; (xii) x₁−1/2, x₂+1/2, x₃+1, x₄; (xiii) x₁−1/2, x₂+3/2, x₃+1, x₄; (xiv) x₁−1/2, x₂+1/2, x₃, x₄.

(III)

Crystal data

CuNa1.61689O2	V = 122.11 (1) Å^3
Mr = 661.6	Z = 2
Monoclinic, C2/m(0β0)s0†	F(000) = 126
q = 0.80844(3)b*‡	Dx = 8.994 Mg m^−3
a = 8.23682 (15) Å	X-ray radiation, λ = 1.54059 Å
b = 2.79269 (4) Å	T = 293 K
c = 5.71224 (10) Å	?, ? × ? × ? mm
β = 111.6696 (9)°

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, x₂, −x₃, 1/2+x₄; (3) −x₁, −x₂, −x₃, −x₄; (4) x₁, −x₂, x₃, 1/2−x₄; (5) 1/2+x₁, 1/2+x₂, x₃, x₄; (6) 1/2−x₁, 1/2+x₂, −x₃, 1/2+x₄; (7) 1/2−x₁, 1/2−x₂, −x₃, −x₄; (8) 1/2+x₁, 1/2−x₂, x₃, 1/2−x₄.

‡ ;

Data collection

2θmin = 9.987°, 2θmax = 79.977°, 2θstep = 0.01°

Refinement

Rp = 0.094	Profile function: Pseudo-Voigt
Rwp = 0.122	37 parameters
Rexp = 0.063	Weighting scheme based on measured s.u.'s
R(F) = 0.056	(Δ/σ)max = 0.049
χ^2 = NOT FOUND	Background function: 5 Legendre polynoms
7000 data points	Preferred orientation correction: none

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

	x	y	z	Uiso*/Ueq
Cu1	0	0.5	0	0.0024 (4)*
O1	0.0526 (3)	0	0.2465 (5)	0.0208 (10)*
Na1	−0.1566 (4)	0.25	0.3717 (5)	0.0183 (9)*

Bond lengths (Å)

	Average	Minimum	Maximum
Cu1—Cu1^i	2.797 (3)	2.781 (4)	2.812 (4)
Cu1—Cu1^ii	2.796 (3)	2.781 (4)	2.812 (4)
Cu1—O1	1.919 (10)	1.857 (12)	1.982 (10)
Cu1—O1^ii	1.918 (10)	1.857 (12)	1.982 (10)
Cu1—O1^iii	1.919 (10)	1.857 (12)	1.982 (10)
Cu1—O1^iv	1.918 (10)	1.857 (12)	1.982 (10)
Cu1—Na1	376.3 (8)	2.876 (8)	4.854 (7)
Cu1—Na1^ii	331.7 (8)	2.876 (8)	4.020 (9)
Cu1—Na1^v	318.7 (6)	2.548 (10)	3.927 (6)
Cu1—Na1^iv	312.9 (8)	2.876 (8)	3.805 (7)
Cu1—Na1^vi	313.0 (6)	2.548 (10)	3.366 (6)
O1—O1^i	2.795 (13)	2.733 (16)	2.915 (16)
O1—O1^ii	2.794 (13)	2.733 (16)	2.915 (16)
O1—O1^iii	2.625 (14)	2.54 (3)	2.711 (18)
O1—Na1	248.1 (14)	2.175 (13)	3.384 (12)
O1—Na1^ii	345.2 (13)	2.214 (14)	4.592 (10)
O1—Na1^vii	266.2 (12)	2.147 (9)	3.710 (11)
O1—Na1^v	346.0 (12)	2.147 (9)	4.741 (9)
O1—Na1^viii	339.6 (12)	2.231 (13)	4.689 (9)
O1—Na1^ix	243.6 (12)	2.210 (12)	3.264 (11)
Na1—Na1^viii	3.038 (9)	2.656 (7)	3.228 (10)
Na1—Na1^ix	3.036 (9)	2.656 (7)	3.228 (10)

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