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A single-phase sample of α′ (O′3)-type layered sodium cobalt oxide NaxCoO2 (x ∼ 0.78) was prepared and its incommensurately modulated crystal structure was analyzed using the (3+1)-dimensional superspace approach to the powder neutron diffraction data. The crystal structure of the cobaltate is accurately described based on the superspace group C2/m(α0γ)00, wherein the positions of Na atoms are most significantly modulated in the monoclinic a direction to form an ordered arrangement. Such a displacive modulation causes a quasi-periodic shift of Na atoms from the centers of the NaO6 polyhedra between undulated CoO2 sheets, changing the form of the NaO6 polyhedron from an octahedral coordination (O) to a trigonal prismatic (P) one, via an intermediate capped trigonal prismatic NaO7 coordination (C). At the positions where the Na atoms are most significantly shifted, the neighboring Na atoms are located at almost touching distances. However, the occupation factor of Na atoms becomes zero at such positions, yielding Na-deficient sites VNa, sandwiched either between C and P, or C and C-type polyhedra.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S205252062100370X/dq5050sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S205252062100370X/dq5050Isup2.hkl
Contains datablock I

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S205252062100370X/dq5050Isup3.rtv
Contains datablock I

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S205252062100370X/dq5050sup4.pdf
Table S1 and Fig. S1

B-IncStrDB reference: 16942E6CXxJ

CCDC reference: 2075708

Computing details top

Cell refinement: JANA2006; program(s) used to solve structure: JANA2006; program(s) used to refine structure: JANA2006.

(I) top
Crystal data top
Na0.779CoO2V = 75.21 (1) Å3
Mr = 108.84Z = 2
Monoclinic, C2/m(α0γ)00†F(000) = 33.752
q = 0.345787a* + -0.262426c*Dx = 4.806 Mg m3
a = 4.88979 (17) ÅNeutron radiation
b = 2.86782 (8) ÅT = 293 K
c = 5.78034 (19) Åblack
β = 111.8897 (16)°
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, −x4; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, x4; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3, −x4; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3, x4.

Data collection top
HRPD
diffractometer
Scan method: energy dispersive
Refinement top
Rp = 0.04842 parameters
Rwp = 0.0620 restraints
Rexp = 0.0340 constraints
R(F) = 0.033Weighting scheme based on measured s.u.'s
2800 data points(Δ/σ)max = 0.049
Excluded region(s): from 10.025 to 10.000, from 150.01 to 150.130Background function: 8 Legendre polynoms
Profile function: Pseudo-VoigtPreferred orientation correction: none
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Na00.50.50.0086 (13)*0.5
Co0000.0110 (9)*
O0.2544 (3)00.8162 (2)0.0104 (4)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
???????
Bond lengths (Å) top
AverageMinimumMaximum
Na—Nai5.176 (6)3.589 (10)5.592 (10)
Na—Naii2.86792.86792.8679
Na—Naiii2.86792.86792.8679
Na—Naiv5.184 (6)3.589 (11)5.592 (11)
Na—Nav3.142 (4)3.142 (8)3.142 (8)
Na—Navi3.142 (4)3.142 (8)3.142 (8)
Na—Navii3.142 (4)3.142 (8)3.142 (8)
Na—Naviii3.142 (4)3.142 (8)3.142 (8)
Na—Naix2.8771 (3)2.8771 (7)2.8771 (7)
Na—Nax0.230 (3)0.230 (9)0.230 (9)
Na—Naxi2.8771 (3)2.8771 (7)2.8771 (7)
Na—Naxii4.995 (7)3.803 (9)5.815 (9)
Na—Naxiii2.946 (3)2.946 (10)2.946 (10)
Na—Naxiv2.946 (3)2.946 (10)2.946 (10)
Na—Naxv3.226 (4)1.797 (8)3.343 (8)
Na—Naxvi3.226 (4)1.797 (8)3.343 (8)
Na—Co3.199 (11)3.00 (2)3.53 (2)
Na—Coxvii3.215 (11)2.998 (19)3.571 (19)
Na—Coiii3.199 (11)3.00 (2)3.53 (2)
Na—Coxviii3.215 (11)2.998 (19)3.571 (19)
Na—Covi3.030 (10)2.747 (17)3.445 (17)
Na—Coxix3.080 (10)2.588 (16)3.381 (16)
Na—O2.356 (5)2.190 (7)2.513 (7)
Na—Oiii2.356 (5)2.190 (7)2.513 (7)
Na—Ovi2.497 (9)2.231 (12)3.134 (12)
Na—Ox2.301 (5)2.237 (7)2.612 (7)
Na—Oxi2.301 (5)2.237 (7)2.612 (7)
Na—Oxvi2.519 (9)2.348 (12)3.061 (12)
Co—Oxx1.918 (16)1.85 (2)1.99 (2)
Co—Oxxi1.920 (8)1.884 (12)1.953 (12)
Co—Oxxii1.920 (8)1.884 (12)1.953 (12)
Co—Ox1.918 (16)1.85 (2)1.99 (2)
Co—Oxv1.920 (8)1.884 (12)1.953 (12)
Co—Oxvi1.920 (8)1.884 (12)1.953 (12)
Symmetry codes: (i) x11, x2, x3, x4; (ii) x1, x21, x3, x4; (iii) x1, x2+1, x3, x4; (iv) x1+1, x2, x3, x4; (v) x11/2, x21/2, x3, x4; (vi) x11/2, x2+1/2, x3, x4; (vii) x1+1/2, x21/2, x3, x4; (viii) x1+1/2, x2+1/2, x3, x4; (ix) x1, x21, x3+1, x4; (x) x1, x2, x3+1, x4; (xi) x1, x2+1, x3+1, x4; (xii) x1+1, x2, x3+1, x4; (xiii) x11/2, x21/2, x3+1, x4; (xiv) x11/2, x2+1/2, x3+1, x4; (xv) x1+1/2, x21/2, x3+1, x4; (xvi) x1+1/2, x2+1/2, x3+1, x4; (xvii) x1, x2, x3+1, x4; (xviii) x1, x2+1, x3+1, x4; (xix) x1+1/2, x2+1/2, x3+1, x4; (xx) x1, x2, x31, x4; (xxi) x11/2, x21/2, x31, x4; (xxii) x11/2, x2+1/2, x31, x4.
 

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