research papers
Incommensurately modulated crystal structure of α′ (O′3)-type sodium cobalt oxide NaxCoO2 (x ∼ 0.78)
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.
Keywords: sodium cobalt oxide; modulated structure; powder neutron diffraction; superspace group; Rietveld analysis.
Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S205252062100370X/dq5050sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S205252062100370X/dq5050Isup2.hkl | |
Rietveld powder data file (CIF format) https://doi.org/10.1107/S205252062100370X/dq5050Isup3.rtv | |
Portable Document Format (PDF) file https://doi.org/10.1107/S205252062100370X/dq5050sup4.pdf |
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
Na0.779CoO2 | V = 75.21 (1) Å3 |
Mr = 108.84 | Z = 2 |
Monoclinic, C2/m(α0γ)00† | F(000) = 33.752 |
q = 0.345787a* + -0.262426c* | Dx = 4.806 Mg m−3 |
a = 4.88979 (17) Å | Neutron radiation |
b = 2.86782 (8) Å | T = 293 K |
c = 5.78034 (19) Å | black |
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. |
Refinement top
Rp = 0.048 | 42 parameters |
Rwp = 0.062 | 0 restraints |
Rexp = 0.034 | 0 constraints |
R(F) = 0.033 | Weighting 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 150.130 | Background function: 8 Legendre polynoms |
Profile function: Pseudo-Voigt | Preferred orientation correction: none |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Na | 0 | 0.5 | 0.5 | 0.0086 (13)* | 0.5 |
Co | 0 | 0 | 0 | 0.0110 (9)* | |
O | 0.2544 (3) | 0 | 0.8162 (2) | 0.0104 (4)* |
Bond lengths (Å) top
Average | Minimum | Maximum | |
Na—Nai | 5.176 (6) | 3.589 (10) | 5.592 (10) |
Na—Naii | 2.8679 | 2.8679 | 2.8679 |
Na—Naiii | 2.8679 | 2.8679 | 2.8679 |
Na—Naiv | 5.184 (6) | 3.589 (11) | 5.592 (11) |
Na—Nav | 3.142 (4) | 3.142 (8) | 3.142 (8) |
Na—Navi | 3.142 (4) | 3.142 (8) | 3.142 (8) |
Na—Navii | 3.142 (4) | 3.142 (8) | 3.142 (8) |
Na—Naviii | 3.142 (4) | 3.142 (8) | 3.142 (8) |
Na—Naix | 2.8771 (3) | 2.8771 (7) | 2.8771 (7) |
Na—Nax | 0.230 (3) | 0.230 (9) | 0.230 (9) |
Na—Naxi | 2.8771 (3) | 2.8771 (7) | 2.8771 (7) |
Na—Naxii | 4.995 (7) | 3.803 (9) | 5.815 (9) |
Na—Naxiii | 2.946 (3) | 2.946 (10) | 2.946 (10) |
Na—Naxiv | 2.946 (3) | 2.946 (10) | 2.946 (10) |
Na—Naxv | 3.226 (4) | 1.797 (8) | 3.343 (8) |
Na—Naxvi | 3.226 (4) | 1.797 (8) | 3.343 (8) |
Na—Co | 3.199 (11) | 3.00 (2) | 3.53 (2) |
Na—Coxvii | 3.215 (11) | 2.998 (19) | 3.571 (19) |
Na—Coiii | 3.199 (11) | 3.00 (2) | 3.53 (2) |
Na—Coxviii | 3.215 (11) | 2.998 (19) | 3.571 (19) |
Na—Covi | 3.030 (10) | 2.747 (17) | 3.445 (17) |
Na—Coxix | 3.080 (10) | 2.588 (16) | 3.381 (16) |
Na—O | 2.356 (5) | 2.190 (7) | 2.513 (7) |
Na—Oiii | 2.356 (5) | 2.190 (7) | 2.513 (7) |
Na—Ovi | 2.497 (9) | 2.231 (12) | 3.134 (12) |
Na—Ox | 2.301 (5) | 2.237 (7) | 2.612 (7) |
Na—Oxi | 2.301 (5) | 2.237 (7) | 2.612 (7) |
Na—Oxvi | 2.519 (9) | 2.348 (12) | 3.061 (12) |
Co—Oxx | 1.918 (16) | 1.85 (2) | 1.99 (2) |
Co—Oxxi | 1.920 (8) | 1.884 (12) | 1.953 (12) |
Co—Oxxii | 1.920 (8) | 1.884 (12) | 1.953 (12) |
Co—Ox | 1.918 (16) | 1.85 (2) | 1.99 (2) |
Co—Oxv | 1.920 (8) | 1.884 (12) | 1.953 (12) |
Co—Oxvi | 1.920 (8) | 1.884 (12) | 1.953 (12) |
Symmetry codes: (i) x1−1, x2, x3, x4; (ii) x1, x2−1, x3, x4; (iii) x1, x2+1, x3, x4; (iv) x1+1, x2, x3, x4; (v) x1−1/2, x2−1/2, x3, x4; (vi) x1−1/2, x2+1/2, x3, x4; (vii) x1+1/2, x2−1/2, x3, x4; (viii) x1+1/2, x2+1/2, x3, x4; (ix) −x1, x2−1, −x3+1, −x4; (x) −x1, x2, −x3+1, −x4; (xi) −x1, x2+1, −x3+1, −x4; (xii) −x1+1, x2, −x3+1, −x4; (xiii) −x1−1/2, x2−1/2, −x3+1, −x4; (xiv) −x1−1/2, x2+1/2, −x3+1, −x4; (xv) −x1+1/2, x2−1/2, −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, x3−1, x4; (xxi) x1−1/2, x2−1/2, x3−1, x4; (xxii) x1−1/2, x2+1/2, x3−1, x4. |