Type II Bi_1 − xW_xO_{1.5 + 1.5x}: a (3 + 3)-dimensional commensurate modulation that stabilizes the fast-ion conducting delta phase of bismuth oxide

The Type II phase in the Bi_1 − xW_xO_{1.5 + 1.5x} system is shown to have a (3 + 3)-dimensional modulated δ-Bi₂O₃-related structure, in which the modulation vector [epsilon] `locks in' to a commensurate value of 1/3. The structure was refined in a 3 × 3 × 3 supercell against single-crystal Laue neutron diffraction data. Ab initio calculations were used to test and optimize the local structure of the oxygen sublattice around a single mixed Bi/W site. The underlying crystal chemistry was shown to be essentially the same as for the recently refined (3 + 3)-dimensional modulated structure of Type II Bi<sub>1 − x</sub>Nb<sub>x</sub>O<sub>1.5 + x</sub> (Ling et al., 2013), based on a transition from fluorite-type to pyrochlore-type via the appearance of W<sub>4</sub>O<sub>18</sub> `tetrahedra of octahedra' and chains of corner-sharing WO₆ octahedra along 〈110〉_F directions. The full range of occupancies on this mixed Bi/W site give a hypothetical solid-solution range bounded by Bi₂₃W₄O_46.5 (x = 0.148) and Bi₂₂W₅O₄₈ (x = 0.185), consistent with previous reports and with our own synthetic and analytical results.

Computing details

(I)

Crystal data

Bi23O46.5W4	F(000) = 10308
Mr = 6285.9	Dx = 9.073 Mg m^−3
Cubic, F43m	Neutron radiation, λ = 1 Å
Hall symbol: F -4;2;3	µ = 0.004 mm^−1
a = 16.633 Å	T = 293 K
V = 4601.63 Å^3	, yellow
Z = 4	0.5 mm (radius)

Data collection

299 measured reflections	h = 2→20
299 independent reflections	k = 0→14
162 reflections with I > 3σ(I)	l = 0→12
θmax = 38.5°, θmin = 5.7°

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.249	8 constraints
wR(F^2) = 0.273	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 11.69	(Δ/σ)max = 0.032
162 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
21 parameters	Absolute structure: 12 of Friedel pairs used in the refinement

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
W1	0.669 (2)	0.831 (2)	0.831 (2)	0.020 (4)*
Bi1	0.0015 (11)	0.8372 (5)	0.8372 (5)	0.020 (4)*
Bi2	0.5	0	0.8356 (11)	0.020 (4)*
Bi3	0.3320 (9)	0.8320 (9)	0.8320 (9)	0.020 (4)*
Bi4	0.5	0.5	0	0.020 (4)*
O1	0.9113 (12)	0.9113 (12)	0.9113 (12)	0.006 (8)*
O2	0.0861 (18)	0.9139 (18)	0.9139 (18)	0.010 (10)*	0.75
O3	0.4166 (13)	0.9166 (13)	0.761 (2)	0.062 (10)*
O4	0.25	0.75	0.75	0.062 (10)*
O5	0.628 (3)	0.75	0.75	0.072 (10)*
O6	0.726 (3)	0.9142 (16)	0.9142 (16)	0.072 (10)*
O7	0.25	0.099 (4)	0.25	0.062 (10)*	0.75
O8	0.410 (2)	0.910 (2)	0.910 (2)	0.062 (10)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

Bond lengths (Å)

W1—O5	2.03 (4)	Bi4—O2^xxv	2.48 (3)
W1—O5^i	2.03 (4)	Bi4—O2^xxvi	2.48 (3)
W1—O5^ii	2.03 (4)	Bi4—O2^xxvii	2.48 (3)
W1—O6	2.17 (5)	O1—O2^xxviii	2.91 (4)
W1—O6^iii	2.17 (5)	O1—O2^xxix	2.91 (4)
W1—O6^ii	2.17 (5)	O1—O2^xxx	2.91 (4)
Bi1—O1^iv	2.30 (2)	O1—O6	3.08 (5)
Bi1—O2	2.29 (3)	O1—O6^xxxi	3.08 (5)
Bi1—O3^v	2.50 (3)	O1—O6^xxxii	3.08 (5)
Bi1—O3^vi	2.50 (3)	O2—O3^v	2.90 (5)
Bi1—O5^vii	2.97 (4)	O2—O3^xv	2.90 (5)
Bi1—O6^viii	2.67 (4)	O2—O3^vi	2.90 (5)
Bi1—O6^ix	2.67 (4)	O3—O6^ii	2.82 (3)
Bi1—O7^x	2.62 (4)	O3—O6^xxxiii	2.82 (3)
Bi2—O3^xi	2.33 (3)	O3—O7^xvii	2.79 (2)
Bi2—O3^xii	2.33 (3)	O3—O7^xix	2.79 (2)
Bi2—O6^xiii	2.27 (3)	O3—O8	2.50 (5)
Bi2—O6^xiv	2.27 (3)	O4—O7^xxxiv	2.50 (7)
Bi2—O8^xi	2.45 (3)	O4—O7^xvii	2.50 (7)
Bi2—O8^xii	2.45 (3)	O4—O7^xxxv	2.50 (7)
Bi3—O3	2.32 (3)	O4—O7^xviii	2.50 (7)
Bi3—O3^xv	2.32 (3)	O4—O7^x	2.50 (7)
Bi3—O3^xvi	2.32 (3)	O4—O7^xix	2.50 (7)
Bi3—O4	2.363 (15)	O5—O5^xxxi	2.88 (5)
Bi3—O7^xvii	2.24 (4)	O5—O5^i	2.88 (5)
Bi3—O7^xviii	2.24 (4)	O5—O5^xxxii	2.88 (5)
Bi3—O7^xix	2.24 (4)	O5—O5^ii	2.88 (5)
Bi3—O8	2.26 (4)	O5—O6^iii	2.85 (3)
Bi4—O1^xx	2.55 (2)	O5—O6^xxxvi	2.85 (3)
Bi4—O1^xxi	2.55 (2)	O5—O6^ii	2.85 (3)
Bi4—O1^xxii	2.55 (2)	O5—O6^xxxvii	2.85 (3)
Bi4—O1^xxiii	2.55 (2)	O6—O6^iii	3.31 (5)
Bi4—O2^xxiv	2.48 (3)	O6—O6^ii	3.31 (5)

Symmetry codes: (i) z, −x+3/2, −y+3/2; (ii) −y+3/2, z, −x+3/2; (iii) −z+3/2, −x+3/2, y; (iv) x−1, y, z; (v) −x+1/2, y, −z+3/2; (vi) −y+1, −z+3/2, x+1/2; (vii) −x+1/2, −y+3/2, z; (viii) z−1, x, y; (ix) y−1, z, x; (x) y, z+1/2, x+1/2; (xi) x, y−1, z; (xii) −x+1, −y+1, z; (xiii) −y+3/2, z−1, −x+3/2; (xiv) y−1/2, −z+1, −x+3/2; (xv) z−1/2, x+1/2, y; (xvi) y−1/2, z, x+1/2; (xvii) −x+1/2, −y+1, z+1/2; (xviii) z, −x+1, −y+1; (xix) −y+1/2, z+1/2, −x+1; (xx) x−1/2, y−1/2, z−1; (xxi) −x+3/2, −y+3/2, z−1; (xxii) −x+3/2, y−1/2, −z+1; (xxiii) x−1/2, −y+3/2, −z+1; (xxiv) x+1/2, y−1/2, z−1; (xxv) −x+1/2, −y+3/2, z−1; (xxvi) −x+1/2, y−1/2, −z+1; (xxvii) x+1/2, −y+3/2, −z+1; (xxviii) x+1, y, z; (xxix) −x+1, −y+2, z; (xxx) −x+1, y, −z+2; (xxxi) z, x, y; (xxxii) y, z, x; (xxxiii) y−1/2, −z+2, −x+3/2; (xxxiv) x, y+1/2, z+1/2; (xxxv) z, x+1/2, y+1/2; (xxxvi) −z+3/2, x, −y+3/2; (xxxvii) −y+3/2, −z+3/2, x.