The incommensurately modulated crystal structure of β-Pb₂BiVO₆: interpretation of the phase transition α → β → δ and conduction properties of related materials

A new polymorph of Pb₂BiVO₆ was prepared under ambient conditions and its crystal structure was determined by single-crystal X-ray diffraction. The phase transitions α → β and β → δ were identified in the mother phase; the high-temperature form δ-Pb₂BiVO₆ eventually decomposes at 753 K to a mixture of Pb₄BiVO₈ and the high-temperature form of PbBiVO₅ before showing recombination at 923 K. β-Pb₂BiVO₆ has an incommensurate monoclinic modulated structure. This crystal structure is twinned and complementary structural investigations of a powder sample of β-Pb₂BiVO₆ by TEM diffraction studies confirmed the lattice and incommensurate modulation character. Log σ = f(T⁻¹) dependences for Pb₂BiVO₆-related materials (6% M-for-V-substituted compositions; M = Cr, Mn, P) are reported, which allow the characterization (E_a and isothermal σ values) of the β- as well as the δ- and α-Pb₂BiVO₆ varieties.

Computing details

Data collection: KM4B8 (Kuma Diffraction Ltd., 1996); cell refinement: KM4B8 (Kuma Diffraction Ltd., 1996); data reduction: Jana2000 (Petricek & Dusek, 2000); program(s) used to solve structure: SIR97 (Altomare et al., 1997); program(s) used to refine structure: Jana2006 (Petricek, Dusek & Palatinus, 2006); molecular graphics: Diamond (Brandenburg, 1999); software used to prepare material for publication: Jana2006 (Petricek, Dusek & Palatinus, 2006).

(I)

Crystal data

BiO6Pb2V	V = 655.37 (6) Å^3
Mr = 770.3	Z = 4
Monoclinic, P21/m(0β0)s0†	F(000) = 1272
q = 0.23382b*	Dx = 7.804 Mg m^−3
Hall symbol: -P 2yb	Mo Kα radiation, λ = 0.71073 Å
a = 15.0501 (5) Å	µ = 81.17 mm^−1
b = 5.9011 (3) Å	T = 298 K
c = 7.5322 (5) Å	Platelet, black
β = 101.5657°	0.21 × 0.12 × 0.05 mm

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

Data collection

Bruker CCD diffractometer	24247 independent reflections
Radiation source: X-ray tube	4097 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.152
ω–scans	θmax = 40.3°, θmin = 1.4°
Absorption correction: analytical Sadabs (Sheldrick 2004)	h = −25→27
Tmin = 0.301, Tmax = 1	k = −11→11
110335 measured reflections	l = −13→13

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.036	1 constraint
wR(F^2) = 0.032	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 1.07	(Δ/σ)max < 0.001
4097 reflections	Δρmax = 3.44 e Å^−3
189 parameters	Δρmin = −6.04 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Bi1	0.80070 (4)	0.25	0.42521 (7)	0.02056 (19)
Bi2	0.71083 (4)	0.75	0.64948 (8)	0.01813 (19)
Pb1	0.95280 (4)	0.75	0.70209 (9)	0.0196 (2)
Pb2	0.55636 (4)	0.25	0.37273 (8)	0.01834 (19)
Pb3	0.84761 (5)	0.25	0.91902 (8)	0.0207 (2)
Pb4	0.64789 (4)	0.75	0.15756 (8)	0.0254 (2)
O1	0.6787 (4)	0.5092 (13)	0.4078 (8)	0.025 (3)
O2	0.8346 (4)	0.9943 (14)	0.6793 (9)	0.026 (3)
V1a	0.59555 (16)	0.2348 (10)	0.8701 (3)	0.0171 (9)	0.5
O11a	0.5883 (7)	0.233 (4)	1.0878 (16)	0.031 (4)*	0.5
O12a	0.6925 (9)	0.340 (3)	0.8386 (19)	0.048 (5)*	0.5
O13a	0.5895 (11)	−0.017 (3)	0.778 (2)	0.041 (5)*	0.5
O14a	0.5093 (9)	0.381 (3)	0.7476 (18)	0.035 (4)*	0.5
V2a	0.1185 (4)	0.25	0.8139 (8)	0.0197 (13)	0.5
O21a	0.0348 (13)	0.25	0.928 (3)	0.051 (4)*	0.5
O22a	0.0827 (13)	0.25	0.595 (2)	0.059 (5)*	0.5
O23a	0.1894 (7)	0.4721 (14)	0.8728 (19)	0.041 (3)*	0.5
V2b	0.1004 (4)	0.25	0.7768 (8)	0.0197 (13)	0.5
O21b	0.0455 (13)	0.25	0.947 (3)	0.051 (4)*	0.5
O22b	0.2104 (11)	0.25	0.844 (3)	0.059 (5)*	0.5
O23b	0.0695 (9)	0.0279 (14)	0.6357 (15)	0.041 (3)*	0.5

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Bi1	0.0194 (3)	0.0219 (3)	0.0200 (3)	0	0.0029 (2)	0
Bi2	0.0166 (3)	0.0161 (3)	0.0215 (3)	0	0.0032 (2)	0
Pb1	0.0152 (3)	0.0216 (4)	0.0214 (3)	0	0.0021 (2)	0
Pb2	0.0168 (3)	0.0201 (3)	0.0179 (3)	0	0.0030 (2)	0
Pb3	0.0245 (4)	0.0198 (3)	0.0169 (3)	0	0.0019 (3)	0
Pb4	0.0235 (3)	0.0310 (4)	0.0209 (3)	0	0.0023 (2)	0
O1	0.028 (4)	0.017 (4)	0.028 (5)	−0.004 (4)	−0.001 (3)	−0.003 (4)
O2	0.026 (4)	0.027 (4)	0.024 (5)	−0.004 (3)	0.001 (3)	−0.002 (4)
V1a	0.0165 (13)	0.0183 (18)	0.0167 (16)	−0.0011 (16)	0.0043 (11)	0.0015 (18)
V2a	0.027 (2)	0.0155 (15)	0.017 (2)	0	0.0071 (17)	0
V2b	0.017 (2)	0.0155 (15)	0.027 (2)	0	0.0073 (17)	0