Structural characterization of YV₄O₈: simultaneous analysis of coexisting polytypes and simulation of diffuse scattering for a stacking disorder model

The structure of a crystal of newly synthesized YV₄O₈ was refined on the assumption that two polytypes and their respective twin forms intergrow. The model was expressed as a commensurate composite crystal with two types of subsystem: one is a V₄O₈ framework with rather large tunnels and the other consists of Y ions. In the tunnels, Y ions and vacancies are located at every second site in an ordered manner that is characteristic of each polytype. Refinement was performed using a high-dimensional formalism and all reflections from all domains. Diffuse streaks observed in the X-ray and electron diffraction patterns were simulated using the matrix method that has been used for one-dimensional disorder such as stacking faults. The unusual diffraction phenomena that occur in a crystal of YV₄O₈ are explained as arising from a multiple-domain structure of coexisting polytypes.

Computing details

Program(s) used to refine structure: FMLSM (Kato, 1994).

Figures

(I)

Crystal data

YV4O8	The diffraction data were collected based on a pseudo-orthorhombic unit cell with lattice constants A=9.109, B=21.356, C=5.774. Strong reflections could be indexed based on a pseudo-orthorhombic cell with a=9.109, b=10.678, c=2.887, and other weak reflections could be considered to come from two kinds of superstructures of CaFe2O4-type, one kind is alpha-form and the other is beta-form. The crystal has been considered to be intergrowths of two forms, and expected to be multiple-domain crystals. The structure of a multiple-domain crystal of YV4O8 was refined on the assumption that alpha-form, beta-form and their respective twin forms intergrowth mutually. The model was expressed as a commensurate composite crystal with two kinds of subsystems, one is V4O8 part and the other is Y part, and refinement was performed using high-dimensional formalism and all reflections from all domains simultaneously. The observed 3546 reflections [I>2s(I)] seem to be of three groups, the first one indexed based on a pseudo-orthorhombic cell with a=9.109, b=10.678, c=2.887, the second one indexed on a monoclinic cell with A1=9.109, B1=11.061, C1=5.774, alpha=105.129deg, and the third one indexed on a pseudo-orthorhombic cell with A2=9.109, B2=10.678, C2=5.774. Relations between the basic vectors are A1=A2=a, B1=b-c, B2=b, C1=C2=2c, which are equivalent to the relations between the reciprocal vectors A1*=A2*=a*, B1*=B2*=b*, C1*=b*/2+c*/2, C2*=c*/2. If five reciprocal basic vectors, a*, b*, c*, k1=b*/2, k2=c*/2, are adopted, each reflection is expressed by q=ha*+kb*+lc*+mk1+nk2. The first group (1615 reflections) is assigned by hkl00, and is considered to be main reflections common to alpha- and beta-YV4O8. The second group (1461 reflections) assigned by hkl11 are super-reflections which come from beta-form, while the third group (470 reflections) assigned by hkl01 are super-reflections which come from alpha-form. Structure models of alpha- and beta-YV4O8 are expressed as commensurate composite crystals consisting of basically common V4O8 frameworks and Y3+ cations ordering with respective manners in the tunnel of the framework. Reciprocal base vectors of the two subsystems of beta-YV4O8, (a*, b*, c*) for the V4O8 part and (a*, b*, C1*=k1+k2) for the Y part, are related to a five-dimensional basis (a*, b*, c*, k1, k2) through Z1=(1 0 0 0 0 | 0 1 0 0 0 | 0 0 1 0 0) and Z2=(1 0 0 0 0 | 0 1 0 0 0 | 0 0 0 1 1). Those of the two subsystems of alpha-YV4O8, (a*, b*, c*) for the V4O8 part and (a*, b*, C2*=k2) for the Y part, are related to the basis (a*, b*, c*, k1, k2) through Z3=(1 0 0 0 0 | 0 1 0 0 0 | 0 0 1 0 0) and Z4=(1 0 0 0 0 | 0 1 0 0 0 | 0 0 0 0 1). Symmetry operations for beta- and alpha-forms are expressed in a five-dimensional formalism based on (a*, b*, c*, k1, k2) in xyzx4x5. Those of beta-form are shown as follows in the beginning four lines, and those of alpha-form are shown in the succeeding four lines.
Mr = 420.67	Dx = 4.98 Mg m^−3
Monoclinic, ?	Mo Kα radiation, λ = 0.70930 Å
a = 9.109 (1) Å	Cell parameters from 22 reflections
b = 10.687 (1) Å	θ = 0–30°
c = 2.887 (1) Å	µ = 165.13 mm^−1
β = 90°	T = 293 K
V = 281.04 (5) Å^3	Block, black
Z = 2	0.12 × 0.11 × 0.10 mm

Data collection

Enraf-Nonius CAD4 diffractometer	3546 reflections with I > 2σ(I)
Radiation source: xray tube	Rint = 0.040
Graphite monochromator	θmax = 30.0°, θmin = 1.7°
ω–2θ scans	h = −12→12
Absorption correction: gaussian ?	k = −30→30
Tmin = ?, Tmax = 0.280	l = 0→7
4443 measured reflections	3 standard reflections every 240 min
4443 independent reflections	intensity decay: none

Refinement

Refinement on F	97 parameters
Least-squares matrix: full	0 restraints
R[F^2 > 2σ(F^2)] = 0.046	Calculated w = 1
wR(F^2) = .055
3546 reflections

Special details

Refinement. Respective two twin domains for alpha- and beta-forms have been considered, and the twin operations for alpha- and beta-forms are x, y, z, x4, x5; x, −y, z, -x4, x5 and x, y, z, x4, x5; x, y, −z, x4, -x5 respectively. Refinement was performed on the basis of |F| through a program FMLSM (Kato, K., Acta Cryst.(1994) A50, 351–357) with unit weight for all reflections. All 3546 intensity data [I>2 s(I)] of the three groups, were used after re-indexing based on (a*, b*, c*, k1, k2), namely 1615 reflections of (hkl00), 1461 reflections of (hkl11), and 470 reflections of (hkl01). In the structure factor calculation a summation over two points along [00011] or [00001] can be used instead of integration. Besides basic atomic coordinates of V and O common to alpha- and beta-forms, atomic coordinates of Y in alpha- and beta-forms and thermal parameters of V, O and Y, the Fourier amplitudes of the modulation functions of V and O atoms which are susceptible to modulation by ordered Y ions in the tunnels with respective manners for alpha- and beta-forms were considered as structural parameters. Furthermore, 4 scale factors and one parameter for extinction correction were considered as parameters. The final F-based scale factors are 0.673 (2), 0.659 (2), 0.231 (4) and 0.277 (4), and they correspond to the volume ratio of twin domains I, II, III, IV 8.48 (5):8.13 (5):1.00:1.44 (7), as the volume of each domain is proportional to the square of the scale factor. Domains I and II correspond to two twin domains of beta-YV4O8 while domain III and IV are two twin domains of alpha-YV4O8. The parameter for extinction correction is 1.12 (4)*10–5. The RF and wRF values for three reflection data groups, superposition of common main reflections (hkl00), super-reflections (hkl11) from domains I and II, super-reflections (hkl01) from domains III and IV are 0.037 and 0.050, 0.052 and 0.065, and 0.108 and 0.129.

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

	x	y	z	Uiso*/Ueq
Y1B	0.24249 (7)	0.34248 (5)	0.5505 (2)	0.00116 (2)
V1B	0.05925 (8)	0.11438 (6)	0.75	0.0051 (2)
V2B	0.41425 (6)	0.10157 (5)	0.25	0.0041 (2)
O1B	0.2059 (2)	0.1561 (2)	0.25	0.0036 (6)
O2B	0.1165 (3)	0.4756 (2)	0.25	0.0039 (6)
O3B	0.4742 (3)	0.2171 (2)	0.75	0.0044 (6)
O4B	0.4168 (2)	0.4289 (2)	0.25	0.0029 (5)
Y1A	0.24249	0.34248	0.8730 (5)	0.0029 (6)
V1A	0.05925	0.11438	0.75	0.0030 (10)
V2A	0.41425	0.10157	0.25	0.005 (2)
O1A	0.2059	0.1561	0.25	0.022 (4)
O2A	0.1165	0.4756	0.25	0.022
O3A	0.4742	0.2171	0.75	0.022
O4A	0.4168	0.4289	0.25	0.022

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Y1B	0.0076 (2)	0.0113 (2)	0.0136 (3)	0.0002 (2)	−0.0001 (4)	−0.0010 (3)
V1B	0.0038 (3)	0.0043 (3)	0.0071 (4)	0.0001 (2)	−0.0002 (7)	−0.0029 (7)
V2B	0.0017 (3)	0.0036 (3)	0.0071 (4)	0.0003 (2)	−0.0030 (10)	−0.0020 (10)