Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768103010450/ck0019sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108768103010450/ck0019Isup2.hkl |
YV_{4}O_{8} | 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. |
M_{r} = 420.67 | D_{x} = 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 |
Enraf-Nonius CAD4 diffractometer | 3546 reflections with I > 2σ(I) |
Radiation source: xray tube | R_{int} = 0.040 |
Graphite monochromator | θ_{max} = 30.0°, θ_{min} = 1.7° |
ω–2θ scans | h = −12→12 |
Absorption correction: gaussian ? | k = −30→30 |
T_{min} = ?, T_{max} = 0.280 | l = 0→7 |
4443 measured reflections | 3 standard reflections every 240 min |
4443 independent reflections | intensity decay: none |
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 |
YV_{4}O_{8} | V = 281.04 (5) Å^{3} |
M_{r} = 420.67 | Z = 2 |
Monoclinic, ? | Mo Kα radiation |
a = 9.109 (1) Å | µ = 165.13 mm^{−}^{1} |
b = 10.687 (1) Å | T = 293 K |
c = 2.887 (1) Å | 0.12 × 0.11 × 0.10 mm |
β = 90° |
Enraf-Nonius CAD4 diffractometer | 3546 reflections with I > 2σ(I) |
Absorption correction: gaussian ? | R_{int} = 0.040 |
T_{min} = ?, T_{max} = 0.280 | 3 standard reflections every 240 min |
4443 measured reflections | intensity decay: none |
4443 independent reflections |
R[F^{2} > 2σ(F^{2})] = 0.046 | 97 parameters |
wR(F^{2}) = .055 | 0 restraints |
3546 reflections |
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. |
x | y | z | U_{iso}*/U_{eq} | ||
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 |
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) |
Experimental details
Crystal data | |
Chemical formula | YV_{4}O_{8} |
M_{r} | 420.67 |
Crystal system, space group | Monoclinic, ? |
Temperature (K) | 293 |
a, b, c (Å) | 9.109 (1), 10.687 (1), 2.887 (1) |
β (°) | 90, 90, 90 |
V (Å^{3}) | 281.04 (5) |
Z | 2 |
Radiation type | Mo Kα |
µ (mm^{−}^{1}) | 165.13 |
Crystal size (mm) | 0.12 × 0.11 × 0.10 |
Data collection | |
Diffractometer | Enraf-Nonius CAD4 diffractometer |
Absorption correction | Gaussian |
T_{min}, T_{max} | ?, 0.280 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 4443, 4443, 3546 |
R_{int} | 0.040 |
(sin θ/λ)_{max} (Å^{−}^{1}) | 0.705 |
Refinement | |
R[F^{2} > 2σ(F^{2})], wR(F^{2}), S | 0.046, .055, ? |
No. of reflections | 3546 |
No. of parameters | 97 |
Δρ_{max}, Δρ_{min} (e Å^{−}^{3}) | ?, ? |
Computer programs: FMLSM (Kato, 1994).