Synchrotron X-ray and TOF neutron powder diffraction study of a lyonsite-type oxide Co3.6Fe3.6(VO4)6

Solid State Sciences 4 (2002) 515–522 www.elsevier.com/locate/ssscie

Synchrotron X-ray and TOF neutron powder diffraction study of a lyonsite-type oxide Co3.6Fe3.6 (VO4 )6 Alexei A. Belik a,∗,1 , Fujio Izumi a , Takuji Ikeda a , Atsushi Nisawa b , Takashi Kamiyama c , Kenichi Oikawa c a Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan b Harima Office, Advanced Materials Laboratory, National Institute for Materials Science, 1-1-1 Kouto, Mikazuki-cho, Sayo-gun, Hyogo 679-5198, Japan c Institute of Materials Structure Science, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan

Received 14 December 2001; accepted 18 December 2001

Abstract Co3.6 Fe3.6 (VO4 )6 was synthesized by solid-state reaction at 900 ◦ C, and its structure was determined by X-ray and neutron powder diffraction. Co3.6 Fe3.6 (VO4 )6 is isotypic with lyonsite (space group: Pnma; Z = 2), having lattice parameters of a = 4.96480(9) Å, b = 10.2245(2) Å, and c = 17.2100(3) Å. Its structure parameters were refined by the Rietveld method with two sets of synchrotron X-ray (wavelengths: 0.85001 and 1.74500 Å) and time-of-flight neutron powder diffraction data. Co2+ and Fe3+ ions are distributed among three different metal sites M1–M3. Not Co2+ ions but Fe3+ ions are mainly contained in face-sharing M3O6 octahedra, forming single chains parallel to the [1 0 0] direction. Edge- and corner-sharing octahedra M2O6 build up layers perpendicular to the [0 0 1] direction. Edge-sharing trigonal prisms M1O6 form zig-zag single chains along the [1 0 0] direction. The M1 and M3 sites are about 6.0(2)% and 34.0(2)% deficient, respectively. The tendency for Co2+ and Fe3+ ions to distribute among the three metal sites is discussed on the basis of the electrostatic valence rule.  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Crystal structure; TOF neutron diffraction; Synchrotron X-ray powder diffraction; Mössbauer spectroscopy; Vanadium oxide; Lyonsite

1. Introduction Vanadium and molybdenum oxides are widely used as catalysts for selective oxidation of hydrocarbons [1]. Some compounds isotypic with the mineral lyonsite, Cu3 Fe4 (VO4 )6 [2], exhibit good catalytic properties as in Mg2.5 VMoO8 [3] and high ionic conductivity as in Li2 Cu2 (MoO4 )3 [4]. Synthetic lyonsite has recently been revealed to have a narrow homogeneous-solution range of Cu3+1.5x Fe4−x (VO4 )6 (0.667
x < 0.778) [5]. Some vanadium oxides, e.g., Co4 Fe3.33(VO4 )6 [6] and Cu4.05Cr3.30 (VO4 )6 [5], with the lyonsite-type structure were synthesized and characterized by various experimental means. Vanadium oxides with a 3+ general formula A2+ 3+1.5x M4−x (VO4 )6 crystallize also in another structure type of howardevansite, NaCuFe2 (VO4 )3 [7],

* Correspondence and reprints.

E-mail address: [email protected] (A.A. Belik). 1 Postdoctoral fellow from Department of Chemistry, Moscow State

University, Leninskie Gory, Moscow 119899, Russia.

or Fe7 (PO4 )6 [8], e.g., Cu3+1.5x Fe4−x (VO4 )6 (−0.333
x
−0.167) [5,9] and Mn3 Fe4 (VO4 )6 [6]. All the vanadium oxides with the lyonsite-type structure contain face-sharing M3O6 octahedra, where the M3 site was believed to be partially occupied by divalent cations. In addition, these vanadium oxides include two sites, M1 and M2, occupied by both divalent and trivalent cations. Wang et al. [6] determined the crystal structure of Co4 Fe3.33(VO4 )6 containing Co2+ and Fe3+ ions by single-crystal X-ray diffraction and reported the following occupancies of the three metal sites: 1 (Co2+ ) for M1, 0.17 (Co2+ ) and 0.83 (Fe3+ ) for M2, and 0.662 (Co2+ ) for M3. However, our simple estimation of electrostatic bond strengths suggested that distribution of Co2+ and Fe3+ among the three metal sites reported by them is doubtful, as discussed later. This paper describes the synthesis and crystal structure of a lyonsite-type vanadium oxide, Co3.6 Fe3.6 (VO4 )6 , isotypic with Co4 Fe3.33(VO4 )6 [6]. We refined its structural parameters by the complementary use of synchrotron X-ray and neutron powder diffraction. Because the atomic scattering factors of Co and Fe are very close to each other, X-ray

1293-2558/02/$ – see front matter  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 2 9 3 - 2 5 5 8 ( 0 2 ) 0 1 2 7 9 - 7

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powder diffraction (XRD) is useful to obtain deficiencies at mixed-metal sites but unable to determine distribution of Co and Fe among the three metal sites. Time-of-flight (TOF) neutron powder diffraction was then used to distinguish Co from Fe unambiguously.

Table 1 Identification of Co3 Fe4 (VO4 )6 annealed at different temperatures Temperature (annealing time) 670 ◦ C (60 h) 750 ◦ C (60 h)

2. Experimental

900 ◦ C (30 h)

Products Co3+1.5x Fe4−x (VO4 )6 , FeVO4 (13.0 mass%), and a howardevansite-type phase (traces) Co3+1.5x Fe4−x (VO4 )6 , a howardevansite-type phase, and an unidentified phase Co3+1.5x Fe4−x (VO4 )6 and Fe2 O3 (4.1 mass%)

2.1. Synthesis Lyonsite-type vanadium oxides were synthesized from mixtures of Co3 O4 , Fe2 O3 , and V2 O5 . The starting materials were contained in platinum crucibles and heated in air at different temperatures in an electric furnace. After annealing, they were quenched in air. All the products were black. Unless otherwise noted, nominal compositions will hereafter be described for these oxides. They were identified by XRD with a SIEMENS D500 Bragg–Brentano-type powder diffractometer equipped with an incident-beam quartzmonochromator to obtain Cu Kα1 radiation and a BRAUN position-sensitive detector and operated at 30 kV and 30 mA. Table 1 lists products obtained by annealing mixtures corresponding to a stoichiometric compound Co3 Fe4 (VO4 )6 at different temperatures. Fig. 1 shows XRD patterns of Co3 Fe4 (VO4 )6 annealed at 670, 750, and 900 ◦ C. Mass fractions of phases given in this paper were calculated from scale factors refined by Rietveld analysis of the XRD data with R IETAN -2000 [10]. Formation of the FeVO4 impurity suggests that Co3 Fe4 (VO4 )6 decomposed to FeVO4 and nonstoichiometric lyonsite-type phases: (1 + 0.5x) Co3 Fe4 (VO4 )6 → 3x FeVO4 + Co3+1.5x Fe4−x (VO4 )6 . An impurity isotypic with howardevansite, which was never detected by Wang et al. [6], was formed slightly at 670 ◦ C (Fig. 1a) and noticeably at 750 ◦ C (Fig. 1b). A lyonsite-type compound, Co3.6 Fe3.6 (VO4 )6 , synthesized by heating the starting materials at 670 ◦ C for 90 h also contained a slight amount of the howardevansite-type phase, as in the case of Co3 Fe4 (VO4 )6 (Fig. 1a). Then, this sample was heated at 900 ◦ C for 1 h and slowly cooled in the furnace. The resultant sample containing about 1.0 mass% of Fe2 O3 was submitted to synchrotron X-ray and TOF neutron diffraction experiments. We also tried to synthesize samples Co3+1.5x Fe4−x (VO4 )6 with different x values in addition to Co3.6 Fe3.6 (VO4 )6 (x = 0.4). However amounts of impurity phases in them were larger than those in Co3.6 Fe3.6 (VO4 )6 . 2.2. Measurements and Rietveld analyses of synchrotron X-ray and neutron powder diffraction data Synchrotron XRD data of Co3.6 Fe3.6 (VO4 )6 were measured at room temperature on a powder diffractometer

Fig. 1. XRD patterns of Co3 Fe4 (VO4 )6 annealed at (a) 670 ◦ C, (b) 750 ◦ C, and (c) 900 ◦ C. Peak positions of Bragg reflections for (1) the lyonsite-type phase, (2) FeVO4 , (3) the howardevansite-type phase, and (4) Fe2 O3 are given below the patterns. Reflections due to unknown compounds are marked with black circles. Arrows indicate the howardevansite-type phase.

(BL15XU at SPring-8) with the Debye–Scherrer geometry using a receiving slit. Incident beams from an undulator were monochromatized to either of two wavelengths, λ1 = 0.85001 Å (SR-1) and λ2 = 1.74500 Å (SR-2) near the absorption edge of Fe, with rotated inclined Si(1 1 1) double crystal monochromators. The sample was contained in a quartz-glass capillary tube with an inner diameter of 0.3 mm and rotated at a speed of 60 rpm. The µr (µ: linear absorption coefficient, r: sample radius) values of the sample and capillary tube were determined with direct incident beams to correct for X-ray absorption. The counting time per step was 1 s for SR-1 and 2 s for SR-2. We analyzed the two sets of the synchrotron XRD data by the Rietveld method with R IETAN -2000 [10] on the basis of space group Pnma (No. 62) using fractional coordinates of lyonsite [2] as initial parameters. Atomic scattering factors for Co, Fe, V, and O were taken from International Tables, Vol. C [11]. Anomalous scattering factors were evaluated with a computer program C ROMER by the Cromer–Liberman method adopting a Kissel–Pratt correction [12]. The split pseudo-Voigt function of Toraya [13] was fit to each profile, and a composite background function, i.e., 11th-order Legendre polynomial multiplied by a set of numerical values to approximate the background, to the background. These numerical values for the background was obtained with P OWDER X [14]. Preferred orientation was corrected with the March–Dollase function on the assumption

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Table 2 Occupancies and isotropic atomic displacement parametersa for the M1–M3 sites in Co3.6 Fe3.6 (VO4 )6 Data

M1

Cations

M2

g

102 U (Å2 )

g

M3 102 U (Å2 )

g

102 U (Å2 )

0.28(6) 0.28(6)

0.575(6) 2.18(2)

1.91(14) 1.90(14)

−0.65(5) 2.19(5)

0.706(5) 0.514(3)

0.65(14) 3.39(14)

Nb

Fe Co

0.295(4) 1.12(2)

0.3(2) 0.3(2)

0.653(3) 2.477(12)

SR-2

Fe Co

1.195(5) 0.874(4)

−1.53(5) 1.30(5)

1.142(4) 0.835(3)

SR-2

Fec Coc

1.319(5) 0.853(3)

1.0 1.0

1.229(4) 0.785(3)

0.9 0.9

0.770(4) 0.481(3)

1.9 1.9

SR-1

Fe Co

0.975(2) 0.938(2)

1.01(3) 1.06(3)

1.0085(13) 0.9690(12)

0.875(13) 0.930(13)

0.661(2) 0.633(2)

1.93(4) 1.95(4)

a The isotropic Debye–Waller factor is computed as exp(−8π 2 U sin2 θ/λ2 ); M3 sites were, respectively, fixed at 0.01, 0.009, and 0.019 obtained for SR-1.

b N: TOF neutron diffraction data;

of a (1 0 0) cleavage plane. Partial profile relaxation [10] was applied to 011, 002, 022, 004, 024, 122, 015, 104 reflections for SR-2 and to the same reflections plus 133 and 039 reflections for SR-1 to improve fits in these reflections at the last stages of the structure refinements. TOF neutron powder diffraction data of Co3.6 Fe3.6 (VO4 )6 were measured at room temperature for 3.5 h on a TOF neutron powder diffractometer Vega [15] at the pulsed spallation neutron facility KENS. The sample (ca. 5.7 g) was contained in a V holder (diameter: 9.2 mm), which was slowly rotated during the measurement. An array of 160 position-sensitive detectors (PSDs) installed in a backward bank (d/d ≈ 2 × 10−3 ) with a 2θ range from 150 to 170◦ was used to collect the intensity data. Incident neutron spectra were monitored with a 3 He monitor counter. Differences in efficiency between the PSDs and the monitor counter were corrected using intensity data taken in a separate measurement of incoherent scattering from V. The resulting neutron diffraction data were analyzed by the Rietveld method with R IETAN -2001T [16]. A composite background function, i.e., 14th-order Legendre polynomial multiplied by a smoothed incident spectrum, was fit to the background. Preferred orientation was corrected with the March–Dollase function on the assumption of the (1 0 0) cleavage plane. Bound coherent scattering lengths, bc , used for the structure refinement were 2.49 fm (Co), 9.45 fm (Fe), −0.3824 fm (V), and 5.803 fm (O) [17]. Structure parameters for vanadium sites were not refined but fixed at those obtained from the SR-1 data because of its very small bc value.

3. Results and discussion

2.3. Mössbauer spectroscopy We measured 57 Fe Mössbauer spectra using a constant acceleration Mössbauer spectrometer coupled with a 1024 multichannel analyzer and a 57 Co/Rh source kept at room temperature. All the isomer shifts, δ, were determined with reference to α-Fe. The resulting spectra were decomposed into symmetric quadrupole doublets with Lorentzian lineshapes.

c U parameters for the M1, M2, and

Metals other than vanadium, M, have possibilities of occupying the three metal sites: M1 (4c; x ≈ 0.24, y = 1/4, and z ≈ 0.80), M2 (8d; x ≈ 0.25, y ≈ 0.42, and z ≈ 0.97), and M3 (4c; x ≈ 0.10, y = 1/4, and z ≈ 0.25). Full occupation of these sites leads to the presence of 16 M atoms per unit cell whereas the chemical formula of Co3.6 Fe3.6 (VO4 )6 gives 14.4 M atoms per unit cell. Therefore, 1.6 vacancies per unit cell have to be assigned to part or all of the three metal sites. To reveal the tendency for Co, Fe, and the vacancies to distribute among the three sites, their occupation factors, g, at these sites were refined with their isotropic atomic displacement parameters, U , on the assumption that only Co or Fe occupies the M1–M3 sites together with vacancies. Table 2 lists the results of such preliminary refinements. The difference in bc between Co and Fe is large enough to distinguish them unambiguously by neutron diffraction. In the SR-2 data, atomic scattering factors for Co and Fe differ considerably because of the anomalous scattering of Fe, which also enables us to distinguish Co and Fe. The occupancies refined with the neutron and SR-2 data are incompatible with those reported for Co4 Fe3.33 (VO4 )6 by Wang et al. [6], i.e., g(M1) = 1, g(M2) = 1, and g(M3) = 0.662, apart from distribution of Co and Fe which are hardly distinguishable from each other by X-ray diffraction. This fact supports the idea that none of the M1–M3 sites is occupied by one kind of a metal (Co or Fe). In other words, Co and Fe are not completely ordered but distributed among the three sites. Nevertheless, the occupancies in Table 2, particularly those refined with the neutron diffraction data, provide us with significant information regarding site preferences. In the neutron Rietveld refinement, the occupancy of Co at the M1 site was a little more than 1, viz., 1.12, whereas that of Fe was only 0.295. This finding, coupled with the g(M1) value obtained by single-crystal X-ray diffraction [6], shows the M1 site to be preferentially occupied by Co. The occupancy of Fe at the M3 site, 0.575, was essentially the same

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Table 3 Distribution of Co2+ and Fe3+ ions among the M1–M3 sites in Co3.6 Fe3.6 (VO4 )6 M1

Data N SR-2

M2

M3

g(Fe)

g(Co)

102 U (Å2 )

g(Fe)

g(Co)

102 U (Å2 )

g(Fe)

g(Co)

102 U (Å2 )

0.096(6) 0.185(10)

0.844 0.755

0.9(2) 1.06(6)

0.555 0.557

0.445 0.443

0.45(6) 1.10(5)

0.594(7) 0.501(9)

0.066 0.159

2.52(14) 1.7(2)

Table 4 Conditions of the diffraction experiments and parts of refinement results for Co3.6 Fe3.6 (VO4 )6 Beam λ (Å) d range (Å) 2θ range (deg) Number of data points Lattice parameters: a (Å) b (Å) c (Å) V (Å3 ) Number of Bragg reflections Variables: Background Profiles Structure Others PPPa Rwp ; Rp RB ; RF b S a Refined primary profile parameters;

SR-1 0.85001 0.648–10.83 4.5–82.0 15503

SR-2 1.74500 0.931–9.54 10.5–139.0 12861

TOF neutron (N) – 0.5–5.0 – 3970

4.96281(1) 10.22010(3) 17.20290(5) 872.538(4) 1764

4.96392(2) 10.22260(3) 17.20710(5) 873.160(5) 605

4.96480(9) 10.2245(2) 17.2100(3) 873.62(3) 3782

12 10 43 9 45 3.57%; 2.73% 2.90%; 2.20% 2.13

12 10 43 9 35 3.22%; 2.53% 8.87%; 5.72% 1.40

15 18 44 9 – 3.20%; 2.52% 1.41%; 1.24% 1.25

b R and R for the lyonsite-type phase. B F

as 0.662 determined by single-crystal X-ray diffraction [6], which presents unambiguous evidence for the preferential occupation of the M3 site by Fe. On the other hand, the occupancies of the three metal sites refined with the SR-1 data give us information concerning vacancy locations. The occupancies were near to 1 for both the M1 and M2 sites but as small as 0.661 for Fe and 0.633 for Co for the M3 site. Vacancies must, therefore, be localized at the M3 site. However, these values are a little larger than 0.6 that would be expected for the nominal composition Co3.6Fe3.6 (VO4 )6 , which indicates partial deficiency at the M1 and/or M2 sites. When Co was positioned at the M1 site, the occupancy of the M1 site deviated from unity, converging at 0.938(2). Locating Fe at the M3 site yielded an occupancy of 0.661(2). The occupancies of the M2 site were nearly unity. In view of the preferential occupation of the M1 site by Co and the M3 site by Fe, the results described above permit us to impose the following linear constraints on the occupancies of the three metal sites: g(Fe) + g(Co) = 0.94 for the M1 site, g(Fe) + g(Co) = 1 for the M2 site, and g(Fe) + g(Co) = 0.66 for the M3 site. Subsequent Rietveld refinements were carried out under these constraints and those based on the total chemical composition. The occupancies of Co and Fe refined for the M1–M3 sites with the neutron and SR-2 data (Table 3) noticeably

differed from each other. In view of the large difference in bc between Co and Fe, neutron diffraction is believed to yield more accurate occupancies. Hence, the occupancies of the three metal sites were fixed at those obtained by neutron diffraction in final structure refinements. Rietveld refinements with the SR-1 and SR-2 data afforded normal U parameters on the adoption of the cation distribution described above. Single-crystal X-ray analyses of isotypic compounds, e.g., lyonsite Cu3 Fe4 (VO4 )6 [2], Co4 Fe3.33(VO4 )6 [6], and NaCo2.31 (MoO4)3 [18], showed that thermal motion of cations at the M1 and M3 sites is highly anisotropic. Then, anisotropic atomic displacement parameters, Uij , were refined at the last stage of the Rietveld refinement using the neutron diffraction data. Because U12 , U13 , and U23 parameters for the M2 site were nearly zero within standard deviations, they were fixed at zero in the last stage of the refinement. The resulting Uij values of the M1, M2, and M3 sites in Co3.6 Fe3.6 (VO4 )6 were comparable to corresponding ones in Cu3 Fe4 (VO4 )6 [2] and Co4 Fe3.33(VO4 )6 [6]. Table 4 lists experimental/refinement conditions, final R factors, and lattice parameters, etc. It should be noted that, with the model adopting isotropic thermal motion, R factors in the neutron Rietveld analysis were Rwp = 3.36% (S = 1.32), Rp = 2.69%, RB = 1.58%, and RF = 1.39%. Final fractional coordinates and atomic displacement parameters

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Table 5 Fractional coordinates and atomic displacement parametersa for Co3.6 Fe3.6 (VO4 )6 y

z

102 U (Å2 )

Atom

Data

Site

x

M1b

SR-1 SR-2 N

4c

0.2459(2) 0.2440(6) 0.2418(14)

1/4 1/4 1/4

0.80274(4) 0.80291(10) 0.8028(5)

1.08(2) 1.46(5) 1.27c

M2b

SR-1 SR-2 N

8d

0.24798(13) 0.2474(5) 0.2480(5)

0.42285(4) 0.42299(12) 0.4235(2)

0.97183(3) 0.97183(8) 0.9721(2)

0.983(11) 1.07(4) 0.55c

M3b

SR-1 SR-2 N

4c

0.0941(2) 0.0902(8) 0.0948(8)

1/4 1/4 1/4

0.25071(8) 0.2508(3) 0.2512(2)

2.38(3) 0.55(12) 2.33c

V1

SR-1 SR-2 Nd

4c

−0.2227(2) −0.2237(5) −0.2227

1/4 1/4 1/4

0.05674(4) 0.05647(10) 0.05674

0.97(2) 1.11(5) 0.97

V2

SR-1 SR-2 Nd

8d

0.72200(14) 0.7232(4) 0.72200

0.47241(5) 0.47235(10) 0.47241

0.84315(3) 0.84335(7) 0.84315

0.98(2) 1.20(4) 0.98

O1

SR-1 SR-2 N

8d

0.6546(5) 0.6603(10) 0.6530(5)

0.6167(2) 0.6172(4) 0.6148(2)

0.79634(12) 0.7964(3) 0.7964(2)

1.35(6) 1.27(14) 1.15(7)

O2

SR-1 SR-2 N

8d

0.4283(5) 0.4257(11) 0.4311(5)

0.3863(2) 0.3904(5) 0.3860(2)

0.87253(13) 0.8717(3) 0.8723(2)

0.89(6) 0.86(13) 0.70(5)

O3

SR-1 SR-2 N

4c

0.0707(6) 0.0764(14) 0.0663(7)

1/4 1/4 1/4

0.9937(2) 0.9961(4) 0.9934(2)

0.75(8) 0.6(2) 0.94(9)

O4

SR-1 SR-2 N

8d

0.5865(4) 0.5925(9) 0.5836(5)

0.3854(2) 0.3846(4) 0.3853(3)

0.03519(13) 0.0355(3) 0.0349(2)

1.08(6) 1.13(13) 0.63(6)

O5

SR-1 SR-2 N

8d

0.9138(5) 0.9110(10) 0.9146(5)

0.5042(2) 0.5034(5) 0.5053(2)

0.92668(13) 0.9278(3) 0.9265(2)

1.24(6) 0.95(14) 0.60(6)

O6

SR-1 SR-2 N

4c

0.6473(7) 0.6496(14) 0.6505(8)

3/4 3/4 3/4

0.6531(2) 0.6537(4) 0.6517(2)

1.18(9) 0.8(2) 0.71(9)

O7

SR-1 SR-2 N

8d

−0.0852(5) −0.0856(12) −0.0864(5)

0.3737(2) 0.3737(4) 0.3731(2)

0.78724(12) 0.7875(3) 0.7877(2)

1.10(6) 1.55(14) 1.00(6)

a The anisotropic Debye–Waller factor is computed as exp[−2π 2 (h2 a ∗2 U 2 ∗2 2 ∗2 ∗ ∗ ∗ ∗ 11 + k b U22 + l c U33 + 2hka b U12 + 2hla c U13 + (Co) for M2, and 0.594 (Fe) and 0.066 (Co) for 2klb∗ c∗ U23 )]. b Occupation factors are 0.096 (Fe) and 0.844 (Co) for M1, 0.555 (Fe) and 0.445

M3. c These are equivalent isotropic atomic displacement parameter, Ueq , defined as Ueq = (1/3) i j Uij ai∗ aj∗ a i a j . Anisotropic atomic displacement

parameters are U11 = 0.011(4) Å2 , U22 = 0.007(4) Å2 , U33 = 0.020(5) Å2 , and U13 = −0.009(4) Å2 for M1; U11 = 0.0048(12) Å2 , U22 = 0.0062(11) Å2 , U33 = 0.0056(12) Å2 , U12 = 0, U13 = 0, and U23 = 0 for M2; U11 = 0.061(3) Å2 , U22 = 0.002(2) Å2 , U33 = 0.007(2) Å2 , and U13 = 0.013(3) Å2 for M3. d Fixed at corresponding values in SR-1.

are listed in Table 5, and metal–oxygen bond lengths in Table 6. Fig. 2 displays observed, calculated, and difference patterns for the synchrotron X-ray and neutron diffraction data. Fig. 3 shows the Mössbauer spectrum of Co3.6 Fe3.6 (VO4 )6 together with that calculated on the basis of the result of least-squares fitting. The spectrum exhibits a slightly asymmetric doublet, which indicates that it consists of at least two doublets. Hyperfine parameters obtained by least-squares fitting were δ = 0.44(1) mm s−1 , EQ = 0.82(1) mm s−1 ,

Γ = 0.36(1) mm s−1 , and S = 63(2)% for one doublet and δ = 0.43(1) mm s−1 , EQ = 0.58(1) mm s−1 , Γ = 0.26(1) mm s−1 , and S = 37(2)% for the other doublet, where EQ is the quadrupole splitting, Γ is the full-width at half-maximum, and S is the area of a profile. Thus, Mössbauer spectroscopy cannot give any additional information about Fe distribution in Co3.6 Fe3.6 (VO4 )6 because the spectrum can unambiguously be decomposed only on the basis of structural data. Fe2 O3 was not detected by Mössbauer spectroscopy in any significant amount. The Mössbauer spectrum

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Table 6 Bond distances (Å) in Co3.6 Fe3.6 (VO4 )6 Bonds

SR-1

SR-2

N

2.049(3) 2.090(2) 2.167(2)

2.068(5) 2.085(6) 2.177(5)

2.061(6) 2.075(6) 2.177(7)

M2–O2i –O3i –O4v –O4vi –O5vii –O5viii

1.964(2) 2.009(2) 2.039(2) 2.128(2) 2.011(2) 2.061(2)

1.965(5) 2.006(4) 2.071(5) 2.125(4) 2.009(5) 2.041(5)

1.980(4) 2.024(3) 2.025(3) 2.130(4) 2.014(3) 2.056(2)

M3–O1ix, x (×2) –O1vi, xi (×2) –O6ix –O6xi

1.999(2) 2.017(2) 2.063(4) 2.094(3)

2.001(5) 2.009(6) 2.051(8) 2.091(7)

2.006(4) 2.037(4) 2.102(6) 2.095(5)

V1–O3xii –O4vii, xiii (×2) –O6ix

1.815(3) 1.717(2) 1.700(3)

1.816(7) 1.690(5) 1.713(7)

1.802(4) 1.726(3) 1.673(4)

V2–O1i –O2i –O5i –O7xiv

1.713(2) 1.776(3) 1.754(2) 1.691(2)

1.716(4) 1.766(6) 1.756(4) 1.685(5)

1.699(3) 1.766(3) 1.756(3) 1.687(3)

M1–O2i, ii (×2) –O7i, ii (×2) –O7iii, iv (×2)

Symmetry codes: ii x, 1/2 − y, z; iii 1/2 + x, 1/2 − y, 3/2 − z; iv 1/2 + x, y, 3/2 − z; v x, y, 1 + z; vi 1 − x, 1 − y, 1 − z; vii −1 + x, y, z; viii 1 − x, 1 − y, 2 − z; ix 1/2 − x, 1 − y, −1/2 + z; x 1/2 − i x, y, z;

x, −1/2 + y, −1/2 + z; xi 1 − x, −1/2 + y, 1 − z; xii x, y, −1 + z; xiii −1 + x, 1/2 − y, z; xiv 1 + x, y, z.

of Co3.6 Fe3.6 (VO4 )6 was similar to that of Cu4 Fe3.33(VO4 )6 [5]. This finding supports the idea that these two compounds have similar Fe distribution among the M1–M3 sites. Fig. 4 illustrates the structure of Co3.6 Fe3.6 (VO4 )6 projected along the [1 0 0] direction. Its structure comprises three types of coordination polyhedra forming chains along the [1 0 0] direction. Face-sharing M3O6 octahedra (Figs. 4 and 5) are not linked with the other types of the polyhedra M1O6 and M2O6 . M2O6 octahedra form zig-zag chains extending parallel with the [1 0 0] direction, sharing O3–O3 and O4–O4 edges. The chains composed of M2O6 octahedra are linked with one another by sharing O2 atoms, building up sheets perpendicular to the c axis. As Fig. 5 shows, edgesharing trigonal prisms, M1O6 , form zig-zag single chains along the [1 0 0] direction. Our structure refinements of Co3.6 Fe3.6 (VO4 )6 show that the M1 and M3 sites are about 6.0(2)% and 34.0(2)% deficient, respectively. Vacancies in its crystal structure are mainly localized at the M3 site. This fact may be ascribable to the small M3–M3 interatomic distance of 2.48 Å (= a/2). In the structure of Co3.6 Fe3.6 (VO4 )6 , the thermal vibration of cations at the M3 site was found to be highly anisotropic with its thermal ellipsoid elongated along the a axis, as can be appreciated from Fig. 5. This apparent anisotropy in thermal motion probably reflects the static displacement

Fig. 2. Rietveld refinement patterns for the (a) TOF neutron, (b) synchrotron X-ray (SR-1), and (c) synchrotron X-ray (SR-2) powder diffraction data of Co3.6 Fe3.6 (VO4 )6 . Bragg reflections for the lyonsite-type phase (upper bars) and Fe2 O3 (lower bars) are indicated by tick marks.

of M3 atoms towards vacancies introduced to reduce the electrostatic repulsion between cations. Despite the short M3–M3 distance, our structure refinements revealed that the M3 site is preferentially occupied not by Co2+ ions but by Fe3+ ions. Such cation distribution can be qualitatively explained in terms of Pauling’s second rule (electrostatic valence rule) [19]. This rule is simply represented as  vi  si = − , V =− Ni i

i

where V is the valence of an anion, si is the electrostatic bond strength of the ith cation, vi and Ni are, respectively, the valence and the coordination number, and i is extended to all the cations coordinated by the anion in question. Table 7 lists V values for oxide ions in Co3.6 Fe3.6 (VO4 )6

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Table 7 Oxidation states calculated for oxygen atoms with the crystal data of Co4 Fe3.33 (VO4 )6 [6] and Co3.6 Fe3.6 (VO4 )6 (this work) Oxygen atom O1 O2 O3 O4 O5 O6 O7

Neighboring cations V2, M3, and M3 V2, M1, and M2 V1, M2, and M2 V1, M2, and M2 V2, M2, and M2 V1, M3, and M3 V2, M1, and M1

Co4 Fe3.33 (VO4 )6 Co3.6 Fe3.6 (VO4 )6 −1.69 −2.06 −2.19 −2.19 −2.19 −1.69 −1.92

−1.89 −2.01 −2.10 −2.10 −2.10 −1.89 −1.91

Note. Occupancies in Co4 Fe3.33 (VO4 )6 [6]: 1 (Co2+ ) for M1, 0.17 (Co2+ ) and 0.83 (Fe3+ ) for M2, and 0.662 (Co2+ ) for M3. Occupancies in Co3.6 Fe3.6 (VO4 )6 : 0.844 (Co2+ ) and 0.096 (Fe3+ ) for M1, 0.445 (Co2+ ) and 0.555 (Fe3+ ) for M2, and 0.066 (Co2+ ) and 0.594 (Fe3+ ) for M3.

Fig. 3. Mössbauer spectrum of Co3.6 Fe3.6 (VO4 )6 at room temperature.

Fig. 4. Crystal structure of Co3.6 Fe3.6 (VO4 )6 viewed along the [1 0 0] direction.

Fig. 5. Linkage of three kinds of the polyhedra in Co3.6 Fe3.6 (VO4 )6 . Thermal ellipsoids for the M1, M2, and M3 atoms are displayed in translucent polyhedra.

(present study) and Co4 Fe3.33 (VO4 )6 [6]. For the M1, M2, and M3 sites, we used average vi ’s calculated from the occupancies of Co2+ and Fe3+ ions. The oxidation state of V was regarded as +5. The estimated oxidation states are much nearer to −2 for cation distribution determined in this work than for that reported by Wang et al. [6] for Co4 Fe3.33(VO4 )6 . Without any experimental evidence, Wang et al. [6] assumed that the M1 and M3 sites are occupied only by Co2+ ions while the M2 is occupied by Fe3+ (g = 0.83) and Co2+ (g = 0.17) ions. The resulting V (O1) and V (O6) values in Co4 Fe3.33(VO4 )6 deviated greatly from −2: −1.69. Because each of O1 and O6 atoms is surrounded by two M3 and one V sites, V (O1) and V (O6) depend only on the average valence of M3. V (O1) and V (O6) approach −2 on introduction of Fe3+ ions into the M3 site as in our metaldistribution model. With the metal-distribution model of Wang et al. [6], the V values for O3, O4, and O5 in Co4 Fe3.33 (VO4)6 also deviated considerably from −2: −2.19, in comparison with our metal-distribution model. Each of O3, O4, and O5 atoms has the three neighboring sites: two M2 and one V site. Decreasing the occupancy of Fe at the M2 site leads to increases in the V values of O3, O4, and O5. The mean valence of M1 obtained by us is nearly the same as that evaluated from the crystal data reported Wang et al. [6] because the incorporation of Fe3+ ions is roughly compensated with that of vacancies. Two M1 and one V sites surround each O7 atom. Therefore, the V (O7) values obtained on the basis of the two metal-distribution models are essentially the same. Thus, not only occupancies of Co and Fe obtained by neutron diffraction but the V values estimated according to Pauling’s second rule deny the validity of the metaldistribution model put forward by Wang et al. [6]. From the present results, we can conclude that the distribution of Co, Fe, and the vacancies is ruled by the local electrostatic balance including the repulsion between M3 cations.

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Acknowledgements We thank the staff of beam line BL15XU at SPring-8 for technical assistance and Dr. K.V. Pokholok of Moscow State University for the measurement of the Mössbauer spectrum.

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