inorganic compounds
On the symmetry of wulfenite (Pb[MoO_{4}]) from Mežica (Slovenia)
^{a}Department of Mineralogy, Eötvös Loránd University, Pázmány P. stny. 1/c, 1117 Budapest, Hungary, ^{b}Institute of Structural Chemistry, Chemical Research Center, Hungarian Academy of Sciences, Pusztaszeri út 59–67, 1025 Budapest, Hungary, and ^{c}Department for Nanostructured Materials, Jožef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia
^{*}Correspondence email: coraildiko@gmail.com
Wulfenite [lead(II) molybdate(VI)] is known as a scheelite structure in the I4_{1}/a The structure of the unusual `hemimorphic' wulfenite crystals from the Mežica mine was refined in the noncentrosymmetric I using a Pb/Mo exchange disorder model with the approximate composition Pb_{0.94}Mo_{0.06}[MoO_{4}]. Pb atoms in the 2b positions are substituted by Mo at about 12%. The crystal is shown to be twinned by inversion. Hemimorphism may result from the shortrange chemical ordering of the metal atoms at the 2b positions.
Comment
The mineral wulfenite (Pb[MoO_{4}]) is a member of the scheelite group of minerals with the general formula ABO_{4}, where the most abundant cations in the A and B positions are Ca, Sr, Ba and Pb, and Mo and W, respectively. Structure determinations for scheelite using singlecrystal Xray and neutron diffraction techniques indicated the I4_{1}/a (Zalkin & Templeton, 1964; Kay et al., 1964). Gürmen et al. (1971) studied the structure of scheelitetype minerals, such as SrMoO_{4}, SrWO_{4}, CaMoO_{4} and BaWO_{4}, using neutron diffraction and compared their Oatom positions. Arakcheeva & Chapuis (2008) gave a comprehensive study of scheelitelike structures with both commensurate and incommensurate modulations in the site occupations and with substitutions along the 〈uv0〉 directions.
The first isotropic (Leciejewicz, 1965; neutron diffraction study) and anisotropic (Lugli et al., 1999; Xray diffraction data) structure refinements of wulfenite from various localities resulted in the same symmetry. Recently, Hibbs et al. (2000) studied `hemihedral' (with polar symmetry along the c axis) tungstenian wulfenite crystals (Pb[Mo_{0.64}W_{0.36}O_{4}]) from Chillagoe (Australia) and found different W–Mo distributions over the 2a and 2c tetrahedral positions, responsible for the reduced I symmetry. Hemihedrism was interpreted as a result of ordered substitution of Mo by W. Their conclusion may be subject to debate, since the difference in the R values resulting from isotropic structure in the I4_{1}/a (R = 0.040) and from anisotropic in the I (R = 0.038) is not very significant.
Hurlbut (1955) first described two types of unusual `hemimorphic' wulfenite crystals from the Mežica mine (Slovenia) showing two habits: (i) pyramidal crystals indicating polar character on the [001] axis; and (ii) tabular crystals twinned on {00}. Based on their morphology and on etch and piezoelectric tests, he suggested that wulfenite from the Mežica mine crystallizes with tetragonal–pyramidal (4) symmetry. (TEM) and highresolution TEM (HRTEM) microdiffraction studies of these hemimorphic wulfenites from the Doroteja locality in the Mežica mine imply I4 (acentric tetragonal–pyramidal) symmetry (Zavašnik et al., 2010). As a result of this lower symmetry, Rečnik (2010) explained a new law of basal inversion the socalled Doroteja Law, macroscopically observable in wulfenite crystals from this locality. These hemimorphic wulfenite crystals are the subject of this work.
Most of the previous structural studies indicated the I4_{1}/a for wulfenite. In contrast, many intense reflections in our data set violate the extinction rules of this symmetry, e.g. for 00l the l = 2n (with l values up to ±22) reflections, and several hk0 reflections (h, k ≠ 2n), are evident. Experimentally, only the Icentring is proven (h + k + l = 2n). The space groups I4, I4/m, I, Imm2, I4/mmm and I2/m were checked in structure refinements, as well as I4_{1}/a. Except for I, the best R values resulting from the refinements in the above space groups converged to only about R = 0.07–0.08.
In the I racemic was indicated as early as the isotropic stage. The volume ratio of the twinned pair refined to 0.50 (6). The Pb and Mo cations were both allocated to two Wyckoff sites (Table 1). The Pb sites at the 2b positions proved to be substituted by ∼12% Mo, which corresponds to the composition Pb_{0.94}Mo_{0.06}[MoO_{4}]. The final anisotropic converged to acceptably low R values for 30 parameters and no restraints. The resulting Pb:Mo ratio is within the range of the quantified energydispersive (EDS) data, the considered uncertainties and the different sample volumes. Final atomic parameters are listed in Table 1.
Besides the explanation of Pb/Mo substitution, the difference between the occupancy of the 2b and 2d Pb positions (and the potentially minor difference between the 2a and 2c Mo positions) could also be regarded as vacancies, which would also be in line with the Pb > Mo content observed from the EDS analyses. However, our Xray model based on Pb/Mo substitution at the 2b site, resulted in consistently lower R, wR^{2} and S values (by about 0.005–0.01%) and also in lower residual densities at the metal sites.
Relevant bond distances for both I4_{1}/a Monte Cengio wulfenite (Lugli et al., 1999) and I Mežica wulfenite are listed for comparison in Table 2. Although the degree of freedom in the I is higher than that in I4_{1}/a, the corresponding atomic distances and bond angles in the MoO_{4} and PbO_{8} groups in both the Mežica wulfenite and wulfenites with I4_{1}/a symmetry are identical within the known s.u. criteria. The hemimorphism of the Mežica wulfenite (cf. Fig. 1) may be interpreted as a result of ordering.
Experimental
A small singlecrystal chip was carefully selected as a good scattering sample for experiments at T = 294 K. EDS analyses were measured on 100–200 nm sized wulfenite crystals using a Technai G^{2} XTwin 200 kV analytical TEM. Besides Pb and Mo, the O content was also measured. The measured Pb:Mo ratios were close to 1 [atoms per formula unit (apfu) for Pb = 0.98 (4)]. These values are consistent with the ∼12% substitution in the 2b Pb site. A slight correlation was observed between the resolution of the data and the refined substitution at the 2b Pb site (at 0.6 Å resolution the substitution at the 2b site is ∼4%, while at 0.83 Å resolution it is ∼12%). Such virtual resolution dependence of the composition might be easily interpreted in terms of the clearly deficient scattering model at a higher than usual (0.6 Å) resolution. Here, the dominant scattering of the core electrons and the use of spherical scattering factors yield an overweighted spherical scattering model. The disorderdependent smearing of the electron densities, as well as the deformation density due to valence and higherorbital electron densities, thus logically provide somewhat lower populations than at a lower (0.83 Å) resolution.
Finally, we note that this model describes a twinned and disordered crystal using a discrete substitution site. This disorder model itself is only an approximation, as other Wyckoff sites might also contain minute contamination of, for example, chalcogenide elements.
Crystal data

‡Occupancy = 0.119 (8). 
Racemic b site.
was indicated during the isotropic and the volume ratio of the twin pairs was refined to 0.50 (6). All atoms were treated anisotropically. An extinction parameter was also refined, and an occupancy constraint was applied for the 2Data collection: CrystalClear (Rigaku, 2008); cell CrystalClear; data reduction: CrystalClear; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: PLATON (Spek, 2009); software used to prepare material for publication: SHELXL97.
Supporting information
https://doi.org//10.1107/S0108270111015769/ku3043sup1.cif
contains datablocks I, global. DOI:Structure factors: contains datablock I. DOI: https://doi.org//10.1107/S0108270111015769/ku3043Isup2.hkl
Data collection: CrystalClear (Rigaku, 2008); cell
CrystalClear (Rigaku, 2008); data reduction: CrystalClear (Rigaku, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: PLATON (Spek, 2009); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).Pb_{0.94}Mo_{0.06}[MoO_{4}]  D_{x} = 6.671 Mg m^{−}^{3} 
M_{r} = 360.42  Mo Kα radiation, λ = 0.71070 Å 
Tetragonal, I4  Cell parameters from 2580 reflections 
Hall symbol: I 4  θ = 3.4–45.3° 
a = 5.442 (1) Å  µ = 47.59 mm^{−}^{1} 
c = 12.1177 (14) Å  T = 294 K 
V = 358.87 (5) Å^{3}  Chip, yellow 
Z = 4  0.10 × 0.10 × 0.05 mm 
F(000) = 614 
Rigaku RAXIS RAPID diffractometer  335 independent reflections 
Radiation source: normalfocus sealed tube  333 reflections with I > 2σ(I) 
Graphite monochromator  R_{int} = 0.120 
Detector resolution: 10.0000 pixels mm^{1}  θ_{max} = 25.3°, θ_{min} = 3.4° 
dtprofit.ref scans  h = −6→6 
Absorption correction: numerical (NUMABS; Higashi, 2002)  k = −6→6 
T_{min} = 0.064, T_{max} = 0.336  l = −14→14 
6322 measured reflections 
Refinement on F^{2}  Secondary atom site location: difference Fourier map 
Leastsquares matrix: full  w = 1/[σ^{2}(F_{o}^{2}) + (0.0244P)^{2} + 3.452P] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
R[F^{2} > 2σ(F^{2})] = 0.025  (Δ/σ)_{max} = 0.049 
wR(F^{2}) = 0.061  Δρ_{max} = 0.71 e Å^{−}^{3} 
S = 1.16  Δρ_{min} = −0.86 e Å^{−}^{3} 
335 reflections  Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
30 parameters  Extinction coefficient: 0.0140 (8) 
0 restraints  Absolute structure: Flack (1983), ???? Friedel pairs 
Primary atom site location: structureinvariant direct methods  Absolute structure parameter: 0.50 (6) 
x  y  z  U_{iso}*/U_{eq}  Occ. (<1)  
Pb1  0.5000  0.0000  0.2500  0.0213 (13)  
Mo2  0.0000  0.0000  0.0000  0.022 (4)  
Pb3  0.5000  0.5000  0.0000  0.025 (2)  0.881 (8) 
Mo3  0.5000  0.5000  0.0000  0.025 (2)  0.119 (8) 
Mo1  0.0000  0.5000  0.2500  0.018 (3)  
O1  0.2344 (13)  −0.1372 (14)  0.0806 (6)  0.0302 (17)  
O2  0.2338 (14)  0.3648 (14)  0.1697 (6)  0.0307 (17) 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
Pb1  0.021 (2)  0.021 (2)  0.022 (2)  0.000  0.000  0.000 
Mo2  0.020 (6)  0.020 (6)  0.025 (7)  0.000  0.000  0.000 
Pb3  0.023 (3)  0.023 (3)  0.027 (4)  0.000  0.000  0.000 
Mo3  0.023 (3)  0.023 (3)  0.027 (4)  0.000  0.000  0.000 
Mo1  0.016 (5)  0.016 (5)  0.021 (6)  0.000  0.000  0.000 
O1  0.033 (5)  0.030 (4)  0.028 (4)  0.002 (3)  −0.005 (3)  0.004 (3) 
O2  0.030 (5)  0.028 (4)  0.034 (4)  0.001 (3)  −0.003 (3)  0.011 (4) 
Pb1—O1  2.619 (7)  Pb3—O2^{viii}  2.620 (7) 
Pb1—O1^{i}  2.619 (7)  Pb3—O2^{ix}  2.620 (7) 
Pb1—O1^{ii}  2.619 (7)  Pb3—O2  2.620 (7) 
Pb1—O1^{iii}  2.619 (7)  Pb3—O1^{v}  2.635 (8) 
Pb1—O2^{i}  2.643 (8)  Pb3—O1^{x}  2.635 (8) 
Pb1—O2^{ii}  2.643 (8)  Pb3—O1^{xi}  2.635 (8) 
Pb1—O2^{iii}  2.643 (8)  Pb3—O1^{iii}  2.635 (8) 
Pb1—O2  2.643 (8)  Mo1—O2^{xii}  1.763 (8) 
Mo2—O1^{iv}  1.772 (7)  Mo1—O2^{xiii}  1.763 (8) 
Mo2—O1  1.772 (7)  Mo1—O2^{xiv}  1.763 (8) 
Mo2—O1^{v}  1.772 (7)  Mo1—O2  1.763 (8) 
Mo2—O1^{vi}  1.772 (7)  O1—Pb3^{xv}  2.635 (8) 
Pb3—O2^{vii}  2.620 (7)  
O1—Pb1—O1^{i}  127.9 (2)  O2^{vii}—Pb3—O2  76.6 (3) 
O1—Pb1—O1^{ii}  127.9 (2)  O2^{viii}—Pb3—O2  128.0 (2) 
O1^{i}—Pb1—O1^{ii}  76.8 (3)  O2^{ix}—Pb3—O2  128.0 (2) 
O1—Pb1—O1^{iii}  76.8 (3)  O2^{vii}—Pb3—O1^{v}  149.2 (2) 
O1^{i}—Pb1—O1^{iii}  127.9 (2)  O2^{viii}—Pb3—O1^{v}  67.4 (3) 
O1^{ii}—Pb1—O1^{iii}  127.9 (2)  O2^{ix}—Pb3—O1^{v}  78.6 (2) 
O1—Pb1—O2^{i}  149.2 (2)  O2—Pb3—O1^{v}  73.9 (3) 
O1^{i}—Pb1—O2^{i}  67.9 (3)  O2^{vii}—Pb3—O1^{x}  73.9 (3) 
O1^{ii}—Pb1—O2^{i}  78.4 (2)  O2^{viii}—Pb3—O1^{x}  78.6 (2) 
O1^{iii}—Pb1—O2^{i}  73.6 (3)  O2^{ix}—Pb3—O1^{x}  67.4 (3) 
O1—Pb1—O2^{ii}  73.6 (3)  O2—Pb3—O1^{x}  149.2 (2) 
O1^{i}—Pb1—O2^{ii}  78.4 (2)  O1^{v}—Pb3—O1^{x}  136.5 (3) 
O1^{ii}—Pb1—O2^{ii}  67.9 (3)  O2^{vii}—Pb3—O1^{xi}  78.6 (2) 
O1^{iii}—Pb1—O2^{ii}  149.2 (2)  O2^{viii}—Pb3—O1^{xi}  149.2 (2) 
O2^{i}—Pb1—O2^{ii}  136.8 (3)  O2^{ix}—Pb3—O1^{xi}  73.9 (3) 
O1—Pb1—O2^{iii}  78.4 (2)  O2—Pb3—O1^{xi}  67.4 (3) 
O1^{i}—Pb1—O2^{iii}  149.2 (2)  O1^{v}—Pb3—O1^{xi}  97.90 (11) 
O1^{ii}—Pb1—O2^{iii}  73.6 (3)  O1^{x}—Pb3—O1^{xi}  97.90 (11) 
O1^{iii}—Pb1—O2^{iii}  67.9 (3)  O2^{vii}—Pb3—O1^{iii}  67.4 (3) 
O2^{i}—Pb1—O2^{iii}  97.79 (12)  O2^{viii}—Pb3—O1^{iii}  73.9 (3) 
O2^{ii}—Pb1—O2^{iii}  97.79 (12)  O2^{ix}—Pb3—O1^{iii}  149.2 (2) 
O1—Pb1—O2  67.9 (3)  O2—Pb3—O1^{iii}  78.6 (2) 
O1^{i}—Pb1—O2  73.6 (3)  O1^{v}—Pb3—O1^{iii}  97.90 (11) 
O1^{ii}—Pb1—O2  149.2 (2)  O1^{x}—Pb3—O1^{iii}  97.90 (11) 
O1^{iii}—Pb1—O2  78.4 (2)  O1^{xi}—Pb3—O1^{iii}  136.5 (3) 
O2^{i}—Pb1—O2  97.79 (12)  O2^{xii}—Mo1—O2^{xiii}  107.8 (2) 
O2^{ii}—Pb1—O2  97.79 (12)  O2^{xii}—Mo1—O2^{xiv}  113.0 (5) 
O2^{iii}—Pb1—O2  136.8 (3)  O2^{xiii}—Mo1—O2^{xiv}  107.8 (2) 
O1^{iv}—Mo2—O1  107.7 (2)  O2^{xii}—Mo1—O2  107.8 (2) 
O1^{iv}—Mo2—O1^{v}  113.1 (5)  O2^{xiii}—Mo1—O2  113.0 (5) 
O1—Mo2—O1^{v}  107.7 (2)  O2^{xiv}—Mo1—O2  107.8 (2) 
O1^{iv}—Mo2—O1^{vi}  107.7 (2)  Mo2—O1—Pb1  135.2 (4) 
O1—Mo2—O1^{vi}  113.1 (5)  Mo2—O1—Pb3^{xv}  120.4 (4) 
O1^{v}—Mo2—O1^{vi}  107.7 (2)  Pb1—O1—Pb3^{xv}  101.6 (2) 
O2^{vii}—Pb3—O2^{viii}  128.0 (2)  Mo1—O2—Pb3  135.6 (4) 
O2^{vii}—Pb3—O2^{ix}  128.0 (2)  Mo1—O2—Pb1  120.4 (3) 
O2^{viii}—Pb3—O2^{ix}  76.6 (3)  Pb3—O2—Pb1  101.4 (3) 
Symmetry codes: (i) y+1/2, −x+1/2, −z+1/2; (ii) −y+1/2, x−1/2, −z+1/2; (iii) −x+1, −y, z; (iv) y, −x, −z; (v) −y, x, −z; (vi) −x, −y, z; (vii) −x+1, −y+1, z; (viii) −y+1, x, −z; (ix) y, −x+1, −z; (x) y+1, −x+1, −z; (xi) x, y+1, z; (xii) −y+1/2, x+1/2, −z+1/2; (xiii) −x, −y+1, z; (xiv) y−1/2, −x+1/2, −z+1/2; (xv) x, y−1, z. 
Wyckoff position  x  y  z  U_{iso}*/U_{eq}  Occ. (<1)  
Pb1  2d  0.5000  0.0000  0.2500  0.0213 (13)  
Mo1  2c  0.0000  0.5000  0.2500  0.018 (3)  
Mo2  2a  0.0000  0.0000  0.0000  0.022 (4)  
Pb3  2b  0.5000  0.5000  0.0000  0.025 (2)  0.881 (8) 
Mo3  2b  0.5000  0.5000  0.0000  0.025 (2)  0.119 (8) 
O1  8g  0.2344 (13)  0.1372 (14)  0.0806 (6)  0.0302 (17)  
O2  8g  0.2338 (14)  0.3648 (14)  0.1697 (6)  0.0307 (17) 
This work  Lugli <it> et al.</it> (1999)  
Pb1—O1  2.619 (7)  2.611 (3) 
Pb1—O2  2.643 (8)  2.636 (3) 
Mo2—O1  1.772 (7)  1.769 (3) 
Pb3—O2  2.620 (7)  2.611 (3) 
Pb3—O1  2.635 (8)  2.636 (3) 
Mo1—O2  1.763 (8)  1.769 (3) 
Symmetry codes: (i) y + 1/2, x + 1/2, z + 1/2; (ii) y + 1/2, x  1/2, z + 1/2; (iii) x + 1, y, z; (iv) y, x, z; (v) y, x, z; (vi) x, y, z; (vii) x + 1, y + 1, z; (viii) y + 1, x, z; (ix) y, x + 1, z; (x) y + 1, x + 1, z; (xi) x, y + 1, z; (xii) y + 1/2, x + 1/2, z + 1/2; (xiii) x, y + 1, z; (xiv) y  1/2, x + 1/2, z + 1/2; (xv) x, y  1, z. 
Acknowledgements
The authors express their sincere thanks to Alajos Kálmán and László Párkányi for their helpful comments and suggestions, and to Tamás Holczbauer for his help. We also thank the HAS CRC for carrying out the Xray data collection. Financial support, administered through OTKA grant Nos. 68562 and K75869 and the ARRS L12232 project, is gratefully acknowledged.
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