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Journal logoSTRUCTURAL SCIENCE
CRYSTAL ENGINEERING
MATERIALS
ISSN: 2052-5206
Volume 70| Part 2| April 2014| Pages 243-258

Superspace description of wagnerite-group minerals (Mg,Fe,Mn)2(PO4)(F,OH)

aMineralogical Crystallography, Institute of Geological Sciences, University of Bern, Freie­strasse 3, 3012 Bern, Switzerland, bLaboratoire de Géologie, Ecole Normale Supérieure – CNRS, 24 Rue Lhomond, 75231 Paris, France, cSchool of Earth and Climate Sciences, University of Maine, Orono, Maine 04469-5790, United States, dAix-Marseille Université, CNRS, CINaM, UMR 7325, 13288 Marseille, France, and eInstitute of Physics of the Academy of Sciences of the Czech Republic, Na Slovance 2, 18221 Prague, Czech Republic
*Correspondence e-mail: biljana.lazic@krist.unibe.ch

(Received 12 June 2013; accepted 14 November 2013; online 4 March 2014)

Reinvestigation of more than 40 samples of minerals belonging to the wagnerite group (Mg, Fe, Mn)2(PO4)(F,OH) from diverse geological environments worldwide, using single-crystal X-ray diffraction analysis, showed that most crystals have incommensurate structures and, as such, are not adequately described with known polytype models (2b), (3b), (5b), (7b) and (9b). Therefore, we present here a unified superspace model for the structural description of periodically and aperiodically modulated wagnerite with the (3+1)-dimensional superspace group C2/c(0β0)s0 based on the average triplite structure with cell parameters a ≃ 12.8, b ≃ 6.4, c ≃ 9.6 Å, β ≃ 117° and the modulation vectors q = βb*. The superspace approach provides a way of simple modelling of the positional and occupational modulation of Mg/Fe and F/OH in wagnerite. This allows direct comparison of crystal properties.

1. Introduction

Wagnerite, first described by Fuchs (1821[Fuchs, J. N. (1821). J. Chem. Phys. Nürnberg, 33, 269-270.]), is a relatively rare accessory mineral in metamorphic rocks, but occurrences in granite pegmatites and the Zechstein salt deposits have also been reported (Anthony et al., 2000[Anthony, J. W., Bideaux, R. A., Bladh, K. W. & Nichols, M. C. (2000). Editors. Handbook of Mineralogy, Vol. IV, Arsenates, Phosphates, Vanadates. Mineralogical Society of America, Chantilly, VA, USA.]). Depending on chemical composition, crystals can be translucent to nearly opaque, with a wide variety of colours: colourless, white, yellowish, orange, flesh red, pink and green (Palache et al., 1951[Palache, C., Berman, H. & Frondel, C. (1951). Dana's System of Mineralogy. Wiley: New York.], and references therein). Ideally Mg2(PO4)F, wagnerite, is better described with the general formula Mg2 − x(Fe, Mn, Ca, Ti…)x(PO4)(F,OH,O) because of an extensive solid solution with related minerals containing Fe2+, Mn2+ and OH (Fig. 1[link]). Pitra et al. (2008[Pitra, P., Boulvais, P., Antonoff, V. & Diot, H. (2008). Am. Mineral. 93, 315-326.]) reported distinct chemical zoning in wagnerite grains: a decrease of Fe [from 0.16 to 0.08 per formula unit (p.f.u.)] and an associated increase of F (0.46–1 p.f.u.), from the centre toward the rims of the grains. When Fe3+ substitutes Mg2+, charge balance requires more negative charge at the anion site, and thus O substitutes for F and OH, as in stanekite (Fe3+, Mn2+, Fe2+, Mg)2(PO4)O (Keller et al., 2006[Keller, P., Lissner, F. & Schleid, T. (2006). Eur. J. Mineral. 18, 113-118.]).

[Figure 1]
Figure 1
Compositional diagrams showing the two groups of phosphate minerals with the formula M2(PO4)X, where M = Mg2+, Fe2+, Mn2+ and X = F, OH. Red lettering indicates structure type.

The structure of wagnerite was first solved by Coda et al. (1967[Coda, A., Giuseppetti, G. & Tadini, C. (1967). Atti Accad. Naz. Lincei, 43, 212-224.]) from single-crystal X-ray data [P21/c, a = 9.44 (7), b = 12.679 (8), c = 11.957 (9) Å, β = 108.18 (9)°]. Another four wagnerite structure types, with different b periodicity (b ≃ 19, b ≃ 32, b ≃ 45 and b ≃ 57 Å) have been reported (Coda et al., 1967[Coda, A., Giuseppetti, G. & Tadini, C. (1967). Atti Accad. Naz. Lincei, 43, 212-224.]; Ren et al., 2003[Ren, L., Grew, E. S., Xiong, M. & Ma, Z. (2003). Can. Mineral. 41, 393-411.]; Chopin, Armbruster & Leyx, 2003[Chopin, C., Armbruster, T. & Leyx, C. (2003). Geophysical Research Abstracts, Vol. 5, 08323. European Geophysical Society.]; Armbruster et al., 2008[Armbruster, T., Chopin, C., Grew, E. S. & Baronnet, A. (2008). Geochim. Cosmochim. Acta, Suppl. 72, 32.]). The close structural relationship between various stacking variants of wagnerite and e.g. triplite (Mn,Fe)2(PO4)F (Waldrop, 1969[Waldrop, L. (1969). Z. Kristallogr. 130, 1-14.]) with b = 6.45 Å led to the proposal of naming wagnerite as a polytypic series based on the triplite cell. Thus, wagnerite with 2b ≃ 13 Å was named wagnerite-Ma2b, and e.g. with 9b ≃ 57 Å wagnerite-Ma9bc (Burke & Ferraris, 2004[Burke, E. A. J. & Ferraris, G. (2004). Am. Mineral. 89, 1566-1573.]).

Our structural reinvestigation of different wagnerite samples showed that the assumed b periodicity often displays small but significant deviations from commensurate values. Moreover, refinement of the few commensurately modulated wagnerite structures, especially with a 7b (b = 45 Å) or 9b (b = 57 Å) supercell, with occupational and positional modulation of Mg/Fe/Mn and F/OH, is much more efficient using a superspace approach. Thus, the aim of this paper is to present a unique superspace model for the structural description of both commensurately and incommensurately modulated wagnerites.

1.1. Origin of modulation in wagnerite

The partial replacement of Mg2+ (0.72 Å) by Fe2+ (0.78 Å), Mn2+ (0.83 Å), Ca2+ (1.00 Å), Ti4+ (0.61 Å) or Fe3+ (0.65 Å) (Shannon & Prewitt, 1969[Shannon, R. D. & Prewitt, C. T. (1969). Acta Cryst. B25, 925-946.]) in the structure of wagnerite, as well as partial F ↔ OH substitution, causes significant variations of bond lengths. As a consequence, individual coordination polyhedra around cation sites are locally modified regarding coordination number and geometry and this may affect the geometry of the whole structure. The key to understanding the influence of chemical composition on structural periodicity in wagnerite is its structural relation to other minerals such as triplite (Mn, Fe)2(PO4)F (Waldrop, 1969[Waldrop, L. (1969). Z. Kristallogr. 130, 1-14.]) and triploidite (Mn, Fe)2(PO4)OH (Waldrop, 1968[Waldrop, L. (1968). Naturwissenschaften, 55, 296-297.]).

Based on chemical compositions and crystal morphologies, Brush & Dana (1878[Brush, G. & Dana, E. (1878). Am. J. Sci. 16, 33-46.]) suggested that the OH group in triploidite plays a corresponding role as fluorine in wagnerite and triplite. The single-crystal X-ray data obtained for wagnerite by Coda et al. (1967[Coda, A., Giuseppetti, G. & Tadini, C. (1967). Atti Accad. Naz. Lincei, 43, 212-224.]) and for triploidite by Waldrop (1968[Waldrop, L. (1968). Naturwissenschaften, 55, 296-297.]) have revealed the same features: reflections on procession photographs could be divided by intensity into two groups. If only strong reflections are indexed, then the resulting unit cell corresponds to that of triplite (a ≃ 12.05, b ≃ 6.45, c ≃ 9.9 Å, β = 105–107 °) with I2/c symmetry. Indexing of all reflections leads to a cell of lower symmetry (P21/c) with doubled b parameter (b ≃ 13 Å) compared with triplite.

Pending a formal classification, we suggest that structurally related minerals having the general formula M2(PO4)F and M2(PO4)OH could be placed into two groups within a triplite supergroup (Fig. 1[link]). Members of the OH-dominant group belong to the (2b) structure type, whereas in the F-dominant group only wagnerite has the (2b) structure type with triplite Mn2(PO4)F and zwieselite Fe2(PO4)F belonging to the (1b) structure type. These minerals form an extensive solid-solution series with each other. Table 1[link] summarizes the unit-cell dimensions of synthetic and natural end-members with different b periodicities. To be consistent with our model for wagnerite, unit-cell parameters are given in a different setting than originally reported. Transformation matrices are given in a footnote to Table 1[link]. The (1b) structure type with space group C2/c is observed in the synthetic end-members Mn2(PO4)F (Rea & Kostiner, 1972[Rea, J. R. & Kostiner, E. (1972). Acta Cryst. B28, 2525-2529.]) and Fe2(PO4)F (Yakubovich et al., 1978[Yakubovich, O., Simonov, M., Matvienko, E. & Belov, N. (1978). Dokl. Akad. Nauk SSSR, 238, 576-579.]) and F-dominant triplite and zwieselite samples (Armbruster et al., 2008[Armbruster, T., Chopin, C., Grew, E. S. & Baronnet, A. (2008). Geochim. Cosmochim. Acta, Suppl. 72, 32.]) such as Mn0.95Fe0.25Mg0.7PO4F (Waldrop, 1969[Waldrop, L. (1969). Z. Kristallogr. 130, 1-14.]) or Fe1.042 + Mn0.86(Fe3+, Ca, Mg, Ti4+, Zn)0.1PO4F0.85OH0.15 (Origlieri, 2005[Origlieri, M. (2005). PhD thesis, University of Arizona, USA.]).

Table 1
Synthetic and natural end-members, with unit-cell dimensions in unified setting

  Space group          
Compound Rep. Transf. a (Å) b (Å) c (Å) β (°) V3)
(1) Mg2(PO4)F P21/n P21/n 12.7631 (4) 12.6565 (4) 9.6348 (3) 117.5954 (11) 1379.32
(2) Fe2(PO4)F I112/a C2/c 13.0211 (39) 6.4890 (10) 9.8900 (30) 118.624 (20) 733.52
(3) Mn2(PO4)F C2/c C2/c 13.4100 (40) 6.5096 (5) 10.0940 (20) 119.990 (10) 763.17
(4) Mg2(PO4)OH P21/c P21/n 12.8445 (55) 12.8590 (30) 9.6560 (10) 116.986 (26) 1421.21
(5) Fe2(PO4)OH P21/a P21/n 12.9983 (17) 13.1970 (10) 9.7385 (9) 116.601 (8) 1493.69
(6) (Mn,Fe)2(PO4)OH P21/a P21/n 13.2232 13.2760 9.9430 117.347 1550.42
Matrices for transformation of reported cells: P21/a [[101/010/\bar 100]]P21/c [[101/010/ \bar 100]]P21/n; I112/aI12/a1 [010/001/100]C2/c [[101/010/ \bar 100]]. Source of samples: (1) this paper (wagnerite from Webing); (2) Yakubovich et al. (1978[Yakubovich, O., Simonov, M., Matvienko, E. & Belov, N. (1978). Dokl. Akad. Nauk SSSR, 238, 576-579.]); (3) Rea & Kostiner (1972[Rea, J. R. & Kostiner, E. (1972). Acta Cryst. B28, 2525-2529.]); (4) Raade & Rømming (1986[Raade, G. & Rømming, C. (1986). Z. Kristallogr. 117, 15-26.]); (5) Hatert (2007[Hatert, F. (2007). Acta Cryst. C63, i119-i121.]); (6) Waldrop (1968[Waldrop, L. (1968). Naturwissenschaften, 55, 296-297.]).
†Natural; synthetic samples have not been reported.

The (1b) structure has two symmetrically independent M-cation positions forming MO4F2 polyhedra and one PO4 tetrahedron (Fig. 2[link]). Fluorine occupies a compromise position and has distorted tetrahedral coordination by four M cations. In this context a `compromise position' means that F occupies a site enabling sixfold coordination of M1 and M2, but one M—F bond in each octahedron is strongly elongated.

[Figure 2]
Figure 2
The (1b) structure type observed in M2(PO4)X minerals (C2/c), where M = Fe2+, Mn2+ and X = F (Rea & Kostiner, 1972[Rea, J. R. & Kostiner, E. (1972). Acta Cryst. B28, 2525-2529.]; Yakubovich et al., 1978[Yakubovich, O., Simonov, M., Matvienko, E. & Belov, N. (1978). Dokl. Akad. Nauk SSSR, 238, 576-579.]). PO4 units are displayed as grey tetrahedra, five- or six-coordinated cations as red spheres and F/O(H) atoms as green spheres.

The structure of the (2b) type with the P21/n space group is represented by three end-members: Mg2(PO4)F (this paper), Mg2(PO4)OH (Raade & Rømming, 1986[Raade, G. & Rømming, C. (1986). Z. Kristallogr. 117, 15-26.]) and Fe2(PO4)OH (Hatert, 2007[Hatert, F. (2007). Acta Cryst. C63, i119-i121.]) and minerals with intermediate composition, such as wagnerite (Mg, Fe)2(PO4)F (Coda et al., 1967[Coda, A., Giuseppetti, G. & Tadini, C. (1967). Atti Accad. Naz. Lincei, 43, 212-224.]), hydroxylwagnerite (Mg, Fe)2(PO4)OH (Brunet et al., 1998[Brunet, F., Chopin, C. & Seifert, F. (1998). Contrib. Mineral. Petrol. 131, 54-70.]; Chopin et al., 2004[Chopin, C., Leyx, C., Armbruster, T. & Medenbach, O. (2004). Hydroxylwagnerite. Proposal IMA No. 2004-009, http://pubsites.uws.edu.au/ima-cnmnc/minerals2004.pdf .]), triploidite Mn1.5Fe0.5(PO4)OH (Waldrop, 1968[Waldrop, L. (1968). Naturwissenschaften, 55, 296-297.]) and Mg-rich wolfeite (Fe, Mg)2(PO4)OH (Kolitsch, 2003[Kolitsch, U. (2003). Acta Cryst. E59, i125-i128.]). The unit-cell parameters of Mn1.5Fe0.5(PO4)OH (Waldrop, 1968[Waldrop, L. (1968). Naturwissenschaften, 55, 296-297.]) are also listed in Table 1[link], because pure Mn2(PO4)OH has not been reported so far.

Due to doubling of the b axis and a decrease in multiplicity of the general positions from 8 in C2/c [(1b) type] to 4 in P21/n [(2b) type], the (2b) structure displays four times more symmetry-independent sites than (1b). Thus there are eight cation sites (M) and four F sites. Nevertheless, the (2b) structure type preserves the same arrangement of cations and O atoms as (1b), but differs in the arrangement of F atoms (Fig. 3[link]). In contrast to the (1b) structure, F atoms are moved out of the compromise position and appear in the ab plane as two distinct arc-like configurations labelled up (U) and down (D). This arc-like arrangement is only an optical illusion originating from the special projection. Actually F sites are not coplanar. As a consequence of the shift, F atoms in (2b) structures are in threefold coordination. Furthermore, half of the M sites are five-coordinated (MO4F) and the other half are six-coordinated (MO4F2). Interestingly, wagnerite and hydroxylwagnerite have the same symmetry (P21/n), whereas the Fe2+ and Mn2+ fluorine and hydroxyl end-members are distinct in symmetry (C2/c and P21/n, respectively). The influence of the F ↔ OH substitution on unit-cell dimensions can be recognized by comparing end-members Mg2(PO4)F (this paper) with Mg2(PO4)OH (Raade & Rømming, 1986[Raade, G. & Rømming, C. (1986). Z. Kristallogr. 117, 15-26.]). The four fluorine positions in Mg2(PO4)F are replaced by four OH groups, thus the geometry of M1 and M2 polyhedra is preserved. In addition to the three bonds to Mg [equivalent to Mg—F in Mg2(PO4)F], O acts as a hydrogen-bond donor. The position of hydrogen is fixed by a weak hydrogen bond to an O acceptor (within 2.1 Å). Two of four such O—H bonds (0.95 Å) are oriented opposite each other, approximately parallel to b (Fig. 3[link]), resulting in an increase of b from 12.755 Å in pure Mg2(PO4)F to 12.859 Å in pure Mg2(PO4)OH. Two other O—H bonds are oriented diagonally between a and c, causing only a slight increase of cell parameters.

[Figure 3]
Figure 3
The (2b) structure type, observed in M2(PO4)X minerals, where M = Mg2+ and X = OH, F or M = Fe2+, Mn2+ and X = OH. Two distinct arc-like configurations of F/O atoms are labelled up (U) and down (D). The example represents synthetic hydroxylwagnerite Mg2(PO4)OH (Raade & Rømming, 1986[Raade, G. & Rømming, C. (1986). Z. Kristallogr. 117, 15-26.]); hydrogen bonds (donor green, hydrogen black spheres) are shown as solid lines.

The influence of the size of M2+ cations, e.g. in Mg2(PO4)F (2b) versus Mn2(PO4)F (1b) and OH or F anions, e.g. in Fe2(PO4)F (1b) versus Fe2(PO4)OH (2b), on the structural periodicity or modulation is evident, especially for end-members. In the case of F end-members, large M2+ radii seem to stabilize the (1b) structure, also confirmed by the structure of Cd2(PO4)F (Rea & Kostiner, 1974[Rea, J. R. & Kostiner, E. (1974). Acta Cryst. B30, 2901-2903.]) with an octahedral Cd2+ radius of 0.95 Å (Shannon, 1976[Shannon, R. D. (1976). Acta Cryst. A32, 751-767.]), whereas cations with a small octahedral radius (Mg 0.72 Å, Zn 0.74 Å) stabilize the (2b) structure characteristic of wagnerite and synthetic Zn2(PO4)F (Taasti et al., 2002[Taasti, K. I., Christensen, A. N., Norby, P., Hanson, J. C., Lebech, B., Jakobsen, H. J. & Skibsted, J. (2002). J. Solid State Chem. 164, 42-50.]). An exception is represented by Cu2(PO4)F (Rea & Kostiner, 1976[Rea, J. R. & Kostiner, E. (1976). Acta Cryst. B32, 1944-1947.]). As a result of the Jahn–Teller effect (Jahn & Teller, 1937[Jahn, H. & Teller, E. (1937). Proc. R. Soc. London Ser. A, pp. 220-235.]) for Cu2+, Cu2PO4F (Rea & Kostiner, 1976[Rea, J. R. & Kostiner, E. (1976). Acta Cryst. B32, 1944-1947.]) has (1b) triplite-like structure, although the ionic radius of Cu2+ is 0.73 Å, similar to Mg with 0.72 Å. Cu2(PO4)OH, with a structure corresponding to the triplite supergroup, has not been reported so far.

Until 2008, among 38 investigated wagnerite samples and related minerals (e.g. triplite), six structural polytypes have been refined from single-crystal data and imaged by high-resolution transmission electron microscopy (HRTEM; Armbruster et al., 2008[Armbruster, T., Chopin, C., Grew, E. S. & Baronnet, A. (2008). Geochim. Cosmochim. Acta, Suppl. 72, 32.]). The (1b) structure type was confirmed only for triplite–zwieselite samples. The remaining five polytypes (2b), (3b), (5b), (7b) and (9b) were identified in compositionally complex wagnerite.

1.2. Wagnerite structure types

Five commensurately modulated wagnerite structures with (2b), (3b), (5b), (7b) and (9b) periodicities have been reported to date (Coda et al., 1967[Coda, A., Giuseppetti, G. & Tadini, C. (1967). Atti Accad. Naz. Lincei, 43, 212-224.]; Ren et al., 2003[Ren, L., Grew, E. S., Xiong, M. & Ma, Z. (2003). Can. Mineral. 41, 393-411.]; Chopin, Armbruster & Leyx, 2003[Chopin, C., Armbruster, T. & Leyx, C. (2003). Geophysical Research Abstracts, Vol. 5, 08323. European Geophysical Society.]; Armbruster et al., 2008[Armbruster, T., Chopin, C., Grew, E. S. & Baronnet, A. (2008). Geochim. Cosmochim. Acta, Suppl. 72, 32.]). The topological arrangement of cations and O atoms is the same in all of them. However, positional modulation of F (OH) is responsible for two distinct arc-like configurations, up (U) and down (D), in projections parallel to c, as emphasized for the (2b) model (Fig. 3[link]). Different ordering sequences of these up (U) and down (D) arrangements lead to varying periodicities along b and hence the various polytypes (2b) (UD), (5b) (UDUDU), (7b) (UDUDUDU) and (9b) (UDUDUDUDU) (Chopin, Armbruster & Leyx, 2003[Chopin, C., Armbruster, T. & Leyx, C. (2003). Geophysical Research Abstracts, Vol. 5, 08323. European Geophysical Society.]). On the proposal of Chopin, Armbruster, Baronnet & Grew (2003[Chopin, C., Armbruster, T., Baronnet, A. & Grew, E. S. (2003). Polytypism in wagnerite, triplite & zwieselite, & discreditation of magniotriplite. Proposal IMA 03-C, approved, unpublished.]), to prevent proliferation of new mineral names, the Commission on New Minerals, Nomenclature and Classification (CNMNC) of the International Mineralogical Association (IMA) has decided that wagnerite polytypes be designated by the suffixes Ma2bc, Ma5bc, Ma7bc and Ma9bc (Burke & Ferraris, 2004[Burke, E. A. J. & Ferraris, G. (2004). Am. Mineral. 89, 1566-1573.]).

Structures of wagnerite-(5b) with composition (Mg1.88Fe0.10Ti0.02)PO4(F0.61OH0.39) (Ren et al., 2003[Ren, L., Grew, E. S., Xiong, M. & Ma, Z. (2003). Can. Mineral. 41, 393-411.]) and wagnerite-(9b) (Mg1.97Fe0.03)PO4(F0.93OH0.07) (Chopin, Armbruster & Leyx, 2003[Chopin, C., Armbruster, T. & Leyx, C. (2003). Geophysical Research Abstracts, Vol. 5, 08323. European Geophysical Society.]) were refined to reasonable residual values R1(5b) = 0.04 and R1(9b) = 0.06 in the non-centrosymmetric space group Ia. This showed that wagnerite structures with (5b) or (9b) periodicity have reduced symmetry, because they lose the 21 axes present in the (2b) structure. Most surprisingly, replacement of 2% Mg by Fe in the structure of wagnerite-(9b) demonstrates that a small change in composition may induce a change of periodicity.

Our reinvestigation of wagnerites from over 40 localities confirms the dependence of periodicity on minor compositional variations, as will be presented below. In addition, it could be shown that the crystal structure of wagnerite may be incommensurate. Therefore, a unique superspace model for the structural description of commensurately and incommensurately modulated wagnerites was created. Of the several refined wagnerite structures using the superspace approach, five examples have been selected for discussion. The criteria for selection are the values of the q vectors and the intensities of satellite reflections. The results of a structural refinement on the following wagnerites will be presented: (1) a pale orange crystal from tungsten mine Panasqueira, near Fundão, Portugal (Kelly & Rye, 1979[Kelly, W. C. & Rye, R. O. (1979). Econ. Geol. 74, 1721-1822.]; Bussink, 1984[Bussink, R. W. (1984). Habilitation thesis. Ultrecht University, The Netherlands.]); (2) an orange crystal from Hålsjöberg, Värmland, Sweden (Henriques, 1956[Henriques, A. (1956). Arkiv Miner. Geol. 2, 149-153.]); (3) an orange variety of wagnerite from Kyakhta, southern Buryatiya, Russia (Fin'ko, 1962[Fin'ko, V. (1962). Dokl. Akad. Nauk SSSR, 143, 1424-1427.]; Izbrodin et al., 2008[Izbrodin, I. A., Ripp, G. S. & Karman, N. S. (2008). Zapiski RMO, 137, 94-106.]); (4) wagnerite from Reynolds Range, Australia, drilled out of a thin section, from Vry & Cartwright (1994[Vry, J. K. & Cartwright, I. (1994). Contrib. Mineral. Petrol. 116, 78-91.]); (5) colourless wagnerite obtained from Webing, Austria (Kirchner, 1982[Kirchner, E. (1982). Mitt. Österr. Mineral. Ges. 128, 29-31.]). Results of the X-ray single-crystal diffraction, electron-microprobe analysis and electron microscopy of other samples of wagnerite and related minerals are listed in Table 2[link].

Table 2
Results of X-ray single-crystal diffraction and electron-microprobe analysis for wagnerite and a few related minerals from different localities

Chemical compositions are presented for M and (F, OH) positions in M2(PO4)(F, OH), where X is mole fraction. The average ionic radii for M is calculated as r(M) (average) = XMg × (0.72 Å) + (1 − XMg) × (0.78 Å), parameters from Shannon (1976[Shannon, R. D. (1976). Acta Cryst. A32, 751-767.]).

No. Origin of the sample a (Å) b (Å) c (Å) β (°) q = βb*, β Period. r(M)ave. XMg XFe XMn XCa XTi XNa XAl XF
(1) Reynolds Range, Australia 12.7707 (2) 6.33940 (10) 9.64620 (10) 117.5242 (5) 0.44652 (2) 0.72127 0.979 0.016 0.001 0.003 0.002 0.000 0.000 0.98
(2) In Ouzzal, NW Hoggar, Algeria 12.7758 (2) 6.3378 (1) 9.6480 (2) 117.5720 (5) 0.44513 (3) 0.72307 0.949 0.032 0.001 0.001 0.017 0.000 0.000 0.84
(3) Kyakhta, Russia; orange 12.7978 (2) 6.35230 (10) 9.66420 (10) 117.5670 (10) 0.427560 (18) 0.72646 0.892 0.078 0.019 0.001 0.010 0.000 0.000 0.87
(4) Kyakhta, Russia; yellow 12.8018 (15) 6.3488 (7) 9.6787 (11) 117.739 (3) 0.39120 (2) 0.72902 0.850 0.124 0.024 0.001 0.001 0.000 0.000 1.00
(5) Skřinářov, Czech Republic 12.7580 (3) 6.3332 (2) 9.6421 (2) 117.5600 (11) 0.40927 (3) 0.72149 0.975 0.019 0.000 0.004 0.002 0.000 0.000 1.00
(6) Mont. St Hilaire, Canada 12.7667 (3) 6.3359 (1) 9.6486 (2) 117.5951 (7) 0.44961 (2) 0.72235 0.961 0.034 0.004 0.000 0.000 0.000 0.000 0.98
(7) Chelyabinsk, S. Urals, Russia 12.771 (3) 6.332 (1) 9.654 (1) 117.63 (2) ≃ (5b) 0.72298 0.950 0.030 0.008 0.008 0.004 0.000 0.000 0.97
(8) Benson Mine, New York, USA 12.8211 (2) 6.35612 (9) 9.6975 (1) 117.7865 (7) 0.39026 (4) 0.73225 0.796 0.142 0.060 0.001 0.001 0.000 0.000 0.95
(9) Mount Pardoe, Antarctica 12.7640 (2) 6.3322 (1) 9.6434 (1) 117.5895 (7) 0.40435 (4) 0.72293 0.951 0.040 0.001 0.001 0.006 0.000 0.000 0.93
(10) Anakapalle, India 12.7676 (2) 6.33236 (8) 9.6472 (1) 117.5707 (5) 0.40600 (5) 0.72177 0.970 0.019 0.000 0.006 0.004 0.000 0.000 0.93
(11) Karasu, Kyrgyzstan 13.026 (3) 6.429 (1) 9.853 (15) 118.46 (14) ≃ (5b) 0.76103 0.316 0.379 0.283 0.009 0.012 0.000 0.000 0.82
(12) Sierra Albarrana, Spain 12.908 (2) 6.398 (1) 9.7636 (8) 117.948 (10) ≃ (5b) 0.74738 0.544 0.320 0.118 0.005 0.013 0.000 0.000 0.80
(13) Kyrk-Bulakh, Kyrgyzstan 12.9769 (8) 6.4340 (4) 9.8119 (6) 117.9842 (8) 0.40741 (6) 0.75347 0.442 0.366 0.170 0.004 0.017 0.000 0.000 0.74
(14) Hålsjöberg, Sweden 12.8840 (2) 6.38890 (10) 9.37840 (10) 117.7994 (4) 0.41066 (3) 0.74141 0.643 0.222 0.112 0.002 0.019 0.001 0.000 0.72
(15) Albères, France 12.9462 (7) 6.4378 (4) 9.7957 (5) 117.8892 (12) 0.40906 (4) 0.75430 0.428 0.426 0.136 0.003 0.007 0.000 0.000 0.72
(16) Tsaobismund, Namibia 13.0731 (2) 6.4513 (1) 9.8789 (1) 118.5113 (6) 0.38714 (6) 0.76389 0.268 0.396 0.320 0.010 0.004 0.001 0.000 0.79
(17) Cap de Creus, Spain 12.9389 (4) 6.4224 (2) 9.7765 (3) 117.861 (1) 0.4193 (1) 0.75229 0.462 0.377 0.126 0.003 0.033 0.000 0.000 0.60
(18) Larsemann Hills, Antarctica 12.766 (4) 6.332 (6) 9.645 (2) 117.589 (3) 0.40000 0.74311 0.916 0.085 0.002 0.002 0.018 0.000 0.000 0.61
(19) Himachal Himalaya, India 12.9242 (7) 6.4122 (3) 9.7716 (5) 117.881 (2) 0.40928 (9) 0.74859 0.507 0.365 0.102 0.004 0.020 0.000 0.000 0.74
(20) Salamanca, Spain 13.0312 (3) 6.4478 (1) 9.8444 (2) 118.2198 (10) 0.40426 (3) 0.76138 0.310 0.385 0.283 0.006 0.015 0.001 0.000 0.68
(21) Webing, Austria 12.7633 (4) 6.3282 (2) 9.6350 (3) 117.5985 (11) 0.50000 0.72015 0.998 0.000 0.002 0.000 0.000 0.000 0.000 0.97
(22) Reyers­hausen, Germany 12.7526 (16) 6.3284 (6) 9.6359 (3) 117.553 (6) ≃ (2b) 0.72027 0.996 0.000 0.000 0.002 0.000 0.000 0.002 0.94
(23) Santa Fe Mountains, USA 12.7783 (9) 6.3410 (5) 9.6494 (7) 117.5278 (9) 0.49841 (5) 0.72236 0.961 0.023 0.013 0.001 0.002 0.000 0.000 0.89
(24) Tonagh Island, Antarctica 12.9084 (17) 6.398 (1) 9.7636 (8) 117.988 (10) ≃ (2b) 0.72306 0.949 0.036 0.001 0.001 0.013 0.000 0.000 0.89
(25) Christmas Point, Antarctica 12.7821 (6) 6.3469 (3) 9.6563 (4) 117.5319 (14) 0.46734 (5) 0.72447 0.926 0.064 0.002 0.001 0.007 0.000 0.000 0.83
(26) Werfen, Austria 12.819 (11) 6.3395 (80) 9.644 (7) 117.4411 (11) 0.5000 0.72244 0.959 0.036 0.003 0.001 0.000 0.000 0.000 0.83
(27) Höllgraben, Austria 12.7694 (2) 6.33423 (1) 9.6365 (1) 117.4808 (6) 0.49914 (3) 0.72065 0.989 0.001 0.000 0.001 0.008 0.000 0.000 0.78
(28) Bamble, Norway 12.7797 (9) 6.3417 (4) 9.6428 (7) 117.5152 (9) 0.49822 (5) 0.72063 0.989 0.001 0.000 0.001 0.008 0.000 0.000 0.78
(29) Miregn, Lepontin Alps, Switzerland 12.8112 (3) 6.3700 (7) 9.6630 (20) 117.384 (4) 0.4990 (11) 0.72514 0.914 0.071 0.011 0.001 0.002 0.000 0.000 0.67
(30) Mount Painter, Australia 12.7957 (2) 6.3590 (1) 9.6510 (1) 117.3995 (6) 0.49957 (4) 0.72254 0.958 0.028 0.010 0.001 0.003 0.000 0.000 0.67
(31) Star Lake, Manitoba, Canada 12.809 (2) 6.366 (1) 9.665 (2) 117.381 (4) 0.4838 (3) 0.72480 0.920 0.065 0.001 0.001 0.013 0.000 0.000 0.65
(32) Panasqueira, Portugal 13.0183 (2) 6.41490 (10) 9.84110 (10) 118.5620 (10) 0.34599 (3) 0.75276 0.402 0.228 0.366 0.000 0.000 0.000 0.000 0.78
(33) OH-wagnerite, Dora Maira, Italy 12.794 (6) 6.3655 (20) 9.646 (3) 117.302 (5) 0.5000 0.72054 0.991 0.004 0.000 0.002 0.002 0.000 0.001 0.47
                                 
(34) Mg-wolfeite, Yukon, USA 13.010 (4) 6.585 (3) 9.754 (2) 116.62 (3) 0.5000 0.77400 0.100 0.825 0.075 0.000 0.000 0.000 0.000 0.05
(35) Triplite, Canyon City, USA 13.1728 (16) 6.4429 (7) 9.9264 (12) 118.927 (6) 0.36536 (5) 0.76073 0.321 0.144 0.518 0.014 0.002 0.000 0.000 0.88
(36) Zwieselite, Olary Block, Australia 13.1770 (3) 6.5020 (1) 9.9523 (2) 118.8378 0.40043 (8) 0.77720 0.047 0.555 0.382 0.014 0.002 0.000 0.000 0.75
(37) Triplite, Chanteloube, France 13.304 (3) 6.508 (2) 10.032 (3) 119.478 (5) No sat. ref. 0.77957 0.007 0.426 0.526 0.038 0.002 0.000 0.000 0.84
(38) Triplite, Mica Lode, USA 13.12036 (30) 6.4575 (15) 9.9511 (22) 119.051 (4) 0.3656 (8) 0.76291 0.284 0.149 0.549 0.015 0.003 0.000 0.000 0.89
(39) Zwieselite, Hagendorf, Germany 13.1957 (18) 6.4889 (9) 9.9764 (8) 119.210 (7) ≃ (1b) 0.77912 0.015 0.591 0.376 0.016 0.003 0.000 0.000 0.83
Source of information on occurrence: (1) Vry & Cartwright (1994[Vry, J. K. & Cartwright, I. (1994). Contrib. Mineral. Petrol. 116, 78-91.]); (2) Ouzegane et al. (2003[Ouzegane, K., Guiraud, M. & Kienast, J. R. (2003). J. Petrol. 44, 517-545.]); (3) and (4) Izbrodin et al. (2008[Izbrodin, I. A., Ripp, G. S. & Karman, N. S. (2008). Zapiski RMO, 137, 94-106.]); (5) Novák & Povondra (1984[Novák, M. & Povondra, B. P. (1984). Neues Jahrb. Mineral. Monatsh. 12, 536-542.]); (6) Wight & Chao (1995[Wight, Q. & Chao, G. Y. (1995). Rocks Miner. 70, 90-138.]); (7) Chesnokov et al. (2008[Chesnokov, B. V., Shcherbakova, Ye, P. & Nishanbayev, T. P. (2008). Minerals of the Burnt Dumps of the Chelyabinsk Coal Basin. Institute of Mineralogy, Russian Academy of Sciences, Urals Division, Miass (in Russian).]); (8) Jaffe et al. (1992[Jaffe, H. W., Hall, L. M. & Evans, H. T. Jr (1992). Mineral. Mag. 56, 227-233.]); (9) Grew et al. (2006[Grew, E. S., Yates, M. G., Shearer, C. K., Hagerty, J. J., Sheraton, J. W. & Sandiford, M. (2006). J. Petrol. 47, 859-882.]); (10) Simmat & Rickers (2000[Simmat, R. & Rickers, K. (2000). Eur. J. Mineral. 12, 661-666.]); (11) Ginzburg et al. (1951[Ginzburg, A. I., Kruglova, N. A. & Moleva, V. A. (1951). Dokl. Akad. Nauk SSSR, 77, 97-100.]); (12) González del Tánago & Peinado (1992[González del Tánago, J. & Peinado, M. (1992). Bol. Soc. Esp. Mineral. 15, 202-206.]); (13) Ginzburg et al. (1951[Ginzburg, A. I., Kruglova, N. A. & Moleva, V. A. (1951). Dokl. Akad. Nauk SSSR, 77, 97-100.]); (14) Henriques (1956[Henriques, A. (1956). Arkiv Miner. Geol. 2, 149-153.]); (15) Fontan (1981[Fontan, F. (1981). Bull. Minéral. 104, 672-676.]); (16) Keller, Fransolet & Fontan (1994[Keller, P., Fransolet, A.-M. & Fontan, F. (1994). Neues Jahrb. Mineral. Abh. 168, 127-145.]), Keller, Fontan & Fransolet (1994[Keller, P., Fontan, F. & Fransolet, A.-M. (1994). Contrib. Mineral. Petrol. 118, 239-248.]); (17) Corbella & Melgarejo (1990[Corbella, M. & Melgarejo, J.-C. (1990). Bol. Soc. Esp. Mineral. 13, 169-182.]); (18) Ren et al. (2003[Ren, L., Grew, E. S., Xiong, M. & Ma, Z. (2003). Can. Mineral. 41, 393-411.]); (19) Wyss (1999[Wyss, M. (1999). PhD thesis. University of Lausanne, Switzerland.]); (20) Roda et al. (2004[Roda, E., Pesquera, A., Fontan, F. & Keller, P. (2004). Am. Mineral. 89, 110-125.]); (21) Kirchner (1982[Kirchner, E. (1982). Mitt. Österr. Mineral. Ges. 128, 29-31.]); (22) Braitsch (1960[Braitsch, O. (1960). Kali Steinsalz, 3, 1-14.]); (23) Sheridan et al. (1976[Sheridan, D. M., Marsch, S. P., Mrose, M. R. & Taylor, R. B. (1976). US Geol. Surv. Prof. Pap. 955, 1-23.]); (24) Roy et al. (2003[Roy, A. J., Grew, E. S. & Yates, M. G. (2003). Abstr. Geol. Soc. Am. 35, 327.]); (25) Grew et al. (2000[Grew, E. S., Yates, M. G., Barbier, J., Shearer, C. K., Sheraton, J. W., Shiraishi, K. & Motoyoshi, Y. (2000). Polar Geosci. 13, 1-40.]); (26) and (27) Hegemann & Steinmetz (1927[Hegemann, F. & Steinmetz, H. (1927). Centr. Mineral. Geol. Paläontol. A, pp. 45-56.]); (28) Nijland et al. (1998[Nijland, T. G., Zwaan, J. C. & Touret, L. (1998). Scr. Geol. 118, 1-46.]); (29) Irouschek-Zumthor & Armbruster (1985[Irouschek-Zumthor, A. & Armbruster, T. (1985). Schweiz. Miner. Petrol. Mitt. 65, 137-151.]); (30) Hejny & Armbruster (2002[Hejny, C. & Armbruster, T. (2002). Am. Mineral. 87, 277-292.]); (31) Leroux & Ercit (1992[Leroux, M. V. & Ercit, T. S. (1992). Can. Mineral. 30, 1161-1165.]); (32) Kelly & Rye (1979[Kelly, W. C. & Rye, R. O. (1979). Econ. Geol. 74, 1721-1822.]); (33) Brunet et al. (1998[Brunet, F., Chopin, C. & Seifert, F. (1998). Contrib. Mineral. Petrol. 131, 54-70.]); (34) Kolitsch (2003[Kolitsch, U. (2003). Acta Cryst. E59, i125-i128.]); (35) Heinrich (1951[Heinrich, E. W. (1951). Am. Mineral. 36, 256-271.]); (36) Lottermoser & Lu (1997[Lottermoser, B. G. & Lu, J. (1997). Mineral. Petrol. 59, 1-19.]); (37) Otto (1935[Otto, H. (1935). Mineral. Petrogr. Mitt. 47, 89-140.]); (38) Heinrich (1951[Heinrich, E. W. (1951). Am. Mineral. 36, 256-271.]); (39) Keller, Fransolet & Fontan (1994[Keller, P., Fransolet, A.-M. & Fontan, F. (1994). Neues Jahrb. Mineral. Abh. 168, 127-145.]), Keller, Fransolet & Fontan (1994[Keller, P., Fontan, F. & Fransolet, A.-M. (1994). Contrib. Mineral. Petrol. 118, 239-248.]).
Source of samples: (1) Julie Vry, X220; (2) J.-R. Kienast, In928; (3) and (4) Fersman Museum #62065; (5) Milan Novák; (6) Canadian Museum of Nature #83763; (7) B. V. Chesnokov #054-473; (8) National Museum of Natural History #170977; (9) E. S. Grew #10508; (10) Ralf Simmat, X-4; (11) P. M. Kartashov; (12) J. González del Tánago from pegmatite #30; (13) Fersman Museum #50653; (14) Ecole des Mines de Paris #16926; (15) Ecole des Mines de Paris #41494; (16) P. Keller, TSAO-103; (17) J. C. Melgarejo; (18) Liudong Ren; (19) Nicolas Meisser, Musée Géologie Lausanne #8.BB.15; (20) F. Fontan; (21) E. Kirchner; (22) University of Göttingen; (23) National Museum of Natural History #160005; (24) E. S. Grew #11412; (25) E. S. Grew #12213; (26) E. Kirchner; (27) Naturhistorisches Museum Bern #A2606; (28) Ecole des Mines de Paris #38513; (29) University of Bern; (30) South Australia Museum #616351; (31) Marc Leroux SC-5-21F; (32) Staatssammlung München #27901; (33) C. Chopin 85DM73c; (34) U. Kolitsch; (35) American Museum of Natural History #21326; (36) American Museum of Natural History #91609; (37) Ecole des Mines de Paris #16925; (38) Harvard University Mineralogical Museum # 97893; (39) Ecole des Mines de Paris #36158.
†Crystals were mesured on an Enraf–Nonius (CAD4) diffractometer with a conventional point detector. The periodicity of the structures was determined using diagnostic `fingerprint' reflections whose hkl indices correspond to the superstructures and not to the basic (1b) type.
‡The cell parameters and chemical compositions of these samples are taken from the cited papers and recalculated in terms of our settings and formula units. Data on all the other samples were obtained in the present study.

2. Experimental

The experimental setting for electron-microprobe analysis of wagnerite is described by Fialin & Chopin (2006[Fialin, M. & Chopin, C. (2006). Am. Mineral. 91, 503-510.]). For investigation with the electron microscope, wagnerite crystals were gently ground separately in an agate mortar under bidistilled water. When crystal fragments reached ∼ 1 µm in size, a droplet of their suspension was deposited onto a mesh copper grid coated with a 10 nm thick amorphous C film.

The high-resolution imaging and selected-area electron diffraction (SAED) patterns reported below were obtained with the Jeol 3010 high-resolution transmission electron microscope at the Centre Interdisciplinaire de Nanoscience de Marseille (CINaM) working at 300 kV and equipped with a LaB6 tip emitter, the 1.6 or 2.1 Å point-to-point pole pieces and a ± 28° double-tilt, side-entry specimen holder. In the absence of cleavage in any of the polytypes, crushing yielded thin shards and wedges with no preferred crystallographic orientation. Electrical conduction of the specimen was achieved without carbon coating. The suitable [001] zone-axis orientation was searched from pseudo-hexagonal hk0 diffraction patterns of the wagnerite substructure. Then the specimen was tilted slightly from this alignment to favour the contribution of satellite reflections to the Fourier summation leading to the high-resolution image contrast.

High-resolution images were typically recorded at 400–600k magnification after tuning the focusing of the objective lens under a weak-beam mode using a low-light Lhesa camera to obtain the quasi-hexagonal network of bright dots supposed to image structure channels containing F and OH. One-second film exposures were then made in full-beam mode after checking for no image drift during an increase in beam intensity. Subsequently, exposed 6 × 9 cm2 negative films were scanned with a Nikon Super Coolscan 8000 scanner at 4000 d.p.i. resolution to generate numerical files. Selected regions were then Fourier transformed (FT) with the NIH image/SXM software working on 2048 × 2048 matrices. The resulting frequency spectra as `numerical diffraction patterns' allowed us to check beam alignment from the shape of the zeroth-order Laue zone. It also allowed further image processing when necessary through image-noise and point-defects Fourier filtering by means of inverse FT after selection of sharp spots and transmitted beam using the same program.

Single-crystal XRD was carried out on a Bruker APEX II diffractometer with Mo Kα (0.71073 Å) X-ray radiation with 50 kV and 40 mA X-ray power. Samples were mounted on the glass needle, and measured at room-temperature conditions with 10–60 s per frame (ω-scans, scan steps 0.5 °). Data were processed using SAINT software (Bruker, 2011[Bruker (2011). RLATT, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]).

3. Results

Table 2[link] lists the formula units calculated from electron-microprobe analyses of 39 samples. Difficulties concerning precise and accurate determination of fluorine contents of wagnerite and other phosphates were the subject of another study (Fialin & Chopin, 2006[Fialin, M. & Chopin, C. (2006). Am. Mineral. 91, 503-510.]). Average ionic radii (Table 2[link]) are calculated multiplying XMg by the radius of Mg, 0.72 Å, and (1 − XMg) by the radius of Fe2+ (0.78 Å; Shannon & Prewitt, 1969[Shannon, R. D. & Prewitt, C. T. (1969). Acta Cryst. B25, 925-946.]), where (1 − XMg) is the sum of the other cations (Mn, Fe, Ca and Ti).

Representative samples of the ≃ (2b), ≃ (3b), ≃ (5b), ≃ (7b) and ≃ (9b) structures were studied by HRTEM (Figs. 4[link]ad). All wagnerite polytypes are subject to electron beam damage. The phosphate grains amorphize readily in the thinnest wedges to coalescing drops lacking diffraction contrast. Substructure diffraction spots weaken concomitantly. When present, modulation fringes are better imaged in thicker regions where dynamical diffraction prevails. Given these operating conditions it is almost impossible for any polytype to record `structure images' displaying all cation positions and the origin of modulation simultaneously. Instead, efforts were made to image correctly F/OH-bearing channels running along c only with the aim of bringing out faint contrast differences which could be indicative of differences in their content and configuration. The `image code' concept (Van Tendeloo et al., 1986[Van Tendeloo, G., Van Dyck, D. & Amelinckx, S. (1986). Ultramicroscopy, 19, 235-252.]) assumes that identical atom configurations within the unit cell display the same image at high resolution. This concept applies even if the contrast departs strongly from the local projected potential density of the structure. The latter is expected only from the thinnest regions at Scherzer underfocusing conditions of the objective lens. The modulation contrast was disappearing much quicker than the substructure contrast. This feature suggests, but does not prove, that modulation may originate from the labile F, OH sites rather than from the more stable P, M1 and/or M2 sites. Some results of electron-microscopic investigation are exemplified for different types of modulated wagnerites (Fig. 4[link]ad).

[Figure 4]
Figure 4
〈001〉 zone axis HRTEM micrographs of four microstructures of wagnerite. Upper left insets: SAED patterns; lower insets: zoomed views with approximate two-dimensional unit-cells as boxes. (a) Wagnerite (2b) from Miregn, Val Ambra, Lepontin Alps, Ticino, Switzerland; (b) wagnerite (5b) from Anakapalle, Andhra Pradesh, India; (c) wagnerite (7b) from Kyakhta, Russia; (d) wagnerite (9b) from Reynolds Range, Australia.

The diffraction pattern of triplite appears to be pseudo-hexagonal because the strongest reflections represent the substructure in the reciprocal lattice. This feature is common to all wagnerites. Superstructure (satellite) reflections are always sharp, i.e. no smearing or streaking is observed. As expected, the satellite reflections are weaker than adjacent substructure reflections. Furthermore, satellite reflections are perfectly aligned along b* (no offset visible), which indicates that the modulations only occur along b. In (2b) structures, modulation spots align perfectly parallel to a, whereas in other `polytypes', modulation spots define a zigzag ribbon resembling a string of the letter w along a. Each structure type has a different strongest satellite reflection along b*, namely at 2/5 corresponding to ≃ 5b, at 3/7 corresponding to ≃ 7b, or at 4/9 corresponding to ≃ 9b.

HRTEM images of the investigated wagnerites display strong contrast differences among the investigated members of this structural series (Figs. 4[link]ad). This is consistent with the exceptional sharpness of modulation reflections (SAED patterns as upper insets in Figs. 4[link]ad). After having been purposely blurred and contrasted, the blown-up raw HRTEM images (lower insets in Figs. 4[link]ad) show linear patterns of bright (+) and weaker (−) dots running along b that mark local periodicities in that direction and from which we can draw local unit cells (lower insets in Figs. 4[link]ad). As expected, these local direct-space asin βb unit cells correspond to the reciprocal unit cells appearing as boxes in the SAED patterns. asin β is invariant for the different wagnerites, whereas b lengths may look at first glance to be integral multiples 2, 5, 7 and 9 of b of triplite.

However, there is a significant difference between (2b) wagnerite and the (5b), (7b) and (9b) wagnerites. The [+ −] motif of (2b) wagnerite propagates well along b (Fig. 4[link]a), whereas any chosen motif is progressively altered along b (Figs. 4[link]bd) for other structures. This indicates that (2b) wagnerite may also be considered as commensurate, and a standard polytype of triplite. The HRTEM image contrast behaviour of other wagnerites is consistent with the incommensurability of their structures. However, it does not prove it due to the narrow field of view with constant and correct HRTEM imaging conditions that precludes long-distance commensurability to be distinguished from true incommensurability.

Owing to the location and dual intensity of light dots, a reasonable correlation may be made between + and U, − and D, i.e. with the arc-like arrangement of F, OH of the wagnerite structures projected along c. Thus, [+ −] corresponds to the [U D] sequence in (2b) wagnerite. For the other wagnerites, we find inside only some of the modulation fringes the following sequences or circular permutations of these, as presented in Table 3[link]. These sequences fit with X-ray structure data for the commensurate approximation of their structure.

Table 3
Correlation between + and − motifs observed in HRTEM images of (5b), (7b) and (9b) wagnerites with U (up) and D (down) arc-like arrangements of F, OH of the wagnerite structures projected along c

Wagnerite [+ −] sequence [U D] sequence
(5b) [+ + − + −] [U U D U D]
(7b) [+ + − + − + −] [U U D U D U D]
  [+ − + − − + −] [U D U D D U D]
(9b) [+ + − + − + − + −] [U U D U D U D U D]

Analysis of sections of reciprocal space in X-ray diffraction patterns clearly showed the presence of strong parent reflections accompanied by a subset of composition-dependent `satellite' reflections along b*. Using the reciprocal lattice viewer RLATT (Bruker, 2011[Bruker (2011). RLATT, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]), stronger reflections were separated and indexed with the C-centred cell corresponding to triplite [(1b) type] a ≃ 12.8, b ≃ 6.4, c ≃ 9.6, β ≃ 117°. All additional weaker satellite reflections were indexed with the q vector (0, β, 0) (de Wolff, 1974[Wolff, P. M. de (1974). Acta Cryst. A30, 777-785.]) using the closest main reflection along b* as reference. First-order satellite reflections found in the X-ray single-crystal diffraction pattern corresponded to strongest satellite reflections seen in SAED patterns recorded by TEM. Subsequently, data were integrated including satellite reflections using SAINT software (Bruker, 2011[Bruker (2011). RLATT, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]). The results are presented in Table 2[link]. The observed systematic absences (hklm) h + k = 2n + 1, (0k0m) m = 2n + 1 and (h0lm) l = 2n + 1 unambiguously give the centrosymmetric superspace group C2/c(0β0)s0 (Wilson & Prince, 2004[Wilson, A. & Prince, E. (2004). International Tables of Crystallography, Vol. C. Dordrecht: Kluwer Academic Publishers.]). The structure of wagnerite from Kyakhta, Russia, was solved with the software SUPERFLIP (Palatinus & Chapuis, 2007[Palatinus, L. & Chapuis, G. (2007). J. Appl. Cryst. 40, 786-790.]). This first solved structure of wagnerite was used as a parent model for structural refinements of all wagnerite crystals. Full-matrix least-squares refinement of all data sets was carried out using JANA2006 (Petříček et al., 2006[Petříček, V., Dusek, M. & Palatinus, L. (2006). JANA2006. Institute of Physics, Praha, Czech Republic.]). Details on data collection and refinement for four aperiodic and one periodic (2b) wagnerite structures are summarized in Table 4[link]. CIF files are provided as supporting information.1

Table 4
Experimental details

For all structures: Z = 8. Experiments were carried out at 293 K with Mo Kα radiation using a Bruker CCD diffractometer. Absorption was corrected for by multi-scan methods, SADABS (Bruker, 2011[Bruker (2011). RLATT, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]).

Wagnerite from Panasqueira, Portugal ≃ (3b) Hålsjöberg, Sweden ≃ (5b) Khyakhta, Russia (orange) ≃ (7b) Reynolds Range, Australia ≃ (9b) Webing, Austria (2b)
Crystal data
Chemical formula Mg0.8Fe0.5Mn0.7(PO4)F0.8(OH)0.2 Mg1.3Fe0.5Mn0.2(PO4)F0.7(OH)0.3 Mg1.7Fe0.25Mn0.05(PO4)F1.0 Mg1.94Fe0.06F0.98(OH)0.02 Mg2(PO4)F
Mr 196.6 183 168.43 163.5 162.6
Crystal system Monoclinic Monoclinic Monoclinic Monoclinic Monoclinic
Space group C2/c(0β0)s0 C2/c(0β0)s0 C2/c(0β0)s0 C2/c(0β0)s0 C2/c(0β0)s0
Wavevectors q = 0.345990b* q = 0.410660b* q = 0.427560b* q = 0.446520b* q = 0.500000b*
a, b, c (Å) 13.0183 (2), 6.4149 (1), 9.8411 (1) 12.8840 (2), 6.3889 (1), 9.7384 (1) 12.7978 (2), 6.3523 (1), 9.6642 (1) 12.7707 (2), 6.3394 (1), 9.6462 (1) 12.7633 (4), 6.3282 (2), 9.6350 (3)
β (°) 118.562 (1) 117.799 (1) 117.567 (1) 117.5240 (5) 117.5985 (11)
V3) 721.82 (2) 709.10 (2) 696.46 (2) 692.55 (2) 689.66 (4)
μ (mm−1) 4.99 3.47 1.8 1.18 1.07
Crystal size 0.16 × 0.16 × 0.06 0.2 × 0.15 × 0.15 0.6 × 0.16 × 0.1 0.25 × 0.25 × 0.1 0.46 × 0.26 × 0.26
           
Data collection
No. of measured, independent and observed [I > 3σ(I)] reflections 9151, 2484, 2086 6943, 2439, 2216 17 606, 7370, 3766 26 453, 7409, 4855 12 149, 3160, 2999
Rint 0.011 0.010 0.016 0.010 0.009
(sin θ/λ)max−1) 0.650 0.649 0.715 0.715 0.715
No. of satellite reflections
First-order obs/all 1262/1653 1413/1625 1684/2106 1847/2106 1939/2102
Second-order obs/all ≤ 10% 344/2102 849/2122
Third-order obs/all ≤ 10% 721/2108 1059/2119
           
Refinement
No. of reflections 2484 2439 7370 7409 3160
No. of parameters 167 228 504 503 227
No. of constraints 2 2 2 2 0
Rint obs/all 0.010/0.009 0.010/0.010 0.016/0.018 0.010/0.009 0.009/0.009
R obs/all 0.022/0.025 0.023/0.024 0.031/0.061 0.033/0.048 0.016/0.017
Main ref. R obs/all 0.019/0.019 0.022/0.022 0.024/0.025 0.023/0.023 0.018/0.018
First-order sat. R obs/all 0.032/0.046 0.025/0.030 0.027/0.038 0.020/0.025 0.014/0.016
Second-order sat. R obs/all Not refined 0.128/0.391 0.197/0.305
Third-order sat. R obs/all Not refined 0.106/0.242 0.111/0.171
wR2 obs/all 0.063/0.064 0.064/0.065 0.079/0.091 0.099/0.104 0.054/0.055
GOF obs/all 0.019/0.019 0.022/0.021 0.021/0.016 0.029/0.024 0.020/0.020

4. Average three-dimensional structure of wagnerite

To describe both periodic and aperiodic wagnerite, a unified superspace model was created using only main reflections. This model is based on an average wagnerite structure (Fig. 5[link]) with C2/c space group and cell dimensions a ≃ 13, b ≃ 6.45, c ≃ 9 Å, β ≃ 117 °. The average structure has two M sites (M1 and M2), one P, four O and two half occupied F sites (F1 and F2) separated by ca 1 Å. M1 and M2 sites are fully occupied with Mg and Fe (the minor Mn is included with Fe). Depending on the arrangement of F1 and F2, both M1 and M2 are five- or six-coordinated.

[Figure 5]
Figure 5
Average structure, obtained only from main reflections, of wagnerite from Khyakta in space group C2/c. PO4 units are displayed as grey tetrahedra, five- or six-coordinated cations as red spheres and F/O(H) as light and dark green spheres. F1 and F2 are half occupied.

M1 has four regular bonds to oxygen (average M1—O 2.07 Å) and one bond to F1 (2.11 Å) or two bonds to F2 (1.85 and 2.29 Å). M2 also has four regular bonds to oxygen (average M2—O = 2.05 Å) and one longer bond to F2 (2.19 Å) or two bonds to F1 (1.83 and 2.14 Å). The PO4 tetrahedra are very regular, with average bond lengths (P—O) of 1.53 Å. Thus, the average structure of wagnerite is built by two slightly distorted MO4F and MO4F2 polyhedra and one regular PO4 tetrahedron.

5. Superspace model

A unified (3+1)-dimensional model includes three major parts: (1) cations: occupational and displacive modulation of Mg/Fe positions; (2) anions: occupational and displacive modulation of F or O (OH); (3) displacive modulation of the PO4 tetrahedron.

As in an average model, the superspace model also has two cation positions, M1 and M2. Both positions are fully occupied. These sites are hosting Mg, which according to the results of chemical analyses can be partially replaced by Fe2+ and Mn2+ and to a smaller amount by Ca and/or Ti. Considering that the scattering factors of Fe and Mn are similar for X-ray data, the amount of Fe2+ and Mn2+ are combined and treated as Fe, and the subordinate elements (Ca, Ti, Na, Al) neglected. Hence, both cation positions M1 and M2 are refined with occupational modulation. Occupational probabilities of Mg and Fe (Fe2+ + Mn2+) are constrained to be complementary. In addition, both species (Mg and Fe) at M sites show displacive modulation, but their coordinates, modulations and atomic displacement parameters (ADP) are constrained to be identical.

For X-ray data, the scattering power of F and O (from OH) cannot be distinguished, in particular not for mixed occupation. Consequently, these sites are refined as F or O depending on the dominant species. In an average structure two F are distributed over two half-occupied positions. In the (3+1)- dimensional model, two fluorine atoms, F1 and F2, also have two distinct positions (in x1, x2, x3), not related by symmetry operations. The alternating occupation of F1 or F2 is modelled with a crenel function (Petříček et al., 1995[Petříček, V., van der Lee, A. & Evain, M. (1995). Acta Cryst. A51, 529-535.]), the results of which can adopt two distinct values only, 0 (vacancy) or 1 (occupied position). The parameters of the crenel function x40 (centre of crenel function) and Δ (width of function) were refined, with the following constraints:

  • (1) Δ[F2] = 1 − Δ[F1];

  • (2) [{{x}}_4^0\left [{{\rm{F}}2} \right] = 0.5 + {{x}}_4^0\left [{{\rm{F}}1} \right] + {\rm{\beta }} \cdot {{x}}_2^0[{\rm{F}}2] - {\rm{\beta }} \cdot {{x}}_2^0[{\rm{F}}1]].

The first constraint fixes the sum of occupancies at F1 and F2 at one. The second constraint takes care that only one F is considered in any t-section (real space section). In addition to occupational modulation, F sites also exhibit positional modulation. A Legendre polynomial is used to combine the crenel function with positional modulation (Dušek et al., 2010[Dušek, M., Petříček, V. & Palatinus, L. (2010). J. Phys. Conf. Ser. 226, 012014, 1-6.]). For all other sites (one P and four O), the modulation of positional and anisotropic displacement parameters was refined with harmonic functions. The sine and cosine terms of up to the third harmonic wave of the modulation functions may be used, depending on the highest observed order of satellites and their number and intensity. In addition, depending on chemical composition (e.g. concentration of OH groups in the anionic part) and data quality, H positions could be found in difference Fourier maps. Four modulated structures of wagnerite will be presented. Figures of t-plots and Fourier maps are only shown for wagnerite from Kyakhta. The type and degree of modulation in four additional samples will be described. Selected bond distances, including average (average) and extreme (minimum and maximum), caused by modulation in the structures of different wagnerites are given in Tables 5–11 of the supporting information. In all investigated wagnerite structures, the PO4 tetrahedron behaves almost as a rigid unit, just tilting a little bit around its centre of gravity. Thus, small variations of the average P—O bonds will be briefly discussed.

5.1. Wagnerite from Kyakhta, Russia (orange variety)

Refinement of the structure was based on all main and satellite reflections up to third order (Table 4[link]). Following the above-described recipe, occupational probabilities of Mg and Fe2+ (Fe2+ + Mn2+) are refined complementarily and they are presented as a function of the internal coordinate t (Fig. 6[link]). The Fe content at M1 varies with modulation from 12 to 18% and at M2 between 3 and 6%. The average composition of the M1 + M2 sites, 90% Mg and 10% (Fe2+ + Mn2+) is very close to the average obtained by electron-microprobe analysis (Table 2[link]). In addition, both M sites exhibit displacive modulation apparent in corresponding Fourier maps (Fig. 7[link]). The modulation of M1 is more pronounced along x2 (b*) and of M2 along x1 (a*). The occupation of F is refined with a crenel function (Fig. 8[link]). The refined value of Δ = 0.5039 (9) indicates that F is equally distributed over two positions. In addition, F1 and F2 show significant displacive modulation in all three directions (Fig. 9[link]). A plot of interatomic distances as a function of t confirms that F1 and F2 are always threefold-coordinated by M1 and M2 (Fig. 10[link]). F1 has three bonds to M sites, F1—M1 = 2.028 (3) Å (average) and F1—M2 = 2.0736 (17) Å and an additional F1—M2 = 1.941 (3) Å (average). F2 has two bonds to M1 [1.955 (2) and 2.221 (2) Å (average)] and one to M2 [2.030 (3) Å (average)].

[Figure 6]
Figure 6
Occupational modulations of Mg and Fe atoms on M1 and M2 sites in wagnerite from Kyakhta: occ (M1) = occ (Mg1) + occ (Fe1) and occ (M2) = occ(Mg2) + occ (Fe2).
[Figure 7]
Figure 7
Displacive modulation of cations on M1 and M2 sites in wagnerite from Kyakhta as a function of t.
[Figure 8]
Figure 8
The crenel function modulation of F1 and F2. x3 − x4 map intersecting the four-dimensional Fobs Fourier synthesis at x1 = 0.006 and x2 = 0.100.
[Figure 9]
Figure 9
Displacive modulations of F(O) in wagnerite from Kyakhta in x, y, z displacement as a function of t.
[Figure 10]
Figure 10
Coordination of F presented as a plot of bond lengths to M sites as a function of t in wagnerite from Kyakhta.

The coordination of M1 and M2 is displayed in Fig. 11[link] and Table 7 of the supporting information . In sections from t = 0 to t = 0.5, M1 is six- coordinated with four regular bonds to O and one to F1 [average 2.027 (3)–2.155 (3) Å] and one longer bond to F2 [average 2.221 (2) Å]. Therefore, M2 is five-coordinated with four O atoms [average 2.012 (3)–2.053 (3) Å] and one shorter bond to F2 [average 1.943 (3) Å]. Between t = 0.5 and t = 1, the situation is reversed. M1 is five-coordinated with four O atoms [average 2.037 (3)–2.096 (3) Å] and a shorter bond to F2 [average 1.955 (2) Å]. M2 has regular sixfold coordination M2O4F2 [average 2.030 (3)–2.118 (2) Å]. In Figs. 12[link](a)–(e) the positional modulation of the PO4 tetrahedron is displayed. The t-plots suggest a very small displacive modulation of P associated with displacement of the pairs O1/O4 and O2/O3. The biggest displacive modulation is found for O2 connecting the PO4 tetrahedron with M1 and M2 polyhedra. Nevertheless, the tetrahedron preserves average P—O distances between 1.533 (2) and 1.540 (3) Å (Table 7 of the supporting information ).

[Figure 11]
Figure 11
Coordination of M1 and M2 atoms with four O and one or two bonds to F presented as the dependence of bond lengths as a function of t in wagnerite from Kyakhta.
[Figure 12]
Figure 12
Displacive modulation of atoms in PO4 units as a function of t in wagnerite from Kyakhta.

In addition, the final difference-Fourier map indicated (residual peak of 0.7 e) the position of partly occupied H close to F1, which represents in this case an O site (OH group).

5.2. Wagnerite from Panasqueira, Portugal

Refinement of the structure was based on all the main and first-order satellite reflections (Table 4[link]). Refined occupational probabilities of Mg and Fe2+ (Fe2+ + Mn2+) converged to 29–33% Mg at M1 and to 51–71% Mg at M2, as well as to 67–71% of (Fe2+ + Mn2+) at M1 and to 29–48% at M2. The average composition of M cations of 46% Mg and 54% (Fe2+ + Mn2+) agrees fairly well with the results (40% Mg) of electron-microprobe analysis (Table 2[link]). The obtained value of ΔF1 = 0.5303 (3) in the crenel occupation function indicates that F slightly prefers F1 over F2. This has consequences on the M1 and M2 coordination (Table 5 of the supporting information ). Between t = 0 and t = 0.53, M1 has five regular bonds to four O and to one F [average 2.085 (11)–2.156 (1) Å]. If F2 is occupied (from t = 0 to t = 0.47) one additional longer bond to F2 [average 2.324 (8) Å] exists. In the section between t = 0.53 and t = 1, M1O4F2 has five average bonds between 2.034 (11) and 2.1431 (10) Å. Between t = 0 and t = 0.53, M2 has five regular bonds, comprising 4 × O and F1 [average 1986 (6) Å]. In the sections from t = 0.53 to t = 1, the M2O4F1F2 polyhedron has six bonds between (average) 1.925 (9) and (average) 2.181 (4) Å. The PO4 tetrahedron shows more pronounced tilting than in the structure of Kyakhta wagnerite. All average P—O bonds are between 1.5314 (11) and 1.5424 (14) Å (Table 5 of the supporting information ).

5.3. Wagnerite from Hålsjöberg, Sweden

From X-ray data of wagnerite from Hålsjöberg, Sweden, up to the third-order satellite reflections are visible (Table 4[link]). Statistically around 10% of second- and third-order reflections were observed, but their intensity was weak. Thus, the refinement was performed with all main reflections and first-order satellites only. Site populations of 52–60% Mg and 40–48% of (Fe2+ + Mn2+) were refined at M1 and 72–86% Mg and 14–28% (Fe2+ + Mn2+) at M2. The average composition at M sites (69% Mg and 31% Fe + Mn) is close to the one obtained by electron-microprobe analysis: 64% Mg, 22% Mn and 11% Fe (Table 2[link]). The width of the crenel function at F1 [Δ = 0.504 (1)] shows a minor preference of F for this position. M1 and M2 are each to 50%, five- and six-coordinated (Table 6 of the supporting information ). Between t = 0 and t = 0.5, M1 has five bonds to O and F1 [average 2.072 (7) to 2.166 (1) Å] and one longer bond to F2 [average 2.241 (5) Å]. M2 has regular fivefold coordination (M2O4F1) with average bonds [average 1.948 (7)–2.068 (1)  Å]. For sections from t = 0.5 to t = 0.1, both polyhedra around M1 and M2 have regular coordination, M1O4F1 [average 1.978 (7)–2.1204 (10) Å] and M2O4F1F2 [average 2.032 (8)–2.1298 (10) Å]. The PO4 tetrahedron shows the same behaviour as in other wagnerite structures, with P—O bond lengths (average) between 1.5334 (10) and 1.5415 (13) Å (Table 6 of the supporting information ).

5.4. Wagnerite from Reynolds Range, Australia

Structure refinement of the wagnerite from Reynolds Range was based on all main and first-order satellite reflections (Table 4[link]). The chemical composition of the investigated crystal was close to the Mg wagnerite end-member (Table 2[link]). Population refinements in our superspace model confirmed this composition. Occupational probabilities of (Fe2+ + Mn2+) at M1 are 2.5–4% and 0–1% at M2. The average Fe + Mn content of 2% confirms the results of the microprobe analysis (Table 2[link]). F is perfectly distributed over two positions [ΔF1 = 0.5016 (7)]. For t = 0 up to t = 0.5, M1 has five bonds to O and F1 [average 2.061 (2)–2.151 (1) Å] and one slightly longer bond to F2 [average 2.2154 (2) Å]. The M2O4F1 polyhedron has five average bonds between 1.938 (2) and 2.051 (2) Å. Between t = 0.5 and t = 1, the M1O4F1 polyhedron has average bonds between 1.940 (2) and 2.087 (2) Å, and the M2O4F1F2 octahedron from (average) 2.044 (2) to 2.1113 (17) Å (Table 8). The PO4 tetrahedron behaves as rigid unit with the average bonds from 1.5328(17) to 1.538(2) Å (Table 8 of the supporting information ).

5.5. Wagnerite from Webing, Austria

Of the structures presented in this paper, only that of wagnerite from Webing, Austria, is periodic. Based on chemical analysis (Table 2[link]) this sample can be considered as the end-member Mg2(PO4)F. Results of refinements both with a periodic supercell (in P21/n space group with 2b parameter) or with superspace formalism [C2/c(0β0)s0 with q = 0.5b*] are deposited to allow easy comparison with other (3)- or (3+1)-dimensional structures. Selected bond distances for both models are presented in Tables 9–11 of the supporting information .

Structure refinement in the superspace group C2/c(0β0)s0 with q = 0.5b* was based on all main and first-order satellite reflections (Table 4[link]). There were no correlations larger than 0.7 in the last refinement cycle. Corresponding to chemical analysis (Table 2[link]), M1 and M2 positions are fully occupied by Mg. F is perfectly distributed over two positions, for which only sine terms of the harmonic wave of the positional and ADP modulation function are refined. For the remaining atoms, two Mg, one P and four O, both sine and cosine terms of the positional and ADP modulation function were refined. As in the above described aperiodic structures, Mg1 and Mg2 atoms are five- or six-coordinated, depending on the position of F (Table 9 of the supporting information ). The average bonds for five- and six-coordinated Mg1 are between 1.9422 (7) and 2.2411 (5) Å and for Mg2 between 1.9371 (4) and 2.0813 (4) Å. The PO4 tetrahedron corresponds to those in other wagnerite structures, with all bonds between 1.5284 (4) and 1.5464 (4) Å (Table 9 of the supporting information ).

Using the supercell formalism a structure refinement was performed in space group P21/n with a doubled b parameter (Table 2[link]). In this structure four Mg sites correspond to M2 and four additional sites to M1. Out of four M1 polyhedra, two have regular sixfold and two fivefold coordination. M—O/F bond distances vary between 1.9414 (5) and 2.2394 (4) Å (Table 10 of the supporting information ). All P—O bond lengths are in the range between 1.5255 (3) and 1.5474 (4) Å (Table 11 of the supporting information ). One difference between the two refinement strategies is a small deviation in unit-cell parameters (Tables 2[link] and 4[link]) as a consequence of differences in the way reflections are integrated.

6. Discussion

There are many examples of minerals having modulated structures that give satellite reflections observable with electron diffraction, but only a few of them have been studied with superstructure formalism (Bindi, 2008[Bindi, L. (2008). Rend. Lincei, 19, 1-16.], and references therein). It is unusual to find minerals giving satellite reflections which are sufficiently strong and sharp enough for structural refinement.

Our investigation shows that most wagnerite samples have modulated structures. Therefore, in refining the average structure, information provided by the satellite reflections is being deliberately neglected. Another approach to handling such structures is to discard any differences between the main and satellite reflections and to treat all reflections equally, that is, the structure is refined in a supercell with pseudo-commensurate periodicity and all observed satellite reflections indexed. Such an approach is successful if satellite reflections are commensurate, as described in the (5b) model by Ren et al. (2003[Ren, L., Grew, E. S., Xiong, M. & Ma, Z. (2003). Can. Mineral. 41, 393-411.]). If the structure is incommensurate, satellite reflections do not fit the grid of the supercell lattice and cause poor agreement factors, large standard deviations, split atom positions and large ADP. The β components of the modulation vectors q = βb* for four wagnerite samples discussed in this paper are close to commensurate values, especially with `larger cells' [e.g. β = 0.34599 (3) ≃ 1/3; β = 0.41066 (3) ≃ 2/5 (0.4); β = 0.427560 (18) ≃ 3/7 (0.42857) and β = 0.44652 (2) ≃ 4/9 (0.4444)]. Therefore, it is not surprising that refinements using superstructure models can also provide reasonable results. However, this refinement strategy entails additional difficulties and problems, as discussed below.

In a refinement of Kyakhta wagnerite with a primitive lattice (space group P21) and sevenfold supercell, there are 56 symmetry-independent M sites, 28 P sites, 112 O and 28 F sites. Simple refinement of atomic coordinates and isotropic displacement parameters, restricted to species, gives a total of 710 parameters, with large correlations among them. In contrast, using a superspace approach for such a commensurate 7b cell, only 166 parameters are needed for the refinement of nine atom sites (two M, one P, four O and two F) and their positional, occupational and anisotropic displacement parameters. Thus, a superspace approach is an efficient tool for dealing with commensurate structures with large unit cells.

Commensurate and incommensurate structures of wagnerite Mg2 − x(Fe, Mn, Ca, Ti…)x(PO4)(F, OH, O) may be considered products of a structural branching process, i.e. increasing complexity of structural modulation with solid solution in which the (1b) and (2b) structure types function as end-members. The modulation complexity is related to a chemical complexity due to different compositions of the various (1b) and (2b) end-members shown in the two triangular diagrams in Fig. 1[link].

This is confirmed by the average structure model with (1b) cell dimensions as for triplite and F distribution conforming to the distributions in both the (1b) and (2b) types. Wagnerite structures with a (5b) (UDUDU), (7b) (UDUDUDU) and (9b) (UDUDUDUDU) cell could be considered as structures with the faults in which the (2b) (UD) periodicity is violated on every fifth, seventh and ninth sequence of the structure. Another indicator for the suggested branching process is that rational β values for observed modulation vectors (q = βb*) are very close to the branches of Farey tree series (Hardy & Wright, 2003[Hardy, G. & Wright, E. (2003). An Intoduction to the Theory of Numbers, 5th ed. New York: Oxford University Press.]). Generating Farey medians successively between [{0 \over 1}] and [{1 \over 2}], the obtained values are [{1 \over 3}], [{2 \over 5}], [{3 \over 7}], [{4 \over 9}] etc. These values correspond to the strongest satellite reflections along b* observed in different wagnerite samples by HRTEM: 2/5 in the ≃ (5b) structure, 3/7 in ≃ (7b) and 4/9 in ≃ (9b) type. Each branch of a Farey tree has two `parents' in the level above, e.g. [{1 \over 3}] is a `child' of [{0 \over 1}] and [{1 \over 2}] or [{2 \over 5}] is a `child' of [{1 \over 3}] and [{1 \over 2}]. In wagnerites, this parent–child relationship is associated with chemical composition, because the value of the modulation vector or branch of the Farey tree can be predicted from the calculated average cation radius on the M position (Fig. 13[link]). For the [{0 \over 1}] branch [(1b) structure type] let us consider pure Fe2(PO4)F, with a cation radius of 0.78 Å and for the [{1 \over 2}] branch [(2b) structure type], Mg2(PO4)F or Mg2(PO4)OH with cation radius 0.72 Å. The average value of the M radius for the child structure should be between the values of the parent structures. For simplicity, only parameters for sixfold coordination are calculated (Shannon & Prewitt, 1969[Shannon, R. D. & Prewitt, C. T. (1969). Acta Cryst. B25, 925-946.]), and the cation composition is restricted to only two species, Mg (radius 0.72 Å) and Fe2+ (radius 0.78 Å), where the latter also accounts for minor Mn2+. Therefore, for the [{1 \over 3}] branch the predicted radius at M is 0.75 Å, for [{2 \over 5}], 0.735 Å, for [{3 \over 7}], 0.7275 Å and for [{4 \over 9}], 0.72375 Å (Fig. 13[link]), values in reasonable agreement with the corresponding average ionic radii determined for our selected wagnerite crystals, respectively, 0.7528 Å [≃ (3b), Panasqueira], 0.7414 Å [≃ (5b), Hålsjöberg], 0.7275 (≃ (7b), orange Kyakhta] and 0.7213 [≃ (9b), Reynolds Range] (Table 2[link]). In summary, the Farey tree series with average ionic radius shows a remarkable qualitative resemblance with the observed modulation in wagnerite and may be used as a simplified approach to explain complex crystal-chemical relationships. In actuality, we expect that the relation between modulation and M-site chemistry is more complex. The different periodicity along b* of wolfeite Fe2(PO4)(OH) and zwieselite Fe2(PO4)F indicates that the OH → F substitution influences the modulation. In addition, the modulation is sensitive to whether the average M ionic radius is increased by Fe2+ or Mn2+ (radius 0.82 Å). Lastly, the pressure–temperature conditions under which wagnerite crystallized and was annealed could affect the modulation, e.g. Fe2+ and Mn2+ should become more disordered with increasing temperature.

[Figure 13]
Figure 13
Farey tree (Hardy & Wright, 2003[Hardy, G. & Wright, E. (2003). An Intoduction to the Theory of Numbers, 5th ed. New York: Oxford University Press.]). The marked branches correspond to the values of the main satellite reflections observed in the crystals studied by us. The corresponding average ionic radii calculated for M sites are presented on the scale: ideal values above and calculated values for our five selected wagnerite crystals below (see text).

Modelling the structure of wagnerite, with a (3+1)-dimensional approach in which F/OH is subject to occupational and displacive modulation appears justified, particularly when we compare bonds and coordination polyhedra around M sites. In all selected wagnerite structures, both sites M1 and M2 are partially five or six coordinated, but mean bond lengths and angles are in very good agreement with expected values for non-modulated structures (Allen et al., 2006[Allen, F., Watson, D., Brammer, L., Orpen, A. & Taylor, R. (2006). International Tables for Crystallography, Vol. C. Berlin: Springer.]).

7. Conclusion

The unified superspace model for the structural description of periodically and aperiodically modulated wagnerite is created with occupational and displacive modulations of Mg/Fe atoms, occupational and displacive modulation of F (O) atoms and displacive modulation of the PO4 tetrahedron.

The superspace model is superior to `average cell' and `supercell' models because: (1) periodic and aperiodic wagnerite structures can be refined with a common space group; (2) it enables refinement of positional and occupational modulation of atoms, which is essential for this structure type; (3) it simplifies the description of positional and occupational modulation of Mg/Fe and F/OH, and their connectivity; (4) it converges to better residual values with a lower number of refined parameters and less correlation among parameters.

Supporting information


Experimental top

Refinement top

Crystal data, data collection and structure refinement details are summarized in Table 1.

Results and discussion top

Computing details top

For all compounds, data collection: SAINT V8.27B (Bruker AXS Inc., 2012); cell refinement: SAINT V8.27B (Bruker AXS Inc., 2012); data reduction: SAINT V8.27B (Bruker AXS Inc., 2012). Program(s) used to solve structure: SUPERFLIP (Palatinus & Chapuis, 2007) for (3b); SUPERFLIP (Palatinus & Chapuis 2007) for (5b), (7b), (9b), (2b). Program(s) used to refine structure: JANA2006(Pertricek,Dusek & Palatinus 2006) for (I), (2b); 'JANA2006(Pertricek,Dusek & Palatinus 2006)' for (3b), (5b), (9b); 'JANA2006(Pertricek,Dusek & Palatinus, 2006)' for (7b). Software used to prepare material for publication: JANA2006(Pertricek,Dusek & Palatinus 2006) for (I), (2b); 'JANA2006(Pertricek,Dusek & Palatinus 2006)' for (3b), (5b), (9b); 'JANA2006(Pertricek,Dusek & Palatinus, 2006)' for (7b).

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
[Figure 7]
[Figure 8]
[Figure 9]
[Figure 10]
[Figure 11]
[Figure 12]
[Figure 13]
(I) top
Crystal data top
FMg2O4PZ = 16
Mr = 162.6F(000) = 1280
Monoclinic, P21/nDx = 3.131 Mg m3
Hall symbol: -P 2yabcMo Kα radiation, λ = 0.71073 Å
a = 12.7628 (4) ŵ = 1.07 mm1
b = 12.6564 (4) ÅT = 293 K
c = 9.6348 (3) ÅPrism, colourless
β = 117.5995 (10)°0.46 × 0.26 × 0.26 mm
V = 1379.22 (8) Å3
Data collection top
Bruker CCD
diffractometer
4216 independent reflections
Radiation source: X-ray tube3753 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.015
Detector resolution: 8.3333 pixels mm-1θmax = 30.6°, θmin = 2.2°
ϕ and ω scansh = 1818
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
k = 1818
Tmin = 0.693, Tmax = 0.746l = 1313
51073 measured reflections
Refinement top
Refinement on F0 restraints
R[F2 > 2σ(F2)] = 0.0230 constraints
wR(F2) = 0.039Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2)
S = 2.71(Δ/σ)max = 0.026
4216 reflectionsΔρmax = 0.65 e Å3
289 parametersΔρmin = 1.40 e Å3
Crystal data top
FMg2O4PV = 1379.22 (8) Å3
Mr = 162.6Z = 16
Monoclinic, P21/nMo Kα radiation
a = 12.7628 (4) ŵ = 1.07 mm1
b = 12.6564 (4) ÅT = 293 K
c = 9.6348 (3) Å0.46 × 0.26 × 0.26 mm
β = 117.5995 (10)°
Data collection top
Bruker CCD
diffractometer
4216 independent reflections
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
3753 reflections with I > 3σ(I)
Tmin = 0.693, Tmax = 0.746Rint = 0.015
51073 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.023289 parameters
wR(F2) = 0.0390 restraints
S = 2.71Δρmax = 0.65 e Å3
4216 reflectionsΔρmin = 1.40 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
P10.425703 (19)0.076466 (18)0.30969 (3)0.00408 (9)
P20.076043 (19)0.071794 (18)0.80361 (3)0.00421 (9)
P30.075387 (19)0.174968 (18)0.30744 (3)0.00414 (9)
P40.424129 (19)0.177235 (18)0.19676 (3)0.00415 (9)
Mg10.91195 (3)0.07041 (2)0.36132 (4)0.00651 (12)
Mg20.59995 (3)0.06944 (3)0.13479 (4)0.00641 (11)
Mg30.91857 (3)0.18215 (2)0.87221 (4)0.00628 (11)
Mg40.60682 (3)0.17777 (3)0.35736 (4)0.00639 (11)
Mg50.19088 (3)0.01888 (3)0.00045 (4)0.00656 (11)
Mg60.30731 (3)0.00470 (3)0.48274 (4)0.00683 (12)
Mg70.31278 (3)0.23253 (3)0.00688 (4)0.00662 (11)
Mg80.19398 (3)0.24447 (3)0.51291 (4)0.00710 (11)
O10.32657 (6)0.11098 (5)0.14876 (8)0.0072 (2)
O20.16464 (6)0.09502 (5)0.63367 (8)0.0076 (2)
O30.17118 (6)0.14367 (5)0.14321 (8)0.0075 (2)
O40.33025 (6)0.15108 (5)0.36360 (8)0.0072 (2)
O50.53641 (6)0.04663 (5)0.29504 (8)0.0072 (2)
O60.95297 (6)0.05275 (6)0.18442 (8)0.0078 (2)
O70.95939 (6)0.20171 (6)0.69681 (8)0.0077 (2)
O80.54107 (6)0.20199 (6)0.19814 (8)0.0072 (2)
O90.62083 (6)0.01785 (5)0.36505 (8)0.0067 (2)
O100.88352 (6)0.02615 (5)0.86120 (8)0.0067 (2)
O110.61859 (6)0.23022 (5)0.13444 (8)0.0068 (2)
O120.88140 (6)0.22592 (5)0.36135 (8)0.0066 (2)
O130.05128 (6)0.08289 (5)0.42166 (8)0.0075 (2)
O140.43958 (6)0.08749 (5)0.07988 (8)0.0072 (2)
O150.45500 (6)0.16598 (5)0.42979 (8)0.0069 (2)
O160.06839 (6)0.16267 (5)0.91490 (8)0.0073 (2)
F10.75481 (5)0.04941 (4)0.34108 (6)0.00959 (19)
F20.71697 (5)0.08346 (4)0.04855 (7)0.0112 (2)
F30.72166 (5)0.16259 (4)0.55240 (7)0.0109 (2)
F40.75948 (4)0.20213 (4)0.15155 (6)0.00925 (19)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
P10.00424 (12)0.00396 (12)0.00353 (12)0.00010 (6)0.00137 (9)0.00003 (7)
P20.00453 (12)0.00423 (12)0.00339 (12)0.00006 (7)0.00142 (9)0.00013 (7)
P30.00447 (12)0.00390 (12)0.00352 (12)0.00007 (6)0.00139 (9)0.00009 (7)
P40.00418 (12)0.00420 (12)0.00350 (12)0.00000 (6)0.00129 (9)0.00005 (7)
Mg10.00768 (15)0.00561 (15)0.00721 (16)0.00026 (10)0.00426 (12)0.00021 (10)
Mg20.00700 (14)0.00561 (15)0.00641 (16)0.00020 (10)0.00293 (12)0.00020 (10)
Mg30.00681 (15)0.00532 (14)0.00752 (16)0.00028 (10)0.00400 (12)0.00008 (10)
Mg40.00683 (15)0.00595 (15)0.00577 (16)0.00015 (10)0.00240 (12)0.00031 (10)
Mg50.00614 (15)0.00734 (15)0.00607 (15)0.00147 (10)0.00270 (12)0.00057 (11)
Mg60.00603 (15)0.00828 (15)0.00611 (16)0.00137 (10)0.00275 (12)0.00085 (11)
Mg70.00651 (15)0.00711 (15)0.00629 (15)0.00142 (10)0.00300 (12)0.00031 (11)
Mg80.00587 (15)0.00925 (15)0.00621 (15)0.00161 (10)0.00282 (12)0.00132 (11)
O10.0063 (3)0.0074 (3)0.0051 (3)0.0006 (2)0.0003 (2)0.0016 (2)
O20.0073 (3)0.0079 (3)0.0048 (3)0.0007 (2)0.0005 (2)0.0011 (2)
O30.0072 (3)0.0075 (3)0.0053 (3)0.0006 (2)0.0006 (2)0.0017 (2)
O40.0065 (3)0.0076 (3)0.0049 (3)0.0004 (2)0.0006 (2)0.0013 (2)
O50.0054 (3)0.0101 (3)0.0071 (3)0.0010 (2)0.0037 (2)0.0006 (2)
O60.0055 (3)0.0116 (3)0.0068 (3)0.0020 (2)0.0033 (2)0.0021 (2)
O70.0058 (3)0.0111 (3)0.0071 (3)0.0017 (2)0.0038 (2)0.0016 (2)
O80.0050 (3)0.0104 (3)0.0066 (3)0.0013 (2)0.0032 (2)0.0012 (2)
O90.0077 (3)0.0049 (3)0.0080 (3)0.0007 (2)0.0042 (2)0.0010 (2)
O100.0081 (3)0.0047 (3)0.0079 (3)0.0002 (2)0.0042 (2)0.0009 (2)
O110.0080 (3)0.0051 (3)0.0078 (3)0.0007 (2)0.0041 (2)0.0009 (2)
O120.0077 (3)0.0047 (3)0.0081 (3)0.0002 (2)0.0043 (2)0.0009 (2)
O130.0093 (3)0.0051 (3)0.0066 (3)0.0007 (2)0.0023 (2)0.0008 (2)
O140.0081 (3)0.0061 (3)0.0064 (3)0.0010 (2)0.0026 (2)0.0010 (2)
O150.0080 (3)0.0053 (3)0.0060 (3)0.0003 (2)0.0021 (2)0.0008 (2)
O160.0082 (3)0.0062 (3)0.0065 (3)0.0012 (2)0.0026 (2)0.0011 (2)
F10.0065 (2)0.0116 (2)0.0106 (3)0.00025 (18)0.0039 (2)0.00256 (19)
F20.0115 (3)0.0103 (2)0.0147 (3)0.00192 (19)0.0086 (2)0.0001 (2)
F30.0115 (3)0.0094 (2)0.0144 (3)0.00207 (18)0.0083 (2)0.0001 (2)
F40.0059 (2)0.0114 (2)0.0104 (3)0.00022 (18)0.0038 (2)0.00235 (19)
Bond lengths (Å) top
P1—O11.5420 (6)Mg3—O16vi2.0712 (7)
P1—O51.5309 (9)Mg3—F4vii1.9515 (7)
P1—O9i1.5349 (8)Mg4—O82.0843 (10)
P1—O151.5367 (7)Mg4—O92.0363 (7)
P2—O21.5265 (7)Mg4—O15viii2.0738 (7)
P2—O6ii1.5398 (8)Mg4—O16v2.0914 (7)
P2—O10i1.5415 (8)Mg4—F3viii2.0302 (9)
P2—O161.5444 (8)Mg4—F42.0599 (5)
P3—O31.5371 (6)Mg5—O12.0292 (7)
P3—O7ii1.5376 (9)Mg5—O32.0321 (8)
P3—O11iii1.5309 (8)Mg5—O6i2.0782 (7)
P3—O131.5330 (8)Mg5—O10ix2.0510 (10)
P4—O41.5312 (6)Mg5—F2i1.9444 (8)
P4—O81.5312 (9)Mg6—O22.0696 (7)
P4—O12iii1.5479 (8)Mg6—O42.1271 (8)
P4—O141.5465 (8)Mg6—O5i2.0805 (7)
Mg1—O62.0138 (10)Mg6—O9x2.0783 (10)
Mg1—O122.0065 (8)Mg6—F1i1.9907 (8)
Mg1—O13iv2.0283 (7)Mg6—F3i2.2000 (6)
Mg1—O13i2.0174 (7)Mg7—O12.0109 (8)
Mg1—F11.9414 (7)Mg7—O32.0495 (7)
Mg2—O52.0700 (10)Mg7—O7iii2.0905 (7)
Mg2—O112.0490 (8)Mg7—O12iii2.0365 (10)
Mg2—O142.1440 (7)Mg7—F3iii1.9441 (8)
Mg2—O14i2.0571 (7)Mg8—O22.1607 (8)
Mg2—F12.0690 (5)Mg8—O42.0428 (7)
Mg2—F22.0254 (9)Mg8—O8iii2.0556 (6)
Mg3—O72.0010 (10)Mg8—O11iii2.0759 (10)
Mg3—O102.0163 (7)Mg8—F2iii2.2402 (7)
Mg3—O15v1.9949 (7)Mg8—F4iii1.9936 (8)
Symmetry codes: (i) x+1, y, z; (ii) x1, y, z1; (iii) x1/2, y+1/2, z1/2; (iv) x+1, y, z+1; (v) x+1/2, y+1/2, z+1/2; (vi) x+1, y, z+2; (vii) x, y, z+1; (viii) x, y, z1; (ix) x+1, y, z+1; (x) x+1, y, z1.
(3b) top
Crystal data top
FFe1.078Mg0.922O4PZ = 8
Mr = 196.6F(000) = 761
Monoclinic, C2/c(0β0)s0†Dx = 3.617 Mg m3
q = 0.345990b*Mo Kα radiation, λ = 0.71073 Å
a = 13.0183 (2) ŵ = 4.99 mm1
b = 6.4149 (1) ÅT = 293 K
c = 9.8411 (1) ÅPrism, dark brown
β = 118.562 (1)°0.16 × 0.16 × 0.06 mm
V = 721.82 (2) Å3
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
2484 independent reflections
Radiation source: X-ray tube2086 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.011
Detector resolution: 8.3333 pixels mm-1θmax = 27.5°, θmin = 2.6°
ϕ and ω scansh = 1616
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
k = 88
Tmin = 0.521, Tmax = 0.745l = 1212
9151 measured reflections
Refinement top
Refinement on F20 restraints
R[F2 > 2σ(F2)] = 0.0222 constraints
wR(F2) = 0.064Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0004I2)
S = 1.75(Δ/σ)max = 0.028
2484 reflectionsΔρmax = 0.40 e Å3
167 parametersΔρmin = 0.45 e Å3
Crystal data top
FFe1.078Mg0.922O4Pβ = 118.562 (1)°
Mr = 196.6V = 721.82 (2) Å3
Monoclinic, C2/c(0β0)s0†Z = 8
q = 0.345990b*Mo Kα radiation
a = 13.0183 (2) ŵ = 4.99 mm1
b = 6.4149 (1) ÅT = 293 K
c = 9.8411 (1) Å0.16 × 0.16 × 0.06 mm
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
2484 independent reflections
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
2086 reflections with I > 3σ(I)
Tmin = 0.521, Tmax = 0.745Rint = 0.011
9151 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.022167 parameters
wR(F2) = 0.0640 restraints
S = 1.75Δρmax = 0.40 e Å3
2484 reflectionsΔρmin = 0.45 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Fe10.058512 (19)0.27144 (4)0.00197 (3)0.00876 (11)0.691 (2)
Mg10.058512 (19)0.27144 (4)0.00197 (3)0.00876 (11)0.309 (2)
Fe20.15729 (3)0.10648 (5)0.14075 (3)0.00817 (13)0.3874 (16)
Mg20.15729 (3)0.10648 (5)0.14075 (3)0.00817 (13)0.6126 (16)
P10.17535 (3)0.59597 (5)0.30569 (4)0.00575 (14)
F10.01035 (14)0.1317 (3)0.13959 (16)0.0248 (5)0.531 (3)
F20.0283 (2)0.0835 (3)0.0704 (4)0.0217 (7)0.469 (3)
O10.08125 (7)0.53788 (14)0.14224 (10)0.0114 (3)
O20.19389 (8)0.41819 (14)0.42004 (11)0.0101 (4)
O30.13343 (9)0.21184 (13)0.14023 (11)0.0099 (4)
O40.29025 (8)0.64362 (15)0.30467 (11)0.0105 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Fe10.00776 (15)0.01085 (14)0.00696 (15)0.00271 (8)0.00296 (11)0.00080 (8)
Mg10.00776 (15)0.01085 (14)0.00696 (15)0.00271 (8)0.00296 (11)0.00080 (8)
Fe20.01027 (17)0.00634 (17)0.00807 (18)0.00035 (10)0.00453 (13)0.00048 (10)
Mg20.01027 (17)0.00634 (17)0.00807 (18)0.00035 (10)0.00453 (13)0.00048 (10)
P10.00524 (18)0.00566 (18)0.00505 (18)0.00003 (11)0.00140 (14)0.00011 (11)
F10.0120 (6)0.0255 (6)0.0372 (8)0.0038 (5)0.0121 (6)0.0173 (6)
F20.0183 (7)0.0155 (6)0.0378 (11)0.0004 (5)0.0187 (8)0.0071 (6)
O10.0097 (5)0.0125 (5)0.0078 (4)0.0009 (3)0.0009 (4)0.0015 (4)
O20.0133 (5)0.0077 (4)0.0088 (5)0.0002 (3)0.0049 (4)0.0018 (3)
O30.0104 (5)0.0080 (4)0.0109 (5)0.0020 (3)0.0047 (4)0.0016 (4)
O40.0078 (5)0.0134 (4)0.0107 (5)0.0020 (3)0.0048 (4)0.0009 (4)
Bond lengths (Å) top
AverageMinimumMaximum
Fe1—F12.103 (6)2.057 (4)2.188 (8)
Fe1—F22.033 (11)2.019 (17)2.044 (5)
Fe1—F2i2.324 (8)2.294 (13)2.334 (3)
Fe1—O12.1297 (13)2.0895 (13)2.1752 (12)
Fe1—O1ii2.0867 (11)2.0792 (11)2.0937 (11)
Fe1—O32.0893 (17)2.0671 (17)2.1135 (17)
Fe1—O4iii2.1431 (10)2.1382 (10)2.1464 (10)
Mg1—F12.103 (6)2.057 (4)2.188 (8)
Mg1—F22.033 (11)2.019 (17)2.044 (5)
Mg1—F2i2.324 (8)2.294 (13)2.334 (3)
Mg1—O12.1297 (13)2.0895 (13)2.1752 (12)
Mg1—O1ii2.0867 (11)2.0792 (11)2.0937 (11)
Mg1—O32.0893 (17)2.0671 (17)2.1135 (17)
Mg1—O4iii2.1431 (10)2.1382 (10)2.1464 (10)
Fe2—F11.983 (7)1.921 (9)2.022 (4)
Fe2—F1iv2.180 (4)2.164 (5)2.192 (4)
Fe2—F22.049 (12)2.031 (7)2.090 (19)
Fe2—O2iv2.0764 (12)2.0697 (12)2.0830 (12)
Fe2—O2v2.1157 (10)2.0845 (10)2.1477 (10)
Fe2—O3i2.0669 (12)2.0591 (12)2.0730 (12)
Fe2—O4vi2.0460 (16)2.0226 (16)2.0725 (17)
Mg2—F11.983 (7)1.921 (9)2.022 (4)
Mg2—F1iv2.180 (4)2.164 (5)2.192 (4)
Mg2—F22.049 (12)2.031 (7)2.090 (19)
Mg2—O2iv2.0764 (12)2.0697 (12)2.0830 (12)
Mg2—O2v2.1157 (10)2.0845 (10)2.1477 (10)
Mg2—O3i2.0669 (12)2.0591 (12)2.0730 (12)
Mg2—O4vi2.0460 (16)2.0226 (16)2.0725 (17)
P1—O11.5314 (11)1.5281 (11)1.5361 (10)
P1—O21.5390 (13)1.5344 (13)1.5438 (13)
P1—O3vii1.5424 (14)1.5358 (14)1.5489 (14)
P1—O41.5325 (15)1.5282 (15)1.5365 (15)
Symmetry codes: (i) x1, x2, x3, x4; (ii) x1, x2+1, x3, x4; (iii) x1+1/2, x21/2, x3+1/2, x4+1/2; (iv) x1, x2, x3+1/2, x4+1/2; (v) x11/2, x2+1/2, x31/2, x4+1/2; (vi) x11/2, x21/2, x3, x4; (vii) x1, x2+1, x3+1/2, x4+1/2.
(5b) top
Crystal data top
FFe0.649Mg1.351O4PZ = 8
Mr = 183F(000) = 711
Monoclinic, C2/c(0β0)s0†Dx = 3.428 Mg m3
q = 0.410660b*Mo Kα radiation, λ = 0.71073 Å
a = 12.8840 (2) ŵ = 3.47 mm1
b = 6.3889 (1) ÅT = 293 K
c = 9.7384 (1) ÅPrism, orange
β = 117.799 (1)°0.2 × 0.15 × 0.15 mm
V = 709.10 (2) Å3
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
2439 independent reflections
Radiation source: X-ray tube2216 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.010
Detector resolution: 8.3333 pixels mm-1θmax = 27.5°, θmin = 2.6°
ϕ and ω scansh = 1614
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
k = 88
Tmin = 0.648, Tmax = 0.746l = 1212
6943 measured reflections
Refinement top
Refinement on F20 restraints
R[F2 > 2σ(F2)] = 0.0232 constraints
wR(F2) = 0.065Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0004I2)
S = 2.06(Δ/σ)max = 0.019
2439 reflectionsΔρmax = 0.48 e Å3
228 parametersΔρmin = 0.57 e Å3
Crystal data top
FFe0.649Mg1.351O4Pβ = 117.799 (1)°
Mr = 183V = 709.10 (2) Å3
Monoclinic, C2/c(0β0)s0†Z = 8
q = 0.410660b*Mo Kα radiation
a = 12.8840 (2) ŵ = 3.47 mm1
b = 6.3889 (1) ÅT = 293 K
c = 9.7384 (1) Å0.2 × 0.15 × 0.15 mm
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
2439 independent reflections
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
2216 reflections with I > 3σ(I)
Tmin = 0.648, Tmax = 0.746Rint = 0.010
6943 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.023228 parameters
wR(F2) = 0.0650 restraints
S = 2.06Δρmax = 0.48 e Å3
2439 reflectionsΔρmin = 0.57 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Fe10.05876 (2)0.27212 (4)0.00649 (3)0.00826 (12)0.429 (2)
Mg10.05876 (2)0.27212 (4)0.00649 (3)0.00826 (12)0.571 (2)
Fe20.15593 (3)0.10788 (5)0.13668 (4)0.00846 (14)0.2019 (17)
Mg20.15593 (3)0.10788 (5)0.13668 (4)0.00846 (14)0.7981 (17)
P10.17494 (3)0.59944 (4)0.30565 (3)0.00481 (12)
F10.00797 (14)0.1513 (3)0.15536 (19)0.0198 (4)0.5042 (19)
F20.03358 (14)0.0799 (2)0.0500 (2)0.0204 (4)0.4958 (19)
O10.08041 (7)0.54146 (13)0.14224 (10)0.0101 (3)
O20.19424 (8)0.42072 (13)0.42064 (10)0.0092 (3)
O30.13283 (8)0.20889 (13)0.13783 (10)0.0085 (3)
O40.29017 (7)0.64788 (13)0.30248 (10)0.0092 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Fe10.00733 (16)0.01029 (14)0.00707 (16)0.00228 (9)0.00327 (12)0.00041 (8)
Mg10.00733 (16)0.01029 (14)0.00707 (16)0.00228 (9)0.00327 (12)0.00041 (8)
Fe20.01196 (18)0.00600 (17)0.00815 (18)0.00030 (11)0.00530 (14)0.00044 (10)
Mg20.01196 (18)0.00600 (17)0.00815 (18)0.00030 (11)0.00530 (14)0.00044 (10)
P10.00453 (17)0.00506 (16)0.00447 (17)0.00009 (10)0.00179 (13)0.00010 (9)
F10.0126 (5)0.0244 (5)0.0221 (5)0.0002 (4)0.0079 (4)0.0071 (4)
F20.0206 (5)0.0170 (5)0.0294 (6)0.0026 (4)0.0166 (5)0.0008 (4)
O10.0087 (4)0.0115 (4)0.0067 (4)0.0010 (3)0.0007 (3)0.0021 (3)
O20.0122 (4)0.0072 (3)0.0078 (4)0.0007 (3)0.0043 (3)0.0015 (3)
O30.0096 (4)0.0063 (4)0.0104 (4)0.0013 (3)0.0052 (4)0.0014 (3)
O40.0069 (4)0.0123 (4)0.0100 (4)0.0016 (3)0.0051 (3)0.0013 (3)
Bond lengths (Å) top
AverageMinimumMaximum
Fe1—F12.072 (7)2.052 (5)2.104 (10)
Fe1—F21.978 (7)1.914 (11)2.017 (3)
Fe1—F2i2.241 (5)2.191 (2)2.343 (8)
Fe1—O12.1154 (12)2.0403 (12)2.2050 (12)
Fe1—O1ii2.0768 (10)2.0707 (10)2.0812 (10)
Fe1—O32.0766 (16)2.0465 (15)2.1123 (16)
Fe1—O4iii2.1252 (10)2.1104 (10)2.1411 (10)
Mg1—F12.072 (7)2.052 (5)2.104 (10)
Mg1—F21.978 (7)1.914 (11)2.017 (3)
Mg1—F2i2.241 (5)2.191 (2)2.343 (8)
Mg1—O12.1154 (12)2.0403 (12)2.2050 (12)
Mg1—O1ii2.0768 (10)2.0707 (10)2.0812 (10)
Mg1—O32.0766 (16)2.0465 (15)2.1123 (16)
Mg1—O4iii2.1252 (10)2.1104 (10)2.1411 (10)
Fe2—F11.947 (7)1.854 (9)1.998 (3)
Fe2—F1iv2.085 (5)2.021 (2)2.197 (6)
Fe2—F22.032 (8)2.009 (4)2.081 (12)
Fe2—O2iv2.0722 (11)2.0475 (11)2.0972 (11)
Fe2—O2v2.0994 (10)2.0402 (10)2.1615 (10)
Fe2—O3i2.0477 (11)2.0288 (11)2.0635 (11)
Fe2—O4vi2.0541 (16)2.0119 (15)2.1046 (16)
Mg2—F11.947 (7)1.854 (9)1.998 (3)
Mg2—F1iv2.085 (5)2.021 (2)2.197 (6)
Mg2—F22.032 (8)2.009 (4)2.081 (12)
Mg2—O2iv2.0722 (11)2.0475 (11)2.0972 (11)
Mg2—O2v2.0994 (10)2.0402 (10)2.1615 (10)
Mg2—O3i2.0477 (11)2.0288 (11)2.0635 (11)
Mg2—O4vi2.0541 (16)2.0119 (15)2.1046 (16)
P1—O11.5334 (10)1.5284 (10)1.5419 (10)
P1—O21.5388 (12)1.5311 (12)1.5474 (12)
P1—O3vii1.5415 (13)1.5333 (13)1.5494 (13)
P1—O41.5335 (14)1.5266 (14)1.5400 (14)
Symmetry codes: (i) x1, x2, x3, x4; (ii) x1, x2+1, x3, x4; (iii) x1+1/2, x21/2, x3+1/2, x4+1/2; (iv) x1, x2, x3+1/2, x4+1/2; (v) x11/2, x2+1/2, x31/2, x4+1/2; (vi) x11/2, x21/2, x3, x4; (vii) x1, x2+1, x3+1/2, x4+1/2.
(7b) top
Crystal data top
FFe0.185Mg1.815O4PZ = 8
Mr = 168.43F(000) = 661
Monoclinic, C2/c(0β0)s0†Dx = 3.223 Mg m3
q = 0.427560b*Mo Kα radiation, λ = 0.71073 Å
a = 12.7978 (2) ŵ = 1.8 mm1
b = 6.3523 (1) ÅT = 293 K
c = 9.6642 (1) ÅPrism, orange
β = 117.567 (1)°0.6 × 0.16 × 0.1 mm
V = 696.46 (2) Å3
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
7370 independent reflections
Radiation source: X-ray tube3766 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.016
Detector resolution: 8.3333 pixels mm-1θmax = 30.5°, θmin = 1.9°
ϕ and ω scansh = 1817
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
k = 1010
Tmin = 0.664, Tmax = 0.746l = 1313
17606 measured reflections
Refinement top
Refinement on F20 restraints
R[F2 > 2σ(F2)] = 0.0312 constraints
wR(F2) = 0.091Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0004I2)
S = 1.63(Δ/σ)max = 0.008
7370 reflectionsΔρmax = 0.68 e Å3
504 parametersΔρmin = 0.95 e Å3
Crystal data top
FFe0.185Mg1.815O4Pβ = 117.567 (1)°
Mr = 168.43V = 696.46 (2) Å3
Monoclinic, C2/c(0β0)s0†Z = 8
q = 0.427560b*Mo Kα radiation
a = 12.7978 (2) ŵ = 1.8 mm1
b = 6.3523 (1) ÅT = 293 K
c = 9.6642 (1) Å0.6 × 0.16 × 0.1 mm
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
7370 independent reflections
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
3766 reflections with I > 3σ(I)
Tmin = 0.664, Tmax = 0.746Rint = 0.016
17606 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.031504 parameters
wR(F2) = 0.0910 restraints
S = 1.63Δρmax = 0.68 e Å3
7370 reflectionsΔρmin = 0.95 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Fe10.05889 (2)0.27302 (4)0.00846 (3)0.00757 (10)0.1456 (14)
Mg10.05889 (2)0.27302 (4)0.00846 (3)0.00757 (10)0.8544 (14)
Fe20.15599 (3)0.10911 (4)0.13584 (3)0.00669 (11)0.0399 (13)
Mg20.15599 (3)0.10911 (4)0.13584 (3)0.00669 (11)0.9601 (13)
P10.174704 (18)0.60129 (3)0.30584 (2)0.00448 (8)
F10.00762 (6)0.15371 (11)0.15615 (8)0.0145 (3)0.5040 (9)
F20.03186 (6)0.07923 (11)0.04913 (8)0.0147 (3)0.4960 (9)
O10.08029 (5)0.54360 (10)0.14142 (7)0.0084 (2)
O20.19394 (6)0.42101 (9)0.42128 (7)0.0080 (2)
O30.13194 (6)0.20713 (9)0.13696 (7)0.0074 (2)
O40.29091 (5)0.65083 (10)0.30309 (7)0.0080 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Fe10.00720 (14)0.00883 (13)0.00658 (13)0.00174 (8)0.00309 (10)0.00026 (8)
Mg10.00720 (14)0.00883 (13)0.00658 (13)0.00174 (8)0.00309 (10)0.00026 (8)
Fe20.00922 (16)0.00469 (14)0.00670 (15)0.00024 (9)0.00414 (12)0.00027 (9)
Mg20.00922 (16)0.00469 (14)0.00670 (15)0.00024 (9)0.00414 (12)0.00027 (9)
P10.00484 (11)0.00405 (11)0.00430 (10)0.00011 (6)0.00191 (8)0.00005 (6)
F10.0095 (4)0.0162 (4)0.0182 (4)0.0000 (3)0.0068 (3)0.0056 (3)
F20.0150 (4)0.0119 (4)0.0220 (4)0.0020 (3)0.0126 (3)0.0002 (3)
O10.0081 (3)0.0087 (3)0.0060 (2)0.0007 (2)0.0011 (2)0.0016 (2)
O20.0106 (3)0.0056 (2)0.0068 (3)0.0007 (2)0.0033 (2)0.0009 (2)
O30.0085 (3)0.0055 (2)0.0089 (3)0.0010 (2)0.0045 (2)0.0011 (2)
O40.0064 (3)0.0106 (3)0.0081 (3)0.0018 (2)0.0042 (2)0.0010 (2)
Bond lengths (Å) top
AverageMinimumMaximum
Fe1—F21.955 (2)1.879 (3)1.981 (3)
Fe1—F2i2.221 (2)2.1813 (19)2.334 (3)
Fe1—O12.096 (3)2.012 (3)2.200 (3)
Fe1—O1ii2.060 (2)2.043 (2)2.083 (2)
Fe1—O32.063 (3)2.033 (3)2.089 (3)
Fe1—O4iii2.095 (2)2.078 (2)2.108 (2)
Mg1—F21.955 (2)1.879 (3)1.981 (3)
Mg1—F2i2.221 (2)2.1813 (19)2.334 (3)
Mg1—O12.096 (3)2.012 (3)2.200 (3)
Mg1—O1ii2.060 (2)2.043 (2)2.083 (2)
Mg1—O32.063 (3)2.033 (3)2.089 (3)
Mg1—O4iii2.095 (2)2.078 (2)2.108 (2)
Fe2—F22.030 (3)2.010 (3)2.088 (3)
Fe2—O2iv2.054 (3)2.015 (3)2.103 (3)
Fe2—O2v2.086 (2)2.020 (2)2.170 (2)
Fe2—O3i2.035 (3)2.015 (3)2.057 (3)
Fe2—O4vi2.045 (3)1.997 (3)2.103 (3)
Mg2—F22.030 (3)2.010 (3)2.088 (3)
Mg2—O2iv2.054 (3)2.015 (3)2.103 (3)
Mg2—O2v2.086 (2)2.020 (2)2.170 (2)
Mg2—O3i2.035 (3)2.015 (3)2.057 (3)
Mg2—O4vi2.045 (3)1.997 (3)2.103 (3)
P1—O11.533 (2)1.523 (2)1.544 (2)
P1—O21.540 (3)1.531 (3)1.548 (3)
P1—O3vii1.539 (3)1.531 (3)1.549 (3)
P1—O41.535 (3)1.529 (3)1.546 (3)
Symmetry codes: (i) x1, x2, x3, x4; (ii) x1, x2+1, x3, x4; (iii) x1+1/2, x21/2, x3+1/2, x4+1/2; (iv) x1, x2, x3+1/2, x4+1/2; (v) x11/2, x2+1/2, x31/2, x4+1/2; (vi) x11/2, x21/2, x3, x4; (vii) x1, x2+1, x3+1/2, x4+1/2.
(9b) top
Crystal data top
FFe0.029Mg1.971O4PZ = 8
Mr = 163.5F(000) = 643
Monoclinic, C2/c(0β0)s0†Dx = 3.135 Mg m3
q = 0.446520b*Mo Kα radiation, λ = 0.71073 Å
a = 12.7707 (2) ŵ = 1.18 mm1
b = 6.3394 (1) ÅT = 293 K
c = 9.6462 (1) ÅPrism, colourless
β = 117.5240 (5)°0.25 × 0.25 × 0.1 mm
V = 692.55 (2) Å3
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
7409 independent reflections
Radiation source: X-ray tube4855 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.010
Detector resolution: 8.3333 pixels mm-1θmax = 30.6°, θmin = 1.8°
ϕ and ω scansh = 1818
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
k = 1010
Tmin = 0.688, Tmax = 0.746l = 1313
26453 measured reflections
Refinement top
Refinement on F20 restraints
R[F2 > 2σ(F2)] = 0.0332 constraints
wR(F2) = 0.104Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0004I2)
S = 2.38(Δ/σ)max = 0.027
7409 reflectionsΔρmax = 0.71 e Å3
503 parametersΔρmin = 0.35 e Å3
Crystal data top
FFe0.029Mg1.971O4Pβ = 117.5240 (5)°
Mr = 163.5V = 692.55 (2) Å3
Monoclinic, C2/c(0β0)s0†Z = 8
q = 0.446520b*Mo Kα radiation
a = 12.7707 (2) ŵ = 1.18 mm1
b = 6.3394 (1) ÅT = 293 K
c = 9.6462 (1) Å0.25 × 0.25 × 0.1 mm
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
7409 independent reflections
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
4855 reflections with I > 3σ(I)
Tmin = 0.688, Tmax = 0.746Rint = 0.010
26453 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.033503 parameters
wR(F2) = 0.1040 restraints
S = 2.38Δρmax = 0.71 e Å3
7409 reflectionsΔρmin = 0.35 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Fe10.05882 (2)0.27289 (4)0.00922 (3)0.00693 (11)0.0292 (16)
Mg10.05882 (2)0.27289 (4)0.00922 (3)0.00693 (11)0.9707 (16)
Fe20.15619 (2)0.10962 (4)0.13559 (3)0.00585 (10)0
Mg20.15619 (2)0.10962 (4)0.13559 (3)0.00585 (10)
P10.174600 (16)0.60201 (3)0.30588 (2)0.00369 (8)
F10.00761 (5)0.15484 (10)0.15630 (7)0.0126 (2)0.5016 (7)
F20.03140 (6)0.07905 (9)0.04856 (7)0.0134 (2)0.4984 (7)
O10.08031 (5)0.54440 (9)0.14104 (7)0.00726 (18)
O20.19384 (5)0.42137 (9)0.42132 (7)0.00723 (18)
O30.13158 (5)0.20648 (9)0.13671 (7)0.00655 (19)
O40.29115 (5)0.65210 (10)0.30350 (6)0.00720 (19)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Fe10.00632 (16)0.00825 (15)0.00614 (14)0.00162 (9)0.00280 (11)0.00055 (8)
Mg10.00632 (16)0.00825 (15)0.00614 (14)0.00162 (9)0.00280 (11)0.00055 (8)
Fe20.00745 (13)0.00435 (13)0.00604 (13)0.00020 (8)0.00336 (10)0.00029 (8)
Mg20.00745 (13)0.00435 (13)0.00604 (13)0.00020 (8)0.00336 (10)0.00029 (8)
P10.00396 (11)0.00329 (11)0.00342 (10)0.00006 (5)0.00136 (8)0.00008 (5)
F10.0073 (3)0.0146 (3)0.0154 (3)0.0001 (2)0.0048 (2)0.0048 (2)
F20.0132 (3)0.0103 (3)0.0205 (3)0.0017 (2)0.0111 (3)0.0011 (2)
O10.0070 (3)0.0072 (3)0.0052 (2)0.00087 (18)0.00078 (19)0.00156 (18)
O20.0093 (2)0.0052 (2)0.0060 (2)0.00108 (18)0.0025 (2)0.00080 (18)
O30.0072 (3)0.0043 (2)0.0084 (2)0.00074 (18)0.0038 (2)0.00104 (17)
O40.0053 (3)0.0098 (3)0.0070 (2)0.00186 (19)0.0032 (2)0.00122 (19)
Bond lengths (Å) top
AverageMinimumMaximum
Fe1—Fe1i3.2195 (14)3.0948 (14)3.3498 (14)
Fe1—Mg1000
Fe1—Mg1i3.2195 (14)3.0948 (14)3.3498 (14)
Fe1—Fe2ii3.2397 (13)3.1325 (13)3.3404 (13)
Fe1—Fe2iii3.3260 (16)3.2304 (16)3.4187 (16)
Fe1—Mg23.6344 (17)3.6188 (17)3.6517 (17)
Fe1—Mg2iv3.8972 (14)3.6988 (14)4.1103 (15)
Fe1—Mg2ii3.2290 (13)3.1257 (13)3.3404 (13)
Fe1—Mg2iii3.3164 (16)3.2164 (16)3.4187 (16)
Fe1—P1v3.0577 (15)2.9473 (15)3.1698 (15)
Fe1—F12.014 (2)1.984 (2)2.073 (2)
Fe1—F21.940 (2)1.861 (2)1.968 (2)
Fe1—F2iii2.2153 (18)2.1759 (16)2.3300 (19)
Fe1—O12.091 (2)2.004 (2)2.196 (2)
Fe1—O1i2.0547 (19)2.0327 (19)2.0819 (19)
Fe1—O32.061 (3)2.033 (3)2.086 (3)
Fe1—O4vi2.0827 (18)2.0604 (18)2.0985 (18)
Mg1—Mg1iii3.7437 (14)3.7336 (14)3.7544 (14)
Mg1—Mg1i3.2195 (14)3.0948 (14)3.3498 (14)
Mg1—Fe23.6450 (17)3.6275 (17)3.6517 (17)
Mg1—Fe2iv3.8075 (14)3.6988 (14)3.9257 (14)
Mg1—Fe2ii3.2397 (13)3.1325 (13)3.3404 (13)
Mg1—Fe2iii3.3260 (16)3.2304 (16)3.4187 (16)
Mg1—Mg23.6344 (17)3.6188 (17)3.6517 (17)
Mg1—Mg2iv3.8972 (14)3.6988 (14)4.1103 (15)
Mg1—Mg2ii3.2290 (13)3.1257 (13)3.3404 (13)
Mg1—Mg2iii3.3164 (16)3.2164 (16)3.4187 (16)
Mg1—Mg2vii4.1557 (12)4.0594 (12)4.2548 (12)
Mg1—P13.2918 (11)3.2496 (11)3.3389 (11)
Mg1—P1vi3.2166 (11)3.1953 (12)3.2521 (11)
Mg1—P1i3.2228 (9)3.1849 (9)3.2583 (9)
Mg1—P1v3.0577 (15)2.9473 (15)3.1698 (15)
Mg1—F12.014 (2)1.984 (2)2.073 (2)
Mg1—F21.940 (2)1.861 (2)1.968 (2)
Mg1—F2iii2.2153 (18)2.1759 (16)2.3300 (19)
Mg1—O12.091 (2)2.004 (2)2.196 (2)
Mg1—O1i2.0547 (19)2.0327 (19)2.0819 (19)
Mg1—O32.061 (3)2.033 (3)2.086 (3)
Mg1—O4vi2.0827 (18)2.0604 (18)2.0985 (18)
Fe2—Fe2viii3.1915 (12)3.1695 (12)3.2078 (12)
Fe2—Mg2000
Fe2—Mg2ii3.5566 (13)3.5498 (13)3.5635 (13)
Fe2—Mg2viii3.1709 (12)3.1465 (12)3.2078 (12)
Fe2—F11.9391 (19)1.852 (2)1.9738 (18)
Fe2—F1ii2.0821 (15)2.0658 (13)2.1314 (15)
Fe2—F22.034 (2)2.020 (2)2.064 (3)
Fe2—O2ii2.037 (2)2.000 (2)2.074 (2)
Fe2—O2ix2.1034 (17)2.0386 (17)2.1659 (17)
Fe2—O3iii2.033 (2)2.018 (2)2.057 (2)
Fe2—O4x2.033 (3)1.995 (3)2.078 (3)
Mg2—Mg2ii3.5566 (13)3.5498 (13)3.5635 (13)
Mg2—Mg2viii3.1580 (12)3.1279 (12)3.2078 (12)
Mg2—P1x3.2650 (16)3.1388 (16)3.3750 (16)
Mg2—P1xi3.2967 (12)3.2535 (12)3.3365 (12)
Mg2—P1ii3.2020 (12)3.1276 (12)3.2831 (12)
Mg2—P1ix3.2009 (10)3.1371 (10)3.2505 (10)
Mg2—F11.936 (2)1.852 (2)1.9738 (18)
Mg2—F1ii2.0760 (14)2.0324 (13)2.1791 (15)
Mg2—F22.037 (2)2.018 (2)2.103 (3)
Mg2—O2ii2.048 (2)2.000 (2)2.105 (2)
Mg2—O2ix2.0813 (17)2.0192 (17)2.1659 (17)
Mg2—O3iii2.030 (2)2.009 (2)2.057 (2)
Mg2—O4x2.043 (3)1.995 (3)2.099 (3)
P1—O11.5328 (17)1.5250 (17)1.5448 (16)
P1—O21.539 (2)1.531 (2)1.546 (2)
P1—O3xii1.538 (2)1.528 (2)1.550 (2)
P1—O41.535 (2)1.530 (3)1.544 (2)
F1—F1ii1.826 (3)1.826 (3)1.826 (3)
Symmetry codes: (i) x1, x2+1, x3, x4; (ii) x1, x2, x3+1/2, x4+1/2; (iii) x1, x2, x3, x4; (iv) x1+1/2, x2+1/2, x3, x4; (v) x1, x2+1, x31/2, x4+1/2; (vi) x1+1/2, x21/2, x3+1/2, x4+1/2; (vii) x1, x2, x31/2, x4+1/2; (viii) x11/2, x2+1/2, x3, x4; (ix) x11/2, x2+1/2, x31/2, x4+1/2; (x) x11/2, x21/2, x3, x4; (xi) x1, x21, x3+1/2, x4+1/2; (xii) x1, x2+1, x3+1/2, x4+1/2.
(2b) top
Crystal data top
FFe0Mg2O4PZ = 8
Mr = 162.6F(000) = 320
Monoclinic, C2/c(0β0)s0†Dx = 3.131 Mg m3
q = 0.500000b*Mo Kα radiation, λ = 0.71073 Å
a = 12.7633 (4) ŵ = 1.07 mm1
b = 6.3282 (2) ÅT = 293 K
c = 9.6350 (3) ÅPrism, colourless
β = 117.5985 (11)°0.46 × 0.26 × 0.26 mm
V = 689.66 (4) Å3
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
3160 independent reflections
Radiation source: X-ray tube2999 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.009
Detector resolution: 8.3333 pixels mm-1θmax = 30.6°, θmin = 2.4°
ϕ and ω scansh = 1818
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
k = 99
Tmin = 0.693, Tmax = 0.746l = 1313
12149 measured reflections
Refinement top
Refinement on F20 restraints
R[F2 > 2σ(F2)] = 0.0162 constraints
wR(F2) = 0.055Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0004I2)
S = 2.01(Δ/σ)max = 0.003
3160 reflectionsΔρmax = 0.43 e Å3
227 parametersΔρmin = 0.31 e Å3
Crystal data top
FFe0Mg2O4Pβ = 117.5985 (11)°
Mr = 162.6V = 689.66 (4) Å3
Monoclinic, C2/c(0β0)s0†Z = 8
q = 0.500000b*Mo Kα radiation
a = 12.7633 (4) ŵ = 1.07 mm1
b = 6.3282 (2) ÅT = 293 K
c = 9.6350 (3) Å0.46 × 0.26 × 0.26 mm
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Data collection top
Bruker CCD
diffractometer
3160 independent reflections
Absorption correction: multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
2999 reflections with I > 3σ(I)
Tmin = 0.693, Tmax = 0.746Rint = 0.009
12149 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.016227 parameters
wR(F2) = 0.0550 restraints
S = 2.01Δρmax = 0.43 e Å3
3160 reflectionsΔρmin = 0.31 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Mg10.058804 (17)0.27328 (3)0.00936 (2)0.00724 (7)
Mg20.155930 (16)0.10997 (3)0.13591 (2)0.00677 (7)
P10.174579 (11)0.60199 (2)0.305995 (17)0.00451 (6)
F10.00712 (3)0.15274 (6)0.15522 (5)0.01013 (14)0.5
F20.03064 (4)0.07910 (6)0.05042 (5)0.01167 (15)0.5
O10.08028 (3)0.54446 (6)0.14062 (5)0.00783 (13)
O20.19369 (4)0.42109 (6)0.42158 (5)0.00767 (13)
O30.13137 (4)0.20622 (7)0.13675 (5)0.00706 (14)
O40.29141 (4)0.65201 (7)0.30402 (5)0.00794 (14)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mg10.00668 (10)0.00846 (9)0.00656 (10)0.00133 (6)0.00304 (8)0.00062 (6)
Mg20.00736 (9)0.00591 (10)0.00729 (11)0.00018 (6)0.00360 (7)0.00025 (6)
P10.00461 (8)0.00443 (8)0.00404 (9)0.00003 (4)0.00162 (6)0.00010 (4)
F10.00704 (17)0.01214 (18)0.0113 (2)0.00020 (13)0.00434 (15)0.00264 (14)
F20.01217 (18)0.01044 (18)0.0153 (2)0.00177 (13)0.00886 (16)0.00015 (15)
O10.00750 (17)0.00798 (17)0.00552 (18)0.00067 (12)0.00092 (14)0.00125 (13)
O20.00915 (16)0.00607 (16)0.00643 (19)0.00069 (12)0.00245 (14)0.00106 (13)
O30.00806 (18)0.00545 (17)0.00824 (19)0.00049 (13)0.00427 (15)0.00094 (13)
O40.00579 (17)0.01112 (18)0.00753 (19)0.00164 (13)0.00361 (15)0.00143 (14)
Bond lengths (Å) top
AverageMinimumMaximum
Mg1—F11.9931 (13)1.9931 (13)1.9931 (13)
Mg1—F21.9416 (10)1.9416 (10)1.9416 (10)
Mg1—O12.0864 (7)2.0121 (7)2.1607 (7)
Mg1—O32.0592 (9)2.0395 (9)2.0789 (9)
Mg1—F21i2.2415 (5)2.2415 (5)2.2415 (5)
Mg1—O11ii2.0481 (6)2.0447 (6)2.0516 (6)
Mg1—O41iii2.0737 (6)2.0560 (6)2.0914 (6)
Mg2—F11.9541 (11)1.9541 (11)1.9541 (11)
Mg2—F1iv2.0578 (8)2.0578 (8)2.0578 (8)
Mg2—F22.0376 (12)2.0376 (12)2.0376 (12)
Mg2—O2iv2.0416 (6)1.9943 (6)2.0890 (6)
Mg2—O2v2.0778 (6)2.0776 (6)2.0779 (6)
Mg2—O31i2.0285 (6)2.0180 (6)2.0390 (6)
Mg2—O41vi2.0429 (9)2.0024 (8)2.0835 (9)
P1—O11.5353 (5)1.5272 (6)1.5433 (5)
P1—O21.5408 (6)1.5373 (6)1.5443 (7)
P1—O41.5388 (7)1.5349 (8)1.5428 (7)
P1—O31vii1.5379 (7)1.5344 (7)1.5413 (7)
Mg11—F2i2.1992 (8)2.1992 (8)2.1992 (8)
Mg11—O1ii2.0480 (6)2.0279 (6)2.0681 (6)
Mg11—O4viii2.0769 (6)2.0754 (6)2.0783 (6)
Mg11—F111.9916 (6)1.9916 (6)1.9916 (6)
Mg11—F211.9449 (7)1.9449 (7)1.9449 (7)
Mg11—O112.0809 (7)2.0336 (7)2.1282 (7)
Mg11—O312.0618 (9)2.0481 (9)2.0755 (9)
Mg21—O3i2.0263 (6)2.0046 (6)2.0479 (6)
Mg21—O42.0423 (9)2.0137 (9)2.0709 (9)
Mg21—F111.9372 (6)1.9372 (6)1.9372 (6)
Mg21—F11viii2.0731 (4)2.0731 (4)2.0731 (4)
Mg21—F212.0203 (8)2.0203 (8)2.0203 (8)
Mg21—O21viii2.0420 (6)2.0223 (6)2.0616 (6)
Mg21—O21ix2.0813 (6)2.0228 (6)2.1399 (6)
P11—O3x1.5373 (7)1.5284 (7)1.5462 (7)
P11—O111.5312 (5)1.5283 (5)1.5341 (5)
P11—O211.5371 (6)1.5298 (6)1.5443 (7)
P11—O411.5332 (7)1.5301 (7)1.5363 (7)
Symmetry codes: (i) x1, x2, x3, x4; (ii) x1, x2+1, x3, x4; (iii) x1+1, x21, x3+1/2, x4+1/2; (iv) x1, x2, x3+1/2, x4+1/2; (v) x11, x2, x31/2, x4+1/2; (vi) x11, x21, x3, x4; (vii) x11, x2+1, x3+1/2, x4+1/2; (viii) x1+1, x2, x3+1/2, x4+1/2; (ix) x11, x2+1, x31/2, x4+1/2; (x) x1, x2+1, x3+1/2, x4+1/2.

Experimental details

(I)(3b)(5b)(7b)
Crystal data
Chemical formulaFMg2O4PFFe1.078Mg0.922O4PFFe0.649Mg1.351O4PFFe0.185Mg1.815O4P
Mr162.6196.6183168.43
Crystal system, space groupMonoclinic, P21/nMonoclinic, C2/c(0β0)s0†Monoclinic, C2/c(0β0)s0‡Monoclinic, C2/c(0β0)s
Temperature (K)293293293293
a, b, c (Å)12.7628 (4), 12.6564 (4), 9.6348 (3)???
β (°)90, 117.5995 (10), 9013.0183 (2), 6.4149 (1), 9.8411 (1)12.8840 (2), 6.3889 (1), 9.7384 (1)12.7978 (2), 6.3523 (1), 9.6642 (1)
V3)1379.22 (8)90, 118.562 (1), 9090, 117.799 (1), 9090, 117.567 (1), 90
Z16721.82 (2)709.10 (2)696.46 (2)
Radiation typeMo Kα???
µ (mm1)1.07???
Crystal size (mm)0.46 × 0.26 × 0.26Dark brownOrangeOrange
Data collection
DiffractometerBruker CCD
diffractometer
Bruker CCD
diffractometer
Bruker CCD
diffractometer
Bruker CCD
diffractometer
Absorption correctionMulti-scan
SADABS V2012/1 (Bruker AXS Inc.)
Multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
Multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
Multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
Tmin, Tmax0.693, 0.7460.521, 0.7450.648, 0.7460.664, 0.746
No. of measured, independent and
observed [I > 3σ(I)] reflections
51073, 4216, 3753 9151, 2484, 2086 6943, 2439, 2216 17606, 7370, 3766
Rint0.0150.0110.0100.016
(sin θ/λ)max1)0.7150.6500.6490.715
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.023, 0.039, 2.71 0.022, 0.064, 1.75 0.023, 0.065, 2.06 0.031, 0.091, 1.63
No. of reflections4216248424397370
No. of parameters289167228504
Δρmax, Δρmin (e Å3)0.65, 1.400.40, 0.450.48, 0.570.68, 0.95


(9b)(2b)
Crystal data
Chemical formulaFFe0.029Mg1.971O4PFFe0Mg2O4P
Mr163.5162.6
Crystal system, space groupMonoclinic, C2/c(0β0)s0††Monoclinic, C2/c(0β0)s0‡‡
Temperature (K)293293
a, b, c (Å)??
β (°)12.7707 (2), 6.3394 (1), 9.6462 (1)12.7633 (4), 6.3282 (2), 9.6350 (3)
V3)90, 117.5240 (5), 9090, 117.5985 (11), 90
Z692.55 (2)689.66 (4)
Radiation type??
µ (mm1)??
Crystal size (mm)ColourlessColourless
Data collection
DiffractometerBruker CCD
diffractometer
Bruker CCD
diffractometer
Absorption correctionMulti-scan
SADABS V2012/1 (Bruker AXS Inc.)
Multi-scan
SADABS V2012/1 (Bruker AXS Inc.)
Tmin, Tmax0.688, 0.7460.693, 0.746
No. of measured, independent and
observed [I > 3σ(I)] reflections
26453, 7409, 4855 12149, 3160, 2999
Rint0.0100.009
(sin θ/λ)max1)0.7150.715
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.033, 0.104, 2.38 0.016, 0.055, 2.01
No. of reflections74093160
No. of parameters503227
Δρmax, Δρmin (e Å3)0.71, 0.350.43, 0.31

† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

‡ Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

§ Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

†† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

‡‡ Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3+1/2, x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3+1/2, −x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3+1/2, x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3+1/2, −x4+1/2.

Computer programs: SAINT V8.27B (Bruker AXS Inc., 2012), SUPERFLIP (Palatinus & Chapuis, 2007), SUPERFLIP (Palatinus & Chapuis 2007), 'JANA2006(Pertricek,Dusek & Palatinus 2006)', 'JANA2006(Pertricek,Dusek & Palatinus, 2006)'.

 

Footnotes

1Supporting information for this paper is available from the IUCr electronic archives (Reference: DK5018 ).

Acknowledgements

We thank Boris Valentinovich Chesnokov, the late François Fontan, J. González del Tánago, Pavel Kartashov, Paul Keller, Jean-Robert Kienast, Elisabeth Kirchner, Friedrich Koller, Marc Leroux, Nicolas Meisser, Juan Carlos Melgarejo, Milan Novák, Gunnar Raade, Günter Schnorrer, Ralf Simmat, Julie Vry, for donating samples; Dmitriy Belakovskiy, Jean-Claude Boulliard, Carl Francis, Robert Gault, George Harlow, Norman Halden, Jeffrey Post, Allen Pring, Gilla Simon, Lydie Touret for arranging donations, and the American Museum of Natural History, Canadian Museum of Nature, Collection de minéraux de l'Université P. et M. Curie, Musée de l'Ecole des Mines de Paris, Fersman Museum, Harvard Mineralogical Museum, National Museum of Natural History (Smithsonian Institution), South Australian Museum, Staatssammlung München, University of Göttingen and Naturhistorisches Museum Bern for samples. CC was supported by CNRS-INSU Dyeti programme, ESG by US National Science Foundation grants OPP-0228842 and EAR 0837980 to the University of Maine, TA and BL by Swiss National Science Foundation, project `Chemistry of Minerals'.

References

First citationAllen, F., Watson, D., Brammer, L., Orpen, A. & Taylor, R. (2006). International Tables for Crystallography, Vol. C. Berlin: Springer.
First citationAnthony, J. W., Bideaux, R. A., Bladh, K. W. & Nichols, M. C. (2000). Editors. Handbook of Mineralogy, Vol. IV, Arsenates, Phosphates, Vanadates. Mineralogical Society of America, Chantilly, VA, USA.
First citationArmbruster, T., Chopin, C., Grew, E. S. & Baronnet, A. (2008). Geochim. Cosmochim. Acta, Suppl. 72, 32.
First citationBindi, L. (2008). Rend. Lincei, 19, 1–16.  Web of Science CrossRef
First citationBraitsch, O. (1960). Kali Steinsalz, 3, 1–14.
First citationBruker (2011). RLATT, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.
First citationBrunet, F., Chopin, C. & Seifert, F. (1998). Contrib. Mineral. Petrol. 131, 54–70.  Web of Science CrossRef CAS
First citationBrush, G. & Dana, E. (1878). Am. J. Sci. 16, 33–46.  CrossRef
First citationBurke, E. A. J. & Ferraris, G. (2004). Am. Mineral. 89, 1566–1573.  CAS
First citationBussink, R. W. (1984). Habilitation thesis. Ultrecht University, The Netherlands.
First citationChesnokov, B. V., Shcherbakova, Ye, P. & Nishanbayev, T. P. (2008). Minerals of the Burnt Dumps of the Chelyabinsk Coal Basin. Institute of Mineralogy, Russian Academy of Sciences, Urals Division, Miass (in Russian).
First citationChopin, C., Armbruster, T., Baronnet, A. & Grew, E. S. (2003). Polytypism in wagnerite, triplite & zwieselite, & discreditation of magniotriplite. Proposal IMA 03-C, approved, unpublished.
First citationChopin, C., Armbruster, T. & Leyx, C. (2003). Geophysical Research Abstracts, Vol. 5, 08323. European Geophysical Society.
First citationChopin, C., Leyx, C., Armbruster, T. & Medenbach, O. (2004). Hydroxylwagnerite. Proposal IMA No. 2004–009, http://pubsites.uws.edu.au/ima-cnmnc/minerals2004.pdf .
First citationCoda, A., Giuseppetti, G. & Tadini, C. (1967). Atti Accad. Naz. Lincei, 43, 212–224.  CAS
First citationCorbella, M. & Melgarejo, J.-C. (1990). Bol. Soc. Esp. Mineral. 13, 169–182.
First citationDušek, M., Petříček, V. & Palatinus, L. (2010). J. Phys. Conf. Ser. 226, 012014, 1–6.
First citationFialin, M. & Chopin, C. (2006). Am. Mineral. 91, 503–510.  Web of Science CrossRef CAS
First citationFin'ko, V. (1962). Dokl. Akad. Nauk SSSR, 143, 1424–1427.  CAS
First citationFontan, F. (1981). Bull. Minéral. 104, 672–676.  CAS
First citationFuchs, J. N. (1821). J. Chem. Phys. Nürnberg, 33, 269–270.
First citationGinzburg, A. I., Kruglova, N. A. & Moleva, V. A. (1951). Dokl. Akad. Nauk SSSR, 77, 97–100.  CAS
First citationGonzález del Tánago, J. & Peinado, M. (1992). Bol. Soc. Esp. Mineral. 15, 202–206.
First citationGrew, E. S., Yates, M. G., Barbier, J., Shearer, C. K., Sheraton, J. W., Shiraishi, K. & Motoyoshi, Y. (2000). Polar Geosci. 13, 1–40.
First citationGrew, E. S., Yates, M. G., Shearer, C. K., Hagerty, J. J., Sheraton, J. W. & Sandiford, M. (2006). J. Petrol. 47, 859–882.  Web of Science CrossRef CAS
First citationHardy, G. & Wright, E. (2003). An Intoduction to the Theory of Numbers, 5th ed. New York: Oxford University Press.
First citationHatert, F. (2007). Acta Cryst. C63, i119–i121.  Web of Science CrossRef CAS IUCr Journals
First citationHegemann, F. & Steinmetz, H. (1927). Centr. Mineral. Geol. Paläontol. A, pp. 45–56.  CAS
First citationHeinrich, E. W. (1951). Am. Mineral. 36, 256–271.  CAS
First citationHejny, C. & Armbruster, T. (2002). Am. Mineral. 87, 277–292.  CAS
First citationHenriques, A. (1956). Arkiv Miner. Geol. 2, 149–153.  CAS
First citationIrouschek-Zumthor, A. & Armbruster, T. (1985). Schweiz. Miner. Petrol. Mitt. 65, 137–151.  CAS
First citationIzbrodin, I. A., Ripp, G. S. & Karman, N. S. (2008). Zapiski RMO, 137, 94–106.  CAS
First citationJaffe, H. W., Hall, L. M. & Evans, H. T. Jr (1992). Mineral. Mag. 56, 227–233.  CrossRef CAS Web of Science
First citationJahn, H. & Teller, E. (1937). Proc. R. Soc. London Ser. A, pp. 220–235.  CrossRef
First citationKeller, P., Fontan, F. & Fransolet, A.-M. (1994). Contrib. Mineral. Petrol. 118, 239–248.  CrossRef CAS Web of Science
First citationKeller, P., Fransolet, A.-M. & Fontan, F. (1994). Neues Jahrb. Mineral. Abh. 168, 127–145.  CAS
First citationKeller, P., Lissner, F. & Schleid, T. (2006). Eur. J. Mineral. 18, 113–118.  Web of Science CrossRef CAS
First citationKelly, W. C. & Rye, R. O. (1979). Econ. Geol. 74, 1721–1822.  CrossRef CAS
First citationKirchner, E. (1982). Mitt. Österr. Mineral. Ges. 128, 29–31.
First citationKolitsch, U. (2003). Acta Cryst. E59, i125–i128.  Web of Science CrossRef CAS IUCr Journals
First citationLeroux, M. V. & Ercit, T. S. (1992). Can. Mineral. 30, 1161–1165.  CAS
First citationLottermoser, B. G. & Lu, J. (1997). Mineral. Petrol. 59, 1–19.  CrossRef CAS Web of Science
First citationNijland, T. G., Zwaan, J. C. & Touret, L. (1998). Scr. Geol. 118, 1–46.
First citationNovák, M. & Povondra, B. P. (1984). Neues Jahrb. Mineral. Monatsh. 12, 536–542.
First citationOriglieri, M. (2005). PhD thesis, University of Arizona, USA.
First citationOtto, H. (1935). Mineral. Petrogr. Mitt. 47, 89–140.  CAS
First citationOuzegane, K., Guiraud, M. & Kienast, J. R. (2003). J. Petrol. 44, 517–545.  Web of Science CrossRef CAS
First citationPalache, C., Berman, H. & Frondel, C. (1951). Dana's System of Mineralogy. Wiley: New York.
First citationPalatinus, L. & Chapuis, G. (2007). J. Appl. Cryst. 40, 786–790.  Web of Science CrossRef CAS IUCr Journals
First citationPetříček, V., Dusek, M. & Palatinus, L. (2006). JANA2006. Institute of Physics, Praha, Czech Republic.
First citationPetříček, V., van der Lee, A. & Evain, M. (1995). Acta Cryst. A51, 529–535.  CrossRef Web of Science IUCr Journals
First citationPitra, P., Boulvais, P., Antonoff, V. & Diot, H. (2008). Am. Mineral. 93, 315–326.  Web of Science CrossRef CAS
First citationRaade, G. & Rømming, C. (1986). Z. Kristallogr. 117, 15–26.  CrossRef Web of Science
First citationRea, J. R. & Kostiner, E. (1972). Acta Cryst. B28, 2525–2529.  CrossRef CAS IUCr Journals Web of Science
First citationRea, J. R. & Kostiner, E. (1974). Acta Cryst. B30, 2901–2903.  CrossRef CAS IUCr Journals Web of Science
First citationRea, J. R. & Kostiner, E. (1976). Acta Cryst. B32, 1944–1947.  CrossRef CAS IUCr Journals Web of Science
First citationRen, L., Grew, E. S., Xiong, M. & Ma, Z. (2003). Can. Mineral. 41, 393–411.  Web of Science CrossRef CAS
First citationRoda, E., Pesquera, A., Fontan, F. & Keller, P. (2004). Am. Mineral. 89, 110–125.  CAS
First citationRoy, A. J., Grew, E. S. & Yates, M. G. (2003). Abstr. Geol. Soc. Am. 35, 327.
First citationShannon, R. D. (1976). Acta Cryst. A32, 751–767.  CrossRef CAS IUCr Journals Web of Science
First citationShannon, R. D. & Prewitt, C. T. (1969). Acta Cryst. B25, 925–946.  CrossRef CAS IUCr Journals Web of Science
First citationSheridan, D. M., Marsch, S. P., Mrose, M. R. & Taylor, R. B. (1976). US Geol. Surv. Prof. Pap. 955, 1–23.
First citationSimmat, R. & Rickers, K. (2000). Eur. J. Mineral. 12, 661–666.  CAS
First citationTaasti, K. I., Christensen, A. N., Norby, P., Hanson, J. C., Lebech, B., Jakobsen, H. J. & Skibsted, J. (2002). J. Solid State Chem. 164, 42–50.  Web of Science CrossRef CAS
First citationVan Tendeloo, G., Van Dyck, D. & Amelinckx, S. (1986). Ultramicroscopy, 19, 235–252.  CrossRef CAS Web of Science
First citationVry, J. K. & Cartwright, I. (1994). Contrib. Mineral. Petrol. 116, 78–91.  CrossRef CAS Web of Science
First citationWaldrop, L. (1968). Naturwissenschaften, 55, 296–297.  CrossRef CAS
First citationWaldrop, L. (1969). Z. Kristallogr. 130, 1–14.  CrossRef CAS Web of Science
First citationWight, Q. & Chao, G. Y. (1995). Rocks Miner. 70, 90–138.  CrossRef
First citationWilson, A. & Prince, E. (2004). International Tables of Crystallography, Vol. C. Dordrecht: Kluwer Academic Publishers.
First citationWolff, P. M. de (1974). Acta Cryst. A30, 777–785.  CrossRef Web of Science IUCr Journals
First citationWyss, M. (1999). PhD thesis. University of Lausanne, Switzerland.
First citationYakubovich, O., Simonov, M., Matvienko, E. & Belov, N. (1978). Dokl. Akad. Nauk SSSR, 238, 576–579.  CAS

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Volume 70| Part 2| April 2014| Pages 243-258
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