Named in honor of the Austrian mineralogist Josef Zemann (born 1923 and died just three weaks ago on the 16th of October 2022 at the age of 99), who had worked extensively on tellurium minerals. An obituary on Zemann in German can be found here.
Type Locality: The Mina La Bomballa near Moctezuma, Sonora, Mexico
Formula: Mg0.5ZnFe3+[TeO3]3 · 4.5 H2O
Space group: P63/m
Crystal system: hexagonal
Crystal class: 6/m
Lattice parameters: a = b = 9.41 Å, c = 7.64 Å, α = β = 90°, γ= 120°
Picture: Christian Rewitzer – CC BY-SA 3.0
Crystal structure (click on the pictures to download the VESTA file):
[1] J.A. Mandarino, E. Matzat, S. J. Wiliams, Zemannite, a zinc tellurite from Moctezuma, Sonora, Mexico.Canadian Mineralogist1976, 14, 387–390.
[2] R. Miletich, Crystal chemistry of the microporous tellurite minerals zemannite and kinichilite, Mg0.5 [(Me2+Fe3+) (TeO3)3] · 4.5 H2O, (Me2+ = Zn, Mn). European Journal of Mineralogy1995, 7, 509–523.
Recently, I have been immersed in the vast world of intermetallic phases, in particular those with an ordered superstructure of either cubic-closest packed (ccp) or body-centred cubic (bcc) parent structure. They caught my interest, because some of the researchers in that field are paying particular attention to how the densest-packed layers/planes look like and how they are organized, i.e., in which direction they are stacked and if they build an cubic (ABC…) or hexagonal (AB…) stacking sequence. They also partly give network-like descriptions of the atomic configurations of the densest layers.
Since densest layers are considered, one enters the field of circle packings. And the densest circle packing of equally sized circles is, of course, the hexagonal packing. If we draw lines from each circle midpoint to every midpoint of the next-neighboring circles, we get the well known hxl net, a uninodal 6-c net. The vertex symbol is 36.
In those densest layers of ordered alloys the atoms within one densest plane are of different kind. If we ignore this – as it is usually the case, when we analyze the topology of an atomic arrangement – then we obtain again the hxl net. But what happens, if we focus only on a subnet, for instance, the net that is built by the major component?
Let’s look at an example.
In the ordered binary intermetallic phase Cu3Au (space group Pm-3m), the Cu atoms in the densest layers, (111) planes, form a continous net as shown in Fig. 1, in which the Au atoms are a kind of decoration, located in the centres of the hexagons. The Cu subnet is the well-known, again a uninodal net, the kagome net kgm. The vertex symbol is 3.6.3.6.
Fig. 1: Kagome net of Cu atoms in the densest layers of Cu3Au, decorated by Au atoms.
Two different binodal nets based on circle packings are realized in the subnets of densest layers in TiAl3 and MoNi4, respectively, shown in Fig. 2 and 3. In TiAl3 the Al atoms form a bew net, and the Ni atoms in MoNi4 form a krh net. The vertex symbols are given in the figures.
Fig. 2: The subnet formed by Al atoms in the binary intermetallic phase TiAl3.
Fig. 3: The subnet formed by Ni atoms in the binary intermetallic phase MoNi4.
Probably, it is hard to find a new uninodal or binodal net that is based on circle packings as it is believed that the RCSR contains all uninodal and binodal (stable) circle packings. In stable circle packings all tiles are strictly convex (angles between adjacent edges < 180°).
But on the other hand, this also means that one or the other higher-nodal net based on circle packings can still be discovered. Indeed, it turned out that the trinodal net that is formed by the Al atoms (see Fig. 4) in the ordered intermetallic phase ZrAl3 is a hitherto unrecognized net, which, of course, is only due to the fact that no one has cared about it yet.
Fig. 4: The subnet of Al atoms in the binary intermetallic phase ZrAl3.
Who knows if there are more undiscovered networks when looking at densest layers of further intermetallic phases. Maybe there is even a previously undiscovered binodal one 🙂
PS: I would like thank Davide Proserpio for confirming that this a new net by carrying out an appropriate analysis with ToposPro, and I would like to thank Michael Fischer for the inspiring exchange we had concerning this topic.
Michael Fischer, known as @ZeoliteMiFi on twitter, created a mock .cif file that allows visualisation of the periodic table in a structure visualisation software like VESTA. With that, one can see at one glance how different elements are shown.
He kindly provided the CIF and you can download it here. May be reused for all purposes, but no warranty is given. Comments and corrections should be send to: michael.fischer@uni-bremen.de.
Three examples in VESTA:
1. Default settings, vdW radii + labels
2. Default settings, atomic radii, no labels
3. Default settings, ionic radii, no labels
This should work equally well with other software packages. The main issue might be an artificial generation of “bonds” between neighbouring elements that one should suppress in the settings (which is straightforward in VESTA).
This is how it looks in Mercury applying the “Ball-and-Stick” style (bond radius set to zero):
In a very interesting article by Giese and Seppelt from 1994 [1] the question of the preferred coordination geometry for the coordination number 7 is explored. Until then, it has been shown that the pentagonal bipyramid is preferred for main group elements (for instance in the compound IF7), although this geometry results in an overall slightly higher ligand repulsion than the alternative arrangements according to a capped octahedron or capped tigonal prism, respectively.
In this article they raised the question if this is also valid for transition elements, and the ideal candidate to answer this question would be the homoleptic compound ReF7. Unfortunately, for various reasons it is very difficult to determine the crystal structure of ReF7.
Alternatively, they synthesized several ionic compounds comprising of anions with transition elements with the coordination number 7 and varied the nature of the cation to exclude lattice energy effects that might influence the arrangement of the ligands.
The results were as follows:
The anions in Cs+MoF7– (see Fig. 1), Cs+WF7–, NO2+MoF7– ∙ CH3CN, and C11H24N+MoF7– (C11H24N+ = 1,1,3,3,5,5-hexamethylpiperidinium) (all belong to the cubic crystal system) as well as (H3C)4N+MoF7– (tetragonal, space group P4/nmm, ) form a capped octahedron coordination polyhedron. The latter result is of special interest as the 7 fluorine atoms around Tellurium in (H3C)4N+TeF7– (again space group P4/nmm) form a pentagonal bipyramid instead.
Fig. 1: The crystal structure of Cs+MoF7– (space group Pa-3, ICSD deposition number = 78390); Cs = purple, Mo = gray, F = green. (Image made with VESTA [2]).
According to the authors, it can therefore be concluded that neither the lattice type nor the crystal packing have an influence on the different structures of the anions.
Now, what will happen, if one of the 7 fluorine ligands is exchanged with a larger atom? As expected, a pentagonal bipyramid is then realised, as in Cs+ReOF6– (space group P21/a), where the larger ligand occupies one of the two axial positions (see Fig. 2).
Fig. 2: The crystal structure of Cs+ReOF6– (space group P21/a, ICSD deposition number = 78392); Cs = purple, Re = gray, O = red, F = green. (Image made with VESTA [2]).
Update:
I have to admit that I was too lazy to check if the structure of ReF7 is known by now. In fact – thanks to Robert McMeeking (from The Chemical Database Service/CrystalWorks, @cds_daresbury) for the hint – the crystal structure of ReF7 was published in Science only a single(!) day after the publication of the Angewandte paper by Giese & Seppelt: ReF7 builds a (slightly distorted) pentagonal bipyramid [3], see Fig. 3!
Fig. 3: The crystal structure of ReF7 (space group C-1, ICSD deposition number = 78311); Re = gray, F = green. (Image made with VESTA [2]).
Of course, the No. 1 source for such diagrams, i.e. symmetry element and general position diagrams, is Volume A of the International Tables for Crystallography (ITA). As valuable as they are for the daily life of a crystallographer, they are unsuitable when it comes to teaching.
Hitherto, there is another extremely valuable online resource for these diagrams:
However, one of the features I don’t like about these diagrams is that they decided to present both diagrams (symmetry elements and general positions) in a superimposed fashion.
For this reason I decided to draw all diagrams again and to make them publicly available (CC license) in various formats (as a PNG picture, a PDF, and a PPT file) – ready for use for teaching purposes.
However, there will be limitations. Different origin choices will be taken into account, but further different settings will be disregarded. And I do not know, if I will be able to manage the drawings of all diagrams for the cubic space groups. Lets see 🙂
Up to now, the first two space groups of the triclinic crystal system are ready. Until the end of the month the diagrams for all monoclinic space groups should be available. Then further diagrams will be added from time to time.
[1] W. Krause, H.-J. Bernhardt, R.S.W. Braithwaite, U. Kolitsch, R. Pritchard Kapellasite, Cu3Zn(OH)6Cl2, a new mineral from Lavrion, Greece, and its crystal structure Mineralogical Magazine, 2006, 70, 329-340 DOI: 10.1180/0026461067030336
Can be formed from liquid water at 11 kbar by lowering the temperature to approx. -3 °C
Density: 1.31 g/cm3
Structural features
Crystal structure of Ice VI
Ice VI is a proton-disordered phase
it is composed of two independent interpenetrating networks of H-bonded water molecules (shown above in blue and red, respectively)
the main structural motif is a tricyclic, cage-like water hexamer, similar as in liquid water
A tricyclic water hexamer composed of four-membered rings
This motif is also found for the silicon atoms in the zeolite edingtonite, see here for comparison.
The respective topology of the underlying net is edi, a binodal (4,4)-c net with transitivity pqrs = 2343
Space group: P42/nmc (No. 137)
Crystal system: Tetragonal
Lattice parameters:
a = b = 6.116(1) Å, c = 5.689(1) Å
α = β = γ = 90°
Literature:
[1] W. F. Kuhs, J. L. Finney, C. Vettier and D. V. Bliss, Structure and hydrogen ordering in ices VI, VII and VIII by neutron powder diffraction. J. Chem. Phys.1984, 81, 3612-3623. DOI: 10.1063/1.448109
VESTA K. Momma and F. Izumi, “VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data,” J. Appl. Crystallogr., 44, 1272-1276 (2011).
For both metal cation positions there is a complete disorder between Ni and Fe.
There are two distinct coordination environments; octahedrally coordinated metals at the center and all edge centers and tetrahedrally coordinated metals for the others.
Eight tetrahedra each form edge-connected Fe/Ni8(µ-S)6S8 motifs, that means cubes of metal ions with six face-capping and eight terminal S atom. If we take now these cubes and octahedra as building blocks they form a NaCl-like structure.
Fe/NiS4 tetrahedra (blue)
Fe/NiS6 octahedra (orange)
Fe (brown)
Ni (green)
For a 3D interactive version on sketchfab, see here:
[1] Tenailleau, C., Etschmann, B., Ibberson, R. M. & Pring, A.
A neutron powder diffraction study of Fe and Ni distributions in synthetic pentlandite and violarite using 60Ni isotope. Am. Mineral. 91, 1442–1447 (2006)
[2] Stacey, T. E., Borg, C. K. H., Zavalij, P. J. & Rodriguez, E. E.
Magnetically stabilized Fe8(µ-S)6S8 clusters in Ba6Fe25S27. Dalton Trans. 43, 14612–14624 (2014)
Here, you can download the 
The Fascination of Crystals and Symmetry 