Net analysis concerning previously unknown crystal structure types with low coordination numbers

[This is a slightly revised version of the original blog post, particularly concerning the hP47-α structure; it turned out that there was a small error in the SI.]

Last year I attended for the first time the annual meeting of the German Society for Crystallography (DGK). It took place in Frankfurt/Main from 27-30 March 2023.

It was an interesting event with a broad spectrum of topics. One lecture in particular caught my interest. It was given by by Julia Dshemuchadse (from the Cornell University, Ithaca/NY) with the title:

Simulating complex crystal structures and their assembly in hard and soft condensed materials

Part of the content of the talk has already been published in a very nice paper:

H. Pan & J. Dshemuchadse
Targeted Discovery of Low-Coordinated Crystal Structures via Tunable Particle Interactions
ACS Nano 2023, 17, 7157–7169
https://doi.org/10.1021/acsnano.2c09131

Here, they report on the self-assembly of 20 previously unknown crystal structure types, 14 of which have low coordination numbers (CN), i.e., those between 2 and 7. The coordination numbers were determined with a radial-distrubution function (RDF) approach.

For the 14 new crystal structure types with <CN> = 2 – 7, I recreated the CIFs from the information given in the Supporting Information of the paper (with one exception, see below) and wanted to know: If the crystal structures are hitherto unknown, do some of them build also a hitherto unrecognized net? This seems to be the case. My outcome is as follows:

1. oI4-α

Space group: Imma (No. 74), a = 5.000, b = 5.500, c = 8.750 Å

Atom A: 4e 0.000, 0.250, 0.5329

This crystal structure does not form a net, there are only 2-c vertices.

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2. hR3-α

Space group: R-3 (No. 148), a = 5.000, b = 5.000, c = 1.550 Å

Atom A: 3a 0.000, 0.000, 0.000

This structure also does not form a net, there are again only 2-c vertices present.

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3. mC32-α

Space group: C2/c (No. 15), a = 5.000, b = 5.000, c = 1.550 Å

Atom A: 8f 0.9364, 0.0010, 0.5622  CN = 2 (light-blue)
Atom B: 8f 0.6882, 0.7457, 0.0580  CN = 2 (light-blue)
Atom C: 8f 0.9398, 0.4528, 0.3197  CN = 3 (dark-blue)
Atom D: 8f 0.8072, 0.2995, 0.1605  CN = 3 (dark-blue)

The light-blue atoms are only 2-coordinated, the dark-blue ones 3-coordinated. After removing the 2-c vertices, which means that the dark-blue ones form a continuous 3-c net, the outcome of the classification with ToposPro is a binodal (3,3)-c net with stoichiometry (3-c)(3-c). The topological type is:

fsg/P m m m –> P b c n (2c,2a,2b; 1/2,0,0); Bond sets: 2,5,6,7:fsg (binodal.ttd) {8^3}
VS [8.8.8(3)] [8.8.8]

This means that it is a subnet of the known fsg net (a binodal (4,6)-c net) and that it can be obtained by transforming the original structure/net in a group-supergroup relationship to the space group Pbcn accompanied with an origin shilft of 0.5 along a and by removing all bonds except the set 2,5,6, and 7. The most important message of this output is, however, that the topology has not yet been found in crystal structures.

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4. cI52-α

Space group: Im-3 (No. 204), a = b = c = 8.000 Å

Atom A: 12e 0.1985, 0.0000, 0.5000 CN = 2 (green)
Atom B: 16f  0.6864, 0.6864, 0.6864 CN = 4 (orange)
Atom C: 24g 0.0000, 0.7017, 0.8828 CN = 4 (orange)

The structure is characterized by pentagonal-dodecahedral cages (here shown in orange) located at the origin (0,0,0) and in the center of the unit cell (0.5, 0.5, 0.5) and therefore is related to the structure of chlathrate type-I that is realized, for instance, in cP54-K₄Si₂₃ (space group Pm-3n, No. 223). While these cages are occupied with K in cP54-K₄Si₂₃, they are empty for cI52-α. Additionally, cP54-K₄Si₂₃ contains another six tetradecahedron-shaped cages (24 vertices, 14 faces) with occupied cage centers, while cI52-α contains no additional cages. Instead, the dodecahedron-shaped cages are linked through 2-coordinated species (shown here in green).

As a 2-c vertex is only an edge, they are removed during the simplification procedure of the topological analysis. The result of the classification with ToposPro is:

It is a hitherto unknown binodal (4,4)-c net.

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5. tI32-α

Space group: I4₁/acd (No. 142), a = b = 8.000, c = 6.400 Å

Atom A: 16e 0.2500, 0.1747, 0.1250 CN = 4 (orange)
Atom B: 16f  0.9217, 0.9217, 0.2500 CN = 3 (blue)

The topological analysis shows that this is an already known 3-periodic binodal (3,4)-c net, which is stored in the ToposPro database under the entry 3,4T261. With the help of the online tool topcryst (a kind of front end for ToposPro, accessible via the browser), you can not only carry out the topological analysis, but also look up occurences of strctures that have this underlying net, but the number of occurences here is indeed zero.

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6. hP44-α

Space group: P6/mmm (No. 191), a = b = 8.000, c = 8.080 Å

Atom A: 2d 0.33333, 0.66667, 0.50000 CN = 0 (pink)
Atom B: 2e 0.00000, 0.00000, 0.28520 CN = 0 (pink)
Atom C: 4h 0.33333, 0.66667, 0.11550 CN = 4 (orange)
Atom D: 6k 0.26650, 0.00000, 0.50000 CN = 4 (orange)
Atom E: 6l  0.13470, 0.26940, 0.00000 CN = 4 (orange)
Atom F: 12n  0.38270, 0.00000, 0.30970 CN = 4 (orange)
Atom G: 12o  0.21020, 0.42040, 0.81160 CN = 4 (orange)

The framework of hP44-α is identical with that of the clathrate type IV with a unit cell containing three 20-vertex pentagonal dodecahedron-, two 24-vertex tetradecahedron-, and two 26-vertex pentadecahedron-shaped cages. However, the hP44-α structure is missing one set of cage centers at Wyckoff position 3f, corresponding to the (smallest) cage centers of the pentagonal-dodecahedron cages.

Not unexpectedly, the underlying net is already known: It is the 5-nodal (4,4,4,4,4)-c net know as zra-d.

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7. hP47-α

Initially, I was not able to infer the given coordination numbers on the basis of the given specificaton of the crystal structure in the SI. After contacting Julia, she was so kind to send me the CIF file and it turned out that there was a small mistake in the SI. The correct specification is as follows:

Space group: P6/mmm (No. 191), a = b = 5.15931, c = 5.23651 Å

Atom A: 2d 0.33333, 0.66667, 0.50000 CN = 0 (pink)
Atom B: 2e 0.00000, 0.00000, 0.70510 CN = 0 (pink)
Atom C: 4h 0.66667, 0.33333, 0.88480 CN = 5.5 (black)
Atom D: 6k 0.69810, 0.00000, 0.50000 CN = 2 (light-blue)
Atom E: 6l  0.87383, 0.74766, 0.00000  CN = 4 (orange)
Atom F: 6l  0.45933, 0.91865, 0.00000  CN = 2, Occ = 0.5 (light-blue)
Atom G: 12n  0.62722, 0.62722, 0.68902 CN = 4 (orange)
Atom H: 12o  0.20991, 0.41982, 0.18906 CN = 4 (orange)

Removing the 0- and 2-c vertices (this implies also a reduction of the CN of the 4h site from 5.5 to 4) leads to the already known 4-nodal (4,4,4,4)-c net doh.

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8. cF144-Na₈Si₁₃₆

Space group: Fd-3m (No. 227), a = b = c = 11.0000 Å

Atom A: 8a 0.0000, 0.0000, 0.0000 CN = 0
Atom B: 8b 0.5000, 0.5000, 0.5000 CN = 4
Atom C: 32e 0.4074, 0.4074, 0.4074 CN = 4
Atom D: 96g 0.4393, 0.4393, 0.2513 CN = 4

The cF144-Na₈Si₁₃₆ structure is strictly speaking not a new crystal structure type that has been discovered in the work of Pan & Dshemuchadse but has already been observed experimentally [1,2]. It corresponds to the clathrate type II structure of cF160-Na₂₄Si₁₃₆ with missing cage centers within the pentagonal dodecahedral cages, whereas the centers of the hexadecahedron-shaped cages are occupied in both structures.

The underlying net is also already known. It is the trinodal (4,4,4)-c net mtn, very well known in the zeolite community; it is the net of the zeolite ZSM-39.

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9. mC32-β

Space group: C2/c (No. 15), a = 7.0000 b = 6.3700, c = 4.6900 Å, β = 132°

Atom A: 4e 0.0000, 0.7746, 0.2500 CN = 4 (orange)
Atom B: 4e 0.0000, 0.3679, 0.2500 CN = 4 (orange)
Atom C: 8f  0.2901, 0.0670, 0.4208 CN = 3 (green)
Atom D: 8f  0.0843, 0.2798, 0.5821 CN = 4 (orange)
Atom E: 8f  0.1184, 0.0797, 0.7191 CN = 5 (purple)

Here, we have again a hitherto unknown net! It is a 5-nodal (3,4,4,4,5)-net.

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10. cP8-α

Space group: Pn-3m (No. 224), a = b = c = 5.000 Å

Atom A: 8e 0.1375, 0.1375, 0.1375 CN = 4

Nothing special here: The underlying net of this structure is very well known, it is the augmented version of diamond net, the uninodal 4-c net dia-d.

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11. mC12-α

Space group: C2/m (No. 12), a = 8.000, b = 4.000, c = 5.360 Å, β = 107.4°

Atom A: 4i 0.0761, 0.0000, 0.1724 CN = 4 (orange)
Atom B: 4i 0.3495, 0.0000, 0.4541 CN = 4 (orange)
Atom C: 4i 0.5018, 0.0000, 0.1967 CN = 5 (blue)

The underlying net of this crystal structure is again new! It is a trinodal (4,4,5)-c net.

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12. hP22-α

Space group: P6₃/mcm (No. 193), a = b = 7.000, c = 7.470 Å

Atom A: 4d  0.3333, 0.6667, 0.0000 CN = 6 (pink)
Atom B: 6g  0.1673, 0.0000, 0.2500 CN = 4 (blue)
Atom C: 12k 0.4258, 0.0000, 0.1149 CN = 5 (green)

Here we have another hitherto unknown net, a trinodal (4,5,6)-c net.

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13. tI16-α

Space group: I4₁/amd (No. 141), a = b = 4.500, c = 9.000 Å

Atom A: 8d  0.0000, 0.2500, 0.6250 CN = 6 (blue)
Atom B: 8e  0.0000, 0.0000, 0.1032 CN = 7 (golden)

This net is also new, a hitherto unknow binodal (6,7)-c net.

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14. cI48-α

Space group: I-43d (No. 220), a = b = c = 10.000 Å

Atom A: 48e 0.0314, 0.8993, 0.0467 CN = 7 (blue)

Finally, we have another structure in which the underlying network is already known, it is the uninodal 7-c net called svx.

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Altogether, out of these 14 new crystal structure types, 5 constitute an underlying network that was previously unknown.

CrystalNets vs. TopCryst – Follow-up

In my previous blog post, I reported on a new Web tool called CrystalNets, a tool for topology identification of crystalline materials, developed by Lionel Zoubritzky and François-Xavier Coudert.

A gathered a test set composed of 100 different MOFs and compared CrystaNets with TopCryst. The topology of the underlying net of these MOFs were correctly identified in 75 cases using CrystalNets (vs. 69 using TopCryst)! Already an impressive number.

It turned out that in most cases disorder was responsible for an erroneous topology analysis. Actually Lionel Zoubritzky did not intend to working further on CrystalNets, but having this test set at hand, he looked at some cases and has taken this as an opportunity to improve the routine with which disorder is treated.

As a result, the topologies for five more MOFs from this test set are correctly recognized:

No. 10 – NU-1351 – cml (see Fig. 1)
No. 58 – MOF-101 – nbo
No. 60 – MOF-907 – nha
No. 64 – NU-1350 – nuc
No. 74 – MOF-177 – qom

This increases the number of correctly recognized topologies to 80/100!

The PDF with all details of the (updated) results can be downloaded here.

Fig. 1: NU-1351 together with the underlying net cml.

CrystalNets is now an even more valuable tool for a fully automatic analysis of the topology!

CrystalNets vs. TopCryst

Determining the topology of the underlying net of a MOF can be a difficult and tedious task, especially if you are a beginner in the field. In order to be able to operate ToposPro on a profound level and to roughly understand how it works, it will ususally take you at least a 5-day workshop 🙂

But meanwhile there are two tools that can save you a lot of work by offering a fully automatic analysis: TopCryst and CrystalNets. The only thing you need is the CIF file of the compound to be analysed.

While I regularly use TopCryst for some years, I came across CrystalNets only a few days ago. Now, I decided to test both Web tools (no installation required, both work simply in a browser window) with a selection of 100 MOFs, all of which (except four) have different topologies of their underlying nets. In two instances I tested two MOFs with the same underlying nets, DUT-6 and MOF-205, both having ith-d topology, as well as PCN-250 and In-soc-MOF-1a, both having edq or soc topology, dependent if the AllNode or SingleNode algorithm is used (see below). I selected only MOFs that have a three-letter code as identifier in the RCSR.

I used the CIF files as provided from the CSD, meaning that they often contain disordered parts. It turned out that this disorder was the most common reason when a topology was not recognised or not recognised correctly, which is not surprising. As both tools have a size limit of the files that you are allowed to upload (TopCryst: 2 MB, CrystalNets: 1 MB), in some cases it is necessary to open the CIF, for instance with VESTA, and to save just the coordinates in the CIF.

Both tools can perform various clustering methods (and subsequent topology identifications). CrystalNets has the two most common clustering methods as default option, namely the AllNode and SingleNode approach. While in the SingleNode approach the organic linker is only represented by one vertex, the AllNode approach takes branching points of the linker explicitely into account. A good illustration of that topic can be found on the general information page of the MOF+ website.

For the evaluation of the results, I referred to the topology that I determined manually with ToposPro using the AllNodes approach. Of course, my determination does not have to be 100% correct… Therefore, I have also considered the cases to be correct when the topology is consistent with the single-node approach.

It took a while to get the evalution done, because TopCryst has a limit of a maximum of 10 topology determinations per user/computer and day. CrystalNets has no such limit.

Some further impressions of CrystaNets:

• CrystalNets is incredibly fast! Usually, the determination takes only a few seconds!

• In CrystalNets, the structure and/or the net is displayed in a separate window after the analysis, which allows for a further inspection how the clustering was done – a feature that I particularly like!

• It can be very helpful to provide information about the connectivity. In most cases the CIF file contains no such information, however in some cases it does. Therefore, it is always a good idea to try also the “Bonding = Input” option.

But now, the most important question: How accurately do these tools determine the topology?

CrystalNets achieved a score of 75/100.

TopCryst identified 69/100 topologies correctly.

A detailled list of the results can be found here (PDF). The CIF files of the MOFs can be downloaded as a ZIP archive file here.

Maybe the list can help the authors of the tools to further improve their algorithms.

And, of course, I will check in which cases I may have determined the topology of the underlying networks incorrectly 🙂

Zemannite

• 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: Mg_0.5ZnFe³⁺[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):

(K. Momma and F. Izumi, “VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data,” J. Appl. Crystallogr., 44, 1272-1276 (2011).)

• Fe/ZnO₆ octahedra (green)
• TeO₃ trigonal-pyramids (blue)
• MgO_x polyhedra (orange)
• Oxygen (red)
• Hydrogen (white)

For a 3D interactive version, see here:

https://skfb.ly/ozQXK

Refs.:

[1] J.A. Mandarino, E. Matzat, S. J. Wiliams, Zemannite, a zinc tellurite from Moctezuma, Sonora, Mexico.Canadian Mineralogist 1976, 14, 387–390.

[2] R. Miletich, Crystal chemistry of the microporous tellurite minerals zemannite and kinichilite, Mg_0.5 [(Me²⁺Fe³⁺) (TeO₃)₃] · 4.5 H₂O, (Me²⁺ = Zn, Mn). European Journal of Mineralogy 1995, 7, 509–523.

A hitherto unrecognized 2-periodic net derived from a circle packing

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.

Visualisation of the Period Table

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):

Pentagonal Bipyramid vs. Capped Octahedron (Updated)

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]).

References:

[1] S. Giese, K. Seppelt, Angew. Chem. Int. Ed Engl. 1994, 33, 461. http://dx.doi.org/10.1002/anie.199404611

[2] K. Momma and F. Izumi, “VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data,” J. Appl. Crystallogr. 2011, 44, 1272-1276).

[3] T. Vogt, A. N. Fitch, J. K. Cockcroft, Science 1994, 263, 1265.
https://doi.org/10.1126/science.263.5151.1265

Despujolsite

• Named in honor of Pierre Despujols (1888–1981), the founder of the Moroccan Geologic Survey (“Service de la carte géologique du Maroc”)
• The mineral was first observed in 1962 in manganese ore samples from Tachgagalt (Anti-Atlas, Morocco).
• Formula: Ca₃Mn(SO₄)₂(OH)₆  · 3 H₂O
• Space group: P-62c
• Crystal system: hexagonal
• Crystal class: -6m2
• Lattice parameters: a = b =  8.5405(5) Å, c = 10.8094(9) Å, α = β = 90°, γ =  120°

Picture: Rob Lavinsky, iRocks.com – CC BY-SA 3.0

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Crystal structure (click on the pictures to download the VESTA file):

(K. Momma and F. Izumi, “VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data,” J. Appl. Crystallogr., 44, 1272-1276 (2011).)

• CaO₈ polyhedra (blue)
• Mn(OH)₆ octahedra (purple)
• SO₄ tetrahedra (yellow)
• Oxygen (red)
• Hydrogen (white)

For a 3D interactive version, see here:

https://skfb.ly/onvGo

Refs:

[1] M.C. Barkley, H. Yang, S.H. Evans, R.T. Downs, M.J. Origlieri, Acta Cryst E 2011, 67, i47-i48.
DOI: 10.1107/S1600536811030911

Space Group Diagrams (not only) for Lecturers

I’ve started another ‘230 project’.

This time it is concerned with space group diagrams.

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:

The Hypertext Book of Crystallographic Space Group Diagrams and Tables

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.

Have fun!

Kapellasite

• Named after Christo Kapellas (1938-2004), collector and mineral dealer of Kamariza, Lavrion, Greece
• Kapellasite is isostructural with Haydeeite [Cu₃Mg(OH)₆Cl₂]
• Kapellasite is a metastable polymorph of Herbertsmithite
• Formula: Cu₃Zn(OH)₆Cl₂
• Space group: P-3m1 (No. 164)
• Crystal system: trigonal
• Crystal class: -3m
• Lattice parameters: a = b = 6.300(1) Å, c =  5.733(1) Å, α = β = 90°, γ = 120°

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Crystal structure^[1] (click on the pictures to download the VESTA file):

(K. Momma and F. Izumi, “VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data,” J. Appl. Crystallogr., 44, 1272-1276 (2011).)

• CuO₄ square-planar coordination polygons (blue)
• ZnO₆ distorted octahedra (gray)
• Oxygen (red)
• Chlorine (green)

For a 3D interactive version, see here:

https://skfb.ly/6ZNHM

References:

[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