Category Archives: Crystal MOOC

Chapter 7 released on YouTube

Dear Friends,

Chapter 7 of our course is now available on YouTube. This is the final chapter of this course and it will be all about nets and topology.

We will show you how to use three programs for the analysis of framework structures: TOPOS, Systre and 3dt.


Michael & Frank



Chapter 6 available on YouTube

Dear friends,

in chapter 6 of our course “The Fascination of Crystals and Symmetry” we will introduce a very special class of crystalline materials, which are called Metal-Organic Frameworks or short MOFs.

Research interest in this kind of materials has intensified immensely over the last decade. As MOFs are also the field of study of our research group, telling you something about these very special crystals is a matter of heart for us.

MOFs are comprised of inorganic and organic secondary building units. We will take a look at different variations of how these secondary building units can be assembled together and we will introduce the principles of classification of these network-like assemblies.

We provide also several crystal structures of MOFs as VESTA files, in order for you to be able to get familiar with the structural features of MOFs at the atomic level. (You can find a tutorial on how to obtain and install VESTA in Unit 2.7)

Please find the playlist of chapter 6 on YouTube here.

Enjoy the beauty of porous crystals!

Michael & Frank


Chapter 5 now on YouTube

Chapter 5 released!

Dear all,

today Chapter 5 of our course has been released on YouTube!

In this chapter we will practise the handling with the International Tables a little further. But in contrast to staring only at circles and commas we will additionally look at real world crystals and some of their symmetry and physical properties.

And you can be curious about the story of one of the most thrilling scientific discoveries of the last century: the discovery of quasicrystals by Dan Shechtman.


Frank and Michael


Chapter 4 released on YouTube

Dear Friends,

Chapter 4 of our course ‘The Fascination of Crystals and Symmetry’ is now available on YouTube.

In this chapter we will focus on symmetry operations that separate crystal structures from (other) macroscopic objects: glide planes and screw axes. After that we are ready to climb up the last step of our “ladder of crystal classification”, reaching, finally, the space groups. We will open the “crystallographers’ bible”, the International Tables for Crystallography, Volume A.

best wishes!

Frank and Michael



Chapter 3 released on YouTube

Chapter 3 is all about symmetry. We will start with the symmetries that can be found in everyday objects.

You will then learn how to classify crystals into their respective classes. We have prepared a small poster, so you can keep track of your very own collection of crystals.

Furthermore, we want to begin to talk about translational symmetry. This symmetry is a particular feature of crystal structures with their repetitive patterns.

Chapter 2 now on YouTube

Today we released the second chapter of our course into the YouTube channel!

It starts with a virtual flight through the Mineralogical Museum of the University of Hamburg. In the following outer shapes of crystals, Miller indices, the Bravais lattices, and fractional coordinates are being discussed. Furthermore, we introduce VESTA, an incredible piece of software (freeware), which not only allows you to analyze crystal structures, but also to build your own crystals structures and visualize crystal shapes!


Michael & Frank

CrystalMOOC goes YouTube

Dear friends,

we decided that we will make our course “The Fascination of Crystals and Symmetry”, which ran twice as a MOOC at the iversity platform, publicly available in the near future.

This MOOC was a great experience for us. And carrying out this course as a MOOC has indeed several advantages, for instance, the defined time window in which the students can learn more or less synchronously and together, the availability of a discussion forum and the ease to integrate and organize several additional materials like quizzes, articles for further reading etc.

However, there are also several disadvantages. Probably, the most obvious one is that the access to the lecture materials is restricted to the students who have been enrolled in this course at the run time. But in addition it is also very demanding, and, of course, time consuming for us as the instructors, because it was always our intention to be responsive teachers.

Currently, we are adopting the screencast videos (removing/updating links etc.) and use this opportunity to eliminate some surprisingly resistant errors 🙂 We will then upload the videos to a YouTube channel. The new base for some of the additional material will be this website.

We will announce further details soon, so stay tuned!

All the best

Frank & Michael

Follow-up: monoclinic symmetry – with almost perfect cubic metric

In the last post we presented a kind of an empirical proof that a crystal belonging to the monoclinic crystal system can have an angle β of exactly 90°. NaKZnP2O7 crystallizes in the space group P21/n, with the following cell parameters: a = 12.585(5) Å, b = 7.277(5) Å, c = 7.428(5) Å, β = 90.00(5)°. Monoclinic symmetry – but orthorhombic metric.

Our blog reader Michael Fischer now found an even more impressive example: The mineral villamaninite (Cu, Ni, Co, Fe)S2 – a pyrite-derivative – is pseudo-cubic with cell parameters a = 5.709 (2), b = 5.707 (2), c = 5.708 (2) Å,  α = 90.00, β = 90.01(1), γ = 90.00°. However, the symmetry is only monoclinic with the space group P21 !

And this is how villamaninite looks like atomistically:


Metal-S6 octahedra, all 6-fold corner-connected to each other but not edge-connected.


The CIF and the reference to the research article can be found here:

The monoclinic crystal system and the skew angle beta

One of the things we have tried to teach in our course is:

It is not the metric that determines to which crystal system a crystal belong. It is the other way round – the symmtry of the crystal determines the metric, although not in a biunique way.

In many textbooks the metric for the monoclinic crystal system is given as:

a ≠ b ≠ c, and αγ = 90°, β ≠ 90°  ;

And this is simply wrong. The correct statement is that there are no restrictions concerning a, b, and c, and there is also no restriction regarding the angle β, hence:

αγ = 90° – that’s it.

The important message here is that it is indeed not very likely that beta equals 90°, but it is not (mathematically) forbidden, the angle β could ‘accidentally’ be 90°.

While it is one thing to show mathematically that in the monoclinic crystal symmetry the maximum symmetry is 2/m and that therefore the angle beta can also be 90° it is another question if nature produces indeed a crystal belonging to the monoclinic crystal system and nonetheless possesses an angle β of 90°. This could then be considered as a sort of empirical proof.

Here it is 🙂

Crystal structure of sodium potassium zinc diphosphate NaKZnP2O7

Yu.F. Shepelev, A.E. Lapshin, M.A. Petrova

Journal of Structural Chemistry

November 2006, Volume 47, Issue 6, pp 1098-1102

Space group P21/n, a = 12.585(5) Å, b = 7.277(5) Å, c = 7.428(5) Å, β = 90.00(5)° (!)

And this is how it looks like:



PO4 tetrahedra (purple)
ZnO4 tetrahedra (grey)
sodium (yellow)
pottassium (blue)