Unit 4.5 - Space Groups and Space Group Symbols

Unit 4.5 of our course The Fascination of Crystals and Symmetry

If we consider translational symmetry only, the repeating lattices, we saw, that there are 14 different possibilities, the 14 Bravais lattices.

If we restrict symmetry considerations to macroscopic crystalline objects, discounting their potentially additional internal translational symmetry, then we end up with 32 crystal classes, describing their different kinds of outer shapes.

And if we now combine all these symmetry elements with pure translations of the lattice and the two symmetry elements with translational components, namely screw axes and glide planes, then one can show that 230 different symmetrical arrangements in 3D are possible - these are the fameous 230 space groups.

In this unit the nomenclature of space groups is introduced. Additionally, the crystallographic viewing directions are elucidated again, and finally we would like to shine some light on the relationship between the three categories ‘space group’ - ‘point group’ and finally ‘crystal system".

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If you prefer books instead of videos, have a look at:

[KSubruu]

I came looking for a good video on space group symbols and stumbled upon this! I am glad that instead of just watching this and leaving, I went through all the videos from Chapter 1. You have done a truly amazing job making this lecture series with immaculate clarity, free materials and zero ads. It was remarkable to see you answering the questions in the comment section even after 7 years of posting the video. The doubts I had were posted in those comments and your responses helped me clear it. You are an amazing teacher and thank you for this series!

[jeoh]

This video helped me pass my qualifying exams for graduate school. Thank you, Dr. Hoffmann!

[joshuajoshua]

very good explanation. you voice makes it really nice to listen and follow what you are saying. i wish you would read something to me when i go to sleep

[mafeflorez]

I don't think I can thank you enough, you're great! keep the good work

[BenjaminPullicino-qxfh]

Heartfelt thanks from a desperate PhD student of Chemistry

[KPLIUC]

Thank you so much, you just saved my final exam!!!

[shaneyaw]

This was a very clear explanation of a complex topic. Thanks

[DeshmukhDevki]

Thanks a lot for the videos. You made crystallography comprehensible.

[senemdemirci]

Thank you!!! You are the reason I passed my exam for my Masters degree!!!

[CpungMaster]

Thank You for the explanation about the viewing axes for different crystal systems :^)

[aryan]

@5:00 sir, you said 2 mirrors automatically generate 2 fold axis. and there are much more like this. can you please tell what are others. what are suh possible cases. please list all. thank you

[Herngg]

Hi Frank, just to clarify, shouldn't the blue mirror plane be perpendicular to the a-axis since we are viewing it in the a direction? 10:33

[pravinkadhane]

Very helpful information about Space group and specially for tetragonal perovskite structure.

[jackcollings]

Dear Frank,
Thank you so much for these videos - they are amazing!
I have a question:
Previously in the video on glide planes, glide plane "a" was described as a reflection in the "ab" plane, and translation in the a-direction by x+1/2.
However in the example at 4:14, it says glide plane "a" is perpendicular to "b". However the "ab" plane is not perpendicular to "b".
So is glide plane "a" free to reflect in any plane, as long as that plane is the one perpendicular to the axis given by the index of the HM notation?
Can glide plane "a" be specified in the first index, such that there is a reflection in "bc", then translation by x+1/2?

[annavladislava]

This helped me a lot, thank you for this amazing work!

[doorash]

You are awesome.
I’m watching it in Korea.

[mvilatusell]

Hi Frank! Awesome video and series of videos! I'm extremely grateful. I have a couple of questions:
1) When you reduce from space group to crystal classes, is the viewing direction maintained?
2) In the example at 10:25, why is not just P4mm with a hat above the 4 to indicate inversion? In other words, why do we need to specify 4-fold rotation + perpendicular mirror insteada of 4-fold rotation + inversion?
Thanks!!!

[v.vigneshvenkatasubramania]

Thanks for the video.

I have a question.

To obtain space groups, we add the following elements:
1) Bravais lattice - Translation symmetry only
2) Point groups - which are applicable to macroscopic shapes of crystals
3) Glide plane and screw axis

Why don't we talk about the symmetries of a unit cell in particular?
It seems point groups must be applicable for unit cells as well. If yes, then how do you combine glide plane and screw axis with the unit cell?

Also, regarding the viewing directions mentioned in this video: It seems to me to be very difficult to obtain the planes' miller indices of a macroscopic crystal shape. For example, let's say a macroscopic crystal has a hexagonal crystal system, how do you determine that it has a hexagonal shape when you cannot identify its [210] viewing direction.

[johndeng]

I am confused about the last example, why don't you combined the two diffrent motif as a new motif. Then the crystal system will be P4/m m m.

[twrikbling]

very easy course for me because i am living in 2 dimension world