Unit 5.6 - Quasicrystals (I)

[@spin3488]

Hi Frank Thanks a lot for your videos! They are great and well explained. I have two questions regarding the image in the video at 3:28. 1) I guess that unit cell has 4-fold rotational symmetry and could be considered to be each of the rectangles shown on the video (I.e the image shows 4 unit cells). Is that correct 2) Where are the 4 fold axes located? Are they in the center of each rectangle and also on each of the 4 vertices? Thank you very much for all your time and work, Frank!!

[@FrankHoffmann1000]

Hi Spin3488! Correct, there are 4 rectangular unit cells shown. But interestingly, the unit cell has no rotational symmetry at all (apart from the 1-fold axis of rotation). The only symmetry element present is a (vertical) reflection line that runs through the middle of the a-axis. The plane group is pm. Best! Frank

[@spin3488]

Thank you very much, Frank! You have to take into account the symmetry of the pentagon as well to check the symmetry of the unit cell, that is why there is no rotational symmetry in the unit cell. Is this correct?@@FrankHoffmann1000

[@FrankHoffmann1000]

@@spin3488 correct!

[@pt9973]

love'd the clifthanger there. I'm so going to find out in the next unit about the 10 f-, f-, f******, fold symmetry Thanx a lot!

[@saketh6261]

Thanks for the video. It really helped me understand

[@bigproton]

Hi Frank Thanks for these great videos! Regarding the example shown with the pentagonal 2D unit cell to prove that rotational symmetry is forbidden, does it mean that unit cells cannot have five-fold rotational symmetry (i.e. the lattice and unit cell cannot have it?) I am not sure if unit cell can be taken a synonym of lattice in this context and if “Symmetry of the Lattice” can be replaced by “Symmetry of the Unit Cell”? What I can understand is that molecules can have five-fold symmetry, but they cannot pack into a unit cell with five-fold symmetry, or in other words, the molecules in the unit cell can have rotational symmetry of the order 5, but the unit cell cannot. Is this correct? Thank you very much Ps, Perhaps you should write a second book with the Questions and Answers of your channel :-)

[@FrankHoffmann1000]

Hi proton! Thanks for your encouring comments! Yes, “Symmetry of the Lattice” can be replaced by “Symmetry of the Unit Cell” in this context. And you are perfectly right regarding your sentence: "that molecules can have five-fold symmetry, but they cannot pack into a unit cell with five-fold symmetry, or in other words, the molecules in the unit cell can have rotational symmetry of the order 5, but the unit cell cannot."! Nice idea with a second book, but maybe an ordered Q & A section on my homepage will suffice? :-) PS: I think with my answer here, your question under unit 5.4 is also answered, right?

[@bigproton]

@@FrankHoffmann1000 Thank you so much, Frank! Yes, it is answered. Sorry, I confused the unit to place the Question and I deleted it later. Maybe it takes sometime to be deleted.

[@kishorebehera1]

Sir In xrd diffractogram normally 2theta vs intensity graph is plotted.How to get the diffraction spot diagram from xrd expeiment

[@FrankHoffmann1000]

I think you talk about _powder_ X-ray diffractometry. But if you have a single crystal at hand you can carry out a single-crystal X-ray diffraction experiment and will get these diffraction patterns from which you can derive the atomic structure of the crystal. kzbin.info/www/bejne/nXPbi4l8aNhnmbc