Unit 3.7 - Glide Planes and Wallpaper Groups

[@julietten5614]

You are a legend. Thank you for the very clear explanations.

[@honestlordcommissarbrighte7921]

Bless you sir, you just summarized my problem in minutes what two one hour and thirty minute lectures tried to do and failed miserably.

[@narminsalimova7334]

Just amazing! Can't be clearer explanation!

[@bina5580]

I am obsessed with your lectures !

[@nuttyjamie2443]

why p2mg can be abbreviated as pmg? Do a mirror plane and a glide plane automatically generate a 2-fold axis? ty for your awesome videos❤

[@FrankHoffmann1000]

Thanks! Yes, exactly!

[@abbes635]

you are amazing, im graduating this year because of you thankyou❤️

[@FrankHoffmann1000]

Thank you very much for your kind words. Glad that you find these videos helpful.

[@deathslayer1411]

Where is the glide plane on the p2mg image at the end? Could you explain that image in more detail please?

[@FrankHoffmann1000]

Have a look at the following image: crystalsymmetry.wordpress.com/fig_4-18/

[@suvarnnacokepaishatsa8195]

Thank you very much! Your materials can be understood easily.

[@FrankHoffmann1000]

Thank you very much - you are very welcome!

[@wenwuxu6300]

Dear Frank, Thank you very much for another excellent lecture. I'm currently trying to understand the plane point group (wallpaper group) p2mg for the pattern shown at the end of the video. The first three symbols-p2m-make sense to me: p represents the primitive rectangular lattice, 2 indicates the two-fold rotational symmetry, and m refers to the mirror lines along the diagonal direction of the pattern. If we assume the mirror line is perpendicular to the x-axis of the lattice, the y-axis would then lie along the diagonal. However, when I try to identify the fourth symbol, I don't observe a glide symmetry with a ½ translation along the y-axis. Instead, it appears to have a full unit length translation. Interestingly, along the x-axis, I do see a ½ translation associated with the glide symmetry. To summarize, I can identify both mirror and glide (with ½ translation) symmetries when viewed along the x-axis, but not a combination of one mirror along the x-axis and one glide along the y-axis. Given this, how is the wallpaper group classified as p2mg? Thank you so much!! Best, Wenwu

[@FrankHoffmann1000]

Can you give me your eMail adress? I can send you at least the solution in which the symmetry elements are overlaid to the pattern.

[@kamalgurnani924]

Could you please explain how do we decide 'p' or 'c' in the p2mg image shown at the end of the video? Thanks for such a clear presentation.

[@FrankHoffmann1000]

Look for the smallest possible unit cell - is this cell already rectangular (angle of 90°)? Then take 'p'! And then the cell should consists of exactly one motif. In a c-centered cell, there were already two motifs in the cell. You would only choose 'c', if the primitive cell had an angle ≠ 90°.

[@gracesolante7357]

Thank you for this. Where can i find the notation names for all those 17 patterns?

[@FrankHoffmann1000]

en.wikipedia.org/wiki/List_of_planar_symmetry_groups

[@wiwiwi6446]

Hi! question, in minute 7:05 tiy say 5 bravais lattices and 17 plane groups. Shouldn't it be 7 and 14?

[@FrankHoffmann1000]

No - you're probably thinking of the number of crystal systems (7) and Bravais lattices (14) in 3D space. The number of space groups is then 230. But here we discuss the symmetry of the plane, i.e. we are in 2D. There are 4 crystal systems, 5 Bravais lattices and 17 plane groups.

[@wiwiwi6446]

@@FrankHoffmann1000 Oh right! Sorry I mixed stuff up. THnak you for answering!!

[@tengocaries]

Thank you so much, you are an amazing teacher! :)

[@meetatrivedi7332]

Thanks for the lectures, can you please explain Fmmm too?

[@FrankHoffmann1000]

Fmmm is not a plane group but a space group - please refer to the units of chapter 4

[@asailingstone]

where can I find all lecture videos?

[@FrankHoffmann1000]

kzbin.info/door/ts9FTFNInqTMvcFpdyap7wvideos?disable_polymer=1

[@Brucebod]

Thank you.

[@azrulazwan6101]

tq for the video

[@beyelear9665]

Dear Sir, Thank you for your great work! I have a question: for the notation say "P3m1", it has a mirror plane perpendicular to the x-axis, but no mirror/glide plane to the y-axis, but how should we define the x and y axis? I'm comparing P3m1 and P31m, they both have the same type of primitive cell with edges 120/60 degrees to each other, I tried to make two neighboring edges of the cell as x-axis and y-axis, but find it hard to explain the mirror plane perpendicular to axis then.

[@FrankHoffmann1000]

For these complicated cases it is always advisable to have a look at the International Tables for Crystallography. First of all, it might be allowed to correct your first statement. In the trigonal crystal system the x and y axis are identical / symmetry equivalent. This means that in the space group P3m1 you have mirrors perpendicular to the x _and_ the y axis. For this reason you are free to define any of the two axes as x or y. The more difficult case is indeed the other space group P31m, whoch can be described as a variant of the space group P3m1 with a different setting (actually the coordinate sytem is rotated by 30° with respect to P3m1). Here the two mirror planes are perpendicular to the direction [210] and [120], directions that are not perpendicular to the x or y axis, indeed. For a sketch of the somewhat simplified (leaving out the glides) symmetry element diagrams see: crystalsymmetry.files.wordpress.com/2022/02/p3m1_vs_p31m.pdf

[@beyelear9665]

@@FrankHoffmann1000 Thank you very much! So the only difference is how the two mirror planes are placed.

[@FrankHoffmann1000]

@@beyelear9665 Exactly!