Professor, at 19:40 you say the water molecule has 2m symmetry, but the water molecule has 2 mirror planes (second one cutting all atoms in half). Is the second mirror plane implied in the 2m notation or is there a mistake in your presentation? Also the video at 23:35 is very confusing and it looks to me more like a mmm symmetry to me. Perhaps the video should contain a more 'skewed' shape that would indicate the lesser symmetry better (as in the real gypsum crystal).
Regarding the water molecule, please see the caption to Figure 1.18, in Geometry of Crystals, Polycrystals and Phase Transformations, that you can download freely from www.phase-trans.msm.cam.ac.uk/2020/Crystallography_book.pdf
Hi professor, I'm also a little unclear about the water molecule. I had a look at the caption in the book, but I can't see how this addresses the presence of another mirror plane that bisects all three atoms at once
@@TheLetterH111 Without considering the electron clouds, the mirror simply reflects each atom on to itself because each atom then lies on the mirror. That is a trivial operation.
a crystal class corresponds to several point groups. Does the crystal class contain the point groups at same time? can it derive other point groups form one point group in a a crystal class?
It is a set of symmetry elements passing through a point. If a macroscopic crystal has its equilibrium shape, then the point group symmetry of that shape can be related to the crystal class.
Count the number of atoms in the cell, and divide by the number of lattice points, and then attribute that number to the chemical formula of calcium fluorite
Professor, at 19:40 you say the water molecule has 2m symmetry, but the water molecule has 2 mirror planes (second one cutting all atoms in half). Is the second mirror plane implied in the 2m notation or is there a mistake in your presentation?
Also the video at 23:35 is very confusing and it looks to me more like a mmm symmetry to me. Perhaps the video should contain a more 'skewed' shape that would indicate the lesser symmetry better (as in the real gypsum crystal).
Regarding the water molecule, please see the caption to Figure 1.18, in Geometry of Crystals, Polycrystals and Phase Transformations, that you can download freely from www.phase-trans.msm.cam.ac.uk/2020/Crystallography_book.pdf
For the Gypsum, one of the angles is not 90 degrees. See page 24 of www.phase-trans.msm.cam.ac.uk/2020/Crystallography_book.pdf
Hi professor, I'm also a little unclear about the water molecule. I had a look at the caption in the book, but I can't see how this addresses the presence of another mirror plane that bisects all three atoms at once
@@TheLetterH111 Without considering the electron clouds, the mirror simply reflects each atom on to itself because each atom then lies on the mirror. That is a trivial operation.
a crystal class corresponds to several point groups. Does the crystal class contain the point groups at same time? can it derive other point groups form one point group in a a crystal class?
The highest symmetry point group is reduced within a class by placing atoms.
Is point group th symmetry of crystal shape or lattice ?
It is a set of symmetry elements passing through a point. If a macroscopic crystal has its equilibrium shape, then the point group symmetry of that shape can be related to the crystal class.
what is motif of calcium fluorite?
Count the number of atoms in the cell, and divide by the number of lattice points, and then attribute that number to the chemical formula of calcium fluorite