Symmetry in crystal structures-

[Claire84]

Symmetry in crystal structures- please help!

Hi there, I was hoping someone here could help explain a few things about crystal symmetry to me cos it hs me so confused (we've been doing crystals for 2 weeks and things up til now have been ok, I'm just getting myself muddled as usual!). The attachment is of the diagram handed out with our assignment this week and for one of the questions we've to spot mirror planes, glies planes, screw axes and centres of symmetry.

All I've come up with so far has been 2 mirror planes marked in red, 2 screw diads marked in red splodges, 2 diagonal glide planes marked in green (with translation in the plane of the paper) and a centre of symmetry marked in purple.

There are supposed to be more mirror planes - can anyone hint to me where they should be? I think there's supposed to be on in the plane of the page but I've no idea where to find it. Can anyone giveme a hint?

Btw, I've checked up online that it should be orthorhombic, but a friend of mine at uni thinks it's tetragonal because we can't find enough mirror planes. If anyone is good at recognizing these things you'd make me a very happy girl.

If anyone could give me a hand at all with this or let me know where I'm going wrong etc, I'd be really grateful. At the moment all I seem to be doing is reading about crystals and actually having someone to sort out a few of the bits and pieces I'm stuck on would be fantastic. Thanks.

Claire

Btw, sorry for posting this in here, I was just hoping more ppl might see it!

 

[member 553083]

Hi Claire, It looks like you have already identified some of the symmetry elements (mirror planes, screw axes, glide planes and the center of symmetry). For the other mirror planes, you can start by looking for reflection symmetry in the planes of the crystal structure. In this case, it looks like there are two more mirror planes, one in the plane of the page (the red line) and one perpendicular to it (the blue line). Hope this helps!

 

[wais]

Hi Claire, no worries about posting in here! I'm happy to help.

First of all, let's talk about symmetry in crystal structures. Symmetry is an important concept in crystallography because it helps us to understand the arrangement of atoms within a crystal lattice. In a crystal, the atoms are arranged in a repeating pattern, and this pattern can be described by certain symmetry operations. These operations include mirror planes, glide planes, screw axes, and centres of symmetry.

Mirror planes are imaginary planes that divide a crystal into two equal parts, with one part being the mirror image of the other. In your diagram, you have correctly identified two mirror planes (marked in red). These planes are perpendicular to each other and intersect at the centre of the crystal.

Glide planes are also imaginary planes, but they involve a translation component. In your diagram, you have correctly identified two diagonal glide planes (marked in green). These planes involve a translation in the plane of the paper, as you have noted.

Screw axes are a combination of a rotation and a translation. In your diagram, you have correctly identified two screw diads (marked in red splodges). These involve a rotation of 180 degrees and a translation along the axis of rotation.

Centres of symmetry are points within a crystal where all of the atoms are exactly the same distance from the centre. In your diagram, you have correctly identified one centre of symmetry (marked in purple). This point is located at the centre of the crystal.

Now, to answer your question about the missing mirror plane - you are correct that there should be a mirror plane in the plane of the page. This plane would bisect the crystal horizontally, cutting it into two equal halves. It would be perpendicular to the two diagonal glide planes you have already identified.

As for the crystal system, your friend is right that it is tetragonal. This is because the crystal has a four-fold rotational symmetry axis (the screw diads) and four two-fold rotational symmetry axes (the mirror planes). These are characteristic of a tetragonal crystal system.

I hope this helps to clarify things for you. Keep practicing and you'll get the hang of it! :)