[MUSIC] So here we are at field exercise number two, and we're back with our focus group. For field exercise number two, you have to deal with plane symmetry. And this is a little bit more involved than the field exercise one, which was about point symmetry. If we look at the rubric for this exercise, you have to take photos of three objects where the plane group is different. So you can't use the same plane group twice. That's not allowed. You have to find three different objects with three different plane groups. The other thing with this exercise is that there are nine marks in total, which effectively means if you do the exercise properly, you'll get a whole extra bonus mark. So that's something to bear in mind. So let's now turn to our focus group and let them describe each of the photos that they've taken and their interpretation in terms of plane symmetry. And we'll begin with Samuel. >> So basically, I chanced upon my friend's tee shirt and the tribal pattern on it In the tutorial, yeah, so I find it quite interesting as an interesting symmetry on it. So it's a primitive two fold rotation with two mirror lines on it. >> Okay, so now let's go to focus group b and here what they think about Samuel's effort. >> Thanks a lot Samuel, very good. The group felt that you identified the unit cell correctly, so you are deserving of two points. Two marks out of two, so very good. Second thing requires you to identify all the Symmetry Operators. We felt, once again, you identified it correctly. The Symmetry Operators, you identified mirror lines and glide lines, but for the final one, for operation diagram, even though you've identified diagonal lines, it wasn't present in the symmetry operating diagram. So we've got to mark you down for that. So for the final one, one out of two. Total five. Two, two, one. >> So let's revise the marks for Samuel based on what I've said. So in terms of the unit cell being there correctly, it wasn't placed on the smaller image, but it was placed the large one, so we'll give you one for that. For identifying all the symmetry operators, you showed a glide, and it wasn't a glide there, and you didn't mention the two fold rotation, so we'll give you one out of two for that. And then I think for the symmetry operation diagram, that's really just gotta be a replication of what's in the plane group tables. So you need to be able to just pull that out and place it. And already we saw there's some problems there like a six-fold rotation that wasn't there and so forth. So I think we'll give you a zero for that. Okay, so that would be my revision of the marks. So having that unit cell drawn on the lower magnification image, that's the first thing to get the first mark. That you've got the unit cell in the correct place. Now the second thing is you've identified the plane group as p2mm. That's correct. Absolutely. I have no problem with that. But it's a good idea, then, once you've identified p2mm, to finish off the information here. That's plane group number six. So, you should always put the plane group number. That's the other point. Now, the exercise should get very easy from there. If you have the right plane group, and the right plane group number, you can go to your diagrams, and you just have to replicate the symmetry diagram, which is in the plane group tables on top. So when you look at this diagram you can see, as was correctly pointed out by the focus group b, you don't have to have a hexagon here at the corner, but they still didn't get it right. It's not a square, it's another two fold rotation. So in fact what you need to do is take away all of these guys here, and finally if you again look at the symmetry diagram for the plain group, you can see there's got to be a two farg rotation axis right in the middle. If you do that then you would get all of the third marks. Up here where you've written symmetry operations you've written mirror lines which is correct, you can see here, and again you refer to the diagram here, there are only mirrors. So you would take glide lines away, but what you would put in addition here, is two fold rotation. And now we're going to talk to Yuh Harn and see what she discovered. >> Okay, so for mine, I found mine in my room. And it's actually a piece of printed paper. There are different rows of flower cutting through the paper. So I actually found this unit here consisting of two columns of the flower. And my symmetry operators mirror lines and glide lines, which can be shown in the symmetry operation diagram. So each mirror line will cut through the row of flower into half, and then the glide line will be between the two rows. >> Okay, so let's see what focus group b has to say about this picture. Yuh Harn, this is a very beautiful example. So from your picture I could see that you identify the unit cell. So two points we can give you for that. And then next you actually identify all the symmetry operators, the mirror line and glide lines so another two points for that. And last but not least, you actually or locate the glide line and the mirror line, on your unit cell, so another two points for this. So to do you achieve a six points for this exercise. >> This would be a better representation of the unit cell. Now you've got the large yellow flower at every corner. It's also drawn as a rectangle, but perhaps for this paper it's a little bit oblique. It's not quite rectangular, but let's call it rectangular for now. So that's the first thing, the unit cell had to be larger than it was. Now the other thing, which is actually tricky, if we look over here at the symmetry operation diagram. You've suggested that there are mirror lines here, so for example if we take this upper mirror and we look for example again at the yellow flower. You're thinking okay, there's a mirror because this flower here is replicated by the mirror down here, but actually that's not true. It cannot be true because it's a chiral object. So the mirror starts, the flower starts by looking perhaps in this orientation. If you've applied a mirror, it's got to look this way. And if you look at those rows of flowers, the yellow flower is always the same way up, there is no mirror. So I suspect that this true symmetry of this particular group is not cm. It's probably p1, number 1. And in fact for this particular case, if you look closely at it, there are no mirrors, there are no rotation points, there are no glides. So here you would have to say no mirror lines, no glide lines, no rotation points. You almost got it right when you compared the size of the unit, so you drew here on the left hand side, you enlarged the size of the unit cell on the right hand side. So you kind of knew something wasn't quite right, okay? So what you would have to do now is just take away all of these guys and that would be your answer. And in the absence of other information, it doesn't matter where you put the origin of the unit cell. Coming back to the marking scheme, I think that the unit cell was not right on the first diagram, but it was getting close in the second one. So we'll give you one out of two for that. In terms of identifying all asymmetry operators the real problem was you identified too many symmetry operators which weren't really there. So I think this one we can't give you a very big mark for that. And then for the super position of the diagram, again I think it's not clear that the mirrors and the glides were there. So I think in this case we would have to give you a zero again, so not a very high mark for that one I'm afraid. >> Okay for mine I took his photo from the tutorial room's locker. He says this rows of lockers among the corridor. Then I consider color hence I took a unit cell four lockers instead of two or one in the sense. Therefore with the consideration of color I managed to find only one Mirror Line within the unit cell and also one Glide line, which is shown in the Symmetry Operation Diagram. Therefore I come up with the name of p m. >> What does focus Group B have to say on this one? >> Thank you Boyd for your good example. And then for symmetry operators, you did mark it correctly. And therefore, the unique cell you also my coloring in the picture itself. So for both of these you will get two marks. And then since you are actually fulfills all the criterias and the last two might also you add easel so total is six months. >> This is interesting because it depends how much of the lockers you look at to create your unit cell >> So if you just consider the top part, the unit cell, as placed, is correct. If you were going to consider the two rows of lockers or the four rows of lockers, actually the unit cell should be expanded to this spot. And you almost have a sense that that's happening, because you found that the plain group was p m. And the plain group is number 3, and if you look at the number 3 symmetry diagram, you'll find it only has mirrors, no glides. But then when we come over to your second diagram here on the right, you started to insert a glide, so you had a sense glide was actually there. So if we stick with the top, what you've said is correct, it would be p m. And there would be a mirror line here and in fact you should then ignore the bottom half. But if you take the whole arrangement as shown here, then this should become a unit cell looking like this. We should also expand the unit cell here so that it looks like that. And then, you would have the playing group, instead of p m, it would be p g, which is number. 4. And if it's playing group number four, then you won't have any mirrors here anymore. What you would have is a glide in the middle. You would have a glide down here at the bottom of the unit cell, and of course another glide at the top of the unit cell. So it really depends how much of this you look at to decide on whether p m or p g. If you just take the top two rows, it's p m. If you take the whole pattern it's p g. So when we come to the marking, let's have a look at that. Providing you work with the top part of the cabinets then you have the position of the unit. So correct, so we give a full two marks for that. Identifying all of the symmetry operators and this is where you got a little bit confused, or bringing in part of the real information. You showed the mirror line, but you also showed a glide, which was inconsistent. So I think you're pretty much there, so maybe one out of two for that part. And then finally, superimposing the diagram. Again, one out of two because you'd identified the correct unit cell and you got most of the diagram there. But not the whole diagram, so I think two one one. If we look at the marking after I have had my say it will come to seven. So I think there is a message here you’ve got to look very carefully at all of these diagrams, at all of your images, and always refer back to the plane group tables. So let's turn the tables. >> I identified my symmetrical object from the library. I found the computer keyboard to showcase such symmetrical properties. So for example, disregarding the letters on the keyboard, right, you notice that it is one of the plane group identify it. Okay, looking through the symmetrical operation diagram, you can see that you have mirror lines, glide lines, 2-fold rotation, 3-fold rotation, as well as 6-fold rotation. Let me elucidate, let me break it down for you. So at any points for the 6-fold rotation for four points of the s square hexagon in a sense. And of course you can replicate the six directions. So six-fold rotation. Now right in the middle in the horizontal lines as well as the frontal lines the diagonal lines you have three fold rotation because you can rotate it three times okay? And then for mirror length is right diagonally across. So again, reflected. That's about it from me. >> No, I think it's a very good example to pick up from the ntwolibrary. Simple and good. So basically by the marking scheme of the Ruby. I'll give you two marks for drawing the position of the unit cell correctly. You identified a unit cell very well, one mark for identifying all the symmetry's operator. Basically I deduct one mark due to your absence of the plain group symbol and a number. Yeah, sorry about that. For the last part, I will give you one mark for the simple imposing of symmetry diagram with all the symmetry operators quietly for you. So a total of four marks are given to you out of six marks. >> All right so let's start at the top. I think it was actually a very good job and it's a nice example to pick the keyboard. There's the plane group that it actually is, p 6 m m. And plane group is number 17. Now there is one thing that's a little tricky here. And this is where you have to compare how you draw the unit cell, as compared to how it appears in the plain group diagrams. So, when we come to look at your symmetry diagram over here, actually it's almost totally correct. There is of, course, a three-fold rotation point in the middle. And it's lying between, if you like, E, D, R, those keys there. So the threefold rotation point is not actually where you've positioned it. It actually has to be moved a little bit into this area here. And that's where the threefold rotation point should be, and the other, these rotation points should be deleted. But I think, actually, that was a very good job. So let's come to the marking rubric. And I would think that for this marking, in terms of the unit cell, definitely in the right place two marks for that. In terms of identifying all the symmetry operators, I agree that should be one, but that's because you didn't write the plane group symbol down. And in turns of cell position, I would also give one but not because of the poorly grown glide line, but because the three fold rotation point was in the wrong place. So in this case I think the prof's marking and the student's marking agree completely. All right let's move on to the next example. >> For this exercise, I show you I found this attractive Met the cover of a drain that actually has a mirror line symmetry. Two fold rotation and involve fold rotation. I a p4mm been group symmetry. So actually we can from the symmetry operation that way we can observe that four fold at the site in the center and then the two fold in between the four fold symbols at each of the sites of this square rotated in diamond shape. >> So let's here what your marker has to say. >> Okay, so far she still doesn't think our example is a good one. And for your unit cell, I think you correctly identified the one, even though it's only this small. And for the Symmetry Operation Diagram, I think there is a few errors. For the horizontal and vertical lines, I think there is no symmetry present, but for the lines and the rotation points, they are correct. And for the symmetry operators, even though you have glide line use in the diagram you didn't mention it. So according to the marking scheme, for the first point, I'll give you two marks for drawing the correct position of the unit cell. And the second part I'll give you one point for identifying half of the symmetry operators. And one point for the super imposing of the symmetry diagram, the symmetry operators, the symmetry lines are not done correctly. So your total will be four out of six. I think this is a really terrific example. I like this one very much. So let's go through. You identified the plain group correctly, p4mm. Probably it would be better to say which number it is, so it's number 11, just to be complete. I agree that once you have done that, then you've got all of the symmetry operators here, mirrored, two fold, full fold rotation, but you did miss the glide, so the glide line should've been placed here. The unit sale is identified correctly, which is terrific. And I would not be so harsh on the drawing in the diagram. I think the intent is clear, that you've got the glidelines in the right place and it matches the diagram in the plane group tables. So when I look at that, how would I do the marking? Well, let's consider. I think in terms of the position of the unit cell diagram, I would give two. In terms of identifying all of the symmetry operators, I would agreed, there was one missed. And also tou missed the number of the plane groups, maybe one for that. And then, for the symmetry diagram overlay, I'd be a little easier in marking for that. I would actually give two, because I think that was pretty well done. So I would give you a total of five out of six for that. So in this case, the student is marking harder than the professor. So, it happens. All right, let's move on to our final example now. >> So this example I actually took in my bedroom. And there is a pattern printing. Pattern from my laptop stand. And then from this printed pattern itself I can identify p four and m. And then which has four fold rotation at its four side and then two fold rotation at the site of the marking. And then it will, it actually also have mirror nines and got nine in this printing. >> All right. So let's hear what the other group has to say about that. >> Okay. I think this lattice done is simple, but yet, it contains everything from mirror lines, glidelines, to even two-four and four-four iterations. So manage to draw the unit cells on the imagery. I'll give you two points for that. And being able to identify all the symmetry operators, I'll give you two points for that. For the symmetry operation diagram, it seems clear] to me, and yeah I'll give you to 100. So out of a total six points, you get six points. Congratulations. All right, so in this final example I have to be honest, I have a difficult time finding anything wrong with it. I think it's almost perfectly done. You have the plane group correctly defined, you have it's number, you've identified all of symmetry operated, you've got the unit cell correct. And you have the overlay of the symmetry diagram correct. So no doubt, has to be six points. I'd only make one small comment in terms of presentation, which might make it easier for people. If you look at the diagram on the right where you've overlayed the symmetry diagram, you could have enlarged that to maybe just have four of the white dots, and then it's much easier to draw the symmetry diagram on top. But no question, six out of six for that. >> Thank you. >> So thank you very much focus group a and b. I'm sure this is a great help to the students trying to do this work at home.
