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The figures given below show the location of atoms in three crystallographic planes in a FCC lattice. Draw the unit cell for the corresponding structures and identify these planes in your diagram.                                                                                                                                                                                                        


6 years ago

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Hi Amrit,


First of all, understand the Q clearly, crystallographic planes are roughly the planes which can be defined in a simple cube. Here we have to identify the planes which might give the given arrangements. FCC lattice has atoms at all the corners + atom present at the center of each face.


Now first check that, the first figure given is the plane of any of the sides (4 at vertices and 1 at the face center).


The third is obtained if we take 2 opposite faces and draw parallel diagonals to both of them and then join them to complete a rectangle(with 2 diagonals and 2 edges of the cube joining them). (For the third case you get 2 at the vertices of one of faces similarly for the opposite face and remaining 2 for the atoms at respective face centers).


 


The visualization of the second is somewhat difficult,( and I am really very sorry that I am not able to draw the figure). But let us try and understand through text, for the second you can't take the plane for a single cube, but you have to consider 2 adjacent cubes. Consider your room. Now take any vertex of your room. There are 3 faces which pass through that point. Take any 2 of those 3 faces. Now draw diagonals to both the faces. There is an atom on both the diagonals' mid point (the face center atoms). These diagonals have other vertex also, 2 for each diagonal, apart from the common one. You will notice that on joining the common point of diagonals and the other 2 vertices you get a triangle involving 3 faces and the 3 sides of the triangle being the 3 diagonals of the 3 faces. Now just extend the common vertex backwards so that it involves the cube just beside that(the room next to your room). The common vertex and the 2 face center atoms of the other cube + all the other atoms of the triangle formed in the first cube gives you the second figure.


Well I am really sorry to be unable to draw the figures. If you have problem in understanding, please post it here. I will try to make the diagram and explain it once again. But only for the second figure, rest both are easy, I guess.   Do post your query or satisfaction here, so that I may help.


Thanks 

6 years ago

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