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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.


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.                                                                                                                                                                                                        


Grade:12

1 Answers

Avijit Arya
33 Points
11 years ago

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 

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