A particular unit cell is cubic with ions of type A located at the corners and f

Question

A particular unit cell is cubic with ions of type A located at the corners and face centers of the unit cell and ions of type B located at the midpoint of each edge of the cube and at the body-centered position. (a) How many ions of each type are there per unit cell? (b) What is the lattice of this structure? Check to be sure that the number of ions per unit cell given by your description of the structure as a lattice is consistent with your answer to part (a). (c) What is the coordination number of each ion? (d) What is the name commonly given to this crystal structure?

Explanation / Answer

a) A = (8x1/8) + (6x1/2) = 4 i.e 8 ions at 8 corners of cube are each shared by 8 other unit cell ions , hence total ions per unit cell =(8x1/8) = 1 atoms at total 6 faces of cube = 6 , each one shared to 2 unit cells hence total ions = (6x1/2) = 3 total A per unit cell = 4 B = (12 x1/4) + 1 = 4 12 ions at mid point of 12 edges , each is coordinated 4 unit cells hence total ions per unit cell = (12 x1/4) = 3 one B present in body centered is not coordinated to other unit cell B so ion B per unit cell =1 total B per unit cell = 3+1 = 4 b) lattice structure is fcc , face centered cubic , NaCl lattice c) coordination number of A = 6 coordination number of B = 6 d) fcc c)

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