A diamond structure has fcc lattice with the side length a with identical basis

Question

A diamond structure has fcc lattice with the side length a with identical basis atoms at (0,0,0) and (a/4, a/4, a/4) (we technically express two staggered fcc cubes this way, look at below). Write down all the atomic coordinates of atoms with a sketch of the diamond structure (below).

(1) Give two examples of materials having the diamond structure.

(2) A zincblende structure has fcc lattice with the side length a with different basis atoms at (0,0,0) and (a/4, a/4, a/4). Write down all the atomic coordinates of atoms with a sketch of the zincblende structure.

(3) Give two examples of materials having the zingblende structure.

(4) If lattice is simple cubic, what is the basis for bcc?

(5) If lattice is simple cubic, what is the basis for fcc?

Explanation / Answer

1) The Fractional coordinates of the eight atoms can be written as,

(0,0,0) , (1/4,1/4,1/4) , (0,1/2,1/2) , (1/2,0,1/2) , (1/2,1/2,0) , (1/4,3/4,3/4) , (3/4,1/4,3/4) , (3/4,3/4,1/4).

The co ordinates of the other equivalent atoms can be obtained by adding proper lattice vectors to the coordinates of the relevant atoms.

each atom has four nearest neighbour, and the relative coordinates of the nearest neighbour atoms at (1/4,3/4,3/4)a can be written as

(-1/4,-1/4,-1/4)a , (-1/4,1/4,1/4)a , (1/4,-1/4,1/4)a , (1/4,1/4,-1/4)a

in other set of relative co-ordinates, all relative co-ordinates will have opposite sign as compared to the above relative coordinates.

similarly the relative co ordinates of all other atoms can be written using proper lattice vectors.

2.) The structure of diamond gives rise to the tetrahedral arrangement of atoms, where each atom is available at the middle of a tetrahedron forming a bond with each of its nearest neighbour

Other Materials which have this structure includes Si (silicon), Sn(tin) and Ge (germanium)

3.)It is similar to the diamond structure except that , the two atoms belonging to the basis are not same.

here one of the atom in basis is zinc(zn) and the other atom in basis is sulphur(S).

there are four molocules of ZnS per unit cell. Each atom is surrounded by four atoms in a regular tetrahedral configuration.

The co ordinates of zinc atoms in this configuration is given by,

(1/4,1/4,1/4) , (1/4,3/4,3/4) ,(3/4,1/4,3/4) , (3/4,3/4,1/4) and

the co ordinates of sulphur atoms in this structure is given by,

(0,0,0) , (0,1/2,1/2) , (1/2,0,1/2) , (1/2,1/2,0) .

4.) Some other materials which has similar structure of zinc blende is given as,

Gallium Arsenide - GaAs,

Silver Iodine - AgI

Gallium nitride - GaN

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