Interstitial Sites in Close-Packed Structures-
Even in the close packing of spheres, there is left some empty space between the spheres. This empty space in the crystal lattice is called site, void or hole. Voids are of following types.
(i) Trigonal void: This site is formed when three spheres lie at the vertices of an equilateral triangle. Size of the trigonal site is given by the following relation.
r = 0.155 R
r = Radius of the spherical trigonal site
R = Radius of closely packed spheres
(ii) Tetrahedral void: A tetrahedral void is developed when triangular voids (made by three spheres in one layer touching each other) have contact with one sphere either in the upper layer or in the lower layer. This type of void is surrounded by four spheres and the centres of these spheres lie at the apices of a regular tetrahedron, hence the name tetrahedral site for this void.
In a close packed structure, there are two tetrahedral voids associated with each sphere because every void has four spheres around it and there are eight voids around each sphere. So the number of tetrahedral voids is double the number of spheres in the crystal structure. The maximum radius of the atom which can fit in the tetrahedral void relative to the radius of the sphere is calculated to be 0.225: 1, i.e.
\(\frac rR = 0.225\)
No. of voids = 2 x No. of atoms or octahedral voids
where is the radius of the tetrahedral void or atom occupying tetrahedral void and R is the radius of spheres forming tetrahedral void
Tetrahedral void formed by covering trigonal void by spheres of lower layer
Tetrahedral void formed by covering trigonal void by spheres of the upper layer
(iii) Octahedral void: This type of void is surrounded by six closely placed spheres, i.e. it is formed by six spheres. Out of six spheres, four are placed in the same plane touching each other, one sphere is placed from above and the other from below the plane of these spheres. These six spheres surrounding the octahedral void are present at the vertices of regular octahedron.
Therefore, the number of octahedral voids is equal to the number of spheres.
The ratio of the radius (r) of the atom or ion which can exactly fit in the octahedral void formed by spheres of radius R has been
calculated to be 0.414, i.e.
\(\frac rR = 0.414\)
(iv) Cubic void: This type of void is formed between 8 closely packed spheres which occupy all the eight corner of a cube i.e. this site is surrounded by eight spheres which touch each other. Here radius ratio is calculated to be 0.732, i.e.
\(\frac rR = 0.732\)
Thus the decreasing order of the size of the various voids is
Cubic > Octahedral > Tetrahedral > Trigonal
