where, M = m .Ne, and m = mass of one atom.
The mass of one atom m may be obtained by
..........(2)
The volume
of cubical unit cell = a3. Thus the density may be calculated by
the given formula
..........(3)
Equation (3) suggests that the
density is directly proportional to the effective number of atoms per unit
cell. Hence elements having FCC structures possess higher densities. Gold (Au)
belonging to this kind of structure has density of 19300 kg/rn3. However only this
fact cannot be taken as a rule. Aluminium (Al) also belongs to FCC structure but
has a lower density of 2700 kg/m3. only.
Q.7 What do you understand by the term “Miller
Indices”? (2009 - 10)
Ans. Miller Indices: -
Miller indices are defined as the
notations which describe about the planes and directions in the unit cells and
crystals. Miller Indices can be represented by (h k l), but the type
of bracket may varies according to their meaning as :
(h k l) : It denotes
a plane.
[h k l] : It denotes
direction of plane.
{h k l} : It denotes
family of planes.
<h k l> : It
denotes family of directions.
Miller indices are also known as the
reciprocal of the intercepts made by the plane on three rectangular axes x, y
and z axes respectively. Let p is the intercept of the plane on x-axis, q is
the intercept of the plane on y-axis and r is the intercept of the plane on
z-axis.
Thus, 
Miller indices can never be fraction
so
Procedure to Find Miller Indices: -
(1) Let us
consider a unit cell with origin at its one corner as shown in following figure
:
(2) Find out the intercepts OA, OB and OC on
the X, Y and Z axes respectively.
