#CRYSTALLOGRAPHY #CRYSTALPHYSICS #FCC #BCC #APF #PACKING FRACTION #DENSITY_OF_UNIT_CELL

1. BY PRASHANT KUMAR
ASST. PROFESSOR
MITS GWALIOR

3.  The group of atoms is called the basis; when repeated in space it forms the
crystal structure.
 The basis consists of a primitive cell, containing one single lattice point.
Arranging one cell at each lattice point will fill up the entire crystal.

5. A crystal is one in which atoms or molecules are in three
dimensional periodic arrangement.
 The periodicity may be same or different in different
directions.
The periodic positions of the atoms or molecules are called
space lattice or crystal lattice.
“The geometrical representation of a crystal structure in
terms of lattice points is called space lattice”

6. The smallest portion of the crystal which can generate the complete
crystal by repeating its own dimensions in various directions is
called UNIT CELL

7. Axial lengths: a, b, c
Interaxial angles : , ,  

8.  AUGUST BRAVAIS in 1848 mathematically proved that there are 14 distinct
ways to arrange points in space. These 14 lattices corresponding to 7 crystal
system are known as BRAVAIS LATTICE.

16.  CONTRIBUTION by atoms at CORNER = 1/8 atom
 Contribution by atoms at Face center =1/2 atom
 Contribution by atoms at Body center= 1 atom
 Contribution by atoms at Base Center/End Center=1/2 atom
 NO. of faces = 6
 NO. of corners=8
 NO. of Bases =2 (top/bottom)

17. Type of unit cell No. of atoms At
corners
No. of atoms In
faces
No. of atoms At the
center
Total
Simple Cubic 8 x 1/8 = 1 0 0 1
Body Centered
Cubic(B.C.C)
8 x 1/8 = 1 0 1 2
Face Centered
Cubic(F.C.C)
8 x 1/8 = 1 6 x 1/2 = 3 0 4
End Centred Cubic 8 x 1/8 = 1 2 x 1/2 = 1 0 2

20. Procedure for finding Miller Indices
Step 1: Determine the intercepts of the plane
along the axes X,Y and Z in terms of
the lattice constants a,b and c.
Step 2: Determine the reciprocals of these
numbers.

21. Step 3: Find the least common denominator (lcd)
and multiply each by this lcd.
Step 4:The result is written in paranthesis.This is
called the `Miller Indices’ of the plane in
the form (h k l).
This is called the `Miller Indices’ of the plane in the form
(h k l).

22. Plane ABC has intercepts of 2 units along X-axis, 3
units along Y-axis and 2 units along Z-axis.
DETERMINATION OF ‘MILLER INDICES’
Step 1:The intercepts are 2,3 and 2 on the three axes.
Step 2:The reciprocals are 1/2, 1/3 and 1/2.
Step 3:The least common denominator is ‘6’.
Multiplying each reciprocal by lcd,
we get, 3,2 and 3.
Step 4:Hence Miller indices for the plane ABC is (3 2 3)

23. Plane parallel to Y and Z axes
In this plane, the intercept along X axis is 1 unit.
The plane is parallel to Y and Z axes. So, the intercepts
along Y and Z axes are .
Now the intercepts are 1, and .
The reciprocals of the intercepts are = 1/1, 1/ and
1/ .
Therefore the Miller indices for the above plane is (1 0
0).

 



26. In such cases (when plane is passing
through origin)the plane is translated
by a unit distance along the non zero
axis/axes
and the Miller indices are computed
1. Intercept of shifted plan =
( 1 ) 
2. Reciprocal 1 1 1
(
1
)
 
Miller Indices (0 1 0)

39.  BRAGG’S DIFFRACTION GRATING

41. • Why X-Ray is selected
for crystallography ?
Ans: because for proper
observation of
diffraction pattern Size
of Obstacle (here it is
Crystal) ~ should be
comparable to
wavelength of ray to be
diffracted
wavelength of X rays
~1Angstron
Atomic distances in
crystal~few angstron

42.  Diffraction is the slight bending of light as it passes around the edge of an object.
 The amount of bending depends on the relative size of the wavelength of light to
the size of the opening.
 If the opening is much larger than the light's wavelength, the bending will be
almost unnoticeable.