Civil mech ppt It is very usefull to everyone

1. ENGINEERING PHYSICS
UNIT IV
CRYSTAL PHYSICS
Muthayammal Engineering College-Rasipuram
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC &
Affiliated to Anna University)

2. INTRODUCTION TO CRYSTAL PHYSICS
‘What is Crystal Physics?
Crystal Physics’ or ‘Crystallography’ is a branch of physics
that deals with the study of all possible types of crystals and
the physical properties of crystalline solids by the
determination of their actual structure by using X-rays,
neutron beams and electron beams.

3. Why we need single crystals?
Car electric lighters use
piezoelectric crystals: A
spark is created by pressing
a button that compresses a
piezoelectric crystal (piezo
ignition), generating an
electric arc.

4. Why we need single crystals?

5. Why we need single crystals?
Crystalline silica
in pc mother board
Semiconducting crystals
in flexible electronics

6. CLASSIFICATION OF SOLIDS
• Crysatalline Materials
❖ The materials in which the atoms in solids are arranged in a regular and
periodical pattern.
❖ Possess directional properties so called anisotropic substances.
❖ crystal has sharp melting point
❖ Possess regular shape
Examples: Metallic crystals – Cu, Ag, Al, Mg etc,
Non-metallic crystals – Carbon, Silicon, Germanium
• Amorphous
The materials in which the atoms in solids are arranged in an
irregular pattern. Examples: Glass, Plastic, Rubber etc.,
Solids
Crystalline Materials
Non- Crystalline Materials
(Amorphous)
Single Crystalline Materials
Poly Crystalline Materials

7. Differences b/n Crystal and amorphous solids
Crystalline Solids Amorphous Solids
1.Atoms or molecules have regular
periodic arrangements
2.They exhibit different magnitudes of
physical properties in different directions.
3.They are anisotropic in nature.
4. They exhibit directional properties.
5.They have sharp melting points.
6. Crystal breaks along regular crystal
planes and hence the crystal pieces have
regular shape
Ex: Copper, Silver, Aluminium etc
Atoms or molecules are not arranged in a
regular periodic manner. They have
random arrangement.
They exhibit same magnitudes of physical
properties in different directions
They are isotropic in nature.
They do not exhibit directional properties.
They do not possess sharp melting points
Amorphous solids breaks into irregular
shape due to lack of crystal plane.
Ex: Glass, Plastic, rubber, etc.

8. Single crystals
substances in which the constituent particles are arranged in a
systematic geometrical pattern are called single crystals.

9. POLYCRYSTALLINE SOLIDS
Polycrystalline materials are made up of an aggregate of many small
single crystals (also called crystallites or grains).
Polycrystalline materials have a high degree of order over many atomic or
molecular dimensions.
Grains (domains) are separated by grain boundaries. The atomic order can vary
from one domain to the next.
The grains are usually 100 nm - 100 microns in diameter.
Polycrystals with grains less than 10 nm in diameter are nanocrystalline
Poly
crystalline
Pyrite form
(Grain)

10. FUNDAMENTAL TERMS OF
CRYSTALLOGRAPHY
• Lattice: A lattice or space lattice
is defined as an array of points in
three dimensions and have
identical surroundings to that of
every other point.
• Lattice Points: Lattice points
representing the locations of
atoms in an imaginary geometry.
The actual array of atoms is
called the structure.
• Basis: The group of atoms that is
associated with every lattice
point is called a basis. The
crystal structure is formed when
a group of atoms is identically
attached to every lattice point.

11. • Unit Cell: The unit cell is defined as the smallest geometrical
unit, which when repeated in space over three dimensions
gives the actual crystal structure (or) a unit cell is the smallest
volume that carries full description of the entire lattice.

12. Lattice parameters
• Length of the unit cell along the x,
y,
and z direction are a, b, and c
(axial lengths)
• x, y and z are crystallographic axes
• Interfacial angles
α = the angle between a and b
β = the angle between b and c
γ = the angle between c and a
a, b, c, α, β, γ are collectively known as the lattice parameters

13. PRIMITIVE CELL
• A unit cell consists of only one full atom
• A primitive cell got the points or atoms
only at the corners
• If a unit cell consists more than one atom,
then it is not a primitive cell.
• Example for primitive cell :
Simple Cubic(SC)
• Examples for non-primitive cell :
BCC and FCC unit cell.

14. Types of Crystals
The crystals are basically classified into 7 types (7-crystal systems)
1. Cubic
2. Tetragonal
3. Ortho – rhombic
4. Monoclinic
5. Triclinic
6. Trigonal (sometimes called rhombohedral)
7. Hexagonal.

15. Seven crystal systems

16. Seven crystal systems and its lattice Parameters

17. BRAVAIS LATTICE
Bravais in 1948 showed that 14 types of unit cells under seven crystal systems are possible.

18. 18
MILLER INDICES
⮚ set of three possible integers represented as (h k l)
⮚ reciprocals of the intercepts made by the plane on the three
crystallographic axes
⮚ designate plane in the crystal.

19. ▪ Step 1 : Determine the intercepts of the plane along the axes
▪ Step 2 : Determine the reciprocals of these numbers.
▪ Step 3 : Find the LCD and multiply each by this LCD
▪ Step 4 : Write it in paranthesis in the form (h k l).
19
Procedure for finding Miller Indices

20. Step 1 : intercepts - 2a,3b and 2c
Step 2 : reciprocals - 1/2, 1/3 and 1/2.
Step 3 : LCD is ‘6’.
Multiply each reciprocal by lcd,
we get, 3,2 and 3.
Step 4 : Miller indices for the plane
ABC is (3 2 3)
ILLUSTRATION
20

21. EXAMPLE
▪ intercepts are 1, ∞ and ∞.
▪ reciprocals of the intercepts are
1/1, 1/∞ and 1/∞.
▪ Miller indices for the plane is (1 0 0).
21

22. 22
Miller Indices of Some Important Planes

24. Important features of miller indices
▪ a plane parallel to the axes has an intercept of infinity (∞).
▪ a plane cuts an axis on the negative side of the origin, is
represented by a bar, as ( ͞1 0 0).
▪ a plane passing through the origin have non zero intercepts
▪ All equally spaced parallel planes have same Miller indices
24

25. Relation Between the Interplanar Distance (or)
D–Spacing in Cubic Lattice
• d-spacing or the interplanar distance is the distance between any two
successive lattice planes.
• consider a plane ABC as shown in Fig .
• The perpendicular ON from the origin O to the plane ABC represents the
distance d between the origin and the first plane.
• OX, OY and OZ represents the axes and OA, OB, OC are the intercepts by
the plane.
• α, β and γ represents the angle between ON and along with other axis OA,
OB and OC respectively .

26. • The intercepts of the plane on the three axes are

27. The above equation gives the relation
between inter atomic distance ‘a’ and
the inter planer distance‘d’ and is
called d-spacing.

28. Parameters Determining The Crystal
Structure
i) Number of atoms per unit cell
The total number of atoms present in a unit cell is called number of atoms
per unit cell.
ii) Atomic radius (r)
Atomic radius is defined as half of the distance between any two nearest
neighbouring atoms in the crystal structure.
iii) Co-ordination number
Co-ordination number is defined as the number of nearest neighbouring
atoms to any particular atom in the crystal structure.
iv) Atomic Packing factor (or) Packing density (or) Density of Packing
It is defined as the ratio of the total volume occupied by the atoms in a
unit cell (v) to the total volume of a unit cell (V).
Atomic Packing Factor (APF)

29. Simple Cubic structure (SC)
Only 8 atoms, one at each corner of
the cube , each corner atom
contribute only 1/8th of its part
No. of atoms/unit cell 1
Atomic Radius a/2
Coordination No. 6
APF 0.52
R=0.5a
a
a = 2r

30. Atomic Packing Factor (APF)
No of atoms present in unit cell x volume of one atom
Packing Factor = ---------------------------------------------------------------
volume of the unit cell
It is understood that only 52 % of volume of the unit cell is only occupied by the
atoms and the remaining area is kept vacant.

31. Body Centered Cubic Structure (BCC)
A
B
C
D
No. of atoms/unit cell 2
Atomic Radius √3 a/4
Coordination No. 8
APF
√3π/8 or
0.68

32. Atomic Radius
Atomic radius of a BCC structure

33. Atomic Packing Factor (APF)
Volume of the unit cell of a cubic system (V) = a3
Atomic Packing Factor =
Atomic packing factor for BCC structure = 0.68
It is understood that 68 % of volume of the unit cell is occupied by
the atoms and the remaining is kept vacant.

34. Face Centered Cubic Structure (FCC)
4r
A
B
C
D
a
a
No. of atoms/unit
cell
4
Atomic Radius √2a/4
Coordination No. 12
APF π /( 3√2 ) or 0.74

35. Atomic radius of FCC structure
AC2 = AB2 + BC2
= a2 + a2
= 2a2
AC = a
From the diagram AC = 4r
4r = a
r =
Atomic radius of FCC structure is =

36. Atomic Packing Factor (APF)
Total number of atoms per unit cell of a FCC structure = 4
Volume of 4 spherical atoms (v) =
= Since
v =
= =
Volume of the unit cell for a cubic structure (V) = a3

37. Atomic packing factor =
=
Atomic packing factor for FCC structure = 0.74
In which 74% of volume of a unit cell is occupied by the
atoms and remaining volume is vacant.

38. HEXAGONAL CLOSE PACKED STRUCTURE
(HCP)
c
a
A sites
A sites

39. • Number of Atoms per Unit Cell
The number atoms per unit cell =
= Top layer atom contribution + middle layer
atom contribution
= No. of corner atoms + No. of base centered atoms +
No. of middle layer atoms present exclusively inside
unit cell
• Coordination Number
The coordination number = 12
• Atomic Radius
The atomic radius , r = a/2
c
a
A sites
A sites

40. Atomic Packing Factor (APF)
Total number of atoms per unit cell of HCP structure = 6
Volume of the atoms in a unit cell, v =
atomic radius
v
v

41. Volume of the HCP unit cell ( V )

42. Volume of the HCP unit cell ( V )
Total volume of the HCP unit cell, V = Area of the base height
Area of the base = Area of 6 triangles
= 6 area of one triangle
(OFA)
area of the triangle OFA = AF OT
Substituting the value of OT and AF = a,
Area of the triangle OFA =
=
Area of the base = =
Total volume of the unit cell (V)

43. Atomic packing factor
Atomic packing factor = = =
= = 0.74
Atomic packing factor for HCP = 0.74
74% of volume of the unit cell of HCP structure is occupied by the atoms and
remaining is kept vacant.
The atomic packing factor of HCP structure is the same as that of FCC
structure and they are called tightly packed structure.

44. Calculation for c/a ratio
In the HCP structure it is found that
=
In the triangle SOP,
We know the distance between the middle layer and bottom layer is c/2
SP = OP = a

45. Thank you