5. Crystal Structure
• Crystal- it is defined as a solid in which a definite arrangement
of atom is observed in three direction.
• Unit cell- it is defined as smallest arrangement of atom which
is true representation of crystal strucrure and repeat in all
possible direction.
• Space Lattice- it is defined as three dimentional network of
imaginary lines connecting the atom
7. Crystal Structure
• Lattice parameter- The distance between the centre of two
atom is defined as Lattice parameter.
• Lattice angle- These are the angle between the edges of unit
cell.
• Miller Indices- The indexing pattern of plane and direction is
called miller indices
8. Crystal Structure in Metals
Majority of Metals falls in either of the
following crystal structure
BCC (Body Centered Cubic)
FCC (Face Centered Cubic)
HCP (Hexagonal Close Packed)
9. Crystal Structure in Metals
BCC (Body Centered Cubic)
Examples:α-iron, Mo, W, V, Ta, Cr, Na, K
13. Crystal Structure in Metals
HCP (Hexagonal Close Packed)
Examples: Mg,Zn,Be,Cd,Co,Zr,Ti
14. Parameters of Unit Cells
Number of Atoms per Unit Cell
Atomic Packing Factor
Co-ordination Number
Planar Atomic Density
Linear Atomic Density
15. Parameters of Unit Cells
No of Atoms per unit Cell
1. BCC:
No of Atoms at corners:8
No of Atoms at faces: 0
No of Atoms at center: 1
No of Atoms per unit cell
= 8/8 +0/2+1/1
=2
16. Parameters of Unit Cells
No of Atoms per unit Cell
1. FCC:
No of Atoms at corners:8
No of Atoms at faces: 6
No of Atoms at center: 0
No of Atoms per unit cell
= 8/8 +6/2+0/1
=4
17. Parameters of Unit Cells
No of Atoms per unit Cell
1. HCP:
No of Atoms at corners:12
No of Atoms at faces: 2
No of Atoms at center: 3
No of Atoms per unit cell
= 12/6 +2/2+3/1
=6
18. Parameters of Unit Cells
• Co-ordination Number :- The number of
nearest equidistant neighboring atoms
surrounding an atom under consideration is
called co-ordination Number (or Ligancy)
BCC:8 FCC: 12 HCP:12
• APF :- The fractional amount of volume
occupied by atoms in unit cell is called atomic
packing factor (APF)
BCC:0.68 FCC: 0.74 HCP:0.74
19. Imperfections in crystals
• Crystal defect, imperfection in the regular geometrical
arrangement of the atoms in a crystalline solid.
• These imperfections result from deformation of the solid, rapid
cooling from high temperature, or high-energy radiation (X-
rays or neutrons) striking the solid. Located at single points,
along lines, or on whole surfaces in the solid.
• these defects influence its mechanical, electrical, and optical
behaviour.
21. Lattice Vibrations
• one of the main types of internal motion of a solid, in which
• the constituent particles (atoms or molecules) oscillate about e
quilibrium positions—the lattice points.
• The nature of lattice vibrations depends on the symmetry of
• the crystal, the number of atoms in its unit cell, the type of che
mical bond, and the type and concentration of the crystal defec
ts.
22. Zero Dimension Defects (Point Defect)
o Vacancy
A vacancy is referred to an atomic site from where
the atom is missing.
o Impurity
An impurity is referred to an foreign atom which
substitutes for or replaces a parent atom in the
crystal (substitutiona impurity) or occupies the
void pace in the parent crystal (interstitial
impurity).
25. How point defects are formed?
Plastic Deformation
High Energy Particle Irradiation
Temperature
26. One Dimension Defects
(Line Defect) :Dislocations
These defects produce lattice distortions
centered about a line.
The Main Two Types of Dislocations:
Edge Dislocation
Screw Dislocation
28. Screw Dislocation
The screw dislocations are formed by shear stresses
which are applied in the regions of perfect crystal
which have been separated by a cutting plane
These shear stresses create a region of distorted
crystal lattice in the form of a spiral ramp of distorted
atoms.
31. One Dimension Defects
(Line Defect) :Dislocations
Dislocations are formed due to:
Plastic Deformation
Solidification
Vacancy Condensation
32. Grain Boundary is a defect which separate
grain of different orientation from each other
in polycrystalline material
Grain
Boundary
Grain 1
Grain 2
Two Dimension Defects
(Surface Defect)
33. Some of important effect of Grain boundaries
As the atomic packing in grain boundaries is lower
than within the grains, atomics diffusion takes
place more rapidly than in the grain.
Because of their high energy grain boundaries
serve as preferential sites for solid state reactions
such as diffusion phase transformations etc.
34. Some of important effect of Grain boundaries
At room temperature grain boundaries also restrict
plastic flow by making it difficult for the movement
of dislocations in the grain boundary region.
High angle grain boundaries are boundaries of high
surface energy (e.g. grain boundary of Cu has a
surface energy of about 600 mJ/m2 as compare to
its twin boundary energy of 25mJ/ m2). Hence grain
boundaries are more suspectitable for corrosion.
Grain boundaries affect on mech properties.
35. Diffusion Mechanism
• Diffusion, from an atomic perspective, is just the stepwise
migration of atoms from lattice site to lattice site. In fact, the
atoms in solid materials are in constant motion, rapidly
changing positions.
36. Cont…
• Diffusion is the shifting of atoms and
molecules to new sites within a material
resulting in the uniformity of composition as a
result of thermal agitation.
37. Importance of Diffusion
• It is important in the annealing, recrystallization and
grain growth of cold worked metal, in doping of
semiconductors and in the formation of metallic
bonds (soldering, welding, powder metallurgy).
• Diffusion occurs more and more rapidly as the
temperature rises and is the basis for most
metallurgical processes
38. Applications of Diffusion:
• 1. Phase changes, e.g., γ to α iron.
• 2. Metal bonding, e.g., welding, brazing, soldering,
galvanising and metal cladding.
• 3. Homogenising treatment, e.g., annealing of castings.
• 4. Oxidation of metals.
• 5. Production of strong bodies by powder metallurgy.
• 6. Doping of semiconductors.
• 7. Recovery and recrystallization.
• 8. Surface treatment of steels, e.g., casehardening:
• 9. Precipitation of phases in age-hardening.
39. Types of Diffusion:
• 1. Self-Diffusion:
• Self-diffusion is the migration of atoms in pure
materials. In a pure substance, a particular atom does
not remain at one equilibrium site indefinitely, rather it
moves from place to place in the material.
• Self-diffusion in a pure material can be detected
experimentally by radioactive tracers.
• 2. Inter-Diffusion:
• It occurs in binary metallic alloys.
• Observed in binary metal alloys such as Cu-Ni system.
40. Cont…
• 3. Volume Diffusion:
• Volume diffusion means atomic migration through the
bulk of the material.
• 4. Grain Boundary Diffusion:
• It implies atomic movement along the grain boundaries
alone.
• The activation energy for grain boundary diffusion is
lower than for volume diffusion.
• 5. Surface Diffusion:
• It implies atomic movement along the surface of a
phase. Example: Solid-vapour interface.
42. Cont….
• 1. Crystal Structure:
• In case of distorted crystal structure, the rate of
diffusion usually increases.
• 2. Concentration:
• When the concentration within a single solid solution
phase varies, the diffusion coefficient also varies.
43. Cont…
• 3. Grain Boundaries, Dislocations and
Surfaces:
• Grain boundary diffusivities decrease with
decreasing angle of tilt between the grains
joined at the boundary.
44. Cont…
• Grain Size:
• Since grain boundary diffusion is faster than diffusion
within the grains, it is to be expected that the overall
diffusion rate would be higher in fine grained
material.
• Temperature:
• Temperature has the most profound influence on the
coefficients and diffusion rates.
45. Cont…
• Pressure:
• Owing to strong binding between atoms in most
metals, it requires high external pressures to effect an
appreciable change in internal conditions, although it
has been accomplished with relatively soft metals
zinc and sodium.
46. Bauschinger effect
• The Bauschinger effect refers to a property of materials where
the material's stress/strain characteristics change as a result of
the microscopic stress distribution of the material. For
example, an increase in tensile yield strength occurs at the
expense of compressive yield strength.
• The Bauschinger effect is normally associated with conditions
where the yield strength of a metal decreases when the
direction of strain is changed. It is a general phenomenon
found in most polycrystalline metals. The basic mechanism for
the Bauschinger effect is related to the dislocation structure in
the cold worked metal.
