Metallurgy Notes - Crystal Structure, Diffusion, and Phase Transformation
1. Introduction, crystal systems and Bravais lattice systems
Crystals are solid materials whose atoms are arranged in a highly ordered repeating pattern. There are 7 crystal
systems: cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, and triclinic. Bravais lattice refers to the
14 possible 3D arrangements of points to form a crystal lattice.
2. Effective number of atoms and packing factor: BCC and FCC
BCC (Body Centered Cubic) has 1 atom at center and 8 at corners. Effective atoms = 2, packing factor approximately
0.68. FCC (Face Centered Cubic) has 1 atom at each face and 8 at corners. Effective atoms = 4, packing factor
approximately 0.74.
3. Effective number of atoms and packing factor: HCP
HCP (Hexagonal Close Packed) has 6 atoms at corners, 2 inside, and 3 mid-layer. Effective atoms = 6, packing factor
approximately 0.74.
4. Types of crystal imperfections, point imperfections
Imperfections are deviations from perfect atomic arrangement. Point defects include vacancies, interstitials, and
substitutional atoms.
5. Dislocation - Screw dislocation, edge dislocation
Edge dislocation involves extra half-plane of atoms. Screw dislocation involves helical twist in lattice. Both are line
defects.
6. Miller indices of planes and directions
Miller indices are a notation to denote crystal planes. It uses intercepts with axes, reciprocals and reduction to lowest
Metallurgy Notes - Crystal Structure, Diffusion, and Phase Transformation
integers, e.g., (100), (111).
7. Diffusion: Types and factors
Diffusion is the movement of atoms. Types: interstitial and substitutional diffusion. Factors: temperature, atomic size,
concentration gradient.
8. Deformation by slip and twinning
Slip involves movement of dislocations along a plane. Twinning is symmetrical deformation about a plane. Both allow
plastic deformation.
9. Difference between slip and twinning
Slip: large, gradual deformation. Twinning: small, sudden shape change. Slip occurs more frequently.
10. Recovery, Recrystallization, and Grain Growth
Recovery: Removal of internal stresses. Recrystallization: Formation of new strain-free grains. Grain growth: Larger
grains form by consuming smaller ones.
11. Grain size measurement
Measured by comparison charts or intercept method (counting grains per unit length).
12. Iron-Iron Carbide Diagram
Fe-C diagram shows equilibrium phases of iron-carbon alloys. Phases include ferrite, austenite, cementite. Important for
steel heat treatment.
Metallurgy Notes - Crystal Structure, Diffusion, and Phase Transformation
13. Invariant Reactions
Peritectic: Liquid + Solid -> Solid; Eutectic: Liquid -> Two solids; Eutectoid: Solid -> Two solids.
14. Upper and lower critical temperature lines
Critical points divide steel phases. Upper (A3/Acm): Austenite begins to form. Lower (A1): Austenite transforms to
pearlite.
15. Transformations in hypo-eutectoid steels (slow cooling)
Steels with <0.8% C form proeutectoid ferrite and pearlite on slow cooling.
16. Transformations in hyper-eutectoid steels (slow cooling)
Steels with >0.8% C form proeutectoid cementite and pearlite on slow cooling.
17. Cooling curve for pure metal
Cooling curve shows temperature vs time. Plateau at phase change indicates latent heat. Sharp transition for pure
metals.