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Physcial Metallurgy Syllabus

April 02, 2025

GATE MT - Physical Metallurgy

Physical Metallurgy

Complete Guide for GATE Metallurgy (MT) - Section 5 (TestUrSelf)

Table of Contents

  1. Chemical Bonding & Crystal Structure
  2. Characterization Techniques
  3. Crystal Imperfections
  4. Diffusion in Solids
  5. Phase Transformations
  6. Heat Treatment
  7. Material Properties
  8. Corrosion

5.1 Chemical Bonding & Crystal Structure

Types of Chemical Bonding

Bond Type Energy Range (kJ/mol) Examples Characteristics
Ionic 600-1500 NaCl, MgO Electron transfer, high melting point
Covalent 150-1100 Diamond, SiO2 Electron sharing, directional
Metallic 100-350 Cu, Fe, Al Electron sea, ductile
Secondary 1-50 Polymers, H2O Van der Waals, hydrogen bonds

Crystal Structures of Solids

NaCl (Rock Salt)

BCC (Fe, W)

FCC (Cu, Al)

HCP (Mg, Zn)

Key Parameters

Atomic Packing Factor (APF) = (Volume of atoms in unit cell)/(Volume of unit cell)
Structure Coordination # APF Examples
BCC 8 0.68 Fe(α), W, Mo
FCC 12 0.74 Cu, Al, Ni, Fe(γ)
HCP 12 0.74 Mg, Zn, Ti(α)

5.2 Characterization Techniques

X-ray Diffraction

nλ = 2d sinθ (Bragg's Law)

Where:

  • n = order of reflection (1, 2, 3...)
  • λ = wavelength of X-rays (Cu Kα = 1.54 Å)
  • d = interplanar spacing
  • θ = Bragg angle

Interplanar Spacing

For cubic crystals:

1/d2 = (h2 + k2 + l2)/a2
Example: FCC Pattern

Allowed reflections: h,k,l all odd or all even

First 5 peaks: (111), (200), (220), (311), (222)

Optical & Electron Microscopy

Optical Metallography

  • Resolution limit: ~0.2 μm
  • Magnification: 50-1000×
  • Sample preparation: Cutting, mounting, grinding, polishing, etching

SEM Imaging

  • Resolution: 1-10 nm
  • Depth of field: 100× better than optical
  • Signals: Secondary electrons (topography), Backscattered electrons (composition)

Comparison

Feature Optical SEM
Resolution ~0.2 μm 1-10 nm
Depth of Field Low High
Sample Prep Polished+etched Conductive coating

5.3 Crystal Imperfections

Point Defects

Types

  • Vacancies: Missing atoms
  • Interstitials: Extra atoms in voids
  • Substitutional: Impurity atoms

Concentration

Nv/N = exp(-Qv/kT)

Where Qv ≈ 1 eV for many metals

Example: Cu Vacancies

At 1000K (Qv = 1 eV):

Nv/N ≈ exp(-1/(8.617×10-5×1000)) ≈ 10-5

Line Defects (Dislocations)

Types

  • Edge: Extra half-plane of atoms
  • Screw: Spiral ramp of atoms
  • Mixed: Combination of edge and screw

Burgers Vector (b)

Magnitude and direction of lattice distortion

τcritical = Gb/L (for Frank-Read source)

Dislocation Density

ρ = (Total dislocation length)/(Volume)

Annealed metals: 106-108 cm/cm3

Heavily deformed: 1011-1012 cm/cm3

Interfaces

Interface Type Misfit Energy (J/m2) Example
Coherent <5% 0.05-0.5 GP zones
Semi-coherent 5-25% 0.5-1.0 θ' in Al-Cu
Incoherent >25% 1.0-2.0 θ in Al-Cu

5.4 Diffusion in Solids

Diffusion Equations

Fick's First Law

J = -D(∂C/∂x)

Fick's Second Law

∂C/∂t = D(∂2C/∂x2)

Solutions

Error function solution for constant surface concentration:

(Cx-C0)/(Cs-C0) = 1 - erf(x/(2√(Dt)))

Types of Diffusion

Kirkendall Effect

Different diffusion rates create voids (e.g., Cu-Ni diffusion couple)

Uphill Diffusion

Diffusion against concentration gradient due to chemical potential gradient

Diffusion Mechanisms

Mechanism Activation Energy Example
Interstitial Low (0.1-1 eV) C in Fe
Vacancy High (1-5 eV) Self-diffusion
Grain Boundary Very Low (~0.5Qv) Fast diffusion paths

5.5 Phase Transformations

Solidification

Nucleation

ΔG* = (16πγ3)/(3ΔGv2)

Where γ = interfacial energy, ΔGv = volume free energy change

Growth

v = μΔT (where μ = growth mobility)

Cast Structures

  1. Chill zone: Fine equiaxed grains
  2. Columnar zone: Dendritic growth
  3. Equiaxed zone: Central coarse grains

Solid State Transformations

Transformation Mechanism Example
Precipitation Nucleation & growth Al-Cu (θ")
Spinoidal Continuous decomposition Cu-Ni-Fe
Eutectoid Cooperative growth Fe-C (pearlite)
Martensitic Diffusionless shear Fe-C, Ti alloys

Gibbs-Thomson Effect

Cr = C∞exp(2γVm/rRT)

Where Cr = solubility of particle with radius r

5.6 Heat Treatment

Heat Treatment of Steels

TTT Diagrams

<div class="diagram" style="background: url('data:image/svg+xml;utf8,<svg xmlns=\"http://www.w3.org/2000/svg\" width=\"500\" height=\"300\" viewBox=\"0 0 500 300\"><path d=\"M50,250 L150,150 L200,100 L300,50 L400,80\" fill=\"none\" stroke=\"%235e35b1\" stroke-width=\"2\"/><path d=\"M50,250 L150,200 L200,180 L250,200 L300,220 L350,240\" fill=\"none\" stroke=\"%23ff7043\" stroke-width=\"2\"/><path d=\"M50,250 L100,200 L150,150 L200,120 L250,150 L300,200\" fill=\"none\" stroke=\"%2326a69a\" stroke-width=\"2\"/><text x=\"100\" y=\"270\" font-size=\"12\">Time (log scale)</text><text x=\"20\" y=\"150\" font-size=\"12\">Temperature (°C)</text><text x=\"200\" y=\"30\" fill=\"%235e35b1\">Martensite</text><text x=\"300\" y=\"270\" fill=\"%23ff7043\">Pearlite</text><text x=\"200\" y=\"180\" fill=\"%2326a69a\">Bainite</text></svg>') no-repeat center; background-size: contain; height: 300px;">

CCT Diagrams

Continuous Cooling Transformation - shows transformation products at different cooling rates

Surface Hardening

  • Carburizing: Add carbon at surface (900-950°C)
  • Nitriding: Add nitrogen at surface (500-550°C)
  • Induction hardening: Localized heating + quenching

Recovery, Recrystallization & Grain Growth

tR = t0exp(QR/RT)

Where tR = recrystallization time, QR ≈ 0.3-0.5Qv

Dn - D0n = kt (Grain growth kinetics)

Where n ≈ 2 for normal grain growth

</div>

5.7 Material Properties

Electronic Properties

Property Metals Semiconductors Insulators
Resistivity (Ω·m) 10-8-10-6 10-5-106 1010-1020
Band Gap (eV) 0 0.1-3.0 >3.0

Magnetic Properties

Type χ (Susceptibility) Examples
Diamagnetic -10-5 Cu, Au, Si
Paramagnetic 10-5-10-3 Al, Ti, Na
Ferromagnetic >103 Fe, Co, Ni

5.8 Corrosion

Basic Forms of Corrosion

⚡

Galvanic

🔄

Uniform

🕳️

Pitting

↔️

Crevice

🧵

Stress

Prevention Methods

  • Material selection (noble metals, stainless steels)
  • Cathodic protection (sacrificial anodes, impressed current)
  • Coatings (paint, plating, anodizing)
  • Corrosion inhibitors (chromates, phosphates)

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