# (Syllabus) GATE Examination (Metallurgical Engineering)

**GATE Syllabus
Metallurgical Engineering**

**ENGINEERING
MATHEMATICS**

**Linear Algebra: **Matrices and
Determinants, Systems of linear equations, Eigen values and Eigen vectors.

**Calculus:** Limit, continuity
and differentiability; Partial Derivatives; Maxima and minima; Sequences and
series; Test for convergence; Fourier series.

**Vector Calculus:** Gradient;
Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and
Green’s theorems.

**Diferential Equations: **Linear
and non-linear first order ODEs; Higher order linear ODEs with constant
coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs –
Laplace, heat and wave equations.

**Probability and Statistics:**
Mean, median, mode and standard deviation; Random variables; Poisson, normal and
binomial distributions; Correlation and regression analysis.

**Numerical Methods: **Solutions
of linear and non-linear algebraic equations; integration of trapezoidal and
Simpson’s rule; single and multi-step methods for differential equations.

**METALLURGICAL
ENGINEERING**

**Thermodynamics and Rate
Processes: **Laws of thermodynamics, activity, equilibrium constant,
applications to metallurgical systems, solutions, phase equilibria, Ellingham
and phase stability diagrams, thermodynamics of surfaces, interfaces and
defects, adsorption and segregation; basic kinetic laws, order of reactions,
rate constants and rate limiting steps; principles of electro chemistry- single
electrode potential, electro-chemical cells and polarizations, aqueous corrosion
and protection of metals, oxidation and high temperature corrosion –
characterization and control; heat transfer – conduction, convection and heat
transfer coefficient relations, radiation, mass transfer – diffusion and
Fick’s laws, mass transfer coefficients; momentum transfer – concepts of
viscosity, shell balances, Bernoulli’s equation, friction factors.

**Extractive Metallurgy:**
Minerals of economic importance, comminution techniques, size classification,
Flotation, gravity and other methods of mineral processing; agglomeration,
pyrohydro- and electro-metallurgical processes; material and energy balances;
principles and processes for the extraction of non-ferrous metals – aluminium,
copper, zinc, lead, magnesium, nickel, titanium and other rare metals; iron and
steel making – principles, role structure and properties of slags,
metallurgical coke, blast furnace, direct reduction processes, primary and
secondary steel making, ladle metallurgy operations including deoxidation,
desulphurization, sulphide shape control, inert gas rinsing and vacuum reactors;
secondary refining processes including AOD, VAD, VOD, VAR and ESR; ingot and
continuous casting; stainless steel making, furnaces and refractories.

**Physical Metallurgy: **Crystal
structure and bonding characteristics of metals, alloys, ceramics and polymers,
structure of surfaces and interfaces, nano-crystalline and amorphous structures;
solid solutions; solidification; phase transformation and binary phase diagrams;
principles of heat treatment of steels, cast iron and aluminum alloys; surface
treatments; recovery, recrystallization and grain growth; industrially important
ferrous and non-ferrous alloys; elements of X-ray and electron diffraction;
principles of scanning and transmission electron microscopy; industrial
ceramics, polymers and composites; electronic basis of thermal, optical,
electrical and magnetic properties of materials; electronic and opto-electronic
materials.

**Mechanical Metallurgy: **Elasticity,
yield criteria and plasticity; defects in crystals; elements of dislocation
theory – types of dislocations, slip and twinning, source and multiplication
of dislocations, stress fields around dislocations, partial dislocations,
dislocation interactions and reactions; strengthening mechanisms; tensile,
fatigue and creep behaviour; super-plasticity; fracture – Griffith theory,
basic concepts of linear elastic and elasto-plastic fracture mechanics, ductile
to brittle transition, fracture toughness; failure analysis; mechanical testing
– tension, compression, torsion, hardness, impact, creep, fatigue, fracture
toughness and formability.

**Manufacturing Processes: **Metal
casting – patterns and moulds including mould design involving feeding, gating
and risering, melting, casting practices in sand casting, permanent mould
casting, investment casting and shell moulding, casting defects and repair; hot,
warm and cold working of metals, Metal forming - fundamentals of metal forming
processes of rolling, forging, extrusion, wire drawing and sheet metal forming,
defects in forming; Metal joining - soldering, brazing and welding, common
welding processes of shielded metal arc welding, gas metal arc welding, gas
tungsten arc welding and submerged arc welding; welding metallurgy, problems
associated with welding of steels and aluminium alloys, defects in welded
joints; powder metallurgy; NDT using dye-penetrant, ultrasonic, radiography,
eddy current, acoustic emission and magnetic particle methods.