# GATE Syllabus for Metallurgical Engineering (MT)

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## Metallurgical Engineering syllabus

Part 1: Engineering Mathematics

Linear Algebra: Systems of linear equations, Matrices and Determinants, Eigen values and Eigen vectors. Calculus: Limit, Partial derivatives; continuity and differentiability; Maxima and minima; Test for convergence; Sequences and series; Fourier series.

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

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

Probability and Statistics: Definitions of probability and sampling theorems, Mean, median, mode and standard deviation; conditional probability, Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis

Numerical Methods: Solutions of linear and non-linear (Bisection, Secant, NewtonRaphson methods) algebraic equations; single and multi-step methods for differential equations; integration by trapezoidal and Simpson’s rule

Part 2: Thermodynamics and Rate Processes

Laws of thermodynamics, activity, applications to metallurgical systems, equilibrium constant, solutions, phase equilibria, thermodynamics of surfaces, Ellingham and phase stability diagrams, interfaces and defects, principles of electro chemistry- single electrode potential, electrochemical cells and polarizations, aqueous corrosion and protection of metals, galvanic corrosion, crevice corrosion, pitting corrosion, intergranular corrosion, selective leaching, oxidation and high temperature corrosion – characterization and control; adsorption and segregation; basic kinetic laws, order of reactions, rate constants and rate limiting steps; 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, friction factors, Bernoulli’s equation

Part 3: Extractive Metallurgy

Minerals of economic importance, comminution techniques, size classification, flotation, gravity and other methods of mineral processing; agglomeration, pyro-, hydro-, 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, desulphurization, sulphide shape control, inert gas rinsing and vacuum reactors, ladle metallurgy operations including deoxidation

Part 4: Physical Metallurgy

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

Part 5: Mechanical Metallurgy

Elasticity, yield criteria and plasticity; 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; defects in crystals; strengthening mechanisms; tensile, fatigue and creep behaviour; superplasticity; fracture – Griffith theory, basic concepts of linear elastic and elastoplastic fracture mechanics, ductile to brittle transition, fracture toughness; mechanical testing – tension, compression, torsion, hardness, impact, creep, fatigue, fracture toughness and formability; failure analysis

Part 6: 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 – production of powders, compaction and sintering; NDT using dyepenetrant, ultrasonic, radiography, eddy current, acoustic emission and magnetic particle methods

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