# GATE Metallurgical Engineering Syllabus

## Subject Code: MT

### Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Vector Calculus
Unit 4 Differential Equations
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Section B Thermodynamics and Rate Processes
Section C Extractive Metallurgy
Section D Physical Metallurgy
Section E Mechanical Metallurgy
Section F Manufacturing Processes

### Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

• Matrices and Determinants
• Systems of linear equations
• Eigen values and Eigen vectors

Unit 2: Calculus

• Limit, continuity and differentiability
• Partial derivatives
• Maxima and minima
• Sequences and series
• Test for convergence
• Fourier series

Unit 3: Vector Calculus

• Divergence and Curl
• Line, Surface and volume integrals
• Stokes, Gauss and Green’s theorems

Unit 4: Differential 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, one dimensional heat and wave equations

Unit 5: Probability and Statistics

• Definitions of probability and sampling theorems
• Conditional probability
• Mean, median, mode and standard deviation
• Random variables
• Poisson, normal and binomial distributions
• Correlation and regression analysis

Unit 6: Numerical Methods

• Solutions of linear and non-linear (Bisection, Secant, Newton Raphson methods) algebraic equations

• Integration by trapezoidal and Simpson’s rule

• Single and multi-step methods for differential equations

Section B: 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, 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

• 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

Section C: Extractive Metallurgy

• Minerals −
• 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 balance
• Principles and processes for the extraction of non-ferrous metals −
• Aluminium
• Copper
• Zinc
• 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
• Vacuum reactors
• Secondary refining processes including −
• AOD
• VOD
• VAR
• ESR
• Ingot and continuous casting
• Stainless steel making, furnaces and refractories

Section D: 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

• 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

Section E: 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 behavior

• Superplasticity

• Fracture – Griffith theory, basic concepts of linear elastic and elastoplastic fracture mechanics, ductile to brittle transition, fracture toughness

• Failure analysis

• Mechanical testing – tension, compression, torsion, hardness, impact, creep, fatigue, fracture toughness and formability

Section F: Manufacturing Processes

• Metal casting −

• 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

• Submerged arc welding

• Welding metallurgy, problems associated with welding of steels and aluminium alloys, defects in welded joints

• Powder metallurgy −

• Production of powders

• Compaction

• Sintering

• NDT using dye penetrant, ultrasonic, radiography, eddy current, acoustic emission and magnetic particle methods