Candidates appearing for the Graduate Aptitude Test in Engineering (GATE) 2022 examination can take their pick from a total of 29 papers. Given below is the detailed syllabus of the subject paper Metallurgical Engineering (Code: MT). The paper contains 7 sections with an array of topics under each section.

**Section 1: Engineering Mathematics **

**Linear Algebra**: Matrices And Determinants, EigenValues And EigenVectors, Systems Of Linear Equations**Calculus:**Test For Convergence, Partial Derivatives, Fourier Series, Limit, Continuity And Differentiability, Sequences And Series, Maxima And Minima

**Vector Calculus**: Line, Surface And Volume Integrals, Stokes, Gauss And Green’s Theorems, Divergence And Curl, Gradient

**Differential Equations**: Cauchy’s And Euler’s Equations, PDEs –Laplace, One Dimensional Heat And Wave Equations, Higher Order Linear ODEs With Constant Coefficients, Linear And Non-Linear First Order ODEs, Laplace Transforms

**Probability and Statistics**: Linear Least Squares Method, Random Variables, Analysis Of Experimental Data, Definitions Of Probability And Sampling Theorems, Conditional Probability, Mean, Median, Mode And Standard Deviation, Poisson, Normal And Binomial Distributions

**Numerical Methods**: Integration By Trapezoidal and Simpson’s Rule, Solutions Of Linear And Non-Linear (Bisection, Secant, Newton- Raphson Methods) Algebraic Equation, Single And Multi-Step Methods For Differential Equations

**Section 2: Metallurgical Thermodynamics**

**Laws of Thermodynamics**: First law – energy conservation, Second law – entropy; Enthalpy, Gibbs and Helmholtz free energy; Maxwell’s relations; Chemical potential; Applications to metallurgical systems, solutions, ideal and regular solutions; Gibbs phase rule, phase equilibria, binary phase diagram and lever rule, free-energy vs. composition diagrams; Equilibrium constant, Activity, Ellingham and phase stability diagrams; Thermodynamics of point defects, surfaces and interfaces, adsorption and segregation phenomena**Electrochemistry**: Potential-Ph Diagrams, Single Electrode Potential, Nernst Equation, Electrochemical Cells

**Section 3: Transport Phenomena and Rate Processes **

**Momentum transfer**: Flow Past Plane Surfaces And Through Pipes, Shell Balances, Concept Of Viscosity, Mechanical Energy Balance Equation, Bernoulli’s Equation**Heat transfer:**Fourier’s Law, Conduction, 1-D Steady State Conduction**Convection**: Heat Transfer Coefficient Relations For Forced Convection**Radiation**: Stefan-Boltzman Law, Black Body Radiation, Kirchhoff’s Law**Mass transfer**: Mass Transfer Coefficients, Diffusion And Fick’s Laws**Dimensional analysis**: Significance Of Dimensionless Numbers, Buckingham Pi Theorem**Basic laws of chemical kinetics**: Heterogeneous Reactions, Arrhenius Relation, First Order Reactions, Oxidation Kinetics, Reaction Rate Constant

**Electrochemical kinetics**: Polarization

**Section 4: Mineral Processing and Extractive Metallurgy **

Comminution techniques, Size classification, Flotation, Gravity and other methods of mineral beneficiation; Agglomeration: sintering, pelletizing and briquetting.

Material and Energy balances in metallurgical processes; Principles and processes for the extraction of non-ferrous metals – aluminum, copper and titanium.

Iron and steel making: Material and heat balance in blast furnace; Structure and properties of slags and molten salts – basicity of slags – sulphide and phosphate capacity of slags; Production of metallurgical coke.

Other methods of iron making (COREX, MIDRE):

**Primary Steel Making**: Oxidation Reactions, Process Dynamics, Basic Oxygen Furnace, Electric Arc Furnace

**Secondary Steel Making**: Ladle process – deoxidation, argon stirring, desulphurization, inclusion shape control, principles of degassing methods; Basics of stainless steel manufacturing**Continuous Casting**: Fluid flow in the tundish and mould, heat transfer in the mould, segregation, inclusion control

**Section 5: Physical Metallurgy **

**Chemical Bonding**: Ionic, covalent, metallic, and secondary bonding in materials, Crystal structure of solids – metals and alloys, ionic and covalent solids, and polymers-
**X-ray Diffraction**– Optical Metallography, Bragg’s Law, Principles Of SEM Imaging **Crystal Imperfections**: Coherent, Semi-Coherent And Incoherent Interfaces, Point, Line And Surface Defects

**Diffusion in solids**: Diffusion equation, steady state and error function solutions; Examples- homogenization and carburization; Kirkendall effect; Uphill diffusion; Atomic models for interstitial and substitutional diffusion; Pipe diffusion and grain boundary diffusion**Phase transformation**: Driving force, Homogeneous and heterogeneous nucleation, growth Kinetics Solidification in isomorphous, eutectic and peritectic systems, cast structures and macrosegregation, dendritic solidification and constitutional supercooling, coring and microsegregation**Solid state transformations:**Precipitation, spinoidal decomposition, ordering, massive

transformation, discontinuous precipitation, eutectoid transformation, diffusionless transformations; Precipitate coarsening, Gibbs-Thomson effect

Principles of heat treatment of steels, TTT and CCT diagrams; Surface hardening treatments; Recovery, recrystallization and grain growth; Heat treatment of cast iron and aluminium alloys, electronic, magnetic and optical properties of materials, basic forms of corrosion and its prevention

**Section 6: Mechanical Metallurgy **

- Strain Tensor And Stress Tensor, Representation By Mohr’s Circle, Elasticity, Stiffness And Compliance Tensor, Yield Criteria, Plastic Deformation By Slip And Twinning

**Dislocation Theory**: Partial Dislocations, Dislocation Interactions And Reactions, Edge, Screw And Mixed Dislocations, Source And Multiplication Of Dislocations, Stress Fields Around Dislocations

**Strengthening Mechanisms**: Work/strain hardening, strengthening due to grain boundaries, solid solution, precipitation and dispersion. Fracture behaviour, Griffith theory, linear elastic fracture mechanics, fracture toughness, fractography, ductile to brittle transition

**Fatigue**: Crack Growth, Mechanisms Of High Temperature Deformation And Failure, Cyclic Stress Strain Behaviour – Low And High Cycle Fatigue, Creep And Stress Rupture, Stress Exponent And Activation Energy

**Section 7: Manufacturing Processes **

**Metal casting**: Mould Design Involving Gating And Risering, Feeding, Casting Defects, Casting Practices

**Hot, Warm And Cold Working Of Metals**: Metal Forming – Fundamentals Of Metal Forming Processes Of Extrusion, Rolling, Forging, Wire Drawing And Sheet Metal Forming, Defects In Forming

**Metal Joining**: Principles Of Brazing And Welding, Soldering, Welding Metallurgy, Defects In Welded Joints In Steels And Aluminum Alloys**Powder Metallurgy:**Production Of Powders, Compaction And Sintering

**Non-destructive Testing (NDT**): Dye-penetrant, ultrasonic, radiography, eddy current, acoustic emission and magnetic particle inspection methods