# 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**

- Gradient
- 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
- 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
- Vacuum reactors

- Secondary refining processes including −
- AOD
- VAD
- 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 −

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

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

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