GATE Metallurgical Engineering Physical Metallurgy Syllabus

Physical Metallurgy syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Physical Metallurgy in GATE Metallurgical Engineering, not a summary of it.

1. 1

   Chemical Bonding

   4 topics

   • Ionic Bonding
   • Covalent Bonding
   • Metallic Bonding
   • Secondary Bonding in Materials
2. 2

   Crystal Structure of Solids

   4 topics

   • Metals and Alloys
   • Ionic Solids
   • Covalent Solids
   • Polymers
3. 3

   X-ray Diffraction

   3 topics

   • Bragg’s Law
   • Optical Metallography
   • Principles of SEM Imaging
4. 4

   Crystal Imperfections

   6 topics

   • Point Defects
   • Line Defects
   • Surface Defects
   • Coherent Interfaces
   • Semi-Coherent Interfaces
   • Incoherent Interfaces
5. 5

   Diffusion in Solids

   10 topics

   • Diffusion Equation
   • Steady State Solutions
   • Error Function Solutions
   • Homogenenization Examples
   • Carburization Examples
   • Kirkendall Effect
   • Uphill Diffusion
   • Atomic Models for Diffusion
     • Interstitial Diffusion
     • Substitutional Diffusion
   • Pipe Diffusion
   • Grain Boundary Diffusion
6. 6

   Phase Transformation

   13 topics

   • Driving Force
   • Homogeneous Nucleation
   • Heterogeneous Nucleation
   • Growth Kinetics
   • Solidification in Isomorphous Systems
   • Solidification in Eutectic Systems
   • Solidification in Peritectic Systems
   • Cast Structures
   • Macrosegregation
   • Dendritic Solidification
   • Constitutional Supercooling
   • Coring
   • Microsegregation
7. 7

   Solid State Transformations

   9 topics

   • Precipitation
   • Spinoidal Decomposition
   • Ordering
   • Massive Transformation
   • Discontinuous Precipitation
   • Eutectoid Transformation
   • Diffusionless Transformations
   • Precipitate Coarsening
   • Gibbs-Thomson Effect
8. 8

   Principles of Heat Treatment

   8 topics

   • TTT Diagrams
   • CCT Diagrams
   • Surface Hardening Treatments
   • Recovery
   • Recrystallization
   • Grain Growth
   • Heat Treatment of Cast Iron
   • Heat Treatment of Aluminium Alloys
9. 9

   Electronic, Magnetic and Optical Properties

   overview

   Examined as a single unit within Physical Metallurgy — no further topic split in the official outline.

10. 10

    Basic Forms of Corrosion

    1 topic

    • Corrosion Prevention

Physical Metallurgy flashcards for GATE Metallurgical Engineering

21 of 56 cards from the Physical Metallurgy deck — real questions with worked answers.

1. What is ionic bonding and between which type of atoms does it form?

   Ionic bonding is a primary bond formed by the electrostatic (Coulombic) attraction between oppositely charged ions, created by complete electron transfer from a low-electronegativity metal to a high-electronegativity non-metal (e.g. $\ce{Na+}$ and $\ce{Cl-}$ in $\ce{NaCl}$).

2. Write the expression for the Coulombic attractive force between two ions of charges $Z_1 e$ and $Z_2 e$ separated by distance $r$.

   $$F = \frac{Z_1 Z_2 e^{2}}{4 \pi \varepsilon_0 r^{2}}$$ where $e$ is the electronic charge and $\varepsilon_0$ is the permittivity of free space.

3. Is the ionic bond directional or non-directional, and what does this imply for ion packing?

   The ionic bond is non-directional; each ion attracts oppositely charged ions equally in all directions, so ions pack to maximize coordination while maintaining charge neutrality.

4. List four characteristic properties of ionically bonded solids.

   High melting point and hardness, brittleness, electrical insulation in the solid state but conduction when molten or dissolved, and transparency to visible light.

5. What is covalent bonding?

   A primary bond formed by the sharing of valence electron pairs between atoms of similar (high) electronegativity, producing a strong, highly directional bond (e.g. the $\ce{C-C}$ bonds in diamond).

6. Why is the covalent bond described as directional, and how does this affect coordination number?

   Electrons are shared in localized orbitals pointing in specific directions, so bonds form at fixed angles. This limits the coordination number, governed by the $8-N$ rule, where $N$ is the number of valence electrons.

7. State the $8-N$ rule for covalently bonded elements.

   A covalently bonded atom forms $8-N$ bonds (and thus has coordination number $8-N$), where $N$ is the number of valence electrons. E.g. for carbon ($N=4$), coordination $= 8-4 = 4$.

8. What is metallic bonding?

   A primary, non-directional bond in which positively charged metal ion cores are held together by a delocalized 'sea' or 'cloud' of valence electrons that are free to move throughout the lattice.

9. How does metallic bonding explain the high electrical and thermal conductivity of metals?

   The delocalized valence electrons are free to move under an applied electric field or thermal gradient, carrying charge and energy through the lattice.

10. Why are metals ductile while ionic and covalent solids are brittle?

    In metals the non-directional electron-sea bonding allows ion cores to slide past one another (slip) without breaking bonds, whereas directional/charged bonds in covalent and ionic solids resist atomic rearrangement, causing fracture.

11. What are secondary (van der Waals) bonds and how do their energies compare with primary bonds?

    Secondary bonds are weak attractions arising from electric dipoles, with energies typically $\sim 0.1$–$10\ \mathrm{kJ/mol}$, far weaker than primary (ionic/covalent/metallic) bonds at $\sim 100$–$1000\ \mathrm{kJ/mol}$.

12. Name the three main types of secondary bonding (van der Waals forces).

    Fluctuating (London dispersion) induced dipole–induced dipole forces, permanent dipole–induced dipole forces (Debye), and permanent dipole–permanent dipole (Keesom) forces; hydrogen bonding is the strongest special case.

13. What is hydrogen bonding and why is it the strongest secondary bond?

    Hydrogen bonding occurs when H is covalently bonded to a highly electronegative atom (F, O, N); the bare proton creates a strong localized positive end of the dipole, giving energies up to $\sim 50\ \mathrm{kJ/mol}$, larger than ordinary van der Waals bonds.

14. Define an alloy and distinguish a substitutional from an interstitial solid solution.

    An alloy is a metallic material composed of two or more elements. In a substitutional solid solution, solute atoms replace solvent atoms on lattice sites; in an interstitial solid solution, small solute atoms occupy the interstitial voids between solvent atoms.

15. State the Hume-Rothery rules for extensive substitutional solid solubility.

    (1) Atomic radii differ by less than $\sim 15\%$; (2) same crystal structure; (3) similar electronegativity; (4) same or compatible valency. Violating these favors compound formation or limited solubility.

16. What is an intermetallic compound, and how does its bonding differ from a solid solution?

    An intermetallic compound is an ordered phase of two metals with a fixed stoichiometric ratio and a distinct crystal structure (e.g. $\ce{Fe3C}$, $\ce{Ni3Al}$); its bonding has partial ionic/covalent character, making it harder and more brittle than a random solid solution.

17. Describe the structure of an ionic solid such as $\ce{NaCl}$, including coordination.

    $\ce{NaCl}$ has the rock-salt structure: an FCC arrangement of $\ce{Cl-}$ ions with $\ce{Na+}$ ions filling all octahedral voids, giving $6{:}6$ coordination. Each ion is surrounded by six oppositely charged neighbors.

18. What determines the coordination number in an ionic solid, and give the radius-ratio range for octahedral (6) coordination.

    The radius ratio $\frac{r_{\text{cation}}}{r_{\text{anion}}}$ determines coordination. Octahedral (CN $=6$) coordination is stable for $0.414 \leq \frac{r_c}{r_a} < 0.732$.

19. Give the radius-ratio ranges for tetrahedral (CN 4) and cubic (CN 8) coordination in ionic solids.

    Tetrahedral (CN $=4$): $0.225 \leq \frac{r_c}{r_a} < 0.414$; cubic (CN $=8$): $0.732 \leq \frac{r_c}{r_a} < 1.0$.

20. Why are covalent solids like diamond extremely hard and high-melting?

    Diamond forms a 3-D network of strong directional $\ce{C-C}$ covalent bonds (each carbon tetrahedrally bonded to four others); breaking or deforming the crystal requires rupturing many strong bonds, giving extreme hardness and a very high melting point.

21. Contrast diamond and graphite as covalent solids in terms of bonding and properties.

    Diamond: $sp^{3}$ tetrahedral 3-D network, hard, electrically insulating. Graphite: $sp^{2}$ hexagonal layers with delocalized $\pi$ electrons within layers and weak van der Waals bonding between layers, making it soft, a lubricant, and electrically conducting along the layers.

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