GATE MT flashcards
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32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Lever rule
- In a two-phase region at equilibrium, the fraction of one phase equals the length of the tie-line segment opposite that phase divided by the total tie-line length.
- Eutectoid reaction
- A solid transforms on cooling into two different solid phases simultaneously, as in austenite decomposing to ferrite and cementite at 727 °C in steel.
- Peritectic reaction
- On cooling, a liquid and a solid phase react to form a single new solid phase, such as liquid plus delta-ferrite forming austenite in iron–carbon alloys.
- Hume-Rothery rules
- Conditions favouring complete solid solubility: atomic radii within about 15 percent, same crystal structure, similar electronegativity, and similar valence.
- Gibbs phase rule
- Degrees of freedom F = C − P + 2 for a system with C components and P phases, counting temperature and pressure as variables.
- Fick's second law
- The rate of composition change at a point equals diffusivity times the second spatial derivative of concentration, describing non-steady-state diffusion.
- Arrhenius diffusivity
- Diffusion coefficient D = D₀ exp(−Q/RT), where Q is the activation energy for atomic migration and D₀ is a pre-exponential constant.
- Hall–Petch equation
- Yield strength equals a friction stress plus a constant divided by the square root of grain diameter, so finer grains give higher strength.
- Critical resolved shear stress
- The shear stress on a slip plane along a slip direction needed to start plastic flow, equal to applied stress times cos φ times cos λ.
- Schmid factor
- The product cos φ cos λ relating applied axial stress to resolved shear stress on a slip system; its maximum value is 0.5.
- Ellingham diagram
- A plot of standard Gibbs energy of oxide formation per mole of oxygen versus temperature, used to compare metal oxide stabilities and reduction feasibility.
- Boudouard reaction
- The equilibrium CO₂ + C → 2CO, which becomes favourable at high temperature and governs the reducing gas composition in blast furnaces.
- Calcination versus roasting
- Calcination is thermal decomposition of carbonates or hydroxides without air; roasting is oxidation of sulfides in air to form oxides and sulfur dioxide.
- Froth flotation collectors
- Reagents such as xanthates that adsorb on sulfide mineral surfaces making them hydrophobic so bubbles lift them into the froth.
- Carbon equivalent
- A weighted sum of alloying elements, CE = C + Mn/6 + (Cr+Mo+V)/5 + (Ni+Cu)/15, predicting weldability and cold-cracking susceptibility.
- Hall–Héroult process
- Electrolytic reduction of alumina dissolved in molten cryolite at about 950 °C, producing aluminium at the cathode and CO₂ at carbon anodes.
- Cyanidation of gold
- Leaching gold in aerated alkaline sodium cyanide solution to form the soluble complex [Au(CN)₂]⁻, later recovered by zinc cementation.
- Martensite tempering stages
- Heating quenched steel precipitates epsilon-carbide near 100–200 °C, decomposes retained austenite near 200–300 °C, and coarsens cementite above 400 °C.
- Hardenability
- The depth to which a steel can be hardened by quenching, increased by alloying elements such as Mn, Cr, Mo, and Ni and by coarse austenite grains.
- Jominy end-quench test
- A standard hardenability test in which a bar is austenitized and water-quenched at one end, then hardness is measured along its length.
- TTT diagram
- A time-temperature-transformation diagram showing when austenite starts and finishes transforming to pearlite, bainite, or martensite at each isothermal hold.
- CCT diagram
- A continuous-cooling-transformation diagram giving transformation start and finish temperatures for constant cooling rates, used to select quench severity.
- Maraging steel hardening
- Low-carbon Fe–Ni martensite strengthened by precipitation of intermetallic phases such as Ni₃Ti and Ni₃Mo during ageing near 480 °C.
- Normalizing treatment
- Austenitizing steel and cooling in still air to refine grain size and produce a more uniform, fine pearlitic structure than annealing.
- Stress intensity factor
- K = Y σ √(πa) quantifies crack-tip stress field; fracture occurs when K reaches the plane-strain fracture toughness K_IC.
- Paris law
- Fatigue crack growth rate per cycle equals C times the stress intensity range raised to power m, typically with m between 2 and 4.
- Considère criterion
- Necking begins in tension when the rate of true-stress increase with true strain equals the current true stress, dσ/dε = σ.
- Griffith fracture criterion
- A brittle crack propagates when applied stress reaches the square root of 2Eγ divided by πa, where γ is surface energy and a crack length.
- Steady-state creep rate
- Strain rate equals A σⁿ exp(−Q/RT); the stress exponent n is about 3–5 for dislocation creep and about 1 for diffusional creep.
- Nernst equation
- Electrode potential E = E° − (RT/nF) ln Q; at 25 °C this becomes E° − (0.0592/n) log Q.
- Faraday's law of electrolysis
- Mass deposited equals MIt/(nF), where M is molar mass, I current, t time, n electrons transferred, and F the Faraday constant 96485 C/mol.
- Pilling–Bedworth ratio
- The ratio of oxide volume to metal volume consumed; values between about 1 and 2 favour protective, adherent scales.