Title MSE_V.Raghavn_Chapter-09-Phase Transformation.pdf ✅

GATE- Metallurgical & Materials Engineering +91 7309432902 Pradeep Gupta Telegram Channel: https://t.me/Gatemetallurgy -----------------------------(1) Where, ---------------------------(2) So, from equation (1) & (2) Q. (4) Calculate the critical radius of the copper nucleus during solidification of liquid copper at 983°C. The enthalpy of fusion of copper is 1.88 GJ m–3 (50 cal/gm). The liquid-crystal interfacial energy is 0.144 J m–2 Ans. Where,
GATE- Metallurgical & Materials Engineering +91 7309432902 Pradeep Gupta Telegram Channel: https://t.me/Gatemetallurgy Q. (5) In a phase transformation, an appreciable rate of nucleation of 106 m–3 s –1 occurs at room temperature when the critical nucleation energy is 2.07 X 10–19 J. The energy of the interface between the product and parent phases is 0.05 J m–2. Calculate the nucleation rate, if the interfacial energy had been 10% larger than this. Ans. Nucleation Rate Equation: Now compute with values: Q. (6) Derive the results given in Eqs. (9.14)–(9.16) Ans. Let's derive the critical values c∗, r∗, and Δf ∗ (Equations 9.14–9.16) from the given expression for Δf We want to find the saddle point where the partial derivatives of Δf with respect to r and c are zero: Now differentiate with respect to c and r: Let A(c/r) be a function of x = (c/r), so that;