Question During the solidification of a binary alloy, with a positive temperature gradient in the melt, a planar solid-liquid interface is moving at the steady state, Fig. Q1(i). The variation of the solute concentration, C, in the melt ahead of the interface is given by, b) If m is the liquidus gradient, or the slope of liquidus, Fig.Q1 (iv), how does the equilibrium temperature, T, vary with the melt composition C? T₁ = R.x C=C1+ exp (equation 1.1) D T L Solid Melt (iv) T₁ S S+L where Co is the nominal solute concentration in the alloy, Ko is the equilibrium distribution coefficient, R is the solid-liquid interface moving rate, D is the solute diffusivity in the melt and x is distance into the liquid phase, Fig. Q1(ii). Answer the questions in the steps below, to show that the level of constitutional supercooling is governed by both the actual temperature, T, and the composition, C, in the solidification front. a) Consider a point in the melt at a distance x away from the solid/melt interface. The temperature at the interface is Ti, and the temperature gradient in the melt is GL, Fig.Q1 (iii). How does the actual temperature, T, vary in the melt? T = C/K [3 marks] Actual T gradient [3 marks] c) In the steady state of solidification, what is the composition of the melt at the interface, C₁? f) C₁ = [3 marks] d) Determine the interface temperature, Ti, as a function of the overall composition Co T₁ = g) Sketch the relationships between the actual and equilibrium temperatures in the melt at a distance x relative to the solid/melt interface, and indicate the constitutionally supercooled zone. [3 marks] Briefly state why the region enclosed by T and T is termed the constitutionally supercooled zone. [3 marks] [3 marks] h) What is the critical condition for constitutional supercooling NOT to occur? What does it depend on? [4 marks] e) Determine the equilibrium temperature of liquidus, T, as a function of the distance from the interface, x: T₁₁ = [3 marks]

ISBN: 9781259696527

Author: J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher: McGraw-Hill Education