# Test%202 - Page 1 of 2 MATLS 3T04"Phase Transformations...

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Page 1 of 2 MATLS 3T04 “Phase Transformations” Test 2 Problem 1 (40 points) Imagine that eutectic solidification results in cylinders (rods) of β phase surrounded by α phase. An arrangement of the β -cylinders is shown in Liquid →α+β Figure 1. λ 0 90 β α Figure 1 If f is a known volume fraction of β phase, then what is the minimal spacing min for a given supercooling ? T Δ Hint: a b c Problem 2 (40 points) Consider a binary solid solution having a uniform composition. The mole fraction of the 2 nd component in this solution is equal to 0 x . Imagine that a very small particle formed within this solution. The particle has the same crystal structure as the solution (the particle, therefore, is a cluster), but the mole fraction of the 2 nd component in it is equal to 0 x x ′ ≠ . Show that the change of the Gibbs energy associated with the formation of one mole of such clusters is equal to () 0 2 22 0 xx Gx x x x = ∂∂ where is a concentration dependency of the molar Gibbs energy of the solid solution.

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Test%202 - Page 1 of 2 MATLS 3T04"Phase Transformations...

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