finalexamsamplequestions2002 - Matsc 503 - Kinetics of...

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Matsc 503 - Kinetics of Materials Processes Sample Final Exam Questions 2. The amplitude of a compositional fluctuation, C-C o , where C o is the average initial composition, may be expressed as ( ) ( ) ( ) [ ] t R A t A β exp 0 , , = where A( β ,0) is the initial amplitude at time zero and R( β ) is an amplification factor which, with the elastic strain energy ignored, is given by R β ( ) =− M β 2 f " + 2 κβ 2 ( ) N v where κ is the gradient energy coefficient, β is the wave vector, and N v is the number of moles per unit volume (assume N v is a constant and independent of C and T). In a regular solution for a binary alloy (components A and B), the homogeneous free energy density is given by fC () = N v α C 1 C ( ) + RT ClogC + 1 C ( ) log 1 C ( ) [ ] {} (a) (10 points) Find the value of α such that the interdiffusion coefficient is zero at a temperature 722 K at C = 0.5 (moles A/mole). (R = 8.314 J/(K mole)). (b) (10 points) The system is quenched from 800 to 541.5 K at a composition C = 0.5. If the gradient energy coefficient, κ = 6 × 10 -13 N v J/m 2 , what is the expected length scale of the decomposed microstructure in the early stages of decomposition? (c) (10 points) Following part (b), what is the shortest wavelength below which a concentration wave cannot grow during a spinodal decomposition at 541.5 K at C = 0.5?
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This note was uploaded on 01/19/2010 for the course MAT SCI 503 taught by Professor Chen during the Spring '02 term at Pennsylvania State University, University Park.

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finalexamsamplequestions2002 - Matsc 503 - Kinetics of...

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