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Unformatted text preview: Solution to Problem Set #8 Problem A binary system AB exhibits the regular solution behavior in the solid state. Answer parts (a) through (e), each when, ε o =(1/ a )(d a /d X A ), the linear strain per unit composition difference, is equal to (i) 0 and (ii) 0.06. Data: The regular solution free energy: f ( X A )= Ω X A (1 X A )+ RT ( X A ln X A +[(1 X A )ln(1 X A )] Ω = 15kJ/mol Gradient energy coefficient, k = 2x109 J m1 Young's modulus, E =2 µ (1+ v ) = 10 11 Pa Poisson's ratio, v = 0.3 Tracer diffusion coefficient, D A * = D B * = 103 exp(100 kJ/ RT ) m 2 s1 Atomic masses, M A = 195 g mol1 , M B = 197 g mol1 Densities, ρ A = 21.5 g cm3 , ρ B = 19.3 g cm3 (a) Calculate the consolute temperature for solid miscibility (the top of the miscibility gap). The consolute temperature for ε o = 0 is given by ( ) A A A X X RT X f − + Ω − = = ∂ ∂ 1 2 2 2 ( ) R X X T A A − Ω = 1 2 For X A = 0.5, we have ( ) K R X X T A A 902 314 . 8 5 . 5 . 10 15 2 1 2 3 = × × × × = − Ω = The consolute temperature for ε o = 0.06 is given by ( ) 2 2 2 2 1 2 1 2 1 2 o...
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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 Penn State.
 Spring '02
 CHEN

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