Mathematics > QUESTIONS & ANSWERS > University of Texas, Arlington - MSE 5321 | Phase Transformation (MSE 5321) Homework #7 (Complete so (All)

University of Texas, Arlington - MSE 5321 | Phase Transformation (MSE 5321) Homework #7 (Complete solutions) 100% scored

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Phase Transformation (MSE 5321) Homework #7 1. (a) Show that surface melting is to be expected below  Tm in gold (1336 K) given   SL = 0.132,  LV =1.128,   SV... =1.400 Jm-2 (b) Given that the latent heat of fusion of gold is 1.2  109 Jm-3 estimate whether sensible liquid layer thicknesses are feasible at measurably lower temperatures than  Tm . 2. Show that differentiation of Equation 4.4 lead to Equation 4.5 and 4.6 3. Use Equation 4.4 and 4.10 to estimate the number of crystal-like clusters in 1 mm3 of copper at its melting point for spherical clusters containing (a) 10 atoms, (b) 60 atoms. What volume of liquid copper is likely to contain one cluster of 100 atoms? The atomic volume of liquid copper is 1.6×10-29m3,  SL is 0.177 J m-2, k =1.38×10-23 J K-1, Tm = 1356 K. 4. Why does rmax in Fig. 4.5 vary with T ? 5. Calculate the homogeneous nucleation rate in liquid copper at undercooling of 180, 200 and 220 K, using the following data: L = 1.88×109 J m-3 Tm = 1356 K  SL = 0.177 J m-2 f0 = 1011 s-1 C0 = 6×1028 atoms m-3 k = 1.38×10-23 J K-1 6. Show that Equation 4.23 applies to homogeneous nucleation and heterogeneous nucleation on a flat mould wall. 7. Show that Equation 4.16 follows from 4.15 using the following relationships for a spherical cap: ASL  2r2(1cos) A r2 sin2  SM  3  3(2  cos)(1cos)2  r VS [Show More]

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