Ch11 -...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: **TI89**##BOOKS#############################################R###Ch11########Z$##¥Z# ###$#BEB#````#######H###¾######################ÿÿÿþ##ÿÿÿý##ÿÿÿü##ÿÿÿû##ÿÿÿú##0##### ÿÿÿú####ÿÿÿû################ÿÿÿý####ÿÿÿû################ÿÿÿü####ÿÿÿû############### #ÿÿÿþ####ÿÿÿû###############$CH 11 PHASE TRANSFORMATIONS # 1. Rewrite the expression for the total free energy change for nucleation (Equation 11.1) for the case of a cubic nucleus of edge length a (instead of a sphere of radius r). Now differentiate this expression with respect to a (per Equation 11.2) and solve for both the critical cube edge length, a*, and also ?G*. a dG = a^3*dG_v + 6a^2*gam d Find a* using dG/da = 0, a F Then dG* = (a*)^3*dG_v + 6(a*)^2*gam T =============== 2. (a) For the solidification of nickel, calculate the critical radius r* and the activation free energy ?G* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are _2.53 × 109 J/m3 and 0.255 J/m2, respectively. (b) calculate the number of atoms found in a nucleus of critical size. Assume a lattice parameter of 0.360 nm for solid nickel at its melting temperature. l A) r* = (-2*gam*T_m/dH_f)(1/(T_m-T)) = -2(.355)(1455+273)/(-2.53E9)*1/319 dG* = (16*pi*gam^3*T_m^3/3dH_f^2)(1/(T_m-T)^2) = 16pi(.255)^3)(1445+273)^2/(3*- 2.53E9)^2 * 1/(319) 2 B) # unit cells/part = crit nuc vol / unit cell vol = (4/3pi*r^3)/a^3 =116 4 atoms / FCC = 116(4) = 464 atoms/crit nuc 4 =============== 3. (a) Assume for the solidification of nickel that nucleation is homogeneous, and the number of stable nuclei is 10^6 nuclei per cubic meter. Calculate the critical radius and the number of stable nuclei that exist at 200 degrees of supercooling (b) What is significant about the magnitudes of these critical radii and the numbers of stable nuclei? n A) For 200K Supercooling, r* = (-2*gam*T_m/dH_f)(1/dT) = (-(2)(.255)(1455+273)/(- 2.53E9))(1/200) Then, K_1 = n*/exp(-dG*/kT) [use n* for homogeneus nucleation, 10^6] and dG*=(16*pi*gam^3*T_m^2/[3dH_f^2](1/(dT)^2) d so # stable nuclei= n_200* = K_1*exp(-dG*/kT) s B) Small changes in radaii and inc in temp result in much higher number of stable nuclei. =============== 5. The kinetics of the austenite-to-pearlite transformation obey the Avrami relationship. Using the fraction transformed_time data given here (.2, 280; .6, 425), determine the total time required for 95% of the austenite to transform to pearlite. p y = y-1 = -e^(-kt^n), t. t = (ln(1-y)/-k)^(1/n) [[1]] Need n and k....
View Full Document

This note was uploaded on 11/16/2009 for the course ENGIN 45 taught by Professor Devine during the Fall '07 term at Berkeley.

Page1 / 51

Ch11 -...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online