Chapter 4.1 Outline
4.1 Nucleation in metals
The method by which solidification occurs is nucleation (formation of very
small solid particles, nuclei)
This is important because even if a liquid is cooled below its equilibrium
at t=24 hr
D=1/(-8.66*10-4 um2*4*86400 s)=3.34*10-15 m2/s
prove C=C+ 0 sin( x /l )exp(t/ ) is a solution of Ficks second law
DB is independent of conce
derive entropy of mixing equation
Smix=( + )
For this derivation, it is assumed that delta Hmix=0, meaning the resultant solution is ideal, and
change of free energy is only due to change in entropy, thus
1. What are the relationships between Figure 1.4 and Figure 1.29? i.e. Which points on Figure
1.29 can be gathered from Figure 1.4?
a- any temperature in figure 4 well above the melting temperature of both element A, B, and an
1. Calculate the self-diffusivities of:
i. Ti at 1125C
D0= 40 mm2/s
D=40 mm2/s*exp(-94.6*10^3 J/mol/(8.134 J/(Kmol)*1398 K)=9.75*10-3 mm2/s
ii. Ti at 450C
D0= 40 mm2/s
Choose a binary alloy system using the TCBIN database.
a. Create an isopleth (phase diagram) of your system
i. If the diagram is very complex, choose a temperature and/or composition
range that is more manageable. (Have a
1. Derive Equation 3.14 by performing a force balance on Figure 3.18. Use a sketch.
assumptions for case
1) steady state
2) two solids in model are similar phase, composition, energy state
3) properties are uniform in bot
Instructional Objectives: Part 2
3. Describe what undercooling is and what are its limits in metallic systems.
Undercooling is the difference in temperature below the melting temperature by
which a material must be cooled in order for nucleation to occur
Instructional Objectives: Part 1
1. Explain quantitatively the difference between homogeneous and
Homogenous nucleation is nucleation of solid without a foreign particle or surface.
In addition, homogenous nucleation will occur i
Instructional Objectives: Part 3
9. Give the corresponding equations for heat flow steady state and unsteady
state similar to the equations for mass flow.
For steady state heat flow, there is no time dependence. Thus heat flux is given
HW #5 Darkens Paper
In his paper, Darken discusses the experiment he completed on the diffusion
of carbon in austenite in welded steel rods. Essentially, he took a baseline steel rod
(alloy a) of a certain composition of carbon, manganese, and s
Apelian HMWK 2
Question, which is which?
Can this be translated to TL? Is this the right equation?
Equilibrium melting temp, at the tips, as found by phase diagram, TR
TL and TR defined by phase diag