Analysis of Electropolishing
acceptor ions in the electrolyte diffuse to the surface allowing
for a metal atom to give up electrons resulting in metal cation
formation metal dissolution.
y
a
b
x
z
Sav
Simple Rate Equations
Consider a chemical reaction: A B
There are two common trends for the time rate of
change of the concentration, CA.
C A = k C
A
C A = k C
2
A
first order reaction kinetics
second
Solutions To The Linear Diffusion Equation
Martin Eden Glicksman
Afina Lupulescu
Rensselaer Polytechnic Institute
Troy, NY, 12180
USA
meg/aol 02
Outline
Transform methods
Linear diffusion into semi
Diffusion in Substitutional Alloys
In a binary substitutional alloy, the rate at which solvent (A) and solute (B)
atoms move into a vacant site is not equal, and each spices will have its own
diffusio
The RMS displacement of particle undergoing a random walk
Consider a 1D random walk: A particle moves left or right in unit jumps on
the x-axis; at each step it has an equal probability of moving left
Point Defects Equilibrium Concentration Single Component
Perfect Crystal
Vacancy
Self - interstitial
N atom lattices with vacancies and self - interstitials
We consider the situation for vacancies. Si
D for a random walk Simple Picture
A simple lookConsider 2 planes of atoms with different concentrations of solute:
n1
n2
x
Plane (1)
Plane (2)
n1 - # at/ unit area on plane (1)
n2 - # at/ unit area o
Diffusion in interfaces on surfaces and along dislocations
Grain Boundary Diffusion :
d
Diffusion along grain boundaries is more rapid than normal lattice diffusion.
Packing density in a grain boundar
Crystal Growth
General Formalism
Phase growing into with velocity v :
v = f k
f ( site factor ) : fraction of sites where a new atom
can be incorporated 0 < f < 1
: interatomic distance
k
: jump freq
Alloy Solidification
Def. Partition coefficient k
k=
T1
T2
T3
xs
xL
xs and xL are the mole fraction of
solute in the solid and liquid
respectively.
kx0 x0
x0 / k
We will consider 3 limiting cases of t
Kinetics of Nucleation
ki+1
(a)
i1 +1 i
(b)
i +1 i +1
ki
For eqn. (a)
Bimolecular reactions describing
flux of atoms into and out of i
sized-clusters
forward Rx
dni
= ki+i ni 1
dt
backward Rx
dni
=kin
Kinetics of Nucleation
ki+1
(a)
i1 +1 i
(b)
i +1 i +1
ki
For eqn. (a)
Bimolecular reactions describing
flux of atoms into and out of i
sized-clusters
forward Rx
dni
= ki+i ni 1
dt
backward Rx
dni
=kin
Thermodynamics of surface and interfaces (Gibbs 1876 -78)
J. W. Gibbs, collected works, Yale Univ. Press, New Haven, vol.1(1957), p. 219 ~ 331.
Define
:
Consider
to be a force / unit length of surfac
Description of Phase Transformation
(i) Equilibrium phase transformations occurring at the transition
temperature ( e. g. freezing at Tm)
(ii) Non-equilibrium phase transformations
(freezing below Tm)
EGN 3365: Structure and Properties of Materials
Assignment No. 5
University of Central Florida
Due Date: April 26, 2016 10:30am
1. Using the isothermal transformation diagram for a 1.13 wt.% C steel a