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
METAL
Reference Plane
Consider roughness in the form o
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 order reaction kinetics
order refers to the exponent o
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-infinite medium
Boundary conditions
Laplace transfor
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
diffusion coefficient, called the intrinsic diffusion coefficie
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 or right.
We want to know the probability that after N
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. Similar arguments can be made for
self-interstitials.
Let
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 on plane (2)
# of atoms leaving (1) = n1, where is the a
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 boundary is less than the perfect lattice so
atoms can change
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 frequency
*at equilibrium temperature and ( T ) the net k
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 the solidification process. :
(a) Infinitely slow (equil
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
=kini
dt
Writing a similar set of eqns. For (b) and combini
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
=kini
dt
Writing a similar set of eqns. For (b) and combini
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 surface perimeter.
(fluid systems)
If a portion of the perime
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)
Equilibrium phase transitions:
Recall the Ehrenfest (c
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 alloy given below, determine the
final microstructure (i