Chapter 4 - Diffusion Flashcards
What type of diffusion controls the material performance in nuclear env?
impurity and solute diffusion
Name the main diffusing species from cladding?
Oxygen from ZrO2
Name a diffusing species from fuel?
Kr, Xe from UO2
Name a diffusing species causing swelling of metals by irradiation?
vacancy and intersticials in Steel Alloys
name a diffusing species of water into cladding?
Hydrogen to Zr from Water
Name a diffusing species causing RPV embrittlement
Copper precipitation in steels
What does 1st ficks law says?
It calculates what is the energy require for an atom to jupy, how likely is it to find a vacancy and how likely is it for the movement to happen in the direction of the vacancy.
What is the diffusion flux proportional to?
the existing concentration gradient
What is the difusion coeficcient?
the frequenzy factor
What is the diffusion coeficcient influced by?
Temperature crystal structure size of diffusing atoms compared to the lattice microstructure concentration impurities
What are the units of the difusion coefficient?
m2 s-1
What is the typical Diffusion coefficient for metals at 2/3 melting temperature?
10^-10 cm2/sec
What are the units of the diffusion coefficient?
cm2/sec
What is the typical Diffusion coefficient for metals at the melting temperature?
10^-8 cm2/sec
What is the approximate magnitude of the diffusion coefficient of H in Fe?
10^-3 to 10^-4
What is the energy Q in diffusion?
It is the sum of the formation energy of a vacancy and the migration energy
What is thicker? The thicknes of the surface or the grain boundaries?
The grain boundary layer which is about 5 A (the surface is only 2.5A)
Order the surface, grain boundaries, and lattice according to the diffusion coefficient?
The lattice has the lowest while the surface has thehighest.
Where is the diffusion rate higher? In the surface or in grain boundaries?
In the surface
What are the two method for measuring diffusion coeffcicients in solids? Explain it.
source method and couple method
What does the source method consists on?
It consists on a side of source of diffusing species and a initially solute-free solid separated by a surface (interface). Once put together the diffusing species migrate to the solute free and the concentration is measured.
What does the couple method consists on?
One side with a solid containing an initially measured concentration of diffusing species while the other side is the same solid but solute-free.
What are the four types of diffusion coefficients?
self difussion
tracer diffusion
intrinsic diffusion
mutual diffusion
What is the self diffusion coefficient?
describes the migration of the atoms of a pure element. There is no direct method for measuring the self-diffusion coefficient.
What is the tracer diffusion coefficient?
describes the self-diffusion of atoms that are radioactive isotopes of the host (solvent) element. Measurement of Dtr requires a gradient (and hence a
flux) of the tracer but without a gradient (flux) of the solvent
What is the intrinsic diffusion coefficient?
describes the mobility of a species in a binary solid.
Each species possesses an intrinsic diffusion coefficient, designated as . The intrinsic diffusivities of the components of a binary solid are in general not equal. These diffusivities imply concentration gradients of the species A and B, in contrast to the gradient-free self- and tracer diffusion coefficients.
What is the mutual diffusion cofficient?
describes the chemical or inter-diffusion coefficient.
Measurement of the A-B concentration gradient relative to the fixed ends of the diffusion couple (rather than relative to the marker wires) produces. The intrinsic diffusivities and the mutual diffusion coefficient are related by the so-called Darken equation:
Does doping affect the anion and cation vacancy diffusion coefficients?
No
Does doping affect the vacancy fraction?
Yes
What is the effect of doping with higher valence cation
It accelerates cation diffusion and impedes anion diffusion.
What happens to oxygen diffusion in ZrO2 if CaO or Y2O3 are use as dopant?
The oxygen ion diffusion is accelerated since the doping is with a lower valence cation which impedes cation diffusion but accelerates anion diffusion.
what is the random walk total distance after N steps a functio of
r = a*sqrt(N)
What is the diffusive flux a function of?
j = -D dc/dx meaning it is proportional to the existing concentration gradient and the diffusion coefficient
What is the diffusion coefficient a function of?
D = Do*exp(-Q/RT) meaning it is a function of the formation energy of a vacancy, the migration energy, the temperature
What is the diffusion coefficient of H in Iron?
10E-3 to 10E-4
What is the diffusion coefficient of Fe in Fe?
10E-14 to 10E-10
What is the energy Q in the diffusion coefficient for self diffusion?
150Tm
What is diffusion?
phenomenon of a spontaneous material transport into/through the solid (from gas, liquid or another solid) by the atomic motion. It means a migration of atoms inside crystal from lattice site to lattice site
what is interdiffusion, or impurity diffusion
type of diffusion whereby atoms of one metal diffuse into another
what is self-diffusion?
all atoms that exchange positions are of the same type
What is the probaiblity for an atom to move from position a to position b a function of?
W = x_v * exp(-Qm/RT) where:
x_v: vacancy concentration
Qm: vibrational energy of a lattice cell atom needed for breaking bonds and its removal from the initial position
What is necessary for an atom to move from one position to another?
- empty site (of appropiate size)
2. atom must have minimum sufficient energy to break bonds with its neighboring atoms
What is substitutional diffusion?
interchange of an atom from the lattice position to an adjacent vacant lattice site
What is interstitial diffusion?
involves atoms that migrate from an interstitial position to a neighboring one that is empty
What and why is faster? Intersittial diffusion or substitutiaonl diffusion?
interstitial diffusion occurs more rapidly than substitutional, since the interstitial atoms are smaller and thus more mobile.
Is diffusion time dependent? What does this imply?
diffusion is time dependent process and it is necessary to know the rate of mass transfer which is expressed as the diffusion flux (j)
What is the diffusion flux?
it is the rate of mass transfer defined as the mass duffising through and perpendicularly to a unit cross sectional area of solid per unit time
j = M/A*t
A is the area across which diffusion is occuring and t is the elapsed difussion time.
What is the concentration profile?
If the diffusion flux doesn’t change with time, a steady state condition exists. When concentration is plotted versus position (distance) within the solid, the resulting curve is known as the concentration profile
What is the slope of the concentration profile?
the slope at a particular point of this curve is the concentration gradient
What is the diffusion flux in a steady state diffusion treatement?
j = -D dc/dx
where D is the coefficient of proporationality called the difufsion coefficient
What is the diffusion coefficient units
m2/s
Why does crystal structure and microstructure affect the diffusion coefficient?
The activation energy for diffusion depends on the melting point and on the number of atoms already difunded in an inverse exponential manner. Impurities present in crystal also affect the diffusion coefficient and the same is with grain boundaries.
What is the activation energy for diffusion
the energy required to produce the diffusive motion of 1 mol of atoms, given in J/mol
What is the couple method?
formed by joining bars of two different metals together so that there is an intimate contact between the two faces. The couple is then heated for an extended period at an elevated temperature (but below the melting temperature of both metals), and cooled to room temperature. Chemical analysis reveals the pure metals at the two extremities of the couple, separated by an alloyed region in the interface zone
