PNM Flashcards
Which are the materials used in a reactor?
Fuel, cladding, moderator, coolant
Which function do we want to use materials for in a nuclear reactor?
- control
- shield
- electronics
- superconductor (accelerators)
Type of radiations?
- photons (we study ionizing photons)
- charged particles, like e- or ions
- neutrons
- elastic scat(energy and momentum conservation)
- inhelastic scat (momentum conservation)
- nuclear reaction (n,gamma)
What does a photon carry?
-Energy (h*nu)
- momentum (mc^2 = pc = sqrt(pc^2+m^2c^4) )
ES: if lambda = 400 nm = c/nu => E = 3 ev
What is the crosssection?
It’s the probability of a certain phenomenon.
photoeletric cross section?
photoeletttic means that a photon hits and releases an electron.
sigma_pe #= E^-3 (decreasing)
We have in order L edge and K edge
Also sigma_pe #= Z^n where
n = 4 @ 0.1 Mev
n = 4.5 @ 3 Mev
What happen if photon moves at E>1.02 Mev?
pair production, electron and positron, each with 511 kev
sigma_pp #= Z^2
What is compton scattering?
Scattering between photon and electron. Results in both a scattered electron and photon.
Decreases with energy
sigma_c #= z
Coherent vs incoherent compton scattering?
It’s coherent (compton scattering) when the photons interact with the entire e- surrounding the atom, causing the cloud to vibrate momentarily. The photons doesn’t change direction.
It’s predominant at low energy
Incoherent scattering is more common at high E and it’s a scatter where a single electron is ejected due to the photons
monopoles, dipoles and quadrupoles electric field dependence on distance r?
Due to series expansion:
- monopoles
E propto 1/r^2 (energy of electric field)
V propto 1/r
- dipoles
E propto 1/r^3
V propto 1/r^2
- quadrupoles
E propto 1/r^4
V propto 1/r^3
so higher poles have a shorter “range of action”
What is a Schottky pair?
It’s when I remove two ions with different charge from a lattice.
What’s a Frenkel pair?
It’s when I remove an ion from the lattice so that a pair (interstitial and vacnacy) is formed. This causes the creation of a dipole.
What is spallation?
(p,n) reaction or (n,2n) reaction, on nuclei
How can photon be emitted by atoms (x-ray)?
by fluorescnece (an internal e- is emitted so an external e- takes his place and emits a x ray
by brehmsstralung electron are slowed down by matter and emits photon
What are L edge or K edge in photoelectric crossection profile?
They are a sudden increase of crossection due to reaching the threeshold for the L or K elettronic states
most probable effect of photon interaction with atom for increasing energy?
- at low energy: photoeletric
- at medium energy. Compton
- at high energy: pair production
What is the stopping power?
The energy loss per unit path dE/dx
What is a vacancy from an electrical pov?
it’s a cumulation of charge so it’s a monopole
are monopoles easier to create?
No. they are associated with higher energy (E #= 1/r^2) so they are harder to create than frenkel or shotty pair.
What a vacancy creation causes thermodinamically? and an interstitials?
It increases enthalpy and entropy.
This is because we start from 4 bounds and getting the atom to the boundary create only 2 bounds (less energy, less stable)
Similarly with an interstitials but the energy changes due to elastic deformation on of the crystal to accomodate the interstitials
How much energy is needed for frenkel pair creation (scatter out of lattice)?
Temperature is not enough (around 10 ev)
What is PKA?What’s a collisional cascade?
Is the Primary knock on atom. It generates a collisional cascade. Primary knocked atom can knock secondary knocked on atom (SKA). It happens for E>E_d (displacement energy)
There is the displacement spike. In the core region there are more vacancies, inthe perifery there are more interstitials
There is the thermal spike where the energy is below the E_d and all the energy is given as thermal oscillation.
All the phenomena happen in picoseconds (very fast)
What has a bigger collisional cascade?
Ion is smaller becuase it immmeidately loses energy also with interactions with electrons.
Neutron do not interact directly with e- but PKA do.
What happens when a neutron is absorbed?
The nucleus moves with the recoil momentum.
momentum balance
m v = (m + M) V
so V = m/(m+M) v = 1/(1+A) v
energy of final nucleus:
T = 0.5 (M+m) V^2 =T_in * m / (m+M)
It can cause collisional cascade only if it’s an epithermal. But epithermal have low absorption crosssection so we have colllsional cascades only due to scattering
What implies talking about a potential?
elastic scattering
What happens if two atoms get closer?
When they are far we can have repulsive or attractive weak forces. When they are closetThe eletronic clouds repel each other due to Pauli principle since I have two set of electrons
How 2 atoms interact with each other?
First there is the electron cloud to break (Born- Mayer potential, it’s an exponential, V(r) = A * exp(-r/B) )
Intermediate region (screened couolmb potential, V(r) = e^2/(4 pi eps_0) * (Z1 Z2)/r * chi(r))
tipically chi(r) = exp(-r/a)
Then the 2 nuclei can be very close but there is still repulsion due to positive charges. (pure coulomb potential, V(r) = e^2/(4 pi eps_0) * (Z1 Z2)/r)
This was achieved with pulses of matter
What is the minimum distance reached between two particles?
Given by kinetic energy (vedi disegno). Changes if we are in 1D or 2D,3D
What is the collision parameter?
It’s the distance between the line of motion of one particle respect to the other one. It’s easy to see that one component of velocity will be slowed down while the other will deviate. (cerca disegno)
The velocity can also be decomposed in radial (which gets to zero) and tangetial (which is deviated)
It’s indicated with b
What is the kinetic energy of a projectile?
It’s composed by two terms
radial which decrease while approaching and then increases again
tangential that is always there
In 2d (or 3d) the minimum energy is not zero so not all the energy will be converted in getting closer so the minimum distance will be higher
2 particle scattering energy balance
T = 0.5 * m * (V_radial^2 + V_tangential^2)
E = T + U = T_r + T_t + U
at r=(-inf):
T_t = 0, U = 0
at R: I have all 3 components
at r = d_0, minimum distance:
T_r = 0
at r = + inf
T_t = 0, U = 0
If T_t = 0 (1D case or head on condition) the kinetic energy become all potential energy while approahing and then revert back to kinetic
What if the potential, in a two atoms interaction, is a step?
Then the distance reached is always the same. This is the case for strong nuclear force.
Hp of point like particles?
only translational degree of freedom and translational inertia, no rotation or rotation inertia
Lab frame and Center of mass frame
slide (4 lezione)
The CM sees a null total momentum
What is the total kinetic energy of a system of particles?
SLIDE 4 lezione
T_tot = 0.5 sum_i (m_i * v_i^2) = T_CM + T_int
external vs internal forces
SLIDE 4 lezione
Extrnal are F_i
Internal are F_ij, due to interaction between two particles, i and j
How can I change the total momentum of a system of 2 particles?
Only with external forces. Internal forces can change only internal motion. If I have three body forces like strong nuclear force this doesn’t hold true.
An isolated system keeps constant:
momentum p_tot
kinetic energy T_tot
center of mass velocity v_CM (the CM frame is inertial)
which forces do we consider during a collision?
before and after: only external forces
during collision: only internal forces since they are tipically higher than the external
It’s an approximation
This implies that collision cannot change the CM momentum
What are B and f in a collsion?
- B = M/m (not impling (M>m)
- f = |p’_c| / |p_c| > 0
- elastic collision if f = 1 so the momentum are conserved but just changed in direction
- T’_int = f^2 * T_int
two colliding particles formulas:
SLIDE 5 lezione
collision geometry?
SIlde 5 lezione
- b is the collision parameter
if b = 0 we have an head on collision
- We have a perfect cylindirical symmetry where angle is theta and Beta = r * sin(Theta)
- Scattering direction is dOmega = sin(Theta) dTheta dBeta
Velocities in collision in lab frame vs collision in CM frame?
SLIDE 5 lezione
The velocity of center of mass plus the velocity of the particle in the CM frame is the velocity in the lab frame
In a collision if the projectile is heavier can it be backscattered?
No, see slide 5 lezione
This is because I cannot exchange a large amount of momentum so also the energy cannot be transferred
What is the final kinetic energy of a target in a collision?
slide 5 lezione
V’^2 = V_CM^2 * (2-2cos(theta_c))
theta_c is the scattering angle in the center of mass
How does a potential effect a collision?
The potential changes the scattering angle but once the scattering angle is chosen the energy transferred is fixed
Whatis the maximum energy transferred to a stationary target in a collision? Example for neutron on steel?
T’_max = 4mM/(m+M)^2 * E = 4B/(1+B)^2 * E
If our projectile is a fission neutron (E = 1MeV) impinging on steel (iron) so B = M/m = A ~ 50 then:
T’_max = 4/50 MeV ~ 80 keV and our E_d = 40 ev.
It can cause a collisional cascade and displace many atoms
What is the maximum energy transferred from electron on steel?
B = A*2000 ~ 10^5
T_max ~ 4/B. To have 1 displacements T’_max > E_d so the minimum energy for electron is 1Mev
Obs: 1MeV electrons are relativistic and our model doesn’t take it into account
We can look at it the other way around and see that ions can give only a fraction of their energy to the electrons
What is DPA?
It’s used for quantify how much a radiation damages matter. It’s the ratio between the displaced atoms over total atoms
We’ll come back to this
Why high electron damage and neutron damage are very different?
Because elcetron creates defects
randomly spread whule neutron create collisional cascade and localized high damage zones.
Ions can be used to simulate neutrons also because they do not activate the material
What is the ENSP?
The ratio between the energy lost per unit path to electron over the one to nuclei. Stands for Electronic Nuclear Stopping Power ratio.
For neutrons we have electrons due to the collisional cascade so it’s not zero (but still very small compared to ions)
What is the difference in energy lost by radiation to nuclei rather than electrons?
- Lost to nuclei creates DPA
- Lost to electrons in ceramic materials it creates ionization and bonding rearrangement
- Lost to electrons bonded in covalent bonding in the end is dissipated as heat, especially in metals
BUT heat is actually a recovery process for damages in lattice
How much energy can an ion give to electrons?
Not much due to their big mass difference.
In ceramic materials we have bands so energy can be absorbed only in packets
In metals we have bands of conduction so energy can be absorbed almost continuously
Actually it needs to be at least a couple of ev so:
2 ev ~4/10^5 * E means that E > 50 keV
So ions created by electrons (80 keV) cannot move electrons with an energy sufficent to create other ions.
I need to pay attention to gamma emitted from tritium (Mev order)
What is the hard sphere potential?
SLIDE 6 lezione
relation between b and sigma_c
What could we say about time of flight of a particle in the influential area of another one?
Faster the particle, smaller the time for interaction, less the deviation will be
Definition of beam quantities?
SLIDE 6 lezione
- no shadowing
- crossection appear to define the rate of collisions
we obtain the classic exponential decreasing equation for flux
How do we measure thickness by mass?
With the product dx*rho
see SLIDE 6 lezione for passages
What is the probablity of interaction for hard spheres?
1if b<r+R = b_max
0 if b>r+R
We call eta the probabilty
What is the probability of interaction in quantum mechanics?
Since we do not know exactly where the particle is we can say:
P(dA(p)|1|1) = prob(dA(p)) * eta(p) = dA(p)/A * eta(p)
(2nd order differential)
so probability in all area is:
P(any|1|1) = 1/A * intint_A 2dA(p) * eta(p) = M(r+R)^2 / A = pi*b_max^2/A = (area of collision)/(total area)
Why and how can we simplify cylindrical symmetry?
beacuse velocities are always in the same plane so we can use a 2D description. so any function dpepnding on b and Beta actually depend only on b cause it can be integrated in the angle Beta (I obtain a 2pi)
how does probability of interaction increrases if I increase the number of targets?
P(any|N_targ|1) = N_targ * P(any|1|1)
Since the number of targets is 1dN_t = n_tAv*dt
Infinitesimal probability of interaction?
If the target has an infinitesimal thickness the probability becomes:
THEORY PAG 10
What is P(b’<b|1|1)?
P(b’<b|1|1) = sigma(b)/A = int_A
what is the scattering angle for hard spheres?
theta_c = 2 * arccos(b/b_max)
So we can express the probability as a function of sigma_c instead of b
P (thet’ in [theta, theta-dtheta]|1|1) = 1/A * dsigma/dtheta * |dtheta|
What’s the relation between dsigma/db and dsigma/dtheta?
1/A * dsigma/db * |db| = 1/A * dsigma/dtheta * |dtheta|
So:
dsigma/dtheta = dsigma/db * |db/dtheta|
What is db/dtheta and dsigma/dtheta for hard spheres?
Since b = b_max * cos(theta/2)
So:
|db/dtheta| = b_max/2*sin(theta/2)
Also since dsigma/db = 2pi b = 2pi b_max cos(theta/2)
Then:
dsigma/dtheta = 2 pi b_max cos (theta/2) * b_max/2 sin(theta/2) = 1/2 * pi + b_max^2 * sin(theta)
In the end since sigma = pi*b_max^2
Then:
dsigma/dtheta = 1/2 * sigma * sin(theta)
What is b_max (or d_0)?
It’s the collisional paramter that we take for each potential to consider as a upper limit for a collision.
Higher b counts as not collided
What is the infinitesimal area around point P in a collision?
dA(P) = b * db * dBeta
What is the differential crossection in b? and the integral crossection?
dsigma/db = 2 pi b up to b_max
increases linearly up to b_max and then drops to zero
The integral crossection increases up to b_max and then is constant. Express the probability
What can we obtain about a collision starting from energy of projectilem, potential and b?
scattering angle and so the transferred energy
How can I calculate T’ in a collision as a funciton of scatterign angle?
T = T_max * (1-cos(theta_c)) /2
dT = T_max * sin(theta_c)/2 * dtheta_c
How it distributed transferred energy ina ahard sphere collision?
It’s a constant so becomes a uniform distribution due to the dependence on the angle.
What is the differential crosssection in the solid angle?
pag 43
dsigma/dtheta = 2 pi dsigma/domega * sin(theta)
What are the probability of head on in a collision in different dimensions?
in 1d is 100%
in 2d is less
in 3d is a uniform distribution
How can I calculate the dpa?
dn_dpa/dt = n_t * phi * sigma_displ
where sigma_displ = int ( sigma_scat* nu(T_PKA) )
where nu = T_PKA / (2 * E_d) = (remaining kinetic energy)/(energy for knocking atoms)
What is the energy necessary to continue the collisional cascade?
2 * E_d so that it can give E_d to next atom.
If E<E_d it doesn’t knock atoms but it’s stil a lot of energy dissipated as thermic energy
How can we account for dpa in time?
I integrate in time.
n_displaced = n_targ * sigma_displ * int_time(phi dt) = n_t * sigma_displ * fluence
dpa = n_displ/n_targ = sigma_displ * fluence
What is the displacement cross section?
sigma_d(E) = int_E_d^T’max (dsigma_s(E)/dT’ dT’ nu(T’)
= int_E_d^T’max (T’/(2E_d) sigma_s(E)/T’_max(E) dT’)
= sigma_s(E)/(2 E_d T’_max(E)) int_E_d^T’max (T’ dT’)
= sigma_s(E)/(2 E_d T’_max(E)) (T’_max^2 - 4E_d^2)/2 ~ sigma_s(E)/(4 E_d) T’_max = sigma_s(E)/(4 E_d) * 4/( A * E)
= sigma_s(E) * E / (A E_d)
What is T’max in a collision?
T’_max = 4mM/(m+M)^2 * E = 4B/(1+B)^2 E = 4A/(1+A)^2 E ~ 4/A E if A»1
What is the dpa taking into account the scattering cross section?
dpa = n_disp/n_targ = sigma_s *E/(A E_d) * fluence
For example for iron (A = 56, E_d = 40 eV, 0.1 MeV, fluence = 3*10^13) we get:
dpa = 1/8
This is the displacement per year in a thermal reactor
In a fast reactor it’s higher
Kinchin - Peas hp and results
- 2 body interaction
- probability of displacement is a step in E_d
- T’ generates T’’. R’’ = T’-T’’, energy given
- The electronic stopping power is a fraction of the total
(dS/dx)elect / (dS/dx)total = It’s a step as well in E_threeshold (thermal spike) - Hard spheres
- negligible effect of crystal
theory PAG 13
What happens if a projectile in a crystal aligns with the crystal or with the voids?
It’s called focusing. If the PKA is deflected at theta0 and SKA at theta1. If theta0>theta1 we are focusing, otherwise we are defocusing.
If it’s in between the lattice we will have channeling instead.
Both effects create a larger region of displacements, focusing creates acrowdion where all the atoms are moved of 1 place, channeling creates a long strip of displacements
Focusing
In hard spheres hp, pag.14
When do we have focusing?
if cos (theta0) > D/4R
if D/4R >1 we always have defocusing
if D/4R <1 we have theta0_crit = D/4R<1
Of course we have energy dispersion.
tipically this is broken by vacancies
What shape has diffusivity ?
Arrenius behaviour:
D = D0 * exp(-E_act/(kT))
What are escaping defects?
Defects created by a collisional cascade that do not recombine and escape from the zone
How can we freeze diffusion?
Liquid Helium but I still have thermal spikes which lead to recovery so if we plot defects over fluence we have first linearity then less than linearity due to recombination
What’s the dimension of metallic crystals?
nanometers
Why disordered structures are more symmetric?
Because they act like continuous. Adding order selects specific symmetry
What is burger vector?
The remaining vector if in a crystal i perform a loop and do not end at the beinning point. It is constant so if the dislocation curves it can transform from a edge dislocation to a screw dislocation
What is creep?
It’s deformation at constant stress and T(above a thresshold)
Primary, secondary and tertiary creep?
curve ( pag16)
It gets faster and higher by increasing T
We want to stay in secondary creep because it’s more predictable
What causes creep?
motion of dislocations. Also climbing of dislocation that allows for overcome of dislocation blocks (precipitates)
Temperature threeshold for creep?
T/T_melt = 0.5 ?
Small temperatures do not show tertiary creep behaviour
What is stress realxation?
In uniaxial tensile test if we impose strain we can see that the stress diminuish asintotvcally (pag 16)
What effect have vacancies on entrophy and energy?
Incresase entropy
decrease energy
increase enthalpic cost
Which free energy is better to describe which system?
helmotz at costant volume
gibbs at costant pressure
For solids these are very similar (they are not gas)
We use Helmotz since it’s easier
How can we estimate the enthalpic cost of vacancies?
Considering N sites in crystal and n vacancies (n«N)
The possible place for our vacancies are:
N * (N-1) * … * (N-(n-1)) = N! / (N-n)! = N_config
But we need to count for permutations (n!):
N_config = N! / ((N-n)! * n!)
Our configurational enthropy will be:
( remember that ln(N!) ~ N * ln(N) -N so)
S = k_b * ln(N_config) = K_b * (N*ln(N)-N - n * ln(n) + n - (N-n) * ln(N-n) + N - n) = (pag.16) ~ k_b * n * (1 + ln( (N-n) / n) )
so F U -TS = n * E_v - k_b * T * n * (1 + ln( (N-n) / n) )
so dF/dn = pag 16 = E_v - k_b * T * ln( (N-n) / n)
at equilibrium, when is df/dn = 0 :
… -> n = N * exp(-E_v / (k_b * T) )
so F/n = E_v - k_b * T * ( ln ((N-n)/n) +1) = -K_b * T
(many passages skipped)
E_v = 1 eV
k_b = 25 meV
so E_v/(k_b T) = 10 - 40
Why can we neglect volume change in computing free energy of a vacancy?
because the bounding energy is eV order while the deformation energy is meV order
vacancy movement analogy with electric charges?
They move according to an external condition. But unlike charges thay can annihilate so that a continuous flow is created. This is creep.
What is dynamic equilibrium?
When defects and interstitals diffuse from and to grain boundary at the same rate so that the total number doesn’t change
What does irradiation do for creep?
Inject lots of dislocation, vacancies and intertistials (I think)
What energy am I missing for a vacancy?
What energy am I missing for 2 close vacancies?
Dislocation loops?
The energy of 4 bounds (in square lattice)
For 2 I miss 7 bonds so it’s advantageous
For many vacancies I get 2 dislocations (pag17)
specular for many interstitials
They are called dislocation loops, because they create a circular region where I have defects. (They are not circular dislocations) They actually reduce the deformation of the lattice
Why under irradiation we have a “creeep” dependent also on temperature?
Irradiation creates a huge number of vacancies. This vacancies for high temperature can move and create dislocations and motion of dislocation.
It’s called irradiation induced creep at low temperature
it’s called irradiation enhanced creep at high temperature
Why creep doesn’t change volume?
Because crystal orientation is random so each crystal will deforme and create internal stress but not deformation.
This doesn’t happen if the crystal are aligned
What is lamination and effect on grains?
I reduce the crosssection of the bar and the grains elongate. This is called growth of grains. It is used for zry cladding (produced by extrusion to not weld it). They expand axially a lot in the end.
What is nabarro Hearring creep?
At very high Temperature (0.8, 0.8 of T_melt) Whawe have a flow of interstitial from compressed to expand fiber in a bar (pag18)
What is coble creep?
Same as nabarro hearring but grain boundaries are preference location for aggregation of interstitials and vacancies
What’s an aggregation of vacancies?
It’s a cavity or void that reduces the energy cost by minimizing the surface. This increases the volume but doesn’t change the shape siince it’s isotropic.
It’s SWELLING
What happens if nuclei do (n,alfa)?
I will have helium bubbles that create pressure (still create sweelling as vacancies but thety are not hollow but full of helium). The effects from vacancies and bubbles attract each other and creates bubbles of helium.
Interstitals do not do anything for this.
Bubbles sink or source of vacancies?
Bubbles can emit or absorb vacancies
Can creep without irradiation?
swelling?
Creep can happen at high temperature.
Swelling cannot
Dislocation loop contribute to hebrittlement?
Yes. They avoid movement of dislocation so the ability to deform plastically
How are single crystal done?
With directional cooling so that the grains grows from one side only. also I use a path so that I select only one single grain between the many that are forming from the one side
What is the typical dislocation density?
In Al we have 1/400, so 1 dislocation for each 400 atoms.
But if we sum all the dislocation we get 10^5 km in 1 cm^3… a lot.
What’s the effect of radiation on sigma eps graph?
(pag18)
Irradiation increases defects (frenkel pair) so the dislocation motion is harder due to dislocation loops. Yiled stress will increase, constant stress is shorter and plastic domain is shorter as well
What happens to Nihil Ductility Temperature after irradiation?
moves to the right (higer T) and to lower energies (more brittle)
What is the Wigner effect?
Especially in graphite (has high temperature for defects mobility) the energy of defects is stored in the crystal and if T increases can recombine them and relases even more energy creating a positive feedback effect.
What is electric resistivity?
(pag19)
Irradiation increases resistivity. More defects, less perfectly periodic crystal, less conduction of electrons
More damage from collisional cascade in the lattice decrease the possibility of a neutron of hitting a “fresh” part of the crystal. If a already damaged zone will be hit the damage will be way lower due to recombination enhancing.
This is why it does not increases linearly
What is isochronal annealhing?
It’s done by irradiating a sample at liquid Helium temperature since it’s the T at which recombination do not happen. By slowly increasing T we get to see the movements that gets activated
(Pag19) + slides
What happens when a bubble is formed?
We can calculate the enrgy related to the volume and area
deltaG = -A r^3 + B r^2
So sphere is the most suitable
(pag20)
This to say that bubbles nucleate on surfaces since a surface already exist it’s easier and more stable (heterogeneous bubble formation, while if it’s spherical is homogeneous)
What’s the difference of nucleation in a liquid vs a solid?
In a solid I have no convection so if an impurities is formed, a nucleation, there is no convection to bring back equilibirum but only conduction which is way slower
What is quenching?
In Al, that has a low melting T (550°C) and always form fcc, we melt it to have a solution of all the species in the Al. By cooling it becomes a super saturated solution so the impurities precipitate and accumulate in some nucleation points and the metal results to be softer than before (called solubilization temper).
Once the precipitate is formed the concentration of that species in the solution decreases so by diffusion attracts more that once again will precipitate in the nucleation point.
This continue in multiple points until the concentration is below solubility limit.
Remember that impurities blocks dislocations
To obtain many small precipitate I bring it fast to sambient temperature so to reduce mobility but not kill precipitation formation (callled aging of aluminium)
Helium solubility?
- We have a costant production due to irradiation.
- We have an incubation time when it just accumulate
- Nucleation starts
- Number of bubbles saturates so they start to grow in size
- There is a diffusive gradient towards boundary due to escape of He at boundary
Hydrogen bubbles ?
We could have them but H is more reactive so it can forms metal hydride with cladding. They are precipitation of hydrides at grain boundary (heterogeneous nucleation)
Are impurities motion random?
No, since we can have some sinks, like crystal boundaries or bubbles that create a diffusive gradient
Which phenomena can happen in the coolant?
- nuclear reaction
- radiolysis (production of H, O, C (from CO2), organic impurities if I use organic coolant (which I do not due to corrosion) )
- corrosion of cladding
What is cladding corrosion?
Solid particles, like powder or hydrated ions (ions circunadated by water called also colloidal particles) in solution can hit the walls and corrode it
Corrosion in Zircalloy?
Zr caratheristics?
Zry is good for corrosion, maybe even better than steel, (but less resistant to creep). Al is better for neutron but has low melting T.
Zr is above Hafnium in periodic table, but Hf has big abs crosssection so it was necessary to divide them to use Zr in nuclear industry.
What can Zr react with in coolant?
With oxygen.
Zr + 2 H2O -> ZrO2 + 2 H2
The oxide layer is protective for succesive oxidation.
Higher thickness of oxide means less reaction but
Pag.20
It’s a power law (^0.2 - ^0.3) but the overall behaviour is linear due to cracking. I have cracking because the oxide grow from the inner side, not from the external!
It start as a self limiting process but when break away happens it starts a cycle of production and break away that corrode the material
Number for Zr breakaway?
Pure Zr
at 300°C is 2000 days
Zry
at 280°C is 3250 days
Zry contains tin (stagno) and others to reduce corrosion
from nitrogen (N), naturally present in water
In Russia they used Niobium since it increases resistance to creep
This limit is the driving factor for water reactor maximum coolant temperature
What about lead reactor chemical reactivity?
It has low reactivity than sodium but needs 300°C to melt and has hgh heat capacity. they are both pro and cons.
Good for safety, hard for design
Lead is very corrosive though. It diultes other metals. An idea is to use SS and mix oxygen in the lead to promote the creation of the oxide layer to protect the steel.
It was observed that a double oxide layer was created, one external with no chromium and one external with one internal with more chromium. This approach is good for T<400°C
Why protective layer aren’t applied in nuclear industry?
Becuase it’s not a self healing process. If they fail they will not reform.
We are thinking about that for gen4 reactors.
Iron oxide has a small region of stability before the creation of lead oxide so we can use different materials like AlO2…
What are the effects of radiation on metals?
2 BIG tables
- Recombination
- Agglomeration of intersititals and vacancies
- Vacancy emission
- Annihilation at sinks
- Interaction with foreign atoms
Each of these can be caused by different phenomena
sigma-eps for reactor pressure vessel?
Irradiating (also low doses)
- increases yield stress
- decrease ductility
- switch from continuous to discontinuous yielding (for fcc)
Decreasing T:
- increase yielding
- decrease plasticity
- decrease energy to rupture (curve moves to right)
What happens if I irradiate at high vs low temperature?
At high T the phneomena are competitive. Radiation introduce defects and T will try to annheal them. In the long nterm for High T we get the same situation, independent of which T the irradiation started
Ashby map?
We can get what is the most probable phenomena to rupture (normalized stress over normalized temperature)
The above limit is the stress for gliding an entire plane
Below that we have the linee for dislocation glide (way easier)
Below that we have different failure mechaniscm
Irradiation (1dpa)
- increase yield stress below a certain T (after that we have annehaling)
- twinning become possible
- NH and coble creep is the same
- dislocation creep is more probable at lower T, due to the injection of defects due to irradiation
Of course it changes for each material
And changes depending on strain rate (fast rate doesn’t allow for irradiation sinduced strain since it’s slower than yielding)
What activation reaction do happen in coolant?
- On oxygen mainly we have capture and gamma emission 7 MeV, other minor reactions (seconds timescale)
- H capture became deuterium (high crossection) and then tritium(low crossection), dangerous for internal contamination
- Ar (from atmosphere), sodium way lower activity but in the hours timescale
- Of coure many others
How can we evaluate how much does the water gets activated?
t_reactor = 5 s
t_cycle = 20 s
t_extern = t_c - t_r
BETTER TO WRITE THEM BY PEN
N is nitrogen which decays emitting 7 MeV gamma, No is oxygen :
dN/dt = sigma * phi * N_O - lambda * N
first cycle in reactor:
N = 0
first cycle out of reactor:
N1 = sigma phi N_O / lambda (1-exp(-lambda t_r)
second cycle in:
N2 = N1 exp(-lambda t_e)
second cycle out:
N3 = N1 + N2 exp(-lambda t_r) = sigma sigma phi N_O / lambda [ (1-exp(-lambda t_r) + (1-exp(-lambda t_r)) exp(-lambda t_c) ]
N_inf = sigma phi N0/lambda (1-exp(
How do we control reactors?
Control rods, poisons, boric acid
How can we uniformize the power in reactor?
With dispersed abrosber like
- Gadolinium in UO2
- boric acid in solution in water (in PWR)
This allows us to have uniform power production
Water radiolisys in coolant?
Neutrons may break water molecules in H and OH. Then H2 and H2O2 that becomes H2O + 0.5 O2 so I’m producing in the end H2 and O2 which may creating bubbles.
In BWR we can extract them after condensation with a degassificator?. They can interact with metal though
In PWR we add H2 to favour recombination of water since H2 is absorbed more by metals.
In BWR we have more oxygen, in PWR we have more H2.
Irradiation acts as a catalizer
WHy Zr and Ti are called “getters”?
Used also in accelerator, They absorb gas like O2 or H2. Also steel do it but less. H2 is the easier to absorb since it’s a small particle.
Where does N ends up in reactor?
In BWR HNO3 (nitric acid)
In PWR NH4OH (ammonium hydroxide)
This is due to the different concentration of O2 and H2
What is water maintenance?
two things:
- adding chemical to balance chemical reaction and corrosion
- feed and bleed, which is substituting water
- flitering, 1 - 2% in cold leg is diverted and filtered mechanically and with ionic exchange with resins
Water filtering?
PAg 21
Nylon tissue pores 20 micrometers
Ion exchange resins 50 micrometers (at 150°C or resins degrades). They release LI+, H+, OH- and capture other ions produced by corrosion
Also colloidal particle could be extracted but it’s hard. They will get activated and are hard to remove. (Ion circundated by water, so they are liquid and not very active
What are the nuclear fuel requisite?
- Thermal conductivity
- chemical compatibility in normal and accident condition
- Resist thermal cycles
- pure from posions
- reasonable cost
- reprocessable
What are the pro and cons of metal fuel?
We are talking about U, Pu and Th.
PRO:
- good neutron economy
- good thermal conductivity
- good against thermal shock
CONS:
- poor strength
- T limit is low
- They have phase transistion
- they do swelling
- they have low melt eutectics?
Pro and cons of oxide fuels?
we are talking about UO2, MOX
PRO:
- High strength at high temperature
- high T melt
- Low thermal expansion
- no corrosion from oxide
- radiation stability
CONS:
- thermal conductivity -> thermal gradient -> thermal stress -> cracks
- brittleness
What is ratcheting?
Thermal cycle brings plastic deformation that is not recovered when reducing T. So with multiple cycles it gets worse and worse. It’s due to different orientatio of crystals which mean they will expand in different directions
Uranium?
alfa phase - ortorombic up to 666°C, 19.04 g/cm^3
beta phase - tetragonal up to 771°C, 18,11 g/cm^3
gamma phase - Cubic, 18,06 g/cm^3
Plutonium?
Has many phase transitions.
alfa phase - monoclinic up to 319°C, 19.81 g/cm^3
delta phase - fcc up to 451°C, 15.92 g/cm^3 (very ductile)
Thorium
alpha phase - fcc up to 1400°C, 11.72 g/cm^3
beta phase - bcc, up to 1750°C, 11,1 g/cm^3
molten
Notice that is always cubic so no ratcheting
