Macro Effects of Nuclear Scattering

Warning!  Nerd Post!

This is another long nerdy post about nuclear stuff - the one I've been warning about.  I broke it down into a few different parts to try and keep it sensible.

Part 1. Nuclear fission:  How and where the energy is released, in its various forms.

Here is what happens at the subatomic level when the nucleus of an atom splits, or undergoes nuclear fission.  This event releases a phenomenal amount of energy, and where this energy ends up being deposited (or lost) is interesting.

Fission of a single U-235 nucleus releases ~200 Million Electron Volts (MeV) of energy.  By comparison, solar panels collect photons of light in the visible spectrum, which are at energy levels of about 2-3 electron volts (eV).  Red light is 2 eV, while blue light has a slightly higher energy at 3 eV.  This means that the energy released by a single fission is roughly 100 Million times more energetic than a visible light photon.

The vast majority of fission energy (~170 MeV) appears as kinetic energy in the two daughter nuclei.  The daughter nuclei fly apart at ~3% of the speed of light, and the reason they reach this velocity is Coulomb Repulsion.  This is the repulsive force between two particles having the same charge.  The tightly packed protons of a nucleus repel one another.  The instant the strong nuclear force is broken, and the atom splits, the Coulomb force repels the two daughter nuclei apart at extremely high velocity.

The temperature equivalent of these fission particles is over 2 trillion degrees kelvin, but it is at a microscopic level, so we are not able to sense the intensity of it.  3% of light speed is 5580 miles/second, or 20 million miles/hour.  You would think these particles would blast right out of the reactor and kill everyone around.  They don't do that though, and here is why: Nuclear Scattering.

What is Nuclear Scattering?  Collisions with other atoms.  These atoms are very quickly going to bounce into other atoms within the fuel and come to rest among them. This leads us to the concept of Mean Free Path.

Mean Free Path is the mean (not average) distance a particle travels before it interacts with another atom.  The concept of Mean Free Path is not difficult, and the math is pretty simple as well.

As a hypothetical, if you shoot a bullet (daughter nuclei) into a pile of gravel (nuclear fuel), eventually the bullet will eventually bounce several times and come to rest.  The Mean Free Path then, is the likely distance your particle travels before encountering one of the surrounding atoms.  The distance traveled before having a collision is is dependent on the number of atoms present and the cross-sectional target area of each atom.  

For example, the mean free path would be greater in a gas than a solid, because the density of atoms is much lower in gas.  This is also why a bullet travels further in air than it does in a pile of gravel.

The formula for Mean Free Path looks like this: where l = the mean free path, σ = the cross sectional area per target atom, and n is the number of those atoms present in the material.  

Due to the bulk and charge of fission daughter nuclei, the mean free path is quite short - far less than a  millimeter.  If you look at the very first image, one of these daughter particles has a mass of 92 AMU and the other has a mass of 141 AMU, which makes them gigantic boulders in the world of subatomic particles.

The daughter nuclei will very quickly undergo several collisions with other large atoms within the fuel and come to rest.  They will have transferred that 170 MeV of kinetic energy to these other atoms in the form of friction, generating microscopic amounts of heat.   When this process is multiplied by billions of fissions in a self-sustaining chain reaction, then useful quantities of heat are created.

This still leaves ~30 MeV of energy from each fission event unaccounted for, and that's where things get interesting, and what I want to discuss a bit more thoroughly in this post.

About 10 MeV of energy from a fission is carried off as antineutrinos.  Antineutrinos are emitted during beta (β⁻) decay to conserve angular momentum (spin).  We know that they exist due to conservation of momentum, but we almost never detect them.  Matter is almost perfectly transparent to neutrinos and antineutrinos!  That energy is gone - pfffft!

7 MeV of the remaining energy is released as prompt gamma rays, and 5 MeV is released as prompt fast neutrons, with an average of 2.5 neutrons released per fission.  Some of the neutrons will be absorbed in other U-235 atoms and thereby maintain the chain reaction.  Others will be absorbed in non-fuel reactor components, others will escape the core, and yet others might be absorbed by U-235 and not cause a fission.

The remaining energy from a fission is released later on as beta (β⁻) decay of the daughter nuclei, and this also results in very significant quantities of heat (see this post about decay heat).

For now, this ends the discussion about fission.

Part 2. Material failures and design philosophy. 

There are two basic types of stress:  Compressive and Tensile.  Tensile stress is "pulling apart", and thus is the opposite of compressive stress.  If you pile a lot of weight on an object, it is under compressive stress.  If you take the same object and try to pull it apart from either end, or bend it, it is under tensile stress.  If you apply enough stress to any object, it will eventually fail.

There are two failure modes associated with tensile stress - ductile failure and brittle failure.  The failure modes are about what they sound like.  Take ordinary glass:  At the temperature where glassblowers work with it, glass is semi-liquid.  If you pull it from both ends, it will separate into different pieces, but the glass doesn't shatter.  It deforms and thins out, and eventually after a stretch, it parts.  Glass at room temperature on the other hand... If you pull on a glass rod from either end, it won't elongate.  Instead it will suddenly break - possibly it will fail catastrophically into many shards.

Steel shares this tendency to fail in a ductile mode or a brittle mode while under tensile stress, and the failure mode is also dependent on its temperature.  With a ductile failure, the steel will deform a bit before failing.  This deformation can be measured, and provides some warning.  Brittle failure happens rapidly, without warning, and fracturing will continue even after the stress has been removed.  

 Importantly, when steel is in a ductile condition, it can tolerate far more tensile stress before failure than it can when it is in a brittle state. 

Historical side-note:  The sudden and puzzling cleaving in half of several "Liberty Ships" during and following World War II led to a greater recognition and understanding of brittle fracture.

Below: T2 Oil Tanker USS Ponaganset AO-86. 

Below: SS Schenectady also broke in two while moored in calm weather.  Initially, poor welding was blamed.  In fact, the cause was brittle fracture, which was unrelated to the welding.

Several other Liberty ships also cracked in half and sank.  Pendleton and Fort Mercer sank within two hours of each other off Cape Cod in February of 1952.

The temperature at which a solid material changes failure modes is called the Ductile-Brittle Transition Temperature (DBTT).  Brittle fracture then, is the sudden and rapid fracture of a metal that has a pre-existing flaw, when that metal is below its DBTT.  The very major pre-existing flaw that the Liberty ships had was welded high sulfur and high carbon steel.  Each of these failures took place in cold water, when the steel was below its DBTT.  

However, every piece of steel contains minute pre-existing flaws, since nothing is perfect.  The pre-existing flaw that could lead to Brittle Fracture does not even have to be a visible scratch or inclusion in a weld.  It might be a very minor or even invisible flaw, but under stress at low temperatures a microscopic flaw can become the starting point of a brittle fracture event.

Engineers have to assume that quality control measures have overlooked the worst-case flaw that testing instruments would be able to detect, and assume that largest possible undetectable flaw is present in the steel.  Then the operating conditions and material thickness are designed from that worst-case material weakness.

Time now to return to nuclear reactors - and more to the point, reactor pressure vessels. 
Below: A brand new reactor pressure vessel:


Part 3. Gamma rays are powerful penetrating electromagnetic waves.  They have a phenomenal amount of energy, and so they can pass through quite a bit of material before they are stopped. 

Fast neutrons have an average energy of ~2 MeV, which is the equivalent of 12,400 miles/second -  pretty fast.  They have very little mass, at just 1 AMU, and they have no electrical charge.  As a result, their mean free path is much greater than that of the fission daughter nuclei discussed in Part 1.
Due to their high speed, low mass, and lack of charge, neutrons readily escape from the reactor core.

Neutron reflectors are often utilized to reduce the amount of fuel needed in smaller reactors, but they are an absolute necessity in a large utility-sized reactor.  This is because reflectors reduce the number of fast neutrons that reach the reactor pressure vessel, or RPV.  It's important to keep fast neutrons from reaching the RPV as much as possible, and that is due to the effect these neutrons have on the steel. 

With that, we have finally arrived at the point of this post, which is:

Part 4. Macro Effects of Nuclear Scattering
What happens when a fast neutron escapes the reactor core and reaches the Reactor Pressure Vessel?  Note: This problem is specific to Pressurized Water Reactors, due to the high operating pressure and high neutron fluxes involved.

The reactor vessel is pressurized during operation, and it is under incredible tensile stress.  The internal pressure is trying to make the reactor vessel expand like a balloon.  The steel of the pressure vessel is also under continuous bombardment from fast neutrons.  Does this have an effect on the steel?

Reactor pressure vessels are made from ferritic steel alloys containing small amounts of nickel, molybdenum, manganese, silicon, and sometimes chromium.  The purpose of adding these specific metals is to increase the toughness and ductility of the reactor pressure vessel.  Over time the fast neutrons will cause the vessel to become brittle.  This process is called neutron embrittlement, and it turns out that this shift in DBTT is actually what limits the life-span of a nuclear power plant.  This is  because replacing a highly radioactive reactor pressure vessel would be prohibitively expensive in an aging power plant.

See?  This is an important topic!

When neutrons escape the reactor core, get past the thermal shields, and scatter inside atoms in the reactor pressure vessel, they physically move them, causing the atoms to migrate slightly.  The strength and physical properties of the RPV are determined by the crystalline matrix of grains in the steel, and this semi-random displacement of atoms causes the steel to develop microsocopic defects, which (as we learned above) are the birth-place for brittle fracture.

As a result of long-term neutron bombardment, the Ductile-Brittle Transition Temperature of the RPV falls over time, to the point where the reactor pressure vessel is no longer safe to operate, even at the elevated temperatures of an operating reactor.  At this point, the RPV, and the power plant must be retired.

Well before the point where the RPV must be retired from service, RPV embrittlement will cause operational limitations.  Heat-up and cool-down rates are reduced, as they add additional thermal stresses that must be minimized with the neutron-damaged RPV.  Also, at reduced temperatures, very strict pressure limitations must be observed.

Interestingly, Rosatom, the Russian state-owned nuclear corporation, announced in 2018 that it has developed an in-situ thermal annealing process.  Annealing increases ductility and reduces hardness, and Rosatom claims that this process can extend the life of a reactor pressure vessel by 15-30 years.   How cool is that!!