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 Post subject: Neutron mean free path
PostPosted: Apr 23, 2013 6:32 am 
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What exactly does the mean free path mean with respect to neutron poison (capture)?

I presume this is a half-distance, that is, if the mean free path for thermal neutrons is 1 mm for a specific neutron poison, then does a 1 mm neutron poison layer stop half of the thermal neutrons? So 10 mm stops 99.9%?

The mean free path of thermal neutrons through Gd203 is only 8.3 microns according to Kloosterman. So just a 1 mm layer of Gd2O3 stops all thermal neutrons?


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PostPosted: Apr 23, 2013 7:20 am 
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Cyril R wrote:
What exactly does the mean free path mean with respect to neutron poison (capture)?

I presume this is a half-distance, that is, if the mean free path for thermal neutrons is 1 mm for a specific neutron poison, then does a 1 mm neutron poison layer stop half of the thermal neutrons? So 10 mm stops 99.9%?

The mean free path of thermal neutrons through Gd203 is only 8.3 microns according to Kloosterman. So just a 1 mm layer of Gd2O3 stops all thermal neutrons?

Gd203 ????? OK I see, Gadolinium Oxide. But there are many stable isotopes of Gd - so is the 8.3 microns referring to a natural isotropic mix or the one isotope that has the biggest cross-section?

No. I think the mean free path is the average distance traveled before any collision not just an absorption. So maybe you could multiply this by the ratio of the absorption cross-section / (total cross-section) to get a mean absorption distance?


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PostPosted: Apr 23, 2013 10:08 am 
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Gadolinium has a huge thermal neutron absorption x-section.
It is used in the form of gadolinium nitrate solution in the second emergency shutdown system of Candu reactors: The poison solution is easily injected into the HW calandria, which is at ambient pressure.

However, not all neutrons are in the far left end of the thermal spectrum (20 degrees Celsius) - particularly in an epithermal MSR: The equivalent temperature is on the order of tens of thousands of degrees, for the neutrons.
The absorption x-section and mean free path will be VERY different, as a result.
A much thicker layer of Gd would be required for a neutron shield: It gets expensive.
Turns out that a much cheaper option is borated concrete & similar low-tech solutions.


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PostPosted: Apr 23, 2013 12:30 pm 
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jaro wrote:
Gadolinium has a huge thermal neutron absorption x-section.
It is used in the form of gadolinium nitrate solution in the second emergency shutdown system of Candu reactors: The poison solution is easily injected into the HW calandria, which is at ambient pressure.

However, not all neutrons are in the far left end of the thermal spectrum (20 degrees Celsius) - particularly in an epithermal MSR: The equivalent temperature is on the order of tens of thousands of degrees, for the neutrons.
The absorption x-section and mean free path will be VERY different, as a result.
A much thicker layer of Gd would be required for a neutron shield: It gets expensive.
Turns out that a much cheaper option is borated concrete & similar low-tech solutions.


I know this, but was still surprised at the low mean free path for thermal neutrons. I wanted to know if mean free path is the same as halving thickness.

Even for 1 MeV neutrons, gadolinium is still better than pretty much anything else, even B4C. B4C makes helium and tritium, not what I want for the application I'm thinking of.

Concrete won't do for shielding the reactor vessel of a molten salt reactor. It can't take high temperatures like that.

If we first thermalize the neutrons with a chunk of graphite, or just a fuel salt annulus, which can take high temperature, then a Gd metal of B4C layer to capture the neutrons, then something heavy like steel to capture the gamma's, we have a highly efficient high temperature shield. Gd metal is better in capture than B4C, doesn't need enrichment, and also shields decently against gammas.


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PostPosted: Apr 23, 2013 1:01 pm 
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Cyril R wrote:
jaro wrote:
Gadolinium has a huge thermal neutron absorption x-section.
It is used in the form of gadolinium nitrate solution in the second emergency shutdown system of Candu reactors: The poison solution is easily injected into the HW calandria, which is at ambient pressure.

However, not all neutrons are in the far left end of the thermal spectrum (20 degrees Celsius) - particularly in an epithermal MSR: The equivalent temperature is on the order of tens of thousands of degrees, for the neutrons.
The absorption x-section and mean free path will be VERY different, as a result.
A much thicker layer of Gd would be required for a neutron shield: It gets expensive.
Turns out that a much cheaper option is borated concrete & similar low-tech solutions.


I know this, but was still surprised at the low mean free path for thermal neutrons. I wanted to know if mean free path is the same as halving thickness.

Even for 1 MeV neutrons, gadolinium is still better than pretty much anything else, even B4C. B4C makes helium and tritium, not what I want for the application I'm thinking of.

Concrete won't do for shielding the reactor vessel of a molten salt reactor. It can't take high temperatures like that.

If we first thermalize the neutrons with a chunk of graphite, or just a fuel salt annulus, which can take high temperature, then a Gd metal of B4C layer to capture the neutrons, then something heavy like steel to capture the gamma's, we have a highly efficient high temperature shield. Gd metal is better in capture than B4C, doesn't need enrichment, and also shields decently against gammas.


The abstract I posted earlier, and don't have on this computer, says hafnium hydride will stand up to temperature enough to boil zinc, although not to steel-melting temperature. It contains lots of well-glued free protons ... OK, well-glued on a nanometre scale, free on a femtometre scale ... which are the best neutron thermalizers by far.

For particles that just stop at their first collision, the mean free path is the e-fold attenuation distance. For non-thermal neutrons that hit a proton in HfH1.5, that's a pretty good approximation.

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PostPosted: Apr 23, 2013 1:24 pm 
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Hafnium hydride, won't that evolve hydrogen in a high neutron and gamma field? I think the board consensus is that there are no hydrides stable under both high temperature and fluence.

Halides are interesting, though. Currently I'm working on gadolinium trichloride filled cans for neutron shielding to solve a number of problems I ran into earlier. GdCl3 melts at 609 degree C, so acts like an insulator in normal operation, but like a massive thermal switch upon overheating (so the passively cooled vessel kicks in as heat sink), and it stops neutrons really well to protect the vessel. The backup option is 7LiF-GdF3, a eutectic with 25% GdF3 and m.p. <700 C. The LiF will do better slowing down than GdCl3.


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PostPosted: Apr 23, 2013 7:05 pm 
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Cyril R wrote:
What exactly does the mean free path mean with respect to neutron poison (capture)?

I presume this is a half-distance, that is, if the mean free path for thermal neutrons is 1 mm for a specific neutron poison, then does a 1 mm neutron poison layer stop half of the thermal neutrons? So 10 mm stops 99.9%?

The mean free path of thermal neutrons through Gd203 is only 8.3 microns according to Kloosterman. So just a 1 mm layer of Gd2O3 stops all thermal neutrons?


As stated above the mean free path generically is the average distance traveled between any interaction Lambda = 1/SigmaT
where:
SigmaT = the total macroscopic interaction cross section for any interaction (e.g. scatter, absorption), but for your case you can still use the mean free path for a thermal neutron prior to a thermal absorption assume Sigma-th .

Attenuation A = exp-(Sigma-th x thk) , where thk = thickness

Substituting Sigma-th = 1/ Lambda-th , and rearranging gives:

thk = - Lambda-th x ln (A)

So, for each mean free path of Gd2O3 of 8.3 microns, you attenuate by e=2.718,
and to get 99.9% reduction A=0.001, requires
thk = -8.3 microns x ln(0.001) = 57.3 microns

Sorry for not knowing how to get equations in here. :-(

You can take it from there to get any number you want. Caveat, there is no such thing as zero on a log scale, so you have to pick an attenuation factor that is close enough to "all" to get what you want. But, also as stated above there are non-thermal neutrons, that will pass through the Gd2O3, and thermalize even in the vessel shell and still cause helium to be created, if that is what you are trying to do. So, there is a limit to how much you need to attenuate thermals before there are diminishing returns, especially if there is moderator on the outside of the vessel, unless laminate the Gd2O3 on that side too.

I also note that Gd will probably be very expensive. B4C is made in to plates already for vehicle and body armour among other things, so would probably be much cheaper. But, like you said it does create helium, so might need replaced too frequently. Maybe you cold use the B4C in powder form in a can to accomodate the helium production, while using a cheaper precursor to the scintered plates.


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PostPosted: Apr 23, 2013 7:24 pm 
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Cyril R wrote:
Hafnium hydride, won't that evolve hydrogen in a high neutron and gamma field? I think the board consensus is that there are no hydrides stable under both high temperature and fluence.

Halides are interesting, though. Currently I'm working on gadolinium trichloride filled cans for neutron shielding to solve a number of problems I ran into earlier. GdCl3 melts at 609 degree C, so acts like an insulator in normal operation, but like a massive thermal switch upon overheating (so the passively cooled vessel kicks in as heat sink), and it stops neutrons really well to protect the vessel. The backup option is 7LiF-GdF3, a eutectic with 25% GdF3 and m.p. <700 C. The LiF will do better slowing down than GdCl3.



If you want to protect the vessel from helium production, you want to absorb all the neutrons both before and after the vessel (backscatter), without thermalizing any more just before the vessel. Otherwise, the benefit of using Gd, would be reduced. Therefore, ignoring materials problems for the moment, 7LiF-GdF3 would probably not do as well as GdCl3 at protecting from helium production. That being said, Gd is so effective, that you might be able to accept the thermalizations, especially if the overall attenuation of neutrons is better. This is a valid prospect for helping protect the vessel, if needed.

And I agree, anything with hydrogen will tend to evolve hydrogen, unless canned to prevent, and even then there will be a pressure build up of driven off hydrogen.


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PostPosted: Apr 24, 2013 2:22 am 
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Thanks Ed. The advantage of thermalizing neutrons with Gd looks much higher than the added backscatter and the like. Any neutrons that are thermalized will be captured, this much is clear. They don't stand a chance even with 1 mm of Gd worth of shielding.

B4C blocks may be somewhat cheaper, but to be effective with reasonable thickness (compared to Gd) it requires very high B-10 enrichment. Which is expensive. Gd requires no enrichment. We don't need that much. Just for a liner, maybe a few cm thick, around the inside of the reactor vessel.

Since it's clear that the fast neutrons are the problem for shielding, and not the thermal neutron capture thickness of Gd, the LiF-GdF3 version may be more attractive. For designs that already use a reflector, GdCl3 looks better, but I don't want to use a reflector.


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PostPosted: Apr 24, 2013 7:31 am 
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Ed P wrote:
Cyril R wrote:
Hafnium hydride, won't that evolve hydrogen in a high neutron and gamma field? I think the board consensus is that there are no hydrides stable under both high temperature and fluence ...


... I agree, anything with hydrogen will tend to evolve hydrogen, unless canned to prevent, and even then there will be a pressure build up of driven off hydrogen.


Evolution of a gaseous electrophile that is not created by neutron reactions is quite different from evolution of helium, which is so created, especially with strong neutron consumers Li and B.

If fluence could destabilize a hydride at a temperature where it otherwise would be stable, it could also destabilize an oxide or nitride or fluoride, and O2 or N2 or F2 would be evolved from these -ides.

It might quicken the attainment of equilibrium hydrogen pressure within the mentioned cans, but this would not thereafter build up, and the same quickening would apply to pressure reduction when the temperature went down.

Here's the abstract I linked earlier ...


Quote:
Study on an innovative fast reactor utilizing hydride neutron absorber - Fabrication and high temperature behavior of hafnium hydride pellets ...

Fabrication tests of hafnium hydride pellets were performed for several sizes in a diameter range of 5 to 10 mm and a height range of 2 to 10 mm in order to establish the fabrication process for hafnium hydride neutron absorber Hafnium metal pellets were hydrogenated at high temperature while controlling the amount of the supplied hydrogen to get hafnium hydride pellets with several different hydrogen to hafnium ratios. The samples were expanded by hydrogen absorption and slight barrel shape transformations were observed. No cracks, however, were observed in the obtained hafnium hydrides. The dependence of density on the hydrogen to hafnium ratio showed good reproducibility without any effects from the experience of hydrogen desorption and/or re-hydrogenation process. This indicated that the hydrogen content can be adjusted easily in the fabrication process of hydride pellets. Out-of-pile experiments were performed at high temperature using the obtained hafnium hydrides to evaluate the integrity of the control rod with hafnium hydride absorbers during heat cycle tests between 500 to 700 deg. C and temperature transient tests at 25 to 30 deg. C/min. After the temperature transient tests and the heat cycle tests, the integrity and the hydrogen to hafnium ratio of hafnium hydrides were evaluated. No cracks were observed in any hafnium specimens after these tests. The amount of hydrogen lost from the hydrides was negligibly small during both heat cycle and temperature transient tests. This indicated that the heat cycle and the temperature transient had negligible effects on the integrity of hafnium hydride.


(http://inis.iaea.org/search/search.aspx?orig_q=RN:42097777)

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PostPosted: Apr 24, 2013 8:08 am 
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The max transient temperature for a molten salt reactor is about 800 degree C for design basis accidents and transients, and as much as 900 degree C for beyond design basis accidents. Can the hafnium hydride take this?


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PostPosted: Apr 25, 2013 11:28 am 
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Cyril R wrote:
The max transient temperature for a molten salt reactor is about 800 degree C for design basis accidents and transients, and as much as 900 degree C for beyond design basis accidents. Can the hafnium hydride take this?


From 2006, Figure 8 of Study on Application of Hafnium Hydride Control Rods to Fast Reactor gives the theoretical hydrogen pressure.

From "On the Comparison of Additive-Free HfB2-SiC Ceramics Sintered by Reactive Hot Pressing and Spark Plasma Sintering", maybe not on the web any more,

Quote:
Table 1 and Fig. 1 show processing parameters and some results from the campaign of
the heat treatments PLSHT-n. In the (untreated) sample PLSHT-0, alpha-Hf, Si and B4C were
separate phases. X-ray diffraction identified also a cubic modified HfH1.5 (ICDD 05-639), and
HfB2. The former phase was initially present in the as-received hafnium powder because of the
wet storage. Such a hafnium hydride proved to be stable up to 1,100 °C ...


An interesting question: if the neutron shield starts to outgas diprotium, what does that do to you?

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Oxygen expands around B fire, car goes


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PostPosted: Apr 25, 2013 9:11 pm 
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I wouldn't mind hearing more about hafnium hydride testing. So, far so good, but these all sound like short term tests. Do you know how they measured to determine hydrogen loss? Weight doesn't work because of the high hydrogen weight. Measuring hydrogen in the autoclave atmosphere vent stream would work, but only for fairly high hydrogen loss rates, which means it is not holding the hydrogen. The real tests needed to determine viability would be long term canned and uncanned auto-clave tests, and hydrogen loss in-pile.

Neutrons are very good at transferring energy to hydrogen because they have the same mass and can transfer up to 100% of their energy in one collision. Water has a balance produced between H2O, H2 & O2, and H2O2 with some radiation driving dissociation, and some driving re-association to water. LiF-BeF is so wonderful because the F REALLY likes to bond with the Li & Be, being a ionic salt. They radiolytically decompose, but immediately re-associate.....as long as it stays a liquid. I don't think most metallic hydrides have that kind of balance relationship. A neutron of less than 30 eV is enough to break hydrogen bond, trying to overcome the Hf ability to hold on, so unless there is cladding/canning there will be loss over long periods. NASA used LiH in the SNAP 10A space reactor, but they canned that in steel to retain the partial pressure of hydrogen from this radiolytic and the thermal (@700C) decomposition mechanism. Nickel alloys, especially thin canning, are terrible at holding in hydrogen. Nickel tends to take up hydrogen, like Hf, but that means it is mobile in the metal, and the hydrogen can pass through. Since Hast-alloy N is a nickel alloy this leads to double canning, both of which can't fail. We probably want the HfH canned to prevent both the Hf and H from the salt anyway. The question of viability in a molten salt depends what the diffusion rate of the hydrogen is out, how much attenuation you lose with hopefully slow hydrogen loss, and how long until the HfH has to be replaced, and how expensive it is. Graphite is fairly cheap to replace, but HfH would not be so cheap. It would be better to stick with a canned solid or liquid, with low vapor pressures for the reactor temperatures possible.

The higher the Z of the atoms forming the poison the less chemical dissociation because the neutron can't transfer as much energy per collision. Metals are very high Z, which is why they can take very high neutron fluences and survive. It takes much higher energy neutrons >> 1 MeV to cause displacement damage, and there are less neutrons at higher energies especially at very high energies that do the most damage to metals. This is one of the disadvantages of fast reactors, they have many more neutrons at very high energy.


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PostPosted: Apr 26, 2013 6:01 am 
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Ed P wrote:
LiF-BeF is so wonderful because the F REALLY likes to bond with the Li & Be, being a ionic salt. They radiolytically decompose, but immediately re-associate.....as long as it stays a liquid. I don't think most metallic hydrides have that kind of balance relationship.


Even if most don't, Ti, Zr, and Hf do seem to.

This is paywalled, but you can see the first two pages: http://link.springer.com/content/pdf/10.1007/BF00790227.pdf.

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