Why beryllium for neutron multiplication

[KarenRei]

I've been going over the cross sections on Sigma, and I'm a little confused as to why beryllium is the most talked about neutron multiplier I've come across. I mean, it does have a few things going for it: multiplication down to lower energy levels than most multipliers, and a very low (n, gamma) cross section at thermal energies (given that one expects a large portion of neutrons to thermalize in the multiplier, that matters). But its multiplication levels at 10MeV and above are unimpressive versus many heavier isotopes, and its light atomic mass looks like it should ruin its practical multiplication efficiency since neutrons will lose so much energy per elastic scatter and they'll elastic scatter more often than they'll multiply. And while beryllium is light, strong, and rather heat tolerant, it's expensive and toxic. And its low density works against it by decreasing its macroscopic cross sections.

Why not heavier elements? Zirconium, for example, also has a low (n, gamma) in the thermal spectrum, a higher cross section at energies over 12.5MeV, and neutrons lose 1/10th as much energy per elastic scatter, and it costs about 1/8th as much as beryllium and is relatively nontoxic. At about 1/3 the cost of beryllium ($300/kg according to one paper I read) one can get nearly isotopically pure 90Zr, which has an even lower (n, gamma) cross section. Natural lead has a rather high (n, gamma) cross section, but 208Pb has a very low one. Lead from thorium ores can be found naturally enriched up to about 90% in 208Pb, and it can be manually enriched beyond that. Lead not only has a very heavy nucleus, meaning little elastic scattering loss, but also gives a wide range of neutron multiplication reactions, even with a high cross section for (n,4n) at some energy levels. These are of course just two examples. Heavier elements also have other advantages, like usually being better gamma absorbers.

Am I missing something? Do heavy isotopes have abnormally high inelastic scattering losses that beryllium doesn't or something? The cross sections aren't bigger, at the very least. Or are people normally not that concerned with multiplication of neutrons over 10MeV? I guess if you're dealing with fission where the average neutron energy is under 1MeV perhaps you don't care about the higher energy stuff and only care about having a low energy multiplication cross section, versus fusion (17 MeV) or spallation (30-40MeV) where your source is much higher energy neutrons.

Could anyone clarify the situation for me?

 

[SteamKing]

I think you are blowing the toxicity of beryllium out of proportion to its usefulness.

Beryllium is toxic when its dust is inhaled, but this hazard can be mitigated by wearing proper protective gear during any milling or other manufacturing process which might create beryllium dust.

Beryllium is used as an alloying agent in making many hand tools and other mechanical parts where high strength, non magnetic, or non sparking characteristics are desirable.

http://americanmachinist.com/machining-cutting/understanding-beryllium

 

[KarenRei]

I don't think I blew it out of proportion - I mentioned it only briefly. You're quite right that except for dust, toxicity from beryllium is generally low. But the dust is indeed very nasty stuff and it does increase manufacturing costs / risks. The amount of beryllium dust one needs to be exposed to in order to get (uncurable, chronic) berylliosis can be under a milligram per cubic meter.

Anyway, that was really a side point; what I'm curious about is the physics of neutron multiplication with beryllium vs. heavier elements. Because it looks like except for "low" (~2,5-8 MeV) energy neutrons, heavier isotopes with low (n,gamma) thermal cross sections should make better multipliers.

 

[mfb]

Beryllium is toxic when its dust is inhaled, but this hazard can be mitigated by wearing proper protective gear during any milling or other manufacturing process which might create beryllium dust.

Which is basically every manufacturing process.
Particle physics experiments often use beryllium beam pipes due to the low radiation length. That leads to safety rules like "you are not allowed to use any hard tools when working above the beam pipe" - it could fall onto the pipe and produce/release dust.

Fission or fusion neutrons fall below 10 MeV quickly compared to the total thermalization time, so a low threshold for multiplication is important.

 

[KarenRei]

This isn't the discussion that I came here to have. But even with precautions, people working with beryllium still get CBD. The CDC for example champions a company that brought down their incidence rates for beryllium sensitization to "only" 0.7 cases per 1000 person-months - they call it the "first known success story":

http://www.cdc.gov/niosh/nas/rdrp/ch3.4.htm

That still means that on average one in four people who work there for 20 years will develop the beryllium sensitization. That rate may sound high, but rate before their process improvements was 5.6 per 1000 person-months. Sensitization can either remain under control indefinitely (most cases), remain dormant for years but then become active, or immediately progress into granulomas in the lungs, loss of lung capacity, and in bad cases, death. Overall, it will progress to an active disease form in "2 to 5% of beryllium-exposed workers despite efforts to reduce workplace exposures", with mortality rates of 5 to 38%.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2774897/

It's simply a fact that beryllium dust is toxic and poses risks during manufacture of beryllium-containing products, including alloys, and even tiny quantities of the dust can cause sensitization and eventual development of granulomas / loss of lung capacity. Obviously one can, should, and is required to take precautions, and these dramatically reduce the risk versus unprotected workers. Reduce, but not eliminate. A lot of people who work with beryllium still get sick from it.

Anyway, all I said was, quite simply, that beryllium is toxic, as a one-word "and" at the end of a sentence. This shouldn't be a controversial claim. Any information site on beryllium will mention exactly what I wrote. And it's entirely tangential, so can we move on from it?

Anyway, back to the actual topic:

Fission or fusion neutrons fall below 10 MeV quickly compared to the total thermalization time, so a low threshold for multiplication is important.

But beryllium doesn't multiply all the way down to thermalization. The cross section is irrelevantly small up until about 2-3 MeV, so it only offers advantages between say 2,5 and 8 MeV. That's only a couple scatters worth of energy. Plus. multiplication is endothermic (what, -1.6 MeV-ish for beryllium?); there's a lot less energy to give up to the process when your starting neutron is low energy. In beryllium, it's likely that a neutron in the 2,5 to 8 MeV spectrum will simply scatter out of range without multiplication, and if it multiplies, it's likely to only happen once.

In lead or other heavy ions, elastic scattering losses are almost irrelevant due to the 23x heavier atomic mass. Which is why heavy ions are well known to make terrible moderators ;) I don't know what the inelastic scattering losses are (unfortunately they're not as easy to figure out as elastic), but it's clearly low because, as is well known, lead is a terrible moderator (hence its use as coolant in fast reactors). Neutrons that aren't scattered down get more chances to be multiplied. The only other option is capture, but the cross sections are tiny - for example, for lead:

http://www.nndc.bnl.gov/sigma/getPlot.jsp?evalid=15294&mf=3&mt=102&nsub=10

Compared to the neutron multiplication cross sections:

http://www.nndc.bnl.gov/sigma/getPlot.jsp?evalid=15294&mf=3&mt=16&nsub=10
http://www.nndc.bnl.gov/sigma/getPlot.jsp?evalid=15294&mf=3&mt=17&nsub=10
http://www.nndc.bnl.gov/sigma/getPlot.jsp?evalid=15294&mf=3&mt=37&nsub=10

... you can pretty much write it off.

Combine this with the fact that some of these lead multiplication cross sections aren't just for 2n, but 3 and even 4n, it just looks vastly better than beryllium for any neutron over the 8-10 MeV ballpark. But maybe there's something I'm not seeing here? Perhaps the multiplication reactions for lead are vastly more endothermic than with beryllium or something? Even given that I would have trouble picturing that it would be worse - I mean, even if neutrons averaged only a single (n,4n) capture and that was the end of it, that would be an incredible overall multiplication rate.

The more I think about it, the more I think that the main reason for using beryllium has to be for when high energy neutrons are rare, like with fission, rather than fusion or especially spallation. I just can't see any other reason why it would be better. But if the lion's share of your neutrons are under 8 MeV, then that would probably make sense.

 

[Genro]

The Beryllium reflector is usually not as thick as the inertial reflector. In the static state the critical mass is determined principally by the latter but after the chain reaction commences the gamma rays will induce neutron generation in the beryllium. The increasing in the dynamic reflectivity will work to reduce the effective critical mass. The increase in the ratio of the product of compressed radius and density to the critical value will result in a greater yield.
In the case of Fat Man where the critical mass is estimated as about 8.5 Kg Assuming the enhanced dynamic reflectivity of a Beryllium shell reduced the critical mass by 20% i.e. 6.8 Kg, then the yield would rise from 21,000 to an estimated 35,000 tons TNT, an almost 70% increase.

 

[KarenRei]

Hmm, interesting Genro, I didn't stop to think about gamma-induced neutron generation. Hmm, I'm not sure where to find the cross section for this reaction, do you know? I thought beryllium was considered rather transparent to high energy EM radiation, that's why it's used in X-ray windows. Is this something that only becomes significant in the extreme environment of an atomic bomb explosion?