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A BWR reactor core may contain up to 146 tons of uranium. Why does it not form a critical mass when molten? Are there any estimates of the critical mass of the resulting zirconium alloy, steel, concrete and uranium oxide mixture?

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Take a look at wikipedia. I think the main point is that the core does not consist of pure uranium. – Tobias Kienzler Mar 18 '11 at 11:02
up vote 14 down vote accepted

If you read Wikipedia page about corium, they say that critical mass can be achieved locally.

But if you are concerned about a critical mass allowing a nuclear explosion, the difficulty in nuclear weapon design, as told here, is to achieve the criticality fast enough. If you do not achieve criticality fast enough, your material heats and its interaction with neutrons decreases, slowing the chain reaction down. And that is with pure ²³⁵U. So basically what happens if criticality happens in a melting nuclear reactor is the release of a lot of heat and radiation, but not in an explosive manner as in an atomic bomb.

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+1 Thank you for your answer. Your point about heat and anna's one on the moderator in the mixture were equally valuable and I'd accept both answers if it were possible to do so. – artistoex Mar 18 '11 at 18:31
Honestly, I think the wording of Wikipedia about a local critical due to a critical mass is likely to reflect an insufficient technical understanding. A prerequisite for critical mass is to have $k_{\infty}>1$ and this is generally not satisfied for the Uranium Oxide or Uranium metal, as per the arguments regarding the moderator. On the full-core scale, a rearrangement could add reactivity although it is more likely it will subtract reactivity, either way it has to do with the neutronic communication across the entire core. – Alan Rominger Apr 23 '12 at 13:26

The probable answer is that to make a bomb one needs a very special design and very pure U235, in a sphere. So even if a critical mass forms in meltdown, a reactor does not have the geometry and purity for a nuclear bomb. No mushrooms.

But it may continue to heat, acting as a reactor, and the problem is in conveying the heat away without building up steam and hydrogen in order to avoid a chemical explosion.

A nuclear engineer should answer whether the amalgam of all the metals does not allow criticallity. Their plans to first cool the melted reactors and then encase them in sand and cement would imply that they do not expect the melted core to be critical. The fact that with the control rods in place the reactor is no longer critical by design, just has residual radioactivity, argues from conservation of mass that even in melt when the metals will be mixed the same will hold true.

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So both the boron from the control rods and the heat (Frédéric) prevent criticality. – artistoex Mar 18 '11 at 18:19
An operating reactor is critical. TO make a bomb you need to get to criticality faster and hold it for long enough to fission enough of the material - it's called a "prompt criticality" – Martin Beckett Mar 18 '11 at 18:37
There's certainly no requirement for a bomb core to be spherical. The Little Boy bomb had a cylindrical core, for example, which was in two parts, a smaller cylinder and a tube, that were brought together. – David Richerby Aug 13 '14 at 13:09
@DavidRicherby a sphere is a geometrical design easy to comprehend. Other symmetric designs would also do, the symmetry being necessary for the time factor . Reactors are designed wit safety factors, so that they cannot become supercritical, i.e. a bomb, even when mechanical safety fails . At worst it is a melt… – anna v Aug 13 '14 at 15:00

One of the questions often being answered is “why don’t meltdowns go supercritical?” ie. “Why don’t they create a nuclear explosion?” A good understanding of why they don’t provides a good framework to understand why corium should not be critical, and why subcritical can be fairly bad.

Critical mass is more a description of neutron flux than actual mass of material. Perhaps a better term would be critical concentration, but I think “critical mass” sounds better; don’t you? In the supercritical mass the fuel can act as moderator and neutron generator. Fission produces mostly fast neutrons which are not absorbed at high probability by fuel nuclei, but if you have enough fuel nuclei this problem is obviated. Some nuclei will absorb fast neutrons and give off slow neutrons, and a gamma ray. Some of the first reactor designs were slurry reactors where finely ground moderator and fuel were mixed together. I suppose if a slurry reactor melted down the corium would be critical. Modern reactors use fuel rods and both solid and liquid moderators.

The fuel in the rods has both an internal and a surface neutron flux. The perfect nuclear reactor would have surface flux where all the fast neutrons escaping the fuel rod were reflected back as slow neutrons. This would allow the fuel to “burn” most efficiently. By arraigning the fuel rods and moderators in an optimal configuration the closest to perfect flux is achieved. If you remove the moderator the fuel is not critical by itself. If you change the arrangement the fuel should go subcritical also. If it were not for the fact that much more fuel is present for the minimal critical configuration it would be so statistically unlikely to even have local areas of critical flux that it would really be impossible. With the overabundance of fuel it is only highly improbable that a local slurry reactor zone could form in the corium blob.

Subcritical neutron flux does not mean that fission has stopped; it only means that fission will eventually drop to the level expected with only spontaneous fission. Depending on how subcritical the reactor is this could take a while.

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Several things are required to cause a nuclear explosion. It is not just about mass... In terms of a melt down, perhaps heat is the real issue, because it expands the gap between atoms and this diminishes the target cross section for a neutron to strike, thus lengthening the mean neutron pathway.

Other issues include isotope purity of the fissile mass... Also impurity from decay products like Xenon 135. In a nuclear melt down like Chernobyl for example there was very high Xenon poisoning before the steam/hydrogen explosion which destroyed containment buildings.

Geometry of a critical mass is a further consideration, but given the two points above once it is too hot and contaminated Geometry is the least consideration.

Compression of the critical mass is another and this is related to heat. If the mass were squashed tight or frozen the chances of explosion would be higher. In a nuclear warhead too much Alpha activity raises the temperature and degrades the bomb. With heat in a reactor melt down there is virtually no compression.

Having an effective reflector would increase the chances of a nuclear explosion, but nuclear reactors are not normally configured to reflect neutrons back into the pile. In any case in a melt down the confinement vessel is usually ruptured.

Even if you somehow overcame all this there still has to be sufficient neutron flux and this is totally unlikely. In terms of Neutron Flux one has to ensure that 35-40% of neutrons do not escape the mass to obtain an explosion.

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My guess would be that the moderator (normally the water, graphite already would have caused the accident) is missing and that is still vital in a compacted mass. The uranium oxide is not enriched to military grade, but I can't speak for MOx-elements.

Should be difficult to say without some decent figures about leftover UO_2, mass, previous distribution.

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The water is said to slow down the neutrons which increases their cross ection wrt fission. So without the water, it is harder to obtain critical mass. I don't know if it is impossible however, I thought it was considered very improbable, which isn't the same thing. – Omega Centauri Mar 18 '11 at 14:28
That is where one would have to need to know details about enrichement. I somehow doubt that even a melted down mass of nuclear fuel pellets will reach criticality without a moderator. That was always a big risk to be avoided in constructing the whole shebang - because then terrorists just could come along, steal a bit here and there and homegrow a small bomb. – Leonidas Mar 18 '11 at 15:09
A reactor bomb would be a variety of dirty bomb, i.e. you can't obtain kilotons or megatons of energy out of it. Slow assembly of materal into a critical mass, means it would get hot and disperse the material before more than a tiny fraction of nuclei are fissioned. It would still make of awful radiological mess however. – Omega Centauri Mar 19 '11 at 19:40

I seriously doubt that any realistic reactor will contain 146 TONS of Uranium at any one time.

Even if it did, it'd be so spaced out as to preclude the creation of a supercritical mass (i.e. a mass that leads to a nuclear explosion).

Of course any operational reactor WILL be critical, if it weren't there'd be no chain reaction going on, no sustained fision reaction, no energy output.

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Maybe artistoex refers to the spent fuel pool, where some years worth of semi-spent nuclear fuel are stored and produce enough decay-heat to melt down too. – Leonidas Mar 18 '11 at 15:10
From : "A 1000 MWe reactor has about 100 metric tons of uranium dioxide fuel, of which 3 to 5 tons consist of the fissile U-235". So I think one can imagine a realistic reactor containing 150 tons of Uranium, even discounting the oxygen in UO₂ – Frédéric Grosshans Mar 18 '11 at 15:34
@leonidas The page cited by Frédéric also mentions 183 kg uranium/assembly for BWRs and in it says "A range between 368 assemblies for the smallest and 800 assemblies for the largest U.S. BWR forms the reactor core". – artistoex Mar 18 '11 at 17:28

if the pressure vessel contained a supper critical mass long enough it could go boom like a nuclear bomb but its more likely to blow the containment before then and lose mass

its about a self compounding reaction that quickly builds on its self if they lost all ability to moderate the reaction a critical mass could be reached much quicker but it still comes down to the containment being intact at the last moment unlikely but some advocates have spoken out about this remote possibility

japan was close to this outcome they had a fizzle type explosion that was more or less a dirty bomb if their containment was stronger they would have likely had a nuclear bomb of some size

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There is no "vessel" that can contain a super critical mass long enough to permit an explosion with any significant nuclear yield. Runaway fission inside a sealed container produces a Chernobyl-type explosion---what the engineers euphamisticly call "spontaneous disassembly of the core." Containment in nuclear weapons is achieved by a shock wave produced by chemical explosives, and "long enough" is roughly one microsecond. The explosions at Fukushima were not nuclear powered. They were due to the detonation of hydrogen gas. – james large Nov 15 '15 at 14:26

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