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.
A nuclear reactor cannot explode like a nuclear weapon.
For a thermal reactor -like Chernobyl or Three Mile Island- the neutron generation lifetime is too long.
For a fast reactor (and a thermal reactor) there is no mechanism for creating and maintaining a super prompt critical assembly sufficiently long for significant release of energy from fission.
You have to really work hard to assemble the correct material to create a nuclear weapon; you need to create a system that is super prompt critical using fast neutrons and remains so sufficiently long for the chain reaction to produce enough energy before pressure causes dis-assembly into a non-critical configuration. By super prompt critical is meant super critical on the prompt neutrons alone without having to wait for the delayed neutrons to contribute. See the Los Alamos Primer by Serber, available from Amazon: the early notes on the physics of a fission weapon from Los Alamos at the beginning of the Manhattan project.
The explosions at Chernobyl were a steam explosion, and a chemical explosion caused by oxygen reacting with aerosolized graphite. (At Three Mile Island the explosion was from oxygen reacting with hydrogen released from oxidation of the over-heated zircalloy fuel cladding.)
For a nuclear reactor, the safety concern is the removal of decay heat from the radioactive decay of fission products after the fission process is terminated. Decay heat is about 5% of full power at shutdown.
A major problem with the Chernobyl design is the core was over-moderated. Specifically, the graphite was the moderator and the cooling water was not needed as a moderator and in fact acted as a neutron poison. So when the cooling water was lost the reactor power increased: positive feedback. The old N reactor in the US was a graphite moderated, water cooled reactor used to produce Pu for the weapons program, but was specifically designed to not have this problem.
Also, Chernobyl did not have a robust reactor containment system, it had a reactor confinement system.
Best Answer
The electric charge difference between the earth and the atmosphere grows with altitude, at around 88 DC volts per meter. This electric potential may be shorted out when a thermonuclear explosion releases radiation which ionizes the atmosphere. About 5% of a nuclear explosion's energy is in the form of ionizing radiation.
A study of lightning flashes caused by a thermonuclear detonation in 1952 may be of interest, though I read only the abstract, as the full article requires payment: http://onlinelibrary.wiley.com/doi/10.1029/JD092iD05p05696/abstract. The lightning started from the surface and was upward propagating. As the earth has a net negative charge, and as thermonuclear explosions deposit negative ions in the atmosphere, I don't know how to explain the upward propagation of that particular test. However, see anna v's comment. Uman, et.al., studied the same detonation in 1972 and found that "the likely mechanism for the necessary charge and electric field generation were Compton electrons produced by gamma rays from the detonation" - Lightning: Physics & Effects, Rakov, Uman; Cambridge University Press, 2003.