In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, its nuclear fission cross-section), density, shape, enrichment, purity, temperature, and surroundings. The concept is important in nuclear weapon design.
Explanation of criticality
When a nuclear chain reaction in a mass of fissile material is self-sustaining, the mass is said to be in a critical state in which there is no increase or decrease in power, temperature, or neutron population.
A numerical measure of a critical mass is dependent on the effective neutron multiplication factor , the average number of neutrons released per fission event that go on to cause another fission event rather than being absorbed or leaving the material. When k = 1, the mass is critical, and the chain reaction is self-sustaining.
A subcritical mass is a mass of fissile material that does not have the ability to sustain a fission chain reaction. A population of neutrons introduced to a subcritical assembly will exponentially decrease. In this case, k < 1. A steady rate of spontaneous fissions causes a proportionally steady level of neutron activity. The constant of proportionality increases as increases.
A supercritical mass is one which, once fission has started, will proceed at an increasing rate. The material may settle into equilibrium (i.e. become critical again) at an elevated temperature/power level or destroy itself. In the case of supercriticality, k > 1.
Due to spontaneous fission a supercritical mass will undergo a chain reaction. For example, a spherical critical mass of pure uranium-235 (235U) with a mass of about would experience around 15 spontaneous fission events per second. The probability that one such event will cause a chain reaction depends on how much the mass exceeds the critical mass. If there is uranium-238 (238U) present, the rate of spontaneous fission will be much higher. Fission can also be initiated by neutrons produced by cosmic rays.
Changing the point of criticality
The mass where criticality occurs may be changed by modifying certain attributes such as fuel, shape, temperature, density and the installation of a neutron-reflective substance. These attributes have complex interactions and interdependencies. These examples only outline the simplest ideal cases:
Varying the amount of fuel
It is possible for a fuel assembly to be critical at near zero power. If the perfect quantity of fuel were added to a slightly subcritical mass to create an "exactly critical mass", fission would be self-sustaining for only one neutron generation (fuel consumption then makes the assembly subcritical again).
Similarly, if the perfect quantity of fuel were added to a slightly subcritical mass, to create a barely supercritical mass, the temperature of the assembly would increase to an initial maximum (for example: 1 K above the ambient temperature) and then decrease back to the ambient temperature after a period of time, because fuel consumed during fission brings the assembly back to subcriticality once again.
Changing the shape
A mass may be exactly critical without being a perfect homogeneous sphere. More closely refining the shape toward a perfect sphere will make the mass supercritical. Conversely changing the shape to a less perfect sphere will decrease its reactivity and make it subcritical.
Changing the temperature
A mass may be exactly critical at a particular temperature. Fission and absorption cross-sections increase as the relative neutron velocity decreases. As fuel temperature increases, neutrons of a given energy appear faster and thus fission/absorption is less likely. This is not unrelated to Doppler broadening of the 238U resonances but is common to all fuels/absorbers/configurations. Neglecting the very important resonances, the total neutron cross-section of every material exhibits an inverse relationship with relative neutron velocity. Hot fuel is always less reactive than cold fuel (over/under moderation in LWR is a different topic). Thermal expansion associated with temperature increase also contributes a negative coefficient of reactivity since fuel atoms are moving farther apart. A mass that is exactly critical at room temperature would be sub-critical in an environment anywhere above room temperature due to thermal expansion alone.