Atomic Energy — The Basics

When we speak of atomic energy, we mean energy which is obtained from some fundamental property of matter itself, rather than from the way that matter is arranged.

The Molecular, Atomic, and Nuclear Nature of Matter

Energy from the Nucleus • Fission, key to atomic energy • Practical Nuclear Reactors

Matter has proven not to be indefinitely divisible. Everyone is familiar with heterogenous forms of matter, such as granite stone, which is composed of variously-sized grains discernable by the eye. Even the purest of substances, however, eventually turns out to have minimum units of identity, a scale of size below which the substance as such no longer exists. Some of the ancient Greek philosophers suspected as much, and gave the postulated minimum unit the name of atom, or ‘uncuttable’.

As the modern science of chemistry began to develop in the eighteenth and nineteenth centuries, it was observed that many chemical reactions followed a ‘law of definite proportions’. In other words, when two substances combined to make a third, there would typically be some of one of the original reagents left over, and the amount which combined would typically be in a particular ratio to the amount of the other which it had to combine with. This led to the definition of chemical equivalents, quantities of material which would be transformed to the same extent. It was soon observed that the masses of these equivalents were often in simple integer ratios — the mass of one equivalent of oxygen, for example, was just sixteen times that of one equivalent of hydrogen.

This led to a revival of the idea of the atom. Perhaps complex substances were made up of ‘compound atoms’, each of which contained a definite number of atoms of basic or ‘elementary’ substances, and perhaps a gram of hydrogen contained a definite number of atoms of hydrogen, while a gram of oxygen contained one-sixteenth that number of atoms. This hypothesis was agreeable to the kinetic theory of gasses, on the basis that the volume occupied by one equivalent of oxygen was the same as that occupied by one equivalent of hydrogen, while the volume of one gram of oxygen was one-sixteenth that of one gram of hydrogen. This could be explained on the basis of vanishingly small particles of discrete mass.

The chemical equivalent became known as a mole or ‘gram-atom’ ; the constant number of atoms in one mole of any substance is known as Avogadro’s number, and has been measured at 6.022×1023. Mendeleeff and his followers, arranging the known elements on the basis of their molar masses, succeeded in predicting the existence of substances which were actually found in the laboratory.

Presently the compound atoms gained the distinguishing name of molecules, ‘little masses’. At this point the general idea was that atoms were, more or less, exceedingly tiny hard balls. Experiments with electricity, however, began to show that this mysterious principle was not a fluid, but something intimately associated with atoms, which could be attached to or detached from them in discrete units, and absorbed and released in the course of chemical transformations. And then came the discovery of radioactive decay, in which atoms definitely changed their chemical identities, and even spit out bits which proved to be other atoms.

The atom, then, was not indivisible after all. To put a cap to this confusion, experiments with the emanations of radioactive atoms showed that the atom itself was mostly empty space, but that it contained a tiny hard kernel — a ‘nucleus’ — in which practically all the mass was concentrated. The nucleus proved to have its own law of definite proportions, its own chemistry in a sense, but one much simpler than that of atomic substances, with only two basic units. If the mass of the hydrogen nucleus was taken as the unit, then helium had four units of mass, carbon twelve, oxygen sixteen, iron fifty-six, and so on. The nucleus also proved to have an electric charge, that of hydrogen being equal and opposite to that of the electron, of helium twice that of hydrogen, of carbon six times, of oxygen eight, of iron twenty-six, and so on.

Ultimately this led to the realization that the nucleus consisted of two types of particles, the proton or hydrogen nucleus, and the neutron, a particle of about the same mass but having no charge. The chemical identity of an atom was determined purely by its number of protons, known as the atomic number. Careful investigation showed that some elements possessed atoms having nuclei varying in the number of neutrons, and thus of total ‘nucleons’ (protons and neutrons together), what is called the mass number. Thus, in every 6500 hydrogen atoms, there proved to be one with a neutron and a proton together, instead of a lone proton, for a nucleus. This became known as hydrogen-2 or deuterium, the ‘second substance’ (as ordinary hydrogen is also known as protium), and notated as either 2H or D.

Generically, these atomic species having the same chemical identity are known as isotopes, to indicate that they occupy the same place, while a particular type of nucleus (identified by mass number and atomic number) is a nuclide. In fact the difference in mass does lead to slight variations in chemical behaviour between isotopes, which can be used to separate them. Some elements have no stable isotopes ; some, such as gold, have only one (197Au) ; and tin has nine, with mass numbers 112, 114, 115, 116, 117, 118, 119, 122, and 124. Different elements can have ‘overlapping’ isotopes with the same numbers, isobars, such as 116Cd, 115In, and 122Te, where cadmium (element atomic number 48), indium (49), and tellurium (51) overlap tin (50). To measure the mass of an atom or molecule, the isotope carbon-12 is defined as equal to twelve daltons (Da, named after the chemist who first articulated the modern atomic theory), which is equivalent to twelve grams per mole.

Energy From the Nucleus

The Atomic, Molecular, and Nuclear Nature of Matter • Fission, key to atomic energy • Practical Nuclear Reactors

Most nuclei have energy to give up, and some do it spontaneously. It is an experimentally-determined fact that the masses of atomic nuclei are not quite in proportion to their mass numbers. The largest mass per nucleon is that of ordinary hydrogen, the plain proton or 1H, 1.007825 dalton ; the smallest, nickel-62, 61.9283 Da, or 0.99884 Da per nucleon. The difference, or “mass defect”, varies in a somewhat regular fashion referred to as the curve of binding energy. This name comes from the consideration that the mass defect represents, by Einstein’s equation E = mc2, the energy which is given up in going from a less stable to a more stable configuration. In other words, a nucleus cannot hold together unless it has less total energy than the raw particles it is composed of ; and it is another experimental fact that the energy released in a nuclear transition exactly balances with the difference in masses of the initial and final states.

In the furnaces of the stars, nuclei are crushed against each other under enormous heat and pressure, and the strong nuclear force causes some of them to fuse together into heavier nuclei. Ordinarily, this only occurs for reactions which release energy, and so most of the elements formed are iron or lighter. Under abnormal conditions, however, such as a supernova explosion, much heavier nuclei may be formed. In more familiar circumstances, such reactions cannot possibly occur. The energy required to overcome the repulsion between positively-charged nuclei is simply too high a barrier. But some nuclei not only have excess energy, but are actually unstable, and give up a part of that energy by a natural process.

The simplest model of the nucleus is a drop of liquid, in which the strong nuclear force takes the role of surface tension. It must be clearly understood that the strong force drops off much more rapidly with distance than the electrostatic force which repels protons from one another. Since the neutrons contribute to the attraction but not the repulsion, it makes sense that elements with larger atomic numbers have more neutrons, proportionally, than those of small atomic number — 3He being the only stable compound nucleus with more protons than neutrons. Nor is it strange that the largest nuclei cannot hold together at all.

In fact the nucleus is not quite so simple. It has other properties suggestive of a geometrical arrangement ; so, there are ‘magic numbers’ of nucleons which are especially stable. Helium-4, for example, has a much greater mass defect than anything nearby, which helps make it extremely stable, while nuclei of mass numbers 5 and 8 exist only momentarily, as transitional states in nuclear reactions. On the whole, even numbers are more stable than odd numbers, which helps to explain why even-numbered isotopes of thorium (90) and uranium (92) are found in sizable quantities, when protactinium (91) is not.

What is radioactivity?

Radiation is energy which travels through space. Normally this refers to electromagnetic radiation, such as light, but the name is also attached to particles which carry with them energy of motion. “Radiation” is often used as an abbreviated term for ionizing radiation, which is capable of causing chemical changes. This includes energetic electromagnetic radiation such as ultraviolet light and X-rays, as well as fast-moving charged particles, because all of these are capable of dislodging electrons from their positions in molecules.

Ionizing radiation is both useful and dangerous — after all, many of our industries rely on chemical changes, but to have them happen where they are not expected can result in equipment failures, poisoning, and other undesirable occurrences. Living organisms, because of their very complex chemistry and physical structure, are especially susceptible to such injurious effects, and it may reasonably be said that life could not exist on Earth today if it did not possess mechanisms for repairing radiation damage.

An atom which undergoes a change in the nucleus from a less stable to a more stable state normally releases its excess energy in the form of radiation, and for this reason, substances or materials containing such atoms are described as radioactive.

How does radioactivity work?

Nobody can say what causes a particular unstable nucleus to change at a given moment. Indeed, a distinctive feature of radioactive decay is that it is spontaneous and inexorable. As an almost invariable rule, neither the state of chemical combination of a radioactive atom, nor its temperature, from very high values down to as near absolute zero as can be attained, has the least effect to encourage or retard the occurrence of nuclear transitions.

What we do know is that, when a large number of unstable nuclei of the same kind is gathered together, their activity makes a perfect fit to what is called an exponential decay curve. This has two properties. Firstly, it is always decreasing — hence ‘decay’, and nuclear transformations are also known as radioactive decay. Secondly, the activity at any moment is related to the quantity of the original substance at that moment, so that the ratio between the activity at any one time and at another time is in constant proportion to the ratio between the quantities of untransformed nuclei remaining at those two times.

As a result, no matter when you start counting, the time required for the activity to die away to half its initial value is a constant. Every radioactive species can be identified by its distinctive “half-life”. Because of the law of constant proportion, this fact provides us with one of the ways we measure radioactivity.

How is radioactivity measured?

There are three ways of measuring radioactivity : by the frequency of transformations, by the amount of energy involved, and by the biological effects.

The becquerel (Bq) measures decay rate.
One becquerel is a quantity of radioactive material in which one transformation occurs each second. The mass of this quantity of any radioactive species can be calculated directly from its half-life and atomic mass. So, for example, 1 Bq of radium-226 (1600 years) is about twenty-seven one-trillionths of a gram ; 1 Bq of thorium-232 (14 billion years) is a quarter of a milligram ; and 1 Bq of bismuth-209, which (with a half-life of 1.9×1019 years) was long thought to be the heaviest stable nuclide, is some 300 kg. An older unit called the curie, equivalent to one gram of 226Ra, or 37 giga-becquerels, is still often used.
The gray (Gy) measures energy absorbed.
One gray is nothing more than one joule of energy deposited in one kilogram of substance. Because different types of matter absorb energy differently, the same amount of radiant energy will give different ‘doses’ to different objects with the same mass, and different kinds of radiation will give different doses to a particular object, all depending on how much is absorbed, and how much passes through. An older unit called the rad, 1/100 Gy, remains in common use.
The sievert (Sv) measures the biological effect of radiation.
The ‘effective’ or equivalent dose to a human being from some radiation exposure, measured in sievert, is equal to the actual dose (the energy absorbed in the tissue, measured in gray) multiplied by a factor called relative biological effectiveness. That is ‘relative’ to electromagnetic radiation, so that the RBE for X-rays or gamma rays is unity. For alpha radiation, on the other hand, it is 20, because of the great power of the massive charged particle to produce ionization. The actual weighting factor may also take into account the sensitivity of particular body tissues exposed. The rem, a similar unit based on the rad, is 0.01 Sv.

What radioactive substances are there?

Every element has radioactive isotopes — indeed, some have no stable isotopes — but only some are found in nature. The lightest radioactive nucleus is tritum, a form of hydrogen with two neutrons. This has a half-life of about twelve years, so any which existed among the matter from which the Earth formed has utterly vanished over the course of time. It is, however, found in very small traces in the water of the oceans and atmosphere, because it is constantly being produced by the action of cosmic rays. (Water from deep springs may be tritium-free.) The same cause is responsible for the occurrence of carbon-14, and of technetium, which was produced artificially before it was discovered in molybdenum ore.

Other than that, most radioisotopes found in nature are either very long-lived, or decay products of a long-lived progenitor. Potassium-40, for example, has a half-life of 1.28 billion years, producing either argon-40 or calcium-40, both of which are stable. Primordial 40K is found in the same proportion in all the potassium on Earth, about one one-thousandth of one per cent, while 40Ar constitutes more than 99% of terrestrial argon, and terrestrial calcium is more than 95% 40Ca. (Because of the ubiquity of 40K, every human being is detectably radioactive!) Radium-226, on the other hand, has a half-life of 1600 years (decaying to radon-218), but is produced from the decay of uranium-238, which has a half-life of 4.5 billion years, about the age of the Earth. For this reason, 226Ra is found in minerals containing uranium, which were sometimes mined for their radium content in the first half of the twentieth century.

This brings us to the concept of a radioactive decay series, which occurs when one radionuclide decays to yield another. If we begin with uranium-238 as our ‘source term’, the steps are 238U (4.51×109 years, α)→ 234Th (2.41 days, β)→ 234Pa (6.75 hours, β)→ 234U (2.47×105 years, α)→ 230Th (8×104 years, α)→ 226Ra (1600 years, α)→ 222Rn (3.82 days, α)→ 218Po (3.05 minutes, α)→ 214Pb (26.8 minutes, β)→ 214Bi (19.7 minutes, β)→ 214Po (1.64×10-4 second, α)→ 210Pb (21 years, β)→ 210Bi (5.01 days, β)→ 210Po (138.4 days, α)→ 206Pb (stable).

It is obvious that, in equilibrium, the number of decays per second of each species will be the same. The half-life of the source term is so long that its decay rate is essentially constant on any time scale shorter than the geologic, and the shorter-lived ‘daughter products’ slowly accumulate. Starting with one gram of pure 238U, which is 12.3 kilobecquerels, after several half-lives of the longest-lived daughter (which is still less than 1% of the half-life of the source term), then, in addition to 12.2 kBq or so of the source term, there will be 12.2 kBq of each of those other nuclides ― a total of 171 kBq of radioactive material altogether. In practice, the radioactivity of newly-refined uranium is that of an equilibrium quantity of 234U, plus 0.71% of 235U, in addition to 238U, or a total of about 25 kBq per gram, and increases only slowly. The series which begins with thorium-232 has only nine intermediate steps to stable lead-208, but the longest-lived of these (228Ra) has a half-life of only 5 years 9 months, so the activity of one gram climbs from 4 to 40 kBq with comparative rapidity.

To these cosmogenic, primordial, and radiogenic radioactive species, we must now add the artificial or anthropogenic radioactives, produced by various human activities, principally bombardment of various targets with neutrons and other particles. Some of these represent entirely new elements, such as technetium, promethium, and neptunium. In general, they do occur in nature somewhere, but not necessarily in forms, quantities, or places accessible to humans.

What are the types of radioactive decay?

There are four main types of nuclear transition, and three main types of radiation they emit. Two of the types of radiation are intimately associated with a particular type of transformation.

Internal Transition
Some unstable nuclei undergo a rearrangement of the protons and neutrons to a more favourable geometry. We know that this has happened because the change in binding energy appears in the form of a photon, known as a gamma (γ) ray. Gammas accompany almost all nuclear changes, and the energy of the photon can be used to identify what particular change has taken place. They can be extremely powerful, far beyond even X-rays, but some are much weaker.
Alpha (α) Decay / Cluster and Miscellaneous Decays
Sometimes, when the nucleus rearranges itself, two protons and two neutrons group together to form a helium nucleus, known as an alpha particle, which escapes, taking a substantial amount of kinetic energy with it. The parent nucleus has its atomic number reduced by two, and its mass number reduced by four. Usually, alpha decay occurs when the ratio of protons to neutrons is too high for stability.
Alpha decay proves to be a special case of a general process, known as cluster decay. Emission of (radioactive) carbon-14 and (stable) oxygen-18 has been observed. A few nuclides, the heaviest being calcium-37, decay by expelling a proton ; a few other light nuclides decay by neutron emission, as do certain short-lived fission products, a fact which is of importance in the operation of nuclear reactors.
Beta (β) Decay, β+ Decay, and Electron Capture
A free neutron will eventually decompose into a proton and an electron. (This occurs according to the usual exponential law, with a half-life measured to be about twelve minutes.) The same may occur in a nucleus which has an excess of neutrons. The electron is typically expelled at high speed, becoming known as a beta particle. The nucleus has its atomic number increased by one, while the mass number remains the same.
Nuclei can not only ‘spit out’ electrons, but also ‘swallow’ them, in which case a proton will be converted into a neutron. This results in a decrease of atomic number by one, and no change in mass number ; characteristic X-rays are emitted, due to the rearrangement of the inner electrons. Alternatively, the nucleus may eject a positron (or anti-electron, a particle resembling an electron but with a positive charge), which is termed a β+ particle. As soon as this encounters an electron, both will vanish, leaving behind only gamma rays, with a total energy of 1.022 million electron-volts, equivalent to the rest-mass of two electrons. (Most often this is evenly divided, and the distinctive 511 keV gamma is known as annihilation radiation.) The nett result of these two “inverse β” processes is the same. Some nuclei, such as potassium-40, are unstable with respect to both β and inverse-β decay modes.
All three processes also involve a particle termed a neutrino (or antineutrino), which is something like an uncharged electron. This particle has an effect on the manner in which the transition occurs, and carries away a part of the total energy, but is generally neglected because it interacts with matter scarcely at all.
Spontaneous Fission
In rare cases, a very heavy nucleus (the lightest known being 232U) will rearrange itself into two medium-sized chunks. Generally, free neutrons are released, and sometimes an alpha particle or a nucleus of deuterium or tritium. This process, as we shall see, is the basis for practical atomic power. Unlike the other decay processes, the outcome of this one is not fixed : spontaneous fission can result in a variety of different final nuclei, as long as the total number of nucleons matches the original nucleus. Often the fission products are themselves unstable, and additional energy is released through other types of radioactivity.

Fission — Key to Atomic Energy

The Atomic, Molecular, and Nuclear Nature of Matter • Energy from the Nucleus • Practical Nuclear Reactors

A spontaneous process is hardly a practical source of power. That, in context, is the sense of Lord Rutherford’s famous remark that the idea of atomic power was “moonshine” ; he spoke from experience, and in context he was quite right. So long as the energy within the nucleus was liberated only by the decay of naturally-occurring radionuclides, its practical uses were strictly limited.

What is wanted is some process which can readily be controlled. In principle, it should be possible to stimulate at least some nuclear transitions by bombardment with high-energy photons, in other words, using artificial gamma rays to boost nuclei over the edge of stability. As Lord Rutherford found, it is also possible to hit a nucleus with another nuclear particle and force a transition. But to obtain useful energy from either of these types of reaction is challenging, not least because neither is self-sustaining.

In the case of ordinary fire, for example, heat excites the molecules of the combustible fuel and atmospheric air, and they undergo a chemical combination. This process, in its turn, releases heat, and so long as that heat is efficiently communicated to more fuel, which is not packed so closely as to shut out air, or scattered so thin as to dissipate all the heat, the fire will continue. In this way, a single spark can initiate the combustion of great quantities of fuel. Some kind of atomic-level analogue to this type of reaction must be found, in order to liberate atomic energy for human uses.

The fission chain reaction meets this requirement. A neutron, because of its lack of electric charge, is not repelled either by the surrounding electrons of an atom, or by the nucleus itself. When it encounters a nucleus, it may be caught by the strong force. If this capture disturbs the nucleus sufficiently that it disintegrates, and if the disintegration releases at least one free neutron, then the phenomenon may propagate itself. Exactly this behaviour is observed in the case of certain very heavy nuclei. In fact even the most massive nuclear species found in nature are only just barely heavy enough to give us access to this source of energy, and we are fortunate indeed that there are a few with long enough half-lives to be found in appreciable quantities in the present-day Earth.

To disrupt the uranium-238 nucleus, for instance, an incident neutron must bring with it a kinetic energy of about one million electron-volts. A slower-moving neutron, if absorbed, will instead transform 238U to 239U, and its contribution to the energy of the nucleus will be re-emitted as a gamma ray ― what is called radiative capture. But the probability that a neutron will be absorbed at all decreases as its velocity increases ; so, even though neutrons released by fission commonly have energies of 1 MeV or more, such a ‘fast’ neutron in 238U will most likely lose energy by repeated collisions until it is no longer energetic enough to provoke fission, and then be absorbed. For this reason, the heavy isotope of uranium cannot sustain a fission chain reaction.

Practical fission requires a nuclide which can be disrupted by a slow neutron. Happily, the light isotope of uranium proves to have this property. A lighter nucleus, ceteris paribus, should be more difficult to disrupt ― but in this case, certain other things are not equal. Specifically, 235U has an odd number of nucleons, and as we observed above, odd numbers are less stable than even ones. As a result, 236U has substantially less available energy than 235U, and when the latter captures a neutron, the excess has to go somewhere. In 16% of cases, it appears as gamma radiation, but in the remaining 84%, it breaks up the nucleus.

This oddity of nuclear structure has another favourable consequence. Because of its shorter half-life, 235U is present in natural uranium to the extent of only 0.71%, or about one atom in 140. At very low neutron energies, however, its probability of accepting a neutron is more than 70 times that of 238U. Since the number of neutrons released per fission in 235U is greater than 2, the number of fast neutrons produced in natural uranium per slow neutron absorbed is greater than unity ― 1.34, to be exact.

This means that a chain reaction can be sustained in natural uranium, if it is diluted with some material which slows down the fast neutrons soon enough to keep them from being caught by 238U. Such a material is termed a moderator, and its properties can be briefly stated. First, and most obviously, its tendency to absorb neutrons of any energy must be small. Second, because the neutrons lose energy by collisions with nuclei, and the fraction of energy lost is greatest when the masses of the colliding bodies are equal, it must have a large fraction of light atoms. (Remember that a neutron is just about as massive as a hydrogen atom.) Third, it must be dense, so that the fuel atoms can be packed together closely enough for the slowed-down neutrons to hit them, instead of escaping uselessly into the surroundings.

The number of practicable moderators is quite limited. For use in a reactor intended to produce power, at least one additional requirement enters in : the moderator must be chemically and physically stable at reasonably high temperatures. This excludes, for instance, liquid hydrogen, which has about the same number of hydrogen atoms per unit volume as water. The substances ordinarily considered are :

The first three entries in this list are the most common choices. Hydride fuels and beryllium are used in some research reactors, but have not found more widespread application ― beryllium is expensive, toxic, and difficult to work, while metallic hydrides tend to be highly inflammable, and to decompose at moderately high temperatures. Solid hydrocarbons (plastics) are used in zero-power experimental assemblies, and organic liquids doing double duty as coolant have been used in power reactor trials, with mixed results. The last two items are essentially theoretical. Lithium, with the 7.4% of neutron-absorbing 6Li separated out, and molten caustic soda (deuterated or not) have both been proposed as coolant-moderators for high-temperature reactors, but appear unfavourable for reasons including corrosion.

Water has, by far, the most moderating power : neutrons slow down in it more rapidly than in any of the other moderators. But it has a definite tendency to absorb neutrons, which makes it unusable with natural uranium. An ‘enriched’ fuel is therefore required. Heavy water has the least propensity to absorb neutrons. And graphite is a solid which maintains its physical integrity to extremely high temperatures. The reactor designer will be guided by these properties in selecting a moderator for a particular design concept.

When each fission provokes one more fission, an assembly of nuclear material is said to be ‘critical’. This is also expressed by stating that the ‘multiplication factor’ k is unity. For k<1, the reaction dies away more or less rapidly ; for k>1, it increases, and may do so with great rapidity. It is for this reason that a neutron source is always used when starting up a fission reactor. Without a constant background, random neutrons from spontaneous fission or even cosmic rays could initiate a chain reaction, causing a sharp rise in power before the operators could become aware of it and compensate. With the neutron source, however, the approach to k=1 can be taken very gradually and carefully.

As mentioned above, a small proportion of the fission neutrons is emitted by decay of fission products (and, in heavy-water- or beryllium-moderated reactors, by the moderator under the influence of gamma rays) after an appreciable lapse of time. So long as k is small enough that these delayed neutrons are required to maintain criticality, the reactor operator has time to make adjustments as the power level varies. A ‘prompt critical’ reaction is much more difficult to control, because most macroscopic physical processes act with glacial slowness in comparison.

Control mechanisms for the fission chain reaction generally operate by changing the ‘reactivity’ of the assembly — basically, the likelihood that any given neutron will cause a fission. There are three ways of effecting this which suggest themselves. The first is to change the geometry or quantity of the fuel, to alter the likelihood that a neutron will encounter a fissile nucleus. The second is to change the degree of moderation somehow, in order to alter the fraction of neutrons which produce fission when absorbed in fuel. And the third, which is very widely used despite its obvious disadvantages, is to introduce a neutron-absorbing ‘poison’ which competes with the fuel for the available neutrons.

The more fissile nuclei are available, the easier criticality is to achieve. Less moderation is required, and more neutron absorption can be tolerated. This creates a strong incentive for separating fissile material. There are two main approaches : fractionation of natural uranium into its isotopes, and chemical extraction of artificially-produced uranium or plutonium.

The first option is known as uranium enrichment. By taking advantage of physical or chemical processes which proceed differently depending on the isotope, the 0.71% of 235U present in natural uranium can be concentrated to any desired degree, leaving behind ‘depleted’ uranium of typically about 0.2% 235U. The two most important methods are gaseous diffusion and gaseous centrifugation, both of which effectively sort molecules of the compound uranium hexafluoride according to their mass. Enrichment by whatever method is energy-intensive (diffusion more so than centrifugation), and an appreciable part (more, the greater the degree of enrichment attained) of the original 235U is dissipated in the ‘enrichment tails’. It is made practicable, for the present, by the relatively low cost of newly-mined uranium, and the very great energy value of fission fuel.

Most civilian power reactors today use either natural uranium, or ‘low-enriched’ uranium with a 235U content of about one to five per cent. Military power reactors may use more highly enriched fuel, to allow for a smaller powerplant and longer intervals between refuellings. At enrichments above about 20%, criticality can be attained with fast neutrons, greatly increasing the fraction of energy from fission of 238U at the cost of requiring a much larger mass of fuel for criticality. A special case of an assembly of nuclear fuel which is critical with prompt fast neutrons and has a high multiplication factor is, of course, the atomic bomb. It should be appreciated that a bomb-type reaction is not possible with any sort of assembly capable of steady-state fission.

The second option involves using fission neutrons to convert a ‘fertile’ nuclide into a fissile one. In a natural-uranium reactor, this process is quite unavoidable, since many of the neutrons produced are absorbed in 238U, creating nuclei of 239U, which rapidly undergo beta decay to neptunium-239 and thence to fissile, long-lived plutonium-239. This plutonium can then be separated from the uranium by straightforward chemical processes. In such a reactor, the conversion ratio will be less than unity (that is, the number of 239Pu nuclei created is less than the number of 235U nuclei consumed), and there are less-obvious complications as well, but the plutonium then obtained can be used in a ‘breeder’ reactor with a conversion ratio greater than unity. That step promises to allow making good use of depleted uranium. A similar process is possible using thorium as the fertile material, which appears significant enough that we have devoted a separate article to it.

Practical Nuclear Reactors

The Atomic, Molecular, and Nuclear Nature of Matter • Energy from the Nucleus • Fission, key to atomic energy

There are many possible designs for a nuclear reactor. Confining ourselves to the topic of reactors for the production of power, we can distinguish four axes on which a given design may be classified.

Breeder / Burner
A breeder reactor produces more fissile atoms (by neutron capture in fertile material) than it consumes. A burner reactor uses up fissile material. A reactor which produces some fissile material, but not enough to meet its total fuel needs, is termed a converter, and up to now, most civilian energy applications have involved reactors of this class.
Because of the limited propensity of the fertile nuclides to absorb neutrons, a breeder reactor requires a large proportion of fertile to fissile material. So that this does not interfere with the chain reaction, and to make chemical processing simpler, the fuel is commonly divided into two zones, with a fissile-rich ‘core’ or ‘seed’, and most of the fertile material in a ‘blanket’.
Solid Fuel / Fluid Fuel
The simplest fluid-fuel reactor, known as a ‘water boiler’, is little more than a bucket containing a solution of uranium salts in water. Most fluid-fuel power reactor concepts involve a circulating fuel, most often in the form of liquid coolant with fissile material dissolved or suspended in it. Because the fuel spends part of its time outside the reaction zone, the required amount of fuel is increased to some extent beyond the theoretical minimum. On the other hand, the energy of the fission fragments is deposited directly into the coolant, making for better thermal characteristics, and fluid-fuel reactors are easily purged of xenon-135, a neutron-absorbing fission product which presents serious challenges in the operation of solid-fuel reactors.
Solid fuels incur costs for fuel fabrication, and pose problems with heat transfer from the fuel to the coolant. In addition, radiation damage limits the total energy which can be obtained from a fuel element, and neutron absorption in the cladding material can require the use of enriched fuels. The use of solid fuels, however, simplifies the retention and handling of the radioactive materials, and can make possible the use of otherwise incompatible materials with desirable nuclear properties.
Thermal / Fast
When neutrons pass through a moderator, they are slowed down to the point where their typical velocity is about that of the atoms or molecules of the moderator. This motion is the result of heat, and slow neutrons are therefore also termed thermal neutrons. A reactor which operates with slowed-down neutrons is accordingly termed a thermal reactor.
Homogeneous / Heterogenous (thermal reactors only)
In a homogeneous reactor, the fuel is blended with or dispersed into the moderator, in a more or less uniform manner. While we can easily envision, for instance, a reactor constructed of graphite containing uranium carbide, most homogeneous reactors are of the fluid-fuel type, with the fuel either dissolved or suspended (a so-called slurry reactor) in water. A molten-salt thermal reactor is generally considered heterogenous, even though the mixed lithium and beryllium fluorides of the carrier salt do have some moderating power, since most of the moderation occurs in graphite.
The heterogenous reactor allows manipulating the neutron distribution in ways which are not possible in a homogeneous fuel-moderator assembly. For instance, a homogeneous graphite-moderated reactor could not use natural uranium as fuel, because fission neutrons are likely to be absorbed in the relatively long distance required to slow them down. By concentrating the fuel in lumps, the 238U is exposed only to fast and slow neutrons, and not those of intermediate energy.

Overview of Power Reactors

A light-water reactor is cooled and moderated by water. Because of the nuclear and thermal properties of this substance, the LWR is inherently inefficient, requiring enriched fuel and delivering saturated steam. It is, however, compact and inexpensive to build by comparison with many other designs, and its engineering properties are familiar. The large investments by governments in uranium enrichment plant, originally for military purposes, made the use of LWRs practicable, and the greater part of the power reactors in the world today are of this type.

Pressurized-Water Reactor
A PWR is essentially an adaptation of the very first submarine propulsion reactor. Its fuel elements, typically long metal (stainless steel or zirconium-alloy) tubes containing pellets of uranium oxide enriched to 3⁓5%, are immersed in water within a heavy pressure vessel, which has to be opened for refuelling. Liquid water under high pressure (provided by an electrically-heated bubble of steam) circulates to receive the fission heat, and transfers it via a heat exchanger to water at lower pressure, which boils to feed steam to the turbogenerators.
Boiling-Water Reactor
The BWR is a modification of the PWR concept to better suit the circumstances of land-based power stations. It takes advantage of the relaxation of space constraints to reduce the power density in the core, allowing the fuel elements to be cooled partly by steam. This steam is then ducted direct to the turbogenerator, without an intermediate heat exchanger, improving cycle performance. Because of the production of radioactive 16N by neutron capture in water, the turbine hall ordinarily cannot be entered while the plant is in operation, which complicates operations and maintenance. The larger size of the pressure vessel, and the more elaborate arrangements for handling the circulating water, keep BWR costs generally on a level with those of PWRs.
Light-Water Breeder Reactor
The LWBR is not a separate type of plant. Rather, it is a PWR or BWR fitted with a thorium-uranium core constructed to achieve as high a neutron efficiency as possible, so as to take advantage of the high excess thermal neutron output of 233U and produce marginally more fissile nuclei than it consumes. The prototype civilian PWR at Shippingport, Pennsylvania, was so equipped from 1977 to 1982, and performed very well, with a modest breeding gain.

A heavy-water reactor is moderated by deuterium oxide. This allows it to achieve superior neutron economy compared to light-water reactors, and HWR designs generally use natural uranium fuel. The high cost of heavy water, and the larger and more complex facilities compared to a LWR, have kept the HWR in second place among power-reactor types.

The “Canadian Deuterium-Uranium Reactor” is the main HWR design in use today. This is a pressure-tube reactor, in which the fuel elements are contained in channels through which heavy water under pressure flows as coolant. These channels pass through a larger vessel termed a calandria, containing heavy water at a much lower temperature and pressure. (As a safety feature, the calandria at some plants can be emptied rapidly, shutting down the reaction.) The CANDU fuel elements are short bundles of zirconium-alloy tubes containing (natural) uranium oxide pellets, and the construction of the reactor allows refuelling by inserting a fresh fuel bundle into a pressure tube (thereby shoving a spent bundle out the other end) while the reactor is operating. In South Korea, where both light-water and heavy-water reactors are in use, there is considerable interest in using expended LWR fuel (which is still enriched above natural uranium) as CANDU fuel without reprocessing, a scheme known as DUPIC.
Other heterogenous HWRs
The CANDU type of design lends itself to the use of coolants other than liquid heavy water. The Gentilly-1 (Quebec), Fugen (Japan), and Winfrith (England) plants performed adequately using boiling light water, as did EL 4 in France with carbon dioxide gas. At Atucha in Argentina is a pair of pressurized-heavy-water reactors designed by Siemens, blending features of the PWR and CANDU types ; Unit 1, in operation since the 1970s, has demonstrated extraordinary fuel utilization with very slightly enrichment (14 megawatt-days per kilogram of metal at 0.9% 235U, as opposed to 7 MWd/kg with natural uranium). The boiling-heavy-water reactor at Halden in Norway, used mostly for research purposes, sometimes furnishes process heat to a paper plant, and so can just barely be considered a power reactor.
Aqueous Homogeneous Breeder Reactor
An AHBR has never been built, but the type deserves mention for the extensive study made of it. This is a heavy-water reactor in which the fuel is uranium-233 dissolved in the moderator, and the neutrons escaping from the core vessel are used to produce additional 233U in a ‘blanket’ of thorium. The design lends itself to continuous reprocessing and extraction of fission products, avoiding the need to handle large quantities of spent fuel which comes with solid-fuel reactors, and its exceptional neutron economy holds out the possibility of very brief fuel ‘doubling times’ in comparison with other breeder-reactor designs. The Homogeneous Reactor Experiments at Oak Ridge, created to study this concept, generated 140 kW of electricity. A related approach, embodied in the Dutch KSTR, is the use of a slurry of uranium-thorium oxide particles, made so small that the fission products escape into the water, from which they can be filtered out.

Graphite-moderated reactors are mostly used to attain high temperatures. Some early graphite-moderated designs, including the very first nuclear reactors, were created simply because the builders had access to neither heavy water nor enriched uranium in sufficient quantities.

Gas-Graphite Reactor
The United States (Oak Ridge “X-Pile”), Great Britain (Windscale), and France (Marcoule G-1, which actually generated electricity on a pilot scale) built air-cooled graphite reactors early on. Britain and France developed these into power reactors, using carbon dioxide coolant. The British type was known as “Magnox” for the magnesium-alloy cladding used on the metallic natural-uranium fuel. The Magnox design was further developed into the “Advanced Gas-cooled Reactor”, using slightly enriched uranium-oxide fuel elements clad in stainless steel, and operating at higher temperature and pressure for better thermal efficiency. The low power density of these reactor types makes them costly to construct, overbalancing their low operating costs, and none have been built in decades save in North Korea (based on the plans for Calder Hall, the Magnox prototype, published as part of the first Geneva “Atoms for Peace” conference).
Various designs for a “High-Temperature Gas-cooled Reactor” have been proposed, mostly using helium as coolant, because carbon dioxide becomes chemically active at high temperatures. These generally involve ceramic fuel elements composed of uranium and thorium carbides with graphite. The Peach Bottom and Fort St Vrain reactors in the United States were HTGR prototypes which achieved some success using block-type fuel elements ; the pebble-bed reactor is a similar concept which circulates small balls of fuel through the core for superior economy. To date, the heat has been used to generate superheated steam, although it is proposed either to supply process heat for industry, or to drive a gas turbine in a direct cycle conceptually similar to a BWR. Helium turbomachinery has proven troublesome to develop, however, and American nuclear engineer Rod Adams has proposed the use of nitrogen coolant instead, paired with standard combustion-turbine components.
RBMK Water-Graphite Reactor
Unique to the Soviet Union, this pressure-tube design uses solid graphite as moderator and boiling light water as coolant. (The “N-Reactor” at Hanford, Washington, intended to reduce the cost of military plutonium by selling by-product electricity, was somewhat similar.) This design has several drawbacks, the most notable being a large positive power coefficient of reactivity. In other words, unlike in a BWR, the effect of the water is more as a neutron absorber than as a moderator, and a sudden increase in the volume fraction of steam can lead to a runaway rise in power. This is exactly what happened in 1986 at Chernobyl Unit 3, in northern Ukraine, after the operating staff deliberately violated the strict safety protocols which had been laid down for their plant. The steam-hydrogen explosion which followed was nothing less than cataclysmic, ejecting much of the fuel to rain down on the surrounding countryside, and igniting metal and possibly graphite inside the reactor, which burned for a week. After this event, the remaining RBMKs were down-rated and modified for greater stability.
Sodium-Graphite Reactor
The enormous energy which can be developed in a small volume of nuclear fuel means that power production in a reactor is limited mainly by the capacity of the cooling system to carry away heat. This has led to continuing interest in liquid-metal coolants, which have excellent thermal properties, and can be used near atmospheric pressure at temperatures where water would unreasonably heavy pressure vessels. Because of its small neutron absorption cross-section, sodium is the only metal usually considered for use with thermal reactors. Despite the advantages of a melting point below 100°C and a density less than one kilogram per litre, the violent oxidative reaction which it undergoes on contact with water (producing hydrogen gas and corrosive sodium hydroxide) has been an obstacle to its development.
The USS Seawolf (SSN-575) was fitted with the sodium-cooled, beryllium-moderated Submarine Intermediate Reactor, which developed pinhole leaks in the sodium-water heat exchanger, resulting in corrosion and a level of noise incompatible with stealth. To limit the damage, the superheater section was cut out of the circuit, and the powerplant never functioned satisfactorily. The concept seemed worth pursuing in the more forgiving environment of a land-based power plant, and the Sodium Reactor Experiment, a modest-sized power-generating prototype, was operated for several years at Santa Susanna, California. SRE inspired only one imitator, the short-lived Hallam plant in Nebraska, and is perhaps most notable for having been returned to service after suffering a partial core meltdown.
Nuclear Rocket Engines
An extensive development program, under the general name of NERVA (Nuclear Engines for Rocket Vehicle Applications), was undertaken by the United States in the 1950s and 1960s to develop high-performance nuclear engines for advanced space travel purposes. Under such names as “Kiwi” and “Rover”, graphite-moderated, liquid-hydrogen-cooled reactors were brought to the point of readiness for flight before American space activities were curtailed under the Nixon administration. More exotic possibilities, such as “Dumbo” (a metal-fuel system with superior heat transfer properties) and the gas-core reactor, were also investigated.
Molten-Salt Reactor
The first fluid-fuel reactor to employ uranium dissolved in a molten salt actually used beryllium as moderator, and was intended for aircraft propulsion. The intent was to operate at a temperature and power density high enough to drive a turbojet engine, while being lightweight, and minimizing the total quantity of nuclear fuel and fission products aboard, in case of an accident. Further development has concentrated on the use of an MSR with graphite (or in some proposals zirconium hydride) moderator as a thorium-cycle breeder reactor for stationary power plants. In addition to its high operating temperature, promising good thermal efficiency, the two main advantages are inherent safety and ease of reprocessing. The salt used, typically a mixture of lithium and beryllium fluorides, has a very high vapour pressure and is not chemically reactive ; in case of a loss-of-coolant accident, not only would the fuel be removed from the reactor, but the fission products would have little tendency to disperse. Chemical processing is simplified by the use of fluoride chemistry, in addition to the general advantages of fluid-fuel systems. As yet, however, no power prototype has been built.

Other types of power reactors have been proposed and built. Some of these were intended for some special purpose, others for general application. None has achieved widespread use, although some still hold out that prospect.

Organic-Moderated Reactor
Work on a reactor type similar to the PWR, but using a non-corrosive, high-boiling-point organic fluid, progressed as far as the commissioning of a pilot-scale power reactor, which delivered steam to the existing coal-fired power station at Piqua, Ohio. No means could be found to keep the coolant, a mixture of polyphenyls, from breaking down under the intense radiation of the reactor core, blocking coolant channels and impeding the action of the control rods with tarry deposits. The resulting maintenance costs were too high for economical operation ; the reactor was shut down, and little further work has been done along this line. A similar fluid was used for many years as coolant in a CANDU-type research reactor at Whiteshell, Manitoba, with admirable results (because the coolant was exposed to less total radiation, and the fuel bundles were replaced before they could foul too badly), but proposals for a power reactor were not taken up.
Metal-Cooled Fast Reactors
The cooling problem tends to be even greater for fast-neutron reactors, with their characteristic high fuel loadings and small core dimensions, than for thermal reactors, and water, because of its powerful moderating effects, cannot be used. As a result, liquid metals have been preferred — mercury to begin with, sodium or sodium-potassium eutectic alloy (which has a freezing point below that of water), and lead or lead-bismuth eutectic alloy. Although the first reactor to generate electricity was the metal-cooled Experimental Breeder Reactor at Idaho Falls, such reactors have not come into common use for power production ; trouble-free operation has proven difficult to achieve, due both to the inherent ‘touchiness’ of fast reactors in general, and to the properties of liquid metal coolants. EBR itself, and the Enrico Fermi power-breeder near Detroit, suffered partial meltdowns, the Japanese Monju sodium reactor had its coolant catch fire, and the Soviet Union lost at least two lead-bismuth submarine reactors to coolant freezing. The so-called Integral Fast Reactor is one of several types of metal-cooled reactor now under study for next-generation atomic power plants.
Liquid Metal Fuel Reactor
For a time, there was considerable interest in liquid-metal-fuel breeder reactors, both thermal and fast, using a fuel dissolved or suspended in a lead-bismuth coolant. This was thought to have some of the same advantages as the molten-salt reactor, such as high operating temperature and simplified continuous reprocessing. A completely different type of liquid-metal-fuel reactor was LAMPRE, an experimental fast reactor using plutonium-iron eutectic alloy as a non-circulating liquid fuel.
Solid State Reactor
From the late 1960s to the late 1980s, the Soviet Union launched more than thirty military radar satellites, energized by various small nuclear reactors through thermoelectric and thermionic power conversion devices. These reactors used highly enriched uranium fuels with graphite, beryllium, molybdenum, and other high-temperature construction materials, in the service of supplying power from the smallest possible package, because of the low-altitude (high-drag) orbits required for their function. A distinctive feature of this type of reactor was that, to better ensure function in weightlessness, circulating coolants were not used. The satellites were designed to eject the reactor cores into a higher orbit at the end of their service lives, but at least one failed, the infamous Cosmos 954. The remainder of the cores remain in space, where their leaking sodium-potassium heat-transfer fluid contributes to the orbital-debris hazard.
Nuclear Ramjet
As part of a cruise-missile development program known as “Project Pluto”, the United States tested a series of beryllium-oxide-moderated, air-cooled reactors codenamed “Tory”. These were successful, but the Kennedy administration cancelled Project Pluto on the grounds that a low-altitude Mach 6 air-breathing vehicle powered by an unshielded half-gigawatt nuclear reactor had no obvious military utility, and with the guidance systems of the day, would be as dangerous to the nation which launched it as to the intended target.

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