The Curve of Binding Energy by John McPhee

Ref: John McPhee (1974). The Curve of Binding Energy. Farrar, Strauss and Giroux.

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Summary

  • A biograph of Ted Taylor, theoretical physicist and nuclear weapon designer (Davy Crockett, Hamlet, Super Orally Bomb), told in parallel with the dangers of the nuclear power and nuclear weapons industries, and the potential for a lone actor, a terrorist group, or a state to steal or produce and detonate its own weapon.

  • The continuing existence of the nuclear-power fuel cycle, for all its problems, seems inevitable. People will live with it in the way that others have lived with fear of the sword. The question is not so much whether it is good or bad as whether mankind can live with the bad part- a bomb now and again going off God knows where- in order to have the good. "Every civilization must go through this"- Taylor.

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Binding Energy

  • Binding Energy: The energy equivalent to the strength of the forces that bind the parts of the atomic nucleus together- they hold the protons and neutrons inside the nucleus as a unit.

    • Protons and neutrons on their own, free, weigh more than it does when it is inside an atomic nucleus. The difference in weight is extraordinarily small-in, a few octillionths of a gram- but a difference is there. What has happened to the neutrons and protons losing weight in the nucleus is that a minute part of each of them has turned from matter into energy. 

    • Curve of Binding Energy: The measurements of the binding energies of all known elements show a remarkable curve. From the lightest elements upward, binding energies grow generally stronger and stronger, until-somewhere in the region of Co, Ni, and Cu, they reach a peak. Binding energies then are seen to grow weaker and weaker as the elements progress in weight toward U. The curve suggests this: If an atom of a very heavy element, with a couple of hundred protons and neutrons in its nucleus, is to be split apart, the protons and neutrons will convert mass into energy as they form other elements higher on the curve. U-235 breaking apart, for example, might become Sn and Mb, and the U-235’s protons and neutrons busily create energy while giving up mass. The same sort of thing happens at the other end of the curve if the atoms of two very light elements, instead of being pulled apart, are pushed together. If two H isotopes are pushed together to make He, the protons and neutrons will have to shrink a little, and in so doing release energy. 

  • Einstein's suggested that the energy would be equal to the mass that disappeared multiplied by the square of the velocity of light (E = mc2). The velocity of light is ~186,000 miles/sec, and the square of that is 34,596,000,000. Thus, the loss of weight in a proton or a neutron might be almost nothing, but to get a sense of the amount of energy derived from the annihilation of such a small amount of matter one would multiply by an extremely large number. If the mass-energy change were to happen to many atoms all at once, the result would be an amazing explosion. A bomb might be made by disintegrating, or fissioning, U.

  • When Fat Man exploded over Nagasaki the amount of matter that changed into energy and destroyed the city was 1g- a third the weight of a penny. A number of kg of Pu were in the bomb, but the amount that actually released its binding energy and created the fireball was 1g.

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Uranium

  • For each atom of U-235 that exists in natural U, there are 140 atoms of U-238.

  • Enrichment: U-238 (Natural U) is combined with F and turned into a gas: UF6. Because the U-235 atoms are a little over 1% lighter, and therefore moving faster, a little extra U-235 goes through the membrane in any given pass, and the U on the other side of the membrane is, enriched. The enrichment is so very slight though, that the process has to be repeated again and again. The gas has to flow through thousands of membranes, cumulatively known as “cascades.” Thousands of miles of tubes, pipes, and other conduits are needed to create a network of flow wherein the gas goes through a membrane, then returns to try again, then goes on to a new membrane, gradually advancing, in a process of separation and elimination, until what had begun as .7% U-235 was more than 90% U-235- fully enriched, weapons grade U.

    • U isotopes can be separated in centrifuges whirling around and flinging the heavier U-238 to the outside. 

  • Transport: As oxide or metal, U travels in small cans that are placed in a cylinder- a 5” pipe- that is braced with welded struts in the center of an ordinary 55gal steel drum. It is for criticality reasons that the U is held in the center with the airspace of the drum around it, for if too much U-235, in any form, were to come too close together it would go critical, start to fission, and irradiate the surrounding countryside. The 55gal drums with interior welding’s are called birdcages, because in a vague way they resemble them. Loaded, they weigh 100 lbs and can be handled by one person, easily by two. The 10-liter bottles of UFg travel in birdcages as well.

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Plutonium (Pu)

  • It has been calculated that 2-3x less Pu-239 than U-235 is required in the making of nuclear explosions.

  • You could hold an ingot of Pu next to your heart or brain, fearing no consequences. But you can't breathe it. A mg of Pu taken into the lungs as invisible specks of dust will kill anyone; death from massive fibrosis of the lungs in a matter of hours, or at most a few days. Even a microgram is likely, eventually, to cause lung or bone cancer. Pu that enters the bloodstream follows the path of Ca. Settling in bones, it gives off short-range alpha particles, a form of radioactivity, and these effectively destroy the ability of bone marrow to produce WBC’s. Pu is rendered generally in one of three forms: metal, nitrate, oxide. The oxide is a fluffy yellow-green powder.

  • Pu production in a nuclear reactor: U-238 + free neutron = U-239 (unstable with 93 protons, 147 neutrons); U-239 decays (n becomes a p in the nucleus + emitted e) with a half-life of 23 minutes = Np-239 (unstable); Np-239 decays (n become a p in the nucleus + emitted e) with a half-life of a few days = Pu-239 (94 p, 145 n, and relatively stable) with a half-life of 24,360 yrs.

  • Enrichment: Heat HF (acid) in a quartz container = HF (gas) comes off and goes into a crucible through a quartz tube. Anhydrous Pu oxalate cooked at 500 C in HF becomes PuF6. Do it in batches of a few hundred grams- small enough to avoid going critical. Build up a stockpile of PuF6. Now line a crucible with MgO. You mix it with water and make a paste. Form it. Work it. Dry it. It's like clay. Now get some metallic Ca and crystalline iodine from a chemical-supply house. Put 500g of PuF6 in the crucible. Add 175g of Ca and 50g of I. Cover with Ar, which is a heavy inert gas. Close the lid. Now heat up the crucible inside an induction furnace to 750 C. At that point, the mixture in the crucible reacts and, in one minute, heats itself up to 1600 degrees. The pressure is considerable. In the next 10 min, the whole thing cools itself to 800 degrees. Now remove the crucible from the induction furnace. Let it stand until it comes to room temperature. Open the lid. Metallic Pu is in there with some Ca-I junk. Use nitric acid to wash off the I flakes and the Ca-F salt. What you have left is a small lump of Pu. You can hold it in your hand. It won't hurt you. It feels a little warm, from alpha decay. You could just boil away the water, get Pu-NO3 crystals, and make a bomb out of the crystals. It would not be much of a bomb, ~.1 kT, enough to knock down the World Trade Center. 

    • When recycle comes in, the reactor-fuel rods will probably contain mixed uranium and plutonium oxides. The U would be only slightly enriched and not usable in a bomb, but the Pu would be. There is good, better, and worse, but there is no non-weapons-grade Pu involved in the nuclear industry. Mixed U and Pu oxides can be separated chemically. It's not difficult, but be careful, because Pu is very poisonous. You would add nitric acid to put the pellets into solution. Then add oxalic acid. The Pu forms Pu-oxalate. The U remains in solution, because it does not combine with oxalic acid. Filter out the Pu-oxalate with filter paper. Now you are where you were when you had Pu-oxalate before and you proceed to make metal. Or you can heat up the Pi-oxalate in a furnace to a 1000 C, and you get Pu.

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Weapon Design

  • Implosion: Explosive compression of a sub-critical mass of SNM into a critical, fissionable, mass. After detonation, about a third of the explosive force of the C4 goes into a compressive shock wave. When it reaches the reflector, the Pu within is still subcritical. The reflector acts like a piston, slamming inward. The radius of the Pu decreases. Its density increases. As the shock wave reaches the outer surface of the Pu, the material is almost exactly at the point of criticality. When the shock wave hits the center, the Pu has been compressed above its normal density and is supercritical. With Pu atoms now so dense in the core, the probabilities of collision between free neutrons and the Pu nuclei are considerably increased. The result is an atomic detonation.

    • Initiator: The small sphere in the center of the pit, designed to give off millions of neutrons when squeezed; Po-210.

    • Special Nuclear Material (SNM): Around the initiator is a ball of fissile material, metallic U-235 or Pu-239, in which the neutrons from the initiator would make fissions. 

    • Reflector (‘tamper’): Around the SNM is the reflector (usually Be). It is made of natural U or some other heavy metal to prevent neutrons from getting out and to contain the explosion just long enough to prolong the fission chain reaction and produce a greater yield. 

    • High Explosives (HE): Around the tamper is ordinary HE, the bulk of the bomb; its purpose is to squeeze the SNM from a subcritical density to a supercritical density, squeezing the initiator at the same time. 

    • To get more efficiency, you need to hit the core harder. When you hammer a nail, what do you do? Do you put the hammer on the nail and push?

  • Gun Type: Two subcritical pieces of metallic U come together very quickly to produce a critical mass. In the presence of a surrounding reflector, which could be made of steel or any other material that would tend to reflect neutrons back into the core, the assembled U would be supercritical.

    • Pu is not right for a gun-type bomb. Pu-240 cannot be completely separated in any practical way from Pu-239, and Pu-240 fissions spontaneously. It does so with such vigor that if a Pu projectile were fired toward a Pu target, neutrons, which travel at speeds > 15M mph, would jump from the one to the other before a proper assembly could be achieved. The result would be a fizzle yield. This problem- pre-detonation- is serious enough with U, because of the unavoidable presence of cosmic rays and other stray neutrons. That is why the assembly of the separate parts has to be fast. The projectile travels at a rate of ~500 ft/s.

    • Government bombs contain very little Pu-240 because its spontaneous fissioning would set off a chain reaction too early in the implosion and thus lower considerably the yield of the fireball. The amount of Pu-240 that exists in a given amount of Pu is determined by the length of time the fuel elements have remained in a reactor. Hence, the fuel elements in the governments Pu-production reactors are removed for chemical separation before much Pu-240 has accumulated. Civilian reactors allow their fuel to burn a lot longer- so the resultant Pu includes an amount of Pu-240 very likely to set off a bomb too soon after the moment of criticality. 

  • Critical Mass: Varies inversely with the square of the density of the metal and reflector. If both the reflector and the core are compressed by the same amount- implosion- the critical mass is reduced by the square of that amount.

  • Neutron Generator: An element that emits neutrons; a tenth of a curie of Po-210 glued to the steel at the far end of a target will emit a burst of neutrons in all directions when struck by Li.

  • Neutron Reflectors: Natural U, Steel, copper, Mg, Pb, Al, Be, water, solder, or wax. Two stainless steel mixing bowls could be lined with wax and soldered together around the Pu sphere. A 3” thickness of wax will reflect as many neutrons as 1.5” of steel, but you will pay a price in yield.

    • Be is an awesome reflector, but among the most poisonous non-radioactive inorganic materials on Earth. It is less dense than Al, but it has so many atoms per cm3 that it makes an especially good reflector. Be, in fact, has more atoms per cm3 than any other element. It is also a good neutron scatterer. The critical mass of Pu is smaller in a Be reflector than in any other reflector of comparable thickness.

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Weapon Effects

  • When an implosion bomb is detonated, the temperature in the core builds up to several hundred million degrees in one hundred-millionth of a second (many times the temperature in the center of the sun), a temperature high enough to strip the electrons off any but the heaviest elements. All you're left with is the bare nucleus in a sea of electrons. (In a H bomb, the temperature can be 5x as high. It strips off electrons even from U- almost all 92 electrons gone). In an implosion, pressures at the center build up to a hundred million atmospheres, and with these pressures the core begins to expand at speeds of 2e8 cm/s, ~5M mph. Meanwhile, neutrons are multiplying, with a whole new generation every hundred-millionth of a second. (At the center of an efficient thermonuclear explosion you have so many neutrons that they actually form a gas with the density of a metal.) Pu and U split unevenly. It is rare that they split into two equal parts, and in the explosion their fragments become every element below them. Anything you can name is there- Mo, Ba, I, Ce, Sr, H, Sn, Cu, C, Fe, Ag, and Au. 

  • On detonation, gamma rays arrive first, next comes visible light, next neutrons, then air shock, then secondary fragmentation.

  • The height of detonation has to be greater than the expected radius of the fireball, so that the shock wave breaking away from the fireball would bounce off the ground and push the fireball upward, preventing it from picking up debris and causing unnecessary fallout.

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Reactor Design

  • High Temperature Gas-Cooled Reactor (HTGR): A nuclear reactor that uses less U per MW and operates at 400 F (most reactors operate at 600 F). The fuel elements of present light- water reactors typically consist of long, thin rods of Zr-alloy packed with U-oxide and sealed at the ends. The graphite blocks of the HTGR are something new in cost, efficiency, fissions per dollar. The HGTR is thrifty with neutrons. It uses less U per MW. Most reactors operate at 600 F. The HTGR functions at 1400 F, a difference that obviously bears ar payload, since heat (that makes steam that drives turbine generators that make electricity) is what all power reactors exist to produce.

  • Nuclear Reactors: 39,372 fuel rods stand together in a nuclear reactor. Among them are 53 rods made of a Ag-In-Cd alloy coated in stainless steel. These control (‘poison’) rods absorb neutrons and stop a fission chain reaction. These-the control rods, the "poison" rods-in their combined elements have a capacity to absorb neutrons and stop a fission chain reaction. When the poison rods are drawn slowly upward, by drive mechanisms in the reactor vessel head, the U in the fuel rods will go past the point of criticality, neutrons by the octillion will start jumping around in the forest, and the temperature of the core will rise. Water flowing among the fuel rods will become extremely hot. The poison rods will move out or in just enough to hold the water temperature at 600 F. The reactor vessel holds water under pressure and is thus an enormous pressure cooker. Flanges join the upper and lower parts and are held together by dozens of steel studs.

  • TRIGA: A nuclear reactor model that takes advantage of the “warm-neutron effect.” TRIGA reactors go subcritical if they get too hot and, in an emergency, shut itself off.

  • Breeder Nuclear Reactor: Uses a combination of fissionable and fertile material, making heat with the one and new fuel with the other. The fissionable material might be Pu-239 and the fertile material U-238- ordinary, natural U. As the Pu fissions, it throws off many more neutrons than are needed to keep the Pu chain reaction going. The excess neutrons go into the nuclei of the U-238, which becomes U-239, which decays to become Np-239, which decays to become Pu-239, ready now to get into the original chain reaction, ready to repeat the process and produce eve more Pu. Because the fissioning Pu puts out many extra neutrons and because there is a high proportion of fertile U-238 in the reactor core, the breeder makes more Pu than it uses up.

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Space Travel

  • During the opposition of Earth and Mars, which occurs every couple of years, the distance between them is between 35M-63M miles; the round trip would take from three to six months.

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Nuclear Weapons

  • Davy Crockett: A nuclear weapon designed by Taylor. At its time, the lightest and smallest fission bomb ever made. It weighed less than 50 lbs.

  • Hamlet: A nuclear weapon designed by Taylor; the most efficient fission bomb ever made in the Kt range. 

  • Super Orally Bomb: A nuclear weapon designed by Taylor; the largest-yield fission bomb ever exploded.

  • Little Boy: The bomb of Hiroshima; fissioned only 1% of its U-235 and yielded only 13 Kt.

  • Mike: A thermonuclear weapon that weighed 21t with a 10 Mt yield.

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Misc Quotes

  • He said he now saw all his work on light weapons as nothing but an implementation of "pseudo-rational military purposes." He said his belief in deterrent postures had eroded to zero. "I thought I was doing my part for my country. I thought I was contributing to a permanent state of peace. I no longer feel that way. I wish I hadn't done it. The whole thing was wrong. Rationalize how you will, the bombs were designed to kill many, many people.

  • “He saw the human race running out of frontiers, and he considered frontiers essential to the human psyche, for without them pressures would build that would implode upon the race and destroy it.”

  • “It is in the long run essential to the growth of any new and high civilization that small groups of men can escape from their neighbors and from their governments, to go and live as they please in the wilderness. A truly isolated, small, and creative society will never again be possible on this planet.”

  • “I think that there is only one realistic way to avoid war, and that is to make the world really afraid of it. I think the world should be afraid of it now, but apparently wishful thinking and ignorance (particularly on the part of those people who have some say in what goes on) have removed much of this.”

  • “He reached the conclusion that an acceptable deterrent posture could only be achieved by making small bombs with a capacity for eradicating specific small targets.”

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Terminology

  • Cherenkov Effect: Purple light emitted by electrons that are created in the nuclei of decaying atoms (‘beta rays’).

  • Critical Mass: The point at which a chain reaction will not stop until a great deal of energy has been released- varies widely, depending on what surrounds it. If U-235 is wrapped in steal, for example, its critical mass is much lower than it would be if the U-235 were standing free. 

  • Materials Unaccounted For (MUF): The inevitable loss of nuclear material as it is machined, sintered, or compacted into pellets. The cumulative MUF at a large fuel-fabricating plant can amount to dozens of kg a year.

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Chronology

  • 1964: China explodes an atomic bomb (Curve of Binding Energy by McPhee).

  • 1958: The USG implements Project Orion to assess the potential of nuclear explosion fueled space travel. The limited test-ban treaty of 1963 forbids nuclear explosions in space and in the atmosphere, and thus leads to the indefinite suspension of Orion (Curve of Binding Energy by McPhee).

  • 1951: Stanislaw Ulam and Edward Teller patent the H-bomb (‘thermonuclear bomb’) (Curve of Binding Energy by McPhee).

  • 9 Aug, 1945: Nagasaki; the USAAF drops “Fat Man”, an implosion type nuclear weapon using Pu-239 on Nagasaki, Japan, detonating the device at 1850’ in the air where the detonation would accomplish the most damage through shock, fire, and radiation effects (Curve of Binding Energy by McPhee).

  • 6 Aug, 1945: Hiroshima; the USAAF drops “Little Boy”, a gun-type nuclear weapon using U-235 on Hiroshima, Japan, detonating the device at 1850’ in the air where the detonation would accomplish the most damage through shock, fire, and radiation effects. Little Boy fissioned only 1% of its U-235 and yielded 13 kt (Curve of Binding Energy by McPhee).

  • 16 Jul, 1945: Trinity; the Manhattan project explodes the first atomic bomb, the trinity device, near Alamogordo, NM. Its core was designed by a man named Christy. The name of the exact place where it was detonated was Jornada del Muerto, the Journey of Death (Curve of Binding Energy by McPhee).

  • 1940: Pu-239 is first created at UC Berkeley (Curve of Binding Energy by McPhee).

  • 5 Jun, 1927: Nine men meet in a restaurant in Breslau, Germany and found the Verein für Raumschiffahrt (VFR) which spends the next 6 yrs carrying through the basic engineering development of liquid-fueled rockets, until Hitler ends the program in 1933 (Curve of Binding Energy by McPhee).

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