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DISCLAIMERNUCLEAR INSTALLATION SAFETY TRAINING SUPPORT GROUP

Lecture L.0.2 Concepts of Reactor Safety

IAEA/ANL Regional Workshop on Establishing a Nuclear Safety Infrastructure for a National Nuclear Power Program

Joseph C. Braun, ANL

29 November 2010 1

Timeline for the Discovery of Nuclear Fission

Carol Caplinger, Andrea Harpen, Cecelia Dygdon, Lisa Tighe,, and Joe Braun

Purpose

The purpose of this lecture is to provide a brief history of significant scientific discoveries and historical events that led to the discovery of nuclear fission and the development of the first nuclear reactor, and to explain some of the fundamental aspects of how nuclear reactors make power.

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ObjectivesAt the end of this lecture the participant will

have a general idea of the following nuclear engineering topics and will be able to describe the phenomena in layman’s terms:

History of the discover of nuclear fission and the developments that led to the first man-made nuclear reactorThe nuclear chain reaction process

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Discovery of Electrons

Richard Laming theorized the presence of the electron to explain the electrical properties of atoms in 1838.

In 1874, George Stoney estimated the charge of the electron and suggested that charges were permanently attached to atom particles. He coined the name electron for the charged particle.

During the 1870’s Sir William Crookes developed a high vacuum tube, when electrified, showed a stream of high energy particles moved from cathode to anode. Furthermore, Crookes was able to manipulate the stream of particles using a magnet.

J.J. Thomson identified that cathode rays were comprised of individual particles instead of waves, and made good estimates as to the particle’s charge and mass. The mass he determined to be approximately 1/1000 the mass of the least massive ion known, Hydrogen

Mass9.109382155 X 10−31 kg;0.510998910 MeV/c2;5.4857990943 X 10-4 u

ElectricalCharge

-1e-1.602176487 X 10-19 C

Particle Radius 2.8179 X 10−15 m

Force Interaction

Gravitational, Electromagnetic, weak,

Parity +1

Composition Leptons – No known substructure

Electromagnetic signature

No known color signature

http://upload.wikimedia.org/wikipedia/commons/4/41/Schattenkreuzr%C3%B6hre-in_use-lateral_view-standing_cross.jpg�

1895 Wilhelm RoentgenRoentgen was a German physicist, a professor at the University of Munich. In 1895, Roentgen was studying cathode ray tubes. He discovered that barium platinocyanide fluoresced when it was painted on a sheet of paper near the cathode ray tube and speculated that a new type of ray caused the fluorescence. He called these new rays x-rays. Roentgen is now a common dosage unit for radiation.

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1895 Roentgen Roentgen continued experiments with x-rays and discovered that the rays could penetrate solid objects. While the rays easily passed through paper or wood, the rays did not easily penetrate more dense objects. Roentgen wrote "If the hand be held before the fluorescent screen, the shadow shows the bones darkly with only faint outlines of the surrounding tissues." Roentgen found he could capture the image on a photographic plate and took the first x-ray of his wife’s hand. He was awarded the Nobel Prize in 1901.

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1896 Curie Marie Curie discovered that thorium gives

off the same radiation as uranium. Schmidt in Germany had discovered this two months earlier.

She also observed that the amount of radiation depended only on the amount of U or Th atoms present, independent of the chemical compound, suggesting that the radiation was coming from the nucleus.

She continued to study pitchblende and was able to isolate polonium and radium. Polonium is a metal chemically similar to bismuth. The Curies named it Polonium, in honor of Marie’s homeland, Poland. Radium is an alkali metal with properties similar to barium.

8

Marie & Pierre Curie

1903 Curie

“In 1903 the French Academy of Sciences nominated Becquerel and Pierre Curie—but not Marie—as candidates for the Nobel Prize in physics. A Swedish mathematician named Magnus Goesta Mittag-Leffler, a member of the nominating committee and an advocate of women scientists,—intervened, and Marie was included in the nomination. The three scientists were honored with the Nobel Prize in December 1903.Marie and Pierre Curie were jointly awarded the Nobel Prize in Physics with Becquerel for their research on radiation.”

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Alfred Nobel established the Nobel Prize in 1896. Following the death of his brother, in 1888, a newspaper erroneously published his obituary and condemned his development of dynamite. Many people think that Nobel established the Prize to change his legacy, so that he would not be known as a “Merchant of Death”.

The spectrum shows the different wavelengths of different “rays”. Today, we know they are not rays, but packets of electromagnetism, called photons; alpha is a nucleus of a helium and beta is an electron.

λ x ν = c, where λ= wavelength, ν = frequency and c = the speed of light.

Electromagnetic Spectrum

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1899-1907 Ernest RutherfordRutherford was originally from New Zealand. He worked at the Cavendish lab at Cambridge, England with J.J. Thomson and later at the University of Manchester. Rutherford showed that radioactivity was caused by the spontaneous decay of atoms. Rutherford noticed that the radioactive materials always took the same amount of time for half the sample to decay and coined the term “half-life”. He realized the practical application as a clock. Named α, β, γ radiation. Worked with Geiger to develop scintillation screens. Geiger went on to use this work to develop the Geiger counter.In 1908, he was awarded the Nobel Prize for Chemistry because of his work in atomic disintegration and the chemistry of radioactive substances

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Earnest Rutherford

1909 The Gold Foil Experiment

The alpha particles were fired at a thin sheet of gold foil Particles that hit on the detecting screen (film) are

recorded http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/ruther14.swf

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This shows the Geiger-Marsden experiment, performed by Geiger, Marsden and Rutherford in 1909.

1911 Rutherford’s Findings

Most of the particles passed right through A few particles were deflected VERY FEW were greatly deflected

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Conclusions:

a) The nucleus is smallb) The nucleus is densec) The nucleus is positively charged

It was almost as incredible as if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you..

1911 Rutherford

Rutherford interpreted this experiment and devised the commonly accepted “Rutherford Model of the Atom”. He concluded:

The atom is mostly empty space.

All the positive charge, and almost all the mass is concentrated in a small area in the center. He called this a “nucleus”

The nucleus is composed of protons and neutrons

The electrons are distributed around the nucleus, and occupy most of the volume

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His model was called a “nuclear model”.

1911 Rutherford

Rutherford thought that the protons and neutrons are at the nucleus with the electrons revolving around the nucleus.

15

The Atom

Smallest particle that retains all the chemical and physical properties of a given element

Comprised of three main subatomic particles– Neutron (neutral)

• In nucleus– Proton (positive)

• In nucleus– Electron (negative)

• Orbiting nucleusThe majority of the atom

is empty space, that space is a void

--

-

+++oo

oo

Subatomic Particles

Particle Electric Charge MassElectron (blue) -1.602 X 10-19 C me = 9.109 X 10-39 kgProton (red) +1.602 X 10-19 C mp = 1.673 X 10-27kgNeutron (white) 0 mn = 1.675 X 10-27kg

Relative Size Scale

1 fm

An Atom

1 cm = 10-2 m 1 mm = 10-3 m1μ = 10-6 m 1 nm = 10-9 m (micron)1 Å = 10-10 m (Ångstrom)

1 fm = 10-15 m

A nucleus

A fingertip

Atomic Size

Comparison of the diameter of a hydrogen atom (electron cloud) vs. a proton.Area of circle: πr2 (where r is

the radius)Cross Sectional Area of

Hydrogen atom = – π 1.2Å2 = 4.524 X 108 b*

Cross Sectional Area of Proton = – π (0.8)2(10-10)Å2 = π(.64)(10-

10)(10-16 cm2)= 2.01 X 10-26 cm2

= 0.02 barns

Hydrogen atom

Diameter of atom (electron cloud)

Diameter of proton

* 1 b = 10-24cm2

Estimates of the Relative Sizes of Various Atoms*Atom Atomic Radius

Atomic Area A=πr2

Nuclear Radius *

Nuclear Area A=πr2

Proton 1.2 Å 4.52 X 108 b 0.8 X 10-5 Å 0.02 b

Hydrogen -2 2.4 Å 1.8096 X 109 b 1.68 X 10-5 Å 0.08 b

Carbon -12 .91 Å 2.602 X 108 b 2.75 X 10-5 Å .237 b

Potassium -39 2.77 Å 2.4105 X 109 b 4.08 X 10-5 Å .523 b

Iodine -127 1.32 Å 5.474 X 108 b 6.03 X 10-5 Å 1.14 b

Cesium -133 3.34 Å 3.5046 X 109 b 6.13 X 10-5 Å 1.18 b

Lead - 208 1.81 Å 1.0292 X 109 b 7.11 X 10-5 Å 1.59 b

Thorium -234 1.79 Å 1.0066 X 109 b 7.37 X 10-5 Å 1.71 b

Uranium -238 1.75 Å 9.621 X 108 b 7.44 X 10-5 Å 1.74 b

* Bethe, H, & Morrison, P. (1956). Elementary nuclear theory. New York: John Wiley & Sons.

Scientific Notation

Scientific Notation is used to accurately represent very large or very small numbers.Scientific notation is based on powers of 10.

1

unit

103

10-2

10-6

10-3

10-9

10-12

10-15

106

1918 Rutherford In 1918, Rutherford noticed that when

alpha particles were shot into nitrogen gas, his scintillation detectors showed the signatures of hydrogen nuclei. Rutherford determined that the only place this hydrogen could have come from was the nitrogen, and therefore nitrogen must contain the hydrogen nucleus, an elementary particle with an atomic number of 1. Many believe that Rutherford became the first person to deliberately split the atom. This hydrogen nuclei was later given the name “proton”.

14N + α → 17O + p. After this discovery, he also speculated

that uncharged particles called “neutrons” existed in the nucleus

22

Rutherford used this chamber to bombard nitrogen atoms with alpha particles, producing oxygen and hydrogen nuclei. This was the first demonstration of the disintegration of a nucleus by a charged particle.

Discovery of Protons

The presence of a positively charged subatomic particle was theorized in 1815 by William Prout

In 1919, Ernest Rutherford proved that every atom contained a Hydrogen atom, which is a single proton.– Further studies by Rutherford

showed that when alpha particles were shot into Nitrogengas, their energy signature was the same as Hydrogen. This particle could only come from the Nitrogen, and must contain the Hydrogen nuclei. The Hydrogen nuclei must therefore be an elementary particle in the nucleus

Rutherford named this particle “Proton” after πρῶτον, the Greek word for “first”

Mass1.672621637×10−27 kg;938.272013 MeV/c2;1.00727646677 u

ElectricalCharge

+1e+1.602176487 X 10-19 C

Charge Radius 0.877 fm

Particle radius1.6 X 10-15 m for hydrogen to1.5 X 10 -10 m for heavier atoms

Force Interaction

Gravitational,Electromagnetic, weak, strong

Parity +1

Composition 2 up quarks, 1 down quark


Each quark has either red, blue, green signature, proton must contain all three colors

http://upload.wikimedia.org/wikipedia/commons/9/92/Quark_structure_proton.svg�

Discovery of Neutrons In 1920, Ernest Rutherford theorized

that an additional particle was present in the nucleus that contributed to the overall mass of an atom.

Irene Joliot-Curie identified an unknown radiation, that when fell on a compound containing hydrogen, it ejected high energy protons.

James Chadwick, in 1932, proved that the unknown radiation could not be gamma radiation, as it added to the overall mass of the atom. Additionally, the particle must have no charge as it did not effect the electrical charge of the atom.

The uncharged particles were named “neutron” after the Latin word for neutral.

Mass1.67492729 X 10−27 kg;939.565560 MeV/c2;1.0086649156 u

ElectricalCharge

+0 e+0 C

Charge Radius 0 fm

Particle Radius 8.0 X 10-14 meters

Force Interaction

Gravitational, weak, strong

Parity +1

Composition 1 up quarks, 2 down quarks


Each quark has either red, blue, green signature, neutron must contain all three colors

http://upload.wikimedia.org/wikipedia/commons/8/81/Quark_structure_neutron.svg�

Nuclear Notation

The composition of the nucleus is illustrated by the chemical symbol of the element combined with a series of numbers.

XMass number Z+N

Proton number

(p)

Neutron number

(n)

Z

A

NU

Mass number Z+N

Proton number

(p)

Neutron number

(n)

238

92

146

Nuclides

A Nuclide characterizes the specific constitution of the nucleus of an atom by identifying Z, (the number of protons) and N (the number of neutrons)

Variations of NuclidesName Characteristi

cExample

Isotopes Equal proton number

Isotones Equal neutron number

Isobars Equal mass number

Minor nuclei

Neutron andproton number exchanged

Nuclear isomers

Different energy states

136

126 C C,

147C N13

6 ,178 O17

9N177 , , F

32H He

31 ,

99m43T

cTc

9943 ,

Chart of the NuclidesA chart identifying all nuclides, half-lifes, decay types, etc. of all known nuclides.

An interactive online chart of the nuclides is available at :http://www.nndc.bnl.gov/chart/

Interpreting the Chart of the Nuclides

Changes Produced by Various Nuclear Reactions

Relative Locations of the Various Nuclear Processes

31

Enrico Fermi was an Italian physicist. Fermi worked at the University of Rome. To investigate “artificial” radioactivity, Fermi bombarded elements with neutrons. To obtain neutrons, Fermi took radon from the disintegration of a radium source and mixed it with beryllium powder and sealed it in a glass tube. The tube was his neutron source. He built a Geiger counter to measure the radioactivity results. He systematically tested elements in the periodic table.

Enrico Fermi

1930’s Fermi

1930’s Fermi Fluorine was the first element

to show radioactivity. He bombarded a sample,

measured the resulting radioactivity, chemically separated the irradiated sample, and measured the radioactivity of each separated element. Fermi showed that the element present after disintegration was close in atomic number to the original target sample.

When Fermi bombarded uranium, the resulting mixture contained a new element with atomic number 93 as well as other elements.

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Enrico Fermi

Next, Fermi noticed that the placement of the sample and the surroundings influenced the outcome of the radiation. Fermi suggested trying a light material, paraffin wax with silver. The results showed a 100x increase in radioactivity.

1930’s Fermi

Paraffin has a large amount of hydrogen. The large amount of hydrogen means a large number of collisions and the similar particle size slows the neutrons' speed when collisions occur. The "slow" neutrons striking the target will be more likely to collide with silver atoms; the increased collisions result in higher radioactivity.

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J. Robert Oppenheimer, E. Fermi, and Ernest O. Lawrence

Meitner Lise Meitner was born in

Austria, but following her doctoral degree went to Germany. She became Max Planck’s lab assistant.

She began working with Otto Hahn in 1908. She collaborated with Hahn for 30 years.

Meitner collaborated on radioactive substances with Hahn from 1912-1933. Meitner worked on physics and Hahn worked on the chemistry.

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Meitner and Hahn

Late 1930’s Meitner,Hahn,StrassmanAfter hearing of

Fermi’s experiments, Lise Meitner, Otto Hahn, and Fritz Strassman began performing similar experiments in Germany.

The experimental apparatus with which the team of Lise Meitner, Otto Hahn, and Fritz Strassmandiscovered Nuclear Fission in 1938.

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1938 Hahn/Strassman On December 19, 1938, Otto Hahn

and Fritz Strassman bombarded elements with neutrons. They found that the uranium nucleus changed and broke into two almost equal pieces. In their products they found barium. The products weighed less than the original uranium. Hahn was confused by these results, but sure of his chemistry.

On 12/19/1939, Hahn wrote about his experiment to Meitner. He also prepared an article for Die Naturwessenshaften and submitted it on 12/22/1939. When Meitner received Hahn’s letter, she was in Kunglav, Sweden to celebrate the holidays with relatives. Otto, Frisch was there and Meitner discussed Hahn’s letter with him. In his letter, Hahn said that he had

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chemical proof that some of the product of the bombardment of uranium with neutrons, was barium, and not barium's much heavier chemical sister element radium (barium's atomic weight is half that of uranium). Marie Curie had been separating barium from radium for many years, and the techniques were well known.

1930’s Meitner, Frisch Frisch wrote, “How could

barium be formed from uranium? No larger fragments than protons or helium nuclei (alpha particles) had ever been chipped away from nuclei, and to chip off a large number not nearly enough energy was available. Nor was it possible that the uranium nucleus could have been cleaved right across. A nucleus was not like a brittle solid that can be cleaved or broken.”

Lise Meitner’s laboratory table

Otto Frisch

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1938 Meitner Meitner calculated that the

charge of a uranium nucleus was indeed large enough to overcome the effect of surface tension almost completely: so the uranium nucleus might indeed resemble a very wobbly unstable drop, ready to divide itself at the slightest provocation, such as the impact of a single neutron.

But there was another problem. After separation, the two drops would be driven apart by their mutual electric repulsion and would acquire high speed and a very large energy.

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Meitner and nephew Otto Frisch used Bohr’s liquid drop model and suggested a giant resonance from neutron bombardment leading to fission.

1938 MeitnerMeitner worked out that the two nuclei formed by the division of a uranium nucleus together would be lighter than the original uranium nucleus by about one-fifth the mass of a proton. Now whenever mass disappears energy is created, according to Einstein's formula E=mc2, and one-fifth of a proton mass was just equivalent to 200MeV. So here was the source for that energy.

39

1938 Hahn & Strassman

Frisch was skeptical, but Meitner trusted Hahn’s ability as a chemist. Hahn had discovered fission.

Meitner wrote back to Hahn confirming his results and included her explanation. Frisch called this result, “nuclear fission.”

Frish confirmed these results experimentally on January 13, 1939.

Hahn won the 1944 Nobel prize in chemistry for his “discovery of the fission of heavy atomic nuclei”.

40

Otto Hahn, with a painting of Max Planck in the background.

Relative Locations of the Various Nuclear Processes

42

The following information was obtained from web.stteresa.edu.hk

1939 Fermi & Szilard In the summer, Fermi and

Szilard proposed the idea of a nuclear reactor (pile) to mediate a nuclear chain reaction. The pile would use natural uranium as fuel and graphite as the moderator.

Fermi had previously shown that neutrons were far more effectively captured by atoms if they were moving slowly, a process called moderation, when the neutrons were slowed after being released from a fission event in a nuclear reactor.

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1939 Szilard Einstein Letter

44

• In August, Hungarian-Jewish refugees, Leo Szilard, Edward Teller and Eugene Wigner thought that Germany might make use of the fission chain reaction to make a bomb. They persuadedGerman-Jewish refugee Albert Einstein to warn President Roosevelt of this possible German menace.

Leó Szilárd (right) and Albert Einstein re-enact the signing of the famous letter

to Franklin Delano Roosevelt.

October 11, 1939• The letter suggested the possibility of a uranium bomb deliverable by ship, which would destroy "an entire harbor and much of the surrounding countryside."

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•After receiving the Einstein-Szilárd letter, President Roosevelt authorized the creation of the Advisory Committee on Uranium.

From Einstein’s summer home in Long Island.

The work moved to University of Chicago and focused on constructing a nuclear reactor (Chicago Pile-1).

46

1942 CP-1

CP 1 during construction

CP 1 Construction

47

1942 Chicago Pile 1 Chicago Pile-1 (CP-1) was

the world's first man-made nuclear reactor. CP-1 was built on a squash court under the stands of the stadium, at the University of Chicago.

48

1942 Chicago Pile 1

CP 1 was a structure of 400 tons of machined graphite blocks, timbers and 34 tons of uranium oxide and 6 tons of uranium. This reactor also had cadmium control rods to control the chain reaction that Fermi hypothesized. The entire structure was inside an open rubber bag, in case it became necessary to remove the air from around the reactor.

49

A drawing of CP 1

50

CP-1 December 2, 1942

Fermi had three of his scientist standing on top of the pile “armed with five-gallon jugs of neutron-absorbing cadmium solution to be poured onto the pile if matters got out of control.” George Weil was standing at the front of the pile. His job was to follow Fermi’s instructions and gradually pull out of the pile the final “control rod”, a 14 foot plank with thin cadmium strips tacked onto it from end to end.

51

1942 Chicago Pile 1

There were two other sets of control rods, one electrically operated and one, called “Zip”, which would be pulled into the pile by a weighted rope if the rope holding it out of the pile were cut from the balcony of the squash court. One of Fermi’s colleagues stood by “Zip’s” rope with a hatchet, ready to cut the rope.

52

December 2, 1942 Chicago Pile 1

At 3:25 p.m. Fermi announced that “The reaction is self-sustaining. The curve is exponential”.

53

http://www.cfo.doe.gov/me70/manhattan/images/CP1PrintoutLarge.jpg�

1942 Chicago Pile 1

CP 1 operated for 28 minutes before Fermi ordered “Zip-in” and stopped the chain reaction.

54

This historic moment—the first man-made self-sustaining, nuclear chain reaction—was reached in great secrecy.

1942 Chicago Pile 1

Back row, left to right, Norman Hilberry, Samuel Allison, Thomas Brill, Robert G. Nobles, Warren Nyer, and Marvin Wilkening. Middle row, Harold Agnew, William Sturm, Harold Lichtenberger, Leona W. Marshall, and Leo Szilard. Front row, Enrico Fermi, Walter H. Zinn, Albert Wattenberg, and Herbert L. Anderson.

55

1942 Chicago Pile 1

After the experiment, the scientists toasted their success with a glass of wine and signed the wine bottle.

56

Admiral Hyman G. Rickover (1900-1986) Born in Poland, in

1900 and migrated to U.S. at age 5Attended U.S. Naval

Academy and served in the Navy from 1919-1982. Rickover directed the

original development of the naval nuclear program for 30 years.

57

Admiral Rickover

Admiral Hyman G. Rickover

Worked with Abelson and Weinberg on developing a pressurized reactor vessel for use on submarinesDeveloped the USS

NAUTILIS (SSN-1), the world’s first high-temperature nuclear reactor (1954)Noted for a strong,

controversial, and political personality, Rickover retired after 63 years of Naval service

58

U.S.S. Chicago

U.S.S. Lincoln

Scientists Honored

59

Curium Fermium

Meitnerium Bohrium

Einsteinium Rutherfordium

Nuclear Reactors

60

1. Thermal Reactors

2. Fast Reactors

1. Thermal refers to the energy of the neutrons that cause most of the fissions. These start as fast neutrons that are slowed down by a moderator.

1-2 MeV Moderator ≈ .0253 eV

2. In Fast reactors the fission is caused by fast neutrons.They have no moderators.

Nuclear energy is produced by a controlled nuclear reaction.

Boiling Water ReactorsPressurized Water Reactors

Boiling Water Reactor(BWR) Pressurized Water Reactor(PWR)

61

Quad Cities Nuclear Generating Station Moline, Illinois

Braidwood Nuclear Generating StationBraidwood, Illinois

http://nuklir.wordpress.com/foto/attachment/68/�

BWR Boiling Water Reactor

62

Boiling water reactors heat the water surrounding the nuclear fuel directly into steam in the reactor vessel. Pipes carry steam directly to the turbine, which drives the electric generator to produce electricity.

Pressurized Water Reactor

63

Pressurized water reactors heat the water surrounding the nuclear fuel, but keep the water under pressure to prevent it from boiling. The hot water is pumped from the reactor vessel to a steam generator. There, the heat from the water is transferred to a second, separate supply of water. This water supply boils to make steam. The steam spins the turbine, which drives the electric generator to produce electricity.

The Fission Process

Typical Fission of U – 235 Atom

Fission Product

No. of Protons

No. of Neutrons

Total

Uranium-235

92 143 235

Neutron 1 1

↓ ↓ ↓Krypton -92 36 56 92Barium 141 56 85 141Released neutrons

0 3 3

Total 92 144 236

A “typical” result of a single fission

Distribution of Fission Products from Different Originating Nuclei

65

The Neutron Chain Reaction

A uranium-235 atom absorbs a neutron, and fissions into two new atoms (fission fragments), releasing three new neutrons and some binding energy.

One of those neutrons is absorbed by an atom of uranium-238, and does not continue the reaction. Another neutron is simply lost and does not collide with anything, also not continuing the reaction. However one neutron does collide with an atom of uranium-235, which then fissions and releases two neutrons and some binding energy.

Both of those neutrons collide with uranium-235 atoms, each of which fission and release between one and three neutrons, and so on.

Energy Released from the Fission of One U-235 Atom

FormEmitted energy,

MeVRecoverable energy,

MeV

Fission fragments 168 168

Fission product decay

β-rays 8 8

γ-rays 7 7

neutrinos 12 -

Prompt γ-rays 7 7

Fission neutrons (kinetic energy) 5 5

Capture γ-rays - 3-12

Total 207 198-207

Fission Products (FP) – A Source of Delayed Neutrons

Some of the Fission Products are rich in neutrons and are a possible source of delayed neutrons

Why are they rich in neutrons? Consider this table of Isotopes:

Z Isotope Protons Neutrons Ratio N/Z Note:

2 He-4 2 2 1.00 Stable

35 Br-87 35 52 1.48 FP36 Kr-92 36 56 1.55 FP

40 Zr-90 40 50 1.25 Stable40 Zr-91 40 51 1.27 Stable

56 Ba-141 56 85 1.52 FP

90 Th-232 90 142 1.58 Stable92 U-238 92 146 1.59 Stable

Fission Products – A Source of Delayed Neutrons (cont.)

Example:

Br-87 decays by emitting a beta particle and becomes Kr-87.

This decay has a half life of 55.9 seconds.

Kr-87, formed in an excited state, ejects a neutron immediately with an energy of about 0.3 Mev

Nuclei such as Br-87 are know as delayed neutron precursors

There are believed to be about 20 such precursors.

The precursors can be divided into six groups, each with its own characteristic half-life. The group half-lives and decay constants for the thermal fission of U-235 are given in the following table.

69


Delayed neutron data for thermal fission in 235U

GroupHalf-life

(sec)Decay constant λi, sec-1

Energy (keV)

Yield, neutrons per fission

Fraction βi

1 55.72 0.0124 250 0.00052 0.0002152 22.72 0.0305 560 0.00346 0.0014243 6.22 0.111 405 0.00310 0.0012744 2.3 0.301 450 0.00624 0.0025685 0.61 1.14 - 0.00182 0.0007486 0.23 3.01 - 0.00066 0.000273

Total Yield: 0.015800 Total delayed fraction(β): 0.006500

Based in part on G. R. Keepin, Physics of Nuclear Kinetics, Reading, Mass.: Addision-Wesley, 1965.

Thermal Reactors

Thermal Reactors

Neutron flux, Cross-Section and Reaction Rates

For a given neutron energy, E, the neutron flux at that energy is expressed as the number of neutrons n, at that energy, in a give volume, times the velocity, v, of the neutrons at the given energy, so that:

Ф(E) = n(E) v(E)

If all of the neutrons in a volume are at the same energy, say, 0.0253 electron-volts then:

Ф = nv If there are materials in that volume, then the number of reactions is given by the cross section times the flux.

Cross sections for specific atoms are represented as the cross sectional area of a single atom (microscopic cross sections, σ,) times the number of atoms in a give volume, N. This is often referred to as the macroscopic cross section, Σ, and expressed by the formula

Σ = σ N

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Neutron flux, Cross-Section and Reaction Rates (cont.)

Since Σ represents an area per atom times a number of atoms per unit volume, it has the dimensions of cm2 / cm3 or 1/cm. Since Σ is used to represent reactions of some type, the average distance between reactions is sometimes called the mean free path λ. In this situation, the mean free path for a given type of interaction is expressed by:

λ = 1/Σ and λ has the dimensions of cm. For scattering of neutrons in a moderating medium such as water or graphite, λ is the average distance between scattering collisions.

The reaction rate, R, for a particular interaction, say the scattering of a neutron, is then given by the expression:

R = Σ Ф

Since Σ has the dimensions of 1/cm, and Ф has the dimensions of 1/cm2 sec, then the reaction rate R has the dimensions of (reactions)/cm3·sec.

Microscopic cross sections, σ, are measured in units called ‘barns’ where one barn is 1 x 10-24 cm2.

74


Q: Why did they choose the name ‘Barn?”A: Because to the early nuclear physicists, 10-24 cm was considered to be ‘as

big as a barn!’

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Atomic densities, N, are measured in terms of atoms per unit volume and can be related to a specific volume, e.g. a cubic centimeter (cm3) by Avogadro's number, 6.02 x 1023. An Avogadro's number of any atom or molecule is equal to the atomic weight of that atom or molecule expressed in grams.

For example, the atomic weight of a molecule of water, H2O, is 18. That is, 16 +1 +1 = 18, which is the atomic weight of one oxygen atom (16) and two hydrogen atoms (1 each).

Then 18 grams of water would contain 6.02 x 1023 molecules of water, and since the density of water at room temperature is about 1 gram/ cm3, then a cubic centimeter of water would contain:

6.02 x 1023 /18 or about 3.34 x 1022 molecules of water.

This implies that a cubic centimeter of water contains 3.34 x 1022 oxygen atoms, and 6.68 x 1022 hydrogen atoms.

In nuclear reactors reaction rates are calculated in specific volumes of a reactor and used to determine, for example, the number of fissions that occur in a certain region, or in the whole reactor.

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Thermal ReactorsThermal reactors are the most common type. These systems contain:

Fuel,a moderator to slow down the fission neutrons to thermal energies,

coolant, – In some reactors, the coolant may be the moderator

various structural materials

The word thermal refers to the energy of the neutrons, and in such a reactor, the fast neutrons born from fission with energies of about 1-2 Mev are slowed down by the moderator to energies compatible with the temperatures of the moderator, about 0.0253 ev (~1/40 ev).

Another reactor type is a fast reactor, which utilizes the fission caused by fast neutrons. Fast reactors have significantly different design features from thermal reactors. Most notably, they have no moderator as such, and do not use water in the reactor core – since water is a moderator.

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Thermal Reactors

Thermal reactors are the most common type. These systems contain:

FuelModerator-to slow down

the fission neutrons to thermal energies

Coolant-in some reactors, the coolant may be the moderator.

Structural materialsControl rods to allow/

stop the nuclear reaction.

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Nuclear Fuels

Currently, PWR and BWR reactors use an Uranium oxide (U-235 and U-238) sintered into ceramic pellets that are placed in tubes, and the tubes are bundled together. Oxide Fuels - low thermal conductivity

– Uranium oxide (UOX) or Mixed oxide (MOX) Metal Fuels – higher thermal conductivity, but cannot survive high temperatures

– TRIGA – Uranium zirconium hydride (UZrH)– Actinide fuel – used in fast neutron reactors

Nitride Fuels – high thermal conductivity and high melting points– Uranium nitride– Uranium carbide

Molten Salts – high thermal conductivity and high melting points, that operate in a liquid state at high temperatures.

http://upload.wikimedia.org/wikipedia/commons/2/28/Fuel_Pellet.jpg�

Infinite Thermal Reactor

Imagine an infinite reactor composed only of fuel and moderator.

If Σa is the macroscopic thermal absorption cross section of mixture, that is,

Σa = ΣaF + ΣaM

where F and M refer to the fuel and moderator respectively, then there will be a total of ΣaФth neutrons absorbed per cm3/sec everywhere in the reactor, where Фth is the thermal flux.

We define a parameter called the thermal utilization factor, f, as the fraction of thermal neutrons absorbed in the fuel vs. the entire reactor. So,

f = ΣaF / Σa

and there are f ΣaФth neutrons absorbed per cm3/sec in the fuel.

Next, we define a parameter named η (eta) as the average number of neutrons emitted per thermal neutron absorbed by the fuel. For U-235 with a temperature of 20 °C η has a value of about 2.065.

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Infinite Thermal Reactor (continuation)

For a uniform mixture of only U-235 and pure water in an infinite reactor f has a value of about 0.484 at room temperature, so we can define a parameter called the multiplication factor kinf for an infinite reactor as,

kinf = η f

The multiplication factor gives the ratio of the number of fissions in one generation vs. the number in the previous generation. If kinf is exactly 1.0, then the reactor is said to be critical, and the number of neutrons as a function of time is neither increasing nor decreasing.

Most nuclear fuel in operating reactors has a mixture of U-235 and U-238. U-238 is able to fission when struck by fast neutron with an energy greater that 0.9 Mev. Because of this, we identify a parameter called the fast fission factor, ε (epsilon).

Epsilon is defined as the ratio of (thermal plus fast fissions) divided by (thermal fissions). So,

ε = (all fissions) / (thermal fissions)

and ε is always greater than or equal to 1.0.81


Also because uranium has the ability to absorb neutrons while they are slowing down, we need to define a parameter to account for this loss. The main method of capturing neutron as they slow down is a process called resonance absorption.

Remember that neutrons born from fission have energies in the order of about 1-2 Mev. These neutrons travel at speeds of about 10 million meters per second. When the are slowed down to thermal energies of about 0.0253 ev, they are traveling at speeds of about 2,200 meters per second. The slowing of neutrons is the result of collisions with lighter nuclei such as the nuclei of hydrogen, and oxygen, found in water, or carbon, found in graphite.

As the neutrons collide with and scatter from lighter nuclei, they could encounter nuclei of uranium. Depending upon the energy of the neutrons, the cross section for absorption by uranium could be quite large. Neutrons slowed to specific energies, called resonance absorption energies, can be absorbed more easily if they come near uranium atoms. A graph of neutron cross section vs energy shows a series of sharp peaks that the neutrons must escape while slowing down. Otherwise, they will be absorbed by the uranium and lost to the fission process.

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The probability of escaping resonance absorption in a reactor is called the resonance escape probability, p, which is a very complex function of the fuel and moderator mixture, and the geometry of the fuel and moderator configurations in heterogeneous reactors. Values of p can vary from 0.8 to 0.95. While most neutrons manage to escape being captured by the resonances, the fraction of neutrons that do get captured have a big effect on the criticality of the reactor. As fuel temperatures increase, a ‘doppler’ effect causes more neutrons to be captured in the fuel.

So, the multiplication factor in an infinite reactor can be expressed by the

Four Factor Formula,kinf = η ε p f

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An easy way to remember this formula is to consider how it follows the (short) life of a neutron from birth to death.

The factor η describes the number of new fast neutrons produced when a thermal neutron is captured in a fuel atom.

The factor ε describes the number of extra fast neutrons that occur from fast fission.

The factor p describes the probability that these neutrons will escape capture in the resonance region, and

The factor f describes the fraction of thermal neutrons will be captured by fuel atoms ( and start the process all over again).

The life cycle for prompt neutrons, those arising directly from fission, in a light water moderated system, is on the order of 10-4 seconds.

It seems that neutrons in a reactor live a short (but exciting) life!

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Finite Thermal Reactor In considering actual reactors, factors are needed to account for the finite size, and the fact that neutrons can be lost from the reactor by leakage out of the surface while slowing down or when they have reached thermal energies.

We define two non-leakage probabilities, one for the leakage of fast neutrons to leak out while slowing down, (NL)F, and one for thermal neutrons leaking out (NL)Th.

So the neutron multiplication factor for a finite reactor, k, can be written as:

k = kinf (NL)F (NL)Th

The non-leakage probabilities NLF and NLTh can be combined into an expression so that

(NL)F(NL)Th ~1/ (1 + B2M2)

Where B2 is known as the ‘Buckling,’ a measure of how the geometry of the reactor impacts the leakage, and M2 is called the thermal migration area, a measure of how far neutrons go in the process of slowing down and being captured. The larger the buckling, and the larger the thermal migration area, the more leakage occurs from the reactor. For an infinite reactor, B2 = 0.0.

85

Finite Thermal Reactor (continued)

The net effect of the leakage of neutrons from a finite reactor is a reduction in the value of k, the multiplication factor for a reactor. The multiplication factor, k is expressed as,

k = kinf /(1 + B2M2)

Hence if an infinite reactor was just critical, kinf = 1, then the effect of leakage would make the reactor subcritical (k < 1).

Now we can use the Four Factor Formula on finite reactors:

k = η ε p f /(1 + B2M2)

This is the four factor formula with a consideration for leakage, (sometimes called the ‘six-factor formula’) and it is a helpful tool for making simple evaluations or estimates of the effects of changes to a reactor configuration to the criticality of the reactor.

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87

Nuclear engineers characterize the operation of a nuclear power plant with a four-factor formula:

Kinf = η * ε * p * f (for an infinite reactor)

To account for leakage, two additional factors have been added:

Keffective= η * (NL)f * ε * p * (NL)th * f

Where (NL) means non-leakage, and f and th refer to fast and thermal neutrons.

Keffective = 1, Critical

Keffective < 1, Subcritical

Keffective > 1, Supercritical

Imagine an Infinite Thermal Reactor An easy way to remember the four-factor formula is to consider how it follows the (short) life of a neutron from birth to death.

The factor η describes the number of new fast neutrons produced when a thermal neutron is captured in a fuel atom.

The factor ε describes the number of extra fast neutrons that occur from fast fission.

The factor p describes the probability that these neutrons will escape capture in the resonance region, and

The factor f describes the fraction of thermal neutrons will be captured by fuel atoms ( and start the process all over again).

The life cycle for prompt neutrons, those arising directly from fission, is on the order of 10-4 seconds.

It seems that neutrons in a reactor live a short (but exciting) life!

Critical Mass

Amount of material needed to just sustain a fission chain reaction

89

– Depends on• Element

• Enrichment

• Shape (sphere is best)

• Density

• Surroundings

90

Just for fun, let’s start with a……

91

neutron source!

Nuclear Reactor Operation

Neutron source

92

Fission NeutronProduction

η=


Neutron source

93


η=

Fast Leakage(NL)f=

Fast neutrons (out of the reactor core)


Neutron source

94


η=

Fast Leakage(NL)f=

Fast Fissionε=

Fast neutronsNuclear Reactor Operation

Neutron source

95

Moderation


η=

Fast Leakage(NL)f=

Fast Fissionε=


Neutron source

96

Moderation

Resonance Escapep=


η=

Fast Leakage(NL)f=

Fast Fissionε=


Neutron source

97

Moderation

Resonance Escapep=

Moderation


η=

Fast Leakage(NL)f=

Fast Fissionε=


Neutron source

98

Moderation

Resonance Escapep=

Moderation

Thermal Leakage(NL)th=


η=

Fast Leakage(NL)f=

Fast Fissionε=


Neutron source

99

Moderation

Resonance Escapep=

Moderation


Thermal Utilizationf =


η=

Fast Leakage(NL)f=

Fast Fissionε=


Neutron source

100

Moderation

Resonance Escapep=

Moderation




η=

Fast Leakage(NL)f=

Fast Fissionε=


Neutron source

101

Delayed Neutron Precursor “Bank”

Moderation

Resonance Escapep=

Moderation




η=

Fast Leakage(NL)f=

Fast Fissionε=


Neutron source

102


103

Some Calculations:

Moderation

Resonance Escapep=.8000

Moderation

Thermal Leakage(NL)th=.9000

Thermal Utilizationf =.6832


η=2.164

Fast Leakage(NL)f=.9000

Fast Fissionε= 1.038

Fast neutrons= Nuclear Reactor Operation

Neutron source

104


n= n=

n=

n=

neutrons

n=

neutrons

n=

neutrons

Moderation

Resonance Escapep=.8000

Moderation

Thermal Leakage(NL)th=.9000

Thermal Utilizationf =.6832


η=2.164

Fast Leakage(NL)f=.9000

Fast Fissionε= 1.038

Fast neutrons= 216Nuclear Reactor Operation

Neutron source

105


n= 2164 n= 1948

n=2022

n=1617

405 neutrons

n=1456

161 neutrons

n=994

462 neutrons

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What is the Keffective for this reactor?

Keffective= η * (NL)f * ε * p * (NL)th * f

= 2.164 * .9000 * 1.038 * .8000 * .9000 * .6832

= .9944

Is it critical, supercritical or subcritical?

It is subcritical, but close to critical.

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What causes this delayed neutron precursor “bank”?

Fission Products: The delayed neutron precursors are often characterized by six groups, each with a characteristicyield and half-life.


Delayed neutron data for thermal fission in 235U

GroupHalf-life

(sec)Decay constant λi, sec-1

Energy (keV)

Yield, neutrons per fission

Fraction βi

1 55.72 0.0124 250 0.00052 0.0002152 22.72 0.0305 560 0.00346 0.0014243 6.22 0.111 405 0.00310 0.0012744 2.3 0.301 450 0.00624 0.0025685 0.61 1.14 - 0.00182 0.0007486 0.23 3.01 - 0.00066 0.000273

Total Yield: 0.015800 Total delayed fraction(β): 0.006500

Based in part on G. R. Keepin, Physics of Nuclear Kinetics, Reading, Mass.: Addision-Wesley, 1965.

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The neutron precursors (fission products) remain in the fuel.For each fission, .0158 precursors are formed. At some pointin time, they decay, releasing a neutron into the reactor. For every thousand fissions: 15.8 neutron precursors are formed.

110

What causes the neutrons in the neutron“bank” to return to the reactor?

The six groups of precursor isotopes decay, each withits own half-life, and every precursor releases a neutron.

111

What factors do these delayed neutrons experience after they return to the reactor?

Moderation

Resonance Escapep=

Moderation




η=

Fast Leakage(NL)f=

Fast Fissionε=


Proton Accelerator

112


113

What factors do these delayed neutrons experience after they return to the reactor?Because they are at a lower energy, they do not experiencefast leakage or fast fission. Otherwise, they experience thesame factors that the other neutrons experience.

→They will be moderated.→They must escape being absorbed by the resonances.→They must avoid leaking out of the reactor.→They will either be absorbed in the fuel, or the

moderator or the structural materials or control rods.

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Conclusions Regarding Nuclear Reactor Criticality1. A combination of prompt and delayed neutrons

are needed to achieve steady state criticality. 2. Delayed neutrons contribute significantly to the

steady state neutron population3. Delayed neutrons prevent a rapid rise in power

when the reactor becomes supercritical 4. Delayed neutrons continue to cause fissions

after a reactor has become subcritical5. If it were not for delayed neutrons we would not

have power reactors.

THE END

Acknowledgements

We would like to acknowledge the work of Carol Caplinger, Andrea Harpen, Cecelia Dygdon and Lisa Tighe, in preparing this lecture. The work was done in the Summer of 2010 as part of the Academies Creating Teacher Scientists/Teachers as Research Associates (ACTS/(TARA) program at Argonne National Laboratory.

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Documents

+0:*3(04,9 - International Atomic Energy Agency · PDF fileTimeline for the Discovery of Nuclear Fission Carol Caplinger, Andrea Harpen, Cecelia Dygdon, Lisa Tighe,, and Joe Braun