Fissile material

In nuclear engineering, fissile material is material that can undergo nuclear fission when struck by a neutron of low energy.^[1] A self-sustaining thermal chain reaction can only be achieved with fissile material. The predominant neutron energy in a system may be typified by either slow neutrons (i.e., a thermal system) or fast neutrons. Fissile material can be used to fuel thermal-neutron reactors, fast-neutron reactors and nuclear explosives.

Fissile vs fissionable

According to the Ronen Fissile rule,^[2] for a heavy element with 90 ≤ Z ≤ 100, its isotopes with 2 × Z − N = 43 ± 2, with few exceptions, are fissile (where N = number of neutrons and Z = number of protons).^[3]^[4]^{[note 1]}

Region of relative stability: radium-226 to einsteinium-252

88

89

90

91

92

93

94

95

96

97

98

99

154

Half-life Key
1	10	100
1k	10k	100k
1M	10M	100M
1G	10G	(a)

²⁵⁰Cm

²⁵²Cf

154

153

²⁵¹Cf

²⁵²Es

153

152

²⁴⁸Cm

²⁵⁰Cf

152

151

²⁴⁷Cm

²⁴⁸Bk

²⁴⁹Cf

151

150

²⁴⁴Pu

²⁴⁶Cm

²⁴⁷Bk

150

149

²⁴⁵Cm

149

148

²⁴²Pu

²⁴³Am

²⁴⁴Cm

148

147

²⁴¹Pu

^242m

²⁴³Cm

147

146

²³⁸U

²⁴⁰Pu

²⁴¹Am

146

145

²³⁹Pu

145

144

²³⁶U

²³⁷Np

²³⁸Pu

144

143

²³⁵U

²³⁶Np

143

142

²³²Th

²³⁴U

²³⁵Np

²³⁶Pu

142

141

²³³U

141

140

²²⁸Ra

²³⁰Th

²³¹Pa

²³²U

Table Axes
Neutrons	(N)
Protons	(Z)

140

139

²²⁹Th

139

138

²²⁶Ra

²²⁷Ac

²²⁸Th

138

88

89

90

91

92

93

94

95

96

97

98

99

Only nuclides with a half-life of at least one year are shown on this table.

The term fissile is distinct from fissionable. A nuclide capable of undergoing nuclear fission (even with a low probability) after capturing a neutron of high or low energy^[5] is referred to as fissionable. A fissionable nuclide that can be induced to fission with low-energy thermal neutrons with a high probability is referred to as fissile.^[6] Fissionable materials include those (such as uranium-238) for which fission can be induced only by high-energy neutrons. As a result, fissile materials (such as uranium-235) are a subset of fissionable materials.

Uranium-235 fissions with low-energy thermal neutrons because the binding energy resulting from the absorption of a neutron is greater than the critical energy required for fission; therefore uranium-235 is fissile. By contrast, the binding energy released by uranium-238 absorbing a thermal neutron is less than the critical energy, so the neutron must possess additional energy for fission to be possible. Consequently, uranium-238 is fissionable but not fissile.^[7]^[8]

An alternative definition defines fissile nuclides as those nuclides that can be made to undergo nuclear fission (i.e., are fissionable) and also produce neutrons from such fission that can sustain a nuclear chain reaction in the correct setting. Under this definition, the only nuclides that are fissionable but not fissile are those nuclides that can be made to undergo nuclear fission but produce insufficient neutrons, in either energy or number, to sustain a nuclear chain reaction. As such, while all fissile isotopes are fissionable, not all fissionable isotopes are fissile. In the arms control context, particularly in proposals for a Fissile Material Cutoff Treaty, the term fissile is often used to describe materials that can be used in the fission primary of a nuclear weapon.^[9] These are materials that sustain an explosive fast neutron nuclear fission chain reaction.

Under all definitions above, uranium-238 (²³⁸
U
) is fissionable, but not fissile. Neutrons produced by fission of ²³⁸
U
have lower energies than the original neutron (they behave as in an inelastic scattering), usually below 1 MeV (i.e., a speed of about 14,000 km/s), the fission threshold to cause subsequent fission of ²³⁸
U
, so fission of ²³⁸
U
does not sustain a nuclear chain reaction.

Fast fission of ²³⁸
U
in the secondary stage of a thermonuclear weapon, due to the production of high-energy neutrons from nuclear fusion, contributes greatly to the yield and to fallout of such weapons. Fast fission of ²³⁸
U
tampers has also been evident in pure fission weapons.^[10] The fast fission of ²³⁸
U
also makes a significant contribution to the power output of some fast-neutron reactors.

Fissile nuclides

Actinides and fission products by half-life v t e
Actinides^[11] by decay chain				Half-life range (a)	Fission products of ²³⁵U by yield^[12]
4n	4n + 1	4n + 2	4n + 3	Half-life range (a)	4.5–7%	0.04–1.25%	<0.001%
²²⁸Ra^№				4–6 a		¹⁵⁵Eu^þ
²⁴⁸Bk^[13]				> 9 a
²⁴⁴Cm^ƒ	²⁴¹Pu^ƒ	²⁵⁰Cf	²²⁷Ac^№	10–29 a	⁹⁰Sr	⁸⁵Kr	^113mCd^þ
²³²U^ƒ		²³⁸Pu^ƒ	²⁴³Cm^ƒ	29–97 a	¹³⁷Cs	¹⁵¹Sm^þ	^121mSn
	²⁴⁹Cf^ƒ	^242mAm^ƒ		141–351 a	No fission products have a half-life in the range of 100 a–210 ka ...
	²⁴¹Am^ƒ		²⁵¹Cf^ƒ^[14]	430–900 a
		²²⁶Ra^№	²⁴⁷Bk	1.3–1.6 ka
²⁴⁰Pu	²²⁹Th	²⁴⁶Cm^ƒ	²⁴³Am^ƒ	4.7–7.4 ka
	²⁴⁵Cm^ƒ	²⁵⁰Cm		8.3–8.5 ka
			²³⁹Pu^ƒ	24.1 ka
		²³⁰Th^№	²³¹Pa^№	32–76 ka
²³⁶Np^ƒ	²³³U^ƒ	²³⁴U^№		150–250 ka	⁹⁹Tc^₡	¹²⁶Sn
²⁴⁸Cm		²⁴²Pu		327–375 ka		⁷⁹Se^₡
				1.33 Ma	¹³⁵Cs^₡
	²³⁷Np^ƒ			1.61–6.5 Ma	⁹³Zr	¹⁰⁷Pd
²³⁶U			²⁴⁷Cm^ƒ	15–24 Ma		¹²⁹I^₡
²⁴⁴Pu				80 Ma	... nor beyond 15.7 Ma^[15]
²³²Th^№		²³⁸U^№	²³⁵U^ƒ№	0.7–14.1 Ga	... nor beyond 15.7 Ma^[15]
₡, has thermal neutron capture cross section in the range of 8–50 barns ƒ, fissile №, primarily a naturally occurring radioactive material (NORM) þ, neutron poison (thermal neutron capture cross section greater than 3k barns)

In general, most actinide isotopes with an odd neutron number are fissile. Most nuclear fuels have an odd atomic mass number (A = Z + N = the total number of nucleons), and an even atomic number Z. This implies an odd number of neutrons. Isotopes with an odd number of neutrons gain an extra 1 to 2 MeV of energy from absorbing an extra neutron, from the pairing effect which favors even numbers of both neutrons and protons. This energy is enough to supply the needed extra energy for fission by slower neutrons, which is important for making fissionable isotopes also fissile.

More generally, nuclides with an even number of protons and an even number of neutrons, and located near a well-known curve in nuclear physics of atomic number vs. atomic mass number are more stable than others; hence, they are less likely to undergo fission. They are more likely to "ignore" the neutron and let it go on its way, or else to absorb the neutron but without gaining enough energy from the process to deform the nucleus enough for it to fission. These "even-even" isotopes are also less likely to undergo spontaneous fission, and they also have relatively much longer partial half-lives for alpha or beta decay. Examples of these isotopes are uranium-238 and thorium-232. On the other hand, other than the lightest nuclides, nuclides with an odd number of protons and an odd number of neutrons (odd Z, odd N) are usually short-lived (a notable exception is neptunium-236 with a half-life of 154,000 years) because they readily decay by beta-particle emission to their isobars with an even number of protons and an even number of neutrons (even Z, even N) becoming much more stable. The physical basis for this phenomenon also comes from the pairing effect in nuclear binding energy, but this time from both proton–proton and neutron–neutron pairing. The relatively short half-life of such odd-odd heavy isotopes means that they are not available in quantity and are highly radioactive.

Nuclear fuel

To be a useful fuel for nuclear fission chain reactions, the material must:

Be in the region of the binding energy curve where a fission chain reaction is possible (i.e., above radium)
Have a high probability of fission on neutron capture
Release more than one neutron on average per neutron capture. (Enough of them on each fission, to compensate for non-fissions and absorptions in non-fuel material)
Have a reasonably long half-life
Be available in suitable quantities.

Capture-fission ratios of fissile nuclides
Thermal neutrons^[16]				Epithermal neutrons
σ_F (b)	σ_γ (b)	%		σ_F (b)	σ_γ (b)	%
531	46	8.0%	²³³U	760	140	16%
585	99	14.5%	²³⁵U	275	140	34%
750	271	26.5%	²³⁹Pu	300	200	40%
1010	361	26.3%	²⁴¹Pu	570	160	22%

Fissile nuclides in nuclear fuels include:

Uranium-233, bred from thorium-232 by neutron capture with intermediate decays steps omitted.
Uranium-235, which occurs in natural uranium and enriched uranium
Plutonium-239, bred from uranium-238 by neutron capture with intermediate decays steps omitted.
Plutonium-241, bred from plutonium-240 directly by neutron capture.

Fissile nuclides do not have a 100% chance of undergoing fission on absorption of a neutron. The chance is dependent on the nuclide as well as neutron energy. For low and medium-energy neutrons, the neutron capture cross sections for fission (σ_F), the cross section for neutron capture with emission of a gamma ray (σ_γ), and the percentage of non-fissions are in the table at right.

Fertile nuclides in nuclear fuels include:

Thorium-232, which breeds uranium-233 by neutron capture with intermediate decays steps omitted.
Uranium-238, which breeds plutonium-239 by neutron capture with intermediate decays steps omitted.
Plutonium-240, which breeds plutonium-241 directly by neutron capture.

Notes

^ The fissile rule thus formulated indicates 33 isotopes as likely fissile: Th-225, 227, 229; Pa-228, 230, 232; U-231, 233, 235; Np-234, 236, 238; Pu-237, 239, 241; Am-240, 242, 244; Cm-243, 245, 247; Bk-246, 248, 250; Cf-249, 251, 253; Es-252, 254, 256; Fm-255, 257, 259. Only fourteen (including a long-lived metastable nuclear isomer) have half-lives of at least a year: Th-229, U-233, U-235, Np-236, Pu-239, Pu-241, Am-242m, Cm-243, Cm-245, Cm-247, Bk-248, Cf-249, Cf-251 and Es-252. Of these, only U-235 is naturally occurring. It is possible to breed U-233 and Pu-239 from more common naturally occurring isotopes (Th-232 and U-238 respectively) by single neutron capture. The others are typically produced in smaller quantities through further neutron absorption.

References

^ "NRC: Glossary -- Fissile material". www.nrc.gov.
^ "Nuclear Science and Engineering -- ANS / Publications / Journals / Nuclear Science and Engineering".
^ Ronen Y., 2006. A rule for determining fissile isotopes. Nucl. Sci. Eng., 152:3, pages 334-335. [1]
^ Ronen, Y. (2010). "Some remarks on the fissile isotopes". Annals of Nuclear Energy. 37 (12): 1783–1784. Bibcode:2010AnNuE..37.1783R. doi:10.1016/j.anucene.2010.07.006.
^ "NRC: Glossary -- Fissionable material". www.nrc.gov.
^ "Slides-Part one: Kinetics". UNENE University Network of Excellence in Nuclear Engineering. Retrieved 3 January 2013.
^ James J. Duderstadt and Louis J. Hamilton (1976). Nuclear Reactor Analysis. John Wiley & Sons, Inc. ISBN 0-471-22363-8.
^ John R. Lamarsh and Anthony John Baratta (Third Edition) (2001). Introduction to Nuclear Engineering. Prentice Hall. ISBN 0-201-82498-1.
^ Fissile Materials and Nuclear Weapons Archived 2012-02-06 at the Wayback Machine, International Panel on Fissile Materials
^ Semkow, Thomas; Parekh, Pravin; Haines, Douglas (2006). "Modeling the Effects of the Trinity Test". Applied Modeling and Computations in Nuclear Science. ACS Symposium Series. Vol. ACS Symposium Series. pp. 142–159. doi:10.1021/bk-2007-0945.ch011. ISBN 9780841239821.
^ Plus radium (element 88). While actually a sub-actinide, it immediately precedes actinium (89) and follows a three-element gap of instability after polonium (84) where no nuclides have half-lives of at least four years (the longest-lived nuclide in the gap is radon-222 with a half life of less than four days). Radium's longest lived isotope, at 1,600 years, thus merits the element's inclusion here.
^ Specifically from thermal neutron fission of uranium-235, e.g. in a typical nuclear reactor.
^ Milsted, J.; Friedman, A. M.; Stevens, C. M. (1965). "The alpha half-life of berkelium-247; a new long-lived isomer of berkelium-248". Nuclear Physics. 71 (2): 299. Bibcode:1965NucPh..71..299M. doi:10.1016/0029-5582(65)90719-4.
"The isotopic analyses disclosed a species of mass 248 in constant abundance in three samples analysed over a period of about 10 months. This was ascribed to an isomer of Bk²⁴⁸ with a half-life greater than 9 [years]. No growth of Cf²⁴⁸ was detected, and a lower limit for the β⁻ half-life can be set at about 10⁴ [years]. No alpha activity attributable to the new isomer has been detected; the alpha half-life is probably greater than 300 [years]."
^ This is the heaviest nuclide with a half-life of at least four years before the "sea of instability".
^ Excluding those "classically stable" nuclides with half-lives significantly in excess of ²³²Th; e.g., while ^113mCd has a half-life of only fourteen years, that of ¹¹³Cd is eight quadrillion years.
^ "Interactive Chart of Nuclides". Brookhaven National Laboratory. Archived from the original on 2017-01-24. Retrieved 2013-08-12.

[5] The fissile rule thus formulated indicates 33 isotopes as likely fissile: Th-225, 227, 229; Pa-228, 230, 232; U-231, 233, 235; Np-234, 236, 238; Pu-237, 239, 241; Am-240, 242, 244; Cm-243, 245, 247; Bk-246, 248, 250; Cf-249, 251, 253; Es-252, 254, 256; Fm-255, 257, 259. Only fourteen (including a long-lived metastable nuclear isomer) have half-lives of at least a year: Th-229, U-233, U-235, Np-236, Pu-239, Pu-241, Am-242m, Cm-243, Cm-245, Cm-247, Bk-248, Cf-249, Cf-251 and Es-252. Of these, only U-235 is naturally occurring. It is possible to breed U-233 and Pu-239 from more common naturally occurring isotopes (Th-232 and U-238 respectively) by single neutron capture. The others are typically produced in smaller quantities through further neutron absorption.

[fissile-1] "NRC: Glossary -- Fissile material". www.nrc.gov.

[2] "Nuclear Science and Engineering -- ANS / Publications / Journals / Nuclear Science and Engineering".

[3] Ronen Y., 2006. A rule for determining fissile isotopes. Nucl. Sci. Eng., 152:3, pages 334-335. [1]

[4] Ronen, Y. (2010). "Some remarks on the fissile isotopes". Annals of Nuclear Energy. 37 (12): 1783–1784. Bibcode:2010AnNuE..37.1783R. doi:10.1016/j.anucene.2010.07.006.

[fissionable-6] "NRC: Glossary -- Fissionable material". www.nrc.gov.

[UNENE-7] "Slides-Part one: Kinetics". UNENE University Network of Excellence in Nuclear Engineering. Retrieved 3 January 2013.

[8] James J. Duderstadt and Louis J. Hamilton (1976). Nuclear Reactor Analysis. John Wiley & Sons, Inc. ISBN 0-471-22363-8.

[9] John R. Lamarsh and Anthony John Baratta (Third Edition) (2001). Introduction to Nuclear Engineering. Prentice Hall. ISBN 0-201-82498-1.

[10] Fissile Materials and Nuclear Weapons Archived 2012-02-06 at the Wayback Machine, International Panel on Fissile Materials

[11] Semkow, Thomas; Parekh, Pravin; Haines, Douglas (2006). "Modeling the Effects of the Trinity Test". Applied Modeling and Computations in Nuclear Science. ACS Symposium Series. Vol. ACS Symposium Series. pp. 142–159. doi:10.1021/bk-2007-0945.ch011. ISBN 9780841239821.

[12] Plus radium (element 88). While actually a sub-actinide, it immediately precedes actinium (89) and follows a three-element gap of instability after polonium (84) where no nuclides have half-lives of at least four years (the longest-lived nuclide in the gap is radon-222 with a half life of less than four days). Radium's longest lived isotope, at 1,600 years, thus merits the element's inclusion here.

[13] Specifically from thermal neutron fission of uranium-235, e.g. in a typical nuclear reactor.

[14] Milsted, J.; Friedman, A. M.; Stevens, C. M. (1965). "The alpha half-life of berkelium-247; a new long-lived isomer of berkelium-248". Nuclear Physics. 71 (2): 299. Bibcode:1965NucPh..71..299M. doi:10.1016/0029-5582(65)90719-4.
"The isotopic analyses disclosed a species of mass 248 in constant abundance in three samples analysed over a period of about 10 months. This was ascribed to an isomer of Bk²⁴⁸ with a half-life greater than 9 [years]. No growth of Cf²⁴⁸ was detected, and a lower limit for the β⁻ half-life can be set at about 10⁴ [years]. No alpha activity attributable to the new isomer has been detected; the alpha half-life is probably greater than 300 [years]."

[15] This is the heaviest nuclide with a half-life of at least four years before the "sea of instability".

[16] Excluding those "classically stable" nuclides with half-lives significantly in excess of ²³²Th; e.g., while ^113mCd has a half-life of only fourteen years, that of ¹¹³Cd is eight quadrillion years.

[17] "Interactive Chart of Nuclides". Brookhaven National Laboratory. Archived from the original on 2017-01-24. Retrieved 2013-08-12.

[1]

[2]

[3]

[4]

[note 1]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

Fissile material

Fissile vs fissionable

Fissile nuclides

Nuclear fuel

See also

Notes

References

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