How To Draw A Decay Scheme Diagram Starting With U-235

Actinium

Actinide Elements

Siegfried Hübener , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

II Radioactivity and Nuclear Reactions of Actinides

All isotopes of the actinides and actinium are radioactive. Table II presents data on several of the most available and important of these. The unstable, radioactive actinide nuclei decay by emission of α particles, electrons, or positrons (β⁻ or β⁺ decay, respectively). Alternatively to the emission of a positron, the unstable nucleus may capture an electron of the electron shell of the atom (symbol ε). In most cases the radioactive decay leads to an excited state of the new nucleus, which gives off its excitation energy in the form of one or several photons (γ rays). In some cases a metastable state results that decays independently of the way it was formed. Spontaneous fission (symbol sf) is another mode of radioactive decay, which was discovered in 1940 by G. N. Flerov and K. A. Petrzhak.

TABLE II. Important Isotopes of the Actinide Elements

Atomic number	Element	Isotope	Half-life	Mode of decay
89	Actinium	227Ac	21.7 years	β−(0.986), α(0.014), γ
		228Ac	6.15   h	β−
90	Thorium	232Th	1.405 · 1010 years	α,
91	Protactinium	231Pa	32760 years	α, γ
	234Pa	6.70   h	β−
92	Uranium	235U	7.038 · 108 years	α
		238U	4.468 · 109 years	α
93	Neptunium	237Np	2.144 · 106 years	α
94	Plutonium	238Pu	87.7 years	α
		239Pu	2.411 · 104 years	α
		242Pu	3.733 · 105 years	α
		244Pu	8.08 · 107 years	α(0.999), sf(0.001)
95	Americium	241Am	432.2 years	α, γ
		243Am	7370 years	α
96	Curium	242Cm	162.8 days	α
		244Cm	18.10 years	α
		248Cm	3.40 · 105 years	α(0.916), sf(0.084)
97	Berkelium	247Bk	1380 years	α(<100%)
		249Bk	320 days	β−(0.99999), α(0.00001)
98	Californium	249Cf	351 years	α
		251Cf	898 years	α
		252Cf	2.645 year	α(0.969), sf(0.031)
99	Einsteinium	252Es	471.7 days	α(0.76, ε(0.24)
		253Es	20.47 days	α
		254Es	275.7 days	α
100	Fermium	252Fm	25.39   h	α(0.99998), sf(0.00002)
		255Fm	20.07   h	α
		256Fm	157.6 min	sf(0.919), α(0.081)
101	Mendelevium	255Md	27 min	ε(0.92), α(0.08)
		256Md	78.1 min	ε(0.907), α(0.093)
102	Nobelium	259No	58 min	α(0.75), ε(0.25)
103	Lawrencium	260Lr	3.0 min	α(0.75), ε(0.25)

The numerous radionuclides present in thorium and uranium ores are members of genetic correlated radioactive decay series, which are represented in Fig. 1. In all of these decay series, only α and β⁻ decay are observed. With emission of an α particle ( ${}_2{}^4\text{H}\text{e}$ ), the atomic number is reduced by 2, the mass number by 4. With emission of a β⁻ particle, the mass number remains unchanged, whereas the atomic number increases by 1. As a result, in these decay series the mass number can differ only by multiples of 4 and there are four such families, designated 4n  +   0 (thorium series), 4n  +   1 (neptunium series), 4n  +   2 (uranium or uranium-radium series), and 4n  +   3 (actinium series). The neptunium series is missing in nature. It was probably present in nature for some million years after the genesis of the elements, but decayed due to the relatively short half-life of ²³⁷Np, compared with the age of the Earth (about 5 · 10⁹ years). Each series contains a number of short-lived nuclides, and the final members of each series are stable nuclides. α Decay is the dominant decay mode of long-lived heavy nuclei with atomic numbers Z  >   83. With increasing atomic numbers spontaneous fission begins to compete with α decay. For ²³⁸U the probability of spontaneous fission is about 10⁻⁴% of that of α decay and is already about 90% for ²⁵⁶Fm.

FIGURE 1.

The radioactive decay is the simplest form of a nuclear reaction according to equation [Eq. (6)]:

(6) $\text{A}\to \text{B}+\text{x}+\Delta \text{E}.$

This is a mononuclear reaction. In nuclear science, however, binuclear reactions are generally understood by the term "nuclear reaction." They are described by the general equation [Eq. (7)]:

(7) $\text{A}+\text{x}\to \text{B}+\text{y}+\Delta \text{E},$

where A is the target nuclide, x is the projectile, B is the product nuclide, and y is the particle or photon emitted. Equations (3)–(5) are examples for neutron- and deuteron-induced nuclear reactions. With heavy ions (heavier than α particles) as projectiles, the heaviest actinides have been synthesized. Targets made from heavy actinide nuclides such as ²⁴⁸Cm and ²⁴⁹Bk have been used to synthesize several transactinide elements in heavy-ion reactions.

Nuclear fission of actinides is, without doubt, the most important nuclear reaction. Nuclear fission by thermal neutrons may be described by the general equation [Eq. (8)]:

(8) $\text{A}+\text{n}\to \text{B}+\text{D}+\nu \text{n}+\Delta \text{E}.$

The fission products B and D have mass numbers in the range between about 70 and 160, the number of neutrons emitted is ν   ≈   2–3, and the energy set free by fission is ΔE  ≈   200   MeV. This energy is relatively high, because the binding energy per nucleon is higher for the fission products than for the actinide nuclei. In the case of nuclei with even proton and odd neutron numbers, such as ²³³U, ²³⁵U, and ²³⁹Pu, the binding energy of an additional neutron is particularly high, and the barrier against fission is easily surmounted. Therefore, these nuclides have high fission yields for fission by thermal neutrons.

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Including Actinides

Karl A. GschneidnerJr., in Handbook on the Physics and Chemistry of Rare Earths, 2016

2.8 Correcting Experimental Results

A problem in developing actinide systematics was the radius of actinium: it appeared to be too small relative to that of Th [19]. The change in radius on going from trivalent Ac to tetravalent Th is much too small when one compares the shifts of the radii due to valence changes for the lanthanide series from 2 to 3 and 3 to 4. Zachariasen [36] recognized this problem over 40 years ago, ie, the reported radius of actinium would suggest Ac has a valence greater than 3, which is impossible since it would require removing an electron from the Rn rare gas core level to attain this higher valence. He estimated a hypothetical radius of 1.977   Å for trivalent Ac, and ignored the then known experimental value of 1.877   Å. The Zachariasen radius for Ac is consistent with these valence changes and this implies that the radii for Am, Cm, Bk, and Cf are more appropriate for a valence of about 3.5, instead of 3 as shown in Fig. 4.

Further evidence supporting the larger lattice parameter for Ac metal is that the lattice parameters for all of the known Ac compound are about 3.0% larger than those of the corresponding isostructural La compounds [19]. The lattice parameter of fcc Ac (a  =   5.670   Å) is 6.9% larger than that of fcc La, which is reasonable since the atomic fraction of Ac (or La) in the various compounds ranges from 0.17 to 0.40, and one would expect smaller increases in the lattice parameters in the compounds owing to this dilution effect.

Finally, the last piece of evidence supporting the larger lattice parameter being the true value for Ac is found in the systematic variation in the metallic radii in the Group 2, 3, and 4 elements, as argued by Gschneidner [19].

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Cosmic Rays Underground, Underwater and Under Ice

Peter K.F. Grieder , in Cosmic Rays at Earth, 2001

Terrestrial Neutrinos of Radioactive Origin

Terrestrial neutrinos from β-decay originate from radioactive isotopes in the Earth, mostly from the Thorium-, Neptunium-, Uranium- and Actinium series of naturally radioactive heavy elements and their daughter products, and are electron antineutrinos. It is estimated that this flux amounts to about 7 · 10 ⁶ cm⁻²s⁻¹, assuming an effective thickness of the Earth's crust of 15 km (Young, 1973). Of this flux only about 10⁵ cm⁻²s⁻¹ have energies above the threshold for detection by the reaction

(4.59) ${\overline{\nu }}_e\left(>1.8\text{MeV}\right)+p\to n+e^{+}$

In addition cosmic ray induced radioactivity in the atmosphere and the top layer of the Earth's crust contribute through beta decay to the terrestrial neutrino and antineutrino flux.

But also the fission processes that take place in nuclear reactors and their by-products make locally significant contributions to the antineutrino flux. Neutrinos from β-decay are electron neutrinos and antineutrinos and are of comparatively low energy, mostly in the keV to MeV range.

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Properties and sources of radiation

Syed Naeem Ahmed , in Physics and Engineering of Radiation Detection (Second Edition), 2015

1.3.A Decay energy or Q-value

Decay energy is a term used to quantify the energy released during the decay process. It can be used to determine whether a certain decay mode for a nucleus is possible or not. To understand this, let us suppose a nucleus X goes through a decay mode that transforms it into a nucleus Y with a subsequent emission of a particle d. This reaction can be written as

(1.3.1) $X\to Y+d.$

According to the law of conservation of energy, the total energy before and after the decay should be equal; that is,

(1.3.2) $E_{0,X}+T_X=E_{0,Y}+T_Y+E_{0,d}+T_d,$

where E ₀ stands for the rest energy and T represents the kinetic energy. The rest energy can be computed from the Einstein relation E ₀=m ₀ c ², where m ₀ is the rest mass. Since the decaying nucleus X can be assumed to be at rest, we can safely use T _X =0 in the above relation. If we represent the rest masses of X and Y by m _X and m _Y , the above equation would read

(1.3.3) $(m_X-m_Y-m_d)c^2=T_Y+T_d.$

Now, it is evident that the left-hand side of this relation must be positive in order for the kinetic energy to be positive and meaningful. In other words, the decay would be possible only if the left-hand side is positive valued. Both the left- and right-hand sides of this relation are termed the decay energy, or the Q-value. That is,

(1.3.4) $Q_d=T_Y+T_d$

or

(1.3.5) $Q_d=(m_X-m_Y-m_d)c^2.$

The first relation above requires knowledge of the kinetic energy taken away by the decaying nucleus and the emitted particle. These energies are difficult to determine experimentally, however. Therefore, generally one uses the second relation containing the mass terms to determine the decay energy. If this energy turns out to be negative, then the decay is not possible unless energy is supplied through an external agent, such as by bombarding the material with high-energy particles. A positive Q-value signifies that the isotope is unstable with respect to that particular mode of decay. Note that if a nucleus has a positive Q-value for one decay mode, this does not guarantee that it can decay through other modes as well (see example below).

Since atomic data tables list isotope masses in a.m.u., one must multiply masses in the above equation by the a.m.u.-to-kg conversion factor. We can also convert Joules to MeV in the above relation to transform it into a more computationally convenient form.

(1.3.6) $Q_d=(m_X-m_Y-m_d)8.94\times {10}^{16}\mathrm{J}(m\mathrm{in}\mathrm{kg})$

(1.3.7) $=(m_X-m_Y-m_d)931.502\mathrm{MeV}(m\mathrm{in}\mathrm{a}.\mathrm{m}.\mathrm{u}.)$

Care should be exercised when substituting masses in the above relation. As it stands, the relation is valid for nuclear masses. If one wishes to use atomic masses, the mass of electrons should be properly accounted for as explained later in this section.

The Q-value can be used to determine the kinetic energies of the daughter nucleus and the emitted particle. To demonstrate this, let us substitute $T=\frac{1}{2}m{v}^2$ in Eq. 1.3.5. This gives

(1.3.8) $T_d=Q_d-\frac{1}{2}{m}_Y{v}_d,$

where m _Y and v _Y represent the mass and velocity of the daughter nucleus, respectively. The velocity of the daughter nucleus can be determined by applying the law of conservation of linear momentum, which in this case gives

(1.3.9) $m_Y{v}_Y=m_d{v}_d.$

Note that here we have assumed that the parent nucleus was at rest before the decay. The velocity v _Y from this equation can now be substituted into equation 1.3.A to get

(1.3.10) $T_d=\left[\frac{m_Y}{m_Y+m_d}\right]Q_d.$

Similarly, the expression for the kinetic energy of the daughter nucleus is given by

(1.3.11) $T_Y=\left[\frac{m_d}{m_d+m_Y}\right]Q_d.$

Let us now write the Q-value relations for α and β decays.

$\begin{array}{cc}\mathrm{\alpha }-\text{decay}:& Q_{\mathrm{\alpha }}=(m_X-m_Y-m_{\mathrm{\alpha }})c^2\\ \mathrm{\beta }-\text{decay}:& Q_{\mathrm{\beta }}=(m_X-m_Y-m_{\mathrm{\beta }})c^2\end{array}$

Note that the above relation is valid for nuclear masses only. For atomic masses, the following equations should be used

$\begin{array}{ll}\mathrm{\alpha }-\text{decay}:\hfill & Q_{\mathrm{\alpha }}=(M_X-M_Y-M_{\mathrm{\alpha }})c^2\hfill \\ \mathrm{\beta }-\text{decay}:\hfill & Q_{\mathrm{\beta }}=(M_X-M_Y)c^2\hfill \end{array}$

Here M stands for atomic mass; that is, M _α is the mass of the helium atom and not the helium nucleus.

Example:

Determine whether actinium-225 can decay through α as well as β modes.

Solution:

The α decay reaction for actinium-225 can be written as

${}_{89}{}^{225}\mathrm{A}\mathrm{c}\to {}_{87}{}^{221}\mathrm{F}\mathrm{r}+{}_2{}^4\mathrm{H}\mathrm{e}.$

The Q-value for this reaction in terms of atomic masses is

$\begin{array}{ll}{Q}_{\mathrm{\alpha }}\hfill & =(M_{\mathrm{Ac}}-M_{\mathrm{Fr}}-M_{\mathrm{\alpha }})931.502\hfill \\ \hfill & =(225.023229)-221.014254-4.002603)931.502\hfill \\ \hfill & =5.93\mathrm{MeV}.\hfill \end{array}$

If actinium went through β-decay, the decay equation would be written as

${}_{89}{}^{225}\mathrm{A}\mathrm{c}\to {}_{90}{}^{225}\mathrm{T}\mathrm{h}+e,$

with a Q-value in terms of atomic masses given by

$\begin{array}{ll}{Q}_{\mathrm{\beta }}& =(M_{\mathrm{Ac}}-M_{\mathrm{Th}})931.502\\ & =(225.023229-225.023951)931.502\\ & =-0.67\mathrm{MeV}.\end{array}$

Since the Q-value is positive for α-decay, we can say with confidence that actinium-225 can emit α-particles. On the other hand, a negative Q-value for β-decay indicates that this isotope cannot decay through electron emission.

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SUPERCONDUCTIVITY IN THE ACTINIDES*

James L. Smith , in Superconductivity in D- and F-Band Metals, 1980

III SUPERCONDUCTIVITY AND f ELECTRONS

In this section a few significant properties of each f-band superconductor are highlighted. The references should be consulted for full discussions since they were selected on that basis. Figure 1 shows lanthanum, actinium, thorium, and americium as superconductors. They have some f character but certainly exhibit no magnetic effects. These elements have f bands above the Fermi energy. (Americium with its six well-localized, f electrons in a nonmagnetic, J = 0 state is included in this nonmagnetic category because of the obvious effect of the additional f levels above the Fermi energy.) The existence of these unfilled bands is shown, for example, by depressed melting points (Matthias et al., 1967), by the double hexagonal close-packed (dhcp) structure of lanthanum and americium (Johansson and Rosengren, 1975), and by the need for including some f character in the calculation of the Fermi surface of thorium (Freeman and Koelling, 1974). These materials are fairly straightforward superconductors with T_c's largely understandable in terms of d-band superconductivity but they are still affected to varying degrees by their f character.

Lanthanum (T_c ∼ 5K, dhcp phase) has been discussed in great detail by Probst and Wittig (1978). It has a high T_c that is increased to ∼13K by a pressure of 200 kbar. Although it has a high γ, this cannot be an important aspect of its superconductivity since the nonsuperconductors scandium, yttrium, and lutetium also have high γ's. As Probst and Wittig conclude, the high T_c must be phonon related. Lanthanum does have a significantly low θ _D . More specifically, the evidence for several pressure-induced phase transitions shows the f character in the bonding and this is the origin of phonon softenings that can raise T_c's so effectively. The feature of f electron bonding that causes the elements to exhibit so many exotic structures, also means that the typical vibrational modes must be more exotic than for non f-band elements (Weling, 1977). Put more simply, lattice instabilities raise T_c 's, and if magnetism did not show up so quickly in the f series, the T_c's might be very high.

Actinium has had no reported low-temperature measurements, and the reasons are obvious. It is a β emitter with a half-life of about twenty years. Pure actinium then generates ∼50 mW/g of radioactive self-heating. Its daughters grow in exponentially in days so that for three-month-old actinium, there is ∼18 W/g heating, 1000 ppm lead, and a gamma ray emission from the daughters that is a major health hazard. Furthermore, its high chemical activity makes it very difficult to purify. On the theoretical side, Johansson and Rosengren (1975) predict a T_c for actinium of more than 10K. This is because their pseudopotential calculation lead them to expect it to resemble lanthanum under pressure. On the other hand, if actinium has no significant f character, it should resemble the trivalent nonsuperconductors scandium, yttrium, and lutetium. (An experiment to resolve these arguments is planned.) I point out that this same Johansson and Rosengren paper anticipated the recent demonstration of superconductivity in americium and trivalent europium.

Thorium (T_C∼1.4K, fcc structure) is in many respects the most puzzling of these elements because it appears to be such an ordinary BCS superconductor (Haskell et al., 1972). This is not inconsistent with the views expressed here, but there does appear to be one measurement that begins to raise suspicions of more interesting behavior. Fertig et al. (1972) showed that under pressure, T_c drops until 60 kbar in a manner consistent with a BCS superconductor (somewhat unusual for a "transition" metal), but then goes through a weak minimum at 75 kbar, and drops slowly up to the highest measured pressure of 160 kbar. They say this behavior could be associated with a variation of the Fermi surface or a phase change. Either of these changes can signal the presence of f character. We also consider some thermodynamic correlations of entropy in f electron metals. It is clear from a correlation of room temperature entropy to the metallic radius that thorium cannot be completely tetravalent but must contain some f character (Ward and Hill, 1976). Furthermore, Ward (1979) speculates that f electron effects will be seen in the description of superconductivity in thorium hydrides. Thorium is not as simple as it has appeared.

Protactinium superconductivity has been the subject of conflicting reports for many years. Recent work of Smith, Spirlet, and Müller (1979) settles this conflict and finds a T_c of 0.43K (body-centered tetragonal structure) for a high purity single crystal. It is satisfying that this T_c falls smoothly between thorium and uranium as suggested by the trends of properties in Fig. 2. Very little other information on protactinium is available, but it seems likely that its T_c is partially depressed by the onset of electron correlations, an effect that is pronounced in uranium. If so, a positive pressure effect on the T_c is certainly to be expected (as reported by Fowler et al., 1974).

Americium was discovered to be superconducting by Smith and Haire (1978) with a T_c of 0.79K for the dhcp structure; and a T_c of 1.05K for the fcc structure. This latter high-temperature phase had been accidentally retained to room temperature with the addition of 2000 ppm ytterbium as an impurity. We then have a remarkable parallel to the situation of lanthanum with 2000 ppm gadolinium (Levgold et al., 1977). Indeed the parallel between lanthanum and americium is even more complete (Smith and Haire, 1978). This correspondence shows that americium with six localized f-electrons must owe many of its properties to the remaining f bands that are above the Fermi energy. However, its density of states(∼γ) is extremely low (Fig. 2) and appears to be the primary cause of its low T_c compared to lanthanum. Americium is also reported to have a rather high critical field (Smith, Stewart, Huang, and Haire, 1979). I speculate that this could be caused by some magnetic nature of the electrons arising from a slightly imperfect J = 0 ground state; that is, the metal might not be exactly trivalent. Determination of the pressure dependence of T_c would also certainly be interesting for a superconductor that has both localized f-electrons and f contributions at the Fermi energy since the separable effects would be mixed. It is clear that sufficient pressure will delocalize the six f-electrons (similar to γ-cerium) and cause the compressed americium to resemble plutonium, as has been suggested by Kmetko (1979) and Johansson (1979).

Closely related to the americium is the recent discovery by Matthias et al. (1979) that EuIr₂ is a superconductor, similar in every respect to ScIr₂, YIr₂, LaIr₂, and LuIr₂. It appears that if europium metal were trivalent, as is the Eu in EuIr₂, pure europium would also be a superconductor similar to americium (its actinide analogue) as expected by Johansson and Rosengren (1975).

The other superconductors in Fig. 1 are cerium, uranium, neptunium, and plutonium in which the effects of magnetism must be considered. Cerium and uranium have been discussed by others in great detail. In contrast, neptunium and plutonium are so close to being magnetic that their inclusion in the "superconducting under pressure" category in Fig. 1 is speculation.

Cerium in its room-temperature fcc phase (γ-Ce) is magnetic, while, its low-temperature fcc phase (α-Ce) and higher pressure phases are superconducting (Probst and Wittig, 1978). There are three models for the γ-α phase transition that recognize that this is not a valence change but is simply a loss of the magnetic nature of the f band in γ-Ce. Johansson (1974) views it as a Mott transition of the f electron, that is, the f electron goes sharply from a localized, magnetic state to an itinerant, band state as the pressure is increased. Hill and Kmetko (1975) see the transition as a hybridization of the d band with the f band to destroy magnetism. Probst and Wittig (1978) suggest a simple band broadening picture. These viewpoints are all in qualitative agreement and the papers contain extensive information.

Uranium cannot be considered a bulk superconductor above ∼0.1K. The study of its low-temperature behavior is too compicated to discuss here. The Hill plot is comprehensive with regard to its superconducting and magnetic compounds and alloys (Lam and Aldred, 1974). The more difficult question of the behavior of pure uranium is summarized by Bader and Knapp (1975). They find that the principal effects involved in the superconducting behavior are large Cooper-pair-weakening interactions and phonon mode shifting. There is not a more typical f-electron superconductor.

Neptunium and plutonium are not superconducting at normal pressure (Smith and Elliott, 1977; Meaden and Shigi, 1964). In view of their strong similarity to uranium, the possibility of their superconductivity under pressure was discussed by Hill (1970). Similarly, in light of the analogy to molybdenum and niobium stabilized γ-U (T_C∼2K), an extrapolated value of T_c for stabilized bcc neptunium is 30 mK (Hill et al., 1974; Smith and Elliott, 1977) and 1 mK for bcc plutonium (Hill et al., 1974). Clearly these elements are so close to being magnetic (Brodsky, 1978) that study of their superconducting properties is difficult.

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The Actinide Elements☆

Rudy J.M. Konings , ... Jean-Christophe Griveau , in Comprehensive Nuclear Materials (Second Edition), 2020

7.01.1 Introduction

The actinides are the 15 elements with atomic number 89–103 in the periodic system. The International Union of Pure and Applied Chemistry (IUPAC) has recommended that they are named actinoids (meaning "like actinium"), but this has never found general acceptance. In these elements the 5 f electron subshell is progressively filled leading to the generalized [Rn 7s ²5f ⁿ ] configuration. Unlike the lanthanides, in which the 4f electrons lie in the interior of the xenon core region and thus hardly contribute to the chemical bonds (called "localized") the 5f electrons show a much more diverse character, particularly in the metallic state. ¹ The 5f electrons in the elements thorium to neptunium are placed in the valence shell (often called 'itinerant' or 'delocalized'), and show substantial covalent bonding, whereas the 5f electrons in the elements americium to lawrencium are localized. Plutonium and americium have a transition position, showing both localized and delocalized behavior depending on temperature, pressure and magnetic field. ^2,3

The actinides are radioactive elements, their isotopes having strongly variable half-lives. Owing to the short half-life, compared to the age of the earth, majority of the actinides have decayed and cannot be found in nature. Only the long-lived isotopes ²³²Th, ²³⁵U and ²³⁸U are of primordial origin, and possibly ²⁴⁴Pu. Also, ²³¹Pa is found in very low concentrations in natural minerals (e.g., pitchblende ores) but it is a product of the ²³⁵U (4n + 3) decay chain. ⁴ Most other actinides are man-made elements. They were synthesized by nuclear reactions using reactors and accelerators in the period 1940 (Np) to 1961 (Lr). The metals from Th to Cm are available in gram quantities that have allowed experimental determination of (some of) their physicochemical properties; Bk and Cf metal have been prepared in milligram quantities, Es in microgram quantities that have allowed very limited investigations. The metals Fm and beyond have not been prepared in pure form.

The main technological relevance of the actinides is their use as fuel for nuclear fission reactors, particularly the nuclides ²³³U, ²³⁵U and ²³⁹Pu, which fission with thermal neutrons. ²³⁵U and ²³⁹Pu occur in the so-called U/Pu fuel cycle. ²³⁵U is present in 0.72% in natural uranium, ²³⁹Pu is formed when uranium is irradiated in a reactor as a result of neutron capture by ²³⁸U. ²³³U is formed by neutron capture of ²³²Th in the Th/U fuel cycle. The vast majority of nuclear power reactors use oxide fuel, but carbide and nitride as well metallic alloys fuels have been studied since the early days of reactor development. ⁵

In this article, we discuss the physico-chemical properties of the actinide metals, with emphasis on the elements Th to Cm for which experimental data on bulk samples are generally existing. The trends and systematics in the properties of the actinide series will be emphasized and compared with those the 4f series. These physicochemical data are essential for understanding and describing the properties of multi-element alloys and actinide containing compounds.

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Sediments, Diagenesis, and Sedimentary Rocks

W.H. Orem , R.B. Finkelman , in Treatise on Geochemistry, 2003

7.08.6.1 Abundance of Elements

Although coal consists largely of organic matter, the inorganic constituents in coal commonly attract a disproportionate amount of attention and may ultimately determine how a coal will be used. Except for a few extremely rare elements (actinium, astatine, francium, polonium, protactinium), every element has been found in coal. In ash (the inorganic residue from the complete incineration of coal), elemental concentrations range from the parts per trillion level to more than 50  wt%. Table 2 contains estimates of the arithmetic and geometric means for 79 elements reported in US coal. Although few, if any, coal samples have compositions similar to that of "average" US coal, these values are useful in establishing norms for comparisons. In most coal samples silicon, aluminum, sulfur, iron, and calcium are present at levels of several percent by weight. All other elements (excluding carbon, oxygen, hydrogen, and nitrogen), are usually present at concentrations below 1wt.% (Bragg et al., 1998).

Table 2. Arithmetic and geometric means for chemical elements in US coal

Component	Arithmetic		Geometric		Max.	Num.
	Mean	SD	Mean	SD
Ash (%)	13.1	8.3	10.9	1.9	50.0	7,976
Aluminum (Al) (%)	1.5	1.1	1.1	2.1	10.6	7,882
Antimony (Sb) (ppm)	1.2	1.6	0.61	3.6	35	7,473
Arsenic (As) (ppm)	24	60	6.5	5.5	2,200	7,676
Barium (Ba) (ppm)	170	350	93	3.0	22,000	7,836
Beryllium (Be) (ppm)	2.2	4.1	1.3	3.5	330	7,484
Bismuth (Bi) (ppm)	(<1.0)	ND	ND	ND	14	920
Boron (B) (ppm)	49	54	30	3.1	1,700	7,874
Bromine (Br) (ppm)	17	19	9.1	4.1	160	4,999
Cadmium (Cd) (ppm)	0.47	4.6	0.02	18	170	6,150
Calcium (Ca) (%)	0.46	1.0	0.23	3.3	72	7,887
Carbon (C) (%)	63	15	62	1.3	90	7,154
Cerium (Ce) (ppm)	21	28	5.1	7.1	700	5,525
Cesium (Cs) (ppm)	1.1	1.1	0.70	3.2	15	4,972
Chlorine (Cl) (ppm)	614	670	79	41	8,800	4,171
Chromium (Cr) (ppm)	15	15	10	2.7	250	7,847
Cobalt (Co) (ppm)	6.1	10	3.7	2.9	500	7,800
Copper (Cu) (ppm)	16	15	12	2.1	280	7,911
Dysprosium (Dy) (ppm)	1.9	2.7	0.008	35	28	1,510
Erbium (Er) (ppm)	1.0	1.1	0.002	73	11	1,792
Europium (Eu) (ppm)	0.40	0.33	0.12	5.8	4.8	5,268
Fluorine (F) (ppm)	98	160	35	15	4,000	7,376
Gadolinium (Gd) (ppm)	(1.8)	ND	ND	ND	39	2,376
Gallium (Ga) (ppm)	5.7	4.2	4.5	2.1	45	7,565
Germanium (Ge) (ppm)	5.7	14	0.59	16	780	5,689
Gold (Au) (ppm)	(<0.05)	ND	ND	ND	ND	ND
Hafnium (Hf) (ppm)	0.73	0.68	0.04	38	18	5,120
Holmium (Ho) (ppm)	(0.35)	ND	ND	ND	4.5	1,130
Hydrogen (H) (%)	5.2	0.09	5.2	1.2	9.5	7,155
Indium (In) (ppm)	(<0.3)	ND	ND	ND	ND	ND
Iodine (I) (ppm)	(<1.0)	ND	ND	ND	ND	ND
Iridium (Ir) (ppm)	(<0.001)	ND	ND	ND	ND	ND
Iron (Fe) (ppm)	1.3	1.5	0.75	2.9	24	7,882
Lanthanum (La) (ppm)	12	16	3.9	6.0	300	6,235
Lead (Pb) (ppm)	11	37	5.0	3.7	1,900	7,469
Lithium (Li) (ppm)	16	20	9.2	3.3	370	7,848
Lutetium (Lu) (ppm)	0.14	0.10	0.06	4.7	1.8	5,008
Magnesium (Mg) (%)	0.11	0.12	0.07	2.7	1.5	7,887
Manganese (Mn) (ppm)	43	84	19	3.9	2,500	7,796
Mercury (Hg) (ppm)	0.17	0.24	0.10	3.1	10	7,649
Molybdenum (Mo) (ppm)	3.3	5.6	1.2	6.5	280	7,107
Neodymium (Nd) (ppm)	(9.5)	ND	ND	ND	230	4,749
Nickel (Ni) (ppm)	14	15	9.0	2.8	340	7,900
Niobium (Nb) (ppm)	2.9	3.1	1.0	7.7	70	6,843
Nitrogen (N) (%)	1.3	0.4	1.3	1.4	13	7,153
Osmium (Os) (ppm)	(<0.001)	ND	ND	ND	ND	ND
Oxygen (O) (%)	16	12	12	2.0	60	7,151
Palladium (Pd) (ppm)	(<0.001)	ND	ND	ND	ND	ND
Phosphorus (P) (ppm)	430	1,500	20	20	58,000	5,079
Platinum (Pt) (ppm)	(<0.001)	ND	ND	ND	ND	ND
Potassium (K) (%)	0.18	0.21	0.10	3.5	2.0	7,830
Praseodymium (Pr) (ppm)	(2.4)	ND	ND	ND	65	1,533
Rhenium (Re) (ppm)	(<0.001)	ND	ND	ND	ND	ND
Rhodium (Rh) (ppm)	(<0.001)	ND	ND	ND	ND	ND
Rubidium (Rb) (ppm)	21	20	0.62	41	140	2,648
Ruthenium (Ru) (ppm)	(<0.001)	ND	ND	ND	ND	ND
Samarium (Sm) (ppm)	1.7	1.4	0.35	13	18	5,151
Scandium (Sc) (ppm)	4.2	4.4	3.0	2.3	100	7,803
Selenium (Se) (ppm)	2.8	3.0	1.8	3.1	150	7,563
Silicon (Si) (%)	2.7	2.4	1.9	2.4	20	7,846
Silver (Ag) (ppm)	(<0.1)	0.35	0.01	9.1	19	5,038
Sodium (Na) (%)	0.08	0.12	0.04	3.5	1.4	7,784
Strontium (Sr) (ppm)	130	150	90	2.5	2,800	7,842
Sulfur (S) (%)	1.8	1.8	1.3	2.4	25	7,214
Tantalum (Ta) (ppm)	0.22	0.19	0.02	13	1.7	4,622
Tellurium (Te) (ppm)	(<0.1)	ND	ND	ND	ND	ND
Terbium (Tb) (ppm)	0.30	0.23	0.09	7.7	3.9	5,024
Thallium (Tl) (ppm)	1.2	3.4	0.00004	205	52	1,149
Thorium (Th) (ppm)	3.2	3.0	1.7	5.0	79	6,866
Thulium (Tm) (ppm)	[0.15]	ND	ND	ND	1.9	365
Tin (Sn) (ppm)	1.3	4.3	0.001	54	140	3,004
Titanium (Ti) (%)	0.08	0.07	0.06	2.2	0.74	7,653
Tungsten (W) (ppm)	1.0	7.6	0.10	14	400	4,714
Uranium (U) (ppm)	2.1	16	1.1	3.5	1,300	6,923
Vanadium (V) (ppm)	22	20	17	2.2	370	7,924
Ytterbium (Yb) (ppm)	[0.95]	ND	ND	ND	20	7,522
Yttrium (Y) (ppm)	8.5	6.7	6.6	2.2	170	7,897
Zinc (Zn) (ppm)	53	440	13	3.4	19,000	7,908
Zirconium (Zr) (ppm)	27	32	19	2.4	700	7,913

All values are on a coal basis. Data are exclusively from the US Geological Survey (USGS) except for estimated values in parenthesis which are based on USGS and literature data. Values in brackets are calculated from cerium and lanthanum data and assuming a chondrite normalized rare-earth-element distribution pattern. (ND=no data; SD=standard deviation; Max.=maximum; Num.=number of samples).

The abundance of the inorganic constituents in coal varies at every level—between coal basins, between coal beds within a basin, and within coal beds—over distances from micrometers to kilometers. These variations are due to differences in the geologic and geochemical processes acting on the peat and the coal over geologic time (Swaine, 1990; Bouska, 1981). Variations in the plant communities, source material, detrital influx, diagenetic processes, and epigenesis all influence the type and abundance of the inorganic chemical constituents of coal.

The plants that were the precursors of the coal required a range of elements as nutrients or for structural support. Elements essential to plant metabolism include phosphorus, potassium, sulfur, calcium, and magnesium. Some plants also require boron, chlorine, copper, iron, manganese, molybdenum, and zinc (Severson and Shacklette, 1988). Plants may contribute inorganic constituents to coal in other ways. Several authors have noted the presence of crystalline and noncrystalline biological material, such as phytoliths and sponge spicules in peats (Andrejko and Cohen, 1984; Raymond et al., 1990). Some of this biogenically derived material may be preserved in coal as discrete particles.

Detrital input (air- and water-borne particulates and dissolved species) is one of the more important sources of the inorganic constituents in coal. Many of the minerals in the moderate- to high-ash coals (5 wt.% to more than 20 wt.%) occur intermixed with fragments of organic matter in distinct bands. Although many of the chemical elements may have been originally associated with the plants or with detrital particles, some of these elements are remobilized during the coalification process. Chemical and mineralogical evidence (Finkelman, 1981b) indicates that some of the remobilized elements are precipitated in the coal as authigenic minerals, whereas other elements, such as calcium, sodium, and magnesium can be lost during the coalification process.

The largest and most obvious minerals in coal are the epigenetic minerals that have precipitated in the cleat and fractures subsequent to coal formation. These minerals include sulfides, carbonates, and kaolinite. They are common but volumetrically minor constituents. Nevertheless, the epigenetic sulfide minerals can have a profound impact on the utility of the coal, because they contain potentially hazardous trace elements.

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Radiation Shielding and Protection

Robert W. Roussin , ... David K. Trubey , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

II.C Neutrons

Neutrons are neutral particles with a rest mass approximately the same as a proton. The most common sources of neutrons are nuclear chain reactors. Neutrons are also created in large quantities in some accelerators and in certain material mixtures by (α, n) reactions. This type of reaction is utilized in building small sources using, for example, a mixture of polonium and beryllium where the α particle from the polonium reacts with the beryllium. This (α, n ) reaction also leads to a neutron hazard from irradiated fuel elements which contain α-emitting actinides (actinium or elements higher than actinium in the periodic table). The element californium and a few other heavy nuclides will spontaneously fission, and therefore can be used as small sources of fission neutrons. A few nuclides, such as ²H and ⁹Be, can be a source of neutrons from the photoneutron reaction, that is, (γ, n).

The energy dependence of the fission neutron spectrum reaches a maximum (most probable energy) at about 0.7   MeV, but the more penetrating higher energies generally dominate shielding requirements. The spectrum is often described by a Maxwellian distribution.

(1) $\text{N}\left(\text{E}\right)=2{\pi }^{-1/2}{\text{T}}^{3/2}{\text{E}}^{1/2}{\text{e}}^{-\text{E}/\text{T}},$

where N(E) is the number of neutrons per unit energy about E and T a parameter equal to 2/3 of the average energy. The value of T for ²³⁵U is 1.29. The number of neutrons per thermal neutron-induced fission is about 2.4 for ²³⁵U. The number increases linearly with the energy of the neutron inducing the fission.

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Basic Concepts and Definitions

Michael F. L'Annunziata , in Radioactivity (Second Edition), 2016

2.5.3 Natural Radioactive Decay Chains

There are three naturally occurring decay chains, which begin with one of three long-lived parent nuclides. The three decay chains, namely the ²³²Th or thorium decay chain (4n), the ²³⁸U or uranium decay chain (4n   +   2), and the ²³⁵ U decay chain, also referred to as the actinium decay chain (4n  +   3), are illustrated in Figs. 2.1–2.3, respectively. The notations 4n, 4n   +   2, and 4n   +   3 refer to the mass number A for all nuclides in the respective decay chains, where n is a positive integer between 50 and 60. The notations are derived from the fact that the mass number (A) for all radionuclides in a given decay chain is a multiple of 4 because α decay results in a mass reduction of 4, whereas the mass number between parent and daughter does not change in β decay. Thus the mass numbers in the respective series agree with the relations 4n   = A, 4n   +   2   = A, and 4n   +   3   = A, where n is an integer between 50 and 60. There are radionuclides in the decay chains with very short half-lives (of the order of minutes and seconds). These short-lived nuclides have survived the billions of years since the formation of the Earth due to an equilibrium that develops between a long-lived parent and its shorter-lived daughters. Equilibrium between parent and daughter nuclides is discussed in detail in the chapter entitled "Radionuclide Decay, Radioactivity Units, and Radionuclide Mass". All radionuclides in the thorium, uranium, and actinium decay chains terminate with a stable isotope of lead, namely ²⁰⁸Pb, ²⁰⁶Pb, and ²⁰⁷Pb, respectively.

Figure 2.1. The ²³²Th natural decay chain.

Figure 2.2. The ²³⁸U natural decay chain.

Figure 2.3. The ²³⁵U natural decay chain, also referred to as the actinium decay chain.

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Including Actinides

Eteri Svanidze , in Handbook on the Physics and Chemistry of Rare Earths, 2019

3 Actinide-based superconductors

Actinide-based superconductors represent the smallest and least-studied group of superconducting materials [19,65,78,97–99]. While one might argue that the average critical temperatures of new actinide-based superconductors have been decreasing over the last five decades [19], the situation for uranium-based systems is not fully clear. What has been observed so far is that in general, the superconducting temperatures of actinide-based systems are typically rather low, requiring measurements in the milli-Kelvin regime for experimental verification. This poses a particular challenge for trans -uranium elements like actinium, protactinium, and plutonium, since their short half-lives (at least on the geological scale) essentially classify them as synthetic elements with rather limited availability [19]. Compounds based on trans-uranium elements suffer from self-heating due to radioactive decay, which means that the corresponding samples are never truly isothermal and could even remain in normal state at the center of the sample. The chemical changes in composition, produced by radioactive decay, often compromise sample purity and reliability of the data [65]. The materials themselves are expensive to obtain and hazardous to work with, requiring special regulatory permissions and laboratory environment. This issue is slightly alleviated, when only thorium- and uranium-containing materials are considered, as the main concern they pose is toxicity and not radioactivity [19].

Among actinide-based materials, the superconducting critical temperatures of uranium-based systems are much smaller, compared to the neptunium- and plutonium-containing compounds. The hybridization between 5f- and conduction electrons increases with increasing atomic number [65], which can perhaps explain higher values of the superconducting temperatures as we move from uranium- to neptunium- and plutonium-based materials. Additionally, one might argue that all of the known Pu-based superconductors belong to a very special family [100–108]. Within the same crystal structure, the superconducting pairing mechanism appear to change as the constituent elements are replaced by one another [109]. Indeed, plutonium-based superconductors seem to occupy a class of their own—a bridge between the low-temperature (heavy-fermion uranium- and cerium-based) superconductors and the high-temperature (non-heavy-fermion and cuprate) superconductors [109,110].

While small critical temperatures of uranium-based superconductors might seem discouraging, they give us a unique opportunity to easily change the ground state by variation of chemical composition, application of magnetic field or pressure. This transformation and accompanying phenomena frequently contradict commonly accepted theoretical models and predictions, giving us new insights into the underlying principles of not only superconductivity, but also other unconventional ground states [101,111–117]. Since f-band superconductors can be understood in a similar manner to d-band superconductors [118], by studying which parameters can be changed and how, we are gaining an invaluable insight into what governs the magnitude of the critical temperatures in other systems, providing a universal avenue toward improvement.

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