2.01 The Actinides Elements: Properties and
Characteristics
R. J. M. Konings, O. Benesˇ, and J.-C. Griveau
European Commission, Joint Research Centre, Institute for Transuranium Elements, Karlsruhe, Germany

ß 2012 Elsevier Ltd. All rights reserved.

2.01.1
2.01.2
2.01.2.1
2.01.2.2
2.01.2.3
2.01.2.4
2.01.3
2.01.3.1
2.01.3.2
2.01.3.3
2.01.4
2.01.4.1
2.01.4.2
2.01.4.3
2.01.4.4
2.01.4.5
2.01.4.6
2.01.4.7
2.01.4.8
2.01.5
References

Introduction
Crystallographic Properties

Crystal Structure
Effects of Pressure
Effects of Temperature
Effects of Radiation
Thermodynamic Properties
Heat Capacity and Entropy of the Crystalline State
Heat Capacity of the Liquid State
Heat Capacity and Entropy of the Gaseous State
Thermophysical and Electronic Properties
Thermal Expansion and Density of the Crystalline State
Electrical Resistivity of the Crystalline State
Thermopower of the Crystalline State
Thermal Conductivity of the Crystalline State
Thermal Conductivity of the Liquid State
Density of the Liquid State
Viscosity
Surface Tension
Summary and Outlook

Abbreviations
dhcp
fcc
IUPAC
OECD/NEA

Double hexagonal close-packed
Face-centered cubic
International Union of Pure and
Applied Chemistry
Organisation for Economic

Cooperation and Development/
Nuclear Energy Agency

2.01.1 Introduction
The actinides are the 15 elements with atomic numbers
89–103 in the periodic system. The International Union
of Pure and Applied Chemistry (IUPAC) has recommended that these elements are named actinoids
(meaning ‘like actinium’), but this has never found general acceptance. In these elements, the 5f electron subshell is progressively filled, leading to the generalized

1
2
2
3
4
5
7
7
10
11
12
12
12
14
15
17
18
18
18
18
19


[Rn 7s25f 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
The actinides are radioactive elements, their isotopes having strongly variable half-lives. Owing to the
short half-life, compared with the age of the earth,
majority of the actinides have decayed and cannot be
found in nature. Only the long-lived isotopes 232Th,
235
U, and 238U are of primordial origin, and possibly
244
Pu. Also, 231Pa is found in very low concentrations
in natural minerals (e.g., pitchblende ores), but it is a
1


2

The Actinides Elements: Properties and Characteristics

product of the 235U (4n þ 3) decay chain.3 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 metals
have been prepared in milligram quantities and Es in
microgram quantities and therefore only limited investigations have been possible. 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 0.7%
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.4

Table 1

Ac
Th
Pa
U

Np

Pu

Am


Cm
Bk
Cf
Es
a

a
a
b
a
b
a
b
g
a
b
g
a
b
g
d
d0
e
a
b
g
a
b
a
a

a

In this chapter, we discuss the physicochemical
properties of the actinide metals, with emphasis on
the elements Th to Cm for which experimental data
on bulk samples generally exist. The trends and systematics in the properties of the actinide series will
be emphasized and compared with those of the 4f
series. These physicochemical data are essential for
understanding and describing the properties of multielement alloys (see Chapter 2.05, Phase Diagrams
of Actinide Alloys) and actinide containing compounds (Chapter 2.02, Thermodynamic and Thermophysical Properties of the Actinide Oxides).

2.01.2 Crystallographic Properties
2.01.2.1

Crystal Structure

The stable crystallographic modifications of the actinides at atmospheric pressure are listed in Table 1.
Compared to the lanthanide series in which the hexagonal close-packed (hcp) and the face-centered
cubic (fcc) structures dominate, the actinide metals
show a remarkable variation in the structural

The crystal structure of the actinide metals
Structure

Space group

a (pm)

Cubic
Cubic

Cubic
Tetragonal
Cubic
Orthorhombic
Tetragonal
Cubic
Orthorhombic
Tetragonal
Cubic
Monoclinic
Monoclinic
Orthorhombic
Cubic
Tetragonal
Cubic
Hexagonal
Cubic
Cubic
Hexagonal
Cubic
Hexagonal
Hexagonal
Cubic

Fm 3 m
Fm 3 m
Im 3 m
I4/mmm
Fm 3 m
Cmcm

Im 3 m
Pnma
P42
Im 3 m
P21/n
I2/m
Fddd
Fm 3 m
I4/mmm
Im 3 m
P63/mmc
Fm 3 m

531.5
508.42
411
392.1
501.8
285.4
565.6
352.4
666.3
489.7
351.8
618.3
928.4
315.9
463.71
334
363.61

346.81
489.4

P63/mmc
Fm 3 m
P63/mmc
P63/mmc
Fm 3 m

349.6
503.9
341.6
338.4
575

a

b (pm)

c (pm)

Angle(s)

323.5
587.0

495.5
1075.9

472.3


488.7
338.8

482.2
1046.3
576.8

1096.3
785.9
1016.2

b ¼ 101.79
b ¼ 93.13

444
1124.1

g ¼ 120

1113.3

g ¼ 120

1106.9
1104.0

g ¼ 120
g ¼ 120


Vm (cm3 molÀ1)

r (g cmÀ3)

22.59
19.79
20.90
14.98
19.02
12.50
12.95
13.18
11.58
11.79
13.11
12.04
13.50
13.94
15.01
14.91
14.48
17.63
17.65

10.05
11.73
11.10
15.43
12.15
19.05

18.37
18.06
20.48
20.11
18.08
19.85
17.71
17.15
15.92
16.03
16.51
13.67
13.66

17.74
19.26
16.84
16.48
28.62

13.76
12.67
14.79
15.23
8.88

P42/mnm, P42/nm or P4n2.
Source: Edelstein, N. M.; Fuger, J.; Katz, J. J.; Morss, L. R. In The Chemistry of the Actinide and Transactinide Elements; Morss, L. R.,
Edelstein, N., Fuger, J., Katz, J. J., Eds.; Springer Verlag, 2006; Chapter 15, pp 1753–1835.



The Actinides Elements: Properties and Characteristics

properties at room temperature, as shown in Figure 1.
Particularly, the elements Pa–Pu have unusual low
symmetry (distorted) crystal structures. a-Pa is
body-centered tetragonal, and a-U and a-Np are
orthorhombic but with slightly different space
groups. a-Pu has a monoclinic crystal structure
with 16 atoms in the unit cell at room temperature.
Plutonium is unique in the periodic table of the
elements with six allotropes at atmospheric pressure
and one more at elevated pressure.
This complexity of the structural properties of
the actinides is also evident from Figure 2, which
shows the variation of the molar volume of the
a-phases of the actinides at room temperature and
atmospheric pressure, indicating that the actinides Pa
to Pu follow the trend in the (itinerant) d-transition

(a)

3

metals, whereas the actinides Am to Bk follow that
of the (localized) 4f metals. It is generally accepted
that this complex behavior is due to the active role
of the f-electron in the metallic bond and the
changes in temperature and pressure by which the
f-electron bonding character is affected. Experimental observations and electronic structure calculations

have indeed shown that the bonding in the transition
metals is dominated by d-electron contributions, that
in the lanthanides there is a lack of f-electron contribution, and that the actinides fall in between.5
2.01.2.2

Effects of Pressure

Pressure is expected to drive the atoms in the crystal
lattice closer to each other, forcing the electrons to

(b)

(c)

(d)
(e)

(f)

Figure 1 The crystal structures of the actinides at room temperatures: (a) a-Th, (b) a-Pa, (c) a-U, (d) a-Np, (e) a-Pu, (f) a-Am.

Vm(cm3 mol−1)

40

Y Zr Nb Mo Tc Ru Rh Pd Ag Cd
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

30
20

10
0

Ac Th Pa

U

Np Pu Am Cm Bk Cf

Es Fm Md No Lr

Figure 2 The molar volume of the actinide elements () compared with that of the lanthanides (○) and the 4d transition
metals (□).


4

The Actinides Elements: Properties and Characteristics

participate in the binding (delocalization),6 which
particularly affects the heavy actinides with localized f-electron behavior at ambient pressure.
Recent studies using diamond anvil cells coupled
to synchrotron radiation have provided strong evidence for that. As discussed by Heathman et al.,7
americium shows a remarkable decrease in volume
with increasing pressure (at ambient temperature)
with three transitions up to 100 GPa (Figure 3). Its
structure changes from hcp (Am-I) through fcc
(Am-II) to orthorhombic (Am-III and Am-IV), indicating the appearance of the itinerant character 5f
electrons. This behavior is also observed in curium,
with a puzzling supplementary magnetically stabilized Cm-III structure at 40–60 GPa.8 Uranium

shows a comparatively straightforward behavior and
the a-structure is stable up to 100 GPa, with a much
smaller volume decrease.6 A similar behavior has been
found for protactinium, its a-form being stable up to

80 GPa. This is clearly reflected in the isothermal bulk
modulus (Table 2), which is around 100 GPa for the
elements Pa to Np but around 30–40 GPa for Am and
Cm. The Am-IV phase shows a large bulk modulus
(more similar to that of uranium), as expected for a
metal with appreciable 5f-electron character in its
bonding. This is also evident from the comparison of
the actinide and lanthanide metals (Figure 4).
Uncertainty still exists about the bulk modulus
of a-plutonium. As discussed by Ledbetter et al.,12
the published B0 values at ambient range show a
large variation, as do the theoretical calculations.
The most accurate results for the isothermal bulk
modulus vary between 51(2) GPa13 and 43(2) GPa.14
2.01.2.3

Effects of Temperature

Detailed studies show that the crystal lattice of most
actinide metals expands with increasing temperature

1.00
0.95
0.90


Cm
I

0.85

α-U

Am
I

0.80

Cm
II

2%

V/Vo

0.75
Am
II

0.70

Cm
III
Am
III


0.65

Pa
I

4.5 %

7%

Pa
II

Cm
IV

0.60
0.55

Cm
V

Am
IV

0.50

11.7 %

0.45
0


10

20

30

40

50

60

70

80

90

100

Pressure (GPa)
Figure 3 The relative volumes as a function of pressure of several actinide metals.

Table 2

B0 (GPa)
0
B0
References


0

The isothermal bulk modulus (B0) and its pressure derivative (B0 ) of the actinide elements at ambient temperature
a-Th

a-Pa

a-U

a-Np

a-Pu

a-Am

a-Cm

58(1)
4.2(3)
9

118(2)
3.3(2)
6

104(2)
6.2(2)
6


118(2)
6.6(6)
10

49
12.4
11

29.8(2)
3.6(2)
6

36.5(3)
4.6(2)
8


The Actinides Elements: Properties and Characteristics

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

150

B0 (GPa)

5

100

50


0

Ac Th Pa

U

Np Pu Am Cm Bk Cf

Es Fm Md No

Lr

Figure 4 The isothermal bulk modulus (B0) of the actinide elements (○) compared with that of the lanthanides ().

8
δ

ε

6
DL/L (%)

δЈ

γ

Liquid

β


4

2
α
0

300

500

700
T (K)

900

1100

Figure 5 The thermal expansion of Pu. Made after
Schonfeld, F. W.; Tate, R. E. Los Alamos National
Laboratory, Technical Report LA-13034-MS; 1996.

Moreover, the stability of the crystalline state of
the actinide metals varies significantly. The melting
temperature is high for thorium, similar to that of the
transition metals in group IVB, and low for Np and
Pu (Figure 6).
When applying high temperature as well as high
pressure to the actinides, phase changes can be suppressed, as is shown in Figure 7. For example, the triple
point for the a–b–g equilibrium in uranium is found at

about 1076 K and 31.5 kbar; above this pressure, orthorhombic a-U directly transforms in fcc g-U.17 In plutonium, the g-, d-, and d0 -phases disappear at relatively
low pressure and are replaced by a new phase designated z. In contrast to the other actinides, plutonium
shows a negative slope for the liquidus down to the
b-z-liquid triple point (773 K, 27 kbar) reflecting
the increase in density upon melting.17
2.01.2.4

and evolves to a simple cubic arrangement close to
their melting temperature, similar to the lanthanide
elements. (For numerical data on the thermal expansion, see Section 2.01.4.1) As the atoms move away
from each other, the electrons in the 5f metals tend
to favor a localized state. As discussed by Vohra and
Holzapfel,15 this is particularly important for Np
and Pu, which are on the threshold of localization/
itinerancy. The case for plutonium is much more
complex, as shown in Figure 5. The crystal lattice
of plutonium expands for the a-, b-, g-, and e-phases,
and the g- to d-transition has a positive expansion.
The d- and d0 -phases have negative thermal expansion and the d- to d0 - and d0 - to e-transitions show a
negative volume change, as is the case upon melting.
Dynamic mean field calculations show that the
monoclinic a-phase of Pu is metallic, whereas fcc d
is slightly on the localized side of the localization–
delocalization transition.16

Effects of Radiation

The a-decay of the actinides taking place in the
crystal lattice creates an alpha particle and a recoil
atom. The recoil atom produced has a range of about

12 nm and causes a dense collision cascade with typically about 2300 displacements (Frenkel pairs) within
a short distance, around 7.5 nm in size. The a-particle
has a path of about 10 mm, with a cascade of about 265
displacements at the end of its range.18 Although
recombination will take place, point defects and
eventually extended defects (dislocations, dislocation
loops) will survive in the crystal lattice, resulting in
changes in the properties of the materials. Computer
simulations of the radiation effects in fcc plutonium
have shown that the defect recombination stage is
much longer than that in other metals and that the
vacancies do not seem to form clusters.19 In addition
to the radiation damage, helium ingrowth takes place.
As discussed by Hecker and Martz,20 the expansion of the lattice of a-Pu is significant due to


6

The Actinides Elements: Properties and Characteristics

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

2500

Tfus (K)

2000
1500
1000
500


Ac Th Pa

U

Np Pu Am Cm Bk Cf

Es Fm Md No Lr

Figure 6 The melting point of the lanthanide () and actinide (○) metals. The estimated values are indicated by .

1100
1200

γ
β
α

800

γ

900

T (K)

T (K)

1000


Liquid

1000

800

Neptunium

β

700

600

Uranium

600

400
0

10

20

30

500

40


α
0

5

10

15

P (kbar)

25

30

35

1600

1000
900

δЈ
ζ

600

γ


γ

1400

T (K)

700

Liquid

1500

Liquid

ε

800

T (K)

20

P (kbar)

δ

1300

β


500

β
400
300
0

1200

Plutonium

α
10

20

30

40

50

60

70

P (kbar)

1100
0


Americium

5

10

15

20

25

30

P (kbar)

Figure 7 The pressure–temperature phase diagrams for U, Pu, Np, and Am. Reproduced from Lee, J. A.; Waldron, M. B.
Contemp. Phys. 1972, 13, 113–133.

self-irradiation, when held at cryogenic temperatures, saturating at about 10 vol.%. In contrast, the
(Ti-stabilized) b-phase shows a slight contraction
and the (Al-stabilized) d-phase a substantial contraction, the latter saturating at 15 vol.%. Of course this
is also reflected in other properties such as electrical
resistivity.21,22 The radiation effects recover upon
annealing to room temperature, a few percent of
the damage remaining. Gorbunov and Seleznev23
observed that a-Pu containing predominantly 239Pu

retains its crystal structure after prolonged storage

at room temperature. A sample of predominantly
shorter lived 238Pu (t1/2 ¼ 87.74 years) contains
both the a- and b-forms at immediate examination
and additionally the g-, Z-, and e-phases after a
similar storage period. Chung et al.24 showed by
X-ray diffraction and dilatometry measurements on
238
Pu-doped d-phase plutonium samples that the
lattice expansion by self-irradiation appears to be
the primary cause for dimensional changes during


The Actinides Elements: Properties and Characteristics

the initial 23 years of aging. Following the initial
transient, the density change is primarily caused by
a constant helium ingrowth rate as a result of particle
decay. The two effects were combined in an equation
for the expansion DL/L with an exponential (radiation damage) and a linear (helium ingrowth) part:
DL=L ffi A½1 À expðÀBt ފ þ Ct

½1Š

where A, B, and C are constants and t is time.
The self-irradiation is one of the main causes that
complicates the study of the heavy actinide metals. For
example, berkelium metal (t1/2 ¼ 314 days; $0.2%
249
Cf growth per day) shows signs of amorphization
(weak and diffuse X-ray spectra) at room temperature,

which improved after annealing and thermal cycling,
and the samples were found to contain two crystallographic structures at room temperature, double hexagonal close-packed (dhcp) and fcc, of which the former is
the stable form.25 An extreme case is Es; its crystal
structure has been resolved only by rapid electron
diffraction of thin film material due to the very short
half-life of the isotope used.26

2.01.3 Thermodynamic Properties
Many critical reviews of the thermodynamic properties of the actinide metals have been made since the
1960s. The first milestone was the review by Oetting
and coworkers,27 which gave recommended values
for Th to Cm. Ward et al.28 treated the same elements
but also gave recommendations for Cf and Es.
In addition, the room temperature thermodynamic
properties for the major actinides Th and U have
been reviewed by the CODATA team for key values
for Thermodynamics,29 while Th, U, Np, Pu, and Am
have been reviewed by the OECD/NEA team.30–33
The most recent evaluation was made by Konings
and Benesˇ,34 with emphasis on the high-temperature
properties. There are no large differences between
these studies for the major actinides and it is thus
clear that the recommendations given in this chapter
rely heavily on these studies (Tables 3 and 4).
2.01.3.1 Heat Capacity and Entropy of
the Crystalline State
The low-temperature heat capacity has been measured for the actinides Th through Am, in most
cases showing anomalies. The origin of these anomalies has generally not been explained adequately35
but is likely related to ordering phenomena and


7

f-electron promotion. The measurements for the
major actinides Th, U, and Pu in the a-structure
were made on gram-scale quantities, and the results
should thus be of an acceptable accuracy.
However, although the low-temperature heat
capacity of plutonium was measured by a remarkably
large number of authors,36–42 there is considerable
scatter among the results above 100 K (see Figure 8),
probably due to self-heating and radiation damage.
But even the results for 242Pu samples from the same
batch,40,41 which are affected less due to its much
longer half-life, differ considerably. The differences
in the heat capacity have a pronounced effect on the
standard entropy at T ¼ 298.15 K: 56.03 J KÀ1 molÀ1,39
56.32 J KÀ1 molÀ1,40 54.46 J KÀ1 molÀ1,41 and 57.1
J KÀ1 molÀ1.42 Especially, the results of Lashley
et al.42 indicate a very different shape of the heat
capacity curve of a-Pu, rising much steeper up to
T ¼ 100 K and saturating at a lower value near room
temperature. Although the relaxation method used
in that study is less accurate (Æ1.5% as claimed by
the authors) than the traditional adiabatic technique
used in the other studies, the difference is significant.
Lashley et al.42 attributed this to the buildup of radiation damage at the lowest temperatures, which they
tried to avoid by measuring upon cooling, and below
T ¼ 30 K by intermediate annealing at room temperature. However, other authors also addressed this
issue. For example, Gordon et al.41 performed a heating run from room temperature to T ¼ 373 K before
each low-temperature run. Moreover, no substantial

difference between the results for 239Pu and 242Pu
was observed in that study.
The electronic Sommerfeld heat capacity coefficient (ge), a property proportional to the density
of states at the Fermi level, varies strongly in the
actinide series (Table 5). It increases steadily up to
Pu but is very low for Am. For d-Pu the electronic
heat capacity coefficient ge is even three times higher
than that of a-Pu. This corresponds well with the
results of photoemission spectra48 that show a-Th
has a small density of states at the Fermi level compared with that of a-U, a-Np, and a-Pu (Figure 9).
In a-Am, the valence band is well removed from
the Fermi level. The low-temperature heat capacity
of other modifications of plutonium has been
measured recently. Specifically, the d-structure stabilized by Am or Ce doping shows clearly enhanced
values of the electronic heat capacity coefficient ge at
very low temperature.50,51
The standard entropies derived from the lowtemperature heat capacity data are given in Table 3,


8

Recommended entropy (J KÀ1 molÀ1) and the heat capacity (J KÀ1 molÀ1) of actinide elements in the solid and liquid phase
Phase

Th

Pa

U


Np

Pu

Am

Cm

a
b
Liquid
a
b
Liquid
a
b
g
Liquid
a
b
g
Liquid
a
b
g
d
d0
e
Liquid
a

b
g
Liquid
a
b
Liquid

S0 (298.15)

51.8 Æ 0.50
–
–
51.6 Æ 0.80
–
–
50.20 Æ 0.20
–
–
–
50.45 Æ 0.40
–
–
–
54.46 Æ 0.80
–
–
–
–
–
–

55.4 Æ 2.0
–
–
–
70.8 Æ 3.0
–
–

Cp ¼ A þ B Â T (K) þ C Â T2 (K) þ D Â T3 (K) þ E Â TÀ2 (K)
A

B

23.435
15.702
46
21.6522
39.7
47.3
28.4264
47.12
61.6420
46.45
30.132
40
36
46
17.6186
27.4160
22.0233

28.4781
35.56
33.72
42.80
30.0399
8.4572
43
52
28.409
28.2
37.2

8.945 Â 10À3
11.950 Â 10À3

Source: Konings, R. J. M.; Benesˇ, O. J. Phys. Chem. Ref. Data 2010, 39, 043102.

C

D or E
E ¼ À1.140 Â 104

12.426 Â 10À3
À6.9587 Â 10À3

29.8744 Â 10À6

E ¼ À1.1888 Â 105
E ¼ À33.1644 Â 106


À36.2372 Â 10À3

1.1589 Â 10À4

45.5523 Â 10À3
13.060 Â 10À3
22.959 Â 10À3
10.807 Â 10À3

À29.053 Â 10À3
33.167 Â 10À3

5.2026 Â 10À5
À7.587 Â 10À6

À4.142 Â 10À4

3.280 Â 10À6

D ¼ À1.8961 Â 10À8

Temperature
range (K)
298–1650
1650–2020
2020–2500
298–1443
1443–1843
1843–2500
298–941

941–1049
1049–1407
1407–2500
298–553
553–850
850–913
913–2500
298–399
399–488
488–596
596–741
741–759
759–913
913–2500
298–1042
1042–1350
1350–1449
1449–2500
298–1569
1569–1619
1619–2500

The Actinides Elements: Properties and Characteristics

Table 3


The Actinides Elements: Properties and Characteristics

Table 4

Recommended transition temperatures (K),
enthalpies (kJ molÀ1), and entropies (J KÀ1 molÀ1) of the
actinide metals

Th
Pa
U

Np

Pu

Am

Cm

Transition

Ttrs (K)

DtrsH

DtrsS

a!b
b!liq.
a!b
b!liq.
a!b
b!g

g!liq.
a!b
b!g
g!liq.
a!b
b!g
g!d
d!d0
d0 !E
e!liq.
a!b
b!g
g!liq.
a!b
b!liq.

1650 Æ 15
2020 Æ 10
1443 Æ 50
1843 Æ 50
941 Æ 2
1049 Æ 2
1407 Æ 2
553 Æ 5
850 Æ 3
913 Æ 3
399 Æ 1
488 Æ 1
596 Æ 2
741 Æ 4

759 Æ 4
913 Æ 2
1042 Æ 10
1350 Æ 5
1449 Æ 5
1569 Æ 50
1619 Æ 50

3.5 Æ 0.1
13.8 Æ 1.3
6.6 Æ 2.0
12.3 Æ 2.0
2.85 Æ 0.15
4.62 Æ 0.50
8.47 Æ 1.00
4.7 Æ 0.5
3.0 Æ 0.5
3.2 Æ 0.5
3.706 Æ 0.030
0.478 Æ 0.020
0.713 Æ 0.050
0.065 Æ 0.020
1.711 Æ 0.050
2.766 Æ 0.1
0.34 Æ 0.10
3.8 Æ 0.4
8.0 Æ 2.0
4.5 Æ 0.5
11.7 Æ 1.0


2.12
6.83
4.57
6.67
3.03
4.40
6.02
8.50
3.53
3.50
9.29
0.98
1.20
0.09
2.25
3.03
0.33
2.81
5.52
0.29
7.23

Source: Konings, R. J. M.; Benesˇ, O. J. Phys. Chem. Ref. Data
2010, 39, 043102.

40

Cp (J K–1 mol–1)

30


20

35

30

10
25
100

0

100

0

200

200
T (K)

300

400

300

400


Figure 8 The low-temperature heat capacity of
plutonium; ◊,37; È,38; È,39; r,40; D,41; ,42; ○,43.

Table 5

and the variation along the actinide metal series is
shown in Figure 10. The entropies of the elements
Th to Am are close to the lattice entropies of the
corresponding lanthanides, showing the absence of
magnetic contributions. The entropies of the other
actinide elements must be derived from estimations,
as experimental studies do not exist. To this purpose Ward et al.28 suggested a general formula by
correlating the entropy with metallic radius (r),
atomic weight (M), and magnetic entropy (Sm):
ru 3
Mu
Su ð298:15K Þ ¼ Sk ð298:15K Þ þ R ln
þ Sm
rk 2
Mk

½2Š

where u refers to the unknown (lanthanide or
actinide) element and k refers to the known element.
Sm is taken equal to Sspin ¼ (2J þ 1), where J is the
total angular momentum quantum number. The
entropy of Cm thus obtained is significantly higher
than that of the preceding elements, showing its
magnetic character.

The heat capacity of the actinide metals from
room temperature up to the melting temperature
has been reported for Th, U, and Pu with reasonable
accuracy and for Np for the a-phase only.
The values for the other metals are based on estimations. For example, Konings52 estimated the heat
capacity of americium metal from the harmonic,
dilatation, electronic, and magnetic contributions,
Cp ¼ Char þ Cdil þ Cele þ Cmag, whereas the heat capacity of g-americium was obtained from the trends in
the 4f and 5f series. The high-temperature heat capacity data for the actinide metals was analyzed in detail
by Konings and Benesˇ,34 who gave recommendations
for the elements Ac to Fm. The results for the elements
Th to Cm are summarized in Table 3.
Figure 11 shows the variation of the sum of
the transition entropies from the crystalline room
temperature phase to the liquid phase for the lanthanide and actinide series. This value is about constant
in the lanthanide series but shows large variation in
the actinide series, particularly for the elements
U–Np–Pu. The deviation from the baseline

The electronic heat capacity coefficient (ge) and Debye temperature (YD) of the actinide elements
Th
À2

À1

ge (mJ K mol )
YD (K)
References

4.3(0.05)

163.3(0.7)
44

Pa
5.0(0.5)
185(5)
45

U
a

9.1
256a
46

Np

Pu

Am

13.7(0.7)
240(4)
41

17(1)
153(2)
42

1(1)

120(20)
47

These values are for single crystal material, ge ¼ 9.9 mJ KÀ2 molÀ1 and YD ¼ 184 K for polycrystalline material.

a

9


10

The Actinides Elements: Properties and Characteristics

correlates well with the atomic volume of the metals
that is also anomalous for these elements, indicating
that the itinerant behavior of the 5f electrons and the
resulting lowering of the room temperature crystal
symmetry require additional entropy to reach a
similar disordered liquid state.

a-Th
Intensity (arb. units)

a-U
a-Np

2.01.3.2
a-Pu
a-Am

a-Cm

0

2

4

6

8

10

Energy below Ef (eV)
Figure 9 Valence-band photoemission spectra of the
actinide metals. Modified from Moore, K. T.; van der Laan, G.
Rev. Mod. Phys. 2009, 81, 235–298 by adding the results for
a-Cm by Gouder et al.49 Note that the spectrum for a-Th is
scaled up compared to the other spectra so that it is easily
visualized. In reality, it is much lower in intensity due to a
small f density of states at the Fermi level.

Heat Capacity of the Liquid State

The heat capacity of the actinide elements in the
liquid state is relatively poorly known. Experimental
data exist for Th, U, and Pu, and only the values
for Th and U are known with an acceptable accuracy. They were measured by drop calorimetric
techniques in a reasonable wide temperature range.

Semi-empirical models for liquid uranium suggest
a large electronic contribution to the heat capacity
of this element.53 The data for Pu, also obtained by
calorimetry, are scattered and measured in a limited
temperature range and the heat capacity value
for the liquid of this element is thus uncertain.
Figure 12 also shows the estimated values for Am
and Cm, based on assumptions considering the electron configurations.52,54

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
SЊ(M) (J K–1 mol–1)

100

80

60

40

Ac Th Pa

U

Np Pu Am Cm Bk

Cf

Es Fm Md No


Lr

Figure 10 The standard entropies of lanthanide () and actinide (○) metals at T ¼ 298.15 K; estimated values are
indicated by ().

S (DtrsS) (J K–1 mol–1)

25

La Ce

Pr

Nd Pm Sm Eu Gd Tb Dy Ho

Th

Pa

U

Er Tm Yb Lu

20
15
10
5
0

Ac


Np Pu Am Cm Bk

Cf

Es Fm Md No

Lr

Figure 11 The sum of the transition entropies of the lanthanide () and actinide (○) metals. The estimated values are
indicated by .


The Actinides Elements: Properties and Characteristics

Cp (liq) (J K–1 mol–1)

60

La Ce

Pr

Nd Pm Sm Eu Gd Tb Dy Ho

11

Er Tm Yb Lu

50


40

30
Ac Th Pa

U

Np Pu Am Cm Bk

Cf

Es Fm Md No

Lr

Figure 12 The heat capacity of the lanthanide () and actinide (○) metals in the liquid phase. Estimated values are
indicated by ().

2.01.3.3 Heat Capacity and Entropy of
the Gaseous State
The heat capacity and standard entropy for the ideal
gas can be calculated from the atomic energy levels
up to about 2000 K with reasonable accuracy using
statistical thermodynamic methods34 from the atomic
energy levels. As discussed in detail by Brewer,55 the
electronic states of the gaseous actinide elements are
complete (through experiments and estimations) to
about 15000 cmÀ1. The energies of the lowest electronic states for the elements Th to Cm are listed in
Table 6. Figure 13 shows a schematic representation

of the atomic spectra of the actinide elements, based
on the most recent assessments.56,57
The derived room temperature values for the
entropy and the high-temperature heat capacity
equations are shown in Table 7 and are taken from
the assessment by Konings and Benesˇ.34
The vapor pressure has been measured for all actinide metals except Md, No, and Lr. The majority of the
results deal with the elements Th–Am. Measurements
have also been made for Ac58 but they are of a very
approximate nature. The vapor pressure measurements for Es59 and Fm60 have been made on samples
containing 10À5–10À7at.% of the actinides in rare
earth alloys in combination with Henry’s law for dilute
solutions. These measurements have been carefully
reviewed by Konings and Benesˇ34 and the recommended enthalpies of sublimation derived from these
studies are listed in Table 7. The assessed vapor pressure curves (ln(p) vs. 1/T) are shown in Figure 14,
indicating that the vapor pressure of the actinide metals
varies strongly within the series. It roughly increases
with the atomic number but with prominent exceptions. For example, americium is much more volatile
than the neighboring Pu and Cm.
The enthalpies of sublimation of the actinides
are plotted in Figure 15 together with the values

Table 6
Spectroscopic characteristics of the ground
state and the lowest lying electronic states of the actinide
elements

Th

Pa


U

Np

Pu

Am

Cm

State

Spectroscopic
term

Energy level
(cmÀ1)

6d27s2
6d27s2
6d27s2
6d27s2
6d27s2
5f26d7s2
5f26d7s2
5f26d7s2
5f6d27s2
5f26d7s2
5f36d7s2

5f36d7s2
5f36d7s2
5f36d7s2
5f36d7s2
5f46d7s2
5f46d7s2
5f46d7s2
5f46d7s2
5f46d7s2
5f67s2
5f67s2
5f67s2
5f67s2
5f56d7s2
5f77s2
5f66d7s2
5f66d7s2
5f76d7s
5f77s2
5f76d7s2
5f76d7s2
5f76d7s2
5f76d7s2
5f76d7s2

3

0
2558.06
2869.26

3687.99
3865.48
0
825.42
1618.325
2659.405
2966.53
0
620.323
3800.830
3868.486
4453.419
0
2033.94
3450.995
3502.855
6643.51
0
2203.61
4299.659
6144.515
6313.866
0
10684
12974
14000
14258
0
302.15
815.655

1764.268
3809.358

F2
P0
3
F3
3
P2
3
P1
4
K11/2
4
I9/2
4
G5/2
4
I9/2
4
H7/2
5 o
L6
5 o
K5
5 o
L7
5 o
H3
5 o

I4
6
L11/2
6
L9/2
6
I7/2
6
L13/2
6
I9/2
7
F0
7
F1
7
F2
7
F3
7
K4
8
S7/2
8
H3/2
8
H5/2
10
D5/2
6

P7/2
9 o
D2
9 o
D3
9 o
D4
9 o
D5
9 o
D6
3

Source: Blaise, J.; Wyart, J. F. />Contents.html, 2009; Worden, E. F.; Blaise, J.; Fred, M.;
Trautmann, N.; Wyart, J. F. In The Chemistry of the Actinide and
Transactinide Elements; Morss, L. R.; Edelstein, N.; Fuger, J.;
Katz, J. J., Eds.; Springer Verlag, 2006; Chapter 16, pp 1836–1892.


12

The Actinides Elements: Properties and Characteristics

50 000

Energy (cm–1)

40 000

30 000


20 000

10 000

0
Ac Th Pa

U

Np Pu Am Cm Bk Cf Es Fm Md No Lr

Figure 13 Schematic representation of the atomic spectra of the actinide elements.

for lanthanide metals. The trend in the latter series
shows a typical pattern, with La, Gd, and Lu forming
an approximate linear baseline from which the others
systematically deviate. This trend can be understood
from the electronic states of the condensed and gaseous atoms, as discussed by Nugent et al.61 These
authors argued that the values for La, Gd, and Lu
are almost identical, due the fact that they have the
same number of valence electrons in the ground
states of the gaseous metal atom and the crystal.
In between, the enthalpy of sublimation decreases
regularly because of a corresponding increase in stability of the divalent ground states in the gaseous metal
atoms. A similar explanation can be applied to the
actinide series, although Th, Pa, U, Np, and Pu deviate
from this trend due to unusually large cohesive energies of the crystalline metals, resulting from the large
number of valence electrons in the metal.


2.01.4 Thermophysical and
Electronic Properties
2.01.4.1 Thermal Expansion and
Density of the Crystalline State
The thermal expansion of a number of actinide metals
has been studied, particularly for uranium and plutonium. The 1975 review by Touloukian et al.62 lists 48
studies for uranium, including single crystal and polycrystalline materials. The data show that a-uranium
has a different expansion along the three crystallographic axes; the a- and c-axis expand whereas the
b-axis shrinks with increasing temperature (Figure 16).

Also, a-Pa shows distinct different expansion along
the crystallographic axes (Figure 16). a-Np, in contrast, expands along the three axes of the crystal.
The complex thermal expansion behavior of plutonium has already been discussed in Section 2.01.2.4
and is shown in Figure 5. Schofeld and Tate63
reviewed the wealth of data for the various plutonium
modifications and the recommended values from
their work are listed in Table 9. a-Pu expands along
all three axes of the crystal, and the lattice expansion
continues for the b- and g-phases, but the cell parameter of the cubic d and d0 modifications decreases.
Americium, the last actinide for which thermal
expansion data exist, shows a regular thermal expansion in both crystallographic directions.68
Table 8 summarizes the linear thermal expansion
(DL/L0) for the actinide metals. The density can be
calculated from these data using the formula:
rðT Þ ¼

M
Vo ð1 þ 3DL=L0 ðT ÞÞ

½3Š


where M is the atomic mass, and V0 is the molar
volume at the reference temperature (see Table 1).
Note that the linear thermal expansion corresponds
to the average of the thermal expansion along the
three crystallographic axes.
2.01.4.2 Electrical Resistivity of
the Crystalline State
The electrical resistivity (r) of the elements Th to
Cm has been measured in the cryogenic temperature
range and the values up to 300 K are shown in


Table 7

The enthalpy of formation (kJ molÀ1), the absolute entropy (J KÀ1 molÀ1), and the heat capacity (J KÀ1 molÀ1) of lanthanide and actinide gas phases

Df H0(298.15)

S0 (298.15)

Cp ¼ A þ B Â T (K) þ C Â T2 (K) þ D Â T3 (K) þ E Â T4 (K) þ F Â TÀ2 (K)
A

Pa
U
Np
Pu
Am


Cm

602 Æ 6
–
548 Æ 26
–
533 Æ 8
–
470 Æ 5
–
348.9 Æ 3.0
–
285.5 Æ 3.0
–
–
389 Æ 10
–

190.171 Æ 0.050
–
198.11 Æ 0.10
–
199.79 Æ 0.10
–
197.72 Æ 0.10
–
177.19 Æ 0.10
–
194.66 Æ 0.20
–

–
197.58 Æ 0.20
–

28.7108
29.8483
21.3965
25.7107
35.1688
4.9298
28.7334
68.4689
24.2954
À112.0172
20.786
19.9856
268.8101
26.1234
22.3529

C
À3

À33.4618 Â 10
9.3756 Â 10À3
8.1883 Â 10À3
15.7656 Â 10À3
À32.2466 Â 10À3
10.4892 Â 10À3
À41.2476 Â 10À3

À48.7544 Â 10À3
À37.0413 Â 10À3
187.5714 Â 10À3
–
0.0434 Â 10À3
À179.4359 Â 10À3
24.8448 Â 10À3
1.7417 Â 10À3

Source: Konings, R. J. M.; Benesˇ, O. J. Phys. Chem. Ref. Data 2010, 39, 043102.

D
À6

45.7409 Â 10
À2.1081 Â 10À6
1.8634 Â 10À6
À5.6052 Â 10À6
27.0474 Â 10À6
3.7043 Â 10À6
76.2347 Â 10À6
28.4161 Â 10À6
95.1224 Â 10À6
À86.6780 Â 10À6
–
1.6974 Â 10À6
45.9178 Â 10À6
À45.9572 Â 10À6
À0.4385 Â 10À6


À9

À14.1005 Â 10
0.2225 Â 10À9
À1.0847 Â 10À9
0.5709 Â 10À9
À5.3433 Â 10À9
À0.7598 Â 10À9
À45.8415 Â 10À9
À6.1153 Â 10À9
À65.8404 Â 10À9
18.8245 Â 10À9
–
À1.5984 Â 10À9
À3.5637 Â 10À9
21.6951 Â 10À9
0.2286 Â 10À9

E

F

–
–
–
–
–
–
9.9079 Â 10À12
4.4618 Â 10À13

16.2344 Â 10À12
À1.5431 Â 10À12
–
4.4407 Â 10À13
–
–
–

À1.4548 Â 105
À1.3137 Â 107
À9.4644 Â 104
À1.1144 Â 107
À3.6652 Â 105
6.8108 Â 106
À1.1134 Â 105
À1.6109 Â 107
6.7865 Â 104
2.7817 Â 107
–
2.1403 Â 105
À1.7767 Â 108
À1.7020 Â 104
2.6514.106

298–1400
1400–4000
298–1800
1800–4000
298–1800
1800–4000

298–1400
1400–4000
298–1400
1400–4000
298–900
900–2400
2400–4000
298–1000
1000–4000

The Actinides Elements: Properties and Characteristics

Th

B

Temperature
range (K)

13


The Actinides Elements: Properties and Characteristics

Figure 17, which reveals a strong variation. Th, Pa, U,
Np, and Am show a regular increase from 0 K to room
temperature, typical for nonmagnetic metals in which
transport carriers (electrons) are scattered by phonons (lattice vibrations). Pu and Cm show, however, a
different behavior. The electrical resistivity of a-Pu
has a maximum of about 150 mO cm at about 100 K.

Boring and Smith71 argue that this high value is an
indication of enhanced scattering of conduction electrons caused by electron correlations involving spin
and charge interactions. Curium is the first actinide
metal that is magnetic. a-Cm orders antiferromagnetically below 65 K,72 while its high-temperature phase,
b-Cm with fcc structure, presents ferromagnetic order
above 200 K similarly to Gd, its 4f counterpart. The
change in the resistivity curve occurs around the ordering temperature, which is similar to that in magnetic
rare earth metals and especially Gd.
The electrical resistivity of the actinide metals above
ambient temperature is well known for the major actinides. Chiotti and coworkers73 showed that this property is very sensitive to impurities in the samples,

0

Fm
Cf

–10

2.01.4.3 Thermopower of
the Crystalline State
The thermopower (S) has been reported for the elements Th to Pu in the cryogenic range and up to
300 K.74 Figure 19 shows the values and the sign of S
for the a-phase of these actinide elements. It can be
observed that it varies from Th to Pu and depends
strongly on temperature range. As no carrier is available at 0 K, S is reduced when approaching very low
temperatures. The thermopower of U and Np at high
temperature shows discontinuities at the structural
phase transition (a–b and consecutive).65 The hightemperature thermopower of Pu is not well known
and is very sensitive to impurities. Experimental


Am
Bk
Pu
Ac
Np
Pa

2

Cm

DL/L (%)

–30
–40

5

3

–20
lnp (bar)

Es

particularly carbon. Sahu et al.64 reported measurements for high purity a-Th in a wide temperature
range, and Arajs et al.65 for uranium up to 1000 K,
covering the a-, b, and g-phases. Sandenaw and
Gibby67 reported measurements for plutonium from
27 to 800 K, covering all allotropes. A large decrease

was observed for the a- to b-transition, as shown in
Figure 18. Neptunium shows a similar behavior as Pu.
The recommended values are summarized in Table 9.

U

Th

3
(100)

1

(001)

DL/L (%)

14

(001)
1

0

–50

(100)

(010)
–1


–60
0.0005

0.0006

0.0007

0.0008

0.0009

0.0010

1/T (K–1)

DsubHЊ(298.15 K) (kJ mol–1)

500

700

900

300

T (K)

Figure 14 The vapor pressure of the actinide elements,
calculated from assessed thermochemical data.


800

–1
300

600

900

1200

T (K)

Figure 16 The thermal expansion of U (left) and
Pa (right) along the different crystallographic axes.

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

600
400
200
0

Ac Th Pa

U

Np Pu Am Cm Bk Cf Es Fm Md No Lr


Figure 15 The sublimation enthalpy at T ¼ 298.15 K of the lanthanide () and actinide (○) metals. The estimated values
are indicated by .


The Actinides Elements: Properties and Characteristics

Table 8

Linear thermal expansion (DL/L0) of the actinide metals; L0 refers to 293 K
DL/L0 (T) ¼ a þ b  T (K) þ c  T2 (K) þ d  T3 (K)

Th
Pa
U

a
a
a
b
g
a
b
a
b
g
d
d0
e
liquid
a

a

Np
Pu

Am
Cm

Table 9

References

a

b

c

d

À2.80Â10À3
À3.745Â10À3
À3.79Â10À3
8.04Â10À5
À1.49Â10À3
À8.381Â10À3
À1.258Â10À2
À9.291Â10À3
2.561Â10À3
3.279Â10À2

7.437Â10À2
0.1189
5.241Â10À2
2.912Â10À2
À2.315Â10À3
À3.262Â10À3

8.190Â10À6
1.555Â10À5
1.264Â10À5
1.729Â10À5
1.775Â10À5
2.848Â10À5
5.282Â10À5
1.266Â10À5
4.249Â10À5
3.469Â10À3
1.208Â10À6
À6.510Â10À3
1.325Â10À3
3.010Â10À3
6.965Â10À6
1.094Â10À5

5.286Â10À9
À1.144Â10À8
À8.982Â10À10

À1.432Â10À12
6.794Â10À12

6.844Â10À12

4.382Â10À11

À1.239Â10À12

7.498Â10À8
À1.048Â10À7

À2.952Â10À11
1.608Â10À8

1.782Â10À9

5.926Â10À12

3.176Â10À9

U

Np

Pu

a
a
a
b
g
a

b
g
a
b
g
d
d0
e

61
61
61
61
61
68
68
62
62
62
62
62
62
62
69
53

Electrical resistivity of the actinide metals
r (mV cm) ¼ a þ b  T (K) þ c  T2 (K) þ d  T3 (K) þ e  T4 (K)

Th


15

a

b

c

d

À1.8305
À18.312
22.455
16.971
67.819
86
À94
110
158.09
117.18
108.87
90.22
À75.08
106.4

0.0593
0.1064
À4.5806Â10À2
8.6655Â10À2

À3.1502Â10À2
0.415
0.7217

À3.3116À3
3.2797Â10À4
À3.8929Â10À9
À4.6720Â10À5
1.8947Â10À5
À1.5Â10À4
3.333Â10À7
À8.5Â10À4

À0.0411
À0.0245
À0.0089
0.0072
0.2315

results indicate that the actinide metals have thermopower values close to those of the lanthanides75 but
larger than the transition metals. This essentially can
be related to large band structures and a huge density
of states at the Fermi level.
2.01.4.4 Thermal Conductivity of
the Crystalline State
The thermal conductivity of the actinide metals
varies strongly within the series. This is particularly
true at low temperatures for which the data for
a-Th and a-Pu differ by two orders of magnitude,


Temperature
range (K)

References

e

1.4372Â10À10

300–800
800–1300
300–941
941–1049
1049–1400
300–553
553–850
850–900
300–399
399–488
488–596
596–741
741–759
759–913

63
63
64
64
64
65

65
65
66
66
66
66
66
66

as shown in Figure 20. This trend is opposite to
that for the electrical conductivity and is in line
with the Wiedemann–Franz law that states that
the ratio between thermal conductivity and electrical
conductivity (s ¼ 1/r) is a constant for any temperature (l=s ¼ LT , where L is the Lorenz number,
2.44 Â10À8 W O KÀ2). One can notice that thermal
conductivity of Pu at 100 K is the lowest reported for
any pure metal (3.5WmÀ1KÀ1).
Experimental data for high temperatures are
known only for the major actinides Th, U, and Pu
in a reasonable temperature range, whereas the measurement for Np is made close to room temperature


16

The Actinides Elements: Properties and Characteristics

15

160
Pu


α-Pu

140
Cm

α-U

Np

100
80

Am

5

S (μV K–1)

r (μΩ cm)

120

10

0

60
40


U

α-Np

Pa
Th

20
0

α-Th

–5

0

50

100

150

200

250

300

–10
0


50

100

150

200

250

300

350

T (K)

T (K)

Figure 17 The low-temperature electrical resistivity of
the actinide elements. Reproduced from Schenkel, R.
Solid State Comm. 1977, 23, 389–392.

Figure 19 The thermopower below 300 K of the
actinide elements. Reproduced from Meaden, G. T. Proc.
Roy. Soc. Lond. 1963, 276A, 553–570.

500
300
180


100

140

α-Np

β-Np

r (μΩ cm)

120

l (W m–1 K–1)

160

γ-Np

100
80

a-Th
50
a-U

30

10
β-U


α-U

60

a-Np

γ-U

5

40

a-Pu

3

20
0

400

600

800
T (K)

(a)

1000


1200

1400

α-Pu

r (μΩ cm)

β-Pu

100

ε-Pu

γ-Pu

δ-Pu
δЈ-Pu

80
60
α-Th

40
20
0

(b)


40

60

80

100

Figure 20 The low-temperature thermal conductivity of
the actinide elements. Reproduced from Lee, J. A.;
Waldron, M. B. Contemp. Phys. 1972, 13, 113–133.

140
120

20

T (K)

180
160

1

400

600

800
T (K)


1000

1200

Figure 18 The high-temperature electrical resistivity of
the actinide elements.

(Figure 21). The recommended equations are given
in Table 10. The values for Th, taken from the
assessment by Touloukian and coworkers,76 show a
slight increase with temperature. It should be noted
that our graphs show a discrepancy between the lowand high-temperature data near T ¼ 300 K, which is
probably related to the purity of the samples, as it is
known that the properties of thorium metal are
highly sensitive to carbon impurities.73 The values
for U, also from the assessment by Touloukian and
coworkers,76 are based on a set of several concordant


The Actinides Elements: Properties and Characteristics

measurements and cover the temperature range for
the a-, b-, and g-phases but do not show distinct
differences.
Thermal conductivity data above ambient temperature exist for all crystal phases of plutonium.
The data for a-Pu from 100 to about 400 K were
reported by Sandenaw and Gibney.40 However, the
agreement with other values at ambient temperature
is poor, which might be due to the differences in

purity and to the accumulated radiation damage.
Wittenberg and coworkers77,78 measured the thermal
diffusivity (D) of the d, d0 , and e phases from which
they derived the thermal conductivity, which was
found to be constant in all three cases. However, the
numbers in the early publication78 for the thermal
diffusivity are different from those in the later publication.77 The values in Table 10 are taken from the
latter work, which we consider to be the final results.
Note that only the early values are cited in the

60

β-U

γ-U

l (W m–1K–1)

40
α-U
30
δЈ-Pu

20

γ-Pu

δ-Pu
ε-Pu


β-Pu

10

Pu-liq.

α-Pu
Np
100

200

300

400

500

600
T (K)

700

800

900 1000 1100

Figure 21 The thermal conductivity of the actinide
elements.


Table 10

2.01.4.5 Thermal Conductivity of
the Liquid State
Only data available for the thermal diffusivity and
conductivity of the liquid state of plutonium have
been reported. Wittenberg and coworkers77,78 measured the thermal diffusivity (D) from which they
derived the thermal conductivity, which is constant in
the measured range (973 to 1073 K). As discussed
above, the two publications by these authors are not
consistent. In the early one,78 Wittenberg gave
0.017–0.021 and 0.022–0.023 cm2 sÀ1 for the thermal
diffusivity in two experiments with different heating

Thermal conductivity (W mÀ1KÀ1) of the actinide metals above room temperature
Phase

Th
U
Np
Pu

Gmelin review from 1976.66 As discussed by Wittenberg, the data indicate that the thermal conductivity
of the g- and d-phases are nearly the same (13 Æ 1)
WmÀ1 KÀ1. These trends are in qualitative agreement with the electrical resistivity measurements, as
discussed in Section 2.01.4.2. Wittenberg also noted
that the large decrease in the thermal conductivity of
the e-phase is not expected to be comparable with
the electrical resistivity measurements, and he suggested that this value may be too low as a result of the
difficulty in maintaining good thermal contact after

the volume contraction during the d- to e-phase
transformation.
Although the Wiedemann–Franz law states that
the ratio between thermal conductivity and electrical
conductivity is almost constant for metals, it was
shown that the value for l/sT at T ¼ 298 K varies
regularly in the lanthanide series, as shown in
Figure 22. The values for Th, U, and Np are close
to the Lorenz value, and that of Pu is slightly higher.
The values for Am and Cm in this figure are suggestions,79 assuming that the thermal conductivity of
Cm is close to that of Gd.

α-Th

50

0

17

a
b
g
d, d0
e
Liquid

l ¼ a þ b  T (K) þ c  T2 (K) þ d  T3 (K)
a


b

c

d

48.101
19.019
4.18
2.264
15.4
3.54
6.94
0.44
16.5

0.00336
0.03256

À1.8235Â10À5

1.0343Â10À5

0.00696

2.5332Â10À5

0.02
0.01
0.01


T (K)

References

100–1000
100–100
300
100–399
399–488
488–596
596–759
759–913
913–1073

75
75
75
75
66
76
76
76
76


18

The Actinides Elements: Properties and Characteristics


La Ce

Pr Nd Pm Sm Eu Gd Tb Dy Ho

Er Tm Yb Lu

(l/sT) ϫ 108 (WW K−2)

6
5
4
3
2
Ac Th Pa

U

Np Pu Am Cm Bk

Cf

Es Fm Md No

Lr

Figure 22 The variation of l/sT of the actinide (○) and lanthanide () metals. The estimated values are indicated by .

rates, yielding to l ¼ 5.4 WmÀ1 KÀ1 and 6.3 WmÀ1 KÀ1,
respectively. In the later publication,77 Wittenberg
reports D ¼ 0.057–0.056 cm2 sÀ1 for the temperature

range 948 to 1073 K, yielding l ¼ (17Æ1) WmÀ1 KÀ1.
This latter value is recommended here.
2.01.4.6

Density of the Liquid State

The density of liquid uranium was measured by
Grosse et al.,80 Rohr and Wittenberg,81 and Shpil’rain
et al.82 The results of the latter two studies are in very
good agreement but deviate significantly from the
results of Grosse et al., which has been explained by
errors caused by surface tension forces in the hydrostatic weighing method used in that work.83 We have
therefore selected the combined results from Rohr
and Wittenberg81 and Shpil’rain et al.,82 as recommended by the latter authors:
rðkg mÀ3 Þ ¼ 20332 À 2:146T ðKÞ

½4Š

The density of liquid plutonium was measured by
Olsen et al.84 and Serpan and Wittenberg.85 The
results are very close and the average of the two
equations is recommended:
rðkg mÀ3 Þ ¼ 18004 À 1:486T ðKÞ

2.01.4.7

½5Š

The viscosity of liquid plutonium was reported in
several studies, and the following equation is the

recommended representation of the results87:
log10 ZðcPÞ ¼ 672=T ðKÞ þ 0:037

½7Š

These equations give for the viscosity at the melting
point 6.5 cP for uranium and 6.0 cP for plutonium.
These values are somewhat higher than the values
predicted by Grosse,88 who used an empirical relationship between the activation energy for viscosity
for liquid metals and their melting points, to obtain
5.9 cP for U, 4.5 cP for Pu, and 5.0 cP for Th at the
melting point.
2.01.4.8

Surface Tension

The surface tension of liquid uranium was measured
by Cahill and Kirshenbaum89 from 1406 to 1850 K.
The results can be represented by the equation:
sðN mÀ1 Þ ¼ 1:747 À 0:1410À3 T ðKÞ

½8Š

This equation yields 1.55 NmÀ1 at the melting point.
The surface tension of plutonium was reported by
Olsen et al.84 These authors obtained s(N mÀ1) ¼
1.29À0.967Â10À3 T(K), yielding 0.40 N mÀ1 at the
melting point. It has been suggested that this value
is too low because of dissolved tantalum. Spriet49
reported the surface tension of liquid plutonium to

be 0.55 N mÀ1, which is generally accepted.

Viscosity

The viscosity of liquid uranium and plutonium has
been measured using a direct oscillating method by
researchers at the Mound Laboratory in the 1960s.
These data are still the only available to date. For
liquid uranium, Ofte86 reported:
log10 ZðcPÞ ¼ 1587:7=T ðKÀ1 Þ À 0:3243

½6Š

2.01.5 Summary and Outlook
The actinide elements pose a very interesting paradox. Uranium and especially plutonium are materials
that are very difficult to handle because of their
radioactive nature, but they are among the most


The Actinides Elements: Properties and Characteristics

extensively studied elements in the periodic table.
This is of course due to the importance of these
two elements in nuclear technology. The properties
of the other actinides are relatively poorly known
and are generally obtained from estimations. However, due to the changes in the electronic properties
of the 5f electrons, varying from delocalized to localized, going from Th to Am, the systematics in the
properties of the actinides are difficult to predict, and
analogies with the 4f lanthanides are not (always)
obvious. Theoretical predictions based on atomistic

calculations could help to solve this, but the predictive potential of such calculations is still being
explored. Clearly, more experimental studies are
needed, particularly on the minor actinides.

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