2.03 Thermodynamic and Thermophysical Properties of
the Actinide Nitrides
M. Uno
University of Fukui, Fukui, Japan

T. Nishi and M. Takano
Japan Atomic Energy Agency, Tokai-mura, Ibaraki, Japan

ß 2012 Elsevier Ltd. All rights reserved.

2.03.1

Introduction

61

2.03.2
2.03.2.1
2.03.2.2
2.03.2.3
2.03.2.4
2.03.2.5
2.03.3
2.03.3.1
2.03.3.2
2.03.3.3
2.03.3.4
2.03.3.4.1
2.03.3.4.2
2.03.3.4.3
2.03.3.4.4

2.03.3.5
2.03.4
2.03.4.1
2.03.4.2
2.03.4.3
2.03.4.4
2.03.5
References

Phase Diagrams and Crystal Structure
Uranium Nitrides
Plutonium Nitride
Thorium Nitride
Neptunium, Americium, and Curium Nitrides
Nitride Solid Solutions and Mixtures
Thermal Properties
Melting or Decomposition
Vaporization Behavior
Heat Capacity
Gibbs Free Energy of Formation
Uranium mononitride
Plutonium mononitride
Uranium and plutonium mononitride
Neptunium mononitride and americium mononitride
Thermal Conductivity
Mechanical Properties
Mechanical Properties of UN
Thermal Expansion of UN
Mechanical Properties of PuN
Mechanical Properties of Other MA or MA-Containing Fuels

Summary

62
62
63
63
64
65
67
67
68
71
72
73
74
75
75
76
79
79
81
81
82
83
83

Abbreviations
ADS
An
CTE

fcc
HD
LTE
TD
MA
MD
XRD

Accelerator-driven system
Actinide
Coefficients of linear thermal expansion
Face-centered cubic
(diamond point) Hardness
Linear thermal expansion
Theoretical density
Minor actinide
Molecular dynamics
X-ray diffraction

2.03.1 Introduction
Uranium nitride UN not only has the same isotropic
crystal structure as uranium dioxide UO2 but also has
a higher melting point, higher metal atom density, and
higher thermal conductivity, compared to UO2. UN
thus has advantages as a nuclear fuel compared to
UO2, is well studied, and many of its material properties have been known for a long time. However, UN
has some disadvantages as a nuclear fuel because of its
low chemical stability and the problem of 14C.

61



62

Thermodynamic and Thermophysical Properties of the Actinide Nitrides

Plutonium nitride and thorium nitride have been
also well studied, mainly with regard to their suitability as nuclear fuels. Other actinide nitrides with
higher atomic number are also important as potential
nuclear fuels but the data on these fuels are insufficient because they are difficult to obtain and handle.
In this section, the physicochemical properties of
the actinide nitrides, mainly uranium nitrides and
plutonium nitride, are discussed. First of all, phase
stability and crystal structures of the nitrides are
described. Then, their thermal, thermodynamic, and
mechanical properties which are relevant to their
suitability as nuclear fuels, are discussed. Characteristics of their preparation and irradiation as nuclear
fuels are described in Chapter 3.02, Nitride Fuel.

2.03.2 Phase Diagrams and Crystal
Structure
2.03.2.1

Uranium Nitrides

References for specific data are given separately for
each section below, but readers are also referred to a
classic, outstanding book1 which summarizes, from
the viewpoint of suitability as nuclear fuels, the various properties of not only the nitrides but also the
other compounds. The binary phase diagram shown

in Figure 12 is taken from data published in 1960,3–7
and is still valid. The phase stability of U–N systems

PN2 >> 105 Pa

Liquid

3000

2850Њ

has been summarized by Chevalier et al.8 There are
two uranium nitrides, UN and U2N3; the former has
an NaCl-type cubic structure, and the latter has an
M2O3-type cubic structure at low temperature
(a-U2N3) and hexagonal structure at higher temperature (b-U2N3), as shown in Figure 2. The lattice
parameter of UN is reported to be about 4.890 A˚
at room temperature9–11; this, however, can vary,
depending on the presence of carbon impurities.10
The lattice parameter of a-U2N3 is 10.688–10.70 A˚,9,11
but U2N3 becomes a solid solution, with N2, at a higher
nitrogen pressure (126 atm); and its lattice parameter
decreases with an increase in nitrogen content. The
lattice parameters of b-U2N3 are reported to be
a ¼ 3.69 and c ¼ 5.83 A˚9 or a ¼ 3.70 and c ¼ 5.80 A˚.10
Although the phase diagram, where nitrogen
pressure is greater than 105 Pa (Figure 1), shows
that UN melts at 3123 K and that UN and U2N3
have a wide range of nonstoichiometry, at lower
nitrogen pressure; UN decomposes such that UN

and U2N3 have little nonstoichiometry, as shown in
Figure 312,13; here the b-U2N3 in the previous graph
is denoted as UN2. The N/U ratio of UN below a
nitrogen pressure of 2 atm is reported to be nearly
1.00 at temperatures between 1773 and 2373 K.14
U2N3 actually decomposes to UN and UN
decomposes to U and nitrogen at nitrogen pressure
below 2.5 atm. As the decomposition of UN must
influence the properties of the fuel pellets, and the
decomposition of U2N3 is the last stage in the formation of UN through carbothermic reduction, the equilibrium nitrogen pressure of UN and U2N3 is very
important from the viewpoint of their use as nuclear

2500

T (ЊC)

UN

UN + Liq.
~1950Њ

2000

UN
a-U2N3 + Liq.

UN + a-U2N3

~1450Њ


1500

a-U2N3 ss

a-U2N3 ss +
b-U2N3 ss

1130Њ
g-U + UN

~970Њ

775Њ
b-U + UN
665Њ
a-U + UN
500

0

2

4

UN + b-U2N3

6
Wt%

8


b-U2N3 ss

1000

(a)

b-U2N3 ss
+ liq.

(b)

U
N

10

12
N

Figure 1 U–N phase diagram at nitrogen pressure larger
than 105 Pa. Data from Levinskii, Yu. V. Atom. Energ. 1974,
37(1), 216–219; Sov. Atom. Energ. (Engl. Transl.) 1974,
37(1), 929–932.

(c)
Figure 2 Crystal structures of (a) UN, (b) a-U2N3, and
(c) b-U2N3.



Thermodynamic and Thermophysical Properties of the Actinide Nitrides

Atom ratio
0

0.2

0.4

0.6

1400
0.8

1200

1000

800

1.6

1.2

5
3000

105 Pa

Liquid


63

T (ЊC)

2.5 ϫ 105 Pa

U2N3

4

2600

log PN2 (Pa)

UN + N2

T (ЊC)

2200
UN1–x + Liq.
1800

3

U + N2

2
1400
1127Њ

1000

UN+
U2N3

UN2
+
N2

UN
+
UN2

105 Pa

g-U + UN
775Њ
668Њ

b-U + UN
a-U + UN

600
0

10

20

30


40

50

1

0
60

70

5

6

7

8

9

10

104/ T (K–1)

(a)

At.%


Figure 3 U–N phase diagram at nitrogen pressure smaller
than 2 atm. Data from Storms, E. K. Special Report to the
Phase Equilibria Program; American Ceramic Society:
Westerville, OH, 1989; Muromura, T.; Tagawa, H. J. Nucl.
Mater. 1979, 79, 264.

2.03.2.2

2.03.2.3

Thorium Nitride

Though thorium is a fertile material, recent research
on thorium and its compounds as nuclear fuel is
scanty. The Th–Th3N4 phase diagram, reported
in 196618, is shown in Figure 6. There are two
solid compounds in this system, ThN and Th3N4;
the former is an NaCl-type cubic structure with

2250

2000

1750

T (ЊC)

UN
4


3

2

Plutonium Nitride

In the Pu–N system, as shown in Figure 5,15 there is
only one structure for the mononitride, PuN: an
NaCl-type face-centered cubic (fcc) structure with
a ¼ 4.904 A˚. PuN is a line compound with little nonstoichiometry, and is reported not to congruently
melt up to 25 bar nitrogen pressure.16 However,
there is a study on the safety assessment of fuels on
the basis of vaporization behavior in which the melting temperature of Pu–N is given as 2993 K under a
nitrogen pressure of 1.7 Â 104 Pa.17

2500

5

log PN2 (Pa)

fuel. The reported decomposition curves are shown in
Figure 4.3 It is seen from these graphs, for example,
that UN decomposes at 3073 K and U2N3 decomposes
1620 K at nitrogen pressure of 1 atm. More detailed
decomposition behavior of UN as well as other actinide nitrides will be discussed in Section 2.03.3.1.

2750

6


U + N2

1

0
(b)

3

3.5

4
104/T (K–1)

4.5

5

Figure 4 (a) Decomposition curve of U2N3. (b)
Decomposition curve of UN. Reproduced from Bugl, J.;
Bauer, A. A. J. Am. Ceram. Soc. 1964, 47(9), 425–429, with
permission from Springer. The dotted line is referred from
P. Gross, C. Hayman and H. Clayton, ‘‘Heats of Formation
of Uranium Silicides and Nitrides’’; In Thermodynamics of
Nuclear Materials- Proceedings of Symposium on
Thermodynamics of Nuclear Materials, Vienna, May 1962,
International Atomic Energy Agency.

a ¼ 5.169 A˚,18 and the latter is a rhombohedron

with a ¼ 9.398 A˚ and a ¼ 23.78 .19 The congruent
melting point is 2820  C at nitrogen pressure of


64

Thermodynamic and Thermophysical Properties of the Actinide Nitrides

3000

0

1

Weight percent nitrogen
2
3

4

5
MP(ssL) 3830 ЊC

Dashed lines schematic
2500
L

PuN
Temperature (ЊC)


2000

1500

1000
-640 ЊC

MP 640 ЊC
TP 483 ЊC
500
TP 483 ЊC
TP 320 ЊC
TP 215 ЊC
TP 125 ЊC

a

-483 ЊC
-320ЊC -483 ЊC
-215 ЊC
-125ЊC

aa
g
b
a

0

0

Pu

5

10

15

20

25

30

35

40

45

50

55

Atomic percent nitrogen

Figure 5 Phase diagram of Pu–N. Reproduced from Wriedt, H. A. Bull. Alloys Phase Diagrams 1989, 10, 593, with
permission from American Chemical Society.

3000

2820 Њ ± 30 Њ

2500

Congruent sublimation
compositions
Thermal arrests
Liquidus
Melting points
Solidus, established
micrographically
Solvus, established
metallographically
N solubility in Th
(Gerds and Mallett)115

2 atm. Hypo- and hyper-ThN appear above 1350  C.
Th3N4 decomposes to ThN in vacuum above
1400  C with the formation of a small amount of
oxide.20 As ThN oxidizes more easily than UN it is
important to consider the temperature and nitrogen
and oxygen pressures during the preparation of ThN
by thermal decomposition of Th3N4.21

Temperature (ЊC)

ThN + Th (liq.)

2.03.2.4 Neptunium, Americium, and
Curium Nitrides


2000
1800 Њ ± 25 Њ

1754
±15

ThN + bccTh
1605 Њ ± 20 Њ

1500
1350

Th3N4
+ ThN

ThN + fccTh

1000

0
Th

0.2

0.4

0.6

0.8


N2: Th ratio

1.0
ThN

1.2

1.4
Th3N4

1.6

Figure 6 Phase diagram of Th–N system. Reproduced
from Benz, R.; Hoffman, C. G.; Rupert, G. N. J. Am. Chem.
Soc. 1967, 89, 191–197, with permission from Elsevier.

These nitrides are also usually prepared by carbothermic reduction of the oxides.22–24 As it is very
difficult to prepare bulk samples due to their high
radioactivity, there have been no systematic studies
on their phase stability. However, it has been established that there is only mono nitride in these systems
from the fact that no nitrogen absorption occurred
upon cooling in nitrogen atmospheres during carbothermic reduction. These mono nitrides have an
NaCl-type face-centered cubic structure, and their
lattice parameter ranges from 0.4899 to 0.5041 A˚,
as shown in Table 1.24 The similarity in the crystal
structure of these three nitrides, as well as uranium
and plutonium nitrides, is advantageous as nuclear



Thermodynamic and Thermophysical Properties of the Actinide Nitrides

Lattice parameter of some actinide nitrides

Mononitride Lattice
parameter
a (nm)

NpN−PuN
|aPuN À a| (nm) |aAmN À a| (nm)

UN
NpN
PuN
AmN
CmN
YN
ZrN
TiN

0.4888
0.4899
0.4905
0.4991
0.5041
0.4891
0.4576
0.4242

0.4905


Lattice parameter difference

0.0017
0.0006
–
0.0086
0.0136
0.0014
0.0329
0.0663

0.0103
0.0092
0.0086
–
0.0050
0.0100
0.0415
0.0749

Source: Minato, K.; et al. J. Nucl. Mater. 2003, 320, 18–24, with
permission from Elsevier.

fuels, especially as accelerator-driven system (ADS)
targets of nitride solid solutions that contain a large
amount of minor actinides (MAs). Experimental
research on their vaporization behavior has revealed
that the congruent melting temperature of NpN was
2830  C.25 There are scarcely any data on the phase

stability and other properties of pure CmN. Some data
on Cm and U or Pu solid solutions have been reported,
and these will be discussed in the next section.
2.03.2.5 Nitride Solid Solutions and
Mixtures
As (U,Pu)N were some of the most promising
candidates for the first breeder reactors, they are the
best studied nitride solid solution fuels. UN and PuN
form a continuous solid solution, and the lattice parameter increases with an increase in the plutonium content, and is accompanied by a large deviation from
Vegard’s law, as shown in Figure 7,26 suggesting the
nonideality of the solution. A diagram of the calculated
U–Pu–N ternary phase at 1000  C, shown in Figure 8,1
suggests that there is a relatively narrow range of possible (U,Pu)N compositions, as is the case with U–N
and Pu–N binary systems. It is suggested that the
sesquinitride solid solution (U,Pu)N1.5 exists in a system in which PuN may constitute up to 15 mol%27,
although this is not depicted in Figure 8.
As uranium monocarbide and plutonium monocarbide, as well as other actinide carbides, have an
NaCl-type fcc structure, actinide nitrides and actinide carbides form solid solutions. Some research
performed on actinide nitride carbides, for example,
U–N–C, Pu–N–C,28–30 have investigated the suitability of these carbonitride fuels and the impurities
in nitride fuels after carbothermic reduction. Phase

Lattice parameter (nm)

Table 1

65

0.4900


0.4895

UN−PuN
UN−NpN

0.4890

0
UN
UN
NpN

Vegard’s law
0.2

0.4

0.6

Composition

0.8

1
PuN
NpN
PuN

Figure 7 Lattice parameter of some actinide nitride
solid solution. Reproduced from Minato, K.; et al. J. Nucl.

Mater. 2003, 320, 18–24.

stability graphs of U and/or Pu–N–C, both with and
without oxygen, also have been constructed in order
to make pure nitride fuels.31,32 The irradiation behavior of (U and/or Pu)–N–C fuels also has been
reported,33 but the details of this data are out of the
scope of this chapter.
As MAs are usually burnt with uranium and plutonium for transmutation, and as Am originally exists
in Pu, (MA,U)N or (MA,Pu)N have also been well
studied. As mentioned above, the vaporization behavior of (Pu,Am)N has been studied34, and abnormal
vaporization of Pu and Am was observed. The lattice
parameters of (U,Np)N and (Np,Pu)N increase with
increase in Np and Pu content, and with a small
deviation from ideality, as shown in Figure 7.24
Although scarcely any data for pure CmN has been
obtained, X-ray diffraction data for (Cm0.4Pu0.6)N
has been reported, as shown in Figure 9.24
Inert matrix fuels, where MA as well as uranium
and plutonium are embedded in a matrix, are also
being considered for use in ADS for transmutation.
Recent research in MAs has focused on using various
nitride solid solutions and nitride mixtures as inert
matrix fuels. For ADS targets, matrices have been
designed and selected so as to avoid the formation
of hot spots and to increase the thermal stability,
especially in the case of Americium nitride. Considering their chemical stability and thermal conductivity, ZrN, YN, TiN, and AlN were chosen as
candidates for the matrix.16,35 ZrN has an NaCl-type


66


Thermodynamic and Thermophysical Properties of the Actinide Nitrides
α-U2N3 + (U, Pu)N + N2

N

U-Pu-N
1000 ЊC

α + β + (U,Pu)N

1 atm
β + (U,Pu)N
UN

PuN

α-U2N3
+ (U,Pu)N

Liquid

Solid
U

Pu

Figure 8 U–Pu–N ternary phase diagram at 1000  C. Reproduced from Matzke, H. J. Science of Advanced LMFBR Fuels;
North Holland: Amsterdam, 1986, with permission from Elsevier.


5000

0.56

111

PuO2

0.54

CmO2

Intensity

Lattice parameter (nm)

4000

200

30 mol% Am
3000
2000

0.52

10 mol% Am
1000
CmN
0

30

0.50
PuN

0.48

0

PuN
PuO2

0.2

0.4

0.6

Composition

0.8

1
CmN
CmO2

Figure 9 Lattice parameter of (Pu,Cm)N and (Pu,Cm)O2.
Reproduced from Minato, K.; et al. J. Nucl. Mater. 2003,
320, 18–24, with permission from Elsevier.


fcc structure with a ¼ 4.580 A˚ and has nearly the same
thermal conductivity as UN, has a high melting point,
good chemical stability in air, and a tolerable dissolution rate in nitric acid. Recently, abundant data
have been made available for ZrN-based inert matrix
fuels. It is planned that (Pu,Zr)N, with about 20–25%
Pu, will be used to burn Pu in a closed fuel cycle.36
The lattice parameter of (Pu,Zr)N decreases with an

AmN(111)
32

ZrN(111)

AmN(200)

34
36
2q (deg)

ZrN(200)
38

40

Figure 10 X-ray diffraction patterns for Am–ZrN.
Reproduced from Minato, K.; et al. J. Nucl. Mater. 2003,
320, 18–24.

increase in the Zr content, and is between that of
PuN and ZrN, in accordance with Vegard’s law.24

It has also been estimated, using a model, that (Pu,
Zr)N with 20–40 mol% PuN, does not melt till up
to 2773 K; this is based on experimental thermodynamic data which show that U0.9Zr0.8N does not melt
till up to 3073 K.37 In the case of (Am,Zr)N, it is
reported that two solid solutions are obtained when
Am content is over 30%24, as shown in Figure 10. The
Am content of the two phases have been estimated,
from the lattice parameter, to be 14.5 and 43.1 mol%.
A thermodynamic modeling of a uranium-free inert


Thermodynamic and Thermophysical Properties of the Actinide Nitrides

T (K)
3200

102

3000

101

PuN
UN

100

10–1

Congruent

melting
ThN

10–2

Melting or Decomposition

In this section, the melting points and decomposition
temperatures of actinide mononitrides are discussed
in conjunction with the nitrogen pressures because
this behavior depends on the nitrogen partial pressure of the system. The vapor pressure of a metal gas
over the solid nitride is discussed in the next section
as ‘vaporization behavior.’
The liquid mononitride MN (liq.) can be observed
when congruent melting occurs under a pressurized
nitrogen atmosphere; otherwise the solid mononitride MN (s) decomposes into nitrogen gas and liquid
metal that is saturated with nitrogen, according to the
following reaction,
MNðsÞ ¼ 1=2N2 þ Mðliq; sat: with NÞ

½1Š

Olson and Mulford have determined the decomposition temperatures of ThN,41 UN,6 NpN,25 and PuN42
by the optical observation of the nitride granules
when they were heated under controlled nitrogen
pressures. Figure 11 shows the relationship between
the nitrogen pressure p (atm) in logarithmic scale and
the reciprocal decomposition temperature 1/T (KÀ1).
The solid curves show the following equations:
ThN : log pðatmÞ ¼ 8:086 À 33224=T þ 0:958 Â 10À17 T 5

ð2689

T ðKÞ

3063Þ

½2Š

UN : log pðatmÞ ¼ 8:193 À 29540=T þ 5:57 Â 10À18 T 5
ð2773

T ðKÞ

3123Þ

½3Š

NpN : log pðatmÞ ¼ 8:193 À 29540=T þ 7:87 Â 10À18 T 5
ð2483

T ðKÞ

3103Þ

2600
UN (Hayes)

2.03.3 Thermal Properties
2.03.3.1


2800

NpN

Nitrogen pressure (atm)

matrix fuel, for example, (Am0.20Np0.04Pu0.26Zr0.60),
has also been accomplished.38
In contrast to ZrN, TiN does not dissolve MA
nitrides even though TiN also has an NaCl-type fcc
structure. This is explained by the differences in
lattice parameter, which was estimated by Benedict.39
A mixture of PuN and TiN was obtained by several
heat treatments above 1673 K, and the product, in
which one phase was formed, did not contain the
other phase.40 TiN, as well as ZrN, have nonstoichiometry. It is also reported that a TiN þ PuN mixture
may be hypostoichiometric although (Pu,Zr)N is
hyperstoichiometric.

67

½4Š

10–3

3

3.2

3.4


3.6

3.8

4

10 000/ T (K–1)
Figure 11 Decomposition pressures of ThN, UN, NpN,
and PuN as a function of reciprocal temperature above
2500 K reported by Olson and Mulford.6,25,41,42

PuN : log pðatmÞ ¼ 8:193 À 29540=T þ 11:28 Â 10À18 T 5
ð2563

T ðKÞ

3043Þ

½5Š

The temperature at which the vertical rise in nitrogen
pressure is observed for ThN, UN, and NpN corresponds to the congruent melting point, and is
3063 Æ 30 K for ThN (p ! 0.7 atm), 3123 Æ 30 K for
UN (p ! 2.5 atm), and 3103 Æ 30 K for NpN (p ! 10
atm). The congruent melting for PuN was not
achieved in the nitrogen pressure range up to 24.5 atm.
The presence of an oxide phase, as an impurity,
seems to lower the melting point and decomposition
temperature. In the case of ThN mentioned above,

the melting point and decomposition temperature
of a specimen containing 0.6 wt% oxygen fell by
$130 K from those of the oxygen-free specimens
($0.04 wt% oxygen). A similar experiment conducted
by Eron’yan et al.43 with ZrN, a transition metal nitride
that has the same crystal structure, has revealed a
decrease in the melting point by 200–300 K when the
oxygen content increased from 0.15 to 0.5–1.0 wt%.
Some data sets on the equilibrium nitrogen pressure, in eqn [1] for UN and uranium carbonitride


68

Thermodynamic and Thermophysical Properties of the Actinide Nitrides

T (K)
2200

2000

UN (Hayes)

UC1–xNx (Ikeda)
1: x = 1
2: x = 0.69
3: x = 0.48
4: x = 0.3
UC1–xNx (Prins)
5: x = 1
6: x = 0.79

7: x = 0.5
8: x = 0.36
9: x = 0.2

5
6

10–4
Nitrogen pressure (atm)

7
8
10–5
4

1800

3

9
10–6

1

16

14

T (K)
3200

3000

3600 3400
Timofeeva
Brundiers
TPRC
Smirnov
Houska
Hayes

Takano
Aldred
Benedict
Kruger

10

AmN

1273 K

PuN

8
NpN

293 K

10–7


2800

12
CTE (10–6 K–1)

2400

10–3

UN

2
6

TiN
ZrN
HfN

10–8

4

4.2

4.4

4.6

4.8


5

5.2

5.4

5.6

10 000/ T (K–1)

log pðatmÞ ¼ 1:8216 þ 1:882 Â 10À3 T À 23543:4=T
3170Þ

3

3.2

3.4

3.6

3.8

Figure 13 Coefficients of linear thermal expansion at 293
(open symbols) and 1273 K (closed symbols) for some
transition metal nitrides and actinide nitrides plotted against
reciprocal decomposition temperature under 1 atm of
nitrogen. For references see Table 2.

U(C,N), as measured by the Knudsen-cell and massspectroscopic technique at lower temperatures, are

available and are shown in Figure 12. The dotted
curve represents the correlation for UN developed
by Hayes et al.46 using eight data sets available
in literature.4–6,44,45,47–49 The nitrogen pressure is
given as:

T ðKÞ

2.8

10 000/T (K–1)

Figure 12 Decomposition pressures of U(C,N) as a
function of reciprocal temperature below 2400 K. Solid
lines by Ikeda et al.44 and broken lines by Prins et al.45
Dotted line for UN reviewed by Hayes et al.46

ð1400

4
2.6

½6Š

The N2 pressure for decomposition of UC1ÀxNx, as
measured by Ikeda et al.44 and Prins et al.45, decreases
with a decrease in x, together with a lowering in the
activity of UN in UC1ÀxNx . The nitrogen pressure
over UC0.5N0.5, at a certain temperature in the graph,
is approximately one-fifth of that of UN. When considering a nitride or carbide as nuclear fuel for fast

reactors, it should be noted that the decomposition
pressure of nitrogen can be lowered and that the
reactivity of carbide with moisture can be moderated
by employing the carbonitride instead of the nitride
or carbide.
No experimental data on the melting behavior of
transplutonium nitrides such as AmN and CmN have

been reported. Takano et al.22 have examined the
relationship between the decomposition temperature
and the instantaneous coefficients of linear thermal
expansion (CTE) and used it to predict the decomposition temperature of AmN. Figure 13 shows the
CTE at 293 and 1273 K plotted against reciprocal
decomposition temperature under 1 atm of nitrogen
for some transition metal nitrides (TiN, ZrN, HfN)
and actinide nitrides (UN, NpN, PuN). The data used
for this is summarized in Table 26,22,25,41–43,50–59 with
references. Except for the large CTE value for PuN at
293 K, a reasonable linear relationship is shown by the
agreement of the broken lines. From the CTE values
for AmN, determined by the high-temperature X-ray
diffraction technique, the decomposition temperature
of AmN under 1 atm of nitrogen was roughly predicted to be 2700 K, which is much lower than that
of PuN.
2.03.3.2

Vaporization Behavior

In this section, the vapor pressure of a metal gas over
a solid actinide nitride is summarized.



Thermodynamic and Thermophysical Properties of the Actinide Nitrides

69

Table 2
Summary of melting point, decomposition temperature and linear thermal expansion coefficient (CTE) for some
transition metal nitrides and actinide nitrides
Nitride

Congruent
melting point (m.p.) (K)

Decomposition
temperaturea (K)

References

CTE (10À6 KÀ1)
293 K

TiN

3550

3180

50


ZrN

3970

3520

43

HfN

NAb

3620

50

ThN
UN

3063
3123

(3063)c
3050

41
6

NpN


3103

2960

25

PuN

NA

2860

42

AmN

NA

($2700?)

22

References

Method or
comment

52
51
53

51
54
55

XRD, TiN0.95
TPRC
XRD, ZrN0.99
TPRC
XRD
XRD

56
51
22
57
22
58
59
22

XRD
TPRC
XRD
XRD
XRD
XRD
Dilatometer
XRD

1273 K


7.0
6.3
6.5
5.7
5.7

10.1
10.4
7.9
8.9
–
8.0
–
10.3
11.1
9.9
–
12.2
–
11.6
13.0

–
–
7.5
7.4
7.9
7.6
10.0

10.3
–
9.4

a

Under 1 atm of nitrogen.
Not available.
Congruent melting under 1 atm of nitrogen.

b
c

6
: N2(g), Hayes et al.46

4

: U(g), Hayes et al.46
: U(g), Suzuki et al.61
: U(g), Alexander et al.62

2
log p (Pa)

The major vapor species observed over UN are
nitrogen gas, N2(g), and mono-atomic uranium gas,
U(g). UN(g) can also be detected in addition to U(g)
and N2(g),60 but its pressure is three orders of magnitude lower than that of U(g); therefore, the contribution of UN(g) can be ignored in practice. Some
data on the pressures of N2(g) and U(g) over solid

UN(s) are shown in Figure 14.
Hayes et al.46 have derived equations for the pressures of N2(g) and U(g), which were developed by
fitting the data from eight experimental investigations.
According to that paper, the reported data on
N2(g) agree with each other, but that of U(g) over
UN(s) vary somewhat. The U(g) pressure obtained by
Suzuki et al.61 is a little higher than that predicted
from the equation developed by Hayes et al., but is
in agreement with values given by Alexander et al.62
It is well known that the evaporation of UN is
accompanied by the precipitation of a liquid phase,
where UN(s) ¼ U(1) þ 1/2N2(g) and U(1) ¼ U(g).
The reported vapor pressure of U(g) over UN(s) is
close to or a little lower than that over metal U.63 It is
suggested that the dissolution of nitrogen and/or
impurity metal from crucibles into the liquid phase
could affect the observed partial pressure. Some scattering of the previously reported data on U(g) over
UN(s) may be also caused by a reaction of the liquid
phase in UN with the crucible material. From this
viewpoint, it appears that the partial pressure of U(g)

0
-2
-4
-6
-8

3

4


5
6
104/T (K-1)

7

8

Figure 14 Partial pressure of N2(g) and U(g) over UN
(s) as a function of temperature. Adapted from
Hayes, S. L.; Thomas, J. K.; Peddicord, K. L. J. Nucl.
Mater. 1990, 171, 300–318; Suzuki, Y.; Maeda, A.; Arai, Y.;
Ohmichi, T. J. Nucl. Mater. 1992, 188, 239–243;
Alexander, C. A.; Ogden, J. S.; Pardue, W. H. J. Nucl.
Mater. 1969, 31, 13–24.

over UN(s) should be a little higher than that proposed by Hayes et al.
The vapor species over PuN are nitrogen
gas N2(g) and mono-atomic plutonium gas Pu(g).
PuN(g) is not detected because PuN is more unstable
than UN.64 The N2 pressure over PuN has been
reported by Alexander et al.,65 Olson and Mulford,42


70

Thermodynamic and Thermophysical Properties of the Actinide Nitrides

3

: Suzuki et al.61
: Kent and Leary68
: Sheth and Leibowitz et al.69

2

log p (Pa)

1
0
–1
–2
–3
–4
4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5


104/T (K–1)
Figure 15 Partial pressure of Pu(g) over PuN(s) as a
function of temperature. Data from Suzuki, Y.; Maeda, A.;
Arai, Y.; Ohmichi, T. J. Nucl. Mater. 1992, 188, 239–243;
Kent, R. A.; Leary, J. A. High Temp. Sci. 1966, 1, 176–183;
Sheth, A.; Leibowitz, L. ANL-AFP-2, Argonne National
Laboratory; Chemical Engineering Division: Argonne,
WI, 1975.

0
: (U0.80Pu0.20)N
: (U0.65Pu0.35)N
log p (Pa)

–1

Pu

: (U0.40Pu0.60)N
: (U0.20Pu0.80)N
: PuN

–2

–3

U

: UN
: (U0.80Pu0.20)N

: (U0.65Pu0.35)N

–4
5.0

5.5

6.0

6.5

7.0

104/T (K–1)
Figure 16 Partial pressure of U(g) and Pu(g) over UN(s),
PuN(s) and mixed nitride as function of temperature.
Reproduced from Suzuki, Y.; Maeda, A.; Arai, Y.; Ohmichi,
T. J. Nucl. Mater. 1992, 188, 239–243.

Table 3

Pardue et al.,66 and Campbell and Leary.67 These data
seem to agree with each other.
The vapor pressure of Pu(g) over PuN(s), as a
function of temperature, is shown in Figure 15. The
values reported in the different studies almost
completely agree with each other.61,68,69
According to Alexander et al.,65 the ratio Pu(g)/
N2(g) is 5.8 throughout the investigated temperature
range of 1400–2400 K, which suggests that PuN evaporates congruently; that is, PuN(s) ¼ Pu(g) þ

1/2N2(g). However, Suzuki et al. have reported that
Pu(g) over PuN(s), at temperatures lower than
1600 K, is a little higher than the values extrapolated
from the high-temperature data, and that it approaches
that over Pu metal with further decrease in temperature. There is some possibility that a liquid phase
forms at the surface of the sample during the cooling
stages of the mass-spectrometric measurements,
because PuN has a nonstoichiometric composition
range at elevated temperatures, while it is a line
compound at low temperatures.
The vapor pressure of U(g) and Pu(g) over UN(s),
(U,Pu)N(s), and PuN(s) are shown in Figure 16.
Table 3 gives the vapor pressures of U(g) and Pu(g)
which are represented in Figure 16 in the form of
logarithmic temperature coefficients. It is noteworthy
that the vapor pressure of Pu(g) over mixed nitride
was observed to increase with an increase in the PuN
content.
Nakajima et al.70 have measured the vapor pressure
of Np(g) over NpN(s) in the temperature range of
1690–2030 K by using the Knudsen-cell effusion mass
spectrometry. This data is plotted in Figure 17 as a
function of temperature. The partial pressure of Np
(g) can be expressed using the following equation:
log p NpðgÞðPaÞ ¼ 10:26 À 22 200=T

½7Š

The vapor pressures of Np(g) over NpN(s) obtained
by Nakajima et al. are similar to those of Np(g) over


Partial pressure of U and Pu over UN, PuN, and (U,Pu)N

Compound

Vapor species

Vapor pressure log p (Pa)

Temperature range (K)

UN
(U0.80Pu0.20)N

U
U
Pu
U
Pu
Pu
Pu
Pu

10.65–25 600T1 (T,K)
10.90–26 400T1 (T,K)
9.86–20 500T1 (T,K)
11.03–26 900T1 (T,K)
9.59–19 600T1 (T,K)
11.14–22 000T1 (T,K)
10.76–21 100T1 (T,K)

11.74–22 500T1 (T,K)

1 753–2 028
1 793–1 913
1 653–1 933
1 813–1 833
1 593–1 833
1 553–1 773
1 553–1 733
1 558–1 738

(U0.65Pu0.35)N
(U0.40Pu0.60)N
(U0.20Pu0.80)N
PuN

Source: Suzuki, Y.; Maeda, A.; Arai, Y.; Ohmichi, T. J. Nucl. Mater. 1992, 188, 239–243.


Thermodynamic and Thermophysical Properties of the Actinide Nitrides

71

Am(g) over AmN
1
log p (Pa)

0
Np(g) over NpN


–1

Pu(g) over PuN

–2
–3
U(g) over UN
–4

Heat capacity (J mol–1 K–1)

2
70

60

: Alexander et al.65
: Oetting75

50

Np(g) over Np(l)
500

–5

5.0

5.5
104/T (K–1)


6.0

Figure 17 Temperature dependence of partial pressure of
Np(g) over Np(1), Np(g) over NpN(s) and Am(g) over AmN(s)
together with those of U(g) and Pu(g) over UN(s) and PuN(s)
as a function of temperature. Adapted from Suzuki, Y.;
Maeda, A.; Arai, Y.; Ohmichi, T. J. Nucl. Mater. 1992, 188,
239–243; Nakajima, K.; Arai, Y.; Suzuki, Y. J. Nucl. Mater.
1997, 247, 33–36; Ackermann, R. J.; Rauh, E. G. J. Chem.
Thermodyn. 1975, 7, 211–218; Takano, M.; Itoh, A.;
Akabori, M.; Minato, K.; Numata, M. In Proceedings of
GLOBAL 2003, Study on the Stability of AmN and (Am,Zr)N,
New Orleans, LA, Nov 16–20, 2003; p 2285, CD-ROM.

liquid Np metal found by Ackermann and Rauh71;
these all are shown in Figure 17. Therefore, the
decomposition mechanism is considered to be
the following reaction: NpN(s) ¼ Np(1) þ 1/2N2(g),
Np(1) ¼ Np(g).
Takano et al.72 have estimated the vapor pressure
of Am(g) over AmN by using values of the Gibbs
free energy of formation available in literature.34
The evaporation of AmN obeys the following reaction: AmN(s) ¼ Am(g) þ 1/2N2(g). The estimated
vapor pressure of Am over AmN, expressed as a
function of temperature, is
log p AmðgÞðPaÞ ¼ 12:913 À 20197=T
ð1623 < T ðKÞ < 1733Þ

½8Š


The calculated vapor pressures of Am over AmN are
plotted in Figure 17 as a function of temperature.
The vapor pressure of Am over AmN is higher than
those of other actinide vapor species over their
respective nitrides.
2.03.3.3

Heat Capacity

Data on the heat capacities of actinide nitrides are
very limited due to the experimental difficulties.
In this section, the heat capacities of uranium nitride

1000
1500
Temperature (K)

2000

Figure 18 Heat capacities of PuN. Data from Alexander,
C. A.; Clark, R. B.; Kruger, O. L.; Robins, J. L. Plutonium
and Other Actinides 1975; North-Holland: Amsterdam,
1976; pp 277; Oetting, F. L. J. Chem. Thermodyn. 1978, 10,
941–948.

UN, plutonium nitride PuN, neptunium nitride NpN,
and americium nitride AmN are summarized.
Hayes et al.46 recommended an equation for the
heat capacity of UN based on a comparison of nine

data sets; these seem to agree with each other at low
temperatures but their data are limited, and to some
extent scattered, at elevated temperatures. The previously reported values for the heat capacity of UN
exhibit an almost linear increase with temperature,
except those reported by Conway and Flagella.73
They report that Cp–T curves exhibit a strong upward
trend at temperatures over 1500 K. This behavior is
analogous to that of the actinide carbides, as pointed
out by Blank.74 The assessment by Hayes et al. uses
the results of Conway and Flagella. Thus, the heat
capacity data reported by Hayes et al. can be considered reliable. The heat capacity of UN, expressed by
Hayes et al., is as follows:
Cp ð JmolÀ1 KÀ1 Þ ¼
À Á
 2
exp Ty
y
À3
51:14
 À Á
à þ 9:491  10 T
T exp y À 1 2
T


11
2:642 Â 10
18081
þ
exp

À
T2
T
ð298 < T ðKÞ < 2628Þ

½9Š

where y is the empirically determined Einstein temperature of UN, 365.7 K.
The heat capacities of PuN are shown in Figure 18.
Information on the heat capacity of PuN is very
scarce and is limited to the low temperatures. Moreover, the two data sets on PuN given by Alexander


72

Thermodynamic and Thermophysical Properties of the Actinide Nitrides

80
: UN (Hayes et al.46)
: PuN (Oetting75)
: (U0.8Pu0.2)N (Alexander et al.65)

100

Heat capacity (J mol–1 K–1)

Heat capacity (J mol–1 K–1)

120


: (U0.45Pu0.55)N (Kandan et al.78)

80

60

40
0

500

1000 1500 2000
Temperature (K)

2500

3000

Figure 19 Heat capacities of UN, PuN, and (U,Pu)N. Data
from Hayes, S. L.; Thomas, J. K.; Peddicord, K. L. J. Nucl.
Mater. 1990, 171, 300–318; Oetting, F. L. J. Chem.
Thermodyn. 1978, 10, 941–948; Alexander, C. A.;
Ogden, J. S.; Pardue, W. M. Thermophysical properties of
(UPu)N. In Plutonium 1970 and Other Actinides PT.1; 1970,
17, 95–103; Kandan, R.; Babu, R.; Nagarajan, K.; Vasudeva
Rao, P. R. Thermochim. Acta 2007, 460, 41–43.

et al.65 and Oetting75 are not consistent. Matsui and
Ohse76 have critically reviewed the heat capacity data
of PuN and have argued that the Oetting correlation

is more reliable. Therefore, the heat capacity data, as
reported by Oetting, is given here. The heat capacity
function of PuN given by Oetting is
À1

À1

À2

Cp ð J mol K Þ ¼ 1:542 Â 10 T þ 45:00
ð298 < T ðKÞ < 1562Þ

60

40
: UN (Hayes et al.46)
: NpN (Nishi et al.79)
: PuN (Oetting75)
: AmN (Nishi et al.79)

20

0

400

600
800
Temperature (K)


1000

Figure 20 Heat capacities of UN, NpN, PuN, and AmN.
Adapted from Hayes, S. L.; Thomas, J. K.; Peddicord, K. L.
J. Nucl. Mater. 1990, 171, 300–318; Oetting, F. L. J. Chem.
Thermodyn. 1978, 10, 941–948; Nishi, T.; Itoh, A.; Takano, M.;
et al. J. Nucl. Mater. 2008, 377, 467–469.

of NpN and AmN were prepared by the carbothermic
reduction of their respective oxides. The enthalpy
increments were measured using a twin-type drop
calorimeter in a glove box. The heat capacities were
determined by derivatives of the enthalpy increments.
The measured heat capacity of NpN is expressed by
Cp ð J molÀ1 KÞ ¼ 1:872 Â 10À2 T þ 42:75
ð334 < T ðKÞ < 1562Þ

½11Š

The measured heat capacity of AmN is expressed by
½10Š

The heat capacities of UN, PuN, and (U,Pu)N are
shown in Figure 19. If the heat capacities of solid
solutions can be estimated from those of its raw
materials with the same structure on the basis of the
additive law, it can be expected that the values for
the (U,Pu)N solid solutions are an intermediate
between those of UN and PuN. However, the heat
capacities of (U,Pu)N, as reported by Alexander

et al.77 and Kandan et al.,78 are smaller than those of
UN, by Hayes et al., and PuN, by Oetting. In addition,
the temperature dependencies of the heat capacities
of PuN and its solid solutions are almost linear,
although it has been suggested that they can shift
toward larger values at elevated temperatures, as
does UN. It is considered that these discrepancies
are probably due to the lack of experimental data.
Thus, it is necessary to obtain the accurate heat
capacity of PuN and (U,Pu)N.
Recently, the heat capacities of NpN and AmN
were determined by drop calorimetry.79 The samples

Cp ð J molÀ1 KÞ ¼ 1:563 Â 10À2 T þ 42:44
ð354 < T ðKÞ < 1071Þ

½12Š

These are shown in Figure 20, together with those of
UN,46 NpN,79 and PuN.75 Although there are no
distinct differences, the heat capacity of AmN was
slightly lower than those of UN, NpN, and PuN.
The heat capacities of (Np,Am)N and (Pu,Am)N
solid solutions were also obtained. The heat capacities decreased slightly with an increase in Am
content. This tendency was attributed to the heat
capacity of AmN being slightly smaller than those
of NpN and PuN.80
2.03.3.4

Gibbs Free Energy of Formation


Some data on the Gibbs free energy of formation for
actinide nitrides exist. In this section, the Gibbs free
energy of formation of uranium nitride, UN, plutonium nitride, PuN, uranium and plutonium mixed
nitride, (U,Pu)N, neptunium nitride, NpN, and
americium nitride, AmN are summarized.


Thermodynamic and Thermophysical Properties of the Actinide Nitrides

Table 4

73

The standard thermodynamic functions of UN

T (K)

Cp (J molÀ1 KÀ1)

HÀH298 (J molÀ1)

S (J molÀ1 KÀ1)

À(GÀH298)/T
(J molÀ1 KÀ1)

DfG (J molÀ1)

298

300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400
2500
2600
2628

47.95
48.04
51.49
53.64

55.27
56.63
57.84
58.98
60.06
61.12
62.18
63.28
64.47
65.81
67.38
69.27
71.59
74.40
77.81
81.86
86.62
92.11
98.35
105.33
113.04
115.32

0
96
5089
10 352
15 801
21 397
27 121

32 963
38 915
44 975
51 140
57 413
63 799
70 312
76 969
83 798
90 837
98 132
105 738
113 716
122 133
131 063
140 580
150 757
161 669
164 866

62.68
63.00
77.34
89.08
99.01
107.63
115.27
122.15
128.42
134.19

139.56
144.57
149.28
153.74
157.98
162.01
165.87
169.58
173.14
176.58
179.90
183.12
186.24
189.28
192.23
193.04

62.68
62.68
64.62
68.37
72.67
77.06
81.37
85.53
89.51
93.31
96.94
100.41
103.71

106.87
109.87
112.72
115.41
117.93
120.28
122.43
124.39
126.14
127.67
128.98
130.05
130.31

À270 978
À270 812
À262 582
À254 530
À246 614
À238 788
À231 011
À223 235
À215 267
À206 948
À198 457
À190 019
À181 626
À172 640
À163 550
À154 384

À145 111
À135 687
À126 062
À116 178
À105 969
À95 367
À84 302
À72 701
À60 489
À56 954

The values of DfG for UN were calculated from the values of DH298 and thermal functions for uranium and nitrogen.
Source: Hayes, S. L.; Thomas, J. K.; Peddicord, K. L. J. Nucl. Mater. 1990, 171, 300–318; Matsui, T.; Ohse, R. W. High Temp. High Press.
1987, 19, 1–17; Cordfunke, E. H. P.; Konings, R. J. M.; Potter, P. E.; Prins, G.; Rand, M. H. Thermochemical Data for Reactor
Materials and Fission Products; Elsevier: Amsterdam, 1990; p 667; Chase, M. W.; Curnutt, J. L.; Prophet, H. JANAF Thermochemical
Tables; Dow Chemical Co.: Midland, MA, 1965.

2.03.3.4.1 Uranium mononitride

The Gibbs free energy (G) for UN has been reported
by Hayes et al.46 On the basis of the equations for Cp
and HÀH298, they have determined other thermal
functions of UN(s) in the temperature range of
298–2628 K. They have then calculated the values
of the thermal functions from their equations for
heat capacity, setting S298 to be 62.68 J molÀ1 KÀ1;
these are given in Table 4. The values of Gibbs
free energy of formation DfG for UN were thus
calculated from the values of DH29876 and thermal
functions of uranium81 and nitrogen.82 The values of

entropy S, free energy function À(GÀH298)/T, and
Gibbs free energy of formation DfG of UN(s) are also
given in Table 4.
The values of DfG at various temperatures were
fitted to a polynomial function of temperature using
the least-squares method. The DfG of UN was thus
expressed as the following equation:

Df GðJmolÀ1 Þ ¼ À2:941 Â 105 þ 80:98T À 0:04640T 2
þ 3:085 Â 10À6 T 3 À 1:710 Â 106 =T
ð298 < T ðKÞ< 2628Þ

½13Š

Matsui and Ohse76 have also reported DfG values for
UN. The temperature dependences of DfG for UN
are shown in Figure 21. The UN DfG values of these
two studies agree well with each other below 1800 K,
but there seems to be some discrepancy between them
at higher temperatures. It should be noted that the
values of DfG for UN contain some uncertainty due
to the inaccuracy of the data on the HÀH298 values.
The values of DfG, as estimated by Matsui and Ohse
have a large range of error because the calculation was
performed by extrapolating the values of HÀH298. Thus,
the data for the DfG of UN, as reported by Hayes et al.,
are considered to be the reference standard at the
present.



74

Thermodynamic and Thermophysical Properties of the Actinide Nitrides

2.03.3.4.2 Plutonium mononitride

Gibbs free energy of formation (kJ mol–1)

The most reliable standard thermodynamic function
data for PuN are those reported by Matsui and
Ohse.76 Matsui et al. have calculated the thermal
functions of PuN(s) using the recommended
0

–100

equations for Cp and the HÀH298 values of Oetting75,
and setting S298 to be 64.81 J molÀ1 KÀ1; these are
summarized in Table 5. The values of Cp and
HÀH298 higher than 1600 K are extrapolations of
the data reported by Oetting.75
The values of DfG for PuN were calculated with
DH298 set at À299 200 J molÀ1(83) and the thermal
functions for plutonium84 and nitrogen.82 The values
of entropy S, the free energy function À(GÀH298)/T,
and Gibbs free energy of formation DfG of PuN(s) are
also given in Table 5.
The DfG of PuN is expressed with the following
equation:
Df GðJmolÀ1 Þ ¼ À3:384 Â 105 þ 152:0T À 0:03146T 2


–200

À 5:998 Â 10À6 T 3 þ 6:844 Â 106 =T

: Hayes et al.46
: Matsui and Ohse76
–300

500

1000

1500 2000 2500
Temperature (K)

Figure 21 Temperature dependences of the Gibbs
free energy of formation, DfG for UN(s). Data from
Hayes, S. L.; Thomas, J. K.; Peddicord, K. L.
J. Nucl. Mater. 1990, 171, 300–318; Matsui, T.; Ohse, R. W.
High Temp. High Press. 1987, 19, 1–17.

Table 5

ð298 < T ðKÞ< 3000Þ

3000

½14Š


The temperature dependencies of the DfG for PuN
are shown in Figure 22. The values of DfG are close to
those derived from the precise vapor pressure measurements by Kent and Leary,68 with a difference of
around 1 kJ molÀ1 at 1000 K and 6 kJ molÀ1 at 2000 K.

The standard thermodynamic functions of PuN

T (K)

Cp (J molÀ1 KÀ1)

HÀH298 (J molÀ1)

S (J molÀ1 KÀ1)

À(GÀH298)/T
(J molÀ1 KÀ1)

DfG (J molÀ1)

298
300
400
500
600
700
800
900
1000
1100

1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400
2500
3000

49.60
49.63
51.17
52.71
54.26
55.80
57.34
58.88
60.42
61.97
63.51
65.05
66.59
68.13

69.68
71.22
72.76
74.30
75.84
77.38
78.93
80.47
82.01
83.55
91.26

0
92
5132
10 326
15 674
21 177
26 834
32 645
38 610
44 729
51 003
57 430
64 012
70 749
77 639
84 685
91 884
99 237

106 744
114 405
122 221
130 191
138 314
146 593
190 296

64.81
65.12
79.61
91.19
100.94
109.42
116.97
123.81
130.09
135.92
141.38
146.53
151.40
156.05
160.50
164.76
168.88
172.85
176.70
180.44
184.08
187.62

191.08
194.46
210.37

64.81
64.81
66.78
70.54
74.81
79.16
83.43
87.54
91.48
95.26
98.88
102.35
105.68
108.88
111.97
114.95
117.83
120.63
123.33
125.96
128.52
131.02
133.45
135.82
146.94


À273 247
À273 073
À264 338
À254 777
À245 152
À235 469
À225 714
À215 918
À205 913
À195 883
À185 888
À175 923
À166 005
À156 135
À146 323
À136 571
À126 892
À117 270
À107 730
À98 274
À88 895
À79 594
À70 388
À61 269
À17

Source: Matsui, T.; Ohse, R. W. High Temp. High Press. 1987, 19, 1–17.


Thermodynamic and Thermophysical Properties of the Actinide Nitrides


2.03.3.4.3 Uranium and plutonium
mononitride

Gibbs free energy of formation (kJ mol–1)

The standard thermodynamic function data for
(U0.8Pu0.2)N were determined using an ideal-solution
model. Matsui et al. have estimated the entropy at
298 K (S298) for (U0.8Pu0.2)N to be 67.07 J molÀ1 KÀ1
0

–100

75

from S298 values for UN (62.43 J molÀ1 KÀ1) and PuN
(64.81 J molÀ1 KÀ1) coupled with an entropy of mixing
term, assuming an ideal solution. The values of the
thermal functions for (U0.8Pu0.2)N have been calculated by Matsui et al. and are summarized in Table 6.
The enthalpy of formation for (U0.8Pu0.2)N was estimated to be À296.5 kJ molÀ1, on the basis of an
ideal-solution model with DH298(UN) ¼ À295.8 kJ
molÀ1 and DH298(PuN) ¼ À299.2 kJ molÀ1. The values
of entropy S, free energy function À(GÀH298)/T, and
Gibbs free energy of formation DfG of (U0.8Pu0.2)N(s)
are also given in Table 6. The equation of DG for
(U0.8Pu0.2)N is given as
Df Gð J molÀ1 Þ ¼ À2:909 Â 105 þ 67:56T þ 0:007980T 2

–200


À 1:098 Â 10À6 T 3 À 7:455 Â 105 =T
: Matsui and Ohse76
: Kent and Leary68

–300

500

1000

1500

2000

2500

3000

Temperature (K)
Figure 22 Temperature dependences of the Gibbs free
energy of formation, DfG for PuN(s). Data from Matsui, T.;
Ohse, R. W. High Temp. High Press. 1987, 19, 1–17;
Kent, R. A.; Leary, J. A. High Temp. Sci. 1969, 1, 176–183.
Table 6

½15Š

ð298 < T ðKÞ < 3000Þ
2.03.3.4.4 Neptunium mononitride and

americium mononitride

Nakajima et al.70 have estimated the values of DfG for
NpN(s). Figure 23 shows the temperature dependence of DfG, together with DfG for UN(s), as given

The standard thermodynamic functions of (U0.8Pu0.2)N

T (K)

Cp (J molÀ1 KÀ1)

HÀH298 (J molÀ1)

S (J molÀ1 KÀ1)

À(GÀH298)/T
(J molÀ1 KÀ1)

DfG (J molÀ1)

298
300
400
500
600
700
800
900
1000
1100

1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400
2500
3000

48.18
48.26
51.46
53.57
55.24
56.71
58.07
59.37
60.63
61.87
63.12
64.35
65.57
66.79

68.01
69.22
70.43
71.64
72.85
74.05
75.26
76.46
77.66
78.87
84.87

0
96
5172
10 354
15 796
21 395
27 134
33 007
39 007
45 184
51 433
57 806
64 302
70 921
77 661
84 522
91 505
98 608

105 832
113 177
120 643
128 228
135 935
143 761
184 696

67.07
67.39
83.85
93.47
103.39
112.02
119.68
126.60
132.92
138.91
144.35
149.45
154.26
158.83
163.18
167.34
171.33
175.17
178.87
182.45
185.93
189.30

192.58
195.77
210.68

67.07
67.07
70.92
72.77
77.07
81.45
85.76
89.92
93.91
97.83
101.49
104.98
108.33
111.55
114.64
117.62
120.49
123.27
125.96
128.56
131.09
133.55
135.94
138.27
149.12


À272 623
À272 463
À264 527
À256 576
À248 723
À240 926
À233 156
À225 395
À217 422
À209 381
À201 030
À192 746
À184 520
À175 853
À167 164
À158 499
À149 859
À141 237
À132 654
À124 114
À115 614
À107 156
À98 723
À90 365
À45 975

Source: Matsui, T.; Ohse, R. W. High Temp. High Press. 1987, 19, 1–17.


Thermodynamic and Thermophysical Properties of the Actinide Nitrides


30
–90
–100

: UN (Hayes et al.46)
: PuN (Matsui and Ohse76)
: NpN (Nakajima et al.70)

25

–110
–120
–130
–140
–150
1600

1700

1800
1900
Temperature (K)

2000

2100

Figure 23 Temperature dependences of the Gibbs free
energy of formation, DfG for NpN(s) compared with those for

UN(s) and PuN(s). Data from Hayes, S. L.; Thomas, J. K.;
Peddicord, K. L. J. Nucl. Mater. 1990, 171, 300–318;
Matsui, T.; Ohse, R. W. High Temp. High Press. 1987, 19,
1–17; Nakajima, K.; Arai, Y.; Suzuki, Y. J. Nucl. Mater. 1997,
247, 33–36.

Thermal conductivity (Wm–1 K–1)

Gibbs free energy of formation (kJ mol–1)

76

UN (Arai et al.86)
20
NpN (Nishi et al.87)
NpN (Arai et al.88)
15
PuN (Arai et al.86)
10

5

by Hayes et al.46 and the DfG for PuN(s), as given by
Matsui and Ohse.76 The line for NpN(s) is that of the
following equation and was determined by a leastsquares treatment of the data:
Df Gð J molÀ1 Þ ¼ À295 900 þ 89:88T
ð1690 < T ðKÞ < 2030Þ

½16Š


Nakajima et al. have evaluated these results in the
temperature range of 1690–2030 K using the data of
N2(g) pressure over NpN(s) þ Np(1) derived upon
extrapolation of the experimental data given by
Olson et al. Then, Nakajima et al.85 have also carried
out a mass-spectrometric study on NpN(s) co-loaded
with PuN(s) in order to control the N2(g) pressure by
the congruent vaporization of PuN(s). The DfG value
calculated for NpN(s) almost completely agrees with
that obtained from eqn [16].
Ogawa et al.34 have estimated the Gibbs free
energy of formation for AmN from the partial pressure of Am(g) over (Pu,Am)N. Their values of DG for
AmN(s) are given by the following equation:
DGð J molÀ1 Þ ¼ À297659 þ 92:054T
ð298 < T ðKÞ < 1600Þ
2.03.3.5

½17Š

Thermal Conductivity

In order to determine the thermal conductivity, it is
necessary to obtain the thermal diffusivity. Thermal
diffusivity is determined by the laser flash method.

AmN (Nishi et al.87)

500

1000

Temperature (K)

1500

Figure 24 Thermal conductivities of actinide
mononitrides. Data from Arai, Y.; Suzuki, Y.; Iwai, T.;
Ohmichi, T. J. Nucl. Mater. 1992, 195, 37–43; Nishi, T.;
Takano, M.; Itoh, A.; Akabori, M.; Arai, Y.; Minato, K.
In Proceedings of the Tenth OECD/NEA International
Information Exchange Meeting on Actinide and Fission
Product Partitioning and Transmutation, Thermal
Conductivities of Neptunium and Americium Mononitrides,
Mito, Japan, Oct 6–10, 2008; 2010, CD-ROM; Arai, Y.;
Okamoto, Y.; Suzuki, Y. J. Nucl. Mater. 1994, 211, 248–250.

The temperature dependence of the thermal
conductivities of actinide mononitrides is shown in
Figure 24. The thermal conductivity of UN was
assessed by Arai et al.,86 that of NpN was assessed
by Nishi et al.87 and Arai et al.,88 that of PuN was
assessed by Arai et al.86 and that of AmN was assessed
by Nishi et al.87 These are plotted here. The thermal
conductivities of the actinide mononitrides increased
with an increase in temperature over the temperature
range investigated. The increase in thermal conductivities of the actinide mononitrides is probably due
to the increase in the electronic component.
Figure 24 clearly shows that the thermal conductivity of the actinide mononitrides decreases with
increase in the atomic number of actinide elements.
Although phonons and electrons both may contribute
to the thermal conductivity of actinide mononitrides,

the electronic contribution is probably predominant at
higher temperatures. The electrical resistivity of actinide mononitrides increases with an increase in the


Thermodynamic and Thermophysical Properties of the Actinide Nitrides

atomic number, so the tendency of the thermal conductivity to decrease with an increase in the atomic number
would indicate a reduction in electronic contribution.89
The thermal conductivity values of NpN, as
reported by Nishi and by Arai, agree well with each
other below 1100 K, but there is some discrepancy
between the two data sets at higher temperatures.
It should be noted that the thermal conductivity values
of NpN have some uncertainty due to the inaccuracy
of the heat capacity data. Nishi has determined thermal conductivity values using experimental heat
capacity values. However, the thermal conductivity
of NpN has a large range of error because the heat
capacity of NpN at temperatures higher than
1067 K were calculated by simply extrapolating
eqn [11]. As a result, the data sets of Arai et al.
are taken here as the reference standard for the thermal conductivities of UN, NpN, and PuN. The thermal conductivities of UN, NpN, and PuN corrected to
100% TD (theoretical density) are given by
UN : l ¼ À17:75 þ 0:08808T À 6:161 Â 10À5 T 2
þ 1:447 Â 10À8 T 3
½18Š

ð680 < T ðKÞ < 1600Þ
NpN : l ¼ 7:89 þ 0:0127T À 4:32 Â 10À6 T 2
ð740 < T ðKÞ< 1600Þ


½19Š

PuN : l ¼ 8:18 þ 0:0522T À 9:44 Â 10À7 T 2
ð680 < T ðKÞ< 1600Þ

½20Š

The thermal conductivity of AmN, corrected to
100% TD, has been reported only by Nishi et al.87

The thermal conductivities of Am, corrected to 100%
TD, in the temperature range from 473 to 1473 K. can
be expressed by
l ¼ 8:99 þ 0:00147T À 2:54 Â 10À8 T 2

30

a

20

b
c
d

UN

15
a : (U0.80Pu0.20)N


PuN

b : (U0.65Pu0.35)N
c : (U0.40Pu0.60)N

5

d : (U0.20Pu0.80)N

Thermal conductivity (Wm–1 K–1)

Thermal conductivity (Wm–1 K–1)

25

0

½21Š

The thermal conductivities of (U,Pu)N solid
solutions have been reported by Arai et al.,86
Ganguly et al.,90 Alexander et al.,77 and Keller.91
The data of Arai et al. for the (U,Pu)N solid solutions
agrees with the data of the other investigations. The
data reported by Arai et al. are plotted in Figure 25.
The temperature dependence of thermal conductivity for (U,Pu)N solid solutions is similar to
the other mononitrides; but thermal conductivity
decreases rapidly with the addition of PuN. This
means that a simple averaging method cannot be
applied for the evaluation of the thermal conductivity

of the solid solutions of actinide mononitrides.
The thermal conductivities of (U,Np)N and
(Np,Pu)N solid solutions have been reported by
Arai et al.89 and those of (Np,Am)N and (Pu,Am)N
solid solutions have been reported by Nishi et al.80
Data on (U,Np)N and (Np,Pu)N solid solutions are
plotted in Figure 26 and the data on (Np,Am)N and
(Pu,Am)N solid solutions are plotted in Figure 27.
The behavior of (U,Np)N, (Np,Pu)N, (Np,Am)N,
and (Pu,Am)N solid solutions was found to be similar
to that of (U,Pu)N.
The composition dependence of the thermal conductivities for (U,Pu)N, (U,Np)N, (Np,Pu)N, (Np,Am)
N, and (Pu,Am)N solid solutions at 773 and 1073 K
are shown in Figure 28. It can be seen from these
graphs that the thermal conductivities of (U,Pu)N and

30

10

77

25
a b
20
15
10

800


1000

1200

1400

1600

Temperature (K)
Figure 25 Thermal conductivity of (U,Pu)N solid
solutions. Reproduced from Arai, Y.; Suzuki, Y.; Iwai, T.;
Ohmichi, T. J. Nucl. Mater. 1992, 195, 37–43.

d
e

NpN
PuN

a : (U0.75Np0.25)N
b : (U0.50Np0.50)N

5

c : (U0.25Np0.75)N
0

600

c


UN

600

800

1000

d : (Np0.67Pu0.33)N
e : (Np0.33Pu0.67)N
1200

1400

1600

Temperature (K)
Figure 26 Thermal conductivity of (U,Np)N and (Np,Pu)N
solid solutions. Reproduced from Arai, Y.; Nakajima, K.;
Suzuki, Y. J. Alloys Compd. 1998, 271–273, 602–605.


78

Thermodynamic and Thermophysical Properties of the Actinide Nitrides

20
(Np,Am)N


15
NpN
a
10 AmN
b
c
5

0

a : (Np0.75Am0.25)N
b : (Np0.50Am0.50)N
c : (Np0.25Am0.75)N

Thermal conductivity (Wm–1K–1)

Thermal conductivity (Wm–1 K–1)

20

(Pu,Am)N
15

10

5

0

500

1000
Temperature (K)

a
AmN
b

PuN

a : (Pu0.75Am0.25)N
b : (Pu0.50Am0.50)N
500
1000
Temperature (K)

Figure 27 Thermal conductivities of (Np,Am)N and (Pu,Am)N solid solutions. Reproduced from Nishi, T.; Takano, M.;
Itoh, A.; et al. IOP Conf. Ser. Mater. Sci. Eng. 2010, 9, 012017.
25
At 773 K
20
15

10

5

: (U,Pu)N
: (U,Np)N
: (Np,Pu)N


: (Np,Am)N
: (Pu,Am)N

0
0.4
0.6
0.8
1.0
0.0
0.2
Compositions of solid solutions
UN
NpN
PuN

NpN
PuN
AmN

Thermal conductivity (Wm–1 K–1)

Thermal conductivity (Wm–1 K–1)

25

At 1073 K
20

15


10

5

: (U,Pu)N
: (U,Np)N
: (Np,Pu)N

: (Np,Am)N
: (Pu,Am)N

0
0.4
0.6
0.8
1.0
0.0
0.2
Compositions of solid solutions
UN
NpN
PuN

NpN
PuN
AmN

Figure 28 Composition dependence of the thermal conductivities of (U,Pu)N, (U,Np)N, (Np,Pu)N, (Np,Am)N, and
(Pu,Am)N solid solutions at 773 and 1073 K. Reproduced from Nishi, T.; Takano, M.; Itoh, A.; et al. IOP Conf. Ser. Mater.
Sci. Eng. 2010, 9, 012017.


(Np,Pu)N decrease with an increase in the Pu content;
that of (U,Np)N decreases with an increase in Np
content, and those of (Np,Am)N and (Pu,Am)N decrease with an increase in Am content.
It has been proposed that the thermal conductivities of the actinide mononitrides decrease with an
increase in the atomic number of the actinide element
because the electrical resistivities of the actinide
mononitrides have a tendency to increase with an
increase in the atomic number.89 Thus, the decrease
in thermal conductivity with an increase in Pu or
Np or Am content may correspond to the lowering
of the electronic contribution. These data suggest
that the thermal conductivities of the binary actinide nitride solid solutions are lower than those

derived from the arithmetic mean of their constituent
nitrides. In addition, the thermal conductivities of
(Np0.33Pu0.67)N, (Np0.25Am0.75)N, and (Pu0.50Am0.50)N,
at 773 and 1073 K, were smaller than those of PuN
or AmN, especially at lower temperature. Although
the mechanism for this degradation in the thermal
conductivity of the solid solutions has not yet been
clarified, it might be caused by phonon scattering
between Np and Pu, and Np or Pu and Am atoms, as
this tendency was prominent at the lower temperature.
Porosity correction is necessary to estimate the
thermal conductivity with 100% TD (lTD) for the
present handbook from the measured values (l), with
lTD being needed to compare the thermal conductivity of the actinide mononitrides. Arai et al. have



Thermodynamic and Thermophysical Properties of the Actinide Nitrides

made this correction using the Maxwell–Eucken
equation:
lTD ¼

ð1 þ bPÞ
l
ð1 À PÞ

½22Š

where P is porosity and the constant b is related to
the characteristics of pores in the matrix. Unity is a
popular value of b, and is used in the case where
samples are fabricated by a conventional powdermetallurgical route. However, it should be noted
that b might be about 3 when samples have large
and closed pores, especially when they are prepared
by using pore formers, as pointed out by Arai et al.86
On the other hand, Nishi et al.80,87,92 have made a
porosity correction using the Schulz equation:
l ¼ lTD ð1 À PÞX

given the above interaction. The swelling behavior is
also important and is described in another chapter.
Thermal expansion is discussed in this chapter.

2.03.4.1

2.03.4 Mechanical Properties

During irradiation in reactors, the fuel pellets are
deformed by various processes, including densification, thermal expansion, swelling by fission products,
and creep. This deformation may eventually lead to
an interaction with the cladding, which has resulted
in reactor failure. The elastic and plastic properties of
fuel pellets, as well as creep rate, are very important,

Mechanical Properties of UN

The mechanical properties of UN have been summarized by Hayes et al.94 A summary of the different
measurements of creep rate is plotted in Figure 29.
As the creep rate depends on many parameters such
as stress level, stoichiometry, density, and impurity, as
well as temperature, there is no systematic trend at
each specific temperature. High temperature, steady
state creep is generally expressed by the following
equation,94

½23Š

They have proposed a parameter X ¼ 1.5 for closed
pores that are spherical in shape. Among a variety of
porosity correction formulas, eqn [23] was in the best
agreement with the results of finite element computations in a wide range of porosities up to 0.3, as
reported by Bakker et al.93

79

e_ ¼ Ad Àm sn expfÀQ =RT g


½24Š

where e_ is creep rate, A is a constant, d is grain size,
s is stress, m is the grain size exponent, n is the stress
exponent, Q is the activation energy, R is the gas
constant, and T is the temperature. n and m are
involved in the creep mechanism, and the value of n
is especially important in determining the mechanism that controls the creep. Hayes et al. have tried
to estimate the n values using several creep data sets
reported in individual studies, and they have found
that almost all n values were in the range of 4.0–5.9,
suggesting a dislocation climb mechanism in UN.
Assuming a dislocation climb mechanism, where
creep rate does not depend on grain size, with an
average n value of 4.5, and an m value of zero, the
following correlation94 is suggested;
e_ ¼ 2:054 Â 10À3 s4:5 expfÀ39369:5=T g

½25Š

10–3

Creep rate (s–1)

10–4

Fassler et al.102
Vandervoort et al.103
Uchida and Ichikawa104


10–5
10–6

10–7
10–8
1300

1400

1500

1600

1700

1800

1900

2000

2100

Temperature (K)
Figure 29 Experimental data for steady sate creep rate of UN. Reproduced from Hayes, S. L.; Thomas, J. K.; Peddicord,
K. L. J. Nucl. Mater. 1990, 171, 271–288, with permission from Elsevier.


80


Thermodynamic and Thermophysical Properties of the Actinide Nitrides

3.0E + 5
This work
Honda and Kikuchi105
Padel and deNovian96
Whaley et al.107

Young’s modulus (MPa)

2.5E + 5

2.0E + 5

Padel and deNovian96
Honda and Kikuchi105
Guinan and Cline106
Whaley et al.107
Speidel and Keller 108
Taylor and McMurtry109
Samsonov and Vinitskii110
Hall111

1.5E + 5

1.0E + 5

5.0E + 4
0.00


0.05

0.10

0.15
Porosity

0.20

0.25

0.30

Figure 30 Measured Young’s modulus and fitting curves for UN. Reproduced from Hayes, S. L.; Thomas, J. K.;
Peddicord, K. L. J. Nucl. Mater. 1990, 171, 271–288, with permission from Elsevier.

This equation is valid only for the creep of theoretically dense UN in the temperature range of 1770–
2083 K and under stress ranging from 20 to 34 MPa. It
has been reported that if the density of UN is below
the TD, the creep rate can be obtained by multiplying it with the following factor,95
f ðpÞ ¼

0:987
expfÀ8:65pg
ð1 À pÞ27:6

½26Š

where p is the porosity.
Various measurements of Young’s modulus at

room temperature are summarized in Figure 30.
Young’s modulus depends not only on temperature
but also on porosity. The variation in Young’s modulus,
as a function of porosity, has been measured by two
different methods, velocity measurement and frequency measurement; but no clear difference between
the results of these two methods has been found.
A power law relation was fitted to these experimental
data at room temperature and was combined with the
linear temperature dependence data reported by
Padel and deNovion96 and the following correlation
was obtained94:
E ¼ 0:258D

3:002

À5

½1 À 2:375  10 T Š

½27Š

where E is the Young’s modulus and D is the ratio of
density with TD in percent. This equation is valid
where the ratio of TD is from 75% to 100% and the
temperature ranges from 298 to 1473 K. As this equation fits well with all the experimental data obtained

from samples with uncontrolled pore shape and orientation, porosity distribution, average grain size,
grain shape, orientation, and impurities, as shown in
Figure 30, the dependence of Young’s modulus on
these parameters is small.

The following correlation94 of the shear modulus
with density and temperature was obtained by a
method similar to that used for determining the
Young’s modulus:
G ¼ 1:44  10À2 D3:446 ½1 À 2:375  10À5 T Š

½28Š

where G is the shear modulus. This relation is valid
under the same density and temperature conditions
as the Young’s modulus.
As the data for the bulk modulus could not be
measured directly and was calculated from measurements of Young’s and shear modulus in the various
studies, the degree of data scatter is larger here, compared to the other properties. The following correlation94 with density and temperature was obtained in a
method similar to that used for Young’s modulus and
shear modulus:
K ¼ 1:33  10À3 D4:074 ½1 À 2:375  10À5 T Š

½29Š

where K is the bulk modulus.
Poisson’s ratio for UN was assumed to be independent of temperature. Similar to the bulk modulus,
Poisson’s ratio can be estimated from measurements
of Young’s modulus and shear modulus, and small
errors in measurements of Young’s and shear


Thermodynamic and Thermophysical Properties of the Actinide Nitrides

81


Lattice parameter (Å)

5.05

5.00

Benz et al.112
Kempter and Elliott113
This work
Kempter and Elliott113

4.95

4.90

4.85
200

700

1200
1700
Temperature (K)

2200

2700

Figure 31 Variation of lattice parameter of UN with temperature. Reproduced from Hayes, S. L.; Thomas, J. K.;

Peddicord, K. L. J. Nucl. Mater. 1990, 171, 262–270, with permission from Elsevier.

modulus have resulted in the large scatter of these
calculations. Under the assumption that Poisson’s
ratio is independent of temperature, the following
correlation94 with porosity is obtained:
n ¼ 1:26 Â 10À3 D1:174

½30Š

where n is Poisson’s ratio and D is the density ranging
70–100%.
The hardness values, which are easily obtained
experimentally, decreased with porosity and temperature. The hardness decrease with porosity linearly
and decrease with temperature exponentially. In the
porosity range of 0–0.26 and the temperature range of
298–1673 K, the following correlation94 is valid:
HD ¼ 951:8f1 À 2:1pgexpfÀ1:882 Â 10À3 T g

½31Š

where HD is the diamond point hardness.

2.03.4.2

Thermal Expansion of UN

The thermal expansion of UN has also been estimated
by Hayes et al.56, as shown in Figure 31. As thermal
expansion, measured by the dilatometer method, is

affected by sample density and has a large degree of
uncertainty, thermal expansion was calculated from
the temperature dependence of the lattice parameter.
The lattice parameter also is influenced by impurities,
but the variation due to impurities is much less than
the variation with temperature.
The temperature dependence of lattice parameter56 is given by:
a ¼ 4:879 þ 3:254  10À5 T þ 6:889  10À9 T 2 ½32Š

where a is the lattice parameter in Angstroms. The
linear thermal expansion coefficient56 is given by:
a ¼ 7:096 Â 10À6 þ 1:409 Â 10À9 T

½33Š

where a is the mean linear thermal expansion coefficient and T is temperature.
2.03.4.3

Mechanical Properties of PuN

There are very few studies on the mechanical properties of pure PuN. Matzke1 has reported the elastic
moduli of (U0.8Pu0.2)N at room temperature, the
porosity dependence of its Young’s modulus, its
Poisson ratio, and the temperature dependence of its
elastic moduli. The Young’s modulus of (U0.8Pu0.2)N is
about 5% higher than that of pure UN. According to
Matzke, the room temperature hardness of pure PuN
is 3.3 GPa, about half that of UN.
Thermal expansion of PuN has been recently
reexamined by Takano et al.22 The temperature

dependence of the lattice parameter of PuN aT (nm)
can be expressed as
aT ¼ 0:48913 þ 4:501 Â 10À6 T þ 6:817 Â 10À10 T 2
À 4:939 Â 10À14

½34Š

The linear thermal expansion of PuN is higher than
that of UN, as shown in Figure 32.22
The recent progress in material chemistry calculation techniques has enabled the prediction of
those properties of the actinide compounds which
have not been experimentally measured. Figure 33
shows the temperature dependence of the linear


82

Thermodynamic and Thermophysical Properties of the Actinide Nitrides

1.4
1.4
UN Takano et al.22
NpN
PuN
AmN

1.2

1.2


1.0
LTE (%)

LTE (%)

(Pu0.59Am0.41)N
(Np0.21Pu0.52Am0.22Cm0.05)N
(Pu0.21Am0.18Zr0.61)N
ZrN

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0
200


400

600

800 1000 1200 1400 1600
T (K)

Figure 32 Temperature dependence of linear thermal
expansion of PuN. Reproduced from Takano, M.;
Akabori, M.; Arai, Y.; Minato, K. J. Nucl. Mater. 2008,
376, 114–118, with permission from Elsevier.

18

0.0
200

400

600

800

1000 1200 1400 1600

T (K)
Figure 34 Temperature dependence of linear thermal
expansion of minor actinide containing nitride fuels.
Reproduced from Takano, M.; Akabori, M.; Arai, Y.;

Minato, K. J. Nucl. Mater. 2009, 389, 89–92, with
permission from Elsevier.

by doping with Pu. This calculation study also
reported the compressibility and other thermal and
thermodynamic properties of PuN.

16

Linear thermal expansion
coefficient, alin, (10–6 K–1)

(Np0.55Am0.45)N

14

2.03.4.4 Mechanical Properties of Other
MA or MA-Containing Fuels

12
10
8
6
0

500

1000 1500 2000 2500 3000 3500
Temperature, T (K)
UN (MD) Kurosaki et al.97

PuN (MD) Kurosaki et al.99
(U0.8Pu0.2)N (MD)

Figure 33 Temperature dependence of calculated
linear thermal expansion of PuN. Reproduced from
Kurosaki, K.; Yano, K.; Yamada, K.; Uno, M.; Yamanaka, S.
J. Alloys Compd. 2001, 319, 253–257, with permission
from Elsevier.

thermal expansion of PuN which was calculated by a
molecular dynamic method.97 It is seen that the calculation predicts a high thermal expansion of PuN
and an increase in the thermal expansion of (U,Pu)N

Recent studies on MA-containing fuels have
measured the thermal expansion of various Np–Pu–
Am–Cm–N compounds (shown in Figure 3498), as
well as those of NpN and AmN (Figure 32).
As shown in Figure 32, the thermal expansion of
AmN is the same as that of PuN; however, the thermal
expansion of NpN is smaller than PuN and AmN, but
is the same as that of UN. The thermal expansion of
Np–Pu–Am–Cm–N fuels decreases with a decrease
in Np content, as shown in Figure 34. The thermal
expansion of ZrN inert matrix fuels also decreases due
to the low thermal expansion of ZrN. Molecular
dynamics (MD) calculations have also predicted the
thermal expansion of some MA nitrides; these are
shown in Figure 35.99
The lack of data on MA nitrides, especially the
nitrides of pure transuranium elements, is due to

the difficulty in obtaining and treating bulk samples.
There have been some attempts to calculate the


Thermodynamic and Thermophysical Properties of the Actinide Nitrides

Linear thermal expansion coefficient , a lin (10–6 K–1)

20.0

20.0

20.0

MD result

MD result
Ref. [56]
Ref. [108]

Ref. [114]

17.5

17.5

15.0

20.0
MD result

Ref. [57]

MD result
Ref. [65]

17.5

17.5

15.0

15.0

15.0

12.5

12.5

12.5

12.5

10.0

10.0

10.0

10.0


7.5

7.5

7.5

7.5

ThN

UN
5.0

5.0
0

1000 2000 3000

Temperature T (K)

NpN
5.0

0

1000 2000 3000

Temperature T (K)


83

PuN
5.0

0

1000 2000 3000

Temperature T (K)

0

1000 2000 3000

Temperature T (K)

Figure 35 Temperature dependence of calculated linear thermal expansion of minor actinide nitrides. Reproduced from
Kurosaki, K.; Adachi, J.; Uno, M.; Yamanaka, S. J. Nucl. Mater. 2005, 344, 45–49, with permission from Elsevier.

mechanical properties of these actinide nitride samples.
One such attempt combined the calculations for
longitudinal velocity and porosity.100 In the method
employed, a newly proposed correlation between Poisson’s ratio and the ultrasonic longitudinal velocity was
utilized, and the elastic properties of uranium nitride
as well as uranium dioxide were estimated from the
porosity and longitudinal velocity derived from ultrasonic sound velocity measurements; these had been
previously used to determine mechanical properties
of actinide materials. Another method estimated fracture toughness from the Young’s modulus, hardness, the
diagonal length and the length of micro cracks. Except

for Young’s modulus, all the other properties were
obtained by an indentation method.101 In this study,
not only was the fracture toughness reported, but its
load dependence, in the case of UN, was also reported.

these are difficult to obtain and handle and are scarce.
Some properties of the inert matrix fuels such as
(An,Zr)N solid solution and AnN and TiN mixture
have been obtained through recent studies on the
targets for transmutation in an ADS. Recent progress
in experimental procedures and estimation methods,
which are supported by developments in model calculation, have also been discussed.
The progress made in experimental techniques
and calculation science has brought about growth in
the understanding of the behavior of these nitrides.
However, we need to accumulate more data, especially in the thermal and mechanical properties
around 1673 K, in-reactor temperature, and the variation of those with burnup, in order to accurately
predict the in-reactor behavior of these fuels (see
Chapter 3.02, Nitride Fuel).

2.03.5 Summary

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hand, some properties (especially physical) need
bulk samples for measurements, especially the transuranium elements such as NpN, AmN, and CmN;


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