2.11

Neutron Reflector Materials (Be, Hydrides)

S. Yamanaka and K. Kurosaki
Osaka University, Suita, Japan

ß 2012 Elsevier Ltd. All rights reserved.

2.11.1

Required Properties

307

2.11.2
2.11.2.1
2.11.2.2
2.11.2.3
2.11.3
2.11.3.1
2.11.3.2
2.11.3.3
2.11.3.4
2.11.3.5
2.11.3.6
2.11.3.7
2.11.3.8
2.11.3.9

Beryllium

Introduction
Production and Processing Methods1
Basic Properties
Fundamental Properties of Metal Hydrides
Introduction
Production of Zirconium Hydride20
Lattice Parameter20
Elastic Modulus and Hardness20,21
Electronic Structure22
Electrical Conductivity22
Heat Capacity20
Thermal Conductivity of Metal Hydrides23
Comparison of Thermal Conductivity of Zirconium Hydride with those of the
Hydrides of Titanium and Yttrium
Conclusion
Summary

308
308
308
308
312
312
312
314
314
315
316
317
317


2.11.3.10
2.11.4
References

Abbreviations
DOS Density of state
MO Molecular orbital

Symbols
B
D
E
G
H
Hv
Tm
Ttr
l
lel

Bulk modulus
Diffusivity
Young’s modulus
Shear modulus
Enthalpy
Vickers hardness
Melting temperature
Transformation temperature
Thermal conductivity

Electronic contribution to thermal
conductivity
Lattice thermal conductivity
llat
r
Electrical resistivity
s
Electrical conductivity
DmH Enthalpy of fusion
DtrsH Enthalpy of transition

318
320
321
321

2.11.1 Required Properties
Two highly desirable properties of both neutron
reflectors and moderators are efficient neutron slowing and low neutron absorption. The first requires
effective slowing of neutrons over short distances,
thus reducing the required volume of the reflector or
moderator in the reactor core. Moreover, in a reactor
core of a given shape and volume, this reduces the
leakage of neutrons in the course of their slowing.
For reflectors in particular, the key requirements
include a high reflectivity, a large macroscopic crosssection, and efficient neutron slowing. The reflectivity
of a material is inversely proportional to its diffusion
ratio (D/L), which is the ratio of its diffusivity (D) to its
diffusion length (L). This ratio is generally considered to
decrease as scattering becomes large in comparison with

absorption. It is essential, moreover, to obtain high
reflectivity without excessive thickness, and for this
purpose, to use a material with a large macroscopic
total cross-section. In a thermal reactor, the performance
of the reflector is enhanced if it does not simply reflect
the neutrons but rather slows and then reflects them,

307


308

Neutron Reflector Materials (Be, Hydrides)

and for this reason, the same material is often used as
both reflector and moderator.
In general, materials whose nuclides have low mass
number and neutron absorption may be used as moderators and reflectors. The most commonly used
materials are light water (H2O), heavy water (D2O),
and graphite (C). In addition, hydrocarbons, zirconium hydride, and other such materials are often
used as moderators. Heavy water is particularly effective because of its very low absorption level. Graphite
is second to heavy water in its low absorption level, is
lower in cost, and has the added advantage of suitability for use at high temperatures. Beryllium is generally used as a reflector rather than as a moderator.
In addition to the aforementioned materials, there
exist other candidates as neutron reflectors. For example, Commissariat a` l’Energie Atomique (CEA) is
studying zirconium silicide as the reflector for next
generation reactors.1 Tungsten carbide has also been
used as neutron reflectors ( />wiki/Tungsten_carbide). For fusion reactors, various
materials such as titanium carbide and boron carbide
are considered as reflectors.2

This chapter outlines the basic properties of beryllium and zirconium hydride that are fundamental
to their utilization as neutron reflectors and moderators in nuclear reactors.

2.11.2 Beryllium
2.11.2.1

Introduction

Apart from its use as a neutron reflector and moderator in nuclear reactors, beryllium is in strong demand
for use in X-ray windows of medical and industrial
equipment, acoustic speaker diaphragms, galvano mirrors for laser drilling, reflected electron guard plates in
semiconductor production equipment, and various
other applications. It is also widely used in the electrical and electronic industry, particularly in beryllium–
copper alloys for wrought metal production and for
molds and other forging tools and dies. In electronics,
in particular, the need for beryllium has been growing
rapidly in recent years with the trend toward lighter,
thinner, and smaller electronic components. In the
following sections, we outline the methods of its production and processing and discuss its basic properties.

10–14% beryllium oxide (BeO). At present, the two
main industrial processes used to extract BeO from
beryl are the fluoride method and the sulfuric acid
method. Both of these yield BeO of industrial-grade
purity, which is used as a raw material for Be–Cu
mother alloys, electronics manufacture, refractories,
and other fields of application. For use in nuclear
reactors, BeO is further purified by recrystallization
or precipitation.
Metallic beryllium (Be) is produced from BeO or

Be(OH)2 by either of two industrial processes. One
involves the formation of BeF2 followed by its thermal reduction with Mg to produce Be pebbles, and
the other involves the formation of BeCl2 followed by
its electrolysis to produce Be flakes. The resulting
pebbles and flakes are high in Mg and Cl2 content,
respectively, and these impurities are removed by
vacuum melting.
The principal techniques of Be processing are
molding by powder metallurgy, warm or hot working,
and joining or welding. In hot-press sintering, which
has been widely developed for Be molding, the starting material is commonly À200 mesh Be powder,
which is inserted between graphite dies and then
pressure molded in vacuum at high temperatures
(1323 K). The resulting moldings are commonly
called ‘hot-press blocks,’ and can be obtained with
high integrity and near theoretical density. Other
molding methods that may be employed include
spark plasma sintering and cold-press sintering.
Cold working of Be at room temperature is
extremely difficult because of its low elongation,
and it is accordingly formed into plates, rods, or
tubes by ‘warm working’ at 773–1173 K or ‘hot working’ at 1273–1373 K. In either case, the Be must be
covered with mild steel or some other material and
the intervening air withdrawn before it is heated, as it
readily oxidizes at high temperatures.
Various methods have been developed for Be joining and welding. These include mechanical joining
and resin bonding, electron-beam and diffusion welding, and brazing and soldering. Because of its high
oxygen affinity, however, any process in which the
Be is heated must be performed under an appropriate
inert gas or vacuum.

2.11.2.3

2.11.2.2 Production and Processing
Methods1
Among the 30 or so naturally occurring ores, the most
economically important is beryl, which contains

Basic Properties

The crystal structure of Be is closed-packed hexagonal with a c/a ratio of 1.5671 and lattice parameters
a ¼ 0.22866 nm and c ¼ 0.35833 nm.3 Table 1 shows
the basic properties of Be.4,5 It weighs only about


Neutron Reflector Materials (Be, Hydrides)

two-thirds as much as aluminum (Al), and both its
melting point and its specific heat capacity are quite
high for a light metal. It is widely known for its high
Young’s modulus and other elastic coefficients. Its
nucleus is small in neutron absorption cross-section
and relatively large in scattering cross-section, both of
which are advantageous for use as a moderator or
reflector. Its superior high-temperature dynamical
Table 1

309

properties are also advantageous for use in nuclear
reactors. It emits neutrons under g-ray irradiation and

can thus be used as a neutron source. Its soft X-ray
absorption is less than one-tenth that of Al, making it
highly effective as a material for X-ray tube windows.
Figure 1 shows the temperature dependence of
the specific heat capacities of various Be samples.3
The following equations describing the specific heat
capacity of Be are reported.3
CP ¼ 11:8 þ 9:12 Â 10À3 T

Basic properties of Be

Crystal structure
Density (near room temperature) (g cmÀ3)
Melting point (K)
Boiling point (K)
Heat of fusion (kJ molÀ1)
Heat of vaporization (kJ molÀ1)
Heat capacity (302 K) (J KÀ1 molÀ1)
Thermal conductivity (300 K) (W mÀ1 KÀ1)
Thermal expansion coefficient (302 K) (KÀ1)
Speed of sound (room temperature) (m sÀ1)
Young’s modulus (GPa)
Shear modulus (GPa)
Bulk modulus (GPa)
Poisson ratio
Vickers hardness (GPa)
Scattering cross-section (barn)
Absorption cross-section (barn)
Moderating ratio
Diffusion ratio


Hexagonal
1.85
1560
2742
7.895
297
16.443
200
11.3 Â 10À6
12 870
287
132
130
0.032
1.67
6
0.009
0.0597
0.0273

Source: Genshiryoku Zairyou Handbook; The Nikkan Kogyo
Shimbun: Tokyo, 1952; />Rare Metals Handbook, 2nd ed.; Reinhold: New York, NY, 1961.

ð J KÀ1 gÀ1 atom; from 600 to 1560 KÞ
CP ¼ 25:4 þ 2:15 Â 10À3 T
ð J KÀ1 gÀ1 atom; from 1560 to 2200 KÞ
Temperature dependences of the thermal expansion
coefficient and the electrical resistivity of Be3 are
given in Figures 2 and 3, respectively. Figure 4

shows the temperature dependence of the thermal
conductivities of various Be samples.3,6 Be exhibits
relatively high thermal conductivity values around
200 W mÀ1 KÀ1 at room temperature, and the values
decrease with temperature. The effect of high-dose
neutron irradiation on the thermal conductibility of
Be has been investigated.7,8 It is reported by Chakin
et al.7 that neutron irradiation at 303 K to a neutron
fluence of 2 Â 1022 cmÀ2 (E > 0.1 MeV) leads to sharp
decrease of thermal conductivity, in particular at
303 K, the thermal conductivity decreases by a factor

Specific heat capacity, CP (J K-1 g-1)

4

3

2

1

0
0

200

400

600

800
Temperature, T (K)

1000

1200

Figure 1 Temperature dependence of the specific heat capacity of various Be samples. Different marks mean different
samples. Reproduced from Beeston, J. M. Nucl. Eng. Des. 1970, 14, 445.


310

Neutron Reflector Materials (Be, Hydrides)

Thermal expansion coefficient (´10-6 K-1)

70
60
50
Volume
40
30

Linear, perpendicular to hexagonal axis

20
10

Linear, parallel to hexagonal axis


0
400

600

800
1000
Temperature, T (K)

1200

1400

Figure 2 Temperature dependence of the thermal expansion coefficient of Be. Reproduced from Beeston, J. M. Nucl. Eng.
Des. 1970, 14, 445.

35

Electrical resistivity, r (μΩ cm)

30
25
20
15
10
5
0
200


400

600
800
Temperature, T (K)

1000

1200

Figure 3 Temperature dependence of the electrical resistivity of Be. Different marks mean different samples.
Reproduced from Beeston, J. M. Nucl. Eng. Des. 1970, 14, 445.

of five, but short-term high-temperature annealing
(773 K for 3 h) leads to partial recovery of the thermal
conductivity.
In addition to the data listed in Table 1, the
thermodynamic properties of Be have been reported
recently,9 in which the temperatures of transformation Ttr and melting Tm, and the enthalpies of transformation DtrH and melting DmH are measured

by difference thermal analysis and by anisothermal
calorimetry. It is reported by Kleykamp9 that the
results for hcp–bcc transformation of Be are
Ttr ¼ 1542 Æ 1 K and DtrH ¼ 6.1 Æ 0.5 kJ molÀ1 and
those for the melting process are Tm ¼ 1556 Æ 2 K
and DmH ¼ 7.2 Æ 0.5 kJ molÀ1.
A fine, transparent BeO film of about 10À6 cm
thickness forms on Be in air, and it therefore retains



Neutron Reflector Materials (Be, Hydrides)

311

Thermal conductivity, l (W m-1 K-1)

250

200

150

100

50

0
400

600

800
1000
Temperature, T (K)

1200

1400

Figure 4 Temperature dependence of the thermal conductivities of various Be samples. Different marks mean different

samples. Adapted from Beeston, J. M. Nucl. Eng. Des. 1970, 14, 445; Chirkin, V. S. Trans. Atom. Ener. 1966, 20, 107.

its metallic gloss when left standing. This results in its
passivation in dry oxygen at up to 923 K, but the
oxidized film breaks down at temperatures above
about 1023 K and it thus becomes subject to progressive oxidation.10 It reacts with nitrogen at 1173 K or
higher, forming Be2N3, and with NH3 at lower temperatures.10 Be undergoes passivation in dry CO2 at
up to 973 K, but only up to 873 K in moist CO2.11,12
Its resistance to corrosion by water varies with temperature, dissolved ion content, pH, and other factors;
it is reportedly poor in water containing ClÀ
(1–10 ppm), SO42À (5–15 ppm), Cu2þ (0.1–5 ppm),
Fe2þ (1–10 ppm), or other such ions.10
Among the various compounds formed by Be, BeO
and Be2C may be taken as typical. The basic properties
of BeO are shown in Table 2.4 Its melting point and
thermal conductivity are both high,13 its heat shock
resistance is excellent, its thermal neutron absorption
cross-section is small, and its corrosion resistance to
CO2 at high temperatures is also excellent. Be2C is
formed by reaction of Be or BeO with C. Its basic
properties are density, 2.44 g cmÀ3; specific heat capacity, 41.47 J KÀ1 molÀ1 (303–373 K); thermal expansion
coefficient, 10.5 Â 10À6 KÀ1 (298–873 K); and electric
resistivity, 0.063 O m (303 K). It is reportedly unstable
in moist air.10
Intrinsically, BeO is an excellent moderator and
reflector material in nuclear reactors. Various utilizations of BeO in reactors14 and behavior of BeO under
neutron irradiation have been reported.15 Especially,

Table 2


Basic properties of BeO

Crystal structure
Density (near room temperature)
(g cmÀ3)
Melting point (K)
Boiling point (K)
Thermal conductivity (293 K)
(W mÀ1KÀ1)
Thermal expansion coefficient
(293–373 K) (KÀ1)
Electrical resistivity (1273 K) (O cm)
Scattering cross-section (barn)
Absorption cross-section (barn)
Moderating ratio
Diffusion ratio

Hexagonal wurtzite
3.02
2780
4173
281
5.5 Â 10À6
8.0 Â 107
9.8
0.0092
0.0706
0.0273

Source: Genshiryoku Zairyou Handbook; The Nikkan Kogyo

Shimbun: Tokyo, 1952; Gregg, S. J.; et al. J. Nucl. Mater. 1961,
4, 46.

the effect of neutron irradiation on the thermal conductivity of BeO has been widely studied.16,17 Figure 5
shows the temperature dependence of the thermal conductivity of unirradiated and irradiated BeO.17 It is
observed that irradiation of BeO with neutrons considerably reduces the thermal conductivity. It has also been
reported that the irradiation-induced change in thermal
conductivity can be removed by thermal annealing, but
complete recovery is not achieved until an annealing
temperature of 1473 K is reached.
One further important property of Be that must
be noted is its high toxicity. The effect of Be dust,
vapor, and soluble solutes varies among individuals,


312

Neutron Reflector Materials (Be, Hydrides)

Thermal conductivity, l (W m-1 K-1)

300

250

Unirradiated

1.2 ´ 1020 nvt

1.5 ´ 1019 nvt


4.0 ´ 1020 nvt

200

150

100

50

0
260

280

300
320
Temperature, T (K)

340

360

Figure 5 Temperature dependence of the thermal conductivity of unirradiated and irradiated BeO. Reproduced from
Pryor, A. W.; et al. J. Nucl. Mater. 1964, 14, 208.

but exposure may cause dermatitis and contact or
absorption by mucous membrane or respiratory tract
may result in chronic beryllium disease, or ‘berylliosis.’

Maximum permissible concentrations in air were
established in 1948 and include an 8-h average concentration of 2 mg mÀ3, a peak concentration of 25 mg mÀ3
in plants, and a peak concentration of 0.01 mg mÀ3
in plant vicinities.18 In relation to workplace health
and safety, particular care is necessary in the control
of fine powder generated during molding and mechanical processing. Dust collectors must be installed at
the points of generation, and dust-proof masks, dustproof goggles, and other protective gear must be worn
during work. In Japan, Be is subject to the Ordinance on
Prevention of Hazards due to Specified Chemical
Substances.

2.11.3 Fundamental Properties of
Metal Hydrides
2.11.3.1

Introduction

Zirconium hydride is used as a material for neutron
reflectors in fast reactors. The evaluation of the thermal conductivity, elastic modulus, and other basic
properties of zirconium hydride is extremely important for assessing the safety and cost-effectiveness of
nuclear reactors. Metal hydrides, of which zirconium
hydride is a typical example, are also very interesting
because they exhibit unique properties and shed light

on some fundamental aspects of physics. As part of
work on metals such as zirconium, Yanamana et al.
have successfully created crack-free, bulk-scale metal
hydrides, and systematically investigated their fundamental properties – particularly at high temperatures. Here, we present an outline of the results on
the fundamental properties of zirconium hydride.
Figure 6 shows the zirconium–hydrogen binary

phase diagram.19
2.11.3.2

Production of Zirconium Hydride20

We used polycrystalline (grain size: 20–50 mm) ingots
of high-purity zirconium as the starting material for
producing hydrides. The main impurities present in
the zirconium were O (0.25 wt%), H (0.0006 wt%),
N (0.0024 wt%), C (0.003 wt%), Fe (0.006 wt%), and
Cr (0.008 wt%). The hydride was generated with
high-purity hydrogen gas (7 N) at a prescribed pressure, using an advanced ultra-high vacuum Sieverts
instrument. Details of the instrument configuration
are given in Figure 7.
The procedure for synthesizing hydrides varies
according to the type of metal. This is due to the
phase transition, from metal to hydride that is accompanied by a massive increase in volume due to hydrogenation, and to differences in the strength of the
hydride. Figure 8 shows the external appearance
of zirconium hydride substances produced by the
author’s group.


Neutron Reflector Materials (Be, Hydrides)

0

0.2

0.4


Weight percent hydrogen
0.6
0.8
1

313

1.2 1.4 1.6 1.8 2

1000

900
863 ЊC
800

(b-Zr)

Temperature (ЊC)

700

600

δ
(a-Zr)

550 ЊC
~37.5

5.93


56.7

ε

500

400

300

200

100

0
10

0
Zr

20

30
40
50
Atomic percent hydrogen

60


70

80

Figure 6 Binary phase diagram of the zirconium–hydrogen system. d and e represent the face-centered cubic d-phase
hydride and the face-centered tetragonal e-phase hydride, respectively. Adapted from Zuzek, E.; Abriata, J. P.;
San-Martin, A.; Manchester, F. D. Bull. Alloy Phase Diagrams 1990, 11(4), 385–395.

13
9
1

2

3

11

14

12

:

8
4
5

15
7


10

11

6

1. Absolute capacitance manometer (25 ktorr)
2. Absolute capacitance manometer (1 ktorr)
3. Absolute capacitance manometer (10 torr)
4. Calibrated vessel (~50 ml)
5. Calibrated vessel (~500 ml)
6. Reactor for high pressure (steel)
7. Mantle heater (<723 K)
8. Metal filter (pore size: 2 mm)

16

9. Low temperature incubator (inner temperature: 298 K)
10. Turbo-molecular pump
11. Oil rotary vacuum pump
12. Ionization vacuum gauge
13. Liquid nitrogen trap
14. Compressed hydrogen gas cylinder
15. Reactor for high temperature (quartz glass)
16. Electric resistance furnace (<1273 K)

Figure 7 Schematic diagram of advanced Sieverts instrument.



314

Neutron Reflector Materials (Be, Hydrides)

2.11.3.3

Lattice Parameter20

2.11.3.4

Zirconium hydride or deuteride described here was
all fcc_C1 (d) ZrH2Àx or ZrD2Àx single-phase crystals with a fluorite structure. The lattice parameters
at ambient temperature of zirconium hydride or deuteride are plotted in Figure 9, as a function of hydrogen content (CH). The lattice parameter of zirconium
hydride increases slightly with increasing hydrogen
content, according to the following formula:
aðnmÞ ¼ 0:4706 þ 4:382 Â 10À3 Â CH ðH=ZrÞ:

Elastic Modulus and Hardness20,21

Figure 10 illustrates the hydrogen content dependence of the elastic modulus of zirconium hydride or
deuteride, determined using an ultrasonic pulse echo
method. The elastic modulus of zirconium hydride is
higher than that of the pure metal, and decreases
slightly with increasing hydrogen content. The
hydrogen content dependence of the elastic modulus
of zirconium hydride is expressed by the following
equations (E: Young’s modulus, G: Shear modulus,
and B: Bulk modulus):
EðGPaÞ ¼ 187:7 À 33:28 Â CH ðH=ZrÞ
GðGPaÞ ¼ 73:59 À 14:19 Â CH ðH=ZrÞ

BðGPaÞ ¼ 130:0 À 2:329 Â CH ðH=ZrÞ

Figure 8 Bulk-scale zirconium hydride.

Figure 11 illustrates the hydrogen content dependence of the Vickers hardness of zirconium hydride
and deuteride. The graph clearly shows that the
Vickers hardness of the hydride is higher than that
of pure zirconium, and that it decreases slightly with
increasing hydrogen content. Generalizing these
results, we can conclude that increasing the hydrogen
content has the effect of making zirconium hydride
and deuteride plastically ‘softer.’ The relationship
between the hardness and hydrogen content dependence for zirconium hydride is expressed by the
following formula:

Lattice parameter, a (nm)

0.479

0.478

Yamanaka
Kempter
Ducastelle
Beck
Sidhu
Moore
Cantel

0.477


0.476
1.45

1.50

1.55
1.60
1.65
Hydrogen content, CH (H–Zr)

1.70

1.75

Figure 9 Hydrogen content dependence of the lattice parameter of zirconium hydride and deuteride.


Neutron Reflector Materials (Be, Hydrides)

315

160

Elastic modulus (GPa)

140
120
100
80

60
40

E G B
a-Zr
d-ZrH2-x
d-ZrD2-x

20
0
0.0

1.5
1.6
1.7
Hydrogen content, CH (H–Zr)

1.8

Figure 10 Hydrogen content dependence of the elastic modulus of zirconium hydride and deuteride.

4.0

Vickers hardness, HV (GPa)

3.5
3.0
2.5
2.0
1.5

α-Zr
δ-ZrH2-x

1.0

δ-ZrD2-x

0.5
0.0
0.0

1.45

1.50

1.55

1.60

1.65

1.70

Hydrogen content, CH (H–Zr)
Figure 11 Hydrogen content dependence of the Vickers hardness of zirconium hydride and deuteride.

HV ðGPaÞ ¼ 7:190 À 2:773 Â CH ðH=ZrÞ

2.11.3.5


Electronic Structure22

Figure 12 shows the density of states (DOS) of zirconium hydride, determined by DV-Xa molecular
orbital (MO) calculations. Here, 0 eV corresponds
to the Fermi energy. The new band resulting

from the hydrogen is generated immediately below
the d-band of the hydride cluster, in the region
of $5–7 eV. Figure 13 shows the bond order of
zirconium hydride. With increasing hydrogen content, there is a marked decrease in the bond order
of Zr–Zr metallic bonds, whereas the bond
order of Zr–H covalent bonds does not change. This
reduction in bond order is likely due to a decrease
in the electric charge of the matrix of Zr bonds.


316

Neutron Reflector Materials (Be, Hydrides)

4

Density of states, D(E) (eV -1)

α-Zr
δ-ZrH1.0
δ-ZrH1.5
3

δ-ZrH2.0


2

1

0
-10

-5
Electron energy, E (eV)

0

Figure 12 Hydrogen content dependence of the DOS of zirconium hydride.

0.30
Zr–Zr bond
Zr–H bond

0.25

Bond order

0.20

0.15

0.10

0.05


0.00
0.0

1.0

1.5

2.0

Hydrogen content, CH (H–Zr)
Figure 13 Hydrogen content dependence of the bond order of zirconium hydride.

Since bond order can be thought to be related to the
spring constant of interatomic bonds, these results
can be understood to mean that the effective spring
constant of zirconium hydride, as a whole, decreases
with increasing hydrogen content. This hypothesis
offers a good explanation for the hydrogen content
dependence of the various properties of zirconium
hydride.

2.11.3.6

Electrical Conductivity22

Figure 14 shows the temperature dependence of
the electrical conductivity of zirconium hydride.
In line with the behavior of most metals, electrical
conductivity decreases with increasing temperature

for zirconium hydride. The hydride has a lower electrical conductivity than the pure metals.


Neutron Reflector Materials (Be, Hydrides)

317

Electric conductivity, s (´106 S m-1)

2.5
α-Zr
δ-ZrH1.56
δ-ZrH1.61
2.0

δ-ZrH1.66

1.5

1.0

300

400

500
Temperature, T (K)

600


700

Figure 14 Temperature dependence of the electrical conductivity of zirconium hydride.

δ-ZrH1.58 Tomasch
δ-ZrH1.65 Weeks
δ-ZrH1.33 Beck
ε-ZrH2.00 Flotow
ε-ZrH1.78 Beck
α-Zr
Dinsdale
δ-ZrH1.53 Yamanaka
δ-ZrH1.58 Yamanaka

Heat capacity of ZrH2-x, CP (J mol-1 K-1)

90
80
70
60
50
40
30
20
10
0
0

200


400

600
800
Temperature, T (K)

1000

1200

Figure 15 Temperature dependence of the heat capacity of zirconium hydride.

2.11.3.7

Heat Capacity20

Figure 15 illustrates the temperature dependence
of the heat capacity of zirconium hydride. It is
clear that the heat capacity of the metal hydride
is higher than that of the pure metal, particularly at
higher temperatures. This behavior can be explained
by the observation that while lattice vibrations are
dominated by the acoustic mode at low temperatures,
the contribution of the optical mode increases steadily
as the temperature increases beyond ambient values.

2.11.3.8 Thermal Conductivity of Metal
Hydrides23
Figure 16 shows the thermal conductivity of zirconium hydride, which is seen to be almost identical to
that of the pure metal, and shows no dependence on

temperature.
In order to analyze the thermal conductivity
results, we expressed thermal conductivity as the
sum of a lattice-vibration contribution (llat) and
an electronic contribution (lel). The electronic


318

Neutron Reflector Materials (Be, Hydrides)

Thermal conductivity, l (W m-1 K-1)

25

20

15

10

α-Zr
δ-ZrH1.49
δ-ZrH1.56

5

δ-ZrH1.59
δ-ZrH1.66


0
300

400

500

600

700

Temperature, T (K)
Figure 16 Temperature dependence of the thermal conductivity of zirconium hydride.

Thermal conductivity, l (W m-1 K-1)

20

15

l el
l lat
l total

10

5

0
300


400

500

600

700

Temperature, T (K)
Figure 17 Temperature dependence of the lattice-vibration and electronic contributions to thermal conductivity for
zirconium hydride (d-ZrH1.66).

contribution was evaluated from the Wiedemann–
Franz relation as follows:
lel ¼ LsT

2.11.3.9 Comparison of Thermal
Conductivity of Zirconium Hydride with those
of the Hydrides of Titanium and Yttrium

Here, L is the Lorentz constant and s is electrical
conductivity. Figure 17 plots the values of each contribution to the thermal conductivity of zirconium
hydride. Here, the electronic contribution is greater
than that of lattice vibrations, and the former increases
with temperature, whereas the latter decreases as the
temperature rises.

Figure 18 shows the thermal conductivity of titanium hydride.24 The thermal conductivity of the
hydride is approximately equal to that of the pure

metal, but in this case, it increases slightly with
hydrogen content. Figure 19 shows the thermal conductivity of yttrium hydride.25 In this case, the thermal conductivity of the hydride is higher than that of


Neutron Reflector Materials (Be, Hydrides)

319

Thermal conductivity, l (W m-1 K-1)

25

20

α-Ti
δ-TiH1.66

15

δ-TiH1.75
0
300

350

400
450
500
Temperature, T (K)


550

600

Figure 18 Temperature dependence of the thermal conductivity of titanium hydride.

Thermal conductivity, l (W m-1 K-1)

90
80

α-Y
δ-YH1.72

70

δ-YH1.86

60
50
40
30
20
10
300

400

500


600

700

800

Temperature, T (K)
Figure 19 Temperature dependence of the thermal conductivity of yttrium hydride.

the metal, and it decreases with increasing hydrogen
content. Additionally, the hydride’s thermal conductivity decreases with decreasing temperature,
whereas that of the metal remains more or less constant. Figure 20 plots the values of a lattice-vibration
contribution and an electronic contribution to the
thermal conductivity of titanium hydride. The results
for titanium hydride are not much different from

those for zirconium hydride, as shown in Figure 17.
However, as shown in Figure 21, the results for the
case of yttrium reveal that both the lattice-vibration
and electronic contributions to thermal conductivity
are greater for yttrium hydride than for the pure
metal. This indicates that the thermal conductivity
characteristics of yttrium are different from those of
zirconium and titanium.


320

Neutron Reflector Materials (Be, Hydrides)


Thermal conductivity, l (W m-1 K-1)

25
l el
l lat
l total

20

15

10

5

0
300

400

500

600

700

Temperature, T (K)
Figure 20 Temperature dependence of the lattice-vibration and electronic contributions to thermal conductivity for
titanium hydride (dTiH1.66).


90
k el k ph k tot

Thermal conductivity, l (W m-1 K-1)

80

α-Y

70

δ-YH1.86

60
50
40
30
20
10
0
300

400

500

600

700


800

Temperature, T (K)
Figure 21 Temperature dependence of the lattice-vibration and electronic contributions to thermal conductivity for
yttrium hydride and yttrium metal.

2.11.3.10

Conclusion

Here, we reviewed the fundamental properties of
metal hydrides, focusing on zirconium hydride,
which is a material used to make the neutron reflectors of fast nuclear reactors, as well as titanium
hydride and yttrium hydride. We discussed the
hydrogen content and temperature dependence of

the elastic modulus, hardness, electrical conductivity,
heat capacity, and thermal conductivity of zirconium
hydride. Values of the physical properties of zirconium hydride (d-ZrH1.66) are summarized in Table 3.
Such data are very important and valuable for the
utilization of metal hydrides as materials for neutron
reflectors in fast reactors.


Neutron Reflector Materials (Be, Hydrides)

Table 3
(d-ZrH1.66)

Physical properties of zirconium hydride


Lattice parameter (nm)
Young’s modulus (GPa)
Shear modulus (GPa)
Bulk modulus (GPa)
Vickers hardness (GPa)
Heat capacity (for d-ZrH1.58) (J KÀ1 molÀ1)
Electrical conductivity (Â106 S mÀ1)
Thermal conductivity (W mÀ1 KÀ1)

0.47782
132
50
124
2.67
39.4 (at 367 K)
54.8 (at 708 K)
1.47 (at 293 K)
0.95 (at 673 K)
16.7 (at 286 K)
18.5 (at 663 K)

The data for the lattice parameter, Young’s modulus, shear
modulus, bulk modulus, and Vickers hardness were obtained at
room temperature.

References
1.
2.
3.

4.
5.
6.
7.
8.
9.
10.
11.
12.

2.11.4 Summary
This chapter has provided a basic outline of neutron
reflectors for nuclear reactors from the perspective
of materials science, beginning with an overview
of the properties required for neutron reflectors,
proceeding to an outline of the production and
processing methods for Be and metal hydrides as
representative reflector materials, and then to a
description of their basic properties. The outline of
metal hydrides has focused on zirconium hydride,
which is currently used mainly in fast reactors, and
has described the influence of temperature and
hydrogen concentration on the basic properties of
zirconium hydride. The data provided in this chapter
are considered to be extremely important and
valuable in regard to the use of Be and zirconium
hydride as neutron reflectors.

321


13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.

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