4.10

Radiation Effects in Graphite

T. D. Burchell
Oak Ridge National Laboratory, Oak Ridge, TN, USA

Published by Elsevier Ltd.

4.10.1

Introduction

300

4.10.2
4.10.3
4.10.4

Nuclear Graphite Manufacture
Graphite-Moderated Reactors
Displacement Damage and Induced Structural and Dimensional
Changes in Graphite
Neutron-Induced Property Changes
Wigner Energy
Mechanical and Physical Properties
Irradiation Creep
The Relevance of Creep to Reactor Design and Operation
The Irradiation-Induced Creep Mechanism (In-Crystal)
Review of Prior Creep Models
Linear viscoelastic creep model

The UK creep model
The Kennedy model
The Kelly and Burchell model
The M2 model
Deficiencies in Current Creep Models at High Neutron Doses
Outlook

302
303

4.10.5
4.10.5.1
4.10.5.2
4.10.6
4.10.6.1
4.10.6.2
4.10.6.3
4.10.6.3.1
4.10.6.3.2
4.10.6.3.3
4.10.6.3.4
4.10.6.3.5
4.10.6.4
4.10.7
References

Abbreviations
AGR
ASTM


Advanced gas-cooled reactor
American Society for Testing and
Materials
CEN
Centre European Nuclear
CP-1
Chicago Pile No. 1
CTE
Coefficient of thermal expansion
DWNTs Double-walled carbon nanotubes
Esu
Elastic strain unit
HFR
High flux reactor
HOPG Highly oriented pyrolytic graphite
HRTEM High-resolution transmission electron
microscope
IV
Interstitial–vacancy
MHTGR Modular high-temperature gas-cooled
reactor
NGNP
Next Generation Nuclear Plant
ORNL
Oak Ridge National Laboratory
PGA
Pile grade A
PKA
Primary knock-on atom
SKA

Secondary knock-on atom
STM
Scanning tunneling microscope

TEM
USSR

305
310
310
311
315
315
316
317
317
317
317
318
319
321
323
323

Transmission electron microscope
Union of Soviet Socialist Republics

Symbols
a
a

b
b
B
c
c
C
Cp
d«c/dg
E
E0

Constant in viscoelastic creep model
Crystallographic a-direction (within the
basal planes)
Burger’s vector
Constant in viscoelastic creep model
Empirical fitting parameter, analogous
to the steady-state creep coefficient
Crystallographic c-direction
(perpendicular to the basal planes)
Flaw size
Specific heat
Specific heat at constant pressure
Initial secondary (steady-state)
creep rate
Elastic modulus
Initial (preirradiated) Young’s modulus

299



300

Radiation Effects in Graphite

Ed

Ep
Eg
Fx
Fx0
G
gx

gx0

h
k
k
k0 (g)
k0
k1
k2
La
Lc
R
S(g)
T
W
(1/Xa)

(dXa/dg)
(1/Xc)
(dXc/dg)
XT
Z
a
aa
ac
ax
a´ x
a(f)

Displacement energy for a carbon
atom from its equilibrium lattice
position
Young’s modulus after initial increase
due to dislocation pinning
Young’s modulus at dose g
Pore generation term
Pore generation term for a crept
specimen
Fracture toughness or strain energy
release rate
Rate of change of dimensions in the
x-direction with respect to neutron
dose
Rate of change of dimensions in the
x-direction for a crept specimen with
respect to neutron dose (dimensional
change component)

Planck’s constant
Boltzmann’s constant
Steady-state creep coefficient
Modified steady-state creep coefficient
Initial secondary creep coefficient
Primary creep dose constant
Recoverable creep dose constant
Mean graphite crystal dimensions in
the a-direction
Mean graphite crystal dimensions in
the c-direction
Gas constant (8.314 J molÀ1K)
Structure factor (E/Ep)
Temperature
Oxidation change factor
Rate of change of crystallite
dimensions perpendicular to the
hexagonal axis
Rate of change of crystallite dimensions
parallel to the hexagonal axis
Crystal shape parameter
Atomic number
Coefficient of thermal expansion
Crystal coefficient of thermal
expansion in the a-direction
Crystal coefficient of thermal
expansion in the c-direction
Coefficient of thermal expansion in the
x-direction
Coefficient of thermal expansion of a

crept specimen in the x-direction
Crystal coefficient of thermal
expansion at angle f to the c-direction

«˙
«c
«´ c
«d
«e
«p
«s
«t
«Total
f
g
l
m
n
uD
r
r0
st
s
v
V
j

Strain rate
Creep strain
Apparent creep strain

Dimensional change strain
Elastic strain
Primary creep strain
Secondary creep strain
Thermal strain
Total strain
Fast neutron flux
Fast neutron fluence
Empirical fitting parameter
Empirical constant ($0.75)
Dislocation velocity
Debye temperature
Density
True density
Tensile strength
Tensile stress
Frequency of vibrational oscillations
Mobile dislocation density
Empirical fitting parameter

4.10.1 Introduction
There are many graphite-moderated, powerproducing, fission reactors operating worldwide today.1
The majority are in the United Kingdom (gas-cooled)
and the countries of the former Soviet Union (watercooled). In a nuclear fission reactor, the energy is
derived when the fuel (a heavy element such as 92U235)
fissions or ‘splits’ apart according to the following
reaction:
235
92 U


þ0 n1 !92 U236Ã ! F1 þ F2 þ n
þg À energy

½IŠ

An impinging neutron usually initiates the fission reaction, and the reaction yields an average of 2.5 neutrons
per fission. The fission fragments (F1 and F2 in eqn [I])
and the neutron possess kinetic energy, which can be
degraded to heat and harnessed to drive a turbinegenerator to produce electricity. The role of graphite
in the fission reactor (in addition to providing mechanical support to the fuel) is to facilitate the nuclear chain
reaction by moderation of the high-energy fission neutron. The fission fragments (eqn [I]) lose their kinetic
energy as thermal energy to the uranium fuel mass in
which fission occurred by successive collisions with the
fuel atoms. The fission neutrons (n in eqn [I]) give up


Radiation Effects in Graphite

their energy within the moderator via the process of
elastic collision. The g-energy given up in the fission
reaction (eqn [I]) is absorbed in the bulk of the reactor
outside the fuel, that is, moderator, pressure vessel, and
shielding. The longer a fission neutron dwells in the
vicinity of a fuel atom during the fission process,
the greater is its probability of being captured and
thereby causing that fuel nucleus to undergo fission.
Hence, it is desirable to slow the energetic fission neutron (E $ 2 MeV), referred to as a fast neutron, to lower
thermal energies ($0.025 eV at room temperature),
which corresponds to a velocity of 2.2 Â 1015 cm sÀ1.
The process of thermalization or slowing down of

the fission fast neutron is called ‘moderation,’ and the
material in a thermal reactor (i.e., a reactor in which
fission is caused by neutrons with thermal energies)
that is responsible for slowing down the fast fission
neutrons is referred to as the moderator. Good
nuclear moderators should possess the following
attributes:

301

target elements. Low atomic number (Z) is thus a
prime requirement of a good moderator. The density
(number of atoms per unit volume) of the moderator
and the likelihood of a scattering collision taking
place must also be accounted for. Frequently used
‘Figures of merit’ for assessing moderators are the
‘slowing down power’ and the ‘moderating ratio.’
Figure 1 shows these Figures of merit for several
candidate moderator materials. The slowing down
power accounts for the mean energy loss per collision,
the number of atoms per unit volume, and the scattering cross-section of the moderator. The tendency for a
material to capture neutrons (the neutron capture
cross-section) must also be considered. Thus, the second figure of merit, the moderation ratio, is the ratio
of the slowing down power to the neutron absorption
(capture) cross-section. Ideally the slowing down
power is large, the neutron capture cross-section is
small, and hence the moderating ratio is also large.
Practically, the choices of moderating materials
are limited to the few elements with atomic number
<16. Gasses are of little use as moderators because of

their low density, but can be combined in chemical
compounds such as water (H2O) and heavy water
(D2O). The available materials/compounds reduce
to the four shown in Figure 1 (beryllium, carbon
(graphite), water, and heavy water). Water is relatively unaffected by neutron irradiation, is easily
contained, and inexpensive. However, the moderating
ratio is reduced by the neutron absorption of hydrogen, requiring the use of enriched (in 235U) fuels to
maintain the neutron economy. Heavy water is a good
moderator because 1H2 and 8O16 do not absorb neutrons, the slowing down power is large, and the moderating ratio is therefore very large. Unfortunately,

 do not react with neutrons (because if they are
captured in the moderator the fission reaction
cannot be sustained);
 should efficiently thermalize (slowdown) neutrons
with few (elastic) collisions in the moderator;
 should be inexpensive;
 compatible with other materials in the reactor
core;
 meet the core structural requirements; and ideally
 do not undergo any damaging chemical or physical changes when bombarded with neutrons.
In the fast neutron thermalization process, the maximum energy lost per collision occurs when the target
nucleus has unit mass, and tends to zero for heavy

1.E + 05

1.6
1.4
1.2

Moderating ratio


Slowing-down power (cm–1)

1.8

1
0.8
0.6
0.4

1.E + 04

1.E + 03

1.E + 02

0.2
0

1.E + 01
5

10
15
20
Mass number (M)

25

5


10
15
20
Mass number (M)

25

Figure 1 Moderator Figures of merit for several candidate moderators: beryllium (M ¼ 9); graphite, C (M ¼ 12); light water,
H2O (M ¼ 18); heavy water, D2O (M ¼ 20).


302

Radiation Effects in Graphite

the cost of separating the heavy hydrogen isotope is
large. Beryllium and beryllium oxide are good moderators but are expensive, difficult to machine, and
suffer toxicity problems. Finally, graphite (carbon) is
an acceptable moderator. It offers a compromise
between nuclear properties, utility as a core structural
material, and cost. It also has the advantage of being
able to operate at very high temperatures (in the
absence of oxygen). Unfortunately, the properties of
graphite are markedly altered by neutron irradiation
and this has to be considered in the design of graphite
reactor cores.

Raw petroleum
or pitch coke

Calcined at 1300 ЊC
Calcined coke
Crushed, ground,
and blended
Blended
particles

Coal tar
binder pitch

Mixed
Cooled
Extruded, molded, or
isostatically pressed
Green artifact

4.10.2 Nuclear Graphite
Manufacture
The invention of an electric furnace2 capable of reaching temperatures approaching 3000  C by Acheson
in 1895 facilitated the development of the process for
the manufacture of artificial polygranular graphite.
Detailed accounts of the manufacture of polygranular
graphite may be found elsewhere.2–4 Figure 2 summarizes the major processing steps in the manufacture
of nuclear graphite. Nuclear graphite consists of two
phases: a filler material and a binder phase. The predominant filler material, particularly in the United
States, is a petroleum coke made by the delayed
coking process. European nuclear graphites are typically made from a coal-tar pitch-derived coke. In the
United Kingdom, Gilsonite coke, derived from naturally occurring bitumen found in Utah, USA, has been
used. Both coke types are used for nuclear graphite
production in Japan. The coke is usually calcined

(thermally processed) at $1300  C prior to being
crushed and blended. Typically, the binder phase is
a coal-tar pitch. The binder plasticizes the filler coke
particles so that they can be formed. Forming processes include extrusion, molding, vibrational molding, and isostatic pressing. The binder phase is
carbonized during the subsequent baking operation
(800–1000  C). Frequently, engineering graphites are
pitch impregnated to densify the carbon artifact, followed by rebaking. Useful increases in density and
strength are obtained with up to six impregnations,
but two or three are more typical.
The final stage of the manufacturing process is
graphitization (2500–3000  C) during which, in simplistic terms, carbon atoms in the baked material
migrate to form the thermodynamically more stable
graphite lattice. Nuclear graphites require high
chemical purity to minimize neutron absorption.

Baked at 800–1000 ЊC
Baked artifact
Impregnated to densify
(petroleum pitch)
Rebaked and
reimpregnated
artifact
Graphitized 2500–2800 ЊC
Graphite
Purified
Nuclear graphite

Figure 2 The major processing steps in the manufacture
of nuclear graphite.


Moreover, certain elements catalyze the oxidation of
graphite and must be reduced to an acceptable level.
This is achieved by selecting very pure cokes, utilizing
a high graphitization temperature (>2800  C), or by
including a halogen purification stage in the manufacture of the cokes or graphite. Recently, comprehensive
consensus specifications5,6 were developed for nuclear
graphites.
The electronic hybridization of carbon atoms (1s2,
2
2s , 2p2) allows several types of covalent bonded
structure. In graphite, we observe sp2 hybridization
in a planar network in which the carbon atom is bound
to three equidistant nearest neighbors 120 apart in a
given plane to form the hexagonal graphene structure.
Covalent double bonds of both s-type and p-type are
present, causing a shorter bond length than in the case
of the tetrahedral bonding (s-type sp3 orbital hybridization only) observed in diamond. Thus, in its perfect form, the crystal structure of graphite (Figure 3)
consists of tightly bonded (covalent) sheets of carbon
atoms in a hexagonal lattice network.7 The sheets are


Radiation Effects in Graphite

A

B

c 0.670 nm

303


(grain sizes <100 mm) formed via isostatic pressing
often exhibit complete isotropy in their properties.
In response to the recent renewed interest in hightemperature gas-cooled reactors, many graphite vendors have introduced new nuclear graphites grades.
Table 1 summarizes some of the grades available currently, although this list is not exhaustive. The graphite
manufacturer is listed along with the coke type and
comments related to the given graphite grade.

4.10.3 Graphite-Moderated Reactors

A

a
0.246 nm
Figure 3 The crystal structure of graphite showing the
ABAB stacking sequence of graphene planes in which
the carbon atoms have threefold coordination. Reproduced
from Burchell, T. D. In Carbon Materials for Advanced
Technologies; Burchell, T. D., Ed.; Elsevier Science:
Oxford, 1999, with permission from Elsevier.

weakly bound with van der Waals type bonds in an
ABAB stacking sequence with a separation of 0.335 nm.
The crystals in manufactured polygranular graphite are less than perfect, with approximately one layer
plane in every six constituting a stacking fault. The
graphite crystals have two distinct dimensions,
the crystallite size La measured parallel to the basal
plane and the dimension Lc measured perpendicular
to the basal planes. In a coke-based nuclear graphite,
values of La $ 80 nm and Lc $ 60 nm are typical.8

A combination of crystal structure bond anisotropy
and texture resulting from forming imparts anisotropic properties to the filler coke and the manufactured nuclear graphite. The coke particles become
preferentially aligned during forming, either with
their long axis parallel to the forming axis in the
case of extrusion, or with their long axis perpendicular to the forming axis in the case of molding or
vibrational molding. Consequently, the graphite artifacts are often attributed with-grain and against-grain
properties as in the American Society for Testing and
Materials (ASTM) specifications.5,6 The degree of
isotropy in manufactured graphite can be controlled
through the processing route. Factors such as the
nature of the filler coke, its size and size distribution,
and the forming method contribute to the degree of
isotropy. Nuclear graphites are typically medium or
fine grain graphites (filler coke size <1.68 mm)5,6 and
are considered near-isotropic. Fine grain graphites

Graphite has been used as a nuclear moderator in
nuclear fission reactors since the very beginning
of the nuclear age.1 Indeed, the Chicago Pile No. 1
(CP-1), constructed by Enrico Fermi under the stands
at Stagg Field, University of Chicago, used The
National Carbon Company’s AGOT grade graphite.
On 2 December 1942, Enrico Fermi and his research
team achieved the world’s first nuclear chain reaction
in CP-1. Subsequently, the early weapons materials
production reactors constructed in the United States,
United Kingdom, France, and the former Union of
Soviet Socialist Republics (USSR) were all graphitemoderated reactors, as were the first commercial
power generating fission reactors.
The core of a graphite-moderated reactor is comprised of stacks of graphite blocks that are usually

keyed to one another to facilitate transmission of
mechanical loads throughout the core. Vertical channels penetrate the core into which fuel stringers are
placed via the reactor charge face using a refueling
machine. The nuclear fuel, which may be natural uranium (a mixture of 238U, 235U, and 234U) or enriched
uranium, is usually sheathed (clad) in a metallic cladding. Typically, the cladding is a light alloy (aluminum
or magnesium), but it can also be stainless steel (requiring enriched fuel) if a higher fuel temperature is
desired (>600  C). The fuel stringer and cladding
material may be one and the same, as in the United
Kingdom designed Magnox reactor,1 or the fuel may
be in the form of stainless steel clad ‘pins’ arranged in
graphite fuel sleeves, which are joined to one another
and form the fuel stringer as in the UK Advanced
Gas-Cooled Reactor1 (AGR). The metallic fuel clad
retains the gaseous fission products that migrate from
the fuel during the fission reaction and prevents contact between the gaseous coolant and the fuel.
An alternative core layout uses integral fuel/moderator elements in which the uranium fuel is placed
directly into cavities in the graphite moderator block,


304
Table 1

Radiation Effects in Graphite

Currently available nuclear grade graphites

Grade

Manufacturer


Coke type

Comments

IG-430

Toyo Tanso

Pitch coke

IG-110

Toyo Tanso

Petroleum coke

NBG-10

SGL

Pitch coke

NBG-17

SGL

Pitch coke

NBG-18


SGL

Pitch coke

PCEA

GrafTech International

Petroleum coke

PGX
2020

GrafTech International
Carbone of America

Petroleum coke
Petroleum coke

2191

Carbone of America

Petroleum (sponge) coke

Isostatically molded, candidate for high-dose regions of
NGNP concepts
Isostatically molded, candidate for high-dose regions of
NGNP concepts
Extruded, candidate for high-dose regions of NGNP

pebble bed concepts; PBMR core graphite
Vibrationally molded, candidate for high-dose regions of
NGNP prismatic core concepts
Vibrationally molded, candidate for high-dose regions of
NGNP pebble bed concepts; PBMR core graphite
Extruded, candidate for high-dose regions of NGNP
prismatic core concepts
Large blocks for permanent structure in a prismatic core
Isostatically molded, candidate for permanent structures
in a prismatic core
Isostatically molded, candidate for permanent structures
in a prismatic core

and the entire block is discharged from the reactor
when the fuel is spent. Fuel elements of this design
typically utilize ceramic (UO2 or UC2) rather that
metallic fuel so as to be capable of reaching higher
fuel temperatures. The ceramic fuel kernel is over
coated with layers of SiC and pyrolytic carbon to provide a fission product barrier and to negate the use of
a metallic fuel clad (see Chapter 3.07, TRISOCoated Particle Fuel Performance), allowing the
reactor core to operate at very high temperatures
(>1000  C).1 The coated particle fuel is usually formed
into fuel pucks or compacts but may be consolidated into fuel balls, or pebbles.1 The US designed
modular high-temperature gas-cooled reactor
(MHTGR) and Next Generation Nuclear Plant
(NGNP), and the Japanese high-temperature test
reactor (HTTR) are examples of gas-cooled reactors
with high-temperature ceramic fuel.
Additional vertical channels in the graphite reactor core house the control rods, which regulate the
fission reaction by introducing neutron-adsorbing

materials to the core, and thus reduce the number
of neutrons available to sustain the fission process.
When the control rods are withdrawn from the core,
the self-sustaining fission reaction commences. Heat
is generated by the moderation of the fission fragments in the fuel and moderation of fast neutrons in
the graphite. The heat is removed from the core by a
coolant, typically a gas, that flows freely through the
core and over the graphite moderator. The coolant is
forced through the core by a gas circulator and passes
into a heat exchanger/boiler (frequently referred to
as a steam generator).

The primary coolant loop (the reactor coolant) is
maintained at elevated pressure to improve the coolant’s heat transfer characteristics and thus, the core is
surrounded by a pressure vessel. A secondary coolant
(water) loop runs through the heat exchanger and cools
the primary coolant so that it may be returned to the
reactor core at reduced temperature. The secondary
coolant temperature is raised to produce steam which
is passed through a turbine where it gives up its energy
to drive an electric generator. Some reactor designs,
such as the MHTGR, are direct cycle systems in which
the helium coolant passes directly to a turbine.
The reactor core and primary coolant loop are
enclosed in a concrete biological-shield, which protects the reactor staff and public from g radiation
and fission neutrons and also prevents the escape of
radioactive contamination and fission product gasses
that originate in the fuel pins/blocks. The charge
face, refueling machine, control rod drives, discharge
area, and cooling ponds are housed in a containment

structure which similarly prevents the spread of any
contamination. Additional necessary features of a
fission reactor are (1) the refueling bay, where new
fuel stringers or fuel elements are assembled prior to
being loaded into the reactor core; (2), a discharge
area and cooling ponds where spent fuel is placed
while the short-lived isotopes are allowed to decay
before the fuel can be reprocessed.
The NGNP, a graphite-moderated, helium cooled
reactor, is designed specifically to generate electricity and produce process heat, which could be
used for the production of hydrogen, or steam generation for the recovery of tar sands or oil shale.


Radiation Effects in Graphite

Two NGNP concepts are currently being considered, a prismatic core design and a pebble bed core
design. In the prismatic core concept, the TRISO fuel
is compacted into sticks and supported within a
graphite fuel block which has helium coolant holes
running through its length.1 The graphite fuel blocks
are discharged from the reactor at the end of the
fuel’s lifetime. In the pebble bed core concept,
the TRISO fuel is mixed with other graphite materials and a resin binder and formed into 6 cm diameter
spheres or pebbles.1 The pebbles are loaded into
the core to form a ‘pebble bed’ through which helium
coolant flows. The pebble bed is constrained by a
graphite moderator and reflector blocks which define
the reactor core shape. The fuel pebbles migrate slowly
down through the reactor core and are discharged at
the bottom of the core where they are either sent

to spent fuel storage or returned to the top of the
pebble bed.
Not all graphite-moderated reactors are gascooled. Several designs have utilized water cooling,
with the water carried through the core in zirconium
alloy tubes at elevated pressure, before being fed to
a steam generator. Moreover, graphite-moderated
reactors can also utilize a molten salt coolant, for
example, the Molten Salt Reactor Experiment
(MSRE)1 at Oak Ridge National Laboratory (ORNL).
The fluid fuel in the MSRE consisted of UF4 dissolved
in fluorides of beryllium and lithium, which was circulated through a reactor core moderated by graphite.
The average temperature of the fuel salt was 650  C
(1200  F) at the normal operating condition of 8 MW,
which was the maximum heat removal capacity of the
air-cooled secondary heat exchanger. The graphite
core was small, being only 137.2 cm (54 in.) in diameter
and 162.6 cm (64 in.) in height. The fuel salt entered the
reactor vessel at 632  C (1170  F) and flowed down
around the outside of the graphite core in the annular
space between the core and the vessel. The graphite
core was made up of graphite bars 5.08 cm (2 in.) square,
exposed directly to the fuel which flowed upward in
passages machined into the faces of the bars. The fuel
flowed out of the top of the vessel at a temperature of
654  C (1210  F), through the circulating pump to the
primary heat exchanger, where it gave up heat to a
coolant salt stream. The core graphite, grade CGB,
was specially produced for the MSRE, and had to
have a small pore size to prevent penetration of the
fuel salt, a long irradiation lifetime, and good dimensional stability. Moreover, for molten salt reactor moderators, a low permeability (preferably <10À8 cm2 sÀ1)

is desirable in order to prevent the build up of

305

unacceptable inventories of the nuclear poison
Xe in the graphite. At ORNL, this was achieved
by sealing the graphite surface using a gas phase
carbon deposition process.1

135

4.10.4 Displacement Damage and
Induced Structural and Dimensional
Changes in Graphite
The discovery of Fullerenes9 and carbon nanotubes,10
and other nanocarbon structures, has renewed interest in high-resolution microstructural studies of carbon nanostructures and the defects within them.11
This in turn has given new insight to the nature of
displacement damage and the deformation mechanisms in irradiated graphite crystals. The binding
energy of a carbon atom in the graphite lattice12 is
about 7 eV. Impinging energetic particles such as fast
neutrons, electrons, or ions can displace carbon atoms
from their equilibrium positions. There have been
many studies of the energy required to displace a
carbon atom (Ed), as reviewed by Kelly,13 Burchell,14
Banhart,11 and Telling and Heggie.15 The value of Ed
lies between 24 and 60 eV. The latter value has gained
wide acceptance and use in displacement damage
calculations, but a value of $30 eV would be more
appropriate. Moreover, as discussed by Banhart,11
Hehr et al.,16 and Telling and Heggie,15 an angular

dependence of the threshold energy for displacement
would be expected. The value of Ed in the crystallographic c-axis is in the range 12–20 eV,11,17 while the
in-plane value is much greater.
The primary atomic displacements, primary
knock-on carbon atoms (PKAs), produced by energetic particle collisions produce further carbon atom
displacements in a cascade effect. The cascade carbon
atoms are referred to as secondary knock-on atoms
(SKAs). The displaced SKAs tend to be clustered in
small groups of 5–10 atoms and for most purposes it
is satisfactory to treat the displacements as if they
occur randomly. The total number of displaced carbon atoms will depend upon the energy of the PKA,
which is itself a function of the neutron energy spectrum, and the neutron flux. Once displaced, the
carbon atoms recoil through the graphite lattice, displacing other carbon atoms and leaving vacant lattice
sites. However, not all of the carbon atoms remain
displaced and the temperature of irradiation has a
significant influence on the fate of the displaced
atoms and lattice vacancies. The displaced carbon
atoms easily diffuse between the graphite layer planes


306

Radiation Effects in Graphite

in two dimensions and a high proportion will recombine with lattice vacancies. Others will coalesce to
form C2, C3, or C4 linear molecules. These in turn
may form the nucleus of a dislocation loop – essentially
a new graphite plane. Interstitial clusters may, on further irradiation, be destroyed by a fast neutron or
carbon knock-on atom (irradiation annealing). Adjacent lattice vacancies in the same graphitic layer are
believed to collapse parallel to the layers, thereby

forming sinks for other vacancies which are increasingly mobile above 600  C, and hence can no longer
recombine and annihilate interstitials. The migration
of interstitials along the crystallographic c-axis is
discussed later.
Banhart11 observed typical basal plane defects in a
graphite nanoparticles using high-resolution transmission electron microscopy (HRTEM). These defects
can be understood as dislocation loops which form
when displaced interstitial atoms cluster and form less
mobile agglomerates. Other interstitials condense onto
this agglomerate which grows into a disk, pushing the
adjacent apart. Further agglomeration leads to the formation of a new lattice planes (Figure 4).
Other deformation mechanisms have been proposed for irradiated graphite. Wallace18 proposed a
mechanism whereby interstitial atoms could facilitate sp3 bonds between the atomic basal planes, this
mechanism allowing the stored energy (discussed
in Section 4.10.5.1) to be explained. Jenkins19
argued that the magnitude of the increase in shear

1 nm
Figure 4 A high-resolution electron micrograph showing
the basal planes of a graphitic nanoparticle with an
interstitial loop between two basal planes, the ends of the
inserted plane are indicated with arrows. Reproduced from
Banhart, F. Rep. Prog. Phys. 1999, 62, 1181–1221, with
permission from IOP Publishing Ltd.

modulus (C44) with low dose irradiation could not be
explained by interstitial clusters pinning dislocations,
but that a few sp3 type covalent bonds between the
planes could easily account for the observed changes.
More recently, Telling and Heggie,15 in their ab-initio

calculations of the energy of formation of the ‘spirointerstitial,’ advocate this mechanism to explain the
stored energy characteristics of displacement damaged graphite, particularly the large energy release
peak seen at $473 K (discussed in Section 4.10.5.1).
The first experimental evidence of the interlayer
interstitial–vacancy (IV) pair defect with partial sp3
character in between bilayers of graphite was recently
reported by Urita et al.20 in their study of doublewalled carbon nanotubes (DWNTs).
Jenkins19 invoked the formation of sp3 bonding to
explain the c-axis growth observed as a result of
displacement damage. If adjacent planes are pinned,
one plane must buckle as the adjacent planes shrink
due to vacancy shrinkage; buckled planes yield the
c-axis expansion that cannot be explained by swelling
from interstitial cluster alone. Telling and Heggie15 are
very much in support of this position on the basis of
their review of the literature and ab-initio simulations of
the damage mechanisms in graphite. Their simulations
showed how the spiro-interstitial (cross-link) essentially locked the planes together. Additionally, divacancies could lead to the formation of pentagons and
heptagons in the basal planes causing the observed
bending of graphene layers and c-axis swelling.11,21,22
The predicted c-axis crystal expansion via this mechanism is in closer agreement with the experimentally
observed single crystal and highly oriented pyrolytic
graphite (HOPG) dimensional change data.
The buckling of basal planes as a consequence of
irradiation damage has been observed in HRTEM
studies of irradiated HOPG by Tanabe21 and Koike
and Pedraza.22 In their study, Koike and Pedraza22
observed 300% expansion of thin HOPG samples
subject to electron irradiation in an in-situ transmission electron microscope (TEM) study. Their experimental temperatures ranged from 238 to 939 K.
They noted that the damaged microstructure showed

retention of crystalline order up to 1 dpa (displacements per atom). At higher doses, they observed the
lattice fringes break up in to segments 0.5–5 nm in
length, with up to 15 rotation of the segments with
respect to the original {0001} planes.
The evidence in favor of the formation of bonds
between basal planes involving interstitials is considerable. However, such bonds are not stable at high
temperature. As reported by numerous authors and


Radiation Effects in Graphite

reviewers11,15,19,20 the sp3 like bond would be expected to break and recombine with lattice vacancies
with increasing temperature, such that at T >500 K
they no longer exist. Indeed, the irradiated graphite
stored energy annealing peak at $473 K, and the
HRTEM observations of Urita et al.20 demonstrate this
clearly. Figure 5 shows a sequential series of HRTEM
images illustrating the formation rates of interlayer
defects at different temperatures with the same time
scale (0–220 s) in DWNTs. The arrows indicate possible interlayer defects. At T ¼ 93 K (Figure 5(a))
the electron irradiation-induced defects are numerous, and the nanotubes inside are quickly damaged
because of complex defects. At 300 K (Figure 5(b)),
the nanotubes are more resistive to the damage from
electron irradiation, yet defects are still viable. At
573 K (Figure 5(c)), defect formation is rarely observed
and the DWNTs are highly resistant to the electron
beam irradiation presumably because of the ease of
defect self-annihilation (annealing).
In an attempt to estimate the critical temperature
for the annihilation of the IV defect pairs, a systematic HRTEM study was undertaken at elevated

temperatures by Urita et al.20 The formation rate
of the IV defects that showed sufficient contrast in
the HRTEM is plotted in Figure 6. The reported
numbers were considered to be an underestimate as
single IV pairs may not have sufficient contrast to be

93 K

0s

300 K

307

convincingly isolated from the noise level and thus
may have been missed. However, the data was considered satisfactory for indicating the formation rate
as a function of temperature. The number of clusters
of IV pairs found in a DWNT was averaged for
several batches at every 50 K and normalized by the
unit area. As observed in Figure 6, the defect formation rate displays a constant rate decline, with a
threshold appearing at $450–500 K. This threshold
corresponds to the stored energy release peak (discussed in Section 4.10.5.1) as shown by the dotted
line in Figure 6. Evidentially, the irradiation damage resulting from higher temperature irradiations
(above $473–573 K) is different in nature from that
occurring at lower irradiation temperatures.
Koike and Pedraza22 studied the dimensional change
in HOPG caused by electron-irradiation-induced displacement damage. They observed in situ the growth
c-axis of the HOPG crystals as a function of irradiation
temperature at damage doses up to $1.3 dpa. Increasing
c-axis expansion with increasing dose was seen at all

temperatures. The expansion rate was however significantly greater at temperatures ≲473 K (their data was
at 298 and 419 K) compared to that at irradiation temperatures ≳473 K (their data was at 553, 693, and
948 K). This observation supports the concept that
separate irradiation damage mechanisms may exist at
low irradiation temperatures ($T <473 K), that is,

573 K

110 s

140 s

220 s

(a)

(b)

(c)

Figure 5 Sequential high-resolution transmission electron microscope images illustrating the formation rates of interlayer
defects at different temperatures with the same time scale (0–220 s). (a) 93 K, (b) 300 K, (c) 573 K, in double-walled carbon
nanotubes. The arrows indicate possible interlayer defects. Scale bar ¼ 2 nm. Reproduced from Urita, K.; Suenaga, K.;
Sugai, T.; Shinohara, H.; Iijima, S. Phys. Rev. Lett. 2005, 94, 155502, with permission from American Physical Society.


308

Radiation Effects in Graphite


Defect formation rate (barns)

200

150

100

50

0

0

200

400
600
Temperature (K)

800

1000

Figure 6 Normalized formation rates of the clusters of
interstitial–vacancy pair defects per unit area of bilayer
estimated in high-resolution transmission electron
microscope images recorded at different temperatures.
The dotted line shows the known temperature for
Wigner-energy release ($473 K). Reproduced from Urita, K.;

Suenaga, K.; Sugai, T.; Shinohara, H.; Iijima, S. Phys. Rev.
Lett. 2005, 94, 155502, with permission from American
Physical Society.

buckling due to sp3 bonded cross linking of the basal
planes via interstitials, and at more elevated irradiation
temperatures (T ≳ 473 K), where the buckling of planes
is attributed to clustering of interstitials which induce
the basal planes to bend, fragment, and then tilt. Koike
and Pedraza22 also observed crystallographic a-axis
shrinkage upon electron irradiation in-situ at several
temperatures (419, 553, and 693 K). The shrinkage
increased with dose at all irradiation temperatures,
and the shrinkage rate reduced with increasing irradiation temperature. This behavior is attributed to buckling and breakage of the basal planes, with the amount
of tilting and buckling decreasing with increasing temperature due to (1) a switch in mechanism as discussed
above and (2) increased mobility of lattice vacancies
above $673 K.
Jenkins19,23 also discussed the deformation of
graphite crystals in terms of a unit c-axis dislocation
(prismatic dislocation), that is, one in which the Burgers vector, b, is in the crystallographic c-direction.
The c-axis migration of interstitials can take place by
unit c-axis dislocations. The formation and growth
of these, and other basal plane dislocation loops

undoubtedly play a major role in graphite crystal
deformation during irradiation.
Ouseph24 observed prismatic dislocation loops (both
interstitial and vacancy) in unirradiated HOPG using
scanning tunneling microscopy (STM). Their study
allowed atomic resolution of the defect structures.

Such defects had previously been observed as regions
of intensity variations in TEM studies in the 1960s.25
Telling and Heggie’s15 first principle simulations
have indicated a reduced energy of migration for a
lattice vacancy compared to the previously established value. Therefore, they argue, the observed limited growth of vacancy clusters at high temperatures
(T >900 K) indicates the presence of a barrier to
further coalescence of vacancy clusters (i.e., vacancy
traps). Telling and Heggie implicate a cross-planer
metastable vacancy cluster in adjacent planes as the
possible trap. The disk like growth of vacancy clusters
within a basal plane ultimately leads to a prismatic
dislocation loop. TEM observations show that these
loops appear to form at the edges of interstitial loops
in neighboring planes in the regions of tensile stress.
The role of vacancies needs to be reexamined on
the basis of the foregoing discussion. If the energy of
migration is considerably lower than that previously
considered, and there is a likelihood of vacancy traps,
the vacancy and prismatic dislocation may well play
a larger role in displacement damage induced incrystal deformation. The diffusion of vacancy lines
to the crystal edge essentially heals the damage, such
that crystals can withstand massive vacancy damage
and recover completely.
Regardless of the exact mechanism, the result of
carbon atom displacements is crystallite dimensional
change. Interstitial defects will cause crystallite growth
perpendicular to the layer planes (c-axis direction),
and relaxation in the plane due to coalescence of
vacancies will cause a shrinkage parallel to the layer
plane (a-axis direction). The damage mechanism and

associated dimensional changes are illustrated (in simplified form) in Figure 7. As discussed above, this
conventional view of c-axis expansion as being caused
solely by the graphite lattice accommodating small
interstitial aggregates is under some doubt, and despite
the enormous amount of experimental and theoretical
work on irradiation-induced defects in graphite, we
are far from a widely accepted understanding. It is
to be hoped that the availability of high-resolution
microscopes will facilitate new damage and annealing
studies of graphite leading to an improved understanding of the defect structures and of crystal deformation under irradiation.


Radiation Effects in Graphite

Collapsing
vacancy
line

(c)

309

Contraction

(a)

Interstitial

Vacancy
New plane

Expansion

Figure 7 Neutron irradiation damage mechanism illustrating the induced crystal dimensional strains. Reproduced from
Burchell, T. D. In Carbon Materials for Advanced Technologies; Burchell, T. D., Ed.; Elsevier Science: Oxford, 1999,
with permission from Elsevier.

100

80

ced shrinkage

Irradiation-indu

(%)

60

40
20

0
20

Ne

15

ro


ut

2000

10

n
do

2500
ЊC)
re (
atu
r
e
mp

5

se

)

pa

(d

Dimensional changes can be very large, as demonstrated in studies on well-ordered graphite materials,
such as HOPG that has frequently been used to study
the neutron-irradiation-induced dimensional changes

of the graphite crystallite.13,26 Price27 conducted a
study of the neutron-irradiation-induced dimensional
changes in pyrolytic graphite. Figure 8 shows the
crystallite shrinkage in the a-direction for neutron
doses up to 12 dpa for samples that were graphitized
at a temperature of 2200–3300  C prior to being irradiated at 1300–1500  C. The a-axis shrinkage increases linearly with dose for all of the samples, but
the magnitude of the shrinkage at any given dose
decreases with increasing graphitization temperature.
Similar trends were noted for the c-axis expansion.
The significant effect of graphitization temperature
on irradiation-induced dimensional change accumulation can be attributed to thermally induced improvements in crystal perfection, thereby reducing the
number of defect trapping sites in the lattice.
Nuclear graphites possess a polycrystalline structure, usually with significant texture resulting from
the method of forming during manufacture. Consequently, structural and dimensional changes in
polycrystalline graphites are a function of the crystallite dimensional changes and the graphite’s texture.
In polycrystalline graphite, thermal shrinkage cracks
that occur during manufacture and that are preferentially aligned in the crystallographic a-direction
will initially accommodate the c-direction expansion,
so mainly a-direction contraction will be observed.
The graphite thus undergoes net volume shrinkage.
With increasing neutron dose (displacements), the
incompatibility of crystallite dimensional changes
leads to the generation of new porosity, and the
volume shrinkage rate falls, eventually reaching
zero. The graphite now begins to swell at an

3000
n te
atio


0
3500

itiz
aph

Gr

Figure 8 Neutron irradiation-induced a-axis shrinkage
behavior of pyrolytic graphite showing the effects of
graphitization temperature on the magnitude of the
dimensional changes. Reproduced from Burchell, T. D. In
Carbon Materials for Advanced Technologies; Burchell,
T. D., Ed.; Elsevier Science: Oxford, 1999, with permission
from Elsevier.

increasing rate with increasing neutron dose. The
graphite thus undergoes a volume change ‘turnaround’ into net growth that continues until the generation of cracks and pores in the graphite, due to
differential crystal strain, eventually causes total disintegration of the graphite.
Irradiation-induced volume and dimensional change
data for H-451 are shown28 in Figures 9–11. The effect
of irradiation temperature on volume change is
shown in Figure 9. The ‘turn-around’ from volume
shrinkage to growth occurs at a lower fluence and


310

Radiation Effects in Graphite


10
H-451 @ 600 ЊC
H-451 @ 900 ЊC

Volume change (%)

8
6
4
2
0
-2
-4
-6
-8
-10
0

1

2

3

4

Fast fluence 1026 n m-2 [E > 0.1 MeV]

Figure 9 Irradiation-induced volume changes for H-451
graphite at two irradiation temperatures. From Burchell,

T. D.; Snead, L. L. J. Nucl. Mater. 2007, 371, 18–27.

H-451 graphite irradiated at 600 ЊC

Dimensional change (%)

1
0
-1
-2
-3
-4

Perpendicular to
extrusion (AG)
Parallel to extrusion
direction (WG)

-5
-6

0

1

2

3

4


5

Fast fluence 1026 n m-2 [E > 0.1 MeV]

Figure 10 Dimensional change behavior of H-451
graphite at an irradiation temperature of 600  C. From
Burchell, T. D.; Snead, L. L. J. Nucl. Mater. 2007, 371, 18–27.

Dimensional change (%)

4.10.5 Neutron-Induced Property
Changes

H-451 graphite irradiated at 900 ЊC

5

4.10.5.1

Perpendicular to
extrusion (AG)
Parallel to extrusion
direction (WG)

4
3
2
1
0

-1
-2
-3

0

0.5
1
1.5
2
2.5
Fast fluence 1026 n m-2 [E > 0.1 MeV]

available at the higher temperatures and the c-axis
growth dominates the a-axis shrinkage at lower doses.
The irradiation-induced dimensional changes
of H-451at 600 and 900  C are shown in Figures 10
and 11, respectively. H-451 graphite is an extruded
material and therefore, the filler coke particles
are preferentially aligned in the extrusion axis (parallel direction). Consequently, the crystallographic
a-direction is preferentially aligned in the parallel
direction and the a-direction shrinkage is more apparent in the parallel (to extrusion) direction, as indicated by the parallel direction dimensional change
data in Figures 10 and 11. The dimensional and
volume changes are greater at an irradiation temperature of 600  C than at 900  C; that is, both the maximum shrinkage and the turnaround dose are greater
at an irradiation temperature of 600  C. This temperature effect can be attributed to the thermal
closure of internal porosity that is aligned parallel to
the a-direction that accommodates the c-direction
swelling. At higher irradiation temperatures, a greater
fraction of this accommodating porosity is closed and
thus the shrinkage is less at the point of turnaround.

A general theory of dimensional change in polygranular graphite due to Simmons29 has been extended
by Brocklehurst and Kelly.30 For a detailed account of
the treatment of dimensional changes in graphite the
reader is directed to Kelly and Burchell.31

3

Figure 11 Dimensional change behavior of H-451
graphite at an irradiation temperature of 900  C. From
Burchell, T. D.; Snead, L. L. J. Nucl. Mater. 2007, 371, 18–27.

the magnitude of the volume shrinkage is smaller
at the higher irradiation temperature. This effect is
attributed to the thermal closure of aligned microcracks in the graphite which accommodate the c-axis
growth. Hence, there is less accommodating volume

Wigner Energy

The release of Wigner energy (named after the physicist who first postulated its existence) was historically the first problem of radiation damage in
graphite to manifest itself. The lattice displacement
processes previously described can cause an excess of
energy in the graphite crystallites. The damage may
comprise Frankel pairs or at lower temperatures the
sp3 type bond previously discussed and observed by
Urita et al.20 When an interstitial carbon atom and a
lattice vacancy recombine, or interplanar bonds are
broken, their excess energy is given up as ‘stored
energy.’ If sufficient damage has accumulated in the
graphite, the release of this stored energy can result
in a rapid rise in temperature. Stored energy accumulation was found to be particularly problematic

in the early graphite-moderated reactors, which
operated at relatively low temperatures. Figure 12
shows the rate of release of stored energy with


Radiation Effects in Graphite

0.7

dS/dT (cal g–1 ЊC–1)

0.6

Exposures in MWd/at and dpa (approximately)

0.5
0.4

Specific
heat

0.3

5700/0.60
1075/0.10

0.2
0.1
0


100/0.01
100

200
300
400
Annealing temperature (ЊC)

500

Figure 12 Stored energy release curves for CSF graphite
irradiated at $30  C in the Hanford K reactor cooled test
hole. Source: Nightingale, R. E. Nuclear Graphite; Academic
Press: New York, 1962. From Burchell, T. D. In Carbon
Materials for Advanced Technologies; Burchell, T. D., Ed.;
Elsevier Science: Oxford, 1999, with permission from
Elsevier.

temperature, as a function of temperature, for graphite samples irradiated at 30  C to low doses in the
Hanford K reactor.32 The release curves are characterized by a peak occurring at $200  C. This temperature
has subsequently been associated with annealing of
interplanar bonding involving interstitial atoms.20
In Figure 12, the release rate exceeds the specific
heat and therefore, under adiabatic conditions, the
graphite would rise sharply in temperature. For ambient temperature irradiations it was found9 that the
stored energy could attain values up to 2720 J gÀ1,
which if released adiabatically would cause a temperature rise of some 1300  C. A simple experiment,8 in
which samples irradiated at 30  C were placed in a
furnace at 200  C and their temperature monitored,
showed that when the samples attained a temperature

of $70  C their temperature suddenly increased to a
maximum of about 400  C and then returned to
200  C. In order to limit the total amount of stored
energy in the early graphite reactors, it became necessary to periodically anneal the graphite. The graphite’s temperature was raised sufficiently, by nuclear
heating or the use of inserted electrical heaters, to
‘trigger’ the release of stored energy. The release then
self-propagated slowly through the core, raising the
graphite moderator temperature and thereby partially annealing the graphite core. Indeed, Arnold33
reports that it was during such a reactor anneal that
the Windscale (UK) reactor accident occurred in
1957. Rappeneau et al.34 report a second release peak
at very high temperatures ($1400  C). They studied
the energy release up to temperatures of 1800  C

311

of graphites irradiated in the reactors BR2 (Mol,
Belgium) and HFR (Petten, Netherlands) at doses
between 1000 and 4000 MWd TÀ1 and at temperatures between 70 and 250  C. At these low irradiation
temperatures, there is little or no vacancy mobility, so
the resultant defect structures can only involve
interstitials. On postirradiation annealing to high temperatures, the immobile single vacancies become
increasingly mobile and perhaps their elimination
and the thermal destruction of complex interstitial
clusters or distorted and twisted basal planes contribute to the high-temperature stored energy peak.
The accumulation of stored energy in graphite is
both dose and irradiation temperature dependent.
With increasingly higher irradiation temperatures,
the total amount of stored energy and its peak rate
of release diminish, such that above an irradiation

temperature of $300  C stored energy ceases to be
a problem. Accounts of stored energy in graphite can
be found elsewhere.1,8,29,32
4.10.5.2 Mechanical and Physical
Properties
The mechanical and physical properties of several
medium-grained and fine-grained nuclear grade graphites currently in production are given in Table 2
(see also Chapter 2.10, Graphite: Properties and
Characteristics). The coke type, forming method, and
potential uses of these grades are in Table 1. The most
obvious difference between the four grades listed in
Table 2 is the filler particle sizes. Grade IG-110 is an
isostatically pressed, isotropic grade, whereas the others
grades shown are near-isotropic and have properties
reported either with-grain or against-grain. As discussed
earlier (see Section 4.10.2), the orientation of the filler
coke particles is a function of the forming method.
The mechanical properties of nuclear graphites
are substantially altered by radiation damage. In the
unirradiated condition, nuclear graphites behave in
a brittle fashion and fail at relatively low strains.
The stress–strain curve is nonlinear, and the fracture
process occurs via the formation of subcritical cracks,
which coalesce to produce a critical flaw.35,36 When
graphite is irradiated, the stress–strain curve becomes
more linear, the strain to failure is reduced, and the
strength and elastic modulus are increased. On irradiation, there is a rapid rise in strength, typically
$50%, that is attributed to dislocation pinning at
irradiation-induced lattice defect sites. This effect is
largely saturated at doses >1 dpa. Above $1 dpa, a

more gradual increase in strength occurs because of


312

Radiation Effects in Graphite

Table 2

Typical physical and mechanical properties of unirradiated nuclear graphites

Property

Graphite grade
IG-110

PCEA

NBG-10

NBG-18

Maximum filler particle size (mm)
Bulk density (g cmÀ3)
Tensile strength (MPa)

10
1.77
24.5


Flexural strength (MPa)

39.2

Compressive strength (MPa)

78.5

800
1.83
21.9 (WG)
16.9 (AG)
32.4 (WG)
23.3 (AG)
60.8 (WG)
67.6 (AG)
11.3 (WG)
9.9 (AG)
162 (WG)
159 (AG)
3.5 (WG)
3.7 (AG)
(30–100  C)
7.3 (WG)
7.8 (AG)

1600
1.79
20.0 (WG)
18.0 (AG)

24.0 (WG)
27.0 (AG)
47.0 (WG)
61.0 (AG)
9.7 (WG)
9.7 (AG)
148 (WG)
145 (AG)
4.1 (WG)
4.6 (AG)
(20–200  C)
9.1 (WG)
9.3 (AG)

1600
1.88
21.5 (WG)
20.5 (AG)
28 (WG)
26 (AG)
72.0 (WG)
72.5 (AG)
11.2 (WG)
11.0 (AG)
156 (WG)
150 (AG)
4.5 (WG)
4.7 (AG)
(20–200  C)
8.9 (WG)

9.0 (AG)

Young’s modulus (GPa)

9.8

Thermal conductivity (W mÀ1 KÀ1)
(measured at ambient temperature)
Coefficient of thermal expansion (10À6 KÀ1)
(over given temperature range)

116

Electrical resistivity (mO m)

11

4.5 (350–450  C)

WG, with-grain; AG, against-grain.

ðE=E0 Þirradiated ¼ ðE=E0 Þpinning ðE=E0 Þstructure

½1Š

where E/E0 is the ratio of the irradiated to unirradiated elastic modulus. The dislocation pinning contribution to the modulus change is due to relatively
mobile small defects and is thermally annealable at
$2000  C. The irradiation-induced elastic modulus
changes for GraphNOL N3M graphite37 are shown
in Figure 13. The low dose change due to dislocation

pinning (dashed line) saturates at a dose <1 dpa.
The elastic modulus and strength are related by a
Griffith theory type relationship.
Strength; st ¼ ½GE=pcŠ1=2

½2Š

50

40
Young’s modulus (GPa)

structural changes within the graphite. For nuclear
graphites, the dose at which the maximum strength is
attained loosely corresponds with the volume change
turnaround dose, indicating the importance of pore
closure and generation in controlling the high-dose
strength behavior, and may be as much as twice the
unirradiated value.
The strain behavior of nuclear graphites subjected
to an externally applied load is largely controlled by
shear of the component crystallites. As with strength,
irradiation-induced changes in Young’s modulus are
the combined result of in-crystallite effects, due to
low fluence dislocation pinning, and superimposed
structural change external to the crystallite. The
effects of these two mechanisms are generally considered separable, and related by

30


20
875 ЊC
600 ЊC

10

0

0

5

10

15
20
Fluence (dpa)

25

30

Figure 13 Neutron irradiation-induced Young’s modulus
changes for GraphNOL N3M at irradiation temperatures
600 and 875  C. From Burchell, T. D.; Eatherly, W. P.
J. Nucl. Mater. 1991, 179–181, 205–208.

where G is the fracture toughness or strain energy
release rate ( J mÀ2), E is the elastic modulus (Pa), and
c is the flaw size (m). Thus, irradiation-induced

changes in st and E (in the absence of changes
in [G/c]) should follow st/E1/2. High-dose data
reported by Ishiyama et al.38 show significant deviation from this relationship for grade IG-110 graphite,
indicating that changes in G and or c must occur.


Thermal conductivity (Wm–1 K–1)

Radiation Effects in Graphite

160
12 dpa
25 dpa
26 dpa
Unirradiated

140
120
100
80
60
40
20
0
0

200

400
600

800
Temperature (ЊC)

1000

1200

Figure 14 Temperature dependence of thermal
conductivity in the irradiated and unirradiated condition
for typical nuclear grade graphite. Irradiation
temperature ¼ 600  C.

Graphite is a phonon conductor of heat. Therefore,
any reduction in the intrinsic defect population causes
a reduction in the degree of phonon-defect scattering,
an increase in the phonon mean free path, and an
increase in the thermal conductivity. In graphite,
such thermally induced improvements are attributable
to increases in crystal perfection and a concomitant
increase in the size of the regions of coherent ordering upon graphitization. With increasing temperature,
the dominant phonon interaction becomes phonon–
phonon scattering (Umklapp processes). Therefore,
there is a reduction of thermal conductivity with
increasing temperature.39 This decrease in the thermal
conductivity with increasing temperature can clearly
be seen in Figure 14.
The mechanism of thermal conductivity and the
degradation of thermal conductivity have been extensively reviewed.13,14,26,40 The increase of thermal resistance due to irradiation damage has been ascribed by
Taylor et al.41 to the formation of (1) submicroscopic
interstitial clusters, containing 4 Æ 2 carbon atoms;

(2) vacant lattice sites, existing as singles, pairs, or
small groups; and (3) vacancy loops, which exist in
the graphite crystal basal plane and are too small to
have collapsed parallel to the hexagonal axis. The
contribution of collapsed lines of vacant lattice sites
and interstitial loops, to the increased thermal resistance, is negligible.
The reduction in thermal conductivity due to
irradiation damage is temperature and dose sensitive.
At any irradiation temperature, the decreasing thermal
conductivity will reach a ‘saturation limit.’ This limit is
not exceeded until the graphite undergoes gross structural changes at very high doses. The ‘saturated’ value
of conductivity will be attained more rapidly, and will
be lower, at lower irradiation temperatures.42 In graphite, the neutron irradiation-induced degradation of

313

thermal conductivity can be very large, as illustrated
in Figure 14. This reduction is particularly large
at low temperatures. Bell et al.43 have reported that
the room temperature thermal conductivity of pile
grade A (PGA) graphite is reduced by more than
a factor of 70 when irradiated at 155  C to a dose
of $0.6 dpa. At an irradiation temperature of 355  C,
the room temperature thermal conductivity of PGA
was reduced by less than a factor of 10 at doses twice
that obtained at 155  C. Above 600  C, the reduction of thermal conductivity is less significant. For
example, Kelly8 reported the degradation of PGA at
higher temperatures: at an irradiation temperature of
600  C and a dose of $13 dpa, the thermal conductivity was degraded only by a factor of $6; at irradiation
temperatures of 920 and 1150  C, the degradation was

minimal (less than a factor of 4 at $7 dpa). For the
fine-grained, isomolded graphite shown in Figure 14,
the degradation of thermal conductivity at the irradiation temperature (600  C) was only by a factor of $3,
but was by a factor $6 at a measurement temperature
of 100  C.
There are two principal thermal expansion coefficients in the hexagonal graphite lattice; ac, the thermal expansion coefficient parallel to the hexagonal
c-axis and aa, the thermal expansion coefficient parallel to the basal plane (a-axis). The thermal expansion coefficient in any direction at an angle f to the
c-axis of the crystal is
aðfÞ ¼ ac cos2 f þ aa sin2 f

½3Š

The value of ac varies linearly with temperature
from $25 Â 10À6 KÀ1 at 300 K to $35 Â 10À6 KÀ1
at 2500 K. In contrast, aa is much smaller and
increases rapidly from À1.5 Â 10À6 KÀ1 at $300 K
to $1 Â 10À6 KÀ1 at 1000 K, and remains relatively
constant at temperatures up to 2500 K.39
The large anisotropy in the crystal coefficient of
thermal expansion (CTE) values is a direct consequence of the bond anisotropy and the resultant
anisotropy in the crystal lattice compliances. The
thermal expansion of polycrystalline graphites is controlled by the thermal closure of aligned internal
porosity which forms as a result of thermal shrinkage
strains on cooling after graphitization. Thus, the
c-axis expansion of the graphite crystals is initially,
partially accommodated by this internal porosity and
a much lower bulk CTE value is observed. On further
heating, the graphite crystals fill more of the available
internal porosity and more of the c-axis expansion is
observed. The bulk CTE thus increases with temperature (Figure 15).



Radiation Effects in Graphite

6

5.0
4.0
3.0
2.0
1.0
0.0
0

200
400
600
800
Measurement temperature (ЊC)

1000

Figure 15 Temperature dependence of the coefficient of
thermal expansion for typical nuclear grade graphite.

As the CTE of polycrystalline graphite is dependent on the pore structure, irradiation-induced
changes in the pore structure (see discussion of
structural changes in Section 4.10.4) can be expected
to modify the thermal expansion behavior of carbon
materials. Burchell and Eatherly37 report the behavior of GraphNOL N3M (which is typical of many

fine-textured graphites), which undergoes an initial
increase in the CTE followed by a steady reduction
to a value less than half the unirradiated value of
5 Â 10À6  CÀ1 (Figure 16). Similar behavior is
reported by Kelly8 for grade IM1-24 graphite.
Heat energy is stored in the crystal lattice in the
form of lattice vibrations. The Debye equation therefore gives the specific heat, C, as follows:

C ¼ 9R

T
yD

y

3 ðT
0

z4 ez
dz
ðez À 1Þ2

½4Š

Coefficient of thermal expansion a(10-6 ЊC-1)

6.0

875 ЊC
600 ЊC

5

4

3

2

0

5

10

15
20
Fluence (dpa)

25

30

Figure 16 The irradiation-induced changes in coefficient
of thermal expansion (25–500  C) for GraphNOL N3M
graphite at two irradiation temperatures. From
Burchell, T. D.; Eatherly, W. P. J. Nucl. Mater. 1991,
179–181, 205–208.

2400
Specific heat (J Kg–1 K–1)


Average coefficient of thermal
expansion (10-6 ЊC-1)

314

2000
1600
1200
800
Calculated value
Experimental data

400
0
0

500

1000 1500 2000
Temperature (K)

2500

3000

where R is the gas constant (8.314 J molÀ1 KÀ1); T,
the temperature; yD , the Debye temperature; and
z ¼ ho/2kTp, where o is the frequency of vibrational
oscillations; k, the Boltzmann’s constant; T, the temperature; and h is the Plank’s constant.

At low temperatures, where (T/yD) <0.1, z in eqn
[4] is large, we can approximate eqn [4] by allowing
the upper limit in the integral to go to infinity such
that the integral becomes $(p4/15), and on differentiating we get

Figure 17 The temperature dependence of the specific
heat of graphite, a comparison of calculated values and
literature data for POCO AXM-5Q graphite. Sources: ASTM
C 781. Standard Practice for Testing Graphite and
Boronated Graphite Materials for High-Temperature
Gas-Cooled Nuclear Reactor Components, Annual Book of
Standards. ASTM International: West Conshohocken, PA;
Vol. 05.05; Hust, J. G. NBS Special Publication 260–89;
US Department of Commerce, National Bureau of
Standards, 1984; p 59.

C ¼ 1941ðT =yD Þ3 J molÀ1 KÀ1

10% of the Debye temperature (0.1yD), the specific
heat should rise exponentially with temperature to a
constant value at T % yD.
Figure 17 shows the specific heat of graphite
over the temperature range 300–3000 K. The data
has been shown to be well represented by the
eqn [6],44,45 and is applicable to all nuclear graphites.
The release of energy from the thermal annealing of
damage accumulated at low irradiation temperature

½5Š


Thus, at low temperatures, the specific heat is proportional to T3 (eqn [5]). At high temperatures, z is
small and the integral in eqn [4] reduces to z2dz;
hence, on integrating we get the Dulong–Petit value
of 3R, that is, the theoretical maximum specific heat
of 24.94 J molÀ1 KÀ1. As we are typically concerned
only with the specific heat at temperatures above


Radiation Effects in Graphite

(Wigner energy) will reduce the effective specific
heat (see Section 4.10.4).
Cp ¼

11:07T À1:644

1
J KgÀ1 KÀ1 ½6Š
þ 0:0003688T 0:02191

The electrical resistivity of graphite is also affected
by radiation damage. The mean free path of the
conduction electron in unirradiated graphite is relatively large, being limited only by crystallite boundary scattering. Neutron irradiation introduces (1)
scattering centers, which reduce charge carrier
mobility; (2) electron traps, which decrease the
charge carrier density; and (3) additional spin resonance. The net effect of these changes is to increase
the electrical resistivity on irradiation, initially very
rapidly, with little or no subsequent change to relatively high fluence.14,37 A subsequent decrease at
very high neutron doses is attributed to structural
degradation.


4.10.6 Irradiation Creep
4.10.6.1 The Relevance of Creep to Reactor
Design and Operation
Graphite will undergo creep (inelastic strain) during
neutron irradiation and under stress at temperatures
where thermal creep is generally negligible. The
phenomenon of irradiation creep has been widely
studied because of its significance to the operation
of graphite-moderated fission reactors. Indeed, if
irradiation-induced stresses in graphite moderators
could not relax via radiation creep, rapid core disintegration would result. The total strain, eTotal, in a graphite component under irradiation in a reactor core is
given by the materials constitutive equation:
eTotal ¼ ee þ et þ ed þ ec

½7Š

where ee is the elastic strain; et, the thermal strain; ed,
the dimensional change strain; and ec is the creep
strain, which is given as
ec ¼ ep þ es

½8Š

where ep and es are the primary and secondary
creep strains, respectively. Tsang and Marsden46
concluded that irradiation creep strain is particularly important in reactor design because without
creep strain self-induced shrinkage stresses would
build up to levels exceeding the graphite component
failure strength.

The significance of irradiation creep to reactor
core design and operation has been the subject

315

of recent work, where it has been shown how
uncertainties in the assumed magnitudes of the
irradiation-induced creep strains in a graphite reactor core component can substantially impact the
predicted stress levels, and hence the predicted failure probabilities of core components.47,48 Li et al.47
assumed the current UK creep law and showed that
a 50% decrease in the assumed creep strain resulted
in a 50% increase in the magnitude of the predicted
hoop stress in a hollow cylindrical core brick. Similarly, a 50% increase in the assumed creep strain
yielded a 30% reduction in the predicted brick
hoop stress.
Wang and Yu48 report the effect of varying creep
strain ratio (analogous to Poisson’s ratio, but where
the two perpendicular strains are creep strains) on the
magnitude of the modified equivalent stress in a
graphite component and the associated probability
of failure, as a function of neutron dose. In addition,
they examined the influence of primary creep in
reducing the magnitudes of stresses and associated
failure probabilities in graphite core components.
Wang and Yu’s results clearly indicate that variations
of the creep strain ratio resulted in considerable
change in the stress distributions and the corresponding failure probabilities of graphite components. In addition, they showed that the primary
creep appears to play the same important role as
secondary creep in certain cases.
Because of the significance of irradiation-induced

creep to the stress levels in graphite core components, accurate models of creep have long been
sought. Recently, the breakdown of the currently
accepted model(s) of creep at high temperatures
and doses has been reported, and possible improvement or alternative models have been postulated.49,50 Analysis of the creep behavior of H-451
at high doses indicated that further modification to
the current Kelly and Burchell51 model is required
to allow for the generation of new porosity at higher
doses and temperatures.50 The extent to which
high-dose creep strain behavior differs between
the compressive load and tensile load situations is
shown in Figure 18, which compares the creep
behavior of ATR-2E graphite for the þ5 MPa and
the À5 MPa loading cases;52 the dashed lines are
polynomial fits to the data. A more rapidly increasing
creep rate in the tensile loading case compared to the
compressive case is clearly observed. Because of
the importance of irradiation-induced creep to the
design and operation of graphite reactor cores, the
subject is treated here in considerable detail,


Radiation Effects in Graphite

Creep strain (%)

316

2
1.8
1.6

1.4
1.2
1
0.8
0.6
0.4
0.2
0

Tensile creep
strain (% MPa)
Compressive
creep strain (%)
Poly tensile
creep strain (%
MPa)
Poly
compressive
creep strain (%)

0

1
2
3
Neutron dose 1022 n cm-2 [E > 50 keV]

4

Figure 18 A comparison of the tensile (þ5 MPa) and compressive creep (À5 MPa) rates of ATR-2E graphite at irradiation

temperature of 500–550  C. Source: Haag, G. Properties of ATR-2E Graphite and Property Changes due to Fast Neutron
Irradiation; Report No. Jul-4183; Published FZ-J, Germany, 2005; Available at .

including a review of the in-crystal creep mechanism
and irradiation-induced graphite creep models.
4.10.6.2 The Irradiation-Induced Creep
Mechanism (In-Crystal)
A mechanism for the irradiation-induced creep of
graphite was proposed by Kelly and Foreman53
which involves irradiation-induced basal plane dislocation pinning/unpinning in the graphite crystals.
Pinning sites are created and destroyed by neutron
irradiation (radiation annealing). Under neutron
irradiation, dislocation lines in the basal planes may
be completely or partially pinned depending upon
the dose and temperature of irradiation. The pinning
points were speculated to be interstitial atom clusters 4 Æ 2 atoms in size,54,55 that is, the same defects
clusters assumed to contribute to the reduction in
thermal conductivity. The interstitial clusters are
temporary barriers as they are annealed (destroyed)
by further irradiation. Thus, irradiation can release
dislocation lines from their original pinning site
and the crystal can flow as a result of basal plane
slip at a rate determined by the rate of pinning and
unpinning of dislocations. Kelly and Foreman’s theory assumes that polycrystalline graphite consists of a
single phase of true density r0 and apparent density r.
The material may be divided into elementary regions
in which the stress may be considered uniform and
which may be identified as monocrystalline graphite.
Significantly, the model excludes porosity. It is further
assumed that the only deformation mode is basal

plane slip for which the strain rate is determined by
e_ xz ¼ kðsxz Þf

½9Š

and
e_ yz ¼ kðsyz Þf

½10Š

where f is the fast neutron flux; k, the steady-state
creep coefficient, and s is the stress in the given direction. The microscopic deformation assumes the usual
relationship between the basal plane shear strain
rate (e_) and the mobile dislocation density (O), and is
given by
e_ ¼ Obn ¼ ksf
½11Š
where b is the Burger’s vector and n is the dislocation
velocity as a function of the pinning point concentration in the basal plane as the pins are created and
destroyed by neutron flux. The dislocation line flow
model used the flexible line approach where the dislocation line is pinned/unpinned and the dislocation
line bowing is a function of the line tension and pin
spacing. The concentration of pinning sites increases
under irradiation from the initial value (from intrinsic
defects) to a steady-state concentration. The initial
creep rate is high and decreases to a steady-state
value as the pinning concentration saturates at a level
controlled by the neutron flux and temperature. This
saturation would be expected to occur over the same
dose scale as the reduction of thermal conductivity to

its saturation limit (see Section 4.10.5.2).
Thus, a two stage model can be envisioned where
the primary creep rate is initially high and falls to a
secondary or ‘steady-state’ creep rate. The steady-state
creep term should be the dominant term when the dose
has reached values at which physical property changes
due to dislocation pinning have saturated (see Section
4.10.5.2). Kelly and Foreman state that at higher temperatures the steady-state (secondary) creep rate (k)


Radiation Effects in Graphite

would be expected to increase because of (1) incompatibility of crystal strains increasing the internal stress
and thus enhancing the creep rate, and (2) additional
effects due to the destruction of interstitial pins by
thermal diffusion of vacancies (thermal annealing as
well as irradiation annealing). Kelly and Foreman53
further speculate that the nonlinearity of creep strain
with stress, which is expected at higher stress levels,
may also be related to the high-dose dimensional
change behavior of polycrystalline graphite.56
The possibility of other dislocation and crystal
deformation mechanisms being involved in irradiation creep must also be considered. For example,
prismatic dislocations may play an enhanced role at
high temperatures (>250  C) when the graphite lattice is under stress, as suggested by others.57 Are there
mechanisms of dislocation climb and glide that need
to be explored? Can dislocation lines climb/glide
past the assumed interstitial cluster barriers via a
mechanism that is active only when structural rearrangements occur during irradiation? This behavior
is analogous to carbons and graphites undergoing

thermal creep when they undergo structural reorganization, that is, during carbonization and graphitization (thermal relaxation or slumping).

317

countries showed the primary creep saturated at
approximately one elastic strain (s/E0) so that the
true creep may be represented as
s
½13Š
ec ¼ þ ksg
E0
This is often normalized to the initial elastic strain and
written as
ec ¼ 1 þ kE0 g

½14Š

in elastic strain units (esu) (esu is defined as the
externally applied stress divided by the initial static
Young’s modulus), or creep strain per unit initial elastic strain; kE is the creep coefficient in units of reciprocal dose [United Kingdom $ 0.23 Â 10À20 cm2 nÀ1
EDN up to Tirr $ 500  C]. (EDN – equivalent DIDO
nickel dose, a unit of neutron fluence used in the
United Kingdom and Europe.)
4.10.6.3.2 The UK creep model

The UK model1,64,65 recognizes that the initial creep
coefficient is modified by irradiation-induced structure changes (i.e., changes to the pore structure).
Hence, the total creep strain is given by
  ðg
s

dec
s S À1 ðgÞdg
ec ¼ þ
dg 0
E0

½15Š

0

4.10.6.3

Review of Prior Creep Models

4.10.6.3.1 Linear viscoelastic creep model

Irradiation-induced (apparent) creep strain is conventionally defined as the difference between the
dimensional change of a stressed specimen and an
unstressed specimen irradiated under identical conditions. Early creep data was found to be well
described by a viscoelastic creep model1,58–63 where
total irradiation creep (ec Þ ¼ primary (transient)
creep þ secondary (steady-state) creep.
as
½12Š
ec ¼ ½1 À expðÀbgފ þ ksg
E0
where ec is the total creep strain; s, the applied stress;
E0, the initial (preirradiated) Young’s modulus;
g, the fast neutron fluence; a and b are constants
(a is usually ¼ 1); and k is the steady-state creep

coefficient in units of reciprocal neutron dose and
reciprocal stress.
Equation [13] thus conforms to the Kelly–Foreman
theory of creep with an initially large primary creep
coefficient, while the dislocation pinning sites develop
to the equilibrium concentration, at which time
the creep coefficient has fallen to the steady-state or
secondary value. Early creep experiments in several

where s is the applied stress; (dec/dg)0, the initial
secondary creep rate; g, the fast neutron fluence; S(g),
the structure factor, given by S(g) ¼ Eg/Ep the ratio of
the Young’s modulus at dose g to the Young’s modulus
after the initial increase due to dislocation pinning.
The structure factor, S(g), thus attempts to separate those effects due to dislocation pinning occurring
within the crystallites and structural effects occurring ex-crystal through changes in the Young’s modulus.
However, the effect of creep strain (tensile or compressive) on modulus is not considered when evaluating
the structure term. The unstressed Young’s modulus
changes are used to establish the magnitude of S(g).
4.10.6.3.3 The Kennedy model

Kennedy et al.66 replaced the structure term in the
UK model with a parameter based on the volume
change behavior of the graphite:
s
½16Š
ec ¼ þ k0 ðgÞsg
E0
where
0


ðg 

k ðgÞ ¼ k0
0


1Àm

DV =V0
ðDV =V0 Þmax


dg

½17Š


318

Radiation Effects in Graphite

Here, m is an empirical constant equal to 0.75 and k0 is
the steady-state creep coefficient established from
low dose creep experiments.
Although the Kennedy et al.66 model was shown to
perform well in the prediction of high-dose tensile
creep data, it did not predict the compressive data
nearly as well. Moreover, as with the UK model,
the sign of the applied stress is not considered

when evaluating the influence of structure change
(as reflected in volume changes). The quotient in
eqn [17] is evaluated solely from unstressed (stressfree) samples irradiation behavior. As discussed by
Kelly and Burchell,51 the term (DV/Vmax) does not
exist at low irradiation temperatures where graphites
expand in volume.
4.10.6.3.4 The Kelly and Burchell model

The Kelly and Burchell50,51 model recognizes that
creep produces significant modifications to the dimensional change component of the stressed specimen
compared to that of the control and that this must
be accounted for in the correct evaluation of creep
strain data.
The rate of change of dimensions with respect to
neutron dose g(n cmÀ2) in appropriate units is given
by the Simmons’ theory29 for direction x in the
unstressed polycrystalline graphite:



ax À aa
dXT
1 dXa
þ
þ Fx
½18Š
gx ¼
ac À aa
dg
Xa dg

where ax is the thermal expansion coefficient in the
x-direction, and ac and aa are the thermal expansion
coefficients of the graphite crystal parallel and perpendicular to the hexagonal axis, respectively, over
the same temperature range. The term Fx is a pore
generation term that becomes significant at intermediate doses when incompatibilities of irradiationinduced crystal strains cause cracking of the bulk
graphite.67 For the purposes of their analysis, Kelly
and Burchell ignored the term Fx . The parameters
(1/Xc)(dXc/dg) and (1/Xa)(dXa/dg) are the rates of
change of graphite crystallite dimensions parallel and
perpendicular to the hexagonal axis, and
dXT
1 dXc
1 dXa
¼
À
dg
Xc dg Xa dg

½19Š

The imposition of a creep strain is known to change
the thermal expansion coefficient of a stressed specimen, increasing it for a compressive strain and
decreasing it for a tensile strain compared to an
unstressed control. Thus, the dimensional change

component of a stressed specimen at dose g(n cmÀ2)
is given by

 0


ax À aa
dXT
1 dXa
0
þ
þ Fx0
½20Š
gx ¼
ac À aa
dg
Xa dg
where a0x is the thermal expansion coefficient of the
crept sample, and Fx0 is the pore generation term for
the crept specimen. The difference between these
two equations is thus the dimensional change correction that should be applied to the apparent creep
strain (the pore generation terms Fx and Fx0 were
neglected):
 0


a À aa
dXT
gx0 À gx ¼ x
ac À a a
dg



ax À aa
dXT

À
ac À aa
dg
 0


a À ax
dXT
¼ x
½21Š
ac À aa
dg
The true creep strain rate can now be expressed as
 0


de de0
a À ax
dXT
À x
½22Š
¼
ac À aa
dg
dg dg
where e is the true creep strain and e0 is the apparent
creep strain determined experimentally in the conventional manner. Thus, the true creep strain (ec)
parallel to the applied creep stress is given by



ðg  0
ax À ax
dXT
0
dg
½23Š
ec ¼ ec À
ac À aa
dg
0

where e0c is the induced apparent creep strain,
ða0x À ax Þ is the change in CTE as a function of
dose, ðac À aa Þ is the difference of the crystal thermal
expansion coefficients of the graphite parallel and
perpendicular to the hexagonal axis, XT is the crystal
shape change parameter given above, and g is the
neutron dose. The apparent (experimental) creep
strain is thus given by


ðg  0
ax À ax
dXT
0
dg
½24Š
ec ¼ ec þ
ac À aa
dg

0

Substituting for ec from eqn [13] gives the apparent
(experimental) creep strain e0c as



 ðg  0
s
ax À ax
dXT
0
dg ½25Š
þ ksg þ
ec ¼
ac À aa
dg
E0
0

with the terms as defined above.
The Kelly–Burchell model is unique in that it
does take account of the sign of the applied stress in


Radiation Effects in Graphite

predicting creep strain through changes in the CTE
of the stressed graphite. While the model gave good
agreement between the predicted H-451 graphite

apparent creep strain and the experimental data at
low doses and high temperatures51 (Figures 19–22),
the creep model was shown to be inadequate at doses
>0.5 Â 1022 n cmÀ2 [E >50 keV] ($3.4 dpa) at an
irradiation temperature of 900  C (Figure 23).50
4.10.6.3.5 The M2 model

Based upon the evidence from UK and US creep
experiments, Davies and Bradford49,68 suggest the
following:
 The strain induced change in CTE is not a function of secondary creep strain, but saturates after a
dose of $30 Â 1020 n cmÀ2 EDN ($3.9 dpa).
 There is evidence, from both thermal and irradiation annealing, for a recoverable strain several

times that of primary creep, and a lower associated
secondary creep coefficient that has been previously assumed.
 The dose at which the recoverable strain saturates
bears a striking similarity to that of the saturation
of the CTE change.
Davies and Bradford49,68 proposed a new creep
model (the M2 model) without the term reflecting
changes in CTE due to creep, but containing one
additional term, recoverable creep:
gð1
lk1
s
Àk1 g1
expk1 g dg
ec ¼ exp
E0

SW

0

gð1
gð1
xk2
s
b s
Àk2 g1
k2 g
exp dg þ
dg
exp
þ
E0
SW
E0 SW
½26Š
0
0

Creep strain (%)

0.5
Experimental
creep strain

0


True creep
strain

-0.5

CTE
correction
strain

-1

Predicted
apparent
creep strain

-1.5
-2
0

0.1

0.2

0.3

0.4

0.5

0.6


Neutron dose 1022 n cm-2 [E > 50 keV]
Figure 19 Comparison of predicted apparent creep strain (from eqn [25]) and the experimental creep strain data for
irradiation creep at 600  C under a compressive stress of 13.8 MPa. The true creep strain is calculated from eqn [13].
From Burchell, T. D. J. Nucl. Mater. 2008, 381, 46–54.

1

Creep strain (%)

0.5

Experimental
creep strain

0

True creep
strain

-0.5
-1

CTE
correction
strain

-1.5

Predicted

apparent
creep strain

-2
-2.5
-3
0

319

0.1
0.2
0.3
0.4
0.5
Neutron dose 1022 n cm-2 [E > 50 keV]

0.6

Figure 20 Comparison of predicted apparent creep strain (from eqn [25]) and the experimental creep strain data for
irradiation creep at 600  C under a compressive stress of 20.7 MPa. The true creep strain is calculated from eqn [13].
From Burchell, T. D. J. Nucl. Mater. 2008, 381, 46–54.


Radiation Effects in Graphite

Creep strain (%)

320


1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
-3.5

Experimental
(apparent)
creep
True creep
strain
CTE
change
correction
Predicted
apparent
creep strain

0

0.1
0.2
0.3
0.4

0.5
Neutron dose 1022 n cm-2 [E > 50 keV]

0.6

Figure 21 Comparison of predicted apparent creep strain (from eqn [25]) and the experimental creep strain data for
irradiation creep at 900  C under a compressive stress of 13.8 MPa. The true creep strain is calculated from eqn [13].
From Burchell, T. D. J. Nucl. Mater. 2008, 381, 46–54.

2

Creep strain (%)

1
Experimental
creep strain

0

True creep
strain

-1

Dimensional
change
correction

-2
-3


Predicted
apparent
creep strain

-4
-5
0

0.1

0.2

0.3
22

Neutron dose 10

n cm-2

0.4

0.5

0.6

[E > 50 KeV]

Figure 22 Comparison of predicted apparent creep strain (from eqn [25]) and the experimental creep strain data for
irradiation creep at 900  C under a compressive stress of 20.7 MPa. The true creep strain is calculated from eqn [13].

From Burchell, T. D. J. Nucl. Mater. 2008, 381, 46–54.

5.0
Apparent
(experimental)
creep

Creep strain (%)

4.0
3.0

True creep

2.0

Dimensional
change
correction

1.0
0.0

Predicted
apparent
creep

-1.0
-2.0


0

0.5
1
1.5
Neutron dose, 1022 n cm-2 [E > 50 KeV]

2

Figure 23 Comparison of predicted apparent creep strain (from eqn [26]) and the experimental creep strain data
for irradiation creep at 900  C under a tensile stress of 6 MPa. The true creep strain is calculated from eqn [13].
From Burchell, T. D. J. Nucl. Mater. 2008, 381, 46–54.


Radiation Effects in Graphite

where ec is the total creep strain; s, the applied stress;
l, x, and b, are the empirical fitting parameters;
k1 and k2, the primary and recoverable dose constants
respectively; and W is the oxidation change factor
(with respect to Young’s modulus) and is analogous
to the structure factor. The terms in the eqn [26] are
proportional to esu and the effects of structural
changes and radiolytic oxidation (gasification of
graphite by an activated species that occurs in CO2
cooled reactors) are also included. The rates of saturation of the primary and recoverable creep components are controlled by the dose constants k1 and k2.
The first and last terms in eqn [26] are primary and
secondary creep as in the prior UK creep model, with
the middle term being recoverable creep.
Primary creep is still fast acting, but in the AGR

temperature range of 400–650  C, appears to act on a
longer fluence scale equivalent to that associated
in the United Kingdom with the Young’s modulus
pinning,69 k1 ¼ 0.1, and saturates at 1 esu (a ¼ 1).
The irrecoverable creep is synonymous with secondary creep, but with a coefficient, b, derived from
the irrecoverable strain postthermal anneal, as
0.15 per 1020 n cmÀ2 EDN ($1.3 dpa) in the AGR
temperature range. The lateral creep strain ratios
for primary and recoverable creep are assumed to
be the Poisson’s ratio and secondary creep is assumed
to occur at constant volume.
Figure 24 shows the performance of the M2
models applied to some high dose ATR-2E tensile
creep data52 when irradiated at 500  C in high flux
reactor (HFR), Petten. The prediction matches
the observed data well up to significant fluence
of $160 Â 1020 n cmÀ2 EDN ($21 dpa). Only beyond

321

this fluence does the new model prediction deviate
from the data with a delay in the increase in creep
strain at high doses that is often referred to as the
‘tertiary’ creep phase.
Figure 25 shows the corresponding compressive
creep data,52 irradiated at 550  C. The model over
predicts the data slightly but follows the trend remarkably well up to a significant fluence of $160 Â 1020
n cmÀ2 EDN ($21 dpa). Beyond this fluence, the
compressive prediction also indicates a ‘tertiary’
creep, but the data does not extend into this region.

The data52 also indicates a possible difference between
tensile and compressive creep (seen more clearly in
Figure 18).
Saturation of CTE with creep strain as reported
by Davies and Bradford49,68 is not however in agreement with other published data. Gray70 reported
CTE behavior with creep strain (up to 3%) for
three different graphites at irradiation temperatures
of 550 and 800  C. Saturation of the CTE in the
manner described by Davies and Bradford49,68 for
UK AGR graphite was not observed.
4.10.6.4 Deficiencies in Current Creep
Models at High Neutron Doses
The poor performance of the Kelly and Burchell
model (eqn [25]) at predicting the high temperature
(900  C) and high dose 6 MPa tensile creep data
suggests that the model requires further revision.50,71
H-451 graphite irradiated at 900  C goes through
dimensional change turn-around in the dose range
1.3–1.5 Â 1022 n cmÀ2 [E >50] ($8.8–10.2 dpa). This
behavior is understood to be associated with the
0.02

0.025
M2 model
500 T

0.015
Creep strain

Creep strain


0.02

Model 550 ЊC
550 ЊC

0.015
0.01

0.01

0.005

0.005
0

0
0

50

100
150
EDND (1020 n cm-2)

200

250

Figure 24 Comparison of the M2 models prediction and

experimental creep strain data for ATR-2E tensile creep
data, when irradiation was at 500  C in Petten. Reproduced
from Davies, M.; Bradford, M. J. Nucl. Mater. 2008, 381,
39–45.

0

50

100
150
Dose (1020 n cm-2 EDN)

200

250

Figure 25 Comparison of the M2 models prediction and
experimental creep strain data for ATR-2E compressive
creep data, when irradiation was at 550  C in Petten.
Reproduced from Davies, M.; Bradford, M. J. Nucl. Mater.
2008, 381, 39–45.


322

Radiation Effects in Graphite

generation of new porosity due to the increasing
mismatch of crystal strains. The Kelly–Burchell

model accounts for this new porosity only to the
extent to which it affects the CTE of the graphite,
through changes in the aligned porosity.
Gray70 observed that at 550  C the creep rate was
approximately linear. However, at 800  C he reported
a marked nonlinearity in the creep rate and the
changes in CTE were significant. Indeed, for the
two high density graphites (H-327 and AXF-8Q)
Gray reports that the 900  C creep strain rate
reverses. Gray postulated a creep strain limit to
explain this behavior, such that a back stress would
develop and cause the creep rate to reduce. Other
workers have shown that a back stress does not
develop.62 However, Gray further argued that a creep
strain limit is improbable as this cannot explain
the observed reversal of creep strain rate. Note that a
reversal of the creep rate is clearly seen in the 900  C
tensile creep strain data reported here for H-451
(Figure 23). Also, a creep strain limit would require
that tensile stress would modify the onset of pore
generation behavior in the same way as compressive
stress, because the direction of the external stress
should be immaterial.70 More recent data52 and the
behavior reported by Burchell71 show that this is not
the case. Gray70 suggests that a more plausible explanation of his creep data is the onset of rapid expansion
accelerated by creep strain; that is, net pore generation
begins earlier under the influence of a tensile applied
stress. Indeed, it has been observed52 that compressive
creep appears to delay the turnaround behavior and
tensile creep accelerates the turnaround behavior

(Figure 18).
In discussing possible explanations for his creep
strain and CTE observations, Gray70 noted that
changes in the graphite pore structure that manifested themselves in changes in CTE did not appear
to influence the creep strain at higher doses. The
classical explanation of the changes in CTE invokes
the closure of aligned porosity in the graphite crystallites. Further crystallite strain can be accommodated only by fracture. A result of this fracture is net
generation of porosity resulting in a bulk expansion
of the graphite. A requirement of this model is that
the CTE should increase monotonically from the
start of irradiation. A more marked increase in CTE
would be seen when the graphite enters the expansion phase (i.e., all accommodating porosity filled).
The observed CTE behavior, reported previously50
and in Gray’s70 work, does not display this second
increase in CTE; thus, the depletion of (aligned)

accommodation porosity is not responsible for the
early beginning of expansion behavior.
The observation by Gray70 and Kennedy63 that
creep occurs at near constant volume (up to moderate fluence) indicates that creep is not accompanied
by a net reduction of porosity compared to unstressed
graphite, but this does not preclude that stress may
decrease pore dimensions in the direction of the
applied stress and increase them in the other, that is,
a reorientation of the pore structure. Pore reorientation could effectively occur as the result of a mechanism of pore generation where an increasing fraction
of the new pores are not well-aligned with the crystallites basal planes (and thus they would not manifest
themselves in the CTE behavior) or accompanied
with the closure of pores aligned with the basal planes.
Kelly and Foreman53 report that their proposed
creep mechanism would be expected to break down

at high doses and temperatures, and thus deviations
from the linear creep law (eqn [12]) are expected.
They suggest that this is due to (1) incompatibility of
crystal strains causing additional internal stress and
an increasing crystal creep rate, (2) destruction of
interstitial pins by diffusion of vacancies (thermal
annealing of vacancies in addition to irradiation annealing), and (3) pore generation due to incompatibility of crystal strains.
It is likely that pore generation can manifest itself
in two ways: (1) changes in CTE with creep strain –
thus, pores aligned parallel to the crystallite basal
planes are affected by creep strain – and (2) at high
doses, pore generation or perhaps pore reorientation,
under the influence of applied and internal stress that
must be accounted for in the prediction of high
neutron dose creep behavior.
Brocklehurst and Brown62 report on the annealing
behavior of specimens that had been subjected to
irradiation under constant stress and sustained up to
1% creep strain. They observed that the increase in
creep strain with dose was identical in compression
and tension up to 1% creep strain, and that the CTE
was significantly affected in opposite directions by
compressive and tensile creep strains. Irradiation
annealing of the crept specimens caused only a small
recovery in the creep strain, and therefore provided
no evidence for a back stress in the creep process,
which has implications for the in-crystal creep mechanism. Thermal annealing also produced a small
recovery of the creep strain at temperatures below
1600  C, presumably because of the thermal removal
of the irradiation-induced defects responsible for

dislocation pinning. Higher temperature annealing


Radiation Effects in Graphite

produced a further substantial recovery of creep
strain. Most significantly, Brocklehurst and Brown62
reported the complete annealing of the creep induced
changes in CTE, in contrast to the total creep strain,
where a large fraction of the total creep strain is
irrecoverable and has no effect on the thermal expansion coefficient. Brocklehurst and Brown62 discuss
two interpretations of their results, but report that
neither is satisfactory. One interpretation requires a
distinction between changes in porosity that affect the
CTE and changes in porosity affecting the elastic
deformation under external loads, that is, two distinct
modes of pore structure changes due to creep in broad
agreement with the mechanism discussed earlier.
The modified Simmons model29,30,67 for dimensional changes (eqn [18]) and that for dimensional
changes of a crept specimen (eqn [20]) both have
pore generation terms which are currently neglected.
It now appears necessary to modify the current
Kelly–Burchell creep model (eqn [25]) to account
for this effect of creep strain on this phenomena;
that is, we need to evaluate and take account of the
terms Fx and Fx0 as well as include the term (Fx0 –Fx) in
eqn [25]. Such a term should account for pore generation and/or reorientation caused by fracture when
incompatibilities in crystallite strains become excessive.71 Clearly, further work is needed in the area of
irradiation-induced creep of graphite.


4.10.7 Outlook
For more than 60 years, nuclear graphite behavior
has been the subject of research and development in
support of graphite-moderated reactor design and
operations. The materials physics and chemistry, as
well as the behavior of nuclear graphite under neutron
irradiation are well characterized and understood,
although new high-resolution characterization tools,
such as HRTEM and STM, and other nanoscale
characterization techniques, coupled with powerful
computer based simulations of crystal deformation
and displacement damage, are yielding new insights
to the deformation mechanisms that occur in graphite
throughout its life in the reactor core.
Perhaps the biggest remaining challenge is to
gain a fuller understanding of irradiation-induced
dimensional change and irradiation creep in graphite.
Currently, new creep irradiation experiments are
underway at ORNL in the High Flux Isotope Reactor,
and at Idaho National Laboratory in the Advanced
Test Reactor. Studies of pore structure change from

323

unirradiated reference samples, irradiated unstressed
samples (controls), and irradiated stressed samples
(crept samples), may advance our understanding of
pore generation. Work in other countries is directed
at reviewing existing creep data and assessing the
observable graphite dimensional changes and creep

strain in currently operating reactors. A recent Coordinated Research Project initiated by the International Atomic Energy Agency (IAEA) has the goal of
bringing these various strands of research together to
form a single unified theory of irradiation-induced
creep deformation in graphites.
The knowledge gained through these many years of
work, and 50 years of graphite-moderated reactor
operating experience is currently being used to underwrite the safety cases of graphite reactors through out
the world. In the first part of the twenty-first century,
more knowledge will be gained from the new graphitemoderated reactors in Japan and China that operate
at higher temperatures. Several nations (within the
Generation IV International Forum) are pursuing
high-temperature, graphite-moderated, gas-cooled
reactor projects with the goal of developing versatile
and inherently safe reactor systems that can efficiently
deliver both process heat and electricity.
With the realization and acceptance that greenhouse gas emissions from fossil fueled power plants
are causing global climate changes, as evidenced by
the Kyoto and recent Copenhagen Agreements, the
nuclear option may once again become attractive for
clean electric power generation. At that time, it is to
be hoped that inherently safe, graphite-moderated,
gas-cooled reactors may find renewed popularity.

Acknowledgments
This work is sponsored by the US Department
of Energy, Office of Nuclear Energy Science and
Technology under contact DE-AC05-00OR22725
with Oak Ridge National Laboratories managed by
UT-Battelle, LLC.


References
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2.

3.

Burchell, T. D. In Carbon Materials for Advanced
Technologies; Burchell, T. D., Ed.; Elsevier Science:
Oxford, 1999; pp 429–484.
Eatherly, W. P.; Piper, E. L. In Nuclear Graphite;
Nightingale, R. E., Ed.; Academic Press: New York, 1962;
pp 21–51.
Ragan, S.; Marsh, H. J. Mater. Sci. 1983, 18,
3161–3176.