4.11

Graphite in Gas-Cooled Reactors

B. J. Marsden and G. N. Hall
The University of Manchester, Manchester, UK

ß 2012 Elsevier Ltd. All rights reserved.

4.11.1
4.11.2
4.11.2.1
4.11.2.2
4.11.2.3
4.11.2.4
4.11.2.5
4.11.3
4.11.3.1
4.11.4
4.11.5
4.11.5.1
4.11.5.2
4.11.5.2.1
4.11.5.3
4.11.5.4
4.11.5.4.1
4.11.5.5
4.11.5.6
4.11.5.7
4.11.5.8
4.11.5.9

4.11.6
4.11.6.1
4.11.7
4.11.7.1
4.11.7.2
4.11.7.2.1
4.11.7.3
4.11.7.4
4.11.7.5
4.11.7.6
4.11.7.7
4.11.8
4.11.9
4.11.9.1
4.11.9.2
4.11.10
4.11.11
4.11.11.1
4.11.11.2
4.11.11.3
4.11.11.4
4.11.11.5
4.11.11.6
4.11.12

Introduction
Graphite Crystal Structures
Graphite Crystal Atomic Structure and Properties
Coefficient of Thermal Expansion
Modulus

Thermal Conductivity
Microcracking (Mrozowski Cracks)
Artificial Nuclear Graphite
Microstructure/Property Relationships
Graphite Core Fast Neutron Fluence, Energy Deposition, and Temperatures
Dosimetry (Graphite Damage Dose or Fluence)
Early Activation Measurements on Foils
Reactor Design and Assessment Methodology: Fuel Burnup
Calder effective dose
Equivalent Nickel Flux
Integrated Flux and Displacements per Atom
DIDO equivalent flux
Energy Above 0.18 MeV
Equivalent Fission Flux (IAEA)
Fluence Conversion Factors
Irradiation Annealing and EDT
Summary of Fast Neutron Dose (Fluence)
Graphite ‘Energy Deposition’ (Nuclear Heating)
The Use of Titanium for Installed Sample Holders
Radiolytic Oxidation
Introduction
Ionizing Radiation
Energy deposition
Radiolytic Oxidation Mechanism
Inhibition
Internal Porosity
Prediction of Weight Loss in Graphite Components
Weight Loss Prediction in Inhibited Coolant
Graphite Temperatures
Variation of Fluence, Temperature, and Weight Loss in a Reactor Core

Fuel End Effects
Temperature and Weight Loss
Distribution of Fluence Within an Individual Moderator Brick
Fast Neutron Damage in Graphite Crystal Structures
Stored Energy
Crystal Dimensional Change
Coefficient of Thermal Expansion
Modulus
Thermal Conductivity
Raman
Property Changes in Irradiated Polycrystalline Graphite

327
327
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328
328
329
329
329
330
332
333
334
335
335
336
336
337
338

339
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325



326

Graphite in Gas-Cooled Reactors

4.11.13
4.11.14
4.11.14.1
4.11.14.2
4.11.14.3
4.11.14.4
4.11.15
4.11.15.1
4.11.15.2
4.11.15.3
4.11.15.4
4.11.16
4.11.16.1
4.11.16.2
4.11.16.3
4.11.16.4
4.11.17
4.11.17.1
4.11.17.2
4.11.17.3
4.11.17.4
4.11.17.5
4.11.17.6
4.11.18
4.11.19

4.11.20
4.11.20.1
4.11.20.2
4.11.20.3
4.11.20.4
4.11.20.4.1
4.11.20.4.2
4.11.20.5
4.11.20.6
4.11.20.6.1
4.11.20.6.2
4.11.20.6.3
4.11.20.6.4
4.11.20.7
4.11.21
References

Averaging Relationships
Dimensional Change
Pile Grade A
Gilsocarbon
Effect of Radiolytic Oxidation on Dimensional Change
Dimensional Change Rate
Coefficient of Thermal Expansion
Pile Grade A
Gilsocarbon
Methodology for Converting Between Temperature Ranges
Effect of Radiolytic Oxidation on CTE
Thermal Conductivity
Pile Grade A

Gilsocarbon
Thermal Conductivity Temperature Dependence of Irradiated Graphite
Predicting the Thermal Conductivity of Irradiated Graphite for
Reactor Core Assessments
Young’s Modulus
Relationship Between Static and Dynamic Young’s Modulus
Pile Grade A
Gilsocarbon
Separation of Structure and Pinning Terms
Effect of Radiolytic Weight Loss on Dimensional Change and
Young’s Modulus
Small Specimen Strength
Effect of Radiolytic Oxidation on Thermal Conductivity, Young’s Modulus,
and Strength
The Use of the Product Rule
Irradiation Creep in Nuclear Graphite
Dimensional Change and Irradiation Creep Under Load
Types of Irradiation Creep Experiments
The UKAEA Creep Law
Observed Changes to Other Properties
Coefficient of thermal expansion
Young’s modulus
Lateral Changes
Creep Models and Theories
UKAEA creep law
German and US creep model
Further modifications to the UKAEA creep law: interaction strain
Recent nuclear industry model
Final Thoughts on Irradiation Creep Mechanisms
Concluding Remark


Abbreviations
AG
AGR
BAF
BEPO
CPV

Against grain
Advanced gas-cooled reactor
Bacon anisotropy factor
British Experimental Pile Zero
Closed pore volume

CTE
DFR
DSC
DYM
EDND
EDNF

Coefficient of thermal expansion
Dounreay Fast Reactor
Differential scanning calorimeter
Dynamic Young’s modulus
Equivalent DIDO nickel dose
Equivalent DIDO nickel flux

357
359

360
363
364
366
366
366
367
367
368
368
369
369
369
370
371
372
372
372
374
374
375
375
375
376
378
378
378
380
380
381

381
381
383
385
385
387
387
387
388


Graphite in Gas-Cooled Reactors

EDT
FWHM
HFR
HOPG
HRTEM

Equivalent DIDO temperature
Full-width, half-maximum
High Flux Reactor
Highly oriented pyrolytic graphite
High-resolution transmission electron
microscopy
HTR
High temperature reactor
IAEA
International Atomic Energy Agency
MTR

Materials test reactor
NDT
Nondestructive testing
OPV
Open pore volume
PGA
Pile Grade A
RBMK Reaktor Bolshoy Moshchnosti Kanalniy
(there are other quoted translations)
RPV
Reactive pore volume
SEM
Scanning electron microscopy
SYM
Static Young’s modulus
TEM
Transmission electron microscopy
TPV
Total pore volume
UKAEA United Kingdom Atomic Energy Authority
WG
With grain

327

This chapter aims to address that need by explaining
the influence of microstructure on the properties of
nuclear graphite and how irradiation-induced changes
to that microstructure influence the behavior of graphite components in reactor. Nuclear graphite is manufactured from coke, usually a by-product of the oil or
coal industry. (Some cokes are a by-product of refining

naturally occurring pitch such as Gilsonite.9) Thus,
nuclear graphite is a porous, polycrystalline, artificially
produced material, the properties of which are dependent on the selection of raw materials and manufacturing route. In this chapter, the properties of the
graphite crystal structures that make up the bulk polycrystalline graphite product are first described and
then the various methods of manufacture and resultant
properties of the many grades of artificial nuclear
graphite are discussed. This is followed by a description
of the irradiation damage to the crystal structure, and
hence the polycrystalline structure, and the implication of graphite behavior. The influence of radiolytic
oxidation on component behavior is also discussed as
this is of interest to operators or designers of graphitemoderated, carbon dioxide-cooled reactors, many of
which are still operating.

4.11.1 Introduction
Nuclear graphite has, and still continues, to act as a
major component in many reactor systems. In practice, nuclear graphite not only acts as a moderator but
also provides major structural support which, in
many cases, is expected to last the life of the reactor.
The main texts on the topic were written in the 1960s
and 1970s by Delle et al.,1 Nightingale,2 Reynolds,3
Simmons,4 in German, and Pacault5 Tome I and II, in
French with more recent reviews on works by Kelly6,7
and Burchell.8 This text is mainly on the basis of the
UK graphite reactor research and operating experience, but it draws on international research where
necessary.
During reactor operation, fast neutron irradiation,
and in the case of carbon dioxide-cooled systems
radiolytic oxidation, significantly changes the graphite component’s dimensions and properties. These
changes lead to the generation of significant graphite
component shrinkage and thermal stresses. Fortunately, graphite also exhibits ‘irradiation creep’

which acts to relieve these stresses ensuring, with
the aid of good design practice, the structural integrity of the reactor graphite core for many years. In
order to achieve the optimum core design, it is
important that the engineer has a fundamental understanding of the influence of irradiation on graphite
dimensional stability and material property changes.

4.11.2 Graphite Crystal Structures
The properties and irradiation-induced changes in
graphite crystals have been studied using both ‘naturally occurring’ graphite crystals and an artificial
product referred to as highly orientated pyrolytic
graphite (HOPG), formed by depositing a carbon
substrate using hydrocarbon gas6 followed by compression annealing at around 3000  C. HOPG is considered to be the most appropriate ‘model’ material
that can be used to study the behavior of artificially
produced polycrystalline nuclear graphite. It has a
density value near to that of a perfect graphite crystal
structure, but perhaps more appropriately, it has
imperfections similar to those found in the structures that make up artificial polycrystalline graphite.
A detailed description of the properties of graphite
can be found in Chapter 2.10, Graphite: Properties
and Characteristics.

4.11.2.1 Graphite Crystal Atomic
Structure and Properties
In this section, the atomic structure of graphite crystal structures is discussed briefly, along with some of
the properties relevant to the understanding of the


328

Graphite in Gas-Cooled Reactors


irradiation behavior of graphite. Graphite can be
arranged in an ABAB stacking arrangement termed
hexagonal graphite (see Figure 1). This is the most
thermodynamically stable form of graphite and has a
density of 2.266 g cmÀ3. The a-spacing is 1.415 A˚ and
the c-spacing is 3.35 A˚.
However, in both natural and artificial graphite
stacking faults and dislocations abound.10

4.11.2.3

The crystal elastic moduli6 are C11 (parallel to the basal
planes) ¼ 1060.0 Â 109 N mÀ2, C12 ¼ 180.0 Â 109 N mÀ2,
C13 ¼ 15.0 Â 109 N mÀ2, C33 (perpendicular to the
basal planes) ¼ 34.6 Â 109 N mÀ2, and C44 (shear of
the basal planes) ¼ 4.5 Â 109 N mÀ2 as defined by
the orthogonal co-ordinates given below:
0

4.11.2.2

Modulus

sxx

0

1


C11 C12 C13 0

0

0

C11 C13 0

0

0

C13 C33 0

0

0

0 C44 0

0

B
C B
B syy C B C12
B
C B
B
C B
B szz C B C13

B
C B
Bt C ¼ B 0
B zx C B
B
C B
Bt C B 0
@ zy A @

Coefficient of Thermal Expansion

The coefficient of thermal expansion (CTE) as
measured for natural graphite and HOPG is temperature dependent (Figure 2) and the data from a
number of authors has been collated by Kelly.6 The
room temperature values of CTE are about
27.5 Â 10À6 KÀ1 and À1.5 Â 10À6 KÀ1 in the ‘c’ and
‘a’ directions, respectively.

txy

0

0
0

0

0 C44

0


0

0

0

10
C
C
C
C
C
C
C
C
C
C
A

0
1ðC ÀC Þ
12
2 11

exx

1

B C

B eyy C
B C
B C
B ezz C
B C
Be C
B zx C
B C
Be C
@ zy A
exy
½1Š

c

c

a

a

Upper layer (A)

a

Lower layer (B)

2

40


1

30

CTE ac (10−6 K−1)

CTE aa (10−6 K−1)

Figure 1 The crystalline structure of graphite.

0
Bailey and Yates
Steward et al.
Harrison
Yates et al.

−1

−2

20
Bailey and Yates
Steward et al.
Harrison
Yates et al.
Nelson and Riley

10


0
0

500

1000
1500
2000
Temperature (K)
‘c’ direction

2500

3000

0

500

1000
1500
2000
Temperature (K)

2500

‘a’ direction

Figure 2 Crystal coefficient of thermal expansion. Modified from Kelly, B. T. Physics of Graphite; Applied Science:
London, 1981.


3000


Graphite in Gas-Cooled Reactors

The strength of the crystallite is also directly related
to the modulus, that is, the strength along the basal
planes is higher than the strength perpendicular
to the planes, and the shear strength between the
basal panes is relatively weak.
4.11.2.4

Thermal Conductivity

The thermal conductivity of graphite along the
basal plane ‘a’ direction is much greater than the
thermal conductivity in the direction perpendicular
to the basal plane ‘c.’ At the temperature of interest
to the nuclear reactor engineer, graphite thermal conduction is due to phonon transport. Increasing the
temperature leads to phonon–phonon or Umklapp
scattering (German for turn over/down). Imperfections
in the lattice will lead to scattering at the boundaries.

329

width and many micrometers in length (as seen in
Figure 3(b)), appears to be counterintuitive and has
led to speculation that these microcracks may contain
some low-density carbonaceous structure. The presence of these microcracks is very important in understanding the properties of nuclear graphite as they

provide accommodation for thermal or irradiationinduced crystal expansion in the ‘c’ direction.
Therefore, two crystal structures are of interest;
the ideal, ‘perfect’ structure and the nonperfect structures as may be defined with reference to HOPG. It is
of the latter that many of the crystal behaviors and
properties have been studied.
Definition: In this chapter on nuclear graphite,
‘crystal’ refers to the perfect crystal structure and
‘crystallite’ refers to the nonperfect crystal structures containing Mrozowski-type microcracks (and
nanocracks).

4.11.2.5 Microcracking (Mrozowski
Cracks)

4.11.3 Artificial Nuclear Graphite

During the manufacture of artificial graphite, very
high temperatures (2800–3000  C) are required in
the graphitization process. On cooling from these
high temperatures, thermoplastic deformation is possible until a temperature of $1800  C is reached.
Below this temperature, the large difference in thermal expansion coefficients between the ‘c’ and ‘a’
directions leads to the formation of long, thin microcracks parallel to the basal planes, often referred to as
‘Mrozowski’ cracks.11 These types of cracks are even
observed in HOPG (Figure 3).
The high density of HOPG when compared to the
large number of microcracks, a few nanometers in

The reactor designer requires a high-density, very
pure graphite, with a high scattering cross-section, a
low absorption cross-section, and good thermal and
mechanical properties, both in the unirradiated and

irradiated condition. The purity is important to ensure
not only a low absorption cross-section but also that
during operation the radioactivity of the graphite
remains as low as possible for waste disposal purposes.
Artificial graphite is manufactured from coke
obtained either from the petroleum or coal industry,
or in some special cases (such as Gilsocarbon, a UK
grade of graphite) from a ‘graphitizable’ coke derived

1 µm
1 µm

(a)
(b)

Figure 3 Transmission electron microscopic images of highly orientated pyrolytic graphite. (a) View into the ‘basal’
plane, ‘c’ direction, of HOPG (reproduced from Kelly, B. T. MSc thesis, University of Cardiff, Cardiff, Wales, 1966) and
(b) Mrozowski cracks in HOPG as seen along the ‘basal’ planes, ‘a’ direction. Courtesy of A. Jones, University of Manchester.


330

Graphite in Gas-Cooled Reactors

from naturally occurring pitch deposits.9 The raw
coke is first calcined to remove volatiles and then
ground or crushed for uniformity, before being blended
and mixed with a pitch binder. (Crushed ‘scrap’ artificial graphite may be added to help with heat removal
during the subsequent baking. For nuclear graphite,
this should be of the same grade as the final product.)

This mixture is then formed into blocks using one of
various techniques such as extrusion, pressing, hydrostatic molding, or vibration molding, to produce the
so-called ‘green article.’ The ‘green’ blocks are then
put into large ‘pit’ or ‘intermittent’ gas or oil-fired
furnaces. The blocks are usually arranged in staggers,
covered by a metallurgic coke, and baked at around
800  C in a cycle lasting about 1 month to produce
carbon blocks. These carbon blocks may be used for
various industrial purposes such as blast furnace liners;
it has even been used for neutron shielding in some
nuclear reactors. (Care must be taken as the carbon
blocks are not as pure as graphite and may lead to
waste disposal issues at the end of the reactor life.)
To improve the properties of the graphite produced from the carbon block, the carbon block is
often impregnated with a low-density pitch under
vacuum in an autoclave. To facilitate the entry of
the pitch into the body of the block, the block surface
may be broken by grinding. After impregnation the
blocks are then rebaked. This process of impregnation and rebaking may be repeated 2, 3, or 4 times.
However, the improvement in the properties by this
process is subject to diminishing rewards.
The next process is graphitization at about 2800–
3000  C by passing a large electrical current at low
voltage through the blocks either in an ‘Acheson
furnace’ or using an ‘in-line furnace.’ In both cases,
the blocks are covered by a metallurgical coke to
prevent oxidation. This graphitization cycle may
take about 1 month. If necessary, there may be a
final purification step. This involves heating the
graphite blocks to around 2400  C in a halogen gas

atmosphere to remove impurities. The final product
can then be machined into the many intricate components required in a nuclear reactor.
For quality assurance purposes, during manufacture the blocks are numbered at an early stage and
this number follows the block through the manufacturing process. This is clearly an expensive
manufacturing process and therefore, at each stage,
quality control is very important. Many samples will
be taken from the blocks to ensure that the final batch
(or heat) is of appropriate quality compared to previous heats. It is important that the reactor operators

retain this data in electronic form as it may be
required to investigate any anomalous behavior as
the reactor ages. Samples of ‘virgin’ unirradiated
graphite blocks should also be retained for future
reference. Records should include information on
the batch or heat, property measurements, nondestructive testing (NDT) results, and measurements
of impurities. It is not enough just to have the ‘ash’
content after incineration and the ‘boron equivalent’
as some impurities, such as nitrogen, chlorine, and
cobalt, will cause significant issues related to reactor
operation and final waste disposal. It is important that
the reactor operator takes responsibility for these
measurements as in the past it has been found that
reactor designers and graphite manufacturers close
down or merge, and records are lost.
Final inspection will uncover issues related to
damage, imperfection, quality, etc. Therefore, a ‘concessions’ policy is required to determine what is
acceptable and where such components can be used
in reactor. Again, the reactor operator will require an
electronic record of these concessions.
4.11.3.1 Microstructure/Property

Relationships
The microstructure of a typical nuclear graphite is
described with reference to Gilsocarbon. This product
was manufactured from coke obtained from a naturally
occurring pitch found at Bonanza in Utah in the
United States. To understand the microstructural
properties, one has to start with the raw coke. The
structure of Gilsonite coke is made of spherical particles about 1 mm in diameter as shown in Figure 4.
This structure is retained throughout manufacture
and into the final product. In Figure 4(b), the spherical shaped cracks following the contours of the
spherical particles are clearly visible. This coke will
be carefully crushed in order to keep the spherical
structures that form the filler particles and help to
give Gilsocarbon its (semi-) isotropic properties.
At a larger magnification in a scanning electron
microscopy (SEM), the complexity of these cracks is
clearly visible, Figure 4(c), and at an even larger
magnification, a ‘swirling structure’ made up of
graphite platelets stacked together is discernable
between the cracks. In essence, the whole structure
contains a significant amount of porosity.
After graphitization, the Gilsonite coke filler particles are still recognizable (Figure 5(a) and 5(b)).
From the polarizing colors, one can see that the main
‘a’ axis orientation of the crystallites follows the


Graphite in Gas-Cooled Reactors

(a)


331

(b)

(c)

(d)

Figure 4 Gilsonite raw-coke microstructure. (a) Photograph of Gilsonite coke, (b) Scanning electron microscopy (SEM)
image of polished Gilsonite coke, (c) detail in an SEM image showing the region around cracks that follow the spherical shape
of the coke particles, and (d) a higher magnification SEM image showing the intricate, random arrangement of platelets.
Courtesy of W. Bodel, University of Manchester.

(a)

(c)

500 µm

(b)

200 µm

(d)

Figure 5 Polarized optical and scanning electron microscopic images of Gilsocarbon graphite. (a) Optical image, (b) optical
image, (c) SEM image, (d) SEM image. Courtesy of A. Jones, University of Manchester.


332


Graphite in Gas-Cooled Reactors

spherical particles circumferentially, as does the orientation of the large calcination cracks. The crystallite structures in the binder phase are much more
randomly oriented, and this phase contains significant amounts of gas-generated porosity. There are
also what appear to be broken pieces of Gilsonite
filler particles contained within the binder phase.
The bulk properties of polycrystalline nuclear
graphite strongly depend on the structure, distribution, and orientation of the filler particles.12 The
spherical Gilsonite particles and molding technique
give Gilsocarbon graphite semi-isotropic properties,
whereas in the case of graphite grades such as the UK
pile grade A (PGA), the extrusion process used during manufacture tends to align the ‘needle’ type coke
particles. Thus, the crystallite basal planes that make
up the filler particles tend to align preferentially,
with the ‘c’ axis parallel to the extrusion direction
and the ‘a’ axis perpendicular to the extrusion direction. The long microcracks are also aligned in the
extrusion direction. The terms ‘with grain (WG)’ and
‘against grain (AG)’ are used to describe this phenomenon, that is, WG is equivalent to the parallel
direction and AG is equivalent to the perpendicular
direction. Thus, the highly anisotropic properties of
the crystallite are reflected in the bulk properties
of polycrystalline graphite (Table 1).
A graphite anisotropy ratio is usually defined by
the AG/WG ratio of CTE values. For needle coke
graphite, this ratio can be two or more, while for a
more randomly orientated structure, values in the
region of 1.05 can be achieved by careful selection
of material and extrusion settings. A more scientific
way of defining anisotropy ratio is by use of the Bacon

anisotropy factor (BAF).13
Other forming methods are usually used to produce isotropic graphite grades such as the Gilsocarbon grade described above. In this case, it was found
that Gilsocarbon graphite produced by extrusion was
not isotropic enough to meet the advanced gascooled reactor (AGR) specifications. Therefore, a
Table 1

Relative properties–grain direction relationships

Property

Coefficient of thermal
expansion (CTE)
Young’s modulus
Strength
Thermal conductivity
Electrical resistivity

With grain (WG)

Against
grain (AG)

Lower

Higher

Higher
Higher
Higher
Lower


Lower
Lower
Lower
Higher

‘molding’ method where the blocks were formed by
pressing in two directions was used. This had the
effect of slightly aligning the grains such that the
AG direction was parallel to the pressing direction
and the WG was perpendicular to the pressing direction. However, Gilsocarbon has proved to be one of
the most isotropic graphite grades ever produced,
even in its irradiated condition.
Another approach is to choose an ‘isotropic coke’
crushed into fine particles and then produce blocks
using ‘isostatic molding’ process. The isostatic molding method involves loading the fine-grained coke
binder mixture into a rubber bag which is then put
under pressure in a water bath. In this way, high
quality graphite can be produced mainly for use for
specialist industries such as the production of electronic components. This type of graphite (such as IG110 and IG-11) has been used for high-temperature
reactor (HTR) moderator blocks, fuel matrix, and
reflector blocks in both Japan and China. However,
even these grades exhibit slight anisotropy.
The final polycrystalline product contains many
long ‘thin’ (and not so ‘thin’) microcracks within the
crystallite structures that make up the coke particles.
Similar, but much smaller, cracked structures are to
be found in the ‘crushed filler flour’ used in the
binder, and in well-graphitized parts of the binder
itself. It is these microcracks that are responsible for

the excellent thermal shock resistance of artificial
polycrystalline graphite. They also provide ‘accommodation,’ which further modifies the response of
bulk properties to the crystal behavior in both the
unirradiated and irradiated polycrystalline graphite.
Typical properties of several nuclear graphite grades
are given in Table 2. One can see that polycrystalline
graphite has about 20% porosity by comparing the
bulk density with the theoretical density for graphite
crystals (2.26 g cmÀ3). About 10% of this is open
porosity, the other 10% being closed.

4.11.4 Graphite Core Fast Neutron
Fluence, Energy Deposition, and
Temperatures
Since the late 1940s, many journal papers, conference
papers, and reports have been published on the
change in properties in graphite due to fast neutron
damage. Many different units have been used to
define graphite damage dose (or fluence). It is important to understand the basis of these units because
historic data are still being used to justify models


Graphite in Gas-Cooled Reactors

Table 2

333

Typical properties of several well-known grades of nuclear graphite


Property

PGA

CSF

Gilsocarbon

IG-110

H451

Production method
Direction
Density (g cmÀ3)
Thermal conductivity
(W mÀ1 K)
CTE, 20–120  C (10À6 KÀ1)
CTE, 350–450  C (10À6 KÀ1)
CTE, 500  C (10À6 KÀ1)
Young’s modulus (GPa)
Poisson’s ratio
Strength, tensile (MPa)
Strength, flexural (MPa)
Strength, compressive (MPa)

Extruded
WG
AG
1.74

200
109

Extruded
WG
AG
1.66
155
97

Press-molded
WG
AG
1.81
131

Iso-molded
WG
AG
1.77
116

Extruded
WG
AG
1.76
158
137

0.9


1.2

3.1

1.5
8.0

3.5
4.8

2.8

4.3
4.5

11.7
5.4
$0.07
17
11
19
12
27
27

used in assessments for component behavior in reactors. Indeed, some of these historic data, for example,
stored energy and strength, will also be used to support decommissioning safety assessments.
Early estimations of ‘graphite damage’ were based
on the activation of metallic foils such as cobalt,

cadmium, and nickel. Later, to account for damage
in different reactors, equivalent units, such as BEPO
or DIDO equivalent dose, were used where the damage is referred to damage at a standard position in the
BEPO, Calder Hall, or DIDO reactors. The designers
of plutonium production reactors preferred to use a
more practical unit related to fuel burnup (megawatts
per adjacent tonne of uranium, MW/Atu). Researchers also found that the calculation of a flux unit, based
on an integral of energies above a certain value, was
relatively invariant to the reactor system and used the
unit En > 0.18 MeV and other variants of this.
Today, the favored option is to calculate the fluence using a reactor physics code to calculate the
displacements per atom (dpa). However, in the field
of nuclear graphite technology historic units are still
widely used in the literature. For example, reactor
operators have access to individual channel burnup
which, with the aid of axial ‘form factors,’ can be used
to give a measure of average damage along the individual channel length.
Fortunately, most, but not all, of these units can be
related by simple conversion factors. However, care
must be taken; for example, the unit of megawatt days
per tonne of uranium (MWd tÀ1) is not necessarily
equivalent in different reactor systems.
When assessing the analysis of a particular component in a reactor, one must be aware that a single
detailed calculation of a peak rated component in the

3.6
10.9
0.21
17.5
23.0

70.0

9.8
0.14
24.5
39.2
78.5

4.0

4.4
8.51

5.1
7.38
0.15

15.2

13.7

55.3

52.7

center of the core may have been carried out to give
spatial, and maybe temporal, distribution of that
component’s fluence (and possibly temperature and
weight loss). These profiles may have then been
extrapolated to all of the other components in the

core using the core axial and radial ‘form factors.’ In
doing this, some uncertainty will be introduced and
clearly, some checks and balances will be required to
check the validity of such an approach.

4.11.5 Dosimetry (Graphite Damage
Dose or Fluence)
In a nuclear reactor, high energy, fast neutron flux
leads to the displacement of carbon atoms in the
graphite crystallites via a ‘cascade.’ Many of these
atoms will find vacant positions, while others will
form small interstitial clusters that may diffuse to
form larger clusters (loops in the case of graphite)
depending upon the irradiation temperature. Conversely, vacancy loops will be formed causing the
lattice structure to collapse. These vacancy loops
will only become mobile at relatively high temperatures. The production of transmutation gas from
impurities is not an issue for highly pure nuclear
graphite, as the quantities of gas involved will be
negligible and the graphitic structure is porous.
The change in graphite properties is a function of
the displacement of carbon atoms. The nature and
amount of damage to graphite depends on the particular reactor flux spectrum, which is dependent on the
reactor design and position, as illustrated in Figure 6.
It is impractical to relate a spectrum of neutron
energies to a dimensional or property change at a


334

Graphite in Gas-Cooled Reactors


1800
TE rig in BEPO
Hollow fuel element in BEPO
Empty fuel channel in BEPO
Empty lattice position in PLUTO

1600

Flux per unit lethargy f (v)

1400

Hollow fuel element in PLUTO
1200
1000
800
600
400
200
0
10

100

1000
Energy (keV)

10000


100000

Figure 6 Flux spectrums for various reactor positions used in graphite irradiation programs. Modified from Simmons, J.
Radiation Damage in Graphite; Pergamon: London, 1965.

single point in a material such as graphite. Therefore,
an ‘integrated flux’ is used and is discussed later.

Table 3
Relationship for BEPO equivalent flux (thermal)
at a central lattice position to other positions in BEPO and
other irradiation facilities

4.11.5.1 Early Activation Measurements
on Foils

Position

Factor

BEPO lattice
BEPO hollow slug
BEPO empty fuel channel
Windscale Piles
Windscale Piles thermostats
NRX fast neutron plug MWHs
American data MWd/CT

1
2.27

0.63
1.29
1.29
1.54 Â 1015
5.5 Â 1017

Although one cannot directly measure the damage to
graphite itself, it is possible to measure the activation
of another material, because of nuclear impacts adjacent to the position of interest. This activation may
then be related to changes in graphite properties.
This was done in early experiments using cobalt
foils and by measuring the activation arising from
the 59Co(n,g)60Co reaction. This reaction has a
cross-section of 38 barns and 60Co has a half-life of
5.72 years, which need to be accounted for in the
fluence calculations. Such foils were included in
graphite experiments in BEPO and the Windscale
Piles, and are still used today for irradiation rig
validation and calibration purposes.
In these early experiments, after removal from the
reactor, cobalt foils were dissolved in acid, diluted, and
the decay rate measured. A measure of fluence could
then be calculated from knowledge of the following:





the solution concentration
the time in the reactor

the decay rate
the activation cross-section

Source: Simmons, J. H. W. The Effects of Irradiation on Graphite;
AERE R R 1954; Atomic Energy Research Establishment, 1956.

Unfortunately the 59Co(n,g)60Co reaction is
mainly a measure of thermal flux and atomic displacements in graphite are due to fast neutrons. An
improvement was the use of cobalt/cadmium foils,
but this was not really satisfactory. Measurements
made in this way are often given the unit, neutron
velocity time (nvt).
Table 3 gives an example of thermal flux determined from cobalt foils defined at a standard position in the center of a lattice cell in BEPO.
Graphite damage at other positions in other reactors could then be related to the standard position
in BEPO.


Graphite in Gas-Cooled Reactors

4.11.5.2 Reactor Design and Assessment
Methodology: Fuel Burnup
When designing a nuclear reactor core, a channel
‘rating’ can be related to the reactor power and weight
of uranium in a particular channel. This channel
‘rating’ can be related to a rate of change in the
graphite properties. The channel rating is given in
MW/Atu and over time the channel burnup as megawatt days per adjacent tonne of uranium (MWd/Atu).
Note that this unit is literally the (power in a particular
channel) Â (number of days) Â (weight of uranium
in that channel). No account is taken of refueling.

However, fuel burnup is a function of reactor design
and therefore, the equivalence concept was used and
damage was related to a standard position.
In the United Kingdom, the change in graphite
property was defined at a standard position in a
Calder Hall reactor to give Calder equivalent dose.
This was defined as the dose at a position on the wall
of a fuel channel in a Calder Hall reactor. In the
Calder Hall design, the lattice pitch is 8 in. The standard position was chosen to be in a 3.55-in.-diameter
fuel channel at a point on the shortest line between
the centers of two fuel channels. The fuel is assumed
to be 1.15-in.-diameter natural uranium metal rods.
Calder equivalent dose was then used as a function to
relate graphite property change to fuel burnup.
Kinchin14 had measured the change in graphite
electric resistivity as a function of distance into the
BEPO reflector. By normalizing this change, he defined
a ‘graphite damage function’; see also Bell et al.15
Thus, graphite damage at some position in a reactor core graphite component could be defined as a
function of the following:
 source strength
 distance between position and source
 attenuation in damage with distance through the
intervening graphite
The damage function is a measure of the last two bullet
points. The source strength is related to fuel burnup.
The graphite damage function df is defined as
fðRg Þ
df ¼
R


½2Š

where f(Rg) is the damage absorption curve for
an equivalent distance through BEPO graphite ‘Rg’
of density 1.6 g cmÀ3, and R is the distance through
graphite between the source and position of interest.
Note that nonattenuating geometric features, that is,
holes, need to be accounted for.

335

Calder equivalent rating Pe can now be defined as
Pe ¼

AdfP
ACalder dfCalder

½3Š

where ‘ACalder’ and ‘A’ are the uranium fuel crosssectional areas in Calder (1.04 in.2) and in the reactor
under consideration, respectively; ‘dfCalder’ and ‘df ’
are the values of the damage at the Calder standard
position (1.395) and in the reactor under consideration, respectively, and ‘P’ is the fuel rating in the
reactor under consideration.
Thus, a graphite property change in a reactor under
assessment can be related to the equivalent graphite
property change at the Calder standard position.
However, in a real reactor there is more than one
fuel channel. There may also be absorbers or empty

interstitial holes, the fuel rating will change with
burnup, and the fuel will be replaced from time to
time. Therefore, a more complex, multiple source calculation is required to take account of the actual channel rating and the geometric features of the core. This
is normally done by considering a 5 Â 5 lattice array:
X Bi fðRg Þ 
i
½4Š
df ¼
B
R
i
i
where Bi and B are the accumulated fuel burnup
at the ith and reference source, respectively, f(Rg)i is
the damage absorption function corresponding to
thickness Rg for ith source, and Rg is the distance
between the ith source and target.
This method was successfully used to design the
Magnox reactors. However, because of the higher
enriched oxide fuel and more complex fuel design
in the AGRs, this approach became less satisfactory
and new ‘damage functions’ that accounted for the
new fuel and geometry were calculated using Monte
Carlo methods (made possible by the introduction of
the digital computer). This method was until recently
still used in industry codes such as ‘Fairy’ (National
Nuclear Company) and ‘GRAFDAM’ (UKAEA).
4.11.5.2.1 Calder effective dose

When only low-dose irradiation graphite property

data were available, it was assumed that irradiation
damage could be obtained at one temperature and
that the property change versus dose (fluence) curves
could be adjusted for all other temperatures using the
so called R(y) curve:
Calder effective
calder equivalent
¼
 RðyÞ ½5Š
dose
dose


336

Graphite in Gas-Cooled Reactors

However, the use of R(y) is valid only for very low
fluence and it should no longer be used, although one
may come across its use in historic papers.
4.11.5.3

Equivalent Nickel Flux

Nickel foils were used to give a measure of the
damage to graphite through the 58Ni(n,p)58Co reaction. This reaction has a mean cross-section of
0.107 barns and 58Co has a half-life of 71.5 days.
The change in graphite thermal resistivity was
measured in the TE10 experimental hole in BEPO
and the nickel flux was also measured at the same

position. It was assumed that the graphite displacement rate fd was equal to the nickel flux fNi at this
position. For comparison, the change in graphite
thermal resistivity was then measured at various
other positions in BEPO, as given in Table 4
Later, the same exercise was repeated in PLUTO,
the sister reactor to DIDO at Harwell, and the ratio
compared to that at other positions. In this case, the
ratio appeared to be largely invariant to position.
Table 5 gives a few examples of the many measurements made.16
It was decided that the activity produced in nickel
fNi could be related to the graphite damage rate by a

Table 4
Ratio of graphite damage to nickel flux as
measured in BEPO
Position

Ratio bfd/fNi

Experimental hole TE10
Hollow fuel element
Empty fuel channel (at three positions)
Experimental hole E2/7

1.0 (definition)
0.43
1.0
0.75

Modified from Bell, J.; Bridge, H.; Cottrell, A.; Greenough, G.;

Reynolds, W.; Simmons, J. Philos. Trans. R. Soc. Lond. A Math.
Phys. Sci. 1962, 254(1043), 361–395.
b is a proportionality factor.

Table 5
Ratio of graphite damage to nickel flux as
measured in PLUTO
Position

Ratio
fd/fNi

C4 – inside fuel element stainless steel thimble
D3 – inside fuel element stainless steel thimble
C4 – inside fuel element aluminum thimble
D4 – empty fuel element

0.518
0.468
0.507
0.564

Modified from Bell, J.; Bridge, H.; Cottrell, A.; Greenough, G.;
Reynolds, W.; Simmons, J. Philos. Trans. R. Soc. Lond. A Math.
Phys. Sci. 1962, 254(1043), 361–395.

factor. However, care was still required with respect
to the choice of reactor and irradiation location.
Thus, a definition of damage based on a standard
position in DIDO and a calculation route for equivalent DIDO nickel flux (EDNF) were devised.

It should be noted that there are difficulties related
to a standard based on measurements made with nickel
foils and the 58Ni(n,p,)58Co reaction because of the
short half-life of 58Co and the interfering effect of
the 58Co(n,g)59Co reaction. A method by Bell et al.15
which went back to measuring activation of cobalt
foils and the 59Co(n,g)60Co reaction, and then calculating the ratio fNi/fCo, was used for a short while.
This method used the following relationships:
115g fuel elements fNi =fCo ¼ 0:378 À 0:504b
150g fuel elements fNi =fCo ¼ 0:502 À 0:530b
where ‘b’ is the fuel burnup. However, this was not very
satisfactory and it was clear that a validated calculation
route was desirable, and is now becoming practicable
through development in computer technology.
4.11.5.4 Integrated Flux and
Displacements per Atom
The rate of change of a material property can be
related to displacement rate of carbon atoms (dpa sÀ1).
However, it is not possible to directly measure dpa sÀ1
in graphite, but dpa sÀ1 can be related to the reactor
flux. The flux depends on reactor design, and varies
with position in the reactor core.
Neutron flux is a measure of the neutron population and speed in a reactor. In a reactor, neutrons
move at a variety of speeds in randomly orientated
directions. Neutron flux is defined as the product of
the number of neutrons per unit volume moving at a
given speed, as given by eqn [6] below.





number
number cm
¼
n
v
½6Š
f
cm2 s
cm3
s
However, as there is a spectrum of neutrons, with
many velocities, this is not a useful unit for the
material scientist. Therefore, integrated flux is used
over a range of energies E1 to E2 as given by eqn [7].
ð E2
fðEÞdE
½7Š
f¼
E1

In this way, a measure of neutron damage at any
position within a structural component can be
defined as follows. For a material such as graphite,


Graphite in Gas-Cooled Reactors

the damaging power (displacement rate), fd, can be
expressed as an integrated flux as given in eqn [8].


337

flux multiplied by the nickel cross-section at the
standard position in DIDO, and s0 is the average
nickel cross-section for energies >1 MeV, which is
equal to 0.107 barn. The value of fs at this position
is 4 Â 1013 n cmÀ2 sÀ1.
The carbon displacement rate can be calculated
using eqn [10].
ðð
fðE1 ÞsðE1 ; E2 ÞnðE2 ÞdE1 dE2
½10Š
fd ¼

energy E1 to produce a recoil atom with energy E2,
and v(E2) is a ‘damage function’ giving the number
of atoms displaced from their lattice site by recoil
energy E2. The carbon displacement rate, fds, at a
standard position in DIDO is 5.25 Â 10À8 dpa.
The derivation of the damage function (Figure 7)
is on the basis of billiard ball mechanics, energy losses
to the lattice due to impacts, and to forces associated
with excitation of the lattice.
The early Kinchin and Pease17 form of the damage function was found to underestimate damage in
graphite. To give greater dpa, it was recommended
that ‘Lc’ was artificially increased, but this was not
satisfactory. The Thompson and Wright18 damage
function was used in the official definition of EDNF.
However, the Norgett et al.19 damage function is used

in most modern reactor physics codes and it has been
recently shown that there is little difference in the
calculation of graphite damage using either of these
latter two functions.20,21
It is assumed that the ratio of dpa to nickel flux
(fds/fs) at the standard position, which is equal
to 1313 Â 10À24 dpa (n cmÀ2 sÀ1)À1, can be equated
to the same ratio fd/fNi in the reactor of interest
as given by eqn [11]:
   
fds
fd
¼
¼ 1313 Â 10À24 dpaðn cmÀ2 sÀ1 ÞÀ1
fs
fNi
½11Š

where f(E1) is the flux of neutrons with energy E1,
s(E1, E2) is the cross-section for a neutron with

This value was derived using the Thompson and
Wright damage function and an early flux spectrum

1
ð

fd ¼

½8Š


cðEÞfðEÞdE
0

where f(E) is the neutron flux with energies from E
to E þ dE and C(E) is a function to describe the
ability of neutrons to displace carbon atoms.
4.11.5.4.1 DIDO equivalent flux

At the standard position in a hollow fuel element, the
nickel flux, fs, can be defined by eqn [9].
1
fs ¼
s

1
ð

fs ðEÞsNi ðEÞdE

½9Š

0

where

1
Ð

fs ðEÞsNi ðEÞdE is the integral of neutron


0

10 000

Number of displaced atoms

1000

Thompson-Wright
Norgett, Robinson, and Torrens
Kinchin-Pease (Lc = 25 keV)
Kinchin-Pease (Lc = 12 keV)

100

10

1

0.1

10

102

103

104
105

Energy (eV)

106

107

108

Figure 7 Comparison of various damage function models that describe the number of displaced atoms versus energy of
primary knock-on atom.


338

Graphite in Gas-Cooled Reactors

Table 6
Comparison of calculated and measured
graphite damage rates using the Thompson and Wright
model

Table 7
Energies, cross-sections, and mean number of
displacement for various particles
Particles

Location

Calculated


Measured/
standard

DIDO hollow fuel element
PLUTO empty lattice position
DR-3 empty lattice position
BR-2, Mol, hollow fuel element
HFR-Petten core
BEPO TE-10 hole
BEPO empty fuel channel
BEPO hollow fuel channel
Windscale AGR replaced fuel
stringer B
Windscale AGR replaced fuel
stringer D
Windscale AGR loop stringer
Windscale AGR loop control
stringer
Windscale AGR fuel element –
inner ring
Windscale AGR fuel element –
outer ring
Calder x-hole
Dounreay fast reactor core

1.00
0.975
0.975
1.00
1.02

2.31
2.36
0.98
2.70

1.00
1.22
0.90
0.90
1.0
2.04
2.04
0.87
2.28

2.71

2.03

2.60
2.60

2.08
2.51

1.18

1.06

1.39


1.06

2.12
0.46

2.10
0.50

Energy (eV) Cross-section Mean number of
(cm2)
displacements
per collision

1 Â 106
2 Â 106
3 Â 106
4 Â 106
Protons
1 Â 106
5 Â 106
10 Â 106
20 Â 106
Deuterons 1 Â 106
5 Â 106
10 Â 106
20 Â 106
a-Particles 1 Â 106
5 Â 106
10 Â 106

20 Â 106
Neutrons 103
104
105
106
107
Electrons

14.5 Â 10À24
15.0 Â 10À24
15.5 Â 10À24
16.0 Â 10À24
7.8 Â 10À21
1.56 Â 10À21
7.8 Â 10À21
3.9 Â 10À21
1.56 Â 10À20
3.12 Â 10À21
1.6 Â 10À21
7.8 Â 10À22
1.25 Â 10À19
2.5 Â 10À20
1.25 Â 10À20
6.25 Â 10À21
4.7 Â 10À24
4.7 Â 10À24
4.6 Â 10À24
2.5 Â 10À24
1.4 Â 10À24


1.6
1.9
2.3
2.5
4–5.5
4–5.5
4–6
4–6
4–5
4–6
4–6
4–6.5
4–5
4–6
4–6.5
4–6.5
2.83
28.3
280
480
500

Modified from Marsden, B. J. Irradiation damage in graphite due to
fast neutrons in fission and fusion systems; IAEA, IAEA TECDOC1154; 2000.

Source: Simmons, J. Radiation Damage in Graphite; Pergamon:
London, 1965.

for the standard position in DIDO. Hence, the EDNF
or fd can be calculated at the position of interest.

The equivalent DIDO nickel dose (fluence) (EDND)
is derived by integrating EDNF over time, as given
in eqn [12]:

Table 8
Displacements (Â10À21) per unit fluence for
energies above E1 for various systems

ðt
EDND ¼ fd ðt Þdt

½12Š

0

Table 6 compares the calculated and measured
graphite damage rates in various systems using the
Thompson and Wright model.
Finally, for those wishing to try and reproduce
damage in graphite using ion beams, Table 7 gives
the energies, cross-sections, and mean number of
displacement for various particles.

4.11.5.5

Energy Above 0.18 MeV

Dahl and Yoshikawa22 noted that for energies above
0.065 MeV, eqn [13] was reasonably independent of
reactor spectrum under consideration:


Spectrum

E1 ¼ 0.067 MeV

E1 ¼ 0.18 MeV

PEGGI
ETR(N-8)
EBR-II
DFR
HFR
Average

0.719
0.697
0.693
0.690
0.683
0.701 Æ 2.6%

0.738
0.810
0.769
0.790
0.779
0.774 Æ 4.5%

Source: Morgan, W. Nucl. Technol. 1974, 21, 50–56.


1
Ð

fðE>E1 Þ ¼

0

fðEÞsðEÞnðEÞdE
1
Ð

½13Š
fðEÞdE

E1

Equation [13] is the integral of graphite displacement for a position in the particular reactor of
interest, divided by the integral of flux from E1
(0.065 MeV in this case) to infinity at the same
position. Table 8 gives this ratio for two other values
of E1.


Graphite in Gas-Cooled Reactors

4.11.5.6

Equivalent Fission Flux (IAEA)

An IAEA committee recommended the use of equivalent fission flux23 as given by eqn [14].

1
Ð P

ðEÞfðE; t ÞdE

d

0
fG ¼ 1
1
Ð P
Ð
ðEÞwðEÞdE= wðEÞdE
0

d

½14Š

0

Equation [14] is essentially graphite dpa divided by
a normalized fission flux. A similar unit is defined
by Simmons4 in his book. However, the use of this
unit was never taken up for general use.
4.11.5.7

Fluence Conversion Factors

Table 9 gives the conversion factor from other units

to EDND. The following should be noted:
 EDND is a definition,
 Calder equivalent dose and other units relating
damage to fuel ratings are approximate,
 BEPO equivalent dose is a thermal unit and should
be avoided,
 Energies above En are a good approximation,
 dpa is directly proportional to EDND.
4.11.5.8

Irradiation Annealing and EDT

The reasoning behind the use of equivalent DIDO
temperature (EDT) is that if two specimens are irradiated to the same fluence over two different time
periods, the specimen irradiated faster will contain the
most irradiation damage. The reasoning is that the specimen irradiated at the slower rate would have a longer
time available to allow for ‘annealing’ out of defects
caused by fast neutron damage as outlined below.
The rate of accumulation of damage dC/dt can be
described by eqn [15].
Table 9

Conversion factors to EDND

Fluence unit
À2

EDND (n cm )
Equivalent fission dose (n cmÀ2)
Calder equivalent dose (MWd AtÀ1)

BEPO equivalent dose (n cmÀ2)
En > 0.05 MeV (n cmÀ2)
En > 0.18 MeV (n cmÀ2)
En > 1.0 MeV (n cmÀ2)
dpa (atom/atom)

Conversion factor
1.0
0.547
1.0887 Â 1017
0.123
0.5
0.67
0.9
7.6162 Â 1020

Modified from Marsden, B. J. Irradiation damage in graphite due to
fast neutrons in fission and fusion systems; IAEA, IAEA
TECDOC-1154; 2000.

dC
/
dt

f


E
exp À
kT


339

½15Š

where f is the flux, E is the activation energy, T is
temperature (K), and k is Boltzmann’s constant.
Equating the damage rate for two identical samples
at different flux levels f1 and f2 and different temperatures T1 and T2,
f
f
 1 ¼
 2 
E
E
exp À
exp À
kT1
kT2

½16Š

Rearranging this gives the EDT relationship:
1
1
k ðf Þ
À ¼ ln d 2
y1 y2 E ðfd Þ1

½17Š


The term on the left is the difference in the reciprocal of the temperatures in the two systems (temperature has traditionally been given the symbol ‘y ’ when
used in this context) and the term on the right contains the natural log of the damage flux (or fluence) in
the two systems divided by each other. In practice,
the activation energy E is an empirical constant.
The use of EDT has recently been investigated24
at temperatures above 300  C. The authors concluded
that the use of EDT was inappropriate (Figure 8).
However, below 300  C, there was some evidence of
the applicability,15 but at these lower temperatures
there is little reliable data. Therefore, the use of the
EDT concept is not recommended for modern graphite moderated reactors where the graphite is usually
irradiated above 300  C.
4.11.5.9 Summary of Fast Neutron Dose
(Fluence)
1. Care must be taken when interpreting graphite
data because of the variety of fast neutron dose
units used. Older data in particular should be
treated with care.
2. ‘Graphite damage’ has been equated to activation
of nickel at a standard position in DIDO. This can
now be calculated and equated to dpa.
3. ‘Graphite damage’ may also be equated to channel
burnup which can also be equated to dpa.
4. ‘Graphite damage’ can also be equated to
En > 0.18 MeV.
5. EDT is not applicable to irradiation temperatures
above 300  C; there is some evidence that it may
be applicable below 300  C.



340

Graphite in Gas-Cooled Reactors

2

Dimensional change (%)

PLUTO
DFR
1

0

−1

−2

−3

0

50

100

150

200


250

300

Fluence (1020 n cm−2 EDND)
Figure 8 Comparison of dimensional changes on Gilsocarbon graphite samples irradiated in DFR with similar samples
irradiated in PLUTO. Reproduced from Eason, E. D.; Hall, G.; Heys, G. B.; et al. J. Nucl. Mater. 2008, 381, 106–113.

6. There are conversion factors between all these
units but these are subject to various degrees of
uncertainty.

4.11.6 Graphite ‘Energy Deposition’
(Nuclear Heating)
The heat generated in the graphite (or energy deposition) is required for the calculation of the graphite
temperatures, and in the case of CO2-cooled systems,
it is required for the calculations of radiolytic weight
loss. Both of these requirements are important in
graphite stress analysis calculations.
In the case of CO2-cooled systems it is assumed that
the graphite radiolytic oxidation rate is proportional to
the heat generated in the graphite. However, it is
ionizing irradiation that causes the dissociation of the
CO2. The energy deposition is produced by the interaction of graphite atoms with three types of particles:
 Neutron interactions with graphite atoms ($40%).
 Fission g-rays ($60%).
 Secondary g-rays caused by absorption by materials outside the moderator (e.g., steel fuel pins in
AGRs) and by inelastic scattering of carbon atoms
($1% in a Magnox reactor and $10% in an AGR).

The main source of gammas and neutrons arises
from the fuel, mainly from prompt fission, but there
are some from delayed fission.
The ratios given above are for a central position in
the core and for initial fuel loading. The ratio may
change with position in the core and with graphite

weight loss. Furthermore, in graphite material test
programs, the ratio between neutron and g-heating is
likely to be significantly different, because of the different materials used to construct the various reactor
cores. It is therefore important that this ratio is known
and the implication of a change in this ratio on material
property changes, that is, the implication of the ratio
between fast neutron damage versus radiolytic weight
loss on graphite property changes, is understood.
The gamma and neutron spectrum varies with
distance from the fuel and will vary with graphite
density (i.e., will change with weight loss) and fuel
design. A reactor is run at constant power, and therefore, as weight loss increases, the spectrum (gamma
and neutron) will change and become harsher (higher
neutron and g-flux).
In the graphite, charged electrons are produced
because of the following:
1. Compton scattering interaction of gamma with
electrons within the carbon atoms.
2. Pair product in electrostatic field associated with
carbon atoms.
3. Photoelectric absorption.
Compton scattering predominates, but electrons
and charged carbon ions are also produced because of

the displacement of carbon atoms in the moderator,
and in principle this could be calculated.
Energy deposition is the energy released from
the first collisions of primary gamma and neutrons.25
Energy deposition is calculated in watts per gram
(W/g) and the spatial distribution can be calculated using reactor physics codes such as McBend


Graphite in Gas-Cooled Reactors

( WIMS,
and WGAM. However, a crude estimation of energy
deposition can be made by assuming that $5% of
the reactor power is generated in the graphite. This
heat can then be proportioned to the rest of the core
using interpolation and form factors, and estimates of
the distribution within a moderator brick.
In conclusion, energy deposition is required to
calculate graphite temperatures and radiolytic oxidation rates. Energy deposition can be estimated but
is most accurately calculated using reactor physics
codes. However, care must be taken because the ratio
between neutron heating and g-heating, or more
appropriately a direct measure of the ionizing irradiation, is important.
4.11.6.1 The Use of Titanium for Installed
Sample Holders
During the construction of the Magnox and AGR
reactors, graphite specimens were placed into
‘installed sample holders,’ the intention being that
these samples could be removed at a later date to
give information on the condition of the graphite

core. To enhance the radiolytic weight loss of the
graphite in the installed sample holders, titanium
was used. Although this only slightly increased the
g-heating, it did increase the number of electrons
produced, because of an increase in pair production
and Compton scattering caused by the higher atomic
number or ‘Z-value’ of titanium compared to graphite
(22 and 6, respectively).

4.11.7 Radiolytic Oxidation
4.11.7.1

in CO2 either directly or indirectly. This leads to the
creation of reactive species, which may react with
the carbon atoms at the surfaces (external and more
importantly internal) of the graphite components.
4.11.7.2.1 Energy deposition

Historically, ‘energy deposition’ has been used for a
surrogate for ionizing irradiation, most probably
because it is easy to measure using calorimetry and
can be estimated from the reactor power. Energy
deposition, sometimes referred as ‘dose rate,’ in the
units of W/g of graphite, is a measure of the total
energy absorbed in the gas in unit time from the
scattering of g-radiation and fast neutrons.
For a typical Magnox reactor, energy deposition is
composed of approximately the following components:
 36% from the neutrons
 58% from the gamma

 6% from the interaction of graphite atoms within
the moderator
Of these, it is only the last two that directly contribute to ionization of the carbon dioxide gas, mainly
through Compton scattering. These ratios will be
slightly different in an AGR.
An assumption is made that the dose rate received
by the graphite is the same as that absorbed by carbon
dioxide within the pores of the graphite and that a
fraction k of the fission energy from the fuel causes
heating in the moderator. For a typical Magnox reactor, k is $5.6% of the thermal power. The unit GÀC
is defined as the number of carbon atoms gasified
by the oxidizing species produced by the absorption
of 100 eV of energy in the CO2 contained within
the graphite pores; GÀC for pure CO2 ¼ 3.

Introduction

In carbon dioxide (CO2)-cooled reactors, two types
of oxidation can occur. The first is thermal oxidation
which is purely a chemical reaction between graphite and CO2. This reaction is endothermic and is
negligible below about 625  C and is not important up to 675  C. The second is radiolytic oxidation
that occurs when CO2 is decomposed by ionizing
radiation (radiolysis) to form CO and an active oxidizing species, which attacks the graphite. Radiolytic
oxidation occurs predominantly within the graphite
open porosity.
4.11.7.2

341

Ionizing Radiation


Ionizing irradiation can be defined as that part of a
radiation field capable of ionization (charge separation)

4.11.7.3

Radiolytic Oxidation Mechanism

The exact mechanism of radiolytic oxidation in a carbon dioxide-cooled reactor is complex and has been a
matter of debate for some time; the most satisfactory
explanation has been given by Best et al.26 However,
in its most simplistic form the mechanism can be
described as follows:
In the gas phase,
ionizing radiation
CO2 À
! CO þ OÃ

½IŠ

CO þ OÃ ! CO2

½IIŠ

where O* is an activated state-oxidizing species.
Thus, after ionization the carbon monoxide and
oxidizing species rapidly recombine back into carbon
dioxide and to an uninformed observer, carbon



Graphite in Gas-Cooled Reactors

Isothermal radiolytic oxidation rate (10−8 h−1 W kg−1)

342

0.8
0.7
0.6

0.4–0.6% CO
1% CO
2% CO

0.5
0.4
0.3
0.2
0.1
0
0

100

200

300

400


500

600

700

800

Calculated CH4 concentration (vpm)

Figure 9 GÀC as function of CO and CH4 concentration (41 bar, 673 K).

OÃ þ C ! CO

3

5 vpm H2O
15 to 30 vpm H2O
200 to 400 vpm H2O

2
G–c

dioxide would appear to be stable in an irradiation
field. However, in the presence of graphite which
typically contains $20% porosity, 10% of which is
initially accessible to the carbon dioxide gas, at the
graphite pore surface (mainly internal) carbon atoms
are oxidized. This can be simplistically described as


1

½IIIŠ

The principal oxidizing species is still under debate,
but the most favored candidate is the negatively
charged ion, COÀ
3.

0
0

1

(a)

2

3

CO (%)

1.5

Inhibition

The rate of oxidation can be reduced by the addition
of carbon monoxide (CO) and moisture (H2O) and
can be greatly reduced by the addition of methane
(CH4), as illustrated in Figures 9 and 10. As

described above the radiolytic oxidation process produces CO and if CH4 is added, moisture will be
one of the by-products of the reaction.

1.0
G–c

4.11.7.4

0.5

0.0
0

(b)

4.11.7.5

Internal Porosity

As supplied, graphite components contain a significant
amount of both open and closed porosity in a variety
of shapes and sizes, from the nm scale to the mm scale,
as illustrated in Section 4.11.3. The open pore volume
(OPV) is defined as the volume of pores accessible to
helium, closed pore volume (CPV) is the volume of
pores not accessible to helium, and the total pore
volume (TPV) is the volume of open and closed pore.
The effect of pore size on the radiolytic oxidation
rate was investigated by Labaton et al.27 who found


200

400

600

800

CH4(vpm)

Figure 10 Inhibition in carbon dioxide due to the
addition of carbon monoxide, moisture, and methane.
(a) GÀC as function of CO and H2O concentration and
(b) GÀC as function of methane (CH4) concentration.
Reproduced from Best, J. V.; Stephen, W.; Wickham, A.
Prog. Nucl. Energy 1985, 16(2), 127–178.

the maximum range to be 2.5–5 mm. Taking this into
account and referring to eqns [I]–[III] above, the
oxidation process will be expected to be more efficient in the smaller pores than in the larger pores.


Graphite in Gas-Cooled Reactors

This is because in the smaller pores the distance to
the wall is less, making it less likely, compared to the
case for larger pores, that the active species would
be deactivated by collision in the gas phase.
To account for this difference in oxidation rate
with pore size for modeling purposes, in the case of

the Magnox reactors which did not have CH4 routinely added to the coolant, a pragmatic approach of
defining ‘pore efficiency’ was adopted, whereas in the
case of the AGRs where CH4 is routinely added,
a reactive pore volume (RPV) was defined as being
the volume of pores oxidizing in CH4-inhibited
coolant gas.
It is also clear that as the oxidation process proceeds, closed porosity will be opened and the pore
size distribution will change, thereby changing the
oxidation rate.
4.11.7.6 Prediction of Weight Loss in
Graphite Components
The methodologies used to predict the oxidation rate
in Magnox reactors are based on work by Standring28
as discussed below:


P 273
Weight of CO2 in the
½18Š
¼ er0
pores of 1g of graphite
14:7 T
where P (psi) is the gas pressure, T (K) the temperature, and r0 is the density of CO2 at standard
conditions for temperature and pressure (STP)
(g cmÀ3). The dose rate to the graphite can then be
given in watts as follows:


P
273

À
W ½19Š
Dose rate to graphite ¼ eDr0
14:7
T
where D (W gÀ1 sÀ1) is the ‘energy deposition rate’ or
‘dose rate’ and e is the OPV (cm3 gÀ1). This reasoning
can be taken further to give


eGÀC DP
Percentage initial
¼ 145
% per year ½20Š
oxidation rate; g0
T
Standring and Ashton29 measured the OPV and CPV
in PGA as a function of weight loss (Figure 11).
In the specimens they examined, there appeared
to be a small amount of pores which opened rapidly
before the pore volume increased linearly as a function of weight loss over the range of the data. To
account for this behavior, they modified eqn [20] by
defining an effective OPV as ‘ee’:

g0 ¼ 145


ee GÀC Dp
% per year
T


½21Š

343

Standring further developed this reasoning into a
relationship for the cumulative weight loss, Ct , at
a constant dose rate:
h g t 
i
0
Ct ¼ A exp
À1
½22Š
A
e
where A ¼ ð100P
1ÀPe Þ and Pe is the effective initial OPV
3
À3
in cm cm .
However, a reactor is operated at constant power.
Replacing the dose rate in eqn [21] by kPt/Wm, where
Pt is the reactor thermal power, k is the fraction of
the reactor power absorbed in the graphite ($5%),
and Wm is the weight of the moderator, gives

g0 ¼ 145ee GÀC

kPt P

% per year
Wm T

½23Š

From eqn [23], it is clear that the rate of oxidation
will increase with loss of moderator mass.
It was shown by Standring that the cumulative
weight loss, Ct, for a reactor operated at constant
power is given by


A2
Ct
A
À
Ct ¼ g0 t
log 1 þ
½24Š
100Pe
A
100
This equation yields higher weight loss than the
constant dose rate equation.
This approach was used to design the early
Magnox stations. However, as higher weight loss
data became available from the operating Magnox
stations, it was found necessary to modify the relationship to account for the pore distribution with
increasing oxidation.
4.11.7.7 Weight Loss Prediction in

Inhibited Coolant
It had not been possible to regularly add CH4 as an
inhibitor to the coolant in the Magnox reactors
because of concerns regarding the metallic components in the coolant circuit. However, the higher
rated AGRs were designed with this in mind by
selecting denser graphite and adding CH4 gas as an
oxidation inhibitor.
The addition of an inhibitor causes the process of
radiolytic weight loss to be more complex than that for
Magnox reactors as the oxidation rate becomes a complex function of the coolant gas composition. This is
because gas composition, and hence, graphite oxidation
rate, is not uniform within the moderator bricks and
keys as CH4 is destroyed by radiolysis and may thus be
depleted in the brick interior. In addition, methane
destruction gives rise to the formation of carbon


344

Graphite in Gas-Cooled Reactors

Open pore volume (cm−3 per 100 cm−3)

50
45
40
35
30
25
20

15
10
5
0
0

5

10

15
20
Weight loss (%)

25

30

35

0

5

10

15
20
Weight loss (%)


25

30

35

(a)

Closed pore volume (cm−3 per 100 cm−3)

7
6
5
4
3
2
1
0

(b)

Initial density ~ 1.68 g cm−3
Initial density ~ 1.74 g cm−3

Figure 11 (a) Open and (b) closed pore volume in pile grade A as a function of radiolytic weight loss.

monoxide and moisture which may be higher in the
brick interior. Graphite oxidation forms carbon monoxide, thereby further increasing CO levels in the brick
interior. These destruction and formation processes are
gas composition dependent and the flow rates of these

gases within the porous structure are dependent upon
graphite diffusivity and permeability values which
change with graphite weight loss.
The exact mechanism of radiolysis in a CH4inhibited coolant is complex and the radicals are
disputed. However, from a practical point of view
the mechanisms for oxidation and inhibition can be
considered as given below:
In the gas phase
ionizing radiation
! CO þ OÃ
CO2 À

½IVŠ

CO þ OÃ ! CO2
CH4 ! P

½VŠ
½VIŠ

where O* is the activated oxidizing species formed
by radiolysis of CO2 and P is a protective species
formed from CH4 oxidation.
At the graphite surface (mainly internal porosity),
OÃ þ C ! CO

½VIIŠ

OÃ þ P ! OP


½VIIIŠ

where OP is the deactivated gaseous product of CH4
destruction.
An altogether more satisfactory explanation and
model for the effect of pore structure on corrosion in
gas mixtures containing carbon monoxide, CH4, and


Graphite in Gas-Cooled Reactors

water was developed by Best and Wood30 and Best
et al.,26 who gave a relationship for GÀC with respect
to a pore structure parameter F and to P, the probability of graphite gasification resulting from species
which reach the pore surface:
GÀC ¼ 2:5FP

½25Š

The inhibited-coolant radiolytic oxidation rate is
usually referred to as the graphite attack rate. Data
on initial graphite attack rate have been obtained in
experiments carried out in various materials test
reactors (MTRs)31 for Gilsocarbon and to some
extent other types of graphite (Figure 12). From
Figure 12, it can be seen that the oxidation rate
does not go on exponentially increasing as predicted
by earlier low-dose work, but the increasing rate
saturates at about 3 times the initial oxidation rate.
The approach to predicting temporal and spatial

weight loss in graphite components irradiated in
inhibited coolant is to use numerical analysis to
solve the diffusion equations given below:
Methane concentrations
rT ðD10 rðC1 Þ À rðn Á C1 ÞÞ À K1 ¼ 0
Moisture concentrations
rT ðD20 rðC2 Þ À rðn Á C2 ÞÞ þ K1 STOX ¼ 0
Carbon monoxide concentrations
rT ðD30 rðC3 Þ À rðn Á C3 ÞÞ
½26Š

þ K1 STOX þ K2 STOX2 ¼ 0

The basic unknowns are the CH4, C1, moisture, C2,
carbon monoxide, C3, and gas concentration profiles.

In the CH4 part of eqn [26], the first term is the
pure diffusion contribution, and D10 is the effective
diffusion coefficient in graphite of CH4 in CO2. The
second term is the contribution from porous flow due
to permeation, and n is the velocity vector for CO2
flow through the graphite pores, and K1 is the sink
term for CH4 destruction.
In the moisture part of eqn [26], the first term is
again the pure diffusion contribution, and D20 is
the effective diffusion coefficient in graphite of
moisture in CO2. The second term is the contribution from porous flow. K1STOX is the source term
for moisture formation from CH4 destruction in
accordance with
CH4 þ 3CO2 ! 4CO þ 2H2 O


Fractional graphite weight loss

0.20

0.15

0.10

0.05

0.00
10

20

½IXŠ

In the carbon monoxide part of eqn [26], the first
term is the pure diffusion contribution, and D30 is
the effective diffusion coefficient in graphite of carbon monoxide in CO2. The second term is the
contribution from porous flow. K1STOX is defined
above and K2STOX2 is the source term of carbon
monoxide formation from graphite oxidation.
The various terms in the diffusion equations must
be updated at each time-step for changes in coolant
composition, dose rate, attack rate, and all parameters
controlling graphite pore structure, diffusivity, and
permeability which change with oxidation. These
equations can be solved numerically using finite difference or finite element techniques to give point

wise, temporal distributions of weight loss in a graphite component.

0.25

0

345

30

40

50

60

Fluence (MWh kg−1)

Figure 12 Typical experimental weight loss dose relationship from materials test reactor experiments.


346

Graphite in Gas-Cooled Reactors

4.11.8 Graphite Temperatures

temperatures are compared with the few brick thermocouples that are installed in the moderator. The
codes are also fine-tuned to these.
In conclusion, the calculation of graphite temperatures is complex and involves the calculation of

heat transfer flow to the fuel and flow calculations.
Graphite temperature predictions should be compared to measurements taken from thermocouples
located in most graphite cores.

Graphite component temperature depends on radiation and convection (and conduction in the case of
light-water gas-cooled reactors) heat transfer from
the fuel and heat generated in the graphite by neutron and g-heating, that is, energy deposition as discussed above. Therefore, a detailed knowledge of the
coolant flow is important.
Thermohydraulic codes such as Panther (http://
www.sercoassurance.com/answers/) are used to calculate heat generated in graphite blocks. These codes
estimate the following:
1.
2.
3.
4.

4.11.9 Variation of Fluence,
Temperature, and Weight Loss in a
Reactor Core

The heat generated in the fuel.
The coolant flow.
The heat transfer to the graphite.
The heat ‘energy deposition’ in the graphite.

The flux, temperature, and weight loss will vary within
each individual graphite component, for example,
moderator brick. In addition, the mean component
flux, temperature, and weight loss will vary throughout the core. When designing a graphite core, in
order to extrapolate data from one component,

which has been analyzed in detail, to the other core
components, ‘form factors’ are often used, as illustrated in Figure 13.
In typical graphite-moderated reactors, the axial
(vertical) flux varies approximately as a cosine with
the maximum at center, whereas the radial flux is
usually a flattened cosine as illustrated in Figure 13.
The exact form of these profiles can be calculated
using reactor physics codes.
The mean core rating can be calculated from
eqn [27]:

The calculations take account of graphite weight
loss and change in thermal conductivity of the graphite due to fast neuron damage and radiolytic oxidation. The largest uncertainty is probably associated
with the size of flow bypass paths and flow resistance.
In an AGR, the temperature at the outside of
the brick is lower than the temperature at the inside
because of the interstitial flow, whereas in an Reaktor
Bolshoy Moshchnosti Kanalniy (RBMK) the temperature is hotter at the brick outside.
Using the brick ‘boundary conditions’ including
energy deposition temperatures calculated by the
thermohydraulic code, a standard finite element
code such as ABAQUS can easily be used to calculate
the spatial distribution of temperature with the
graphite component. Thermal transient temperatures can also be calculated using a standard finite
element code. Often, the temperature distribution
is calculated for a central brick, and the temperatures
in the bricks in the rest of the core are calculated using interpolation/extrapolation, that is, form
factors as described in Section 4.11.9. The calculated

Rating ¼


(a)

½27Š

and at the time of interest the mean core burnup can
be calculated by eqn [28]:
Core
reactor
days at
¼
Â
burnup
power
power

Reflector

Core

=

reactor weight of fuel
power in reactorðMWd tÀ1 Þ

=

weight of
fuel in reactor ½28Š
ðMWd tÀ1 Þ


MHA

Individual
channel
About 320
channels
in an AGR

Core

(b)

Figure 13 Form factors. (a) Graphite moderator with reflector and (b) graphite moderator flux profile (form factors).


Graphite in Gas-Cooled Reactors

Thus, a mean moderator brick burnup can be calculated by multiplying the mean core burnup by the
axial and radial form factor for the particular brick
of interest.
4.11.9.1

code. The radial temperature can be assumed to
follow the radial flux profile. Thus, an approximate
mean gas temperature for an individual moderator
brick may be obtained.

Fuel End Effects


4.11.10 Distribution of Fluence
Within an Individual Moderator Brick

The relatively small gap between fuel elements has
a pronounced effect on the damage to the graphite
moderator bricks. This is particularly noticeable in
the brick dimensional changes, in both AGRs and
RBMK reactors. In assessments, this detail needs to
be accounted for and may require a three-dimensional
reactor physics calculation.
4.11.9.2

Having obtained the component mean fluence, temperature, and weight loss, the variation of these parameters throughout the particular component of
interest is required.
The fluence reduces exponentially away from
the fuel in the radial direction, but is influenced
by surrounding fuel sources. The exact distribution
is usually calculated using a reactor physics code
for a 5 Â 5 array pertinent to the area of interest.
Figure 14 is an example for the Windscale Piles.
Thus, the spatial and temporal fluence distribution throughout a graphite component can be calculated. The component temperature can be calculated
using finite element analysis through knowledge of
the surrounding gas temperature, accounting for the

Temperature and Weight Loss

By using the same ‘form factors,’ the moderator brick
mean weight loss can be estimated, assuming that
weight loss is proportional to burnup or fluence.
The gas temperature will vary roughly linearly in

the axial (vertical) direction from the inlet temperature T1 to the outlet temperature T2. A more detailed
profile may be calculated using a thermohydraulics

1.94

All values ϫ 1011
1.97
2.03
2.14
2.05
2.31
2.21

2.64
2.95

2.11
2.28

2.44
2.39

2.32
2.41

2.61
2.49

3.04


3.42

2.52

2.69
3.44

4.13

2.56

2.99
2.63

4.15

3.41

2.79
3.06

4.19

2.72

3.55
4.14

2.83


18.26
21.18
23.48

347

4.21

4.06

3.44

3.47

2.72

3.08
2.69

3.05

2.80

2.70

Figure 14 Nickel flux distribution in a quarter cell calculated for the Windscale Piles. Courtesy of A. Avery.


348


Graphite in Gas-Cooled Reactors

5% of the reactor heat which is generated within
the graphite. Graphite weight loss variation within a
component is more complex and is calculated by
various empirical industry codes. If the axial variation
in fluence, temperature, and weight loss along the
brick length is deemed to be important, three-dimensional physics, temperature, and weight loss calculations will be required.

4.11.11 Fast Neutron Damage in
Graphite Crystal Structures
Atomic displacements due to fast neutron irradiation
modify the ‘crystallite’ dimensions and most of their
material properties. Neutron energies of around
60 eV are required to permanently displace carbon
atoms from the lattice. However, most damage in
graphite is due to fast neutron energies >0.1 MeV; a
typical thermal reactor has neutron energies of up to
10 MeV, with an average of 2 MeV. High-energy
neutrons knock an atom out of the lattice, leading
to a cascade of secondary knock-ons. This process
knocks atoms into interstitial positions between the
basal planes, leaving vacant positions within the lattice. Many of the interstitial atoms will immediately
find and fill these vacancies. However, others may
form semistable Frenkel pairs or other small clusters
or ‘semistable’ clusters. With increasing fast neutron
damage, the stability, size, and number of these clusters will change depending on the irradiation temperature. The higher the irradiation temperature, the
larger are the interstitial clusters or ‘loops.’ This
process leads to considerable expansion in the graphite crystal ‘c’ axis. Conversely, vacancy loops also
form and grow in size with increased irradiation

temperature. It has been postulated that this process
will cause the lattice to collapse leading to the ‘a’ axis
shrinkage observed on irradiating graphite crystal
structures. This process is illustrated in Figure 15.
Thrower32 carried out an extensive review of
transmission electron microscopic (TEM) studies
of defects in graphite, particularly those produced
by fast neutron irradiation. He demonstrated that
interstitial loops and vacancy loops could be distinguished by tilting the specimen. He was able to
observe vacancy loops in graphite irradiated only at
and above 650  C, whereas interstitial loops and
defects were observed at all temperatures of interest
to reactor graphite. It is proposed that the dimensional change in bulk polycrystalline graphite may be
understood by eqn [29]33:

 2
DLc Dc
r0
þ
ffi
Lc
r1
c

½29Š

where Lc is the crystal dimension perpendicular to the
basal plane, ‘c’ is the atomic lattice parameter, and r0
and r1 are the mean defect radius and mean half
separation of defects in the basal plane, respectively.

However, it was noted that this does not completely
explain the expansion. In order to explain basal plane
contraction it is necessary to postulate that vacancy
lines cause the collapse of the basal planes.34–36
More recent atomistic calculations due to Telling
and Heggie37 have sought to explain the process by
the ‘buckling’ of basal planes until they twist round
upon themselves. This latter explanation is more
satisfying as it accounts for the atomistic bonding
around the edges of the interstitial loops and vacancies. However, more HRTEM (high-resolution transmission electron microscopy) observations and other
techniques are required to validate these theories.
Whichever mechanism is correct, empirical
observations made on HOPG, and some natural
crystal flakes,35 show that graphite crystal structures
expand in ‘c’ axis and shrink in the ‘a’ axis, the
degree of deformation being a function of fast neutron fluence and irradiation temperature. Crystal
dimensional change is discussed in more detail
later in this section.
4.11.11.1

Stored Energy

It would not be appropriate to continue without
some discussion on stored (or Wigner) energy. The
perfect crystal configuration is the lowest energy
state for the graphite lattice. However, irradiation
damage will considerably alter that configuration.
Wigner38 predicted that the increased lattice vibration due to heating would allow carbon atoms to
rearrange themselves into lower energy states, and
that in doing so energy would be released in the

form of heat. Early experience in operating graphitemoderated plutonium production and research reactors at low temperatures in the United States,
Russia, France, and the United Kingdom proved
that this assumption was correct. The highest value
of stored energy measured was $2700 J gÀ1.15 If all
of this were released under adiabatic conditions, the
temperature rise would be 1500  C. Fortunately, that
is not the case. Furthermore, the accumulation of
stored energy is insignificant above an irradiation
temperature of $300  C, it is difficult to accidentally
release the stored energy above an irradiation


Graphite in Gas-Cooled Reactors

~0.01 µm

~500 eV

349

0.001 µm

1 keV

Vacant lattice site
Interstitial atom

Displacement cascade

Interstitial defects


Vacancy defects

Layer
plane

Dose
increase

Interstitial
loop

Single vacancy

Submicroscopic
cluster of 4 ± 2 atoms

Interstitial
diffusing to
loop

Layer
increase

Di vacancy

Dose
increase

Vacancy

line

Vacancy
loop
Figure 15 Formation of interstitial and vacancy loops in graphite crystals. Modified from Simmons, J. Radiation Damage in
Graphite; Pergamon: London, 1965.

temperature of $150  C, and only limited self-sustaining energy release of stored energy can be
achieved in graphite irradiated below $100  C.
Thus, stored energy is now of consideration in the
United Kingdom only in the decommissioning of
shutdown reactors such as the Windscale Piles and
BEPO and other similar overseas systems, although
there are graphite ‘thermal columns’ in some research
reactors that may require periodic assessment.
The reason for this is the nature of the irradiation damage sites with respect to irradiation temperature. In graphite irradiated in the early facilities,

at temperatures between about ambient and 150  C,
point defects associated with Frenkel pairs and
small loops can diffuse only slowly through the lattice
to form larger, more stable loops because of the low
irradiation temperature. However, thermal annealing
at temperatures above the irradiation temperature can
readily release the stored energy, and under certain
circumstances, this release can be self-sustaining over
certain temperature changes. (A ‘rule of thumb’ temperature of 50  C above the irradiation temperature is
often cited as a ‘start of release temperature.’ However, this is misleading as a heat balance needs to be