Comprehensive nuclear materials 4 11 graphite in gas cooled reactors

Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 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.

4.11.4 Graphite Core Fast Neutron Fluence, Energy Deposition, and Temperatures 332

4.11.5.2 Reactor Design and Assessment Methodology: Fuel Burnup 335

4.11.9 Variation of Fluence, Temperature, and Weight Loss in a Reactor Core 346

4.11.10 Distribution of Fluence Within an Individual Moderator Brick 3474.11.11 Fast Neutron Damage in Graphite Crystal Structures 348

4.11.13 Averaging Relationships 357

4.11.14.3 Effect of Radiolytic Oxidation on Dimensional Change 364

4.11.15.3 Methodology for Converting Between Temperature Ranges 367

4.11.17.5 Effect of Radiolytic Weight Loss on Dimensional Change and

4.11.18 Effect of Radiolytic Oxidation on Thermal Conductivity, Young’s Modulus,

4.11.20.1 Dimensional Change and Irradiation Creep Under Load 378

4.11.20.6.3 Further modifications to the UKAEA creep law: interaction strain 385

Abbreviations

BEPO British Experimental Pile Zero

CTE Coefficient of thermal expansion

DSC Differential scanning calorimeter

EDND Equivalent DIDO nickel dose EDNF Equivalent DIDO nickel flux

EDT Equivalent DIDO temperature

FWHM Full-width, half-maximum

HOPG Highly oriented pyrolytic graphite

HRTEM High-resolution transmission electron

microscopy

IAEA International Atomic Energy Agency

MTR Materials test reactor

RBMK Reaktor Bolshoy Moshchnosti Kanalniy

(there are other quoted translations)

TEM Transmission electron microscopy

UKAEA United Kingdom Atomic Energy Authority

Nuclear graphite has, and still continues, to act as a

major component in many reactor systems In

prac-tice, 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,4in German, and Pacault5Tome I and II, in

French with more recent reviews on works by Kelly6,7

and Burchell.8This text is mainly on the basis of the

UK graphite reactor research and operating

experi-ence, 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

graph-ite component’s dimensions and properties These

changes lead to the generation of significant graphite

component shrinkage and thermal stresses

Fortu-nately, graphite also exhibits ‘irradiation creep’

which acts to relieve these stresses ensuring, with

the aid of good design practice, the structural

integ-rity 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

under-standing of the influence of irradiation on graphite

dimensional stability and material property changes

This chapter aims to address that need by explainingthe influence of microstructure on the properties ofnuclear graphite and how irradiation-induced changes

to that microstructure influence the behavior of ite components in reactor Nuclear graphite is manu-factured from coke, usually a by-product of the oil orcoal industry (Some cokes are a by-product of refiningnaturally occurring pitch such as Gilsonite.9) Thus,nuclear graphite is a porous, polycrystalline, artificiallyproduced material, the properties of which are de-pendent on the selection of raw materials and man-ufacturing route In this chapter, the properties of thegraphite crystal structures that make up the bulk poly-crystalline graphite product are first described andthen the various methods of manufacture and resultantproperties of the many grades of artificial nucleargraphite are discussed This is followed by a description

graph-of the irradiation damage to the crystal structure, andhence the polycrystalline structure, and the implica-tion of graphite behavior The influence of radiolyticoxidation on component behavior is also discussed asthis is of interest to operators or designers of graphite-moderated, carbon dioxide-cooled reactors, many ofwhich are still operating

The properties and irradiation-induced changes ingraphite crystals have been studied using both ‘natu-rally occurring’ graphite crystals and an artificialproduct referred to as highly orientated pyrolyticgraphite (HOPG), formed by depositing a carbonsubstrate using hydrocarbon gas6 followed by com-pression annealing at around 3000
C HOPG is con-sidered to be the most appropriate ‘model’ materialthat can be used to study the behavior of artificiallyproduced polycrystalline nuclear graphite It has adensity value near to that of a perfect graphite crystalstructure, but perhaps more appropriately, it hasimperfections similar to those found in the struc-tures that make up artificial polycrystalline graphite

A detailed description of the properties of graphitecan be found inChapter2.10, Graphite: Propertiesand Characteristics

4.11.2.1 Graphite Crystal AtomicStructure and Properties

In this section, the atomic structure of graphite tal structures is discussed briefly, along with some ofthe properties relevant to the understanding of the

crys-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 cm3 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

4.11.2.2 Coefficient of Thermal Expansion

The coefficient of thermal expansion (CTE) as

measured for natural graphite and HOPG is

temper-ature dependent (Figure 2) and the data from a

number of authors has been collated by Kelly.6The

room temperature values of CTE are about

27.5 106K1 and1.5  106K1in the ‘c’ and

‘a’ directions, respectively

4.11.2.3 ModulusThe crystal elastic moduli6are C11(parallel to the basalplanes)¼ 1060.0  109

N m2, C12¼ 180.0  109

N m2,C13¼ 15.0  109

N m2, C33 (perpendicular to thebasal planes)¼ 34.6  109

N m2, and C44(shear ofthe basal planes)¼ 4.5  109

N m2 as defined bythe orthogonal co-ordinates given below:

@

1CCCCCA

@

1CCCCCA

@

1CCCCCA

½1

a a

a

c

Figure 1 The crystalline structure of graphite.

‘c’ direction

0 10 20 30 40

Nelson and Riley

Bailey and Yates

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

con-duction 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

4.11.2.5 Microcracking (Mrozowski

Cracks)

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

pos-sible until a temperature of 1800
C is reached.

Below this temperature, the large difference in

ther-mal expansion coefficients between the ‘c’ and ‘a’

directions leads to the formation of long, thin

micro-cracks parallel to the basal planes, often referred to as

‘Mrozowski’ cracks.11These 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

width and many micrometers in length (as seen inFigure 3(b)), appears to be counterintuitive and hasled to speculation that these microcracks may containsome low-density carbonaceous structure The pres-ence of these microcracks is very important in under-standing the properties of nuclear graphite as theyprovide accommodation for thermal or irradiation-induced crystal expansion in the ‘c’ direction.Therefore, two crystal structures are of interest;the ideal, ‘perfect’ structure and the nonperfect struc-tures as may be defined with reference to HOPG It is

of the latter that many of the crystal behaviors andproperties have been studied

Definition: In this chapter on nuclear graphite,

‘crystal’ refers to the perfect crystal structure and

‘crystallite’ refers to the nonperfect crystal tures containing Mrozowski-type microcracks (andnanocracks)

The reactor designer requires a high-density, verypure graphite, with a high scattering cross-section, alow absorption cross-section, and good thermal andmechanical properties, both in the unirradiated andirradiated condition The purity is important to ensurenot only a low absorption cross-section but also thatduring operation the radioactivity of the graphiteremains as low as possible for waste disposal purposes.Artificial graphite is manufactured from cokeobtained either from the petroleum or coal industry,

or in some special cases (such as Gilsocarbon, a UKgrade of graphite) from a ‘graphitizable’ coke derived

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’

artifi-cial 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,

hydro-static 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

pro-duced 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

impregna-tion 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

com-ponents required in a nuclear reactor

For quality assurance purposes, during

manufac-ture the blocks are numbered at an early stage and

this number follows the block through the

manu-facturing 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

previ-ous heats It is important that the reactor operators

retain this data in electronic form as it may berequired to investigate any anomalous behavior asthe reactor ages Samples of ‘virgin’ unirradiatedgraphite blocks should also be retained for futurereference Records should include information onthe batch or heat, property measurements, nonde-structive 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, andcobalt, will cause significant issues related to reactoroperation and final waste disposal It is important thatthe reactor operator takes responsibility for thesemeasurements as in the past it has been found thatreactor designers and graphite manufacturers closedown or merge, and records are lost

Final inspection will uncover issues related todamage, imperfection, quality, etc Therefore, a ‘con-cessions’ policy is required to determine what isacceptable and where such components can be used

in reactor Again, the reactor operator will require anelectronic record of these concessions

4.11.3.1 Microstructure/PropertyRelationships

The microstructure of a typical nuclear graphite isdescribed with reference to Gilsocarbon This productwas manufactured from coke obtained from a naturallyoccurring pitch found at Bonanza in Utah in theUnited States To understand the microstructuralproperties, one has to start with the raw coke Thestructure of Gilsonite coke is made of spherical parti-cles about 1 mm in diameter as shown in Figure 4.This structure is retained throughout manufactureand into the final product InFigure 4(b), the spher-ical shaped cracks following the contours of thespherical particles are clearly visible This coke will

be carefully crushed in order to keep the sphericalstructures that form the filler particles and help togive Gilsocarbon its (semi-) isotropic properties

At a larger magnification in a scanning electronmicroscopy (SEM), the complexity of these cracks isclearly visible, Figure 4(c), and at an even largermagnification, a ‘swirling structure’ made up ofgraphite platelets stacked together is discernablebetween the cracks In essence, the whole structurecontains a significant amount of porosity

After graphitization, the Gilsonite coke filler ticles are still recognizable (Figure 5(a) and 5(b)).From the polarizing colors, one can see that the main

par-‘a’ axis orientation of the crystallites follows the

spherical particles circumferentially, as does the

ori-entation of the large calcination cracks The

crystal-lite structures in the binder phase are much more

randomly oriented, and this phase contains

signifi-cant 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,

distribu-tion, 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

dur-ing 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

direc-tion The long microcracks are also aligned in the

extrusion direction The terms ‘with grain (WG)’ and

‘against grain (AG)’ are used to describe this

phe-nomenon, 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

pro-duce isotropic graphite grades such as the

Gilsocar-bon grade described above In this case, it was found

that Gilsocarbon graphite produced by extrusion was

not isotropic enough to meet the advanced

gas-cooled reactor (AGR) specifications Therefore, a

‘molding’ method where the blocks were formed bypressing in two directions was used This had theeffect of slightly aligning the grains such that the

AG direction was parallel to the pressing directionand the WG was perpendicular to the pressing direc-tion However, Gilsocarbon has proved to be one ofthe 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 blocksusing ‘isostatic molding’ process The isostatic mold-ing method involves loading the fine-grained cokebinder mixture into a rubber bag which is then putunder pressure in a water bath In this way, highquality graphite can be produced mainly for use forspecialist industries such as the production of elec-tronic components This type of graphite (such as IG-

110 and IG-11) has been used for high-temperaturereactor (HTR) moderator blocks, fuel matrix, andreflector blocks in both Japan and China However,even these grades exhibit slight anisotropy

The final polycrystalline product contains manylong ‘thin’ (and not so ‘thin’) microcracks within thecrystallite structures that make up the coke particles.Similar, but much smaller, cracked structures are to

be found in the ‘crushed filler flour’ used in thebinder, and in well-graphitized parts of the binderitself It is these microcracks that are responsible forthe excellent thermal shock resistance of artificialpolycrystalline graphite They also provide ‘accom-modation,’ which further modifies the response ofbulk properties to the crystal behavior in both theunirradiated and irradiated polycrystalline graphite.Typical properties of several nuclear graphite gradesare given inTable 2 One can see that polycrystallinegraphite has about 20% porosity by comparing thebulk density with the theoretical density for graphitecrystals (2.26 g cm3) About 10% of this is openporosity, the other 10% being closed

Fluence, Energy Deposition, and Temperatures

Since the late 1940s, many journal papers, conferencepapers, and reports have been published on thechange in properties in graphite due to fast neutrondamage Many different units have been used todefine graphite damage dose (or fluence) It is impor-tant to understand the basis of these units becausehistoric data are still being used to justify models

Table 1 Relative properties–grain direction relationships

Property With grain (WG) Against

grain (AG) Coefficient of thermal

expansion (CTE)

Thermal conductivity Higher Lower

Electrical resistivity Lower Higher

used in assessments for component behavior in

reac-tors Indeed, some of these historic data, for example,

stored energy and strength, will also be used to

sup-port 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

dam-age is referred to damdam-age 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)

Research-ers 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

flu-ence 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

indi-vidual 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 t1) is not necessarily

equivalent in different reactor systems

When assessing the analysis of a particular

com-ponent in a reactor, one must be aware that a single

detailed calculation of a peak rated component in the

center of the core may have been carried out to givespatial, and maybe temporal, distribution of thatcomponent’s fluence (and possibly temperature andweight loss) These profiles may have then beenextrapolated to all of the other components in thecore using the core axial and radial ‘form factors.’ Indoing this, some uncertainty will be introduced andclearly, some checks and balances will be required tocheck the validity of such an approach

Dose or Fluence)

In a nuclear reactor, high energy, fast neutron fluxleads to the displacement of carbon atoms in thegraphite crystallites via a ‘cascade.’ Many of theseatoms will find vacant positions, while others willform small interstitial clusters that may diffuse toform larger clusters (loops in the case of graphite)depending upon the irradiation temperature Con-versely, vacancy loops will be formed causing thelattice structure to collapse These vacancy loopswill only become mobile at relatively high tempera-tures The production of transmutation gas fromimpurities is not an issue for highly pure nucleargraphite, as the quantities of gas involved will benegligible and the graphitic structure is porous.The change in graphite properties is a function ofthe displacement of carbon atoms The nature andamount of damage to graphite depends on the partic-ular reactor flux spectrum, which is dependent on thereactor design and position, as illustrated inFigure 6

It is impractical to relate a spectrum of neutronenergies to a dimensional or property change at a

Table 2 Typical properties of several well-known grades of nuclear graphite

single point in a material such as graphite Therefore,

an ‘integrated flux’ is used and is discussed later

4.11.5.1 Early Activation Measurements

on Foils

Although one cannot directly measure the damage to

graphite itself, it is possible to measure the activation

of another material, because of nuclear impacts

adja-cent 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

Unfortunately the 59Co(n,g)60Co reaction ismainly a measure of thermal flux and atomic displa-cements in graphite are due to fast neutrons Animprovement was the use of cobalt/cadmium foils,but this was not really satisfactory Measurementsmade in this way are often given the unit, neutronvelocity time (nvt)

Table 3gives an example of thermal flux mined from cobalt foils defined at a standard posi-tion in the center of a lattice cell in BEPO.Graphite damage at other positions in other reac-tors could then be related to the standard position

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

Table 3 Relationship for BEPO equivalent flux (thermal)

at a central lattice position to other positions in BEPO and other irradiation facilities

4.11.5.2 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

mega-watt days per adjacent tonne of uranium (MWd/Atu)

Note that this unit is literally the (power in a particular

channel) (number of days)  (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

stan-dard 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

reac-tor 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

df ¼fðRgÞ

where f(Rg) is the damage absorption curve for

an equivalent distance through BEPO graphite ‘Rg’

of density 1.6 g cm3, 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

Calder equivalent rating Pecan now be defined as

Pe¼ AdfP

ACalderdfCalder ½3where ‘ACalder’ and ‘A’ are the uranium fuel cross-sectional areas in Calder (1.04 in.2) and in the reactorunder consideration, respectively; ‘dfCalder’ and ‘df ’are the values of the damage at the Calder standardposition (1.395) and in the reactor under consider-ation, respectively, and ‘P’ is the fuel rating in thereactor under consideration

Thus, a graphite property change in a reactor underassessment can be related to the equivalent graphiteproperty change at the Calder standard position.However, in a real reactor there is more than onefuel channel There may also be absorbers or emptyinterstitial holes, the fuel rating will change withburnup, and the fuel will be replaced from time totime Therefore, a more complex, multiple source cal-culation is required to take account of the actual chan-nel rating and the geometric features of the core This

is normally done by considering a 5 5 lattice array:

where Bi and B are the accumulated fuel burnup

at the ith and reference source, respectively, f(Rg)iisthe damage absorption function corresponding tothickness Rg for ith source, and Rg is the distancebetween the ith source and target

This method was successfully used to design theMagnox reactors However, because of the higherenriched oxide fuel and more complex fuel design

in the AGRs, this approach became less satisfactoryand new ‘damage functions’ that accounted for thenew fuel and geometry were calculated using MonteCarlo methods (made possible by the introduction ofthe digital computer) This method was until recentlystill used in industry codes such as ‘Fairy’ (NationalNuclear Company) and ‘GRAFDAM’ (UKAEA)

4.11.5.2.1 Calder effective doseWhen only low-dose irradiation graphite propertydata were available, it was assumed that irradiationdamage could be obtained at one temperature andthat the property change versus dose (fluence) curvescould be adjusted for all other temperatures using the

so called R(y) curve:

Calder effectivedose ¼ calder equivalentdose  RðyÞ ½5

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 the58Ni(n,p)58Co

reac-tion This reaction has a mean cross-section of

0.107 barns and58Co 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

displace-ment rate fdwas equal to the nickel flux fNiat this

position For comparison, the change in graphite

thermal resistivity was then measured at various

other positions in BEPO, as given inTable 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 5gives a few examples of the many

measure-ments made.16

It was decided that the activity produced in nickel

fNicould be related to the graphite damage rate by a

factor However, care was still required with respect

to the choice of reactor and irradiation location.Thus, a definition of damage based on a standardposition in DIDO and a calculation route for equiva-lent DIDO nickel flux (EDNF) were devised

It should be noted that there are difficulties related

to a standard based on measurements made with nickelfoils and the 58Ni(n,p,)58Co reaction because of theshort half-life of 58Co and the interfering effect ofthe58Co(n,g)59Co reaction A method by Bell et al.15which went back to measuring activation of cobaltfoils and the59Co(n,g)60Co reaction, and then calcu-lating the ratio fNi/fCo, was used for a short while.This method used the following relationships:

115g fuel elements fNi=fCo¼ 0:378  0:504b150g fuel elements fNi=fCo¼ 0:502  0:530bwhere ‘b’ is the fuel burnup However, this was not verysatisfactory and it was clear that a validated calculationroute was desirable, and is now becoming practicablethrough development in computer technology

4.11.5.4 Integrated Flux andDisplacements per AtomThe rate of change of a material property can berelated to displacement rate of carbon atoms (dpa s1).However, it is not possible to directly measure dpa s1

in graphite, but dpa s1can be related to the reactorflux The flux depends on reactor design, and varieswith position in the reactor core

Neutron flux is a measure of the neutron tion and speed in a reactor In a reactor, neutronsmove at a variety of speeds in randomly orientateddirections Neutron flux is defined as the product ofthe number of neutrons per unit volume moving at agiven speed, as given byeqn [6]below

 

½6

However, as there is a spectrum of neutrons, withmany velocities, this is not a useful unit for thematerial scientist Therefore, integrated flux is usedover a range of energies E1to E2as given byeqn [7]

Table 4 Ratio of graphite damage to nickel flux as

measured in BEPO

Experimental hole TE10 1.0 (definition)

Empty fuel channel (at three positions) 1.0

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

Reynolds, W.; Simmons, J Philos Trans R Soc Lond A Math.

C 4 – inside fuel element stainless steel thimble 0.518

D 3 – inside fuel element stainless steel thimble 0.468

C 4 – inside fuel element aluminum thimble 0.507

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.

the damaging power (displacement rate), fd, can be

expressed as an integrated flux as given ineqn [8]

where f(E) is the neutron flux with energies from E

to Eþ 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 byeqn [9]

fsðEÞsNiðEÞdE is the integral of neutron

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 fsat this position

where f(E1) is the flux of neutrons with energy E1,

s(E1, E2) is the cross-section for a neutron with

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 recoilenergy E2 The carbon displacement rate, fds, at astandard position in DIDO is 5.25 108dpa.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 associatedwith excitation of the lattice

The early Kinchin and Pease17form of the age function was found to underestimate damage ingraphite To give greater dpa, it was recommendedthat ‘Lc’ was artificially increased, but this was notsatisfactory The Thompson and Wright18 damagefunction was used in the official definition of EDNF.However, the Norgett et al.19damage function is used

dam-in most modern reactor physics codes and it has beenrecently shown that there is little difference in thecalculation of graphite damage using either of theselatter 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 1024dpa (n cm2s1)1, can be equated

to the same ratio fd/fNiin the reactor of interest

10 000

Thompson-Wright Norgett, Robinson, and Torrens

Kinchin-Pease (Lc= 25 keV)

Kinchin-Pease (Lc= 12 keV) 1000

for the standard position in DIDO Hence, the EDNF

or fdcan be calculated at the position of interest

The equivalent DIDO nickel dose (fluence) (EDND)

is derived by integrating EDNF over time, as given

ineqn [12]:

ðt 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 Yoshikawa22noted that for energies above

0.065 MeV, eqn [13]was reasonably independent of

reactor spectrum under consideration:

fðE>E1Þ¼

Ð

1 0

fðEÞsðEÞnðEÞdEÐ

displace-of E1

Table 6 Comparison of calculated and measured

graphite damage rates using the Thompson and Wright

model

standard DIDO hollow fuel element 1.00 1.00

PLUTO empty lattice position 0.975 1.22

DR-3 empty lattice position 0.975 0.90

BR-2, Mol, hollow fuel element 1.00 0.90

BEPO empty fuel channel 2.36 2.04

BEPO hollow fuel channel 0.98 0.87

Windscale AGR replaced fuel

Windscale AGR loop stringer 2.60 2.08

Windscale AGR loop control

Dounreay fast reactor core 0.46 0.50

Modified from Marsden, B J Irradiation damage in graphite due to

fast neutrons in fission and fusion systems; IAEA, IAEA

5  10 6 1.56  10 21 4–5.5

10  10 6 7.8  10 21 4–6

20  10 6 3.9  10 21 4–6 Deuterons 1  10 6 1.56  10 20 4–5

5  10 6 3.12  10 21 4–6

10  10 6 1.6  10 21 4–6

20  10 6 7.8  10 22 4–6.5 a-Particles 1  10 6 1.25  10 19 4–5

104 4.7  10 24 28.3

105 4.6  10 24 280

106 2.5  10 24 480

10 7 1.4  10 24 500 Source: Simmons, J Radiation Damage in Graphite; Pergamon: London, 1965.

Table 8 Displacements ( 10 21 ) per unit fluence for energies above E 1 for various systems

Spectrum E 1 ¼ 0.067 MeV E 1 ¼ 0.18 MeV

4.11.5.6 Equivalent Fission Flux (IAEA)

An IAEA committee recommended the use of

equiv-alent fission flux23as given byeqn [14]

fG ¼

Ð

1 0

P

d

ðEÞfðE; tÞdEÐ

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 9gives 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 Enare 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

irra-diated to the same fluence over two different time

periods, the specimen irradiated faster will contain the

most irradiation damage The reasoning is that the

spec-imen 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 byeqn [15]

dC

exp EkT

where f is the flux, E is the activation energy, T istemperature (K), and k is Boltzmann’s constant.Equating the damage rate for two identical samples

at different flux levels f1and f2and different peratures T1and T2,

tem-f1exp  E

recipro-at temperrecipro-atures above 300
C The authors concludedthat the use of EDT was inappropriate (Figure 8).However, below 300
C, there was some evidence ofthe applicability,15 but at these lower temperaturesthere is little reliable data Therefore, the use of theEDT concept is not recommended for modern graph-ite moderated reactors where the graphite is usuallyirradiated above 300
C

4.11.5.9 Summary of Fast Neutron Dose(Fluence)

1 Care must be taken when interpreting graphitedata because of the variety of fast neutron doseunits used Older data in particular should betreated with care

2 ‘Graphite damage’ has been equated to activation

of nickel at a standard position in DIDO This cannow be calculated and equated to dpa

3 ‘Graphite damage’ may also be equated to channelburnup 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 temperaturesabove 300
C; there is some evidence that it may

be applicable below 300
C

Table 9 Conversion factors to EDND

Equivalent fission dose (n cm2) 0.547

Calder equivalent dose (MWd At1) 1.0887  10 17

BEPO equivalent dose (n cm2) 0.123

E n > 0.05 MeV (n cm 2 ) 0.5

E n > 0.18 MeV (n cm 2 ) 0.67

E n > 1.0 MeV (n cm 2 ) 0.9

Modified from Marsden, B J Irradiation damage in graphite due to

fast neutrons in fission and fusion systems; IAEA, IAEA

TECDOC-1154; 2000.

6 There are conversion factors between all these

units but these are subject to various degrees of

uncertainty

(Nuclear Heating)

The heat generated in the graphite (or energy

depo-sition) 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

inter-action 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

materi-als 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 testprograms, the ratio between neutron and g-heating islikely to be significantly different, because of the dif-ferent materials used to construct the various reactorcores It is therefore important that this ratio is knownand the implication of a change in this ratio on materialproperty changes, that is, the implication of the ratiobetween fast neutron damage versus radiolytic weightloss on graphite property changes, is understood.The gamma and neutron spectrum varies withdistance from the fuel and will vary with graphitedensity (i.e., will change with weight loss) and fueldesign A reactor is run at constant power, and there-fore, as weight loss increases, the spectrum (gammaand neutron) will change and become harsher (higherneutron and g-flux)

In the graphite, charged electrons are producedbecause of the following:

1 Compton scattering interaction of gamma withelectrons within the carbon atoms

2 Pair product in electrostatic field associated withcarbon atoms

3 Photoelectric absorption

Compton scattering predominates, but electronsand charged carbon ions are also produced because ofthe displacement of carbon atoms in the moderator,and in principle this could be calculated

Energy deposition is the energy released fromthe first collisions of primary gamma and neutrons.25Energy deposition is calculated in watts per gram(W/g) and the spatial distribution can be calcu-lated using reactor physics codes such as McBend

0

−3

−2

−1 0 1

PLUTO DFR 2

(http://www.sercoassurance.com/answers/), 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

oxida-tion rates Energy deposioxida-tion 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

irradi-ation, 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)

4.11.7.1 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

graph-ite and CO2 This reaction is endothermic and is

negligible below about 625
C and is not

impor-tant 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

oxi-dizing species, which attacks the graphite Radiolytic

oxidation occurs predominantly within the graphite

open porosity

4.11.7.2 Ionizing Radiation

Ionizing irradiation can be defined as that part of a

radiation field capable of ionization (charge separation)

in CO2either directly or indirectly This leads to thecreation of reactive species, which may react withthe carbon atoms at the surfaces (external and moreimportantly internal) of the graphite components.4.11.7.2.1 Energy deposition

Historically, ‘energy deposition’ has been used for asurrogate for ionizing irradiation, most probablybecause it is easy to measure using calorimetry andcan be estimated from the reactor power Energydeposition, sometimes referred as ‘dose rate,’ in theunits of W/g of graphite, is a measure of the totalenergy absorbed in the gas in unit time from thescattering of g-radiation and fast neutrons

For a typical Magnox reactor, energy deposition iscomposed of approximately the following components:

 36% from the neutrons

 58% from the gamma

 6% from the interaction of graphite atoms withinthe moderator

Of these, it is only the last two that directly tribute to ionization of the carbon dioxide gas, mainlythrough Compton scattering These ratios will beslightly different in an AGR

con-An assumption is made that the dose rate received

by the graphite is the same as that absorbed by carbondioxide within the pores of the graphite and that afraction k of the fission energy from the fuel causesheating in the moderator For a typical Magnox reac-tor, k is5.6% of the thermal power The unit GC

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 withinthe graphite pores; GCfor pure CO2¼ 3

4.11.7.3 Radiolytic Oxidation MechanismThe exact mechanism of radiolytic oxidation in a car-bon dioxide-cooled reactor is complex and has been amatter of debate for some time; the most satisfactoryexplanation has been given by Best et al.26 However,

in its most simplistic form the mechanism can bedescribed as follows:

In the gas phase,

CO2ionizing radiation!COþ O ½I

COþ O ! CO2 ½IIwhere O* is an activated state-oxidizing species.Thus, after ionization the carbon monoxide andoxidizing species rapidly recombine back into carbondioxide and to an uninformed observer, carbon

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

The principal oxidizing species is still under debate,

but the most favored candidate is the negatively

charged ion, CO3

4.11.7.4 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

pro-duces CO and if CH4 is added, moisture will be

one of the by-products of the reaction

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 inSection 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

the maximum range to be 2.5–5 mm Taking this intoaccount and referring to eqns [I]–[III] above, theoxidation process will be expected to be more effi-cient in the smaller pores than in the larger pores

0.8 0.7 0.6 0.5 0.4 0.3 0.2

Calculated CH4 concentration (vpm)

0.4–0.6% CO 1% CO 2% CO

Figure 9 GCas function of CO and CH 4 concentration (41 bar, 673 K).

0 1 2 3

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

rou-tinely 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

pro-ceeds, 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

½18

where P (psi) is the gas pressure, T (K) the

tem-perature, and r0 is the density of CO2 at standard

conditions for temperature and pressure (STP)

(g cm3) The dose rate to the graphite can then be

given in watts as follows:

Dose rate to graphite¼ eDr0

P14:7

273T

W ½19

where D (W g1s1) is the ‘energy deposition rate’ or

‘dose rate’ and e is the OPV (cm3g1) This reasoning

can be taken further to give

Standring and Ashton29measured 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

func-tion of weight loss over the range of the data To

account for this behavior, they modifiedeqn [20]by

defining an effective OPV as ‘ee’:

1P e

ð Þand Peis the effective initial OPV

in cm3cm3.However, a reactor is operated at constant power.Replacing the dose rate ineqn [21]by kPt/Wm, where

Pt is the reactor thermal power, k is the fraction ofthe reactor power absorbed in the graphite (5%),and Wmis the weight of the moderator, gives

g0¼ 145eeGCkPt

Wm

P

T% per year ½23From eqn [23], it is clear that the rate of oxidationwill increase with loss of moderator mass

It was shown by Standring that the cumulativeweight loss, Ct, for a reactor operated at constantpower is given by

A2100Pe

This approach was used to design the earlyMagnox stations However, as higher weight lossdata became available from the operating Magnoxstations, it was found necessary to modify the rela-tionship to account for the pore distribution withincreasing oxidation

4.11.7.7 Weight Loss Prediction inInhibited Coolant

It had not been possible to regularly add CH4as aninhibitor to the coolant in the Magnox reactorsbecause of concerns regarding the metallic compo-nents in the coolant circuit However, the higherrated AGRs were designed with this in mind byselecting denser graphite and adding CH4 gas as anoxidation inhibitor

The addition of an inhibitor causes the process ofradiolytic weight loss to be more complex than that forMagnox reactors as the oxidation rate becomes a com-plex function of the coolant gas composition This isbecause gas composition, and hence, graphite oxidationrate, is not uniform within the moderator bricks andkeys as CH4is destroyed by radiolysis and may thus bedepleted in the brick interior In addition, methanedestruction gives rise to the formation of carbon

monoxide and moisture which may be higher in the

brick interior Graphite oxidation forms carbon

mon-oxide, 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

CH4-inhibited 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

CO2ionizing radiation!COþ O ½IV

where O* is the activated oxidizing species formed

by radiolysis of CO2 and P is a protective speciesformed from CH4oxidation

At the graphite surface (mainly internal porosity),

50

40 35 30 25 20 15

35 30

25 20

5 0

7

6

5 4

3

2

1 0

45

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.

water was developed by Best and Wood30 and Best

et al.,26who gave a relationship for GCwith respect

to a pore structure parameter F and to P, the

proba-bility of graphite gasification resulting from species

which reach the pore surface:

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:

The basic unknowns are the CH4, C1, moisture, C2,

carbon monoxide, C3, and gas concentration profiles

In the CH4part ofeqn [26], the first term is thepure diffusion contribution, and D10 is the effectivediffusion coefficient in graphite of CH4in CO2 Thesecond term is the contribution from porous flow due

to permeation, and n is the velocity vector for CO2flow through the graphite pores, and K1 is the sinkterm for CH4destruction

In the moisture part ofeqn [26], the first term isagain the pure diffusion contribution, and D20 isthe effective diffusion coefficient in graphite ofmoisture in CO2 The second term is the contribu-tion from porous flow K1STOX is the source termfor moisture formation from CH4 destruction inaccordance with

CH4þ 3CO2! 4CO þ 2H2O ½IX

In the carbon monoxide part of eqn [26], the firstterm is the pure diffusion contribution, and D30 isthe effective diffusion coefficient in graphite of car-bon monoxide in CO2 The second term is thecontribution from porous flow K1STOX is definedabove and K2STOX2 is the source term of carbonmonoxide formation from graphite oxidation.The various terms in the diffusion equations must

be updated at each time-step for changes in coolantcomposition, dose rate, attack rate, and all parameterscontrolling graphite pore structure, diffusivity, andpermeability which change with oxidation Theseequations can be solved numerically using finite dif-ference or finite element techniques to give pointwise, temporal distributions of weight loss in a graph-ite component

4.11.8 Graphite Temperatures

Graphite component temperature depends on

radia-tion and convecradia-tion (and conducradia-tion in the case of

light-water gas-cooled reactors) heat transfer from

the fuel and heat generated in the graphite by

neu-tron and g-heating, that is, energy deposition as

dis-cussed above Therefore, a detailed knowledge of the

coolant flow is important

Thermohydraulic codes such as Panther (http://

www.sercoassurance.com/answers/) are used to

cal-culate heat generated in graphite blocks These codes

estimate the following:

1 The heat generated in the fuel

2 The coolant flow

3 The heat transfer to the graphite

4 The heat ‘energy deposition’ in the graphite

The calculations take account of graphite weight

loss and change in thermal conductivity of the

graph-ite due to fast neuron damage and radiolytic

oxida-tion 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

temper-ature 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

tempera-tures 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

calcu-lated using interpolation/extrapolation, that is, form

factors as described inSection 4.11.9 The calculated

temperatures are compared with the few brick mocouples that are installed in the moderator Thecodes are also fine-tuned to these

ther-In conclusion, the calculation of graphite peratures is complex and involves the calculation ofheat transfer flow to the fuel and flow calculations.Graphite temperature predictions should be com-pared to measurements taken from thermocoupleslocated in most graphite cores

In typical graphite-moderated reactors, the axial(vertical) flux varies approximately as a cosine withthe maximum at center, whereas the radial flux isusually a flattened cosine as illustrated inFigure 13.The exact form of these profiles can be calculatedusing reactor physics codes

The mean core rating can be calculated fromeqn [27]:

Rating¼ reactor

power =weight of fuel

in reactorðMWd t1Þ ½27and at the time of interest the mean core burnup can

be calculated byeqn [28]:

Coreburnup ¼ reactor

power  days at

power =weight of

fuel in reactorðMWd t1Þ

½28

Reflector

Individual channel

MHA

About 320 channels

Thus, a mean moderator brick burnup can be

calcu-lated by multiplying the mean core burnup by the

axial and radial form factor for the particular brick

of interest

4.11.9.1 Fuel End Effects

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 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

tempera-ture T1to the outlet temperature T2 A more detailed

profile may be calculated using a thermohydraulics

code The radial temperature can be assumed tofollow the radial flux profile Thus, an approximatemean gas temperature for an individual moderatorbrick may be obtained

Within an Individual Moderator BrickHaving obtained the component mean fluence, tem-perature, and weight loss, the variation of these para-meters throughout the particular component ofinterest is required

The fluence reduces exponentially away fromthe fuel in the radial direction, but is influenced

by surrounding fuel sources The exact distribution

is usually calculated using a reactor physics codefor a 5 5 array pertinent to the area of interest.Figure 14is an example for the Windscale Piles.Thus, the spatial and temporal fluence distribu-tion throughout a graphite component can be calcu-lated The component temperature can be calculatedusing finite element analysis through knowledge ofthe surrounding gas temperature, accounting for the

1.94

1.97 2.03 All values ⫻ 10 11

2.05 2.14

2.11

2.28

2.32 2.41

2.21 2.39 2.44 2.31

2.64 2.95 3.04 3.42

3.44 3.41 2.99 2.69 2.49

2.63 2.79 3.06 3.55 4.14

4.21 21.18

2.72 4.19

4.15

2.52 2.61

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

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-dimen-sional physics, temperature, and weight loss

calcula-tions will be required

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

lat-tice 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

clus-ters will change depending on the irradiation

tem-perature The higher the irradiation temperature, the

larger are the interstitial clusters or ‘loops.’ This

process leads to considerable expansion in the

graph-ite 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 inFigure 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

distin-guished 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

dimen-sional change in bulk polycrystalline graphite may be

4.11.11.1 Stored Energy

It would not be appropriate to continue withoutsome discussion on stored (or Wigner) energy Theperfect crystal configuration is the lowest energystate for the graphite lattice However, irradiationdamage will considerably alter that configuration.Wigner38 predicted that the increased lattice vibra-tion due to heating would allow carbon atoms torearrange themselves into lower energy states, andthat in doing so energy would be released in theform of heat Early experience in operating graphite-moderated plutonium production and research reac-tors at low temperatures in the United States,Russia, France, and the United Kingdom provedthat this assumption was correct The highest value

of stored energy measured was 2700 J g1.15 If all

of this were released under adiabatic conditions, thetemperature rise would be 1500
C Fortunately, that

is not the case Furthermore, the accumulation ofstored energy is insignificant above an irradiationtemperature of300
C, it is difficult to accidentally

release the stored energy above an irradiation

temperature of 150
C, and only limited

self-sus-taining 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

irradia-tion damage sites with respect to irradiairradia-tion

tempera-ture In graphite irradiated in the early facilities,

at temperatures between about ambient and 150
C,point defects associated with Frenkel pairs andsmall loops can diffuse only slowly through the lattice

to form larger, more stable loops because of the lowirradiation temperature However, thermal annealing

at temperatures above the irradiation temperature canreadily release the stored energy, and under certaincircumstances, this release can be self-sustaining overcertain temperature changes (A ‘rule of thumb’ tem-perature of 50
C above the irradiation temperature isoften cited as a ‘start of release temperature.’ How-ever, this is misleading as a heat balance needs to be

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.

considered when assessing energy release rates Thus,

50
C above the irradiation temperature can be

con-siderably overconservative.)

The accumulation of stored energy, measured by

burning irradiated graphite samples in a bomb

calo-rimeter, is given as a function of fluence and

temper-ature in Figure 16 At low fluence, stored energy

quickly accumulates reaching a plateau at high

flu-ence Many measurements were made in the

Wind-scale Piles, BEPO, Hanford, and Magnox reactors

that clearly illustrated this behavior.15

To fully understand the thermal stability of

graph-ite containing stored energy, the most appropriate

measure is the rate of release of stored energy

measured using a differential scanning calorimeter

(DSC) as illustrated inFigure 17

A graphite sample is heated in the DSC usually at

a constant rate of 2.5
C min1 In simple terms, two

runs are made and the heat capacity of the samples

measured in each case When the heat capacities from

the two runs are subtracted, the energy release rate is

easily obtained as a function of heating temperature

This can be compared to the specific heat of graphite

as given in Figure 17 When the rate of release of

energy is below the specific heat, energy needs to

be added to continue the process When the rate

of release is above the specific heat, the process is

self-sustaining This behavior was used to ‘anneal’ the

Windscale Piles; a ‘hit and miss’ strategy that ended

in damage to the fuel cartridges and eventually a

‘metal uranium fire.’ (Contrary to ‘common folklore,’the graphite did not burn in the Windscale incident

A limited amount of graphite was oxidized leading toenlargement of fuel and control channels but it wasthe metal uranium that burnt Graphite is very diffi-cult to burn and requires large amounts of heat andoxygen or air, applied to crushed graphite in a flui-dized bed or in similar form.39)

The form of this rate of release curve is a tion of (1) the amount of stored energy in thesample, (2) the temperature the sample was irra-diated at, (3) the fluence the sample had beenirradiated to, (4) the release temperature, and(5) the heating rate Unfortunately, there are no com-prehensive datasets of these five parameters thatallow a robust empirical model to be derived forassessing the stability of graphite containing storedenergy The models that usually exist take the worst-case rate of release curve and fit an Arrhenius typeequation to the rate of release curve

is temperature in (K) as a linear function of time(T¼at in the case of the DSC test and is nonlinear

in most practical cases), K is Boltzmann’s constant, andE(T, S) is the activation energy as a function of thestored energy remaining and temperature and u is afrequency factor usually taken as 7.5 1013

It can be appreciated that the exact solution ofeqn

[30]requires a substantial amount of information from

several rate of release curves from several samples,

which is seldom available Thus, a practical approach

is usually taken, the simplest of which is to assume a

single activation energy However, this is not very

satisfactory and more elegant approaches using

vari-able or discrete activation energies can be found.41–44

Having derived a satisfactory model for the rate of

release using a DSC, it then can be applied to a

practi-cal situation using commercially available computer

codes such as ‘user subroutine’ facilities.42

In assessing practical situations, it is important to

use an energy balance that accounts for heat applied,

heat generated by the release of stored energy, the

heat capacity of the graphite itself, and heat lost to

the surroundings If the heat generation is intense and

oxygen is available, the heat generated by graphite

oxidation should be taken into account However, the

latter case should be unnecessary as a professional

scientist or engineer would not design a system or

process that would approach such conditions It

should be noted that irradiated graphite thermal

conductivity and total stored energy are directly

cor-related15; seeeqn [31] Therefore, the thermal

con-ductivity will improve as energy is released

S¼ 27:2 K0

K  1

The data thateqn [30]is based on is derived from rate

of release curves obtained using a relatively fast heatingrate In dealing with irradiated graphite waste, muchslower rates of heating are often required Graphitesamples taken from the Windscale Piles 40 years afterthe incident showed little change in the dS/dt curves,45indicating that diffusion of atoms at around ambienttemperature is extremely slow Nevertheless, condi-tions relevant to any proposed encapsulation techniqueand repository will need to be accounted for in deter-mining if heat released from stored energy is an issue.The rate of release curves given inFigure 17areonly to a temperature of around 450
C It had beenobserved, by comparing the energy released in theDSC with the energy released on a similar sample in

a bomb calorimeter, that not all of the stored energyhad been released in the samples heated to a maxi-mum of 450
C in the DSC It was found that onincreasing the temperature to around 1600
C, a sec-ond peak could exist46,47; seeFigure 18

It was observed that the ‘200
C’ peak reduced insize and moved to a slightly higher temperature withincreased irradiation, presumably as the irradiationinduced defects became more stable, and the plateaubetween the two peaks increased in height andapproached the specific heat value.15 The first ofthese phenomena could explain why it becamemore and more difficult to ‘anneal’ the WindscalePiles39 and the second had the implication that

Figure 17 Typical rate of release of stored energy Modified from Bell, J C.; Gray, B S Stored Energy Studies Made

on Windscale Pile Graphite Since October 1957; TRG Report 84(W), UKAEA, 1961.

eventually the rate of release curve would remain

above the specific heat up to 1600
C with the

conse-quent safety implications Fortunately, the second of

these phenomena proved to be incorrect

It is interesting to note that there is a

correla-tion (eqn [32]) between the height of the plateau

at400
C and total stored energy.15

dS

dT½400¼ S

1670J g

1
C1 ½32

This equation, although not exact, was often used in

reactor graphite sampling programs to avoid having

to measure total stored energy

Most of the discussion on stored energy above is

relevant only to low temperature reactor systems,

with graphite temperatures operating from ambient

to 150
C When graphite is irradiated at higher

tem-peratures, in practice above about 100
C, the dS/dt

does not exceed the graphite specific heat One of the

operating rules for the UK Magnox reactors was that

the dS/dt, as measured on surveillance samples,

should always be below 80% of the specific heat,

which proved to be the case

4.11.11.2 Crystal Dimensional Change

As previously discussed, graphite crystal structures,

in the form of HOPG, have been observed to swell in

the ‘c’ axis direction and contract in the ‘a’ axisdirection for all measured fluence and irradiationtemperatures Figure 19 shows early data obtained

by Kelly et al.35It is clear fromFigure 19that the rate

of swelling and shrinkage significantly changesbetween 200 and 250
C, indicating that the defectpopulation is becoming more stable above this tem-perature range

HOPG data is an important input into multiscalemodels of irradiation damage in graphite.48 For thepurpose of understanding irradiation damage inoperating reactors, data would be required ideallyfrom 140 to 1400
C, the maximum fluence beingdependent on the irradiation temperature Unfortu-nately, the dataset is far from complete The data due

to Brockelhurst and Kelly49is the most complete set

of HOPG irradiation data covering the fluence andpart of the temperature range appropriate to AGRs(Figure 20) In the same paper, the authors show theeffect of final heat treatment, between 2000 and

3000
C, on the crystal dimensional change rate ofHOPG The data showed that the lower the heattreatment, the faster is the dimensional change rate,indicating that the dimensional change rate of a poorlygraphitized component would be expected to begreater than that of majority of the components.50Pre-viously, Kelly and Brocklehurst51had shown that borondoping also significantly increased the dimensional

Figure 18 Schematic of the high-temperature rate of release curve Reproduced from Rappeneau, J.; Taupin, J L.; Grehier, J Carbon 1966, 4(1), 115–124.

change rate in HOPG, and this was again reflected in

the behavior of doped polycrystalline graphite.50

HOPG high-temperature data was mainly obtained

by investigators interested in the behavior of HTR

fuel coatings.52 Some of this data is for low-density

pyrolytic carbons and it is not always made clear which

material the data refers to Figure 21 shows all the

data known to the author, and it is clear that there is

some inconsistency

4.11.11.3 Coefficient of Thermal Expansion

There are only two reasonable sets of data for the

CTE in HOPG Data for the lower temperatures

(150–250
C) is given in Figure 22 This data is

associated with the dimensional change data given

inFigure 19 At these low temperatures, there is asignificant increase in dimensional changes withincreased fluence This could explain the increase,and the subsequent decrease, in CTE in the ‘c’ direc-tion It is interesting that this is reminiscent of thebehavior of medium grained, semi-isotropic poly-crystalline data, as discussed later In the ‘a’ direction,there is significant scatter in the data, possibly due tothe difficulty in measuring such low values of CTE.However, the behavior appears to indicate anincrease to a plateau, reminiscent of the behavior ofneedle coke anisotropic polycrystalline data.The higher temperature HOPG CTE data given

inFigure 23appears to be invariant to the increasing

0 0 5 10 15 20

25 30

-7 -6 -5

-3 -4

-1 -2

0 1

Figure 19 Dimensional changes in highly orientated pyrolytic graphite as a function of fast neutron fluence and

temperature Modified from Kelly, B T.; Martin, W H.; Nettley, P T Philos Trans R Soc Lond A Math Phys Sci 1966, 260 (1109), 37–49.

fluence, although the maximum fluence is limited to

30 1020

n cm2EDND The author is not aware of

any data at higher irradiation temperatures

4.11.11.4 Modulus

Changes to C33and C44in HOPG and natural

graph-ite crystals have been reported at 50, 650, and

1000
C53 and at 150
C.54 For HOPG, the 150
C

data indicated that C33slightly reduced with

increas-ing irradiation (Figure 24) and this was attributed to

the increase in ‘c’ axis lattice spacing However, there

is no clear trend at the other temperatures (Figure 24)

In the case of shear, at a very low temperature of

50
C there was a significant increase in C44, but at

higher temperatures the increase was less (Figure 25)

The data for natural crystal showed similar trends

but there was significantly more scatter The trend

in the increase in C44 at the lower temperature

would go towards explaining the increase in modulus

in polycrystalline data at low fluence However, it is

surprising that the increase is only modest at the

higher temperatures, although the maximum fast

neutron fluence is very low and data is required at

the intermediate temperatures

Seldin and Nezbeda53 also measured the shear

strength but unfortunately there is considerable

scat-ter and no definite trend

4.11.11.5 Thermal Conductivity

Taylor et al.55 measured the change in thermal

conductivity in HOPG with fast neutron

irradiation The thermal conductivity along thebasal planes (the ‘a’ direction) is much greaterthan the value perpendicular to the basal planes(the ‘c’ direction) Taylor et al also measured thechange in thermal resistivity in irradiated graphite,and when this data is normalized, the data indicatedthat thermal resistivity temperature dependencechanged with irradiation as given in Figure 26.This is the so-called ‘d’ curve that is used in theUnited Kingdom to predict thermal resistivity inirradiated graphite

4.11.11.6 RamanFigure 27gives Raman spectra for unirradiated andirradiated graphite as well as for baked carbon

In the spectral range shown, there is a prominentG-peak at 1580 cm1associated with the basal planebond stretching of ‘c’ axis sp2atoms The D-peak at

1350 cm1is associated with the breathing mode of

sp2atoms and disordered carbon structure The ond D-peak at 2700 cm1is indicative of the crystal-line structure of the graphite

sec-In Figure 28 the normalized positions of theG- and D-peaks, and the ratio of the peak intensitiesare compared for various graphites (unirradiated andirradiated) HOPG is obviously the most orderedstructure followed by the PGA needle coke graphiteand then the medium grained graphite grades Themost disordered materials are the baked carbon(NBG-18 baked) followed by irradiated BEPO(a UK test reactor) graphite

70

c-axis, 600⬚C a-axis, 430⬚C

a-axis, 600⬚C

50 40 30 20 10

Figure 29qualitatively demonstrates that there is

a relationship between Raman spectra and crystal

structure disorder The higher the disorder, the

higher are the D- and G-peak wave number and

I(D/G) ratio

In Figure 29(a), the crystal length La has been

calculated from the full width at half maximum

(FWHM) using the method proposed by Tuinstra

and Koenig.56 Both figures demonstrate that Raman

can be used to quantify the disorder in the graphite

structure, either as manufactured or due to irradiation

Irradiated Polycrystalline Graphite

Fast neutron irradiation and, in the case of

car-bon dioxide-cooled reactors, radiolytic oxidation

change many of the properties of graphite The

properties of interest to the nuclear engineer arethe following:

 Stored energy – a function of fast neutron damageand temperature, due to damage to the graphitecrystallites, but not affected by radiolytic oxidationother than by a reduction in mass

 Specific heat – a function of temperature but notaffected by fast neutron irradiation or radiolyticoxidation other than by stored energy, which may

be considered separately

 Dimensional changes – a function of fast neutrondamage and irradiation temperature There is alsosome evidence of modification by radiolytic oxida-tion It is also modified by stress (see irradiation creep)

 CTE – a function of temperature, fast neutrondamage, irradiation temperature, and stress.There is evidence that it is not modified by radio-lytic weight loss

 Thermal conductivity – a function of temperature,

fast neutron damage, and irradiation

tempera-ture It is significantly modified by radiolytic

weight loss

 Young’s modulus – a function of temperature,

fast neutron damage, and irradiation temperature

It is significantly modified by radiolytic weight

loss

 Strength (tensile, compressive, flexural, and

frac-ture) – a function of temperature, fast neutron

damage, and irradiation temperature It is

signifi-cantly modified by radiolytic weight loss

 Electrical resistivity – a function of temperature,

fast neutron damage, and irradiation temperature

It is probably modified by radiolytic weight loss

 Irradiation creep – a function of fast neutron age, irradiation temperature, and stress

dam-These property changes are illustrated inFigure 30.These dimensional changes, property changes andcreep mechanisms are correlated, some morestrongly than others This has been taken advantage

of in various semiempirical models for irradiationdamage in graphite.57–60

In discussing the irradiation behavior of line graphite, it is useful to split these changes into low,medium, and high fluence effects At low irradiation,fluence changes in polycrystalline graphite are stronglycorrelated with the crystallite changes discussed else-where; seeSection 4.11.11 Typical mechanisms would

polycrystal-30 28 26 24 22 20 18

2.0 1.5 1.0 0.5 0.0

Modified from Kelly, B T.; Martin, W H.; Nettley, P T Philos Trans R Soc Lond A Math Phys Sci 1966, 260(1109), 37–49.

be the accumulation of stored energy, pinning (leading

to a rapid increase in Young’s modulus), and the rapid

decrease in thermal conductivity At medium fluence,

several of the properties saturate, such as Young’s

mod-ulus and thermal conductivity At high fluence, when

crystallite growth in the ‘c’ direction has taken up much

of the accommodation provided by Mrozowski

cracks,11and larger ‘cracks,’ the polycrystalline

struc-ture starts to become strained, thereby generating new

cracking At extremely high fluence, beyond that

expe-rienced in a modern power production reactor, the

crystallite swelling becomes so large that the

polycrys-talline structure completely breaks down leading to a

rapid decrease in modulus and strength

Each of the property changes is discussed in moredetail below In attempting to understand the behavior

of polycrystalline graphite, reference is made to theirradiation behavior of HOPG, as previously discussed

inSection 4.11.11 This is because HOPG is considered

to be a representative model material for the individualcrystallite structures in polycrystalline graphite

Before looking at each of the properties individually,

it is first worth considering the methods developed

to relate changes in the crystallites to the bulk

Figure 23 High-temperature changes to coefficient of thermal expansion in highly orientated pyrolytic graphite.

Reproduced from Brocklehurst, J E.; Kelly, B T Carbon 1993, 31(1), 179–183.