Comprehensive nuclear materials 4 10 radiation effects in graphite

Comprehensive nuclear materials 4 10 radiation effects in graphite Comprehensive nuclear materials 4 10 radiation effects in graphite Comprehensive nuclear materials 4 10 radiation effects in graphite Comprehensive nuclear materials 4 10 radiation effects in graphite Comprehensive nuclear materials 4 10 radiation effects in graphite Comprehensive nuclear materials 4 10 radiation effects in graphite Comprehensive nuclear materials 4 10 radiation effects in graphite

ASTM American Society for Testing and

Materials

CTE Coefficient of thermal expansion

DWNTs Double-walled carbon nanotubes

Esu Elastic strain unit

HOPG Highly oriented pyrolytic graphite

HRTEM High-resolution transmission electron

microscope

MHTGR Modular high-temperature gas-cooled

reactor

NGNP Next Generation Nuclear Plant

USSR Union of Soviet Socialist Republics

Symbols

basal planes)

to the steady-state creep coefficient

(perpendicular to the basal planes)

d« c /dg Initial secondary (steady-state)

creep rate

E 0 Initial (preirradiated) Young’s modulus

299

E d Displacement energy for a carbon

atom from its equilibrium lattice

position

E p Young’s modulus after initial increase

due to dislocation pinning

F x0 Pore generation term for a crept

specimen

release rate

x-direction with respect to neutron

dose

g x0 Rate of change of dimensions in the

x-direction for a crept specimen with

respect to neutron dose (dimensional

change component)

k0(g) Modified steady-state creep coefficient

k 0 Initial secondary creep coefficient

the a-direction

the c-direction

S(g) Structure factor (E/E p )

(1/X a )

(dX a /dg)

Rate of change of crystallite

dimensions perpendicular to the

hexagonal axis

(1/X c )

(dX c /dg)

Rate of change of crystallite dimensions

parallel to the hexagonal axis

a a Crystal coefficient of thermal

expansion in the a-direction

a c Crystal coefficient of thermal

expansion in the c-direction

a x Coefficient of thermal expansion in the

x-direction

a´ x Coefficient of thermal expansion of a

crept specimen in the x-direction

a(f) Crystal coefficient of thermal

expansion at angle f to the c-direction

« Total Total strain

4.10.1 Introduction

There are many graphite-moderated, producing, fission reactors operating worldwide today.1The majority are in the United Kingdom (gas-cooled)and the countries of the former Soviet Union (water-cooled) In a nuclear fission reactor, the energy isderived when the fuel (a heavy element such as92U235)fissions or ‘splits’ apart according to the followingreaction:

power-92U235þ0n1!92U236! F1þ F2þ n

þg  energy ½I

An impinging neutron usually initiates the fission tion, and the reaction yields an average of 2.5 neutronsper fission The fission fragments (F1andF2ineqn [I])and the neutron possess kinetic energy, which can bedegraded to heat and harnessed to drive a turbine-generator to produce electricity The role of graphite

reac-in the fission reactor (reac-in addition to providreac-ing cal support to the fuel) is to facilitate the nuclear chainreaction by moderation of the high-energy fission neu-tron The fission fragments (eqn [I]) lose their kineticenergy as thermal energy to the uranium fuel mass inwhich fission occurred by successive collisions with thefuel atoms The fission neutrons (n ineqn [I]) give up

mechani-their energy within the moderator via the process of

elastic collision The g-energy given up in the fission

reaction (eqn [I]) is absorbed in the bulk of the reactor

outside the fuel, that is, moderator, pressure vessel, and

shielding The longer a fission neutron dwells in the

vicinity of a fuel atom during the fission process,

the greater is its probability of being captured and

thereby causing that fuel nucleus to undergo fission

Hence, it is desirable to slow the energetic fission

neu-tron (E  2 MeV), referred to as a fast neuneu-tron, to lower

thermal energies (0.025 eV at room temperature),

which corresponds to a velocity of 2.2 1015

cm s1.The process of thermalization or slowing down of

the fission fast neutron is called ‘moderation,’ and the

material in a thermal reactor (i.e., a reactor in which

fission is caused by neutrons with thermal energies)

that is responsible for slowing down the fast fission

neutrons is referred to as the moderator Good

nuclear moderators should possess the following

attributes:

 do not react with neutrons (because if they are

captured in the moderator the fission reaction

cannot be sustained);

 should efficiently thermalize (slowdown) neutrons

with few (elastic) collisions in the moderator;

 should be inexpensive;

 compatible with other materials in the reactor

core;

 meet the core structural requirements; and ideally

 do not undergo any damaging chemical or

physi-cal changes when bombarded with neutrons

In the fast neutron thermalization process, the

maxi-mum energy lost per collision occurs when the target

nucleus has unit mass, and tends to zero for heavy

target elements Low atomic number (Z) is thus aprime requirement of a good moderator The density(number of atoms per unit volume) of the moderatorand the likelihood of a scattering collision takingplace must also be accounted for Frequently used

‘Figures of merit’ for assessing moderators are the

‘slowing down power’ and the ‘moderating ratio.’

Figure 1 shows these Figures of merit for severalcandidate moderator materials The slowing downpower accounts for the mean energy loss per collision,the number of atoms per unit volume, and the scatter-ing cross-section of the moderator The tendency for amaterial to capture neutrons (the neutron capturecross-section) must also be considered Thus, the sec-ond figure of merit, the moderation ratio, is the ratio

of the slowing down power to the neutron absorption(capture) cross-section Ideally the slowing downpower is large, the neutron capture cross-section issmall, and hence the moderating ratio is also large.Practically, the choices of moderating materialsare limited to the few elements with atomic number

<16 Gasses are of little use as moderators because oftheir low density, but can be combined in chemicalcompounds such as water (H2O) and heavy water(D2O) The available materials/compounds reduce

to the four shown in Figure 1 (beryllium, carbon(graphite), water, and heavy water) Water is rela-tively unaffected by neutron irradiation, is easilycontained, and inexpensive However, the moderatingratio is reduced by the neutron absorption of hydro-gen, requiring the use of enriched (in235U) fuels tomaintain the neutron economy Heavy water is a goodmoderator because1H2and8O16 do not absorb neu-trons, the slowing down power is large, and the mod-erating ratio is therefore very large Unfortunately,

0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

the cost of separating the heavy hydrogen isotope is

large Beryllium and beryllium oxide are good

mod-erators but are expensive, difficult to machine, and

suffer toxicity problems Finally, graphite (carbon) is

an acceptable moderator It offers a compromise

between nuclear properties, utility as a core structural

material, and cost It also has the advantage of being

able to operate at very high temperatures (in the

absence of oxygen) Unfortunately, the properties of

graphite are markedly altered by neutron irradiation

and this has to be considered in the design of graphite

reactor cores

Manufacture

The invention of an electric furnace2capable of

reach-ing temperatures approachreach-ing 3000C by Acheson

in 1895 facilitated the development of the process for

the manufacture of artificial polygranular graphite

Detailed accounts of the manufacture of polygranular

graphite may be found elsewhere.2–4Figure 2

sum-marizes the major processing steps in the manufacture

of nuclear graphite Nuclear graphite consists of two

phases: a filler material and a binder phase The

pre-dominant filler material, particularly in the United

States, is a petroleum coke made by the delayed

coking process European nuclear graphites are

typi-cally made from a coal-tar pitch-derived coke In the

United Kingdom, Gilsonite coke, derived from

natu-rally occurring bitumen found in Utah, USA, has been

used Both coke types are used for nuclear graphite

production in Japan The coke is usually calcined

(thermally processed) at 1300C prior to being

crushed and blended Typically, the binder phase is

a coal-tar pitch The binder plasticizes the filler coke

particles so that they can be formed Forming

pro-cesses include extrusion, molding, vibrational

mold-ing, and isostatic pressing The binder phase is

carbonized during the subsequent baking operation

(800–1000C) Frequently, engineering graphites are

pitch impregnated to densify the carbon artifact,

fol-lowed by rebaking Useful increases in density and

strength are obtained with up to six impregnations,

but two or three are more typical

The final stage of the manufacturing process is

graphitization (2500–3000C) during which, in

sim-plistic terms, carbon atoms in the baked material

migrate to form the thermodynamically more stable

graphite lattice Nuclear graphites require high

chemical purity to minimize neutron absorption

Moreover, certain elements catalyze the oxidation ofgraphite and must be reduced to an acceptable level.This is achieved by selecting very pure cokes, utilizing

a high graphitization temperature (>2800C), or byincluding a halogen purification stage in the manufac-ture of the cokes or graphite Recently, comprehensiveconsensus specifications5,6were developed for nucleargraphites

The electronic hybridization of carbon atoms (1s2,2s2, 2p2) allows several types of covalent bondedstructure In graphite, we observe sp2 hybridization

in a planar network in which the carbon atom is bound

to three equidistant nearest neighbors 120apart in agiven plane to form the hexagonal graphene structure.Covalent double bonds of both s-type and p-type arepresent, causing a shorter bond length than in the case

of the tetrahedral bonding (s-type sp3orbital dization only) observed in diamond Thus, in its per-fect form, the crystal structure of graphite (Figure 3)consists of tightly bonded (covalent) sheets of carbonatoms in a hexagonal lattice network.7The sheets are

hybri-Raw petroleum

or pitch coke

Calcined coke

Blended particles

Coal tar binder pitch

Mixed Cooled Extruded, molded, or isostatically pressed

Baked at 800–1000⬚C

Impregnated to densify (petroleum pitch) Rebaked and

reimpregnated artifact Graphitized 2500–2800 ⬚C

Nuclear graphite Purified

Figure 2 The major processing steps in the manufacture

of nuclear graphite.

weakly bound with van der Waals type bonds in an

ABAB stacking sequence with a separation of 0.335 nm

The crystals in manufactured polygranular

graph-ite are less than perfect, with approximately one layer

plane in every six constituting a stacking fault The

graphite crystals have two distinct dimensions,

the crystallite sizeLameasured parallel to the basal

plane and the dimensionLcmeasured perpendicular

to the basal planes In a coke-based nuclear graphite,

values of La 80 nm and Lc 60 nm are typical.8

A combination of crystal structure bond anisotropy

and texture resulting from forming imparts

aniso-tropic properties to the filler coke and the

manufac-tured nuclear graphite The coke particles become

preferentially aligned during forming, either with

their long axis parallel to the forming axis in the

case of extrusion, or with their long axis

perpendicu-lar to the forming axis in the case of molding or

vibrational molding Consequently, the graphite

arti-facts are often attributed with-grain and against-grain

properties as in the American Society for Testing and

Materials (ASTM) specifications.5,6 The degree of

isotropy in manufactured graphite can be controlled

through the processing route Factors such as the

nature of the filler coke, its size and size distribution,

and the forming method contribute to the degree of

isotropy Nuclear graphites are typically medium or

fine grain graphites (filler coke size<1.68 mm)5,6

andare considered near-isotropic Fine grain graphites

(grain sizes<100 mm) formed via isostatic pressingoften exhibit complete isotropy in their properties

In response to the recent renewed interest in temperature gas-cooled reactors, many graphite ven-dors have introduced new nuclear graphites grades

high-Table 1summarizes some of the grades available rently, although this list is not exhaustive The graphitemanufacturer is listed along with the coke type andcomments related to the given graphite grade

The core of a graphite-moderated reactor is prised of stacks of graphite blocks that are usuallykeyed to one another to facilitate transmission ofmechanical loads throughout the core Vertical chan-nels penetrate the core into which fuel stringers areplaced via the reactor charge face using a refuelingmachine The nuclear fuel, which may be natural ura-nium (a mixture of238U,235U, and234U) or enricheduranium, is usually sheathed (clad) in a metallic clad-ding Typically, the cladding is a light alloy (aluminum

com-or magnesium), but it can also be stainless steel ing enriched fuel) if a higher fuel temperature isdesired (>600C) The fuel stringer and claddingmaterial may be one and the same, as in the UnitedKingdom designed Magnox reactor,1or the fuel may

(requir-be in the form of stainless steel clad ‘pins’ arranged ingraphite fuel sleeves, which are joined to one anotherand form the fuel stringer as in the UK AdvancedGas-Cooled Reactor1 (AGR) The metallic fuel cladretains the gaseous fission products that migrate fromthe fuel during the fission reaction and prevents con-tact between the gaseous coolant and the fuel

An alternative core layout uses integral erator elements in which the uranium fuel is placeddirectly into cavities in the graphite moderator block,

Figure 3 The crystal structure of graphite showing the

ABAB stacking sequence of graphene planes in which

the carbon atoms have threefold coordination Reproduced

from Burchell, T D In Carbon Materials for Advanced

Technologies; Burchell, T D., Ed.; Elsevier Science:

Oxford, 1999, with permission from Elsevier.

and the entire block is discharged from the reactor

when the fuel is spent Fuel elements of this design

typically utilize ceramic (UO2 or UC2) rather that

metallic fuel so as to be capable of reaching higher

fuel temperatures The ceramic fuel kernel is over

coated with layers of SiC and pyrolytic carbon to

pro-vide a fission product barrier and to negate the use of

a metallic fuel clad (see Chapter 3.07,

TRISO-Coated Particle Fuel Performance), allowing the

reactor core to operate at very high temperatures

(>1000C).1

The coated particle fuel is usually formed

into fuel pucks or compacts but may be

consoli-dated into fuel balls, or pebbles.1The US designed

modular high-temperature gas-cooled reactor

(MHTGR) and Next Generation Nuclear Plant

(NGNP), and the Japanese high-temperature test

reactor (HTTR) are examples of gas-cooled reactors

with high-temperature ceramic fuel

Additional vertical channels in the graphite

reac-tor core house the control rods, which regulate the

fission reaction by introducing neutron-adsorbing

materials to the core, and thus reduce the number

of neutrons available to sustain the fission process

When the control rods are withdrawn from the core,

the self-sustaining fission reaction commences Heat

is generated by the moderation of the fission

frag-ments in the fuel and moderation of fast neutrons in

the graphite The heat is removed from the core by a

coolant, typically a gas, that flows freely through the

core and over the graphite moderator The coolant is

forced through the core by a gas circulator and passes

into a heat exchanger/boiler (frequently referred to

as a steam generator)

The primary coolant loop (the reactor coolant) ismaintained at elevated pressure to improve the cool-ant’s heat transfer characteristics and thus, the core issurrounded by a pressure vessel A secondary coolant(water) loop runs through the heat exchanger and coolsthe primary coolant so that it may be returned to thereactor core at reduced temperature The secondarycoolant temperature is raised to produce steam which

is passed through a turbine where it gives up its energy

to drive an electric generator Some reactor designs,such as the MHTGR, are direct cycle systems in whichthe helium coolant passes directly to a turbine.The reactor core and primary coolant loop areenclosed in a concrete biological-shield, which pro-tects the reactor staff and public from g radiationand fission neutrons and also prevents the escape ofradioactive contamination and fission product gassesthat originate in the fuel pins/blocks The chargeface, refueling machine, control rod drives, dischargearea, and cooling ponds are housed in a containmentstructure which similarly prevents the spread of anycontamination Additional necessary features of afission reactor are (1) the refueling bay, where newfuel stringers or fuel elements are assembled prior tobeing loaded into the reactor core; (2), a dischargearea and cooling ponds where spent fuel is placedwhile the short-lived isotopes are allowed to decaybefore the fuel can be reprocessed

The NGNP, a graphite-moderated, helium cooledreactor, is designed specifically to generate elec-tricity and produce process heat, which could beused for the production of hydrogen, or steam gener-ation for the recovery of tar sands or oil shale

Table 1 Currently available nuclear grade graphites

IG-430 Toyo Tanso Pitch coke Isostatically molded, candidate for high-dose regions of

NGNP concepts IG-110 Toyo Tanso Petroleum coke Isostatically molded, candidate for high-dose regions of

NGNP concepts NBG-10 SGL Pitch coke Extruded, candidate for high-dose regions of NGNP

pebble bed concepts; PBMR core graphite NBG-17 SGL Pitch coke Vibrationally molded, candidate for high-dose regions of

NGNP prismatic core concepts NBG-18 SGL Pitch coke Vibrationally molded, candidate for high-dose regions of

NGNP pebble bed concepts; PBMR core graphite PCEA GrafTech International Petroleum coke Extruded, candidate for high-dose regions of NGNP

prismatic core concepts PGX GrafTech International Petroleum coke Large blocks for permanent structure in a prismatic core

2020 Carbone of America Petroleum coke Isostatically molded, candidate for permanent structures

in a prismatic core

2191 Carbone of America Petroleum (sponge) coke Isostatically molded, candidate for permanent structures

in a prismatic core

Two NGNP concepts are currently being

consid-ered, a prismatic core design and a pebble bed core

design In the prismatic core concept, the TRISO fuel

is compacted into sticks and supported within a

graphite fuel block which has helium coolant holes

running through its length.1The graphite fuel blocks

are discharged from the reactor at the end of the

fuel’s lifetime In the pebble bed core concept,

the TRISO fuel is mixed with other graphite

materi-als and a resin binder and formed into 6 cm diameter

spheres or pebbles.1 The pebbles are loaded into

the core to form a ‘pebble bed’ through which helium

coolant flows The pebble bed is constrained by a

graphite moderator and reflector blocks which define

the reactor core shape The fuel pebbles migrate slowly

down through the reactor core and are discharged at

the bottom of the core where they are either sent

to spent fuel storage or returned to the top of the

pebble bed

Not all graphite-moderated reactors are

gas-cooled Several designs have utilized water cooling,

with the water carried through the core in zirconium

alloy tubes at elevated pressure, before being fed to

a steam generator Moreover, graphite-moderated

reactors can also utilize a molten salt coolant, for

example, the Molten Salt Reactor Experiment

(MSRE)1at Oak Ridge National Laboratory (ORNL)

The fluid fuel in the MSRE consisted of UF4dissolved

in fluorides of beryllium and lithium, which was

circu-lated through a reactor core moderated by graphite

The average temperature of the fuel salt was 650C

(1200F) at the normal operating condition of 8 MW,

which was the maximum heat removal capacity of the

air-cooled secondary heat exchanger The graphite

core was small, being only 137.2 cm (54 in.) in diameter

and 162.6 cm (64 in.) in height The fuel salt entered the

reactor vessel at 632C (1170F) and flowed down

around the outside of the graphite core in the annular

space between the core and the vessel The graphite

core was made up of graphite bars 5.08 cm (2 in.) square,

exposed directly to the fuel which flowed upward in

passages machined into the faces of the bars The fuel

flowed out of the top of the vessel at a temperature of

654C (1210F), through the circulating pump to the

primary heat exchanger, where it gave up heat to a

coolant salt stream The core graphite, grade CGB,

was specially produced for the MSRE, and had to

have a small pore size to prevent penetration of the

fuel salt, a long irradiation lifetime, and good

dimen-sional stability Moreover, for molten salt reactor

mod-erators, a low permeability (preferably<108cm2s1)

is desirable in order to prevent the build up of

unacceptable inventories of the nuclear poison

135

Xe in the graphite At ORNL, this was achieved

by sealing the graphite surface using a gas phasecarbon deposition process.1

Induced Structural and Dimensional Changes in Graphite

The discovery of Fullerenes9and carbon nanotubes,10and other nanocarbon structures, has renewed inter-est in high-resolution microstructural studies of car-bon nanostructures and the defects within them.11This in turn has given new insight to the nature ofdisplacement damage and the deformation mechan-isms in irradiated graphite crystals The bindingenergy of a carbon atom in the graphite lattice12 isabout 7 eV Impinging energetic particles such as fastneutrons, electrons, or ions can displace carbon atomsfrom their equilibrium positions There have beenmany studies of the energy required to displace acarbon atom (Ed), as reviewed by Kelly,13Burchell,14Banhart,11and Telling and Heggie.15The value ofEd

lies between 24 and 60 eV The latter value has gainedwide acceptance and use in displacement damagecalculations, but a value of 30 eV would be moreappropriate Moreover, as discussed by Banhart,11Hehr et al.,16

and Telling and Heggie,15 an angulardependence of the threshold energy for displacementwould be expected The value ofEdin the crystallo-graphicc-axis is in the range 12–20 eV,11,17

while thein-plane value is much greater

The primary atomic displacements, primaryknock-on carbon atoms (PKAs), produced by ener-getic particle collisions produce further carbon atomdisplacements in a cascade effect The cascade carbonatoms are referred to as secondary knock-on atoms(SKAs) The displaced SKAs tend to be clustered insmall groups of 5–10 atoms and for most purposes it

is satisfactory to treat the displacements as if theyoccur randomly The total number of displaced car-bon atoms will depend upon the energy of the PKA,which is itself a function of the neutron energy spec-trum, and the neutron flux Once displaced, thecarbon atoms recoil through the graphite lattice, dis-placing other carbon atoms and leaving vacant latticesites However, not all of the carbon atoms remaindisplaced and the temperature of irradiation has asignificant influence on the fate of the displacedatoms and lattice vacancies The displaced carbonatoms easily diffuse between the graphite layer planes

in two dimensions and a high proportion will

recom-bine with lattice vacancies Others will coalesce to

form C2, C3, or C4 linear molecules These in turn

may form the nucleus of a dislocation loop – essentially

a new graphite plane Interstitial clusters may, on

fur-ther irradiation, be destroyed by a fast neutron or

carbon knock-on atom (irradiation annealing)

Adja-cent lattice vacancies in the same graphitic layer are

believed to collapse parallel to the layers, thereby

forming sinks for other vacancies which are

increas-ingly mobile above 600C, and hence can no longer

recombine and annihilate interstitials The migration

of interstitials along the crystallographic c-axis is

discussed later

Banhart11observed typical basal plane defects in a

graphite nanoparticles using high-resolution

trans-mission electron microscopy (HRTEM) These defects

can be understood as dislocation loops which form

when displaced interstitial atoms cluster and form less

mobile agglomerates Other interstitials condense onto

this agglomerate which grows into a disk, pushing the

adjacent apart Further agglomeration leads to the

for-mation of a new lattice planes (Figure 4)

Other deformation mechanisms have been

pro-posed for irradiated graphite Wallace18 proposed a

mechanism whereby interstitial atoms could

facili-tate sp3bonds between the atomic basal planes, this

mechanism allowing the stored energy (discussed

in Section 4.10.5.1) to be explained Jenkins19

argued that the magnitude of the increase in shear

modulus (C44) with low dose irradiation could not beexplained by interstitial clusters pinning dislocations,but that a few sp3 type covalent bonds between theplanes could easily account for the observed changes.More recently, Telling and Heggie,15in theirab-initiocalculations of the energy of formation of the ‘spiro-interstitial,’ advocate this mechanism to explain thestored energy characteristics of displacement dam-aged graphite, particularly the large energy releasepeak seen at473 K (discussed inSection 4.10.5.1).The first experimental evidence of the interlayerinterstitial–vacancy (IV) pair defect with partial sp3character in between bilayers of graphite was recentlyreported by Urita et al.20

in their study of walled carbon nanotubes (DWNTs)

double-Jenkins19invoked the formation of sp3bonding toexplain the c-axis growth observed as a result ofdisplacement damage If adjacent planes are pinned,one plane must buckle as the adjacent planes shrinkdue to vacancy shrinkage; buckled planes yield thec-axis expansion that cannot be explained by swellingfrom interstitial cluster alone Telling and Heggie15arevery much in support of this position on the basis oftheir review of the literature andab-initio simulations ofthe damage mechanisms in graphite Their simulationsshowed how the spiro-interstitial (cross-link) essen-tially locked the planes together Additionally, diva-cancies could lead to the formation of pentagons andheptagons in the basal planes causing the observedbending of graphene layers andc-axis swelling.11,21,22

The predictedc-axis crystal expansion via this nism is in closer agreement with the experimentallyobserved single crystal and highly oriented pyrolyticgraphite (HOPG) dimensional change data

mecha-The buckling of basal planes as a consequence ofirradiation damage has been observed in HRTEMstudies of irradiated HOPG by Tanabe21 and Koikeand Pedraza.22 In their study, Koike and Pedraza22observed 300% expansion of thin HOPG samplessubject to electron irradiation in anin-situ transmis-sion electron microscope (TEM) study Their exper-imental temperatures ranged from 238 to 939 K.They noted that the damaged microstructure showedretention of crystalline order up to 1 dpa (displace-ments per atom) At higher doses, they observed thelattice fringes break up in to segments 0.5–5 nm inlength, with up to 15 rotation of the segments withrespect to the original {0001} planes

The evidence in favor of the formation of bondsbetween basal planes involving interstitials is consid-erable However, such bonds are not stable at hightemperature As reported by numerous authors and

1 nm

Figure 4 A high-resolution electron micrograph showing

the basal planes of a graphitic nanoparticle with an

interstitial loop between two basal planes, the ends of the

inserted plane are indicated with arrows Reproduced from

Banhart, F Rep Prog Phys 1999, 62, 1181–1221, with

permission from IOP Publishing Ltd.

reviewers11,15,19,20 the sp3 like bond would be

ex-pected to break and recombine with lattice vacancies

with increasing temperature, such that at T >500 K

they no longer exist Indeed, the irradiated graphite

stored energy annealing peak at 473 K, and the

HRTEM observations of Uritaet al.20

demonstrate thisclearly.Figure 5shows a sequential series of HRTEM

images illustrating the formation rates of interlayer

defects at different temperatures with the same time

scale (0–220 s) in DWNTs The arrows indicate

possi-ble interlayer defects At T ¼ 93 K (Figure 5(a))

the electron irradiation-induced defects are

numer-ous, and the nanotubes inside are quickly damaged

because of complex defects At 300 K (Figure 5(b)),

the nanotubes are more resistive to the damage from

electron irradiation, yet defects are still viable At

573 K (Figure 5(c)), defect formation is rarely observed

and the DWNTs are highly resistant to the electron

beam irradiation presumably because of the ease of

defect self-annihilation (annealing)

In an attempt to estimate the critical temperature

for the annihilation of the IV defect pairs, a

system-atic HRTEM study was undertaken at elevated

temperatures by Urita et al.20

The formation rate

of the IV defects that showed sufficient contrast in

the HRTEM is plotted in Figure 6 The reported

numbers were considered to be an underestimate as

single IV pairs may not have sufficient contrast to be

convincingly isolated from the noise level and thusmay have been missed However, the data was con-sidered satisfactory for indicating the formation rate

as a function of temperature The number of clusters

of IV pairs found in a DWNT was averaged forseveral batches at every 50 K and normalized by theunit area As observed in Figure 6, the defect for-mation rate displays a constant rate decline, with athreshold appearing at 450–500 K This thresholdcorresponds to the stored energy release peak (dis-cussed in Section 4.10.5.1) as shown by the dottedline in Figure 6 Evidentially, the irradiation dam-age resulting from higher temperature irradiations(above 473–573 K) is different in nature from thatoccurring at lower irradiation temperatures

Koike and Pedraza22studied the dimensional change

in HOPG caused by electron-irradiation-induced placement damage They observedin situ the growthc-axis of the HOPG crystals as a function of irradiationtemperature at damage doses up to1.3 dpa Increasingc-axis expansion with increasing dose was seen at alltemperatures The expansion rate was however signifi-cantly greater at temperatures≲473 K (their data was

dis-at 298 and 419 K) compared to thdis-at dis-at irradidis-ation peratures ≳473 K (their data was at 553, 693, and

tem-948 K) This observation supports the concept thatseparate irradiation damage mechanisms may exist atlow irradiation temperatures (T <473 K), that is,

buckling due to sp3bonded cross linking of the basal

planes via interstitials, and at more elevated irradiation

temperatures (T ≳ 473 K), where the buckling of planes

is attributed to clustering of interstitials which induce

the basal planes to bend, fragment, and then tilt Koike

and Pedraza22 also observed crystallographic a-axis

shrinkage upon electron irradiation in-situ at several

temperatures (419, 553, and 693 K) The shrinkage

increased with dose at all irradiation temperatures,

and the shrinkage rate reduced with increasing

irradia-tion temperature This behavior is attributed to

buck-ling and breakage of the basal planes, with the amount

of tilting and buckling decreasing with increasing

tem-perature due to (1) a switch in mechanism as discussed

above and (2) increased mobility of lattice vacancies

above673 K

Jenkins19,23 also discussed the deformation of

graphite crystals in terms of a unitc-axis dislocation

(prismatic dislocation), that is, one in which the

Bur-gers vector, b, is in the crystallographic c-direction

Thec-axis migration of interstitials can take place by

unit c-axis dislocations The formation and growth

of these, and other basal plane dislocation loops

undoubtedly play a major role in graphite crystaldeformation during irradiation

Ouseph24observed prismatic dislocation loops (bothinterstitial and vacancy) in unirradiated HOPG usingscanning tunneling microscopy (STM) Their studyallowed atomic resolution of the defect structures.Such defects had previously been observed as regions

of intensity variations in TEM studies in the 1960s.25Telling and Heggie’s15first principle simulationshave indicated a reduced energy of migration for alattice vacancy compared to the previously estab-lished value Therefore, they argue, the observed lim-ited growth of vacancy clusters at high temperatures(T >900 K) indicates the presence of a barrier tofurther coalescence of vacancy clusters (i.e., vacancytraps) Telling and Heggie implicate a cross-planermetastable vacancy cluster in adjacent planes as thepossible trap The disk like growth of vacancy clusterswithin a basal plane ultimately leads to a prismaticdislocation loop TEM observations show that theseloops appear to form at the edges of interstitial loops

in neighboring planes in the regions of tensile stress.The role of vacancies needs to be reexamined onthe basis of the foregoing discussion If the energy ofmigration is considerably lower than that previouslyconsidered, and there is a likelihood of vacancy traps,the vacancy and prismatic dislocation may well play

a larger role in displacement damage induced crystal deformation The diffusion of vacancy lines

in-to the crystal edge essentially heals the damage, suchthat crystals can withstand massive vacancy damageand recover completely

Regardless of the exact mechanism, the result ofcarbon atom displacements is crystallite dimensionalchange Interstitial defects will cause crystallite growthperpendicular to the layer planes (c-axis direction),and relaxation in the plane due to coalescence ofvacancies will cause a shrinkage parallel to the layerplane (a-axis direction) The damage mechanism andassociated dimensional changes are illustrated (in sim-plified form) in Figure 7 As discussed above, thisconventional view ofc-axis expansion as being causedsolely by the graphite lattice accommodating smallinterstitial aggregates is under some doubt, and despitethe enormous amount of experimental and theoreticalwork on irradiation-induced defects in graphite, weare far from a widely accepted understanding It is

to be hoped that the availability of high-resolutionmicroscopes will facilitate new damage and annealingstudies of graphite leading to an improved under-standing of the defect structures and of crystal defor-mation under irradiation

Figure 6 Normalized formation rates of the clusters of

interstitial–vacancy pair defects per unit area of bilayer

estimated in high-resolution transmission electron

microscope images recorded at different temperatures.

The dotted line shows the known temperature for

Wigner-energy release ( 473 K) Reproduced from Urita, K.;

Suenaga, K.; Sugai, T.; Shinohara, H.; Iijima, S Phys Rev.

Lett 2005, 94, 155502, with permission from American

Physical Society.

Dimensional changes can be very large, as

demon-strated in studies on well-ordered graphite materials,

such as HOPG that has frequently been used to study

the neutron-irradiation-induced dimensional changes

of the graphite crystallite.13,26 Price27 conducted a

study of the neutron-irradiation-induced dimensional

changes in pyrolytic graphite Figure 8 shows the

crystallite shrinkage in the a-direction for neutron

doses up to 12 dpa for samples that were graphitized

at a temperature of 2200–3300C prior to being

irra-diated at 1300–1500C The a-axis shrinkage

in-creases linearly with dose for all of the samples, but

the magnitude of the shrinkage at any given dose

decreases with increasing graphitization temperature

Similar trends were noted for the c-axis expansion

The significant effect of graphitization temperature

on irradiation-induced dimensional change

accumula-tion can be attributed to thermally induced

improve-ments in crystal perfection, thereby reducing the

number of defect trapping sites in the lattice

Nuclear graphites possess a polycrystalline

struc-ture, usually with significant texture resulting from

the method of forming during manufacture

Con-sequently, structural and dimensional changes in

polycrystalline graphites are a function of the

crys-tallite dimensional changes and the graphite’s texture

In polycrystalline graphite, thermal shrinkage cracks

that occur during manufacture and that are

prefer-entially aligned in the crystallographic a-direction

will initially accommodate thec-direction expansion,

so mainly a-direction contraction will be observed

The graphite thus undergoes net volume shrinkage

With increasing neutron dose (displacements), the

incompatibility of crystallite dimensional changes

leads to the generation of new porosity, and the

volume shrinkage rate falls, eventually reaching

zero The graphite now begins to swell at an

increasing rate with increasing neutron dose Thegraphite thus undergoes a volume change ‘turn-around’ into net growth that continues until the gen-eration of cracks and pores in the graphite, due todifferential crystal strain, eventually causes total dis-integration of the graphite

Irradiation-induced volume and dimensional changedata for H-451 are shown28inFigures 9–11 The effect

of irradiation temperature on volume change isshown in Figure 9 The ‘turn-around’ from volumeshrinkage to growth occurs at a lower fluence and

Collapsing vacancy line

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

3500 0 5 10

Neutron dose (dpa) 15 0

Irradiation-induced shrinkage (%)

20

20 40

60 80 100

3000 Graphitization temperature (

⬚C) 2500

2000

Figure 8 Neutron irradiation-induced a-axis shrinkage behavior of pyrolytic graphite showing the effects of graphitization temperature on the magnitude of the dimensional changes Reproduced from Burchell, T D In Carbon Materials for Advanced Technologies; Burchell,

T D., Ed.; Elsevier Science: Oxford, 1999, with permission from Elsevier.

the magnitude of the volume shrinkage is smaller

at the higher irradiation temperature This effect is

attributed to the thermal closure of aligned

micro-cracks in the graphite which accommodate thec-axis

growth Hence, there is less accommodating volume

available at the higher temperatures and the c-axisgrowth dominates thea-axis shrinkage at lower doses.The irradiation-induced dimensional changes

of H-451at 600 and 900C are shown inFigures 10and11, respectively H-451 graphite is an extrudedmaterial and therefore, the filler coke particlesare preferentially aligned in the extrusion axis (par-allel direction) Consequently, the crystallographica-direction is preferentially aligned in the paralleldirection and thea-direction shrinkage is more appar-ent in the parallel (to extrusion) direction, as indi-cated by the parallel direction dimensional changedata in Figures 10 and 11 The dimensional andvolume changes are greater at an irradiation temper-ature of 600C than at 900C; that is, both the maxi-mum shrinkage and the turnaround dose are greater

at an irradiation temperature of 600C This perature effect can be attributed to the thermalclosure of internal porosity that is aligned parallel tothe a-direction that accommodates the c-directionswelling At higher irradiation temperatures, a greaterfraction of this accommodating porosity is closed andthus the shrinkage is less at the point of turnaround

tem-A general theory of dimensional change in nular graphite due to Simmons29 has been extended

polygra-by Brocklehurst and Kelly.30For a detailed account ofthe treatment of dimensional changes in graphite thereader is directed to Kelly and Burchell.31

Changes4.10.5.1 Wigner EnergyThe release of Wigner energy (named after the phys-icist who first postulated its existence) was histori-cally the first problem of radiation damage ingraphite to manifest itself The lattice displacementprocesses previously described can cause an excess ofenergy in the graphite crystallites The damage maycomprise Frankel pairs or at lower temperatures the

sp3type bond previously discussed and observed byUritaet al.20

When an interstitial carbon atom and alattice vacancy recombine, or interplanar bonds arebroken, their excess energy is given up as ‘storedenergy.’ If sufficient damage has accumulated in thegraphite, the release of this stored energy can result

in a rapid rise in temperature Stored energy mulation was found to be particularly problematic

accu-in the early graphite-moderated reactors, whichoperated at relatively low temperatures Figure 12

shows the rate of release of stored energy with

Figure 9 Irradiation-induced volume changes for H-451

graphite at two irradiation temperatures From Burchell,

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

Fast fluence 10 26 n m -2 [E > 0.1 MeV]

Figure 10 Dimensional change behavior of H-451

graphite at an irradiation temperature of 600C From

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

Fast fluence 10 26 n m-2 [E > 0.1 MeV]

Figure 11 Dimensional change behavior of H-451

graphite at an irradiation temperature of 900C From

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

temperature, as a function of temperature, for

graph-ite samples irradiated at 30C to low doses in the

Hanford K reactor.32The release curves are

character-ized by a peak occurring at200C This temperature

has subsequently been associated with annealing of

interplanar bonding involving interstitial atoms.20

InFigure 12, the release rate exceeds the specific

heat and therefore, under adiabatic conditions, the

graphite would rise sharply in temperature For

am-bient temperature irradiations it was found9that the

stored energy could attain values up to 2720 J g1,

which if released adiabatically would cause a

temper-ature rise of some 1300C A simple experiment,8in

which samples irradiated at 30C were placed in a

furnace at 200C and their temperature monitored,

showed that when the samples attained a temperature

of70C their temperature suddenly increased to a

maximum of about 400C and then returned to

200C In order to limit the total amount of stored

energy in the early graphite reactors, it became

nec-essary to periodically anneal the graphite The

gra-phite’s temperature was raised sufficiently, by nuclear

heating or the use of inserted electrical heaters, to

‘trigger’ the release of stored energy The release then

self-propagated slowly through the core, raising the

graphite moderator temperature and thereby

par-tially annealing the graphite core Indeed, Arnold33

reports that it was during such a reactor anneal that

the Windscale (UK) reactor accident occurred in

1957 Rappeneauet al.34

report a second release peak

at very high temperatures (1400C) They studied

the energy release up to temperatures of 1800C

of graphites irradiated in the reactors BR2 (Mol,Belgium) and HFR (Petten, Netherlands) at dosesbetween 1000 and 4000 MWd T1 and at tempera-tures between 70 and 250C At these low irradiationtemperatures, there is little or no vacancy mobility, sothe resultant defect structures can only involveinterstitials On postirradiation annealing to high tem-peratures, the immobile single vacancies becomeincreasingly mobile and perhaps their eliminationand the thermal destruction of complex interstitialclusters or distorted and twisted basal planes contrib-ute to the high-temperature stored energy peak.The accumulation of stored energy in graphite isboth dose and irradiation temperature dependent.With increasingly higher irradiation temperatures,the total amount of stored energy and its peak rate

of release diminish, such that above an irradiationtemperature of 300C stored energy ceases to be

a problem Accounts of stored energy in graphite can

(see also Chapter 2.10, Graphite: Properties andCharacteristics) The coke type, forming method, andpotential uses of these grades are inTable 1 The mostobvious difference between the four grades listed in

Table 2is the filler particle sizes Grade IG-110 is anisostatically pressed, isotropic grade, whereas the othersgrades shown are near-isotropic and have propertiesreported either with-grain or against-grain As discussedearlier (seeSection 4.10.2), the orientation of the fillercoke particles is a function of the forming method.The mechanical properties of nuclear graphitesare substantially altered by radiation damage In theunirradiated condition, nuclear graphites behave in

a brittle fashion and fail at relatively low strains.The stress–strain curve is nonlinear, and the fractureprocess occurs via the formation of subcritical cracks,which coalesce to produce a critical flaw.35,36Whengraphite is irradiated, the stress–strain curve becomesmore linear, the strain to failure is reduced, and thestrength and elastic modulus are increased On irra-diation, there is a rapid rise in strength, typically

50%, that is attributed to dislocation pinning atirradiation-induced lattice defect sites This effect islargely saturated at doses >1 dpa Above 1 dpa, amore gradual increase in strength occurs because of

100/0.01

Figure 12 Stored energy release curves for CSF graphite

irradiated at 30 C in the Hanford K reactor cooled test

hole Source: Nightingale, R E Nuclear Graphite; Academic

Press: New York, 1962 From Burchell, T D In Carbon

Materials for Advanced Technologies; Burchell, T D., Ed.;

Elsevier Science: Oxford, 1999, with permission from

Elsevier.