Đang tải... (xem toàn văn)
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
4.10 Radiation Effects in Graphite T D Burchell Oak Ridge National Laboratory, Oak Ridge, TN, USA Published by Elsevier Ltd 4.10.1 Introduction 300 4.10.2 4.10.3 4.10.4 Nuclear Graphite Manufacture Graphite-Moderated Reactors Displacement Damage and Induced Structural and Dimensional Changes in Graphite Neutron-Induced Property Changes Wigner Energy Mechanical and Physical Properties Irradiation Creep The Relevance of Creep to Reactor Design and Operation The Irradiation-Induced Creep Mechanism (In-Crystal) Review of Prior Creep Models Linear viscoelastic creep model The UK creep model The Kennedy model The Kelly and Burchell model The M2 model Deficiencies in Current Creep Models at High Neutron Doses Outlook 302 303 4.10.5 4.10.5.1 4.10.5.2 4.10.6 4.10.6.1 4.10.6.2 4.10.6.3 4.10.6.3.1 4.10.6.3.2 4.10.6.3.3 4.10.6.3.4 4.10.6.3.5 4.10.6.4 4.10.7 References Abbreviations AGR ASTM Advanced gas-cooled reactor American Society for Testing and Materials CEN Centre European Nuclear CP-1 Chicago Pile No CTE Coefficient of thermal expansion DWNTs Double-walled carbon nanotubes Esu Elastic strain unit HFR High flux reactor HOPG Highly oriented pyrolytic graphite HRTEM High-resolution transmission electron microscope IV Interstitial–vacancy MHTGR Modular high-temperature gas-cooled reactor NGNP Next Generation Nuclear Plant ORNL Oak Ridge National Laboratory PGA Pile grade A PKA Primary knock-on atom SKA Secondary knock-on atom STM Scanning tunneling microscope TEM USSR 305 310 310 311 315 315 316 317 317 317 317 318 319 321 323 323 Transmission electron microscope Union of Soviet Socialist Republics Symbols a a b b B c c C Cp d«c/dg E E0 Constant in viscoelastic creep model Crystallographic a-direction (within the basal planes) Burger’s vector Constant in viscoelastic creep model Empirical fitting parameter, analogous to the steady-state creep coefficient Crystallographic c-direction (perpendicular to the basal planes) Flaw size Specific heat Specific heat at constant pressure Initial secondary (steady-state) creep rate Elastic modulus Initial (preirradiated) Young’s modulus 299 300 Radiation Effects in Graphite Ed Ep Eg Fx Fx0 G gx gx0 h k k k0 (g) k0 k1 k2 La Lc R S(g) T W (1/Xa) (dXa/dg) (1/Xc) (dXc/dg) XT Z a aa ac ax a´ x a(f) Displacement energy for a carbon atom from its equilibrium lattice position Young’s modulus after initial increase due to dislocation pinning Young’s modulus at dose g Pore generation term Pore generation term for a crept specimen Fracture toughness or strain energy release rate Rate of change of dimensions in the x-direction with respect to neutron dose Rate of change of dimensions in the x-direction for a crept specimen with respect to neutron dose (dimensional change component) Planck’s constant Boltzmann’s constant Steady-state creep coefficient Modified steady-state creep coefficient Initial secondary creep coefficient Primary creep dose constant Recoverable creep dose constant Mean graphite crystal dimensions in the a-direction Mean graphite crystal dimensions in the c-direction Gas constant (8.314 J molÀ1K) Structure factor (E/Ep) Temperature Oxidation change factor Rate of change of crystallite dimensions perpendicular to the hexagonal axis Rate of change of crystallite dimensions parallel to the hexagonal axis Crystal shape parameter Atomic number Coefficient of thermal expansion Crystal coefficient of thermal expansion in the a-direction Crystal coefficient of thermal expansion in the c-direction Coefficient of thermal expansion in the x-direction Coefficient of thermal expansion of a crept specimen in the x-direction Crystal coefficient of thermal expansion at angle f to the c-direction «˙ «c «´ c «d «e «p «s «t «Total f g l m n uD r r0 st s v V j Strain rate Creep strain Apparent creep strain Dimensional change strain Elastic strain Primary creep strain Secondary creep strain Thermal strain Total strain Fast neutron flux Fast neutron fluence Empirical fitting parameter Empirical constant ($0.75) Dislocation velocity Debye temperature Density True density Tensile strength Tensile stress Frequency of vibrational oscillations Mobile dislocation density Empirical fitting parameter 4.10.1 Introduction There are many graphite-moderated, powerproducing, fission reactors operating worldwide today.1 The majority are in the United Kingdom (gas-cooled) and the countries of the former Soviet Union (watercooled) In a nuclear fission reactor, the energy is derived when the fuel (a heavy element such as 92U235) fissions or ‘splits’ apart according to the following reaction: 235 92 U ỵ0 n1 !92 U236 ! F1 ỵ F2 ỵ n ỵg À energy ½I An impinging neutron usually initiates the fission reaction, and the reaction yields an average of 2.5 neutrons per fission The fission fragments (F1 and F2 in eqn [I]) and the neutron possess kinetic energy, which can be degraded to heat and harnessed to drive a turbinegenerator to produce electricity The role of graphite in the fission reactor (in addition to providing mechanical support to the fuel) is to facilitate the nuclear chain reaction by moderation of the high-energy fission neutron The fission fragments (eqn [I]) lose their kinetic energy as thermal energy to the uranium fuel mass in which fission occurred by successive collisions with the fuel atoms The fission neutrons (n in eqn [I]) give up Radiation Effects in Graphite their energy within the moderator via the process of elastic collision The g-energy given up in the fission reaction (eqn [I]) is absorbed in the bulk of the reactor outside the fuel, that is, moderator, pressure vessel, and shielding The longer a fission neutron dwells in the vicinity of a fuel atom during the fission process, the greater is its probability of being captured and thereby causing that fuel nucleus to undergo fission Hence, it is desirable to slow the energetic fission neutron (E $ MeV), referred to as a fast neutron, to lower thermal energies ($0.025 eV at room temperature), which corresponds to a velocity of 2.2 Â 1015 cm sÀ1 The process of thermalization or slowing down of the fission fast neutron is called ‘moderation,’ and the material in a thermal reactor (i.e., a reactor in which fission is caused by neutrons with thermal energies) that is responsible for slowing down the fast fission neutrons is referred to as the moderator Good nuclear moderators should possess the following attributes: 301 target elements Low atomic number (Z) is thus a prime requirement of a good moderator The density (number of atoms per unit volume) of the moderator and the likelihood of a scattering collision taking place must also be accounted for Frequently used ‘Figures of merit’ for assessing moderators are the ‘slowing down power’ and the ‘moderating ratio.’ Figure shows these Figures of merit for several candidate moderator materials The slowing down power accounts for the mean energy loss per collision, the number of atoms per unit volume, and the scattering cross-section of the moderator The tendency for a material to capture neutrons (the neutron capture cross-section) must also be considered Thus, the second figure of merit, the moderation ratio, is the ratio of the slowing down power to the neutron absorption (capture) cross-section Ideally the slowing down power is large, the neutron capture cross-section is small, and hence the moderating ratio is also large Practically, the choices of moderating materials are limited to the few elements with atomic number 2800 C), or by including a halogen purification stage in the manufacture of the cokes or graphite Recently, comprehensive consensus specifications5,6 were developed for nuclear graphites The electronic hybridization of carbon atoms (1s2, 2s , 2p2) allows several types of covalent bonded structure In graphite, we observe sp2 hybridization in a planar network in which the carbon atom is bound to three equidistant nearest neighbors 120 apart in a given plane to form the hexagonal graphene structure Covalent double bonds of both s-type and p-type are present, causing a shorter bond length than in the case of the tetrahedral bonding (s-type sp3 orbital hybridization only) observed in diamond Thus, in its perfect form, the crystal structure of graphite (Figure 3) consists of tightly bonded (covalent) sheets of carbon atoms in a hexagonal lattice network.7 The sheets are Radiation Effects in Graphite A B c 0.670 nm 303 (grain sizes 1000 C).1 The coated particle fuel is usually formed into fuel pucks or compacts but may be consolidated into fuel balls, or pebbles.1 The US designed modular high-temperature gas-cooled reactor (MHTGR) and Next Generation Nuclear Plant (NGNP), and the Japanese high-temperature test reactor (HTTR) are examples of gas-cooled reactors with high-temperature ceramic fuel Additional vertical channels in the graphite reactor core house the control rods, which regulate the fission reaction by introducing neutron-adsorbing materials to the core, and thus reduce the number of neutrons available to sustain the fission process When the control rods are withdrawn from the core, the self-sustaining fission reaction commences Heat is generated by the moderation of the fission fragments in the fuel and moderation of fast neutrons in the graphite The heat is removed from the core by a coolant, typically a gas, that flows freely through the core and over the graphite moderator The coolant is forced through the core by a gas circulator and passes into a heat exchanger/boiler (frequently referred to as a steam generator) The primary coolant loop (the reactor coolant) is maintained at elevated pressure to improve the coolant’s heat transfer characteristics and thus, the core is surrounded by a pressure vessel A secondary coolant (water) loop runs through the heat exchanger and cools the primary coolant so that it may be returned to the reactor core at reduced temperature The secondary coolant temperature is raised to produce steam which is passed through a turbine where it gives up its energy to drive an electric generator Some reactor designs, such as the MHTGR, are direct cycle systems in which the helium coolant passes directly to a turbine The reactor core and primary coolant loop are enclosed in a concrete biological-shield, which protects the reactor staff and public from g radiation and fission neutrons and also prevents the escape of radioactive contamination and fission product gasses that originate in the fuel pins/blocks The charge face, refueling machine, control rod drives, discharge area, and cooling ponds are housed in a containment structure which similarly prevents the spread of any contamination Additional necessary features of a fission reactor are (1) the refueling bay, where new fuel stringers or fuel elements are assembled prior to being loaded into the reactor core; (2), a discharge area and cooling ponds where spent fuel is placed while the short-lived isotopes are allowed to decay before the fuel can be reprocessed The NGNP, a graphite-moderated, helium cooled reactor, is designed specifically to generate electricity and produce process heat, which could be used for the production of hydrogen, or steam generation for the recovery of tar sands or oil shale Radiation Effects in Graphite Two NGNP concepts are currently being considered, a prismatic core design and a pebble bed core design In the prismatic core concept, the TRISO fuel is compacted into sticks and supported within a graphite fuel block which has helium coolant holes running through its length.1 The graphite fuel blocks are discharged from the reactor at the end of the fuel’s lifetime In the pebble bed core concept, the TRISO fuel is mixed with other graphite materials and a resin binder and formed into cm diameter spheres or pebbles.1 The pebbles are loaded into the core to form a ‘pebble bed’ through which helium coolant flows The pebble bed is constrained by a graphite moderator and reflector blocks which define the reactor core shape The fuel pebbles migrate slowly down through the reactor core and are discharged at the bottom of the core where they are either sent to spent fuel storage or returned to the top of the pebble bed Not all graphite-moderated reactors are gascooled Several designs have utilized water cooling, with the water carried through the core in zirconium alloy tubes at elevated pressure, before being fed to a steam generator Moreover, graphite-moderated reactors can also utilize a molten salt coolant, for example, the Molten Salt Reactor Experiment (MSRE)1 at Oak Ridge National Laboratory (ORNL) The fluid fuel in the MSRE consisted of UF4 dissolved in fluorides of beryllium and lithium, which was circulated through a reactor core moderated by graphite The average temperature of the fuel salt was 650 C (1200 F) at the normal operating condition of MW, which was the maximum heat removal capacity of the air-cooled secondary heat exchanger The graphite core was small, being only 137.2 cm (54 in.) in diameter and 162.6 cm (64 in.) in height The fuel salt entered the reactor vessel at 632 C (1170 F) and flowed down around the outside of the graphite core in the annular space between the core and the vessel The graphite core was made up of graphite bars 5.08 cm (2 in.) square, exposed directly to the fuel which flowed upward in passages machined into the faces of the bars The fuel flowed out of the top of the vessel at a temperature of 654 C (1210 F), through the circulating pump to the primary heat exchanger, where it gave up heat to a coolant salt stream The core graphite, grade CGB, was specially produced for the MSRE, and had to have a small pore size to prevent penetration of the fuel salt, a long irradiation lifetime, and good dimensional stability Moreover, for molten salt reactor moderators, a low permeability (preferably 500 K they no longer exist Indeed, the irradiated graphite stored energy annealing peak at $473 K, and the HRTEM observations of Urita et al.20 demonstrate this clearly Figure shows a sequential series of HRTEM images illustrating the formation rates of interlayer defects at different temperatures with the same time scale (0–220 s) in DWNTs The arrows indicate possible interlayer defects At T ¼ 93 K (Figure 5(a)) the electron irradiation-induced defects are numerous, and the nanotubes inside are quickly damaged because of complex defects At 300 K (Figure 5(b)), the nanotubes are more resistive to the damage from electron irradiation, yet defects are still viable At 573 K (Figure 5(c)), defect formation is rarely observed and the DWNTs are highly resistant to the electron beam irradiation presumably because of the ease of defect self-annihilation (annealing) In an attempt to estimate the critical temperature for the annihilation of the IV defect pairs, a systematic HRTEM study was undertaken at elevated temperatures by Urita et al.20 The formation rate of the IV defects that showed sufficient contrast in the HRTEM is plotted in Figure The reported numbers were considered to be an underestimate as single IV pairs may not have sufficient contrast to be 93 K 0s 300 K 307 convincingly isolated from the noise level and thus may have been missed However, the data was considered satisfactory for indicating the formation rate as a function of temperature The number of clusters of IV pairs found in a DWNT was averaged for several batches at every 50 K and normalized by the unit area As observed in Figure 6, the defect formation rate displays a constant rate decline, with a threshold appearing at $450–500 K This threshold corresponds to the stored energy release peak (discussed in Section 4.10.5.1) as shown by the dotted line in Figure Evidentially, the irradiation damage resulting from higher temperature irradiations (above $473–573 K) is different in nature from that occurring at lower irradiation temperatures Koike and Pedraza22 studied the dimensional change in HOPG caused by electron-irradiation-induced displacement damage They observed in situ the growth c-axis of the HOPG crystals as a function of irradiation temperature at damage doses up to $1.3 dpa Increasing c-axis expansion with increasing dose was seen at all temperatures The expansion rate was however significantly greater at temperatures ≲473 K (their data was at 298 and 419 K) compared to that at irradiation temperatures ≳473 K (their data was at 553, 693, and 948 K) This observation supports the concept that separate irradiation damage mechanisms may exist at low irradiation temperatures ($T 900 K) indicates the presence of a barrier to further coalescence of vacancy clusters (i.e., vacancy traps) Telling and Heggie implicate a cross-planer metastable vacancy cluster in adjacent planes as the possible trap The disk like growth of vacancy clusters within a basal plane ultimately leads to a prismatic dislocation loop TEM observations show that these loops appear to form at the edges of interstitial loops in neighboring planes in the regions of tensile stress The role of vacancies needs to be reexamined on the basis of the foregoing discussion If the energy of migration is considerably lower than that previously considered, and there is a likelihood of vacancy traps, the vacancy and prismatic dislocation may well play a larger role in displacement damage induced incrystal deformation The diffusion of vacancy lines to the crystal edge essentially heals the damage, such that crystals can withstand massive vacancy damage and recover completely Regardless of the exact mechanism, the result of carbon atom displacements is crystallite dimensional change Interstitial defects will cause crystallite growth perpendicular to the layer planes (c-axis direction), and relaxation in the plane due to coalescence of vacancies will cause a shrinkage parallel to the layer plane (a-axis direction) The damage mechanism and associated dimensional changes are illustrated (in simplified form) in Figure As discussed above, this conventional view of c-axis expansion as being caused solely by the graphite lattice accommodating small interstitial aggregates is under some doubt, and despite the enormous amount of experimental and theoretical work on irradiation-induced defects in graphite, we are far from a widely accepted understanding It is to be hoped that the availability of high-resolution microscopes will facilitate new damage and annealing studies of graphite leading to an improved understanding of the defect structures and of crystal deformation under irradiation 310 Radiation Effects in Graphite 10 H-451 @ 600 ЊC H-451 @ 900 ЊC Volume change (%) -2 -4 -6 -8 -10 Fast fluence 1026 n m-2 [E > 0.1 MeV] Figure Irradiation-induced volume changes for H-451 graphite at two irradiation temperatures From Burchell, T D.; Snead, L L J Nucl Mater 2007, 371, 18–27 H-451 graphite irradiated at 600 ЊC Dimensional change (%) -1 -2 -3 -4 Perpendicular to extrusion (AG) Parallel to extrusion direction (WG) -5 -6 Fast fluence 1026 n m-2 [E > 0.1 MeV] Figure 10 Dimensional change behavior of H-451 graphite at an irradiation temperature of 600 C From Burchell, T D.; Snead, L L J Nucl Mater 2007, 371, 18–27 Dimensional change (%) 4.10.5 Neutron-Induced Property Changes H-451 graphite irradiated at 900 ЊC 4.10.5.1 Perpendicular to extrusion (AG) Parallel to extrusion direction (WG) -1 -2 -3 0.5 1.5 2.5 Fast fluence 1026 n m-2 [E > 0.1 MeV] available at the higher temperatures and the c-axis growth dominates the a-axis shrinkage at lower doses The irradiation-induced dimensional changes of H-451at 600 and 900 C are shown in Figures 10 and 11, respectively H-451 graphite is an extruded material and therefore, the filler coke particles are preferentially aligned in the extrusion axis (parallel direction) Consequently, the crystallographic a-direction is preferentially aligned in the parallel direction and the a-direction shrinkage is more apparent in the parallel (to extrusion) direction, as indicated by the parallel direction dimensional change data in Figures 10 and 11 The dimensional and volume changes are greater at an irradiation temperature of 600 C than at 900 C; that is, both the maximum shrinkage and the turnaround dose are greater at an irradiation temperature of 600 C This temperature effect can be attributed to the thermal closure of internal porosity that is aligned parallel to the a-direction that accommodates the c-direction swelling At higher irradiation temperatures, a greater fraction of this accommodating porosity is closed and thus the shrinkage is less at the point of turnaround A general theory of dimensional change in polygranular graphite due to Simmons29 has been extended by Brocklehurst and Kelly.30 For a detailed account of the treatment of dimensional changes in graphite the reader is directed to Kelly and Burchell.31 Figure 11 Dimensional change behavior of H-451 graphite at an irradiation temperature of 900 C From Burchell, T D.; Snead, L L J Nucl Mater 2007, 371, 18–27 the magnitude of the volume shrinkage is smaller at the higher irradiation temperature This effect is attributed to the thermal closure of aligned microcracks in the graphite which accommodate the c-axis growth Hence, there is less accommodating volume Wigner Energy The release of Wigner energy (named after the physicist who first postulated its existence) was historically the first problem of radiation damage in graphite to manifest itself The lattice displacement processes previously described can cause an excess of energy in the graphite crystallites The damage may comprise Frankel pairs or at lower temperatures the sp3 type bond previously discussed and observed by Urita et al.20 When an interstitial carbon atom and a lattice vacancy recombine, or interplanar bonds are broken, their excess energy is given up as ‘stored energy.’ If sufficient damage has accumulated in the graphite, the release of this stored energy can result in a rapid rise in temperature Stored energy accumulation was found to be particularly problematic in the early graphite-moderated reactors, which operated at relatively low temperatures Figure 12 shows the rate of release of stored energy with Radiation Effects in Graphite 0.7 dS/dT (cal g–1 ЊC–1) 0.6 Exposures in MWd/at and dpa (approximately) 0.5 0.4 Specific heat 0.3 5700/0.60 1075/0.10 0.2 0.1 100/0.01 100 200 300 400 Annealing temperature (ЊC) 500 Figure 12 Stored energy release curves for CSF graphite irradiated at $30 C in the Hanford K reactor cooled test hole Source: Nightingale, R E Nuclear Graphite; Academic Press: New York, 1962 From Burchell, T D In Carbon Materials for Advanced Technologies; Burchell, T D., Ed.; Elsevier Science: Oxford, 1999, with permission from Elsevier temperature, as a function of temperature, for graphite samples irradiated at 30 C to low doses in the Hanford K reactor.32 The release curves are characterized by a peak occurring at $200 C This temperature has subsequently been associated with annealing of interplanar bonding involving interstitial atoms.20 In Figure 12, the release rate exceeds the specific heat and therefore, under adiabatic conditions, the graphite would rise sharply in temperature For ambient temperature irradiations it was found9 that the stored energy could attain values up to 2720 J gÀ1, which if released adiabatically would cause a temperature rise of some 1300 C A simple experiment,8 in which samples irradiated at 30 C were placed in a furnace at 200 C and their temperature monitored, showed that when the samples attained a temperature of $70 C their temperature suddenly increased to a maximum of about 400 C and then returned to 200 C In order to limit the total amount of stored energy in the early graphite reactors, it became necessary to periodically anneal the graphite The graphite’s temperature was raised sufficiently, by nuclear heating or the use of inserted electrical heaters, to ‘trigger’ the release of stored energy The release then self-propagated slowly through the core, raising the graphite moderator temperature and thereby partially annealing the graphite core Indeed, Arnold33 reports that it was during such a reactor anneal that the Windscale (UK) reactor accident occurred in 1957 Rappeneau et al.34 report a second release peak at very high temperatures ($1400 C) They studied the energy release up to temperatures of 1800 C 311 of graphites irradiated in the reactors BR2 (Mol, Belgium) and HFR (Petten, Netherlands) at doses between 1000 and 4000 MWd TÀ1 and at temperatures between 70 and 250 C At these low irradiation temperatures, there is little or no vacancy mobility, so the resultant defect structures can only involve interstitials On postirradiation annealing to high temperatures, the immobile single vacancies become increasingly mobile and perhaps their elimination and the thermal destruction of complex interstitial clusters or distorted and twisted basal planes contribute to the high-temperature stored energy peak The accumulation of stored energy in graphite is both dose and irradiation temperature dependent With increasingly higher irradiation temperatures, the total amount of stored energy and its peak rate of release diminish, such that above an irradiation temperature of $300 C stored energy ceases to be a problem Accounts of stored energy in graphite can be found elsewhere.1,8,29,32 4.10.5.2 Mechanical and Physical Properties The mechanical and physical properties of several medium-grained and fine-grained nuclear grade graphites currently in production are given in Table (see also Chapter 2.10, Graphite: Properties and Characteristics) The coke type, forming method, and potential uses of these grades are in Table The most obvious difference between the four grades listed in Table is the filler particle sizes Grade IG-110 is an isostatically pressed, isotropic grade, whereas the others grades shown are near-isotropic and have properties reported either with-grain or against-grain As discussed earlier (see Section 4.10.2), the orientation of the filler coke particles is a function of the forming method The mechanical properties of nuclear graphites are substantially altered by radiation damage In the unirradiated condition, nuclear graphites behave in a brittle fashion and fail at relatively low strains The stress–strain curve is nonlinear, and the fracture process occurs via the formation of subcritical cracks, which coalesce to produce a critical flaw.35,36 When graphite is irradiated, the stress–strain curve becomes more linear, the strain to failure is reduced, and the strength and elastic modulus are increased On irradiation, there is a rapid rise in strength, typically $50%, that is attributed to dislocation pinning at irradiation-induced lattice defect sites This effect is largely saturated at doses >1 dpa Above $1 dpa, a more gradual increase in strength occurs because of 312 Radiation Effects in Graphite Table Typical physical and mechanical properties of unirradiated nuclear graphites Property Graphite grade IG-110 PCEA NBG-10 NBG-18 Maximum filler particle size (mm) Bulk density (g cmÀ3) Tensile strength (MPa) 10 1.77 24.5 Flexural strength (MPa) 39.2 Compressive strength (MPa) 78.5 800 1.83 21.9 (WG) 16.9 (AG) 32.4 (WG) 23.3 (AG) 60.8 (WG) 67.6 (AG) 11.3 (WG) 9.9 (AG) 162 (WG) 159 (AG) 3.5 (WG) 3.7 (AG) (30–100 C) 7.3 (WG) 7.8 (AG) 1600 1.79 20.0 (WG) 18.0 (AG) 24.0 (WG) 27.0 (AG) 47.0 (WG) 61.0 (AG) 9.7 (WG) 9.7 (AG) 148 (WG) 145 (AG) 4.1 (WG) 4.6 (AG) (20–200 C) 9.1 (WG) 9.3 (AG) 1600 1.88 21.5 (WG) 20.5 (AG) 28 (WG) 26 (AG) 72.0 (WG) 72.5 (AG) 11.2 (WG) 11.0 (AG) 156 (WG) 150 (AG) 4.5 (WG) 4.7 (AG) (20–200 C) 8.9 (WG) 9.0 (AG) Young’s modulus (GPa) 9.8 Thermal conductivity (W mÀ1 KÀ1) (measured at ambient temperature) Coefficient of thermal expansion (10À6 KÀ1) (over given temperature range) 116 Electrical resistivity (mO m) 11 4.5 (350–450 C) WG, with-grain; AG, against-grain E=E0 ịirradiated ẳ E=E0 ịpinning E=E0 ịstructure ẵ1 where E/E0 is the ratio of the irradiated to unirradiated elastic modulus The dislocation pinning contribution to the modulus change is due to relatively mobile small defects and is thermally annealable at $2000 C The irradiation-induced elastic modulus changes for GraphNOL N3M graphite37 are shown in Figure 13 The low dose change due to dislocation pinning (dashed line) saturates at a dose 250 C) when the graphite lattice is under stress, as suggested by others.57 Are there mechanisms of dislocation climb and glide that need to be explored? Can dislocation lines climb/glide past the assumed interstitial cluster barriers via a mechanism that is active only when structural rearrangements occur during irradiation? This behavior is analogous to carbons and graphites undergoing thermal creep when they undergo structural reorganization, that is, during carbonization and graphitization (thermal relaxation or slumping) 317 countries showed the primary creep saturated at approximately one elastic strain (s/E0) so that the true creep may be represented as s ẵ13 ec ẳ ỵ ksg E0 This is often normalized to the initial elastic strain and written as ec ẳ ỵ kE0 g ẵ14 in elastic strain units (esu) (esu is defined as the externally applied stress divided by the initial static Young’s modulus), or creep strain per unit initial elastic strain; kE is the creep coefficient in units of reciprocal dose [United Kingdom $ 0.23 Â 10À20 cm2 nÀ1 EDN up to Tirr $ 500 C] (EDN – equivalent DIDO nickel dose, a unit of neutron fluence used in the United Kingdom and Europe.) 4.10.6.3.2 The UK creep model The UK model1,64,65 recognizes that the initial creep coefficient is modified by irradiation-induced structure changes (i.e., changes to the pore structure) Hence, the total creep strain is given by ðg s dec s S gịdg ec ẳ ỵ dg E0 ½15 4.10.6.3 Review of Prior Creep Models 4.10.6.3.1 Linear viscoelastic creep model Irradiation-induced (apparent) creep strain is conventionally defined as the difference between the dimensional change of a stressed specimen and an unstressed specimen irradiated under identical conditions Early creep data was found to be well described by a viscoelastic creep model1,5863 where total irradiation creep (ec ị ẳ primary (transient) creep ỵ secondary (steady-state) creep as ẵ12 ec ẳ ẵ1 expbgị ỵ ksg E0 where ec is the total creep strain; s, the applied stress; E0, the initial (preirradiated) Young’s modulus; g, the fast neutron fluence; a and b are constants (a is usually ¼ 1); and k is the steady-state creep coefficient in units of reciprocal neutron dose and reciprocal stress Equation [13] thus conforms to the Kelly–Foreman theory of creep with an initially large primary creep coefficient, while the dislocation pinning sites develop to the equilibrium concentration, at which time the creep coefficient has fallen to the steady-state or secondary value Early creep experiments in several where s is the applied stress; (dec/dg)0, the initial secondary creep rate; g, the fast neutron fluence; S(g), the structure factor, given by S(g) ¼ Eg/Ep the ratio of the Young’s modulus at dose g to the Young’s modulus after the initial increase due to dislocation pinning The structure factor, S(g), thus attempts to separate those effects due to dislocation pinning occurring within the crystallites and structural effects occurring ex-crystal through changes in the Young’s modulus However, the effect of creep strain (tensile or compressive) on modulus is not considered when evaluating the structure term The unstressed Young’s modulus changes are used to establish the magnitude of S(g) 4.10.6.3.3 The Kennedy model Kennedy et al.66 replaced the structure term in the UK model with a parameter based on the volume change behavior of the graphite: s ẵ16 ec ẳ þ k0 ðgÞsg E0 where ðg k ðgÞ ¼ k0 1Àm DV =V0 ðDV =V0 Þmax dg ½17 318 Radiation Effects in Graphite Here, m is an empirical constant equal to 0.75 and k0 is the steady-state creep coefficient established from low dose creep experiments Although the Kennedy et al.66 model was shown to perform well in the prediction of high-dose tensile creep data, it did not predict the compressive data nearly as well Moreover, as with the UK model, the sign of the applied stress is not considered when evaluating the influence of structure change (as reflected in volume changes) The quotient in eqn [17] is evaluated solely from unstressed (stressfree) samples irradiation behavior As discussed by Kelly and Burchell,51 the term (DV/Vmax) does not exist at low irradiation temperatures where graphites expand in volume 4.10.6.3.4 The Kelly and Burchell model The Kelly and Burchell50,51 model recognizes that creep produces significant modifications to the dimensional change component of the stressed specimen compared to that of the control and that this must be accounted for in the correct evaluation of creep strain data The rate of change of dimensions with respect to neutron dose g(n cmÀ2) in appropriate units is given by the Simmons’ theory29 for direction x in the unstressed polycrystalline graphite: ax aa dXT dXa ỵ ỵ Fx ½18 gx ¼ ac À aa dg Xa dg where ax is the thermal expansion coefficient in the x-direction, and ac and aa are the thermal expansion coefficients of the graphite crystal parallel and perpendicular to the hexagonal axis, respectively, over the same temperature range The term Fx is a pore generation term that becomes significant at intermediate doses when incompatibilities of irradiationinduced crystal strains cause cracking of the bulk graphite.67 For the purposes of their analysis, Kelly and Burchell ignored the term Fx The parameters (1/Xc)(dXc/dg) and (1/Xa)(dXa/dg) are the rates of change of graphite crystallite dimensions parallel and perpendicular to the hexagonal axis, and dXT dXc dXa ẳ dg Xc dg Xa dg ẵ19 The imposition of a creep strain is known to change the thermal expansion coefficient of a stressed specimen, increasing it for a compressive strain and decreasing it for a tensile strain compared to an unstressed control Thus, the dimensional change component of a stressed specimen at dose g(n cmÀ2) is given by ax À aa dXT dXa ỵ ỵ Fx0 ẵ20 gx ẳ ac À aa dg Xa dg where a0x is the thermal expansion coefficient of the crept sample, and Fx0 is the pore generation term for the crept specimen The difference between these two equations is thus the dimensional change correction that should be applied to the apparent creep strain (the pore generation terms Fx and Fx0 were neglected): a À aa dXT gx0 À gx ¼ x ac À a a dg ax À aa dXT À ac À aa dg a ax dXT ẳ x ẵ21 ac aa dg The true creep strain rate can now be expressed as de de0 a À ax dXT x ẵ22 ẳ ac aa dg dg dg where e is the true creep strain and e0 is the apparent creep strain determined experimentally in the conventional manner Thus, the true creep strain (ec) parallel to the applied creep stress is given by ðg ax À ax dXT dg ½23 ec ¼ ec À ac À aa dg where e0c is the induced apparent creep strain, ða0x À ax Þ is the change in CTE as a function of dose, ðac À aa Þ is the difference of the crystal thermal expansion coefficients of the graphite parallel and perpendicular to the hexagonal axis, XT is the crystal shape change parameter given above, and g is the neutron dose The apparent (experimental) creep strain is thus given by ðg ax À ax dXT dg ½24 ec ẳ ec ỵ ac aa dg Substituting for ec from eqn [13] gives the apparent (experimental) creep strain e0c as ðg s ax ax dXT dg ẵ25 ỵ ksg ỵ ec ¼ ac À aa dg E0 with the terms as defined above The Kelly–Burchell model is unique in that it does take account of the sign of the applied stress in Radiation Effects in Graphite predicting creep strain through changes in the CTE of the stressed graphite While the model gave good agreement between the predicted H-451 graphite apparent creep strain and the experimental data at low doses and high temperatures51 (Figures 19–22), the creep model was shown to be inadequate at doses >0.5 Â 1022 n cmÀ2 [E >50 keV] ($3.4 dpa) at an irradiation temperature of 900 C (Figure 23).50 4.10.6.3.5 The M2 model Based upon the evidence from UK and US creep experiments, Davies and Bradford49,68 suggest the following: The strain induced change in CTE is not a function of secondary creep strain, but saturates after a dose of $30 Â 1020 n cmÀ2 EDN ($3.9 dpa) There is evidence, from both thermal and irradiation annealing, for a recoverable strain several times that of primary creep, and a lower associated secondary creep coefficient that has been previously assumed The dose at which the recoverable strain saturates bears a striking similarity to that of the saturation of the CTE change Davies and Bradford49,68 proposed a new creep model (the M2 model) without the term reflecting changes in CTE due to creep, but containing one additional term, recoverable creep: gð1 lk1 s Àk1 g1 expk1 g dg ec ¼ exp E0 SW gð1 gð1 xk2 s b s Àk2 g1 k2 g exp dg ỵ dg exp ỵ E0 SW E0 SW ½26 0 Creep strain (%) 0.5 Experimental creep strain True creep strain -0.5 CTE correction strain -1 Predicted apparent creep strain -1.5 -2 0.1 0.2 0.3 0.4 0.5 0.6 Neutron dose 1022 n cm-2 [E > 50 keV] Figure 19 Comparison of predicted apparent creep strain (from eqn [25]) and the experimental creep strain data for irradiation creep at 600 C under a compressive stress of 13.8 MPa The true creep strain is calculated from eqn [13] From Burchell, T D J Nucl Mater 2008, 381, 46–54 Creep strain (%) 0.5 Experimental creep strain True creep strain -0.5 -1 CTE correction strain -1.5 Predicted apparent creep strain -2 -2.5 -3 319 0.1 0.2 0.3 0.4 0.5 Neutron dose 1022 n cm-2 [E > 50 keV] 0.6 Figure 20 Comparison of predicted apparent creep strain (from eqn [25]) and the experimental creep strain data for irradiation creep at 600 C under a compressive stress of 20.7 MPa The true creep strain is calculated from eqn [13] From Burchell, T D J Nucl Mater 2008, 381, 46–54 Radiation Effects in Graphite Creep strain (%) 320 1.5 0.5 -0.5 -1 -1.5 -2 -2.5 -3 -3.5 Experimental (apparent) creep True creep strain CTE change correction Predicted apparent creep strain 0.1 0.2 0.3 0.4 0.5 Neutron dose 1022 n cm-2 [E > 50 keV] 0.6 Figure 21 Comparison of predicted apparent creep strain (from eqn [25]) and the experimental creep strain data for irradiation creep at 900 C under a compressive stress of 13.8 MPa The true creep strain is calculated from eqn [13] From Burchell, T D J Nucl Mater 2008, 381, 46–54 Creep strain (%) Experimental creep strain True creep strain -1 Dimensional change correction -2 -3 Predicted apparent creep strain -4 -5 0.1 0.2 0.3 22 Neutron dose 10 n cm-2 0.4 0.5 0.6 [E > 50 KeV] Figure 22 Comparison of predicted apparent creep strain (from eqn [25]) and the experimental creep strain data for irradiation creep at 900 C under a compressive stress of 20.7 MPa The true creep strain is calculated from eqn [13] From Burchell, T D J Nucl Mater 2008, 381, 46–54 5.0 Apparent (experimental) creep Creep strain (%) 4.0 3.0 True creep 2.0 Dimensional change correction 1.0 0.0 Predicted apparent creep -1.0 -2.0 0.5 1.5 Neutron dose, 1022 n cm-2 [E > 50 KeV] Figure 23 Comparison of predicted apparent creep strain (from eqn [26]) and the experimental creep strain data for irradiation creep at 900 C under a tensile stress of MPa The true creep strain is calculated from eqn [13] From Burchell, T D J Nucl Mater 2008, 381, 46–54 Radiation Effects in Graphite where ec is the total creep strain; s, the applied stress; l, x, and b, are the empirical fitting parameters; k1 and k2, the primary and recoverable dose constants respectively; and W is the oxidation change factor (with respect to Young’s modulus) and is analogous to the structure factor The terms in the eqn [26] are proportional to esu and the effects of structural changes and radiolytic oxidation (gasification of graphite by an activated species that occurs in CO2 cooled reactors) are also included The rates of saturation of the primary and recoverable creep components are controlled by the dose constants k1 and k2 The first and last terms in eqn [26] are primary and secondary creep as in the prior UK creep model, with the middle term being recoverable creep Primary creep is still fast acting, but in the AGR temperature range of 400–650 C, appears to act on a longer fluence scale equivalent to that associated in the United Kingdom with the Young’s modulus pinning,69 k1 ¼ 0.1, and saturates at esu (a ¼ 1) The irrecoverable creep is synonymous with secondary creep, but with a coefficient, b, derived from the irrecoverable strain postthermal anneal, as 0.15 per 1020 n cmÀ2 EDN ($1.3 dpa) in the AGR temperature range The lateral creep strain ratios for primary and recoverable creep are assumed to be the Poisson’s ratio and secondary creep is assumed to occur at constant volume Figure 24 shows the performance of the M2 models applied to some high dose ATR-2E tensile creep data52 when irradiated at 500 C in high flux reactor (HFR), Petten The prediction matches the observed data well up to significant fluence of $160 Â 1020 n cmÀ2 EDN ($21 dpa) Only beyond 321 this fluence does the new model prediction deviate from the data with a delay in the increase in creep strain at high doses that is often referred to as the ‘tertiary’ creep phase Figure 25 shows the corresponding compressive creep data,52 irradiated at 550 C The model over predicts the data slightly but follows the trend remarkably well up to a significant fluence of $160 Â 1020 n cmÀ2 EDN ($21 dpa) Beyond this fluence, the compressive prediction also indicates a ‘tertiary’ creep, but the data does not extend into this region The data52 also indicates a possible difference between tensile and compressive creep (seen more clearly in Figure 18) Saturation of CTE with creep strain as reported by Davies and Bradford49,68 is not however in agreement with other published data Gray70 reported CTE behavior with creep strain (up to 3%) for three different graphites at irradiation temperatures of 550 and 800 C Saturation of the CTE in the manner described by Davies and Bradford49,68 for UK AGR graphite was not observed 4.10.6.4 Deficiencies in Current Creep Models at High Neutron Doses The poor performance of the Kelly and Burchell model (eqn [25]) at predicting the high temperature (900 C) and high dose MPa tensile creep data suggests that the model requires further revision.50,71 H-451 graphite irradiated at 900 C goes through dimensional change turn-around in the dose range 1.3–1.5 Â 1022 n cmÀ2 [E >50] ($8.8–10.2 dpa) This behavior is understood to be associated with the 0.02 0.025 M2 model 500 T 0.015 Creep strain Creep strain 0.02 Model 550 ЊC 550 ЊC 0.015 0.01 0.01 0.005 0.005 0 50 100 150 EDND (1020 n cm-2) 200 250 Figure 24 Comparison of the M2 models prediction and experimental creep strain data for ATR-2E tensile creep data, when irradiation was at 500 C in Petten Reproduced from Davies, M.; Bradford, M J Nucl Mater 2008, 381, 39–45 50 100 150 Dose (1020 n cm-2 EDN) 200 250 Figure 25 Comparison of the M2 models prediction and experimental creep strain data for ATR-2E compressive creep data, when irradiation was at 550 C in Petten Reproduced from Davies, M.; Bradford, M J Nucl Mater 2008, 381, 39–45 322 Radiation Effects in Graphite generation of new porosity due to the increasing mismatch of crystal strains The Kelly–Burchell model accounts for this new porosity only to the extent to which it affects the CTE of the graphite, through changes in the aligned porosity Gray70 observed that at 550 C the creep rate was approximately linear However, at 800 C he reported a marked nonlinearity in the creep rate and the changes in CTE were significant Indeed, for the two high density graphites (H-327 and AXF-8Q) Gray reports that the 900 C creep strain rate reverses Gray postulated a creep strain limit to explain this behavior, such that a back stress would develop and cause the creep rate to reduce Other workers have shown that a back stress does not develop.62 However, Gray further argued that a creep strain limit is improbable as this cannot explain the observed reversal of creep strain rate Note that a reversal of the creep rate is clearly seen in the 900 C tensile creep strain data reported here for H-451 (Figure 23) Also, a creep strain limit would require that tensile stress would modify the onset of pore generation behavior in the same way as compressive stress, because the direction of the external stress should be immaterial.70 More recent data52 and the behavior reported by Burchell71 show that this is not the case Gray70 suggests that a more plausible explanation of his creep data is the onset of rapid expansion accelerated by creep strain; that is, net pore generation begins earlier under the influence of a tensile applied stress Indeed, it has been observed52 that compressive creep appears to delay the turnaround behavior and tensile creep accelerates the turnaround behavior (Figure 18) In discussing possible explanations for his creep strain and CTE observations, Gray70 noted that changes in the graphite pore structure that manifested themselves in changes in CTE did not appear to influence the creep strain at higher doses The classical explanation of the changes in CTE invokes the closure of aligned porosity in the graphite crystallites Further crystallite strain can be accommodated only by fracture A result of this fracture is net generation of porosity resulting in a bulk expansion of the graphite A requirement of this model is that the CTE should increase monotonically from the start of irradiation A more marked increase in CTE would be seen when the graphite enters the expansion phase (i.e., all accommodating porosity filled) The observed CTE behavior, reported previously50 and in Gray’s70 work, does not display this second increase in CTE; thus, the depletion of (aligned) accommodation porosity is not responsible for the early beginning of expansion behavior The observation by Gray70 and Kennedy63 that creep occurs at near constant volume (up to moderate fluence) indicates that creep is not accompanied by a net reduction of porosity compared to unstressed graphite, but this does not preclude that stress may decrease pore dimensions in the direction of the applied stress and increase them in the other, that is, a reorientation of the pore structure Pore reorientation could effectively occur as the result of a mechanism of pore generation where an increasing fraction of the new pores are not well-aligned with the crystallites basal planes (and thus they would not manifest themselves in the CTE behavior) or accompanied with the closure of pores aligned with the basal planes Kelly and Foreman53 report that their proposed creep mechanism would be expected to break down at high doses and temperatures, and thus deviations from the linear creep law (eqn [12]) are expected They suggest that this is due to (1) incompatibility of crystal strains causing additional internal stress and an increasing crystal creep rate, (2) destruction of interstitial pins by diffusion of vacancies (thermal annealing of vacancies in addition to irradiation annealing), and (3) pore generation due to incompatibility of crystal strains It is likely that pore generation can manifest itself in two ways: (1) changes in CTE with creep strain – thus, pores aligned parallel to the crystallite basal planes are affected by creep strain – and (2) at high doses, pore generation or perhaps pore reorientation, under the influence of applied and internal stress that must be accounted for in the prediction of high neutron dose creep behavior Brocklehurst and Brown62 report on the annealing behavior of specimens that had been subjected to irradiation under constant stress and sustained up to 1% creep strain They observed that the increase in creep strain with dose was identical in compression and tension up to 1% creep strain, and that the CTE was significantly affected in opposite directions by compressive and tensile creep strains Irradiation annealing of the crept specimens caused only a small recovery in the creep strain, and therefore provided no evidence for a back stress in the creep process, which has implications for the in-crystal creep mechanism Thermal annealing also produced a small recovery of the creep strain at temperatures below 1600 C, presumably because of the thermal removal of the irradiation-induced defects responsible for dislocation pinning Higher temperature annealing Radiation Effects in Graphite produced a further substantial recovery of creep strain Most significantly, Brocklehurst and Brown62 reported the complete annealing of the creep induced changes in CTE, in contrast to the total creep strain, where a large fraction of the total creep strain is irrecoverable and has no effect on the thermal expansion coefficient Brocklehurst and Brown62 discuss two interpretations of their results, but report that neither is satisfactory One interpretation requires a distinction between changes in porosity that affect the CTE and changes in porosity affecting the elastic deformation under external loads, that is, two distinct modes of pore structure changes due to creep in broad agreement with the mechanism discussed earlier The modified Simmons model29,30,67 for dimensional changes (eqn [18]) and that for dimensional changes of a crept specimen (eqn [20]) both have pore generation terms which are currently neglected It now appears necessary to modify the current Kelly–Burchell creep model (eqn [25]) to account for this effect of creep strain on this phenomena; that is, we need to evaluate and take account of the terms Fx and Fx0 as well as include the term (Fx0 –Fx) in eqn [25] Such a term should account for pore generation and/or reorientation caused by fracture when incompatibilities in crystallite strains become excessive.71 Clearly, further work is needed in the area of irradiation-induced creep of graphite 4.10.7 Outlook For more than 60 years, nuclear graphite behavior has been the subject of research and development in support of graphite-moderated reactor design and operations The materials physics and chemistry, as well as the behavior of nuclear graphite under neutron irradiation are well characterized and understood, although new high-resolution characterization tools, such as HRTEM and STM, and other nanoscale characterization techniques, coupled with powerful computer based simulations of crystal deformation and displacement damage, are yielding new insights to the deformation mechanisms that occur in graphite throughout its life in the reactor core Perhaps the biggest remaining challenge is to gain a fuller understanding of irradiation-induced dimensional change and irradiation creep in graphite Currently, new creep irradiation experiments are underway at ORNL in the High Flux Isotope Reactor, and at Idaho National Laboratory in the Advanced Test Reactor Studies of pore structure change from 323 unirradiated reference samples, irradiated unstressed samples (controls), and irradiated stressed samples (crept samples), may advance our understanding of pore generation Work in other countries is directed at reviewing existing creep data and assessing the observable graphite dimensional changes and creep strain in currently operating reactors A recent Coordinated Research Project initiated by the International Atomic Energy Agency (IAEA) has the goal of bringing these various strands of research together to form a single unified theory of irradiation-induced creep deformation in graphites The knowledge gained through these many years of work, and 50 years of graphite-moderated reactor operating experience is currently being used to underwrite the safety cases of graphite reactors through out the world In the first part of the twenty-first century, more knowledge will be gained from the new graphitemoderated reactors in Japan and China that operate at higher temperatures Several nations (within the Generation IV International Forum) are pursuing high-temperature, graphite-moderated, gas-cooled reactor projects with the goal of developing versatile and inherently safe reactor systems that can efficiently deliver both process heat and electricity With the realization and acceptance that greenhouse gas emissions from fossil fueled power plants are causing global climate changes, as evidenced by the Kyoto and recent Copenhagen Agreements, the nuclear option may once again become attractive for clean electric power generation At that time, it is to be hoped that inherently safe, graphite-moderated, gas-cooled reactors may find renewed popularity Acknowledgments This work is sponsored by the US Department of Energy, Office of Nuclear Energy Science and Technology under contact DE-AC05-00OR22725 with Oak Ridge National Laboratories managed by UT-Battelle, LLC References Burchell, T D In Carbon Materials for Advanced Technologies; Burchell, T D., Ed.; Elsevier Science: Oxford, 1999; pp 429–484 Eatherly, W P.; Piper, E L In Nuclear Graphite; Nightingale, R E., Ed.; Academic Press: New York, 1962; pp 21–51 Ragan, S.; Marsh, H J Mater Sci 1983, 18, 3161–3176 324 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Radiation Effects in Graphite Inagaki, M In Graphite and Precursors; Delhae`s, P., Ed.; Gordon & Breach Science: The Netherlands, 2001; pp 179–198 ASTM D 7219 Standard Specification for Isotropic and Near-Isotropic Nuclear Graphites, Annual Book of Standards; ASTM International: West Conshohocken, PA, 2010; Vol 05.05 ASTM D 7301 Standard Specification for Nuclear Graphite Suitable for Components Subjected to Low Neutron Irradiation Dose, Annual Book of Standards; ASTM International: West Conshohocken, PA, 2010; Vol 05.05 Ruland, W Chem Phys Carbon 1968, 4, 1–84 Kelly, B T In Materials Science and Technology: A Comprehensive Treatment: Vol 10A – Nuclear Materials; Cahn, R W., Haasen, P., Kramer, E J., Eds.; Wiley-VCH: Weinheim, 1994; pp 365–417 Kroto, H W.; Heath, J R.; O’Brien, S C.; Curl, R F.; Smalley, R E Nature 1985, 318, 162–163 Iijima, S Nature 1991, 354, 56–58 Banhart, F Rep Prog Phys 1999, 62, 1181–1221 Thrower, P A.; Meyer, R M Phys Status Solidi A 1978, 47, 11–37 Kelly, B T Physics of Graphite; Applied Science: London, 1981 Burchell, T D In Physical Processes of the Interaction of Fusion Plasmas with Solids; Hofer, W O., Roth, J., Eds.; Academic Press: San Diego, CA, 1996; pp 341–384 Telling, R H.; Heggie, M I Philos Mag 2007, 87, 4797–4846 Hehr, B D.; Hawari, A I.; Gillette, V H Nucl Technol 2007, 160, 251–256 Nakai, K.; Kinoshita, C.; Matsunaga, A Ultramicroscopy 1991, 39, 361–368 Wallace, P R Solid State Commun 1966, 4, 521–524 Jenkins, G M Chem Phys Carbon 1973, 11, 189–242 Urita, K.; Suenaga, K.; Sugai, T.; Shinohara, H.; Iijima, S Phys Rev Lett 2005, 94, 155502 Tanabe, T Phys Scripta 1996, T64, 7–16 Koike, J.; Pedraza, D F J Mater Res 1994, 9, 1899–1907 Jenkins, G M Carbon 1969, 7, 9–14 Ouseph, P J Phys Status Solidi A 1998, 169, 25–32 Amelinckx, S.; Dellavignette, P.; Heerschap, M Chem Phys Carbon 1965, 1, 1–71 Engle, G B.; Eatherly, W P High Temp High Press 1972, 4, 119–158 Price, R J Carbon 1974, 12, 159–169 Burchell, T D.; Snead, L L J Nucl Mater 2007, 371, 18–27 Simmons, J W H Radiation Damage in Graphite; Pergamon: Oxford, 1965 Brocklehurst, J E.; Kelly, B T Carbon 1993, 31, 155–178 Kelly, B T.; Burchell, T D Carbon 1994, 32, 499–505 Nightingale, R E Nuclear Graphite; Academic Press: New York, 1962 Arnold, L Windscale 1957, Anatomy of a Nuclear Accident; St Martin Press: London, 1992 Rappeneau, J.; Taupin, J L.; Grehier, J Carbon 1966, 4, 115–124 Tucker, M O.; Rose, A P G.; Burchell, T D Carbon 1986, 24, 581–602 Burchell, T D Carbon 1996, 34, 297–316 Burchell, T D.; Eatherly, W P J Nucl Mater 1991, 170–181, 205–208 Ishiyama, S.; Burchell, T D.; Strizak, J P.; Eto, M J Nucl Mater 1996, 230, 1–7 Burchell, T D In Graphite and Precursors; Delhae`s, P., Ed.; Gordon & Breach Science: The Netherlands, 2001; pp 87–109 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 Burchell, T D MRS Bull 1997, XXII, 29–35 Taylor, R.; Kelly, B T.; Gilchrist, K E J Phys Chem Solids 1969, 30, 2251–2267 Snead, L L.; Burchell, T D J Nucl Mater 1995, 224, 222–229 Bell, J C.; Bridge, H.; Cottrell, A H.; Greenough, G B.; Reynold, W N.; Simmons, J W H Phil Trans R Soc London Ser A 1962, 245, 361–395 ASTM C 781 Standard Practice for Testing Graphite and Boronated Graphite Materials for High-Temperature Gas-Cooled Nuclear Reactor Components, Annual Book of Standards; ASTM International: West Conshohocken, PA, 2010; Vol 05.05 Hust, J G NBS Special Publication 260–89; U.S Department of Commerce, National Bureau of Standards: Gaithersburg, MD, USA, 1984; p 59 Tsang, D K L.; Marsden, B J In Management of Ageing Processes in Graphite Reactor Cores; Neighbour, G., Ed.; RSC: Cambridge, 2007; pp 158–166 Li, H.; Fok, A S L.; Marsden, B J J Nucl Mater 2006, 372, 164–170 Wang, H.; Yu, S Nucl Eng Des 2008, 238, 2256–2260 Davies, M.; Bradford, M J Nucl Mater 2008, 381, 39–45 Burchell, T D J Nucl Mater 2008, 38, 146–154 Kelly, B T.; Burchell, T D Carbon 1994, 32, 119–125 Haag, G Properties of ATR-2E Graphite and Property Changes due to Fast Neutron Irradiation; Report No Jul-4183; Published FZ-J, Germany, 2005; Available at http://juwel.fz-juelich.de Kelly, B T.; Foreman, A J E Carbon 1974, 12, 151–158 Martin, D G.; Henson, R W Philos Mag 1967, 9, 659–672 Martin, D G.; Henson, R W Carbon 1967, 5, 313–314 Kelly, B T.; Simmons, J H W.; Gittus, J H.; Nettley, P T In Proceedings of the Third United Nations Conference on Peaceful Uses of Atomic Energy; IAEA: Vienna, 1972; Vol 10, p 339 Heggie, M I.; Davidson, C R.; Haffenden, G L.; Suarez-Martinez, I.; Campanera, J.-M.; Savini, G In Proceedings of CARBON 2007; American Carbon Society: Oak Ridge, TN, 2007 Kelly, B T.; Brocklehurst, J E J Nucl Mater 1977, 65, 79–85 Jouquet, G.; Kleist, G.; Veringa, H J Nucl Mater 1977, 65, 86–95 Oku, T.; Eto, M.; Ishiyama, S J Nucl Mater 1990, 172, 77–84 Hansen, H.; Loelgen, R.; Cundy, M J Nucl Mater 1977, 65, 148–156 Brocklehurst, J E.; Brown, R G Carbon 1969, 7, 487–497 Kennedy, C R In Conference 901178-1; ORNL: Oak Ridge, TN, 1990 Brocklehurst, J E.; Kelly, B T Carbon 1993, 31, 155–178 Kelly, B T Carbon 1992, 30, 379–383 Kennedy, C R.; Cundy, M.; Kliest, G In Proceedings of CARBON’88, Newcastle upon Tyne, UK, July 1988; Institute of Physics: London, 1988; pp 443–445 Kelly, B T.; Martin, W H.; Nettley, P T Philos Trans R Soc 1966, A260, 51–71 Davies, M A.; Bradford, M R In Management of Ageing Processes in Graphite Reactor Cores; Neighbour, G B., Ed.; RSC: Cambridge, 2007; pp 100–107 Bradford, M R.; Steer, A G J Nucl Mater 2008, 381, 137–144 Gray, W J Carbon 1973, 11, 383–392 Burchell, T D Irradiation Induced Creep in Graphite at High Temperature and Dose – A Revised Model; ORNL/TM-2008/098; Oak Ridge National Laboratory: Oak Ridge, TN, Feb 2009 ... Burchell, T D In Graphite and Precursors; Delhae`s, P., Ed.; Gordon & Breach Science: The Netherlands, 2001; pp 87 109 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66... 310 Radiation Effects in Graphite 10 H -45 1 @ 600 ЊC H -45 1 @ 900 ЊC Volume change (%) -2 -4 -6 -8 -10 Fast fluence 102 6 n m-2 [E > 0.1 MeV] Figure Irradiation-induced volume changes for H -45 1 graphite. .. irradiation-induced creep of graphite was proposed by Kelly and Foreman53 which involves irradiation-induced basal plane dislocation pinning/unpinning in the graphite crystals Pinning sites are