Discussion of the diffusion mechanism in graphite with particular reference to irradiated material

Carbon

1969, Vol. 7. pp. 119-147.

Pergamon

Press.

Printed

in Great

Britain

DISCUSSION OF THE DIFFUSION MECHANISM IN GRAPHITE WITH PARTICULAR REFERENCE TO IRRADIATED MATERIAL C. ROSCOE Department of Materials Science, Fuel Science Section, The Pennsylvania State University, University Park, Pa. 16802, U.S.A. (Received 12June 1968) Abstract-Principally due to doubt concerning the activation energy of interstitial formation, Eli, it has been difficult to differentiate between an interstitial and vacancy mechanism for self-diffusion in graphite. However, the recent studies of Turnbull and Stagg, which have been verified by Thrower, yield a value of 8.3 rt 0.3 eV for the activation energy of diffusion occurring both in pyrolytic and naturally occurring gra hites. This value was identified with E,+ +(E, + E,,). By considering the structural pe K ection of the graphites employed by the above authors, it has been concluded here that there is no necessity to assume a discrete value describing E,. Rather the observed activation energy, E*, is interpreted as the summation of +(E,‘+ Efu)+ EL,, which implies that self diffusion occurs via a dynamic interchange mechanism. It is implicit for the operation of this mechanism that the matrix should contain sites of high vacancy concentrations, such as intercrystallite boundaries. If the value of Ef is assumed to be 7.0 -C0.5 eV, the values of 8.8 k O-6 and 9-4 +-O-6 eV are derived for E,‘, when the experimental and theoretical values of Eim are substituted, respectively. The latter number is in fairly close agreement with both Coulson’s theoretical value and that determined experimentally by Murty 9% +- 043 eV. 1. INTRODUCTION There seems little to dispute the fact that graphite will in the future retain its unique role in the fabrication of nuclear reactors. Despite this, the processes which occur in this material both during irradiation and subsequent high temperature annealing remain imprecisely understood. The literature does. however, contain a considerable number of attempts to identify both the activation energies for the formation and mobility of the point defects incurred during irradiation r1,21. The experimental values for the activation energies of vacancy formation EfD = 7-O+ 0.5 eV, and vacancy diffusion in (0001) a planes E,& = 3-l 20.2 eV, have gained of acceptance [3-51. The large measure modified calculations of Coulson et al. [6] do in fact provide confirmation for this value of

Ef’. These values, which imply that the activation energy for self-diffusion occurring via a vacancy mechanism is 2 10.1 eV, will be adopted throughout the remainder of this text. The data concerning the corresponding values for interstitials are more confused. The theoretical calculations of Co&on et aZ.[7] predict that Ef’ should correspond to 9.76 eV. However, this value is highly dependent on the particular model taken to represent the interaction potential between the appropriate carbon atoms. The same authors calculate E&, as 0~14eV which is somewhat lower than that determined experimentally, O-4 f O-1 eV, by Goggin and Reynolds [8]. The desirability for further fundamental research in this same general area has gained even more impetus since the observation of the anomalous behaviour of graphite when irradiated to doses in excess of lO*Oneutrons/ 119

C. ROSCOE

120

cm5, i.e. above the so termed breakaway value[9-111. The resulting studies of Turnbull and Stagg[l2] and Thrower[2,5] are particularly informative. The most pertinent features of this work will now be summarized and subsequently discussed in terms of the structural perfection of the various graphites employed. Finally two modes of diffusion are considered to explain the experimental observations made during irradiation and thermal annealing above 2100°C. 1.1 TurnbuUandStagg[l2] By employing a succession of isothermal anneals at temperatures between 2100” and 2600% Turnbud and Stagg were able to conclude that both interstitial and vacancy loops annealed with a common activation energy, E * = 8.3 zt 0.3 eV. The observed rate of change of the loop radius with time, R, was found to be represented by

R =-A

exp(-E*IkT)

- {B/R-G}

(la)

where A and B are constants, and, G is a function of temperature. Since R varies linearly with l/R, and in the case of an interstitial loop, is either positive or negative depending on the loop being larger or smaller than a critical radius, R,, the kinetic processes must be diffusion controlled. Consequently_, in the theoretical approach of calculating R derived by Baker and Kelly@41 from Friedel’s theory of dislocation climb, fi=-

Zxvdaexp (y)

exp (G)

*

C, # Co. Here C, is the concentration of defects at a site adjacent to the defect loop and CO the predicted thermal equilibrium concentration. a&/R and /3 are respectively, the driving forces for climb due to the line tension and the stacking fault energy. By solving the appropriate time independent

diffusion equations for C1 and substituting in equation (1b), Turnbull and Stagg were able to show that an expression of the form represented by equation (la) was possible only for diffusion occurring in an anisotropic crystal, with the dislocation loop approximated to a long straight dislocation. E* was identified with E,++(E,+E,,), where E, is the activation energy for the diffusion of the appropriate type of point defect along the c-axis. However, it is suggested here that a clearer insight into the implications of the value of E* can be gained by considering the modifications to the structural perfection of the naturally occurring crystals employed, during the introduction of the imperfections, (see Section 3). Vacancy loops were introduced to the crystals in two ways: namely, by annealing between 2ooo” and 2200% in a vacuum of - lo+ Tot-r. and annealing crystals substitutionally boronated to the extent of 4 per cent. The authors state that the first of these methods introduces loops predominantly in deformed crystals containing twist boundaries or twins. It is now assumed that the loops were in fact formed at the more favorable sites of intercrystallite boundaries [13,14]. The method for the growth of the boronated crystals[15] also strongly suggests that the thermal annealing of vacancy loops formed in this material would be influenced by the presence of intercrystallite boundaries. (The crystals were actually grown by heating amorphous boron at 2500% in a crucible made from reactor grade graphite.) The L, dimensions of these crystals would be expected to be relatively small, since it is known that the addition of only 05-1.0 per cent substitutional boron markedly increases the number of intercrystallite boundaries traversing Ticonderoga crystals [ 161. Interstitial loops were formed by irradiating the crystals to doses of 3 and 5 X loZ” neutrons/cm* at temperatures of 150 and 260°C respectively. The character of the damage to the crystal lattice under these

DIFFUSION

MECHANISM

conditions is such that an appreciable concentration of interstitials is formed which cannot be removed by thermal annealing. The effect this distortion of the lattice can exert on the diffusion mechanism is discussed more fully in Section 3.2. 1.2 Thrower[2,5] By investigating the modes of defect nucleation and thermal annealing in three different graphites irradiated to doses of 11.7 x loZ” neutrons/cm* at 135O”C, Thrower was able to confirm the anisotropic diffusion model of Turnbull and Stagg (Section 2.1). Moreover, the author has pointed out that the overall change in entropy, AS, occurring during the diffusion process can be determined by considering the pre-exponential component of equation (la), Ahs A = Zxual’* expk - F-l.

(2)

IN GRAPHITE

121

material, respectively. In the single crystals the damage took the form of the familiar large interstitial loops surrounded by clusters of much smaller vacancy loops. However, in the 2900P material only a homogeneous distribution of vacancy loops, radius - 40 A, and very large interstitial loops, - lop, residing within twist boundaries were observed. The character of the defects in the 3600P material varied between that described for single crystals and the 2900P material. The above observations were explained in terms of anisotropic diffusion rates of single interstitials parallel and perpendicular to the {OOOZ} planes. The value of EI, was then derived from the thermal annealing processes occurring in the pyrolytic material by making the following assumptions: The mean half separation distance between interstitial nuclei in a basal plane, rl, is - 3.5 CL.This is the value observed in single crystals. The average value of L, in the 2!WOP material is 6d(OOO1). The crystal perfection in the basal plane is equivalent to that of single crystals. Roscoe and Baker [ 141 have subsequently shown that this is not a valid assumption (see Section 3). There will be a critical crystallite thickness, tc, below which the interstitials will diffuse to a twist boundary rather than to an interstitial nucleus. Then, from the equations representing diffusion of an interstitial perpendicular,

(In equation (2), 2 H coordination number, u - geometric mean of the atomic vibration frequencies parallel and perpendicular to the basal planes, a = area per atom in the basal plane, and x = jog density. F = 1+ l-4 xui’*/ 2&ln l2/e,, where lz/e1, represents the ratio of the outer boundary to that of the inner boundary for diffusion). From the data of Turnbull and Stagg, A = 101s-1019 which yields a value of - 11 K for AS. Thrower assumed that the principal contribution to this latter value comes from AS, and hence concluded that diffusion must be controlled by the formation and mobility of interstitials D, = 3d,%, = D, exp (-E&&T) as opposed to vacancies It was inferred that (3) AS, is so large because the interstitial is in and parallel to the {OOOZ}planes, some manner bound to the lattice. D, = &.&,%I,= D, exp (-&Ml Another important observation made by (4) Thrower[5] concerns the significant difference in the defects nucleated in the three a value for ELEf, was derived assuming different materials employed, which were D,. Thrower modifies the number of &namely single crystals and two pyrolytic jumps required to reach a twist boundary, so graphites heat treated to 2!900 and 3600°C. that (3) and (4) yield, These two pyrolytic graphites will sub lSu,-’ < : (r&.&)‘LJ,-’ sequently be referred to as 2900P and 36OOP

l!?!?

C. ROSCOE

extremely important conclusion reached by the authors was that the observed basal plane contraction could not be attributed merely or l&= 2.8 f 0.2 eV. (5) to the contraction expected by relaxation at single vacancies, together with a Poisson ratio Substituting the values E, = 2.8 f O-2 eV contraction due to the expansion along the andE* = 8.3 -C0.3 eV in (0001) direction. Both Kelly et uZ.[9, lo] and Williamson and Horner [ 1l] found it necessE* = E/i++(Ejj+EL) ary to postulate the occurrence of irregular vacancy lines in the layer planes, which Ej = 67 2 0.5 eV. (6) collapsed above a critical length. Since the maximum irradiation temperature employed This value for Ef’ is appreciably lower than was only 65O”C, it was necessary to postulate that calculated by Co&on, but it does concur that the formation of these lines was governed with the value for the activation energy of either, by the presence of an existing defect or, the statistical probability of forming a self diffusion in the basal planes as determined by Kanter, Es0 = 7-l + 0.5. row of vacancies under the conditions of The value of Efm was tentatively assumed irradiation. At the time the former possibility to arise from the interaction potential as- was thought unlikely. Although Mayer [19] was principally consociated with an interstitial diffusing through with substitutionally boronated the open hexagons of the basal planes. Some cerned verification for this assumption is forthgraphite, his notions with regard to the coming from theoretical calculations of this mechanism of boron diffusion within the interaction potential using the approach of graphite lattice are very pertinent to this Setton[7]. However, as pointed out by discussion. He considered that self-diffusion Thrower, similar calculations do not lead to and the diffusion of substituted boron may acceptable values for E&,. well occur by the same process. A dynamic Another objection to the model described interchange mechanism, as opposed to a above concerns its inability to satisfactorily direct interchange mechanism, was proposed explain the observation that the dimensions in which interstitials move rapidly between of the loops residing in the twist boundaries the layer planes until they are able to reenter decrease with increasing c-axis perfection. the lattice by recombination with a vacancy. It However, this and the other anomalies as- was assumed that E’,, = Eim and D, > D,, sociated with this model are more readily conditions which are directly opposed to explained if one assumes a decrease in interthose postulated by Thrower. The initial diffusion of boron was assumed stitial loop size, within the twist boundaries, to occur via the spiral ramps present at the with increasing values of L, (see Section 3). sites of forest screws. In cognizance of the 1.3 Related studies exceedingly large Burgers vectors of these It is relevant at this juncture to mention the dislocations, >500 A in Ticonderoga crystals, studies of Kelly et al.[9] concerning the it is reasonable to assume that diffusion of dimensional changes occurring during irraboron will also occur via the dislocation core. dination to neutron doses of 1-15 x lO*O/cm*. However, this would merely promote the formation of large boron interstitial clusters In the hope of simulating the effects expected the authors used the in the twist boundaries: in a monocrystal, diffusion of this same pyrolytic materials mentioned above in boron to substitutional sites must then occur mechanism. connection with the studies of Thrower. One by the dynamic interchange (where u, and u, - the respective jump frequencies) when, F* - E’,, = 2.3 f O-2 eV.

DIFFUSION MECHANISM IN GRAPHITE

(Since crystals boronated to an extent of 10 ppm to 1 per cent wt/wt were employed, the possibility again exists that intercrystallite boundaries play some role in the diffusion process.) 0. MODELS FOR DIFFUSION The possible models for diffusion are now discussed first in terms of the thermal annealing studies of Thrower, Section 2.2, on irradiated 2900P and 36OOP pyrolytic graphites. Roscoe and Baker [14] have found the average value of L, for a material similar to the 36OOP graphite to lie on average between l-40 /.L.The value of L, for this same material varied from 100 A to that normally associated with naturally occurring single crystals. Consequently, the intercrystallite boundaries can afford the interstitials a pathway for diffusion along the c-axis and there is no necessity to assume interstitials diffuse through the open hexagons of a basal plane. The threedimensional network of pathways for diffusion are schematically represented in Fig. 1. Other possibilities for diffusion along the ‘c’-axis include the sites of substitutional boron [ 191, present as an impurity, and forest screws. Roscoe and Baker [14] observed the concentrations of the latter defects within the confines of the intercrystallite boundaries to be variable between 103-1V cm+. Although it must be stated that the screws were predominantly of unit Burgers vector and traversed only a few basal planes. However,

123

there appeared to be a much higher density of screws contained within the boundaries and, moreover, these screws traversed the material for appreciably greater distances along the ‘c’axis. 2.1 Two mechanisms fo7 C-axis intemystallite boundaries

via

The intercrystallite boundaries in high temperature stress-annealed pyrolytic graphites are known to vary widely in their complexity. This variation extends from the low angle tilt boundaries comprised of forest edges, which are prevalent in Ticonderoga crystals, to high-angle boundaries where there is considerable lattice distortion across’s ribbon >lOO 8, in width, as measured in a direction perpendicular to the boundary trace. The high-angle boundaries are in fact by far the most numerous, but it remains a possibility that the kinetics of diffusion may be dependent on the boundary type as discussed in Sections 2.2 and 2.3. 2.2 Dajksion dislocations

controlled by freest edge and screw

The activation energy of dislocation loop annealing on any model in which diffusion along the ‘c’-axis is controlled by forest dislocations can be described by, E* = EI’++(E&+EL). For

forest

edge

dislocations

tFig. 1. The three dimensional

da&km

network of pathways

for diffusion.

the minimum

124

C. ROSCOE

interaction potential with an interstitial, calculated after the manner of Setton[7,17], yields a value of -2 eV for &. Then assuming forest edge dislocations are responsible for the value of E * = 8.3 rf: O-3 eV, and that EL, = O-4i- 0.1 eV , Ef’ d 7+1eV.

(7)

For forest screws, the value of EfK might be expected to decrease with increasing values of their Burgers vector. In the case of TiconF;;T c~tals, where the latter are usually fm = E’,. This result is also expected ;br diffusion down the spiral ramp of a forest screw, so that E* = E,1+EL when Eff = 7.9kO.4 eV.

(8)

Consequently on this model the value of E’! and E* can be variant because of their dependency on the nature, and possibly the Burgers vector, of the lattice imperfections which determine the kinetics of diffusion in the ‘c’direction. It is emphasized that the same value of E* has been obtained using several types of material. Thii implies that in all probability the same imperfections were responsible for the rate controlling step determining diffusion along the c-axis. By making thii premise, it becomes extremely unlikely that the measured value of 8.3 ItO- eV includes a term indicative of diffusion occurring at forest screws. The probability of preparing a &itable sample of Ticonderoga graphite for transmission electron microscopy which contains such a dislocation is very slightf201. Hence, this casts considerable doubt upon the validity of the value, E,’ = 7*9_tO-4 eV, obtained from equation (8). 2.3 ~~~ v&a~~~~~ As stated earlier there is considerable distortion of the crystal lattice at the sites of

high-angle intercrystallite boundaries. It is now postulated that for this reason, both under the conditions of irradiation and high temperature annealing, >21OO*C, the equilibrium concen~ation of vacancies in the region of intercrystallite boundaries is far in excess of that pertaining to the relatively more perfect portions of the material. Some experimental verification for this assumption was obtained by determining the concentrations of su~dtution~ boron in a stress annealed pyrolytic graphite[l4]. (Because of its smaller atomic volume boron should preferentially residue at sites of lattice distortion ordinarily occupied by vacancies.) Although the overall impurity level for this element was between i-2 ppm wtlwt, the concentration within the boundaries was found to be - 10s ppm wt/wt. Even so, the overall boron concentration is very low, and it is far from certain that the lattice distortion was completely accommodated by boron atoms. Therefore, particularly above 21OO”C, the vacancy concentrations at intercrystallite boundaries should be in excess of 1 per 103 carbon atoms. Under the conditions of irradiation empbyed[5,9,12] there is a distinct ~sibi~~ that the vacancy lines psotulated by Kelly et a1.[9, lo] will in fact be nucleated in these boundaries. Collapse of the vacancy lines would then facilitate shrinkage of the crystall&es across the basal planes, but would not alleviate the lattice distortion associated with the relative misorientation between neighbouring crystallites. This implies that at least the enhanced thermal equilibrium concentration of vacancies will be maintained irrespective of the number of vacancy tines that are formed and subsequently collapse at the boundaries. At the temperatures employed for thermal annealing, >21WC, this concentration of vacancies would allow a dynamic interchange mechanism for diffusion to take place. This implies that the recombination of vacancies and interstitials occurs at the intercrystallite

DIFFUSION

MECHANISM

boundaries, with the subsequent formation of a Frenkel pair to satisfy the physical constraints of the lattice at these sites. The operation of this model obviously entails the diffusion of interstitials both in the ‘a’ and ‘c’directions. The observed activation energy can then be represented by,

IN GRAPHITE

125

where E, = sublimation energy, 744 eV [21]; EST= the self energy, or strain energy

associated with an interstitial in the position of minimal interaction energy with the lattice when inserted between two adjacent (0001) planes. Coulson[7] obtained a value of EST= 2.32 eV assuming the interaction energy could be represented by the model of E*=#(E,'+E,")+EL,. (9) Crowell[22]; Eb * binding energy of the interstitial; EP = energy change due to the In order to satisfy the condition C, > C,, change in position of an atom in the lattice. Both EQ and EP were neglected in the calcu(Section 2.1) it is merely necessary to assume lations of Coulson, EP will also be neglected that the diffusing atoms, which are emitted here. Substituting in equation 10 the value from interstitial loops, must compete for the available vacancy sites at the boundaries. For En = 2.32 eV and the conditions R < R, a greater proportion E'< 7*1eV of the total number of interstitials, N, emitted (i) E',z 2-7 eV from such a loop will recombine with the available vacancies than for the case R > R,. (ii) (a) Ef'= ;_;+;;',"v *2 . OR (b) E,'=9.4a0.6 This simply follows from the direct relationEB= -. EB = O-3(* 0.8)eV. ship that exists between N and R. Consequently, the concentration of diffusing Since the value of EB should be G Efma, the interstitials in the proximity of the small value of E,'= 8.8 2 0~6 eV (or alternatively loops is depleted and the latter shrink, whilst 9.4&O*6) obtained using the dynamic interthere must be a net flow of interstitials to the change model certainly appears the more immediate vicinity of the larger loops causing realistic. It must then be concluded that them to grow. whilst some diffusion may take place in the Substituting the experimentally deterpyrolytic material via forest dislocations, the mined values for E*, 8-3&O-3 eV, and EL dynamic interchange mechanism postulated 0-4-t O-1 eV, in equation (9), above is rate controlling. Consequently, value of 7-l + O-5 Ef ’ = 8.8 + O-6 eV. (9a) Kanter’s [23] experimental eV for the activation energy of self diffusion, Alternatively, if the theoretically calculated even when restricted to (0001) planes, is value of Efno, O-14 eV, is used, too low. The very recent work of Murty et a1.[15] Ef'= 9*4&0.6eV. (9b) does in fact provide further experimental support for the value of Effderived from This latter value is in fairly close agreement equation (9). This author found that the with Coulson’s value of 9.76 eV. activation energy for the graphitization of It is pertinent at this juncture to compare three different cokes had the discrete value the values of E,'predicted by the first model for diffusion, s 7-l eV, and the present of 9.8 &O-6 eV. In this instance the graphitimodel, either 8*8+0*6 eV or 9*4&O-6 eV, zation process can only proceed via an interwith that predicted theoretically. According stitial mechanism [ 151, in which to Thrower [2],

E*=Efi+Ed.

Ef’

=E,+EST-E,,+EP

(10) It might be expected that Em*,which probably

126

C. ROSCOE

denotes the activation energy for the migration of an interstitial along the surface of a crystalhte, would be lower than EL, which describes diffusion between planes separated by only 335 A, Therefore from this work the value of 9.6 +- 0.8 eV can be ascribed to Efi, Finally, the observed entropy change can be related to the difference between E* for the diffusion of inter&As at the intercrystallite boundaries, 8-3 +0+3 eV, and the formation and migration of interstitials at the periphery of an interstitial loop. From the calculations of Coulson, E* in the latter instance should correspond to 9*9eV, provided Em = 2.32 eV at a lattice site adjacent to an interstitial loop. (In the limiting case it is possible that E* = Es, when EL = Esr+E’,,). Note, the experimentally determined activation energy always describes the rate controlling process which is assumed here to involve diffusion at intercrystilite boundaries. Then,

8.3 A O-3 eV for E*. The annealing behaviour exhibited by the interstitial and vacancy loops introduced by the neutron irradiation of Ticonderoga crystals still requires explanation. Perhaps the most plausible interpretation is to assume that under the conditions of irradiation severe distortion was induced in the crystal lattice, so that sites analogous to intercrystallite boundaries were created. This distortion could well have originated in the stress field of forest screws, as the irradiations were carried out on the bulk crystals. These dislocations are known to be associated with both the alignment of vacancies and, under the appropriate conditions, the formation of boundaries in stress-annealed pyrolytic graphite[l4]. The net result of the proposed distortion would be to allow once again the operation of a dynamic interchange mechanism for diffusion.

3.3 Fe of large in~sti~ loops within tit boundaries during irradiator ~=~9~9--8~3)x1~6x10-“,~=g~ The formation of the large interstitial loops 2100 x 1.38 x lo-r6 occurs in the bulk crystal and therefore it is where T is taken as 2100°C. The value of as‘ possible to invoke the model of Section 2.1 to describe their kinetics of formation. The obtained in this manner is in good agreement activation energy for interstitial loop formawith the number derived from equation (2). tion will in this instance be given by E* = 2.4 A#&cahnz of the d@sion models to thL? )(Et,, +Ek,) or alternatively if diffusion along studies involving Ticmuieroga mystais the ‘c’-axis occurs only via the spiral ramps associated with forest screws, E* = EL,. ft has already been stated, Section 2.2 that diffusion in the (0001) direction is unlikely Thrower found that the interstitial loops to be controlled by forest screws. However, lying in the twist boundaries of Ticonderoga for the experiments of Turnbull and Stagg crystals were the same size as normal interstitial loops. This result would be expected which involved the annealing of vacancy for at least three reasons. First, the pathways loops, the method of introducing the latter for ‘&‘-axis diffusion, for example forest almost certainly implies that the diffusion screws, are considerably more numerous in kinetics were modified by the close proximity of intercrystallite boundaries, (Section 2.1). pyrolytic graphites than in most Ticonderoga crystals. Second, whereas a great majority of Under these conditions a dynamic interthe forest screws in pyrolytic graphite are change process is undoubtedly an integral terminated at the twist boundaries, this is and rate controlling part of the observed certainly not the case in Ticonderoga crysanisotropic diffusion mechanism, It is therefore no surprise that both singie crystals and stals[26]. Finally, although some large pyrolytic material yield the same value of interstitial loops should be formed in the

DIFFUSION MECHANISM IN GRAPHITE

immediate region of a forest screw, it is unlikely that they will be observed because of the process of sample preparation. Acknowledgmtntc-The author wishes to thank Dr. P. L. Walker, Jr. for his continued interest in this work and the A.E.C. for financial support on project AT(SO-l)-1710. REFERENCES

1. Reynolds W. N ., &m&y and Physics ofCarbon, Vol. 1, p. 1. Marcel Dekker, New York (1965). 2. Thrower P., Che&try and Physics of Carbon, Vol. 4. Marcel Dekker, New York (1968). 3. Hennig G. R., I. Cha. Phw. 42,1167 (1965). 4. Henso; R. W.“and Reynolds W. N., ‘Carbon 3, 277 (1965). 5. Thrower P. A., Eighth Biennial Conf: on Carbon, Buffalo. 6. Co&on C. A., Herraez M. A., Lea1 M., Santos E. and Sennet S., Proc. Roy. Sot. A273, 461 (1963). 7. Coulson C. A., Sennet S., Herraez M. A., Leal M. and Santos E., Carbon& 445 (1966). a. Goggin P. R. and Reynolds W. N., Phil. Mag. 8,265 (1963). 9. Kelly B. T., Martin W. H. and Nettley P. T., Phil. Trans. Roy. Sot. 460,37 (1966).

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10. Kelly B. T., Proc. Second Industrial Carbon and Graphite Con., London. 11. Williamson G. K. and Horner P., J. Br. Nucl. Enqy Sot. 3,269 (1964). 12. Turnbull J. A. and Stagg M. S., Phil. Mag. 14, 1049 (1966). 13. Roscoe C. and Thomas J. M., Carbon 3, 373 (1965). 14. Roscoe C. and Baker J., J. A#. Phys. To be published (1969). 15. Turnbull J. A., Stagg M. S. and Eeles W. T., Carbon 3,387 (1966). 16. Thomas J. M. and Roscoe C., Eighth Biennial Conf. on Carbon, Buffalo. 17. Setton R., Bull. Sot. Chim. 1758 (1960). 18. Bollman J. W., J. Appl. Phys. 34,869 (1961). 19. Mayer R. M., Ph.D. Thesis, University of Cambridge. 20. Hennig G. R.. Sctie 147.733 (1965). Phys. 29, 21. Knigh; H. T. and Rink J. P., j. CL. 449 (1958). 22. Crowell A. D., J. C/m. Phys. 29,446 (1958). 23. Kanter M. A., Phys. Rev. 107,655 (1957). 24. Baker C. and Kelly A., Nature 193,235(1962). 25. Murty H. N., Biederman D. L. and Heintz E. A., Carbon To be published (1969). 26. Roscoe C. and Thomas J. M., Proc. Roy. Sot. A!z97,397 (1967).