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Internal friction study of annealing processes in pile-irradiated graphite
Cnrbon
1969, Vol. 7, pp. 379-384.
Pergamon
Press.
Pnoted
in Great
Britain
INTERNAL FRICTION STUDY OF ANNEALING PROCESSES IN PILE-IRRADIATED GRAPHITE M. SAITO*, M. BABA*, K. KAWAMURA and T. TSUZUKU College of Science and Engineering, Nihon University, Kanda-Surugadai, Chiyoda-ku, Tokyo,Japan
Abstract-A reactor grade graphite irradiated by fast neutrons at 30°C to the total dose of 5% x 102* nvt was stepwise annealed between 100” and 23OO”C,and was examined each time by measuring the internal friction and dynamic modulus at temperatures from 300” down to 80°K. The recovery process has been found to consist of three stages; the first stage occurring between 100” and 5OO”C,the second one in the range from 660” to 115O”C, and the third one between 1200” and 2300°C. In the first stage the dynamic modulus recovers for the most part, while the internal friction indicates little change. On the other hand, the recovery of internal friction arises mostly in the third stage where the dynamic modulus shows only a slight fall-off. In the second stage no serious change arises in the anelastic properties. A qualitative explanation for the formation and decomposition processes of interstitial clusters is given within the framework of the Granato-Liicke theory in relation to the behavior of such anelastic properties. 1. INTRODUCTION Internal
friction
(mechanical
expected to play the principal role in the damping mechanism [Z]. As stated in a previous paper[2], the impurity atoms and their clusters which have precipitated onto dislocations through Cottrell’s mechanism [3] are believed to behave because of the extremely anisotropic crystal structure of graphite in such a complicated way that they act either as pinning agents or as viscous drag, in accordance with their geometrical size relative to the size of the dislocation core. This situation would be common to the knocked-on atoms, vacancies and their clusters in the radiationdamaged graphite. are
damping)
is defined as the rate of internal energy dissipation per cycle in a vibrating solid specimen; it is, in practice, represented by the logarithmic decrement of freely-decaying vibration or the half-value width of the resonance curve. In the case of crystalline solids, such a mechanical damping is thought to be caused mainly by the oscillatory motion of dislocation lines undergoing some viscous friction. In this context, a theory based on the so-called vibrating-string model has been proposed by Granato and Liicke[l] and was greatly successful in dealing with a number of experimental data. Hence, it is worthwhile attempting to test this theory in describing the annealing process of radiationdamaged graphite, since dislocations interacting with the radiation-induced defects *Present address: College of Medicine, University, Oyaguchi, Itabasji-ku, Tokyo.
Nihon
2. EXPERIMENTAL METHOD SPECIMENS
AND
A reactor-grade polycrystalline graphite prepared by the Tokai Eiectrode Manufacturing Co., Ltd. was bombarded by fast neutrons at 30°C in the Material Testing Reactor at Hanford, U.S.A. to the total 379
380
M. SAITO
dose of 5-8 X 10zo nvt. A long slab test piece cut out of this parent material was isothermally annealed for 30-60 min in vacuum at twenty-one temperature steps ranging from 100” up to 2300°C. Such an annealed specimen was examined each time by measurements of internal friction and dynamic modulus at temperatures between 80” and 300°K. The experimental arrangements were almost the same as those previously reported [2]. 3. RESULTS AND DISCUSSION 3.1 Temper-atwe
dependence of internull @&on
Although the internal friction (Q-l) as a function of temperature (2) shows a variety of absolute values for different annealing temperatures (A.T.), one can find some similarity in the relative changes irrespective of the absolute value. Taking this point of view, the e’ vs. T curves have been classified into three groups as shown in Fig. 1.
“0 x4 b z0 80 ’
I20
I 160 No
240
260
Tempwture, 3-C
Fig. 1. Representative behavior of temperature dependence of internal friction of irradiated graphite in the three stages of annealing. The curve (1) for the lOO”C-annealed specimen is well representative of the first group consisting of samples annealed between 100” and 1150°C. This group is characterized by the monotonic increase of Q-’ with increasing ambient temperature. In this range of annealing temperature, the vacancies produced by radiation are known to be immobile[4], the X-ray diffraction showing C~(~Z) = 6.88 A even after annealing at
et al,
l~O’C[5]. Hereupon, the specimens are concluded to possess still a heavily damaged structure so that the internal friction can not appropriately be ascribed to dislocations. The second group annealed between 1250” and 1600°C is represented by the curve (2). The curve shape is apparently similar to that for usual polycrystalline graphite subjected to no damage, whereas the absolute values of Q-’ are considerably higher than those for the f&y-recovered material. Therefore, this curve may be Iikened rather to that for the samples intercalated with impurity atoms and/or molecules such as Br2 and ICI. In this annealing range, vacancies become sufficiently mobile to begin to recombine with knocked-on atoms, and the structure is suspected to have recovered the graphitic crystallinity fairly well. Therefore, the steep rise of Q-” around 200°K can be appropriately attributed to the thermal depinning of dislocations in the same manner as previously found for impurity-doped graphites 121. The curve for the third group annealed between 1800” and 2150°C exhibits a maximum around 230°K irrespective of annealing temperature. So far as the X-ray diffraction is concerned (see [4], p.126) the structure of this group appears to have fully recovered. However, according to Turnbull[6], some Iarge clusters of point defects still remain. Therefore, the foregoing maximum seems to be a relaxation peak caused by the interaction between such clusters and dislocations. Finally, the internal friction curve obtained after annealing at 2300°C is shown separately in the lower diagram of Fig. 2, while the upper gives the resonant frequency (fo) as a measure of the modulus change. One can see that the internal friction peak under consideration is still present though it has considerably been flattened out. Hence, the third stage of recovery seems not to be readily completed untess the treatment is made at quite high temperature.
ANNEALING PROCESSES Tatat don frSXK+
381
that most of interstitial clusters (except the extremely large ones) have already undergone recombination with vacancies.
nut& 30 -C
A.T. 2300%
3.3 Pinning energy of dislocations
Fig. 2. Temperature dependence of internal friction and resonant frequency for an irradiated graphite specimen annealed at 2300°C. 3.2 Stepwise recovery of anelastic properties Figure 3 shows the resonant frequency (fO) and the internal friction (Q-l) at 80” and 280°K as functions of annealing temperature. The first stage in recovery appears strongly in the f0 curves. That is, in the A.T. range between 100” and 600°C the elastic modulus recovers for the most part, while the change in Q-l is scarcely detectable. The next recovery stage shows up in the room-temperature internal friction as a broad hump extending over the range from 1200” up to l?OO”C, while f0 shows only a slight fall-off. In the range A.T. > lSOO”C, both Q-l and f0 show no appreciable change, implying
Previously, two of the authors[2] were successful in calculating the interaction impurity pins and disenergy between locations in graphite. Herewith, a similar analysis has been applied to specimens which are recovering from radiation damage. In the theory of Granato and Liicke[l], the change in modulus due to the presence of dislocations (AE) is related to the free length of dislocation strings (L) in a simple form: hElEO = (uL2
where E,, is the pure elastic modulus of graphite lattice, and cy is a temperaturethe containing independent parameter orientation factor, Poisson’s ratio, the dislocation density and a factor dependent on the distribution function of L. On the other hand, according to Cottrell’s pinning mechanism [3], the impurity concentration (C) in the neighborhood of a dislocation is given by an Arrhenius-type expression b/l = C = COexp ( W/kT)
AEEIE, = a(b/CJ2exp t
I
400
800 Anneding
4
1200
(2)
where W denotes the interaction energy between pinning agent (radiation-induced defects in this case) and dislocations, b the Burgers vector of dislocations and C, the average impurity concentration in bulk. From equations (1) and (2), one obtains the following:
28O’K
0
(1)
1600
lemperaiure
ZOO0
2400
,“c
Fig. 3. The relationship of the resonant frequency and of the internal friction vs. annealing temperature at 80” and 280°K for irradiated graphite.
(-2WlkT).
(3)
Since the pure elastic modulus, E,, is much more temperature-insensitive than the modulus change due to dislocations [T-9], A E can directly be related to Tin equation (3) as an approximation. Thus, by taking the
382
M. SAITO et al.
general relationship that elastic modulus is proportional to the square of resonance equation (3) is converted to frequency, log {df,/d( I/?“)} = /3 - 2WlkT
(4)
where the constant /3 involving cr, b, Co, fO, E,, and W is assumed to be independent of temperature. Figure 4 gives log {df,ld( l/T)} vs. l/T plot for the specimen annealed at 23OO”C, from which the activation energy for depinning dislocations (w) is determined to be 0.046 eV+ Told dare
30 T
5*BXlO%vl,al
A.T. 2300 T
II
1 4
6
5
7
I/T XIO’
Fig. 4. Log {dfo/d( l/T)} vs. l/T plot for a specimen of irradiated graphite annealed at temperature of 2300°C. Similarly, the evaluation of W was successful for samples anneafed between 1050” and 1600°C. For the specimens annealed below lOOO*C, however, such an analysis does not work; which means that the crystal structure is too imperfect to contain well-defined dislocations in it. On the other hand, although dislocation theory ought to be still applicable to samples annealed between 1800” and 215O”C, estimation of U’ was also unsuccessful, because the modulus change is accompanied by the presence of an internal friction peak around 230°K (see Fig. 1). Numerical values of W obtained are tabulated as follows:
A.T. (“Q
Gh
1050 1150 1250 1440 1600 2300
0.012 0*013 0.016 0.021 0.038 O-046
Although W shows a systematically increasing trend with the rise of annealing temperature, the values corresponding to the annealing below 1250°C are too small to have any real meaning in the ambient temperature range examined. Even values for the specimens annealed above 1440°C are still small by a factor of ten than the migration energy of interstitial carbon atoms as evaluated by Goggin [lo]. Such a discrepancy could be removed by assuming that in the present case the so-called pipe diffusion of interstitials along edge dislocations play an essential role. W = 0.038 eV for the specimen annealed at 1600°C is nearly equal to that previously reported [2] for the unirradiated graphite, 0.04 eV. This means that at this temperature the graphitic lattice has almost recovered its tri-dimensional periodicity so as to permit the presence of normal dislocations. This has also been verified by the X-ray diffraction analysis as stated before[5]. In this sense, W = 0.046 eV for A.T. = 2300°C seems to be too large and may probably be due to the growth of interstitial clusters such as proposed by Turnbull[6]; i.e. such large clusters growing with the increase of A.T. would react with dislocations as pinning agents more firmly than those smaller ones formed at lower stages of annealing. 3.4 Free bngth of dislocation and damping constant From the expressions for the internal friction and the dynamic modulus given by Granato and Liicke, one can derive the
ANNEALING
free length of dislocations (L) and the damping constant (B) as function of annealing temperature: Namely the internal friction (Q-‘) in the amplitude independent region is simply related to those quantities by Q-l a BL4.
(5)
Taking equations (1) and (5) and using the data on the room-temperature anelasticity, the relative change of B and L with the annealing temperature was obtained and is shown schematically in Fig. 5. t.)(o)
5’ ob
T&aldoss5.exicPnvt,or so%
400
600
Am&q
I605 t$ZotuapC 2ooo
2400
Fig. 5. Free loop length of disiocation (L) and damping constant (B) vs. annealing temperature for irradiated graphite at room temperature. As stated before, due to the extremely anisotropic structure of graphite, the inelastic core of dislocations is presumably spread along the basal plane and has an section. elliptic cross Therefore, single atoms and/or molecules precipitated into may not such widely-cored dislocations effectively pin them down, but rather react with them causing viscous drag. Based on such an understanding of the situation, a consistent account can be given even though qualitatively, for the behavior of B and L in Fig. 5, which is, of course, closely connected with the clustering of knocked-on atoms in the recovery process. In Fig. 5, it is noted that in the first stage of annealing up to 500°C L greatly increases, while R shows a remarkable decrease. This
PROCESSES
383
may appropriately be explained in the following way: First, the single atoms and/or molecules working as viscous drag migrate along dislocations, by pipe diffusion, and consolidate into larger clusters. This in due course leads to the marked decrease in the damping constant B. Similar consolidation takes place also for the small interstitial clusters working as pinning agents, and causes such a steep increase in L as found in Fig. 5. The plateaux found in the range 500”1100°C for both L and B imply that no serious change arises in the fundamental nature of pinning agents and of viscous drag; that is, the consolidation of interstitials has come to an end, yielding some stability in the size distribution. When A.T. comes up to 12OO”C,some interstitial clusters become thermally unstable and begin to decompose into smaller fragments: such fragments maybe, including molecular-size ones, would enhance the viscous drag effect again, giving rise to an increase of B in Fig. 5. On the other hand, the radiation-induced vacancies become fairly mobile in this stage, and meet the interstitials more frequently than before. Such annihilation of point defects tends not only to lower B but to increase L. In the range A-T. >1300”C, the latter mechanism seems to overcome the former, to which the fall-off of B as well as the gradual increase of L also displayed in Fig. 5 can be ascribed. 4. CONCLUDING
REMARKS
The behavior of internal friction and of dynamic modulus in the annealing process of pile-irradiated graphite has been investigated under the light of the dislocation theory. It is of deep interest that the qualitative description of the behavior of B and L in terms of dislocations is successful even for such poorly-crystalline specimens as those annealed below 100°C. Actually, the X-ray diffraction indicates that the structure of such materials is too imperfect to contain
3%
M. SAITO
definite dislocations. However, it is still possible to suppose dislocation-iike line defects as one of the macroscopic phase patterns in a continuous body, e.g. glassy solid and even liquid@]. In the pioneering work of Burgers, the concept of dislocation was introduced in such a way. Accepting this hypothesis, one can see than the essential nature of such line defects satisfies the dislocation-string model utilized for the present purpose. The interaction energy obtained from the temperature dependence of dynamic modulus is seen to increase rapidiy with A.T., amounting to 0438 eV for the specimens annealed at 1600°C. This value is almost the same as that for unirradiated graphite, in good agreement with the fact that so far as the X-ray diffraction is concerned the recovery has apparently become complete at this temperature. A&kno~~e~g~~n~-Thanks are Noma~uchi of Tokai Electrode
due to Mr. Manufacturing
et al
Co., Ltd. for furnishing the irradiated graphite, and also to Dr. E. Hoda, Dr. K. Kobavashi and Mr. K. Furuta for affording us their facilities for anneals at high temperature.
REFERENCES 1. Cranato A. and Liicke K., J. A#d. Phys. 27, 589,789 (1956). 2. Tsuzuku T. and Saito M.,Ja@n J. A#. Phys. 6.54 (1967). Flow 3. dottr‘ell A: H., In ~~~cu~o~ an& P&IS&& iti Crystals; p. 133. Oxford University Press, Oxford (1953). 4. Simmons J. H. W., In Radiation Damage in Graphite, p. 73. Pergamon Press, Oxford (1965). 5. Tsuzuku T. and Ishihara Y., JSPS-Rep. No. 117-94-C-1 (1966); Inagaki M., Private communication. 6. Turnbull J. A. and Stagg M. S., Phil. Mag. 14,1049 (1966). 7. Tsuzuku T., Carbon 1,25 (1964). 8. Baker C. and Kelly A., P&E. Msg. 9,927 (1964). 9. Kelly B. T., Phil. Msg. 2,721 (1964). 10. Goggin P. R., VP Gol~oqued.eMe~~~ur~e, p. 181 (1962).
1969, Vol. 7, pp. 379-384.
Pergamon
Press.
Pnoted
in Great
Britain
INTERNAL FRICTION STUDY OF ANNEALING PROCESSES IN PILE-IRRADIATED GRAPHITE M. SAITO*, M. BABA*, K. KAWAMURA and T. TSUZUKU College of Science and Engineering, Nihon University, Kanda-Surugadai, Chiyoda-ku, Tokyo,Japan
Abstract-A reactor grade graphite irradiated by fast neutrons at 30°C to the total dose of 5% x 102* nvt was stepwise annealed between 100” and 23OO”C,and was examined each time by measuring the internal friction and dynamic modulus at temperatures from 300” down to 80°K. The recovery process has been found to consist of three stages; the first stage occurring between 100” and 5OO”C,the second one in the range from 660” to 115O”C, and the third one between 1200” and 2300°C. In the first stage the dynamic modulus recovers for the most part, while the internal friction indicates little change. On the other hand, the recovery of internal friction arises mostly in the third stage where the dynamic modulus shows only a slight fall-off. In the second stage no serious change arises in the anelastic properties. A qualitative explanation for the formation and decomposition processes of interstitial clusters is given within the framework of the Granato-Liicke theory in relation to the behavior of such anelastic properties. 1. INTRODUCTION Internal
friction
(mechanical
expected to play the principal role in the damping mechanism [Z]. As stated in a previous paper[2], the impurity atoms and their clusters which have precipitated onto dislocations through Cottrell’s mechanism [3] are believed to behave because of the extremely anisotropic crystal structure of graphite in such a complicated way that they act either as pinning agents or as viscous drag, in accordance with their geometrical size relative to the size of the dislocation core. This situation would be common to the knocked-on atoms, vacancies and their clusters in the radiationdamaged graphite. are
damping)
is defined as the rate of internal energy dissipation per cycle in a vibrating solid specimen; it is, in practice, represented by the logarithmic decrement of freely-decaying vibration or the half-value width of the resonance curve. In the case of crystalline solids, such a mechanical damping is thought to be caused mainly by the oscillatory motion of dislocation lines undergoing some viscous friction. In this context, a theory based on the so-called vibrating-string model has been proposed by Granato and Liicke[l] and was greatly successful in dealing with a number of experimental data. Hence, it is worthwhile attempting to test this theory in describing the annealing process of radiationdamaged graphite, since dislocations interacting with the radiation-induced defects *Present address: College of Medicine, University, Oyaguchi, Itabasji-ku, Tokyo.
Nihon
2. EXPERIMENTAL METHOD SPECIMENS
AND
A reactor-grade polycrystalline graphite prepared by the Tokai Eiectrode Manufacturing Co., Ltd. was bombarded by fast neutrons at 30°C in the Material Testing Reactor at Hanford, U.S.A. to the total 379
380
M. SAITO
dose of 5-8 X 10zo nvt. A long slab test piece cut out of this parent material was isothermally annealed for 30-60 min in vacuum at twenty-one temperature steps ranging from 100” up to 2300°C. Such an annealed specimen was examined each time by measurements of internal friction and dynamic modulus at temperatures between 80” and 300°K. The experimental arrangements were almost the same as those previously reported [2]. 3. RESULTS AND DISCUSSION 3.1 Temper-atwe
dependence of internull @&on
Although the internal friction (Q-l) as a function of temperature (2) shows a variety of absolute values for different annealing temperatures (A.T.), one can find some similarity in the relative changes irrespective of the absolute value. Taking this point of view, the e’ vs. T curves have been classified into three groups as shown in Fig. 1.
“0 x4 b z0 80 ’
I20
I 160 No
240
260
Tempwture, 3-C
Fig. 1. Representative behavior of temperature dependence of internal friction of irradiated graphite in the three stages of annealing. The curve (1) for the lOO”C-annealed specimen is well representative of the first group consisting of samples annealed between 100” and 1150°C. This group is characterized by the monotonic increase of Q-’ with increasing ambient temperature. In this range of annealing temperature, the vacancies produced by radiation are known to be immobile[4], the X-ray diffraction showing C~(~Z) = 6.88 A even after annealing at
et al,
l~O’C[5]. Hereupon, the specimens are concluded to possess still a heavily damaged structure so that the internal friction can not appropriately be ascribed to dislocations. The second group annealed between 1250” and 1600°C is represented by the curve (2). The curve shape is apparently similar to that for usual polycrystalline graphite subjected to no damage, whereas the absolute values of Q-’ are considerably higher than those for the f&y-recovered material. Therefore, this curve may be Iikened rather to that for the samples intercalated with impurity atoms and/or molecules such as Br2 and ICI. In this annealing range, vacancies become sufficiently mobile to begin to recombine with knocked-on atoms, and the structure is suspected to have recovered the graphitic crystallinity fairly well. Therefore, the steep rise of Q-” around 200°K can be appropriately attributed to the thermal depinning of dislocations in the same manner as previously found for impurity-doped graphites 121. The curve for the third group annealed between 1800” and 2150°C exhibits a maximum around 230°K irrespective of annealing temperature. So far as the X-ray diffraction is concerned (see [4], p.126) the structure of this group appears to have fully recovered. However, according to Turnbull[6], some Iarge clusters of point defects still remain. Therefore, the foregoing maximum seems to be a relaxation peak caused by the interaction between such clusters and dislocations. Finally, the internal friction curve obtained after annealing at 2300°C is shown separately in the lower diagram of Fig. 2, while the upper gives the resonant frequency (fo) as a measure of the modulus change. One can see that the internal friction peak under consideration is still present though it has considerably been flattened out. Hence, the third stage of recovery seems not to be readily completed untess the treatment is made at quite high temperature.
ANNEALING PROCESSES Tatat don frSXK+
381
that most of interstitial clusters (except the extremely large ones) have already undergone recombination with vacancies.
nut& 30 -C
A.T. 2300%
3.3 Pinning energy of dislocations
Fig. 2. Temperature dependence of internal friction and resonant frequency for an irradiated graphite specimen annealed at 2300°C. 3.2 Stepwise recovery of anelastic properties Figure 3 shows the resonant frequency (fO) and the internal friction (Q-l) at 80” and 280°K as functions of annealing temperature. The first stage in recovery appears strongly in the f0 curves. That is, in the A.T. range between 100” and 600°C the elastic modulus recovers for the most part, while the change in Q-l is scarcely detectable. The next recovery stage shows up in the room-temperature internal friction as a broad hump extending over the range from 1200” up to l?OO”C, while f0 shows only a slight fall-off. In the range A.T. > lSOO”C, both Q-l and f0 show no appreciable change, implying
Previously, two of the authors[2] were successful in calculating the interaction impurity pins and disenergy between locations in graphite. Herewith, a similar analysis has been applied to specimens which are recovering from radiation damage. In the theory of Granato and Liicke[l], the change in modulus due to the presence of dislocations (AE) is related to the free length of dislocation strings (L) in a simple form: hElEO = (uL2
where E,, is the pure elastic modulus of graphite lattice, and cy is a temperaturethe containing independent parameter orientation factor, Poisson’s ratio, the dislocation density and a factor dependent on the distribution function of L. On the other hand, according to Cottrell’s pinning mechanism [3], the impurity concentration (C) in the neighborhood of a dislocation is given by an Arrhenius-type expression b/l = C = COexp ( W/kT)
AEEIE, = a(b/CJ2exp t
I
400
800 Anneding
4
1200
(2)
where W denotes the interaction energy between pinning agent (radiation-induced defects in this case) and dislocations, b the Burgers vector of dislocations and C, the average impurity concentration in bulk. From equations (1) and (2), one obtains the following:
28O’K
0
(1)
1600
lemperaiure
ZOO0
2400
,“c
Fig. 3. The relationship of the resonant frequency and of the internal friction vs. annealing temperature at 80” and 280°K for irradiated graphite.
(-2WlkT).
(3)
Since the pure elastic modulus, E,, is much more temperature-insensitive than the modulus change due to dislocations [T-9], A E can directly be related to Tin equation (3) as an approximation. Thus, by taking the
382
M. SAITO et al.
general relationship that elastic modulus is proportional to the square of resonance equation (3) is converted to frequency, log {df,/d( I/?“)} = /3 - 2WlkT
(4)
where the constant /3 involving cr, b, Co, fO, E,, and W is assumed to be independent of temperature. Figure 4 gives log {df,ld( l/T)} vs. l/T plot for the specimen annealed at 23OO”C, from which the activation energy for depinning dislocations (w) is determined to be 0.046 eV+ Told dare
30 T
5*BXlO%vl,al
A.T. 2300 T
II
1 4
6
5
7
I/T XIO’
Fig. 4. Log {dfo/d( l/T)} vs. l/T plot for a specimen of irradiated graphite annealed at temperature of 2300°C. Similarly, the evaluation of W was successful for samples anneafed between 1050” and 1600°C. For the specimens annealed below lOOO*C, however, such an analysis does not work; which means that the crystal structure is too imperfect to contain well-defined dislocations in it. On the other hand, although dislocation theory ought to be still applicable to samples annealed between 1800” and 215O”C, estimation of U’ was also unsuccessful, because the modulus change is accompanied by the presence of an internal friction peak around 230°K (see Fig. 1). Numerical values of W obtained are tabulated as follows:
A.T. (“Q
Gh
1050 1150 1250 1440 1600 2300
0.012 0*013 0.016 0.021 0.038 O-046
Although W shows a systematically increasing trend with the rise of annealing temperature, the values corresponding to the annealing below 1250°C are too small to have any real meaning in the ambient temperature range examined. Even values for the specimens annealed above 1440°C are still small by a factor of ten than the migration energy of interstitial carbon atoms as evaluated by Goggin [lo]. Such a discrepancy could be removed by assuming that in the present case the so-called pipe diffusion of interstitials along edge dislocations play an essential role. W = 0.038 eV for the specimen annealed at 1600°C is nearly equal to that previously reported [2] for the unirradiated graphite, 0.04 eV. This means that at this temperature the graphitic lattice has almost recovered its tri-dimensional periodicity so as to permit the presence of normal dislocations. This has also been verified by the X-ray diffraction analysis as stated before[5]. In this sense, W = 0.046 eV for A.T. = 2300°C seems to be too large and may probably be due to the growth of interstitial clusters such as proposed by Turnbull[6]; i.e. such large clusters growing with the increase of A.T. would react with dislocations as pinning agents more firmly than those smaller ones formed at lower stages of annealing. 3.4 Free bngth of dislocation and damping constant From the expressions for the internal friction and the dynamic modulus given by Granato and Liicke, one can derive the
ANNEALING
free length of dislocations (L) and the damping constant (B) as function of annealing temperature: Namely the internal friction (Q-‘) in the amplitude independent region is simply related to those quantities by Q-l a BL4.
(5)
Taking equations (1) and (5) and using the data on the room-temperature anelasticity, the relative change of B and L with the annealing temperature was obtained and is shown schematically in Fig. 5. t.)(o)
5’ ob
T&aldoss5.exicPnvt,or so%
400
600
Am&q
I605 t$ZotuapC 2ooo
2400
Fig. 5. Free loop length of disiocation (L) and damping constant (B) vs. annealing temperature for irradiated graphite at room temperature. As stated before, due to the extremely anisotropic structure of graphite, the inelastic core of dislocations is presumably spread along the basal plane and has an section. elliptic cross Therefore, single atoms and/or molecules precipitated into may not such widely-cored dislocations effectively pin them down, but rather react with them causing viscous drag. Based on such an understanding of the situation, a consistent account can be given even though qualitatively, for the behavior of B and L in Fig. 5, which is, of course, closely connected with the clustering of knocked-on atoms in the recovery process. In Fig. 5, it is noted that in the first stage of annealing up to 500°C L greatly increases, while R shows a remarkable decrease. This
PROCESSES
383
may appropriately be explained in the following way: First, the single atoms and/or molecules working as viscous drag migrate along dislocations, by pipe diffusion, and consolidate into larger clusters. This in due course leads to the marked decrease in the damping constant B. Similar consolidation takes place also for the small interstitial clusters working as pinning agents, and causes such a steep increase in L as found in Fig. 5. The plateaux found in the range 500”1100°C for both L and B imply that no serious change arises in the fundamental nature of pinning agents and of viscous drag; that is, the consolidation of interstitials has come to an end, yielding some stability in the size distribution. When A.T. comes up to 12OO”C,some interstitial clusters become thermally unstable and begin to decompose into smaller fragments: such fragments maybe, including molecular-size ones, would enhance the viscous drag effect again, giving rise to an increase of B in Fig. 5. On the other hand, the radiation-induced vacancies become fairly mobile in this stage, and meet the interstitials more frequently than before. Such annihilation of point defects tends not only to lower B but to increase L. In the range A-T. >1300”C, the latter mechanism seems to overcome the former, to which the fall-off of B as well as the gradual increase of L also displayed in Fig. 5 can be ascribed. 4. CONCLUDING
REMARKS
The behavior of internal friction and of dynamic modulus in the annealing process of pile-irradiated graphite has been investigated under the light of the dislocation theory. It is of deep interest that the qualitative description of the behavior of B and L in terms of dislocations is successful even for such poorly-crystalline specimens as those annealed below 100°C. Actually, the X-ray diffraction indicates that the structure of such materials is too imperfect to contain
3%
M. SAITO
definite dislocations. However, it is still possible to suppose dislocation-iike line defects as one of the macroscopic phase patterns in a continuous body, e.g. glassy solid and even liquid@]. In the pioneering work of Burgers, the concept of dislocation was introduced in such a way. Accepting this hypothesis, one can see than the essential nature of such line defects satisfies the dislocation-string model utilized for the present purpose. The interaction energy obtained from the temperature dependence of dynamic modulus is seen to increase rapidiy with A.T., amounting to 0438 eV for the specimens annealed at 1600°C. This value is almost the same as that for unirradiated graphite, in good agreement with the fact that so far as the X-ray diffraction is concerned the recovery has apparently become complete at this temperature. A&kno~~e~g~~n~-Thanks are Noma~uchi of Tokai Electrode
due to Mr. Manufacturing
et al
Co., Ltd. for furnishing the irradiated graphite, and also to Dr. E. Hoda, Dr. K. Kobavashi and Mr. K. Furuta for affording us their facilities for anneals at high temperature.
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