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Specific heat of soft carbons between 0·6 and 4·2°K—II
Carbm,
1972, Vol. 10, pp. 267-275.
Pergamon
Press.
Printed
in Great
Britain
SPECIFIC HEAT OF SOFT CARBONS BETWEEN 0.6 AND 4.2”K- II* K. KAMIYA,? S. MROZOWSKI and A. S. VAGH Carbon Research Laboratory and Department of Physics, State University of New York at Buffalo,Buffalo, N.Y. 14214, L’.S.A. (Keceived 2OJuly 1971) AbstractIn extension of the work of Delhaes and Hishiyama, measurements of specific heat in the temperature range 0.55-5°K were carried out for a soft carbon heattreat.ed to various temperatures (HTT 600-1650°C) and for a polycrystalline nuclear graphite neutron irradiated to different doses. A large increase in both the linear and the cubic temperature components is observed for the soft carbon with decrease in HTT. The sharp specific heat peak at around 0.65”K is found again, this time for a soft carbon of different origin; the peak becomes particularly strong for low heattreated materials. Although little change in the cubic components of the specific heat is found for the nuclear graphite, apparently the same anomalous carbon peak emerges at around 0.7”K as the result of irradiation. This peak and its high temperature wing (believed to be due to secondary effects) dominate the shape of the specific heat curve in the lower temperature range for the irradiated material. The importance and implications of these findings are discussed. 1. INTRODUCTION In the first part of this work, Delhaes
and Hishiyama [l] have reported the results of their studies of the low temperature specific heat of a soft carbon heattreated to temperatures in the range 1600°C to 3100°C. They confirmed that the specific heat dependence on temperature in addition to the regular lattice term a7’” (with 2 < n G 3) contains a linear temperature contribution yT, with y rapidly increasing with decreasing degree of graphitization. In fact, the values of y seem
*Research partly supported by theJoint Awards Council of the Research Foundation of the State University of New York. These results were originally presented at the first U.S.-Japan Carbon Seminar in Tokyo (September 1970) and later at the Washington, D.C. Meeting, American Physical Society (April 1971) and at the 10th Carbon Conference in Bethlehem, Pa. (June 1971). ton leave of absence from Nagoya University, Nagoya, Japan. Present address: Mie University, ‘l‘su, Mie-ken,,Japan.
much too large to be explainable solely as a contribution of free carriers. The presence of a small linear term of a non-carrier origin was established earlier by Van Hoeven, et al., [2], in case of polycrystalline graphite for which a somewhat higher specific heat is found than for natural crystalline material, the difference being inexplainable by any reasonable deformation of the band structure and/or minor shift of the Fermi level. Although the work of Delhaes and Hishiyama has shown even more convincingly the presence of this linear contribution of non-carrier origin, the uncertainty remained as to the exact interpretation of the effect. The non-carrier value is estimated by subtracting the carrier contribution which in turn had to be determined b); other means or calculated from a band model of questionable validity (for incompletely graphitized materials). In the range of heattreatments investigated by Delhaes and Hishiyama, the carrier density of states at the Fermi level increases continuously with decrease of
268
K. KAMIYA, S. MROZOWSKI and A. S. VAGH
HTT (heattreatment temperature), so that an increasing carrier contribution is to be subtracted from the (increasing) total observed linear term. The original purpose of the work reported here, was to extend the specific heat investigations to lower heattreatments, in particular to a region where the carrier contribution starts to decrease, or even further where it becomes so small as to be negligible. The presence of a linear term for such materials would then be a direct and convincing proof of its lattice origin. Should the new non-carrier linear contribution to the specific heat happen to be due to lattice vibrations of a special type, appearing only when disorder and/or defects are introduced into the lattice, studies of neutron irradiated graphite would be of special interest. Since Delhaes and Hishiyama have found in incompletely graphitized materials an anomalous specific heat peak at around 0*6”K, which was believed at that time to be due to an impurity (possibly iron), and which interfered with a proper extrapolation of the data to O”K, working with a graphite of nuclear purity would permit a more precise determination of the linear term and a better estimate of the effect of disorder. With this in mind, the proper irradiations were carried out. However, it was early realized that the anomalous peak does not seem to be due to an impurity and that the whole situation might be more complicated than anticipated. As it turned out, our experiments brought to light some important facts concerning the specific heat of carbons and imperfect graphites, and opened up new opportunities for study of defect structures in carbons.
2. EXPERIMENTAL To extend the study of Delhaes and Hishiyama to lower heattreatments, a completely new set of samples was needed, since their starting material was a commercial carbon: baked probably only to about 9OO”C, but containing petroleum filler calcined to
about 1200°C. For this work therefore a set of raw coke carbons was prepared in the following way: raw coke was made from Resin C pitch so that at no time the material was heated to a temperature exceeding 600°C. This coke was ground and a mix prepared using a 50-50 proportion of sizes -65 + 100 and -200, and adding about 35 parts of Resin C as binder. Extruded green rods of 0.75 in. dia. were baked using an exceptionally slow baking cycle (to avoid cracking and disintegration) to top temperature of 500, 600, 700 and 900°C. Later the 900°C baked material was heattreated in a graphite tube furnace to higher temperatures in rapid operation with a 15 min holding time at the top temperature. It is well known that (very roughly) a slow heattreatment to a definite temperature produces material similar to a faster heattreatment to a higher temperature. To provide some kind of comparison HTT scale for the two groups of rods-baked only (500-900°C) and the higher heattreated ones, checks using the ESR technique were made. It was found that the materials baked to 500, 600, 700 and 900°C are roughly equivalent to samples heattreated in a rapid operation with 15 min holding time at the top temperature of 600, 680, 800 and 1000°C. In the following these last four numbers will be used to designate the HTT of the baked samples, so as to provide a more uniform and consistent scale for comparison of the effects of heattreatment throughout the whole range from raw to graphitized materials. For the neutron irradiation experiments, nuclear graphite of very high purity (chlorine treated), kindly supplied by the Airco-Speer Co., was irradiated in the reactor of the Western New York Nuclear Center to three doses: 10, 50, and 250 hr. Samples were enclosed in aluminum capsules and placed exactly in the same position in relation to the reactor core as in case of our previous work on magnetoresistance [3]. Almost identical dependence of the Hall coefficient on the irradiation time was
SPECIFIC
HEAT
OF SOFT
CARBONS
obtained for the Airco-Speer graphite as for the soft type polycrystalline graphite used in the magnetoresistance work. Thus the degree of damage obtained can be directly evaluated from the Hall coefficient curves Fig. 3 and F’ig. 6 of Ref. [3]. It might be here sufficient to note that the maximum of the Hall coefficient at liquid nitrogen temperature is reached after 15 hr irradiation, so that 250 hr, can be considered as a reasonably heavy irradiation dose. Experiln~ntal procedures described by Delhaes and Hishiyama in Part I were followed throughout the present study and the same equipment used. However, in view of the large porosity and adsorption areas of carbons in the low heattreatment range, it took much longer to outgas the samples to a reasonably low level. To avoid all possibility of some He exchange gas desorbing in the higher temperature region, no exchange gas at all was used when experiments were done on the He4 apparatus. The He* apparatus was improved by introduction of a set of radiation shielding baflles which decreased the consumption of helium to such a low level that at the end of the first series of experiments, the sample holder could be withdrawn and a new one (precooled) inserted in its place. The work could be continued on the second sample after addition of a few liters (3-4) of liquid helium. With three sample holders available in evacuated and precooled state, a large amount of data could be obtained in an efficient manner. When a sample was investigated, usually three runs were made by reconnecting the sample to the block at the end of a run and cooling it down for a next run. Different settings of the heater current and sensitivity were used in various runs to avoid systematic errors. Most of the samples were investigated at least twice, the samples being taken out, inspected and reinserted again for the next series of runs, the agreement of the data being considered as a proof of their reliability.
BETWEEN
0% AND
4.2X-11
2fi0
3. RESULTS
Figure 1 gives the results of measurements for the Resin C carbons with the individual experimental points indicated. No distinction is made between different runs and tests. In case of low heattreatments due to the high specific heat after initial tests, the sample volume was reduced to about a half to keep the total capacity of the samples in reasonable limits. The size could not be reduced however much more since some of these samples were to be used after heattreatment to higher temperature. Again no distinction is made between the data originating from such differently sized samples. In case of a few experimental points clearly deviating from the smooth relationship the data fed into computer were rechecked: invariably errors were found either in determination of the temperature jump or in punching of the cards. Thus it is believed that the real scatter of the data is even smaller than seen in Fig. 1. The rough data taken for the Resin C carbon HTT 1650 to compare our soft carbon with the one used by Delhaes and Hishiyama (NCC) are not included. The specific heat values for the Resin C HTT 16.50 are located above the NCC 1600 curve, the raw coke carbons not grahitizing as well as the c-ommercial calcined coke product. The curves obtained by Delhaes and Hishiyama are redrawn in Fig. 1 without experimental points indicated. Efforts were made to go to the extreme in low heattreatment and try to measure the specific heat of the Resin C pitch, from which the raw carbon was made. Two difficulties defeated our efforts: first of all the very low heat conductivity of’ the solidified pitch extending the duration of the transmission of’ a temperature shock beyond reasonable limits and the cracking (shattering) of‘ the sample. It is not clear if the cracking occurs on the cooling cycle and is responsible for the extremely slow heat transx~lissi~~n,or happens later during the upheat. Various arrange-
270
IL KAMIYA,
S. MROZOWSKI
ments were tried, to avoid cracking, but without success. For the two lowest heattreatments no data was obtained in the low temperature region. An unfortunate accident put our He3 cryostat out of order for quite a while, so that when it became operational again, to save time, only the most essential runs were performed. The two next higher heattreatments make it most evident however that the 0*65”K peak would be found also for the lowest heattreatments, and so such data would not help any in improving the accuracy of the linear extrapolation of the curves down to 0°K. The perfect linearity of the plots C/T vs. T2 for lower heattreatments (Fig. 1) shows that such carbons follow (except for the linear term) surprisingly well the Debye T3 relation anyway. Naturally, it would be interesting to know if the 0*65”K peak does increase or decrease in intensity at lower heattreatments. This was our main interest in unsuccessfully trying to investigate the pitch. Unfortunately, the lack of time prevented us from carrying out such additional runs for I-ITT 600 and 680°C. It was believed at first that the anomalous peak is due to some impurity, such as iron or Commercial cokes and something else. pitches contain many impurities, and usually in carbon production iron oxide is added to the binder to prevent puffing. Consequently, we have tried to purify a sample of the NCC carbon (1800) in a stream of HCl and HF vapors at a temperature of about 4OO”C, but as a neutron activation analysis has shown with little success. However, as data were collected and evaluated for the Resin C carbons, the Resin C being a pretty clean coal tar pitch devoid of the second phase and the NCC carbon of Delhaes and Hishiyama being commercial petroleum a regular coke material, the presence of the peak in both materials and its similar dependence on heattreatment made the impurity interpretation very questionable. As will be seen in the next section this suspicion has been fully
and A. S. VAGH
supported ments.
by the neutron
irradiation
experi-
3.2. Spec;fic heat of neutron irradiated
graphite
By introducing defects and disorder into highly pure material, we hoped to clarify the origin of the specific heat peak. We began to suspect that it will emerge as a result of neutron irradiation, but should it turn out to be due to an impurity after all, and not appear after irradiation, at least very good extrapolated values of the linear term would be obtained by having curves devoid of this anomaly down to the lowest temperature. Either way results of interest were expected. Figure 2 presents the results of the specific heat runs on irradiated material. The spectacular emergence of a specific heat peak at low temperature end of the scale, increasing in height with increasing dose is the main feature of these curves. Unfortunately, after repairs the cryostat did not function very efficiently and we did not succeed in cooling the 250 hr sample so low as to reach and cross over the peak-it took a long time to cool the sample, we were running out of He4 in the evaporator, and we had to start the measurements for fear of losing the whole run. However, we did reach the peak at 0*7”K (and went over it) in case of the 50 hr sample; this result gives an idea of how high the peak for 250 hr sample would be since, as checked by ESR, only a relatively small saturation in damage occurs at a 250 hr dose. Clearly, we still had some way to go to reach the peak. Samples of 10 hr dose and of unirradiated graphite were studied only in the He4 apparatus. The results for the latter one coincide sufficiently well with other results on polycrystalline graphite [ 1, %] to guarantee the absence of the peak at low temperature; somewhat higher values found for the specific heat are consistent with the somewhat lower temperature of ~aphitization (- 2700°C). As one can see from Fig. 2, in the upper part of the temperature range investigat.ed,
c .p
. f
“K
Fig. 1. Specific heat of Kesin (: carbon heattreated to various temperatures (FlTT) from 600°C to 1250°C. The curves for a petroleum coke base carbon heattreated from 1600°C To 3 lOO”(; were taken from Part I [l].
T2,
5ooo[ HTT600f ./
6000
Fig. 2. Specific
1000
“K heat of Airco-Speer nuclear irradiated to various doses.
T2,
rystalline
graphite
graphite
neutron
I
K. KAMIYA,
272
2000
S. MROZOWSKI
n
Temperature,
“K
Fig. 3. Decomposition of the high temperature tail of the specific heat anomaly of the 250
hr irradiated graphite into several partly overlapping peaks (broken curves) as obtained by comparison with the shape of the simple peak observed for the unirradiated soft carbon material. only a small increase in specific heat is found to occur as a result of the introduced lattice disorder even for the heavily irradiated sample. Since little change with irradiation throughout the He4 range was found in earlier experiments by other investigators [4], it must be assumed that only lightly irradiated materials were used in their work. More recently, larger differences were found by Kimura and Suzuki [5] for a heavily irradiated material, the deviations found being essentially similar to ours. Except for the high temperature tail, the peak created by irradiation bears great similarity to the peaks observed in unirradiated low heattreated carbons (Fig. 1). The difference in the exact location of the peak should not be taken too seriously, since in the technique used (sample not separated from the block) poor heat conduction along the axis of the block and differences in resistance
and A. S. VAGH
of the contact with the block can cause some inconsistencies in readings of the temperature at the other end of the sample (this was observed in the previous work, see Fig. 3 of Ref. [I]). Thus, we do believe that the peaks in Fig. 1 and Fig. 2 have the same origin. It does seem however that in both cases, as the peak grows in intensity, it does shift in position slightly towards higher temperature values. When the irradiation dose is heavier, the high temperature tail becomes easily noticeable. This tail seems to be an addition caused by some secondary effects. In Fig. 3, the anomalous parts of the specific heat as obtained after subtraction of the regular lattice and conduction components (yT+ crTn) are drawn for the carbon HTT 800°C Fig. 1 and for the 250 hr irradiated graphite from Fig. 2. In case of the 250 hr specimen, the estimated regular part (dotted line on Fig. 2) is based on an educated guess rather than on experimental evidence. However, the conclusion as to the formation of a separate hump on the high temperature side of the peak is quite independent of the exact height and shape of the regular part subtracted. In Fig. 3, the 250 hr peak is split by taking the shape of the main peak to be similar to the 800 HTT, the remaining part of the anomalous specific heat forming a secondary hump at 1.8”K. When the anomalous part for the 50 hr sample is multiplied by a factor of about 4.3”” to bring the main peak to overlap the 250 hr curve an indication for a tertiary peak at 3.1”K is obtained. The final decomposition of the tail into not less than two (or maybe more) peaks is given in Fig. 3 by the broken curves. It is easily seen that the decomposition is not essentially affected by changes or adjustments of the extrapolated linear component. j’The
factor being smaller than 5 indicates
the incipient than 4 was determinations.
saturation. A factor slightly lower obtained for this case from ESR
SPECIFIC
HEAT
OF SOFT
CARBONS
Figure 4 gives the plot of the linear temperature component of specific heat in its dependence on heattreatment temperature (HTT) as determined from extrapolation of the curves Fig. 1. This total effect is composed of the regular conduction carrier contribution and of the new, not yet understood, lattice contribution. The conduction carrier part is indicated by a partly continuous and partly broken curve enclosing a crosshatched area. This part is pr~)portio!lal to the density of electronic energy states at the Fermi level, u(E,. f . The curve was obtained by applying the ESR technique described previously [6-S] consisting of a determination of the total ESR intensity and of its temperature dependence, from which the part due to conduction carriers can be calculated. The four samples of Delhaes and Hishiyama were so analyzed and led to the continuous parr of the curse. The shape of this curve for a soft carbon is somewhat different from the corres~~orldirIg curve f-or the P33 carbon black (Fig. 10 of Ref. [T]) has almost no minim urn at beginning of graphitization, but a long flat plateau at high tIT’I7 is
BETWEEN
0.6 AND 4*2”Ii-Ii
observed. The broken part of the curve in Fig. 4 represents roughly the expected change in tz(EF)-as explained in Ref.[7]. The unshaded white area below the experimental curve of the total linear contribution, Fig. 4, gives then the variation with heattreatment temperature HTT of the new lattice linear contribution of non-carrier origin. The circles in Fig. -I are the linear term values obtained by very rough extrapolation for the neutron irradiated graphite as shown in Fig. 2. They are plotted at HTT’s corresponding to the irradiation doses. the correspondence being based on equivalent depression of the Fermi level. (The correspondence is obtained by consideration of the evolution of the Hall coefficient, see Ref. [3]). The fact that the circles are not located on the HT’I‘ curve, Fig. 4, is a demonstration that a new linear lattice effect has nothing to do with the electronic state of‘ the material or with the type of’ defects (traps) which control directI)’ or indirectly the position of the Fermi level iIt the material. 4. GENERAL Of the three
- -..-
r---40” i
‘.
!
’
HTT,
O’c
Fig. 3. Plot of the coefficient y of the lirwar temperature contribution to specific heat as ohtainetl for the two soft carbons by extrapolat.iort (Fig. I ) in drpendence on heattreatment temperature (HT’I‘). ‘l‘he shaded part represents thug conductiorl carrier contribution as evaluated for these carbons hp art analysis of the ESK dat.a. On the same graph rough values of the coefficient y founcl for irradiated graphite (Fig. 2) are plcttteci fitr equivalent posttions of the Fermi level.
279
REMARKS
results of this work, the first one concerns the large increase in specific heat with decrease in i-ITT. This is an effect connected with some tarure of the structure of the raw and baked carbons. hug. definitely is not simply the result of such tiisorder as introduced bv neutron irradial.ion (3.2). The parti!; square Lattice term LYLE”I&polycrystalllne graphite changes for baked carbon into an exact. cubic tiependen~, as expected for nonplanar three dimensional systems. The large increase in the slope of the curves Fig. 1, seems to indicate ;I considerable decrease in the Debye temperature 0. l‘he Debye temperature H calculated from the data of Fig. 1, turns out to be about 2,.i-S times lower for the HI?’ 600” material than the average H for graphite. Thus the gradual transition from graphitic structure toward a regular oqganic polvmcr seems to be
274
K. KAMIYA,
S. MROZOWSKI
reflected in specific heat of carbons by a gradual decrease of the Debye temperature 6. The second result is the definite proof of the non-carrier origin of the anomalous linear temperature component of the specific heat. Such linear term appears only when the system loses its perfect periodicity by becoming a polycrystal or a carbon polymer. It seems probable therefore that such linear term may be found also in other polymeric materials. Fujita and Bug1191 have proposed an explanation of the anomalous linear term, by considering vibrational modes on the surface of plates-clearly such a model might apply to neutron damaged polycrystalline graphite where the rudiments of the crystal structure are still present, but not to three dimensional polymeric structures. Thus the origin of the lattice term remains unexplained. However Fig. 4 seems to indicate that one has to look for a structural feature which is created by strong neutron irradiation in greater abundance than is present in baked material. The third result is the one which might find the most application, since it gives us a tool for study of some specific type (or types) of defects in carbon and graphite and of their interactions. Judging from the gradual decay of the main peak on the high temperature side (excluding the secondary humps), the specific heat peak at 0~7°K could be a Schottky type peak. If so, the sharpness of the main peak would be surprising; it is hard to see how in such haphazardly occurring destruction of the lattice as happens under neutron irradiation so many systems (defects) with exactly the same energy level splitting would be created, unless this would be some atomic or molecular excitation. On the other hand, as we suggested at the Tokyo and at the Washington APS [lo] Meetings, the peak could be due to some cooperative effect, for instance an exchange interaction between localized electronic spins via the intermediary of the conduction carriers. Such an interaction was actually found in
and A. S. VAGH
the ESR work, the exchange causing a fusion of the two ESR lines and mixing of their g-values[5]. A rough consideration of changes of the intensity of the peak with HTT and a comparison with its intensity for irradiated materials shows a pretty good correlation with the concentration of the localized spins as determined by the ESR technique. Closer look however reveals also some discrepancies (for instance the peak for HTT 2400 is much too strong for such an interpretation). Surprisingly, the linear component shows also a reasonably good correlation with the localized spin concentration; if there is any deeper meaning to this it is hard to assess at present. Recently Delhaes, Lemerle and BlondeGonte [l l] have carried out specific heat measurements on neutron irradiated graphite in magnetic field up to 40 kG. Their work covers only the He* temperature range (1+5-4*4”K), and so nothing can be inferred about the behavior of the 0.7”K peak itself. But their results show at least that the region of secondary peak at first increases in intensity with the magnetic field up to about 30 kG, and then starts to decrease at higher fields. On the other hand, the tertiary hump continues to increase in intensity up to the highest fields. The effect of the magnetic field is large and so indicates that the process responsible for the specific heat humps must be either of electronic origin or be a lattice effect strongly coupled to some electronic process. It is interesting to note that the reversal in magnetic field dependence of the secondary peak occurs for an external field corresponding to a spin-spin exchange interaction equivalent to an internal field of 27 kG (1.8”K). Should this relationship be general, a turnaround point for the tertiary hump would be expected at about 46 kG (3.1”K) and for the main peak at around 10 kG. Thus at the present state of affairs, it seems most imperative to investigate very carefully the position and the shape of the main peak at various magnetic fields- extending the work
SPECIFIC
HEAT OF SOFT CARBONS BETWEEN
to well below 0.3”K. Only then an identification of the structures responsible for the specific heat peak (or peaks) can be expected. Ack~~~~e~~erne~~~-~~~ authors like CO express their sincere thanks to Dr. J. Bulawa for purification of a carbon sample, to Dr. Y. Hishiyama, for helping in several introductory runs and for transmitting all his experience, information and instructions concerning experimentat details and setup of our equipment, to Dr. E. Kluth, for helping in some intrwductory runs and for rewiring the circuits, and to Messrs. J. Mooney and E. Pruuii for their genera1 assistance with the apparatus and the experiments. Thanks are again due to Prof. P. H. Keesom of Purdue Universiry and to Dr. Paul Dust.in of the Janis Research Co. for their friendly help and advice. REFERENCES I. Delhaes P. and Hishiyama Part f (1970).
Y., Car&an 8, 31
0.6 AND 4.2”K-II
275
2. Van Hoeven B. J. C., Keesom P. H., McCfure J. W. and Wagoner C., Phys. Rev. 159, 796 (1966). 3. Hishiyama Y., Mrozowski S. and Vagh A. S., Cnrbon 9,367 (1971). 4. See for instance Simmons J. H. W., Rada‘ation Damage in Graphite, p. 103-4, Pergamon Press, Oxford (1965). 5. Kimura 0. and Suzuki H., Tokyo .~wposium on Car&n 1964, ~~~s~ru~~VI-I. 6. Mrozowski S., Car&on 3,305 (1965). 7. Arnold C. and Mrozowski S,, G&on 6, 243 (1968). 8. Mrozowski S., Carbon6,841 (1968). 9. Fujita S. and Bug1 P., Phys. Rev. 185, 1094 (1969). 10. Mrozowski S., Vagh A. S. and Kamiya K., Bull. Am. Phys. Sot. 16,493 (1971). 11. Delhaes P., Lemerle M. Y. and Blonde-Gonte G., Abstract EP191 I&h Am. G&on. Co$, Bethlehem, Pa., DCIC, 301 f 1971).
1972, Vol. 10, pp. 267-275.
Pergamon
Press.
Printed
in Great
Britain
SPECIFIC HEAT OF SOFT CARBONS BETWEEN 0.6 AND 4.2”K- II* K. KAMIYA,? S. MROZOWSKI and A. S. VAGH Carbon Research Laboratory and Department of Physics, State University of New York at Buffalo,Buffalo, N.Y. 14214, L’.S.A. (Keceived 2OJuly 1971) AbstractIn extension of the work of Delhaes and Hishiyama, measurements of specific heat in the temperature range 0.55-5°K were carried out for a soft carbon heattreat.ed to various temperatures (HTT 600-1650°C) and for a polycrystalline nuclear graphite neutron irradiated to different doses. A large increase in both the linear and the cubic temperature components is observed for the soft carbon with decrease in HTT. The sharp specific heat peak at around 0.65”K is found again, this time for a soft carbon of different origin; the peak becomes particularly strong for low heattreated materials. Although little change in the cubic components of the specific heat is found for the nuclear graphite, apparently the same anomalous carbon peak emerges at around 0.7”K as the result of irradiation. This peak and its high temperature wing (believed to be due to secondary effects) dominate the shape of the specific heat curve in the lower temperature range for the irradiated material. The importance and implications of these findings are discussed. 1. INTRODUCTION In the first part of this work, Delhaes
and Hishiyama [l] have reported the results of their studies of the low temperature specific heat of a soft carbon heattreated to temperatures in the range 1600°C to 3100°C. They confirmed that the specific heat dependence on temperature in addition to the regular lattice term a7’” (with 2 < n G 3) contains a linear temperature contribution yT, with y rapidly increasing with decreasing degree of graphitization. In fact, the values of y seem
*Research partly supported by theJoint Awards Council of the Research Foundation of the State University of New York. These results were originally presented at the first U.S.-Japan Carbon Seminar in Tokyo (September 1970) and later at the Washington, D.C. Meeting, American Physical Society (April 1971) and at the 10th Carbon Conference in Bethlehem, Pa. (June 1971). ton leave of absence from Nagoya University, Nagoya, Japan. Present address: Mie University, ‘l‘su, Mie-ken,,Japan.
much too large to be explainable solely as a contribution of free carriers. The presence of a small linear term of a non-carrier origin was established earlier by Van Hoeven, et al., [2], in case of polycrystalline graphite for which a somewhat higher specific heat is found than for natural crystalline material, the difference being inexplainable by any reasonable deformation of the band structure and/or minor shift of the Fermi level. Although the work of Delhaes and Hishiyama has shown even more convincingly the presence of this linear contribution of non-carrier origin, the uncertainty remained as to the exact interpretation of the effect. The non-carrier value is estimated by subtracting the carrier contribution which in turn had to be determined b); other means or calculated from a band model of questionable validity (for incompletely graphitized materials). In the range of heattreatments investigated by Delhaes and Hishiyama, the carrier density of states at the Fermi level increases continuously with decrease of
268
K. KAMIYA, S. MROZOWSKI and A. S. VAGH
HTT (heattreatment temperature), so that an increasing carrier contribution is to be subtracted from the (increasing) total observed linear term. The original purpose of the work reported here, was to extend the specific heat investigations to lower heattreatments, in particular to a region where the carrier contribution starts to decrease, or even further where it becomes so small as to be negligible. The presence of a linear term for such materials would then be a direct and convincing proof of its lattice origin. Should the new non-carrier linear contribution to the specific heat happen to be due to lattice vibrations of a special type, appearing only when disorder and/or defects are introduced into the lattice, studies of neutron irradiated graphite would be of special interest. Since Delhaes and Hishiyama have found in incompletely graphitized materials an anomalous specific heat peak at around 0*6”K, which was believed at that time to be due to an impurity (possibly iron), and which interfered with a proper extrapolation of the data to O”K, working with a graphite of nuclear purity would permit a more precise determination of the linear term and a better estimate of the effect of disorder. With this in mind, the proper irradiations were carried out. However, it was early realized that the anomalous peak does not seem to be due to an impurity and that the whole situation might be more complicated than anticipated. As it turned out, our experiments brought to light some important facts concerning the specific heat of carbons and imperfect graphites, and opened up new opportunities for study of defect structures in carbons.
2. EXPERIMENTAL To extend the study of Delhaes and Hishiyama to lower heattreatments, a completely new set of samples was needed, since their starting material was a commercial carbon: baked probably only to about 9OO”C, but containing petroleum filler calcined to
about 1200°C. For this work therefore a set of raw coke carbons was prepared in the following way: raw coke was made from Resin C pitch so that at no time the material was heated to a temperature exceeding 600°C. This coke was ground and a mix prepared using a 50-50 proportion of sizes -65 + 100 and -200, and adding about 35 parts of Resin C as binder. Extruded green rods of 0.75 in. dia. were baked using an exceptionally slow baking cycle (to avoid cracking and disintegration) to top temperature of 500, 600, 700 and 900°C. Later the 900°C baked material was heattreated in a graphite tube furnace to higher temperatures in rapid operation with a 15 min holding time at the top temperature. It is well known that (very roughly) a slow heattreatment to a definite temperature produces material similar to a faster heattreatment to a higher temperature. To provide some kind of comparison HTT scale for the two groups of rods-baked only (500-900°C) and the higher heattreated ones, checks using the ESR technique were made. It was found that the materials baked to 500, 600, 700 and 900°C are roughly equivalent to samples heattreated in a rapid operation with 15 min holding time at the top temperature of 600, 680, 800 and 1000°C. In the following these last four numbers will be used to designate the HTT of the baked samples, so as to provide a more uniform and consistent scale for comparison of the effects of heattreatment throughout the whole range from raw to graphitized materials. For the neutron irradiation experiments, nuclear graphite of very high purity (chlorine treated), kindly supplied by the Airco-Speer Co., was irradiated in the reactor of the Western New York Nuclear Center to three doses: 10, 50, and 250 hr. Samples were enclosed in aluminum capsules and placed exactly in the same position in relation to the reactor core as in case of our previous work on magnetoresistance [3]. Almost identical dependence of the Hall coefficient on the irradiation time was
SPECIFIC
HEAT
OF SOFT
CARBONS
obtained for the Airco-Speer graphite as for the soft type polycrystalline graphite used in the magnetoresistance work. Thus the degree of damage obtained can be directly evaluated from the Hall coefficient curves Fig. 3 and F’ig. 6 of Ref. [3]. It might be here sufficient to note that the maximum of the Hall coefficient at liquid nitrogen temperature is reached after 15 hr irradiation, so that 250 hr, can be considered as a reasonably heavy irradiation dose. Experiln~ntal procedures described by Delhaes and Hishiyama in Part I were followed throughout the present study and the same equipment used. However, in view of the large porosity and adsorption areas of carbons in the low heattreatment range, it took much longer to outgas the samples to a reasonably low level. To avoid all possibility of some He exchange gas desorbing in the higher temperature region, no exchange gas at all was used when experiments were done on the He4 apparatus. The He* apparatus was improved by introduction of a set of radiation shielding baflles which decreased the consumption of helium to such a low level that at the end of the first series of experiments, the sample holder could be withdrawn and a new one (precooled) inserted in its place. The work could be continued on the second sample after addition of a few liters (3-4) of liquid helium. With three sample holders available in evacuated and precooled state, a large amount of data could be obtained in an efficient manner. When a sample was investigated, usually three runs were made by reconnecting the sample to the block at the end of a run and cooling it down for a next run. Different settings of the heater current and sensitivity were used in various runs to avoid systematic errors. Most of the samples were investigated at least twice, the samples being taken out, inspected and reinserted again for the next series of runs, the agreement of the data being considered as a proof of their reliability.
BETWEEN
0% AND
4.2X-11
2fi0
3. RESULTS
Figure 1 gives the results of measurements for the Resin C carbons with the individual experimental points indicated. No distinction is made between different runs and tests. In case of low heattreatments due to the high specific heat after initial tests, the sample volume was reduced to about a half to keep the total capacity of the samples in reasonable limits. The size could not be reduced however much more since some of these samples were to be used after heattreatment to higher temperature. Again no distinction is made between the data originating from such differently sized samples. In case of a few experimental points clearly deviating from the smooth relationship the data fed into computer were rechecked: invariably errors were found either in determination of the temperature jump or in punching of the cards. Thus it is believed that the real scatter of the data is even smaller than seen in Fig. 1. The rough data taken for the Resin C carbon HTT 1650 to compare our soft carbon with the one used by Delhaes and Hishiyama (NCC) are not included. The specific heat values for the Resin C HTT 16.50 are located above the NCC 1600 curve, the raw coke carbons not grahitizing as well as the c-ommercial calcined coke product. The curves obtained by Delhaes and Hishiyama are redrawn in Fig. 1 without experimental points indicated. Efforts were made to go to the extreme in low heattreatment and try to measure the specific heat of the Resin C pitch, from which the raw carbon was made. Two difficulties defeated our efforts: first of all the very low heat conductivity of’ the solidified pitch extending the duration of the transmission of’ a temperature shock beyond reasonable limits and the cracking (shattering) of‘ the sample. It is not clear if the cracking occurs on the cooling cycle and is responsible for the extremely slow heat transx~lissi~~n,or happens later during the upheat. Various arrange-
270
IL KAMIYA,
S. MROZOWSKI
ments were tried, to avoid cracking, but without success. For the two lowest heattreatments no data was obtained in the low temperature region. An unfortunate accident put our He3 cryostat out of order for quite a while, so that when it became operational again, to save time, only the most essential runs were performed. The two next higher heattreatments make it most evident however that the 0*65”K peak would be found also for the lowest heattreatments, and so such data would not help any in improving the accuracy of the linear extrapolation of the curves down to 0°K. The perfect linearity of the plots C/T vs. T2 for lower heattreatments (Fig. 1) shows that such carbons follow (except for the linear term) surprisingly well the Debye T3 relation anyway. Naturally, it would be interesting to know if the 0*65”K peak does increase or decrease in intensity at lower heattreatments. This was our main interest in unsuccessfully trying to investigate the pitch. Unfortunately, the lack of time prevented us from carrying out such additional runs for I-ITT 600 and 680°C. It was believed at first that the anomalous peak is due to some impurity, such as iron or Commercial cokes and something else. pitches contain many impurities, and usually in carbon production iron oxide is added to the binder to prevent puffing. Consequently, we have tried to purify a sample of the NCC carbon (1800) in a stream of HCl and HF vapors at a temperature of about 4OO”C, but as a neutron activation analysis has shown with little success. However, as data were collected and evaluated for the Resin C carbons, the Resin C being a pretty clean coal tar pitch devoid of the second phase and the NCC carbon of Delhaes and Hishiyama being commercial petroleum a regular coke material, the presence of the peak in both materials and its similar dependence on heattreatment made the impurity interpretation very questionable. As will be seen in the next section this suspicion has been fully
and A. S. VAGH
supported ments.
by the neutron
irradiation
experi-
3.2. Spec;fic heat of neutron irradiated
graphite
By introducing defects and disorder into highly pure material, we hoped to clarify the origin of the specific heat peak. We began to suspect that it will emerge as a result of neutron irradiation, but should it turn out to be due to an impurity after all, and not appear after irradiation, at least very good extrapolated values of the linear term would be obtained by having curves devoid of this anomaly down to the lowest temperature. Either way results of interest were expected. Figure 2 presents the results of the specific heat runs on irradiated material. The spectacular emergence of a specific heat peak at low temperature end of the scale, increasing in height with increasing dose is the main feature of these curves. Unfortunately, after repairs the cryostat did not function very efficiently and we did not succeed in cooling the 250 hr sample so low as to reach and cross over the peak-it took a long time to cool the sample, we were running out of He4 in the evaporator, and we had to start the measurements for fear of losing the whole run. However, we did reach the peak at 0*7”K (and went over it) in case of the 50 hr sample; this result gives an idea of how high the peak for 250 hr sample would be since, as checked by ESR, only a relatively small saturation in damage occurs at a 250 hr dose. Clearly, we still had some way to go to reach the peak. Samples of 10 hr dose and of unirradiated graphite were studied only in the He4 apparatus. The results for the latter one coincide sufficiently well with other results on polycrystalline graphite [ 1, %] to guarantee the absence of the peak at low temperature; somewhat higher values found for the specific heat are consistent with the somewhat lower temperature of ~aphitization (- 2700°C). As one can see from Fig. 2, in the upper part of the temperature range investigat.ed,
c .p
. f
“K
Fig. 1. Specific heat of Kesin (: carbon heattreated to various temperatures (FlTT) from 600°C to 1250°C. The curves for a petroleum coke base carbon heattreated from 1600°C To 3 lOO”(; were taken from Part I [l].
T2,
5ooo[ HTT600f ./
6000
Fig. 2. Specific
1000
“K heat of Airco-Speer nuclear irradiated to various doses.
T2,
rystalline
graphite
graphite
neutron
I
K. KAMIYA,
272
2000
S. MROZOWSKI
n
Temperature,
“K
Fig. 3. Decomposition of the high temperature tail of the specific heat anomaly of the 250
hr irradiated graphite into several partly overlapping peaks (broken curves) as obtained by comparison with the shape of the simple peak observed for the unirradiated soft carbon material. only a small increase in specific heat is found to occur as a result of the introduced lattice disorder even for the heavily irradiated sample. Since little change with irradiation throughout the He4 range was found in earlier experiments by other investigators [4], it must be assumed that only lightly irradiated materials were used in their work. More recently, larger differences were found by Kimura and Suzuki [5] for a heavily irradiated material, the deviations found being essentially similar to ours. Except for the high temperature tail, the peak created by irradiation bears great similarity to the peaks observed in unirradiated low heattreated carbons (Fig. 1). The difference in the exact location of the peak should not be taken too seriously, since in the technique used (sample not separated from the block) poor heat conduction along the axis of the block and differences in resistance
and A. S. VAGH
of the contact with the block can cause some inconsistencies in readings of the temperature at the other end of the sample (this was observed in the previous work, see Fig. 3 of Ref. [I]). Thus, we do believe that the peaks in Fig. 1 and Fig. 2 have the same origin. It does seem however that in both cases, as the peak grows in intensity, it does shift in position slightly towards higher temperature values. When the irradiation dose is heavier, the high temperature tail becomes easily noticeable. This tail seems to be an addition caused by some secondary effects. In Fig. 3, the anomalous parts of the specific heat as obtained after subtraction of the regular lattice and conduction components (yT+ crTn) are drawn for the carbon HTT 800°C Fig. 1 and for the 250 hr irradiated graphite from Fig. 2. In case of the 250 hr specimen, the estimated regular part (dotted line on Fig. 2) is based on an educated guess rather than on experimental evidence. However, the conclusion as to the formation of a separate hump on the high temperature side of the peak is quite independent of the exact height and shape of the regular part subtracted. In Fig. 3, the 250 hr peak is split by taking the shape of the main peak to be similar to the 800 HTT, the remaining part of the anomalous specific heat forming a secondary hump at 1.8”K. When the anomalous part for the 50 hr sample is multiplied by a factor of about 4.3”” to bring the main peak to overlap the 250 hr curve an indication for a tertiary peak at 3.1”K is obtained. The final decomposition of the tail into not less than two (or maybe more) peaks is given in Fig. 3 by the broken curves. It is easily seen that the decomposition is not essentially affected by changes or adjustments of the extrapolated linear component. j’The
factor being smaller than 5 indicates
the incipient than 4 was determinations.
saturation. A factor slightly lower obtained for this case from ESR
SPECIFIC
HEAT
OF SOFT
CARBONS
Figure 4 gives the plot of the linear temperature component of specific heat in its dependence on heattreatment temperature (HTT) as determined from extrapolation of the curves Fig. 1. This total effect is composed of the regular conduction carrier contribution and of the new, not yet understood, lattice contribution. The conduction carrier part is indicated by a partly continuous and partly broken curve enclosing a crosshatched area. This part is pr~)portio!lal to the density of electronic energy states at the Fermi level, u(E,. f . The curve was obtained by applying the ESR technique described previously [6-S] consisting of a determination of the total ESR intensity and of its temperature dependence, from which the part due to conduction carriers can be calculated. The four samples of Delhaes and Hishiyama were so analyzed and led to the continuous parr of the curse. The shape of this curve for a soft carbon is somewhat different from the corres~~orldirIg curve f-or the P33 carbon black (Fig. 10 of Ref. [T]) has almost no minim urn at beginning of graphitization, but a long flat plateau at high tIT’I7 is
BETWEEN
0.6 AND 4*2”Ii-Ii
observed. The broken part of the curve in Fig. 4 represents roughly the expected change in tz(EF)-as explained in Ref.[7]. The unshaded white area below the experimental curve of the total linear contribution, Fig. 4, gives then the variation with heattreatment temperature HTT of the new lattice linear contribution of non-carrier origin. The circles in Fig. -I are the linear term values obtained by very rough extrapolation for the neutron irradiated graphite as shown in Fig. 2. They are plotted at HTT’s corresponding to the irradiation doses. the correspondence being based on equivalent depression of the Fermi level. (The correspondence is obtained by consideration of the evolution of the Hall coefficient, see Ref. [3]). The fact that the circles are not located on the HT’I‘ curve, Fig. 4, is a demonstration that a new linear lattice effect has nothing to do with the electronic state of‘ the material or with the type of’ defects (traps) which control directI)’ or indirectly the position of the Fermi level iIt the material. 4. GENERAL Of the three
- -..-
r---40” i
‘.
!
’
HTT,
O’c
Fig. 3. Plot of the coefficient y of the lirwar temperature contribution to specific heat as ohtainetl for the two soft carbons by extrapolat.iort (Fig. I ) in drpendence on heattreatment temperature (HT’I‘). ‘l‘he shaded part represents thug conductiorl carrier contribution as evaluated for these carbons hp art analysis of the ESK dat.a. On the same graph rough values of the coefficient y founcl for irradiated graphite (Fig. 2) are plcttteci fitr equivalent posttions of the Fermi level.
279
REMARKS
results of this work, the first one concerns the large increase in specific heat with decrease in i-ITT. This is an effect connected with some tarure of the structure of the raw and baked carbons. hug. definitely is not simply the result of such tiisorder as introduced bv neutron irradial.ion (3.2). The parti!; square Lattice term LYLE”I&polycrystalllne graphite changes for baked carbon into an exact. cubic tiependen~, as expected for nonplanar three dimensional systems. The large increase in the slope of the curves Fig. 1, seems to indicate ;I considerable decrease in the Debye temperature 0. l‘he Debye temperature H calculated from the data of Fig. 1, turns out to be about 2,.i-S times lower for the HI?’ 600” material than the average H for graphite. Thus the gradual transition from graphitic structure toward a regular oqganic polvmcr seems to be
274
K. KAMIYA,
S. MROZOWSKI
reflected in specific heat of carbons by a gradual decrease of the Debye temperature 6. The second result is the definite proof of the non-carrier origin of the anomalous linear temperature component of the specific heat. Such linear term appears only when the system loses its perfect periodicity by becoming a polycrystal or a carbon polymer. It seems probable therefore that such linear term may be found also in other polymeric materials. Fujita and Bug1191 have proposed an explanation of the anomalous linear term, by considering vibrational modes on the surface of plates-clearly such a model might apply to neutron damaged polycrystalline graphite where the rudiments of the crystal structure are still present, but not to three dimensional polymeric structures. Thus the origin of the lattice term remains unexplained. However Fig. 4 seems to indicate that one has to look for a structural feature which is created by strong neutron irradiation in greater abundance than is present in baked material. The third result is the one which might find the most application, since it gives us a tool for study of some specific type (or types) of defects in carbon and graphite and of their interactions. Judging from the gradual decay of the main peak on the high temperature side (excluding the secondary humps), the specific heat peak at 0~7°K could be a Schottky type peak. If so, the sharpness of the main peak would be surprising; it is hard to see how in such haphazardly occurring destruction of the lattice as happens under neutron irradiation so many systems (defects) with exactly the same energy level splitting would be created, unless this would be some atomic or molecular excitation. On the other hand, as we suggested at the Tokyo and at the Washington APS [lo] Meetings, the peak could be due to some cooperative effect, for instance an exchange interaction between localized electronic spins via the intermediary of the conduction carriers. Such an interaction was actually found in
and A. S. VAGH
the ESR work, the exchange causing a fusion of the two ESR lines and mixing of their g-values[5]. A rough consideration of changes of the intensity of the peak with HTT and a comparison with its intensity for irradiated materials shows a pretty good correlation with the concentration of the localized spins as determined by the ESR technique. Closer look however reveals also some discrepancies (for instance the peak for HTT 2400 is much too strong for such an interpretation). Surprisingly, the linear component shows also a reasonably good correlation with the localized spin concentration; if there is any deeper meaning to this it is hard to assess at present. Recently Delhaes, Lemerle and BlondeGonte [l l] have carried out specific heat measurements on neutron irradiated graphite in magnetic field up to 40 kG. Their work covers only the He* temperature range (1+5-4*4”K), and so nothing can be inferred about the behavior of the 0.7”K peak itself. But their results show at least that the region of secondary peak at first increases in intensity with the magnetic field up to about 30 kG, and then starts to decrease at higher fields. On the other hand, the tertiary hump continues to increase in intensity up to the highest fields. The effect of the magnetic field is large and so indicates that the process responsible for the specific heat humps must be either of electronic origin or be a lattice effect strongly coupled to some electronic process. It is interesting to note that the reversal in magnetic field dependence of the secondary peak occurs for an external field corresponding to a spin-spin exchange interaction equivalent to an internal field of 27 kG (1.8”K). Should this relationship be general, a turnaround point for the tertiary hump would be expected at about 46 kG (3.1”K) and for the main peak at around 10 kG. Thus at the present state of affairs, it seems most imperative to investigate very carefully the position and the shape of the main peak at various magnetic fields- extending the work
SPECIFIC
HEAT OF SOFT CARBONS BETWEEN
to well below 0.3”K. Only then an identification of the structures responsible for the specific heat peak (or peaks) can be expected. Ack~~~~e~~erne~~~-~~~ authors like CO express their sincere thanks to Dr. J. Bulawa for purification of a carbon sample, to Dr. Y. Hishiyama, for helping in several introductory runs and for transmitting all his experience, information and instructions concerning experimentat details and setup of our equipment, to Dr. E. Kluth, for helping in some intrwductory runs and for rewiring the circuits, and to Messrs. J. Mooney and E. Pruuii for their genera1 assistance with the apparatus and the experiments. Thanks are again due to Prof. P. H. Keesom of Purdue Universiry and to Dr. Paul Dust.in of the Janis Research Co. for their friendly help and advice. REFERENCES I. Delhaes P. and Hishiyama Part f (1970).
Y., Car&an 8, 31
0.6 AND 4.2”K-II
275
2. Van Hoeven B. J. C., Keesom P. H., McCfure J. W. and Wagoner C., Phys. Rev. 159, 796 (1966). 3. Hishiyama Y., Mrozowski S. and Vagh A. S., Cnrbon 9,367 (1971). 4. See for instance Simmons J. H. W., Rada‘ation Damage in Graphite, p. 103-4, Pergamon Press, Oxford (1965). 5. Kimura 0. and Suzuki H., Tokyo .~wposium on Car&n 1964, ~~~s~ru~~VI-I. 6. Mrozowski S., Car&on 3,305 (1965). 7. Arnold C. and Mrozowski S,, G&on 6, 243 (1968). 8. Mrozowski S., Carbon6,841 (1968). 9. Fujita S. and Bug1 P., Phys. Rev. 185, 1094 (1969). 10. Mrozowski S., Vagh A. S. and Kamiya K., Bull. Am. Phys. Sot. 16,493 (1971). 11. Delhaes P., Lemerle M. Y. and Blonde-Gonte G., Abstract EP191 I&h Am. G&on. Co$, Bethlehem, Pa., DCIC, 301 f 1971).