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Specific heat of soft carbons between 0.4 and 4.5°K—III
Carbon, 1916. Vol. 14, pp. 21 I-218.
Pergamon Press.
Printed in Great Britain
SPECIFIC HEAT OF SOFT CARBONS BETWEEN 0.4 AND 4S°K-III* S. MROZOWW and A. S. VAGH Carbon Research Laboratory, State University of New Yorkat Buffaloand Departmentof Physicsand Astronomy, BallStateUniversity,Muncie, IN 47306,U.S.A. (Received 25 February 1976) Abstract-A more extensive and thorough investigation of the specific heat of two series of soft carbons heattreated to various temperatures from 600to 3OOO’C and of a series of samples of an AS graphite neutron irradiated to various doses, was carried out. In particular, efforts were concentrated on mapping out the exact shape and position of the low temperature peak. A spectroscopic analysis of the impurity content of several of the investigated samples was made and the concentrations of localized spins were determined for all samples by means of the ESR technique. The most important result of this study is, that as the temperature is lowered, a fraction of all localized spins condenses at around 0.65”Kinto an antiferromagnetic phase, the fraction varying from about 2% for lowest up to 20% or more for the highest spin concentrations. An interpretation of the results is suggested and some other questions and difficulties brought out by this work are discussed.
1. INTRODUCllON
Whereas the theory of lattice vibrations and of the electronic band structure of a perfect graphite crystal has been developed to a pretty high degree of perfection, the nature of defects introduced by various means and their influence on various properties of graphite is much less understood. Still less so are the nature and peculiarities of the disorder in carbons on their way to graphitization. A partial disorder is composed of the sum of many defects of various kinds, and any technique which permits to study the influence and behavior of selected type of defects becomes a valuable tool in the quest to unravel the secrets of the disordered state. In two earlier papers under the same title (Part I [ 1] and Part 11[2])we have reported our findings on the anomalies observed in the specilic heat of soft carbons in the temperature range 0.6-4.2”K. When defects are present in the lattice, due either to the disorder resulting in the process of carbonization, or to lattice damage inflicted upon a graphitic structure by neutron irradiation a formation of a specific heat peak at around 0.6-0.7”K and an appearance of a large linear term of noncarrier origin were observed. Similar anomalies have been found by us to show up in Glassy Carbon, with a peak being located at temperature below our reach ( < 0.4”K)[3,4]. However, the observation of the tail of the peak (above 0.4”K) has supported the earlier suspicions that the development of the peak goes in parallel with the linear term, and that both these anomalies are directly related to the presence in the material of localized free electronic spins. The absence of a tail and the small value of the linear term for Glassy Carbon heattreated to 3OOO”C, which still remains in a highly disordered state and thus possesses many defects of various kinds, but for which the localized free spins are annealed out by such heattreatment [5], serves as a case in point. Extending the magnetic field dependence study of *Researchsupportedby the National Science Foundation.
Delhaes, Lemerle and Blondet-Gonte [6] and of BlondetGonte, Delhaes and Daure1[7] to sufficiently low temperature, so as to observe the behavior of the peak itself, we have found[8] that the peak is affected by the magnetic field in a general manner indicating its nature to be of a cooperative magnetic origin. Whereas the linear term might find an explanation analogous to the one of a linear term observed for some metal alloys and believed to be connected with presence of randomly distributed spins (for older literature on the subject see Gopal[9], pp. 71 and 82. In the newer literature a name of “spin glasses” was introduced by Anderson [ lo], see also Ref. [ 1l]), no magnetic phase transition has been found to occur in such disordered spin systems. To obtain more information about the transition observed in carbons (which we believe to be antiferromagnetic) a more detailed and precise study of the peak’s shape than in the exploratory work carried out previously[2], was undertaken for soft carbons. The results of this new series of measurements are presented below. 2. EXPERIMENTAL 2.1 Apparatus and measuring techniques The same ‘He cryostat built by Janis Research Co. was used in this work as previously [1,2,8]. However, after having finished the magnetic field dependence studies [8], the wide tail was reinstalled, so as to accommodate all the samples, of which some were of a larger size. AU measurements at temperature below 2°K were made with the sample in contact with the cooling block. The sample was held against the block by strings and springs, and was surrounded by a radiation shield attached to the block. The heat pulses were applied to the sample after its temperature equilibrated with that of the block in their very slow warming up process. To avoid any possible small differences in standardization of the thermometers, one and the same Germanium thermometer was used for all the series of measurements reported in this paper. A few series of measurements were carried out in the 211
212
S.
MROZOWSKI and
temperature range l.S-45°K using our regular He4 apparatus, some of the individual points being obtained with the sample in contact, and some others after separation, in order to check the reliability of both procedures. Good agreement was always found. The electronics was further improved and interferences reduced. The evaluation of data, and corrections for the heat capacity of the thermometer glue and strings were introduced the same way as previously.
2.2 Materials In these studies of the heattreatment dependence of the specific heat, we have investigated two sets of samples of soft carbons. They were the same as used in our previous work[2]. National Carbon Company commercial baked carbon rods (here designated NCC) were heattreated to various temperatures in a graphite tube electric furnace. The NCC carbon is a material composed mostly of calcined petroleum coke with some addition of carbonized coal tar binder (about 15% of total weight), the material having been baked to a temperature of about 900°C. Since the petroleum coke previous to baking was calcined in a commercial operation to about 1250°C to avoid inhomogeneities the NCC carbon was heattreated to no less than 1250°C. The second set of samples was made in our laboratory entirely from Resin C pitch. The Resin C is a pitch obtained from coal tar by distillation and thus does not contain the so-called second phase of colloidal benzol-insoluble particles. We have prepared a raw coke from it (at about 600°C) and then made carbon rods by extruding the finely ground raw coke with Resin C pitch as binder. These RC rods were baked to various temperatures up to 900°C in our laboratory baking furnace, and then higher in the graphite tube furnace. The kinetics of the carbonization and graphitization process is such that the properties of the material depend strongly on heattreatment temperature and on residence time at the top temperature. In all graphite tube furnace runs the residence time was 15 min (this happens to be about equal to the duration of the calcination in commercial operations). In baking, however, the residence time had to be necessarily much longer, being of an order of no less than 6 hr in case of our laboratory baking furnace. Such an increase in residence time by a factor of 25 is known to be roughly equivalent to an increase in the heattreatment temperature by about 100°C. In order to assign a common HTT scale to all samples of the series, we have determined the equivalent 15min heattreatment temperature for the samples baked to 500,600 and 700°C by establishing the temperature above which the ESR intensity begins to change when the sample is submitted to a sequence of increasing 15min heattreatments. The equivalent temperatures so obtained and recently rechecked of 600, 680 and 800°C are accurate to about * 10°C. Although both types of carbon (NCC and RC) are of the soft variety, the fact that the Resin C coke was ground at the raw stage and also that the binder was introduced at that stage, causes some small differences in response to heattreatment, in particular at higher temperatures, where
A. S. VAGH
the graphitization process is somewhat hindered by the structural deformation introduced into the raw coke [ 121. The composition of the two groups of samples was given here in detail to emphasize the differences in their origin. Whereas the petroleum coke contains little of inorganic impurities incorporated into the structure (metals, sulfur, etc.), the Resin C possesses some impurities characteristic to coal, of which only those which are chemically bonded to organic molecular systems are transported into the Resin C in the distillation process. But the two groups of impurities coming from petroleum and from coal have a very different distribution in concentration (some of the impurities contained in one are entirely absent in the other). Thus when concordant results are obtained from both series of carbons, this indicates strongly that the effects observed are not caused by impurities, but are due to the carbon structure itself. In order to satisfy our curiosity as to the degree of purity of the commercial product, we have submitted a sample of the NCC 1250carbon to a spectrographic check at the NASA analytical laboratory. The following impurities were found in ppm: Al, 50; Ca, 30; Co, 10; Cr, 10; Cu, 10; Fe, 60; Mg, 20; Ni, 50; Si, 75; Ti, 15; all of the others being below the limits of detection. All of these impurities are known to be characteristic to the nonpurified calcined petroleum cokes. Apparently very little or no iron oxide was added in the manufacturing process. Since both materials retain some impurities even after highest heattreatments, a study of a very pure carbon was considered imperative. For the study of the influence of neutron irradiation, a so-called high purity nuclear polycrystalline graphite made by the Airco Speer Company was used. This is a material very similar in composition to the NCC carbon, heattreated to about 2800°C and subjected during the heattreatment to the F-process high temperature purification (chlorinefluorine). Such material is pure as far as inorganic impurities are concerned down to millionth parts per weight of carbon, the only larger impurity concentration corresponding to gases adsorbed on the surfaces of pores and to dust picked up while the material is handled in air. The AS graphite samples were subjected to neutron irradiation in Western New York Reactor facility for various lengths of time, by placing the samples in sealed aluminum capsules. In the case of the hole used by us, the total flux of neutrons with energies above 10KV was 3.6 x lOI nv, the thermal flux being considerably lower (around 2 x 10” nv). But the exact energy distribution of neutrons causing the damage (and their effectiveness) being unknown for this and many other reactors, comparisons based on the total dose applied are not very meaningful. We have found in our work that it is much better to compare the doses by their effectiveness in damaging the lattice, the damage being evaluated by measurements of the Hall coefficient[l3]. In the case of the AS graphite (and other polycrystalline graphites) the Hall coefficient measured at 78°K reaches its positive maximum after a 12hr exposure in the WNY reactor (1.5 x lOI*nvt dose of fast neutrons), and this figure should be used in comparing our results to others. In the case of all irradiations, with the exception of the
Specific heat of soft carbons between 0.4 and 4S”K-III
heaviest one, the radioactivity of the samples decayed in few weeks to a level at which we were permitted to use them in our laboratory. This was a good proof of the high purity of the AS graphite. In the case of the heaviest dose (1250hr), the cool-off period extended, however, over several months. Although the impurities can be easily identified by the decay periods involved, and their concentrations estimated, to remove all doubts of those less acquainted with the purity levels achieved in nuclear graphites, we have taken small slices from the ends of our rods, and subjected them to a spectrographic check at the NASA analytical laboratory. The sample of unirradiated Airco-Speer graphite was found to contain only measurable amounts of Al (10 ppm) and Mg (2 ppm) and some Cu (< 1 ppm), all the other elements being below detection limits, whereas the same material after the heaviest irradiation (1250hr = 1.6 x 102’ fast neutron dose) was found to contain less Al (4ppm) and Mg (< 1 ppm), but more Cu (1.5 ppm), with all other elements being again below the limits of detection. The small amounts of aluminum found are probably due to the Al-foil in which samples were kept and of the copper to the contact with the copper He3 condensing container in the specific heat experiments (slices of the outside surface of rods end were submitted to the analysis!). Thus, whereas the total concentration of impurities in carbons is of the same order as the concentration of defects responsible for the specific heat peak, the impurity level in AS graphite is by at least two orders of magnitude lower, removing all doubts as to the origin of the anomalies observed being due to defects in the carbon lattice. 3. RESULTS
3.1 The heattreatment series The results of the detailed mapping out of the specific heat peak for the two series of variously heattreated soft carbons are shown in Fig. 1 on a C/T vs T2 graph. The thin straight lines drawn indicate the combined cubic
T2.
OK’
Fig. 1. Specific heat data obtained in the temperature range
0.4-2°Kfor two series of soft carbons RCand NCC heattreated to various temperatures. The curve for RC 1000is taken from older data[Z]. The thin lines indicate the linear and cubic components extrapolated down from higher temperature.
213
(oT’) and linear (yT) contributions to the specific heat, and were obtained by extrapolation of the straight line portions of the curves at temperatures well above the peak taken from Fig. 2. Figure 2 shows the results plotted on a compressed scale, with all earlier results [ 1,2] added to the new ones. In order not to crowd the graphs, the
5
IO
15
20
TZ. OK2
Fig. 2. Specific heat data for the two series of soft carbons RC and NCC over a wider temperature range (0.4-4S”K), combining the results of Fig. 1witholder data[l, 21.
individual experimental points are omitted in this case. A number of regularities are right away noticeable in perusing the Figs. 1 and 2: (1) The concentration of defects responsible for the peak itself decreases continuously with increasing temperature of heattreatment (HIT). The peak disappears when the material is heattreated to or above 2800°C. (2) The position of the peak is not constant, but shifts gradually to lower temperature as the HTT increases and the height of the peak diminishes (see Table 1). (3) On the low temperature side of the peak the specific heat variation with temperature is cubic (/3T’) with a linear component (ST) which varies from high positive to negative values as the HTT increases. The coefficient /3 of the cubic term varies only little with heattreatment. The data are collected in Table 1. The meaning of a negative linear term is obscure. It seems, however, that probably the cubic relationship does not extend much farther into the lower temperatures anyway. When we happened to reach temperatures below 0.45”K in case of the NCC 1250 sample, the cubic decrease was found to terminate, the curve indicating possibly a turnaround (which seems quite definite, in spite of the low reliability of the extrapolation of the thermometer calibration below 0.45”K). (4) On the high temperature side of the peak, the specific heat falls off very steeply for higher HTT’s and much less so for the lower HTT’s but in any case the decrease is too rapid (and the peak too sharp) to be consistent with a Schottky type of anomaly. Clearly the peak must be due to some kind of cooperative effect.
214
S. MROZOWSKI
and A. S.
VAGH
Table 1. Low temperaturespecificheatdatafor the heattreatmentseries of soft carbons Sample RC 600 RC 680 RC 800 RC 1000 RC 1250 NCC 1250 NCC 1600 RC 1700 NCC 2000 NCC 2400 NCC 3100
Height of peak alone
S
B (relat.)
2900 1900 1100
3.4 4.6 4.3
T,‘eK’)
T,(OK)
0.53 0.50 0.47
0.726 0.707 0.686
3300 2840 2OOtJ
0.405
0.637
515
-200
3.4
0.38 0.357
0.610 0.598
285 140 110
- 320 -560
3.1 3.9
(5) The coefficient y of the linear term increases greatly with decrease in heattreatment temperature (and increase in concentration of defects) down to HlT 800°C and stays about constant below that. (6) The cubic part aT3 increases greatly with decrease in HTT and with increase in lattice disorder, particularly so for heattreatments below 1000°Cwhere the carbon is essentially still a kind of organic polymer. It was shown that this increase in (Yresults directly from a decrease in the Debye temperature 8[14]. (7) The quadratic deviation, caused by the twodimensionality of the benzene ring planes being held mutually by weak Van der Waals forces, and evidenced in Fig. 2 by the curving of the lines (above T*= 3), is greatest for HZT between 2000 and 24OO”C,and completely disappears (in the temperature range investigated) for HTT 1250°Cand lower. (8) As expected, only small differences between the two series are observable on Fig. 2. Whereas the RC carbon seems to be slightly ahead of the NCC at HTT 125O”C,it begins to lag behind at higher heattreatment, so that RC at HTT 1700°Cis not much ahead of NCC 1600. This is explainable by the slight retardation in crystallite growth observed for carbons prepared from the raw coke[l2]. 3.2 Neutron damage series Whereas in our exploratory work[2] we concentrated on the similarities between the anomalies observed in the carbonization-graphitization ordering process and in the inverse process of destruction of order by neutron irradiation (something like degraphitization), the present more precise study has revealed interesting differences in detailed behavior. The results of the mapping out of the specific heat peak for the neutron irradiated Airco-Speer polycrystalline graphite are presented in Fig. 3 on a C/T vs T graph. Figure 4 shows the same on a compressed temperature scale, with the earlier results [2] added to the new ones in drawing all curves. The data for the 125Ohr irradiation dose in the range 1.S4S”K in Fig. 4 are new, and were obtained using our old He4 cryostat. The thin lines on Fig. 3 are the extrapolations obtained from Fig. 4. On Figs. 3 and 4 a number of regularities are noticeable: (1) The concentration of defects responsible for the peak increases with the irradiation dose, the rate of
0.5.
2,
05
a (relat.)
490 420 445 260 170 145 100 120 95 55 25
11.6 7.7 3.9 3.3 2.5 2.6 2.2 1.85 1.85 1.2 1.0
sin50
___*zL
As
"O-
y
-
~~
ml0 IO
15
20 25 T',OK2
3.0 35
4.0
Fig. 3. Specific heat data obtained in the temperature range 0.4-2°K for the Airco-Speer graphite neutron irradiated to various doses. The thin lines indicate the linear and cubic components extrapolated down from higher temperatures.
Fii. 4. Specitic heat data for the series of AS samples over a wider temperature range (0.4-45°K). combining the results of Fig. 3 with older data[f]. The data for AS 1250hr from 1.5to 45°K are new, and were obtained in a He4cryostat.
215
Specific heat of soft carbons between 0.4 and 4.5”K-III increase of the height of the peak decreasing at higher
doses indicating incipient saturation at higher doses. (2) The position of the peak shifts gradually to higher temperature with increase of the dose. In relation to the carbonization peaks (Fig. 1) of comparable height all the irradiation peaks are located at temperatures higher by about 0.06S”K (see Table 2). (3) On the low temperature side of the peak the specific heat varies with cube of temperature (/.X3), with a linear component ST changing from a negative to a large positive as the dose increases. The data are collected in Table 2. The coefficient /3 of the cubic term varies strongly with the height of the peak, a behavior remarkably different from the behavior observed in the carbonizationgraphitization series. (4) On the high temperature side of the peak the specific heat falls off steeply for the lowest dose, but for the 50 hr dose some kind of high temperature tail builds up, which then moves away from the peak to higher temperature as the dose increases, as shown by the breaks in the two upper curves. (5) The extrapolated linear coefficient y increases greatly with the dose and the height of the peak, and does not show the saturation effect at and around y = 0.5, as observed for the carbonization series. Although it might be argued that in case of the 1250hr dose our y is too high, because we have not extended our measurements to sufficiently high temperature so as to obtain a reliable extrapolation, such correction could not lower y so much as to wipe out this difference in behavior. It seems that the y saturation effect in the case of the carbonization series must be in some way connected with the presence of the organic groups on the peripheries of the carbon structure and/or with the disappearance of the electronic conductivity (see discussion, Section 4). (6) In the range of higher temperatures the cubic term crT’ decreases with increase of the dose and with increase of the disorder, a behavior opposite to the one observed in the carbonization-graphitization series. This decrease is, however, not reflected in any change in the Debye temperature [ 141,so that this must be an effect limited to a narrow range of the low temperatures. 3.3 Analysis of the data The curves Fig. 1 were replotted on a C/T vs T plot and the areas corresponding to the peaks, that is areas above the extrapolated linear and the cubic terms (AC = C - yT - aT3), were determined using a planimeter. To have closed areas, the C/T curves were extrapolated to lower temperatures following the dependence ST + :$T3 down to 0°K when S > y, or to the crossing
point with the yT + aT’ curve in case of S < y. The concentration of the defects responsible for the peak obtained from integration of such areas, assuming two space alignments possible for each defect, are given below in Table 3. The specific heat curves corresponding to the peaks alone, that is AC = C - yT - aT3, are presented in Fig. 5. For low concentrations, the tips of the peaks are very sharp and so on the figure they were left open, since with our equipment the presence of a phase discontinuity, if present, could not be ascertained. For the two highest concentrations, the relatively slow cubic decay on the high temperature side in Fig. 1, causes the peaks to round off and AC to reach a maximum above and beyond the location of the peak in Fig. 1, the AC/T peak showing up only as a break in the AC vs T curve. The locations of the AC/T peaks are indicated on Fig. 5 by downward pointing
T, “K
Fig. 5. Plots of the contribution of the specific heat peak alone for the heattreatment series, obtained from Fig. 1 after subtracting the extrapolated linear and cubic terms. The positions of the peaks from Fig. I are indicated by downward pointing arrows.
Table 2. Low temperature specific heat data for the AS graphite neutron irradiated series Sample dose (hr)
T,,,*(“K*)
2-m(“K)
Height of peak alone
0.44 0.50 0.55 0.62
0.662 0.706 0.742 0.775
85 560 2110 2920
0
IO 50 250 1250
CAR Vol. 14, No. 4-C
S
P (relat.)
Y
a (relat.)
-130 50 950 2020
1.0 2.2 4.5 6.0
25 55 260 425 1550
1.1 1.1 0.57 0.57 0.65
0
S. MROZOWSKI and A. S. VAGH
216
arrows. We were wondering if the effect of rounding off is possibly due to some deficiencies in our equipment or in our procedures, but this does not look probable; the peculiarity seems to be real and corresponds to some kind of nonhomogeneity among the various domains occurring at high spin concentrations. The curves Fig. 3 were also replotted on a C/T vs T plot and the areas AC/T for the peaks alone determined similarly as in the case of the carbonization peaks, except that in the cases of S < y (the two lower doses) no extrapolation was necessary. Both experimental curves cross the extrapolated yT f aT’ curves, possibly showing that a yT t aT’ curve is not the real asymptotic relation for T + 0°K. The concentrations of the defects responsible for the peak obtained by such integration are given below in Table 3. The specific heat curves corresponding to the peaks themselves, are presented in Fig. 6. The downward pointing arrows indicate the location of each peak taken from Fig. 3, whereas the upward pointing arrows focus the attention on breaks in the curves. At the tip of the uppermost curve an incipient effect of rounding off of the peak is seen, analogous to the effect observed on Fig. 3 for RC 680 and RC 600. Not wanting to destroy our samples, we have not yet
2.:
50 c
I
K-S irr.dose 7~10~ I-& B irr.dose6 xlOI nvtinterpolated L500hrsv/
-I J -L =U
Fig. 7. Plot of specific heat data obtained by Kimura and Suzuki[lS] for a neutron irradiated polycrystalline graphite in the temperature range 1.7-12°Kand for the same graphite after it was annealed at 700 and 1750°C.A low temperature curve B, for our AS graphite irradiated to a dose of 5OOhr calculated by interpolation between the curves of Fig. 3, is inserted to emphasize the influence of anneal on the low temperature part of the curve.
shows the data of Kimura and Suzuki combined with a hypothetical curve which would be obtained by us, if we would have had irradiated the AS graphite for about 500 hr (curve calculated by interpolation between the 250 and 1250hr doses). The Fig. 7 shows quite convincingly that: (a) The anneal to 700°C cuts down the anomalously large value of the linear term yT, at the same time increasing the cubic component aT3 (as it looks, most probably wipes out also the anomalous peak). (b) Further anneal to 175O”C,which almost completely reverts the polycrystalline graphite from the partially disordered 700°C state to its original well ordered state, brings a decrease in the cubic component.
2c
T
performed experiments on annealing the defects by re-heattreatment of the irradiated material, but work done by Kimura and Suzuki[lS] some years ago, when combined with our results, furnishes some important insight into the nature of the effects in question. Figure 7
15
F ? s E -z 3 IO
4. DISCUSSION 05
J
0
T. OK Fig. 6. Plots of the contribution of the specific heat peak alone for the irradiation series, obtained from Fig. 3 after subtracting the extrapolated linear and cubic terms. The position of the peaks from Fig. 3 are indicated by downward pointing arrows. The upward pointing arrows direct the attention to breaks in the high temperature tails, evidencing some kind of structure in these tails.
As stressed in the introduction and discussed in more detail in our recent publication[8], it seems pretty certain now that the two anomalies, that is the appearance of the peak and of the linear term are both caused by the presence in the material of localized free spin centers. We believe that the peak corresponds to a A-phase transition of an antiferromagnetic type. As it was found, however [8], only a small fraction of all spins takes part in this transition. With the new data available from this work, a broader view and better understanding of the reasons involved in this can be obtained. In Table 3 are presented all the data obtained (Section 3.3) for the concentrations of spins taking part in the A-transition (peak alone) and below of each of these values is given the
Specificheat of soft carbons between 0.4 and 4.5”K-III
217
consequence of the statistics of density flu~t~tions in local distribution of spins. One has to bear in mind that even for the highest spin concentrations obtainable in carbons (KIT - 65O”C,or for heaviest neutron dose) the spin systems are still quite diluted, the average distance between spins being not less than 6 atomic distances. Somehow the spins pair off by an unknown but very effective mechanism, when they find themselves at a closer distance than that. As the average concentration of spins increases, this pairing off process d~inishes greatly the effectiveness of the statistical fluctuations and, consequently, the density of the spins tends to become more and more uniform throughout the material.
corresponding concentration of the localized spins as determined by us by the use of the ESR technique[X]. The values for the irradiated AS samples and for the two RC 600 and RC 680 should be quite reliable. However, for the heattreatment series starting from RC 800 up all the ESR estimates are pretty rough, because for these types of soft carbons the ESR line is wide and unsymmetric, the shape and width changing with temperature. Thus all the concentrations of localized spins found by us were lower than those measured for equally heattreated P33 carbon black, this agreeing with observations of others on other soft carbons. The Table 3 shows clearly a very interesting trend of an increasing percentagewise contribution of the localized
Table 3. Concentrations of defects responsible for the specific heat alone compared with localized Spin concentrations as determined by the ESR technique Sample Spec. H. Peak (cone. per g) ESR (cont. per g) Ratio (%) Sample Spec. H. Peak (cont. per g) ESR (cont. per g) Ratio (%)
NCC 2000
RC 680
RC 800
2.5 x IOi9
2.0 x lOI
8.4 x 10”
1.4x lo’*
3.0 x 10”
2.5-5 x 1o’9
2-3 x lOI
4.2-8.4 x 10”
1.65-4.2x lo’* s-2
1.05x IOZD 1.25x to**
NCC 1250
RC 1700
RC 600
23
16
33-16
7-5
7-3.6
AS 1250
AS 250
AS 50
AS 10
AS0 0
2 x lOi
1.45x lOi
2.5 x 1o’s
8.4 x lO’=
9.5 x 10’9
7.8 x lOi
2.5 x 1019
3.7 x 1018
21
18.5
10
spins to the antiferromagnetic phase as the total concentration of localized spins increases. At low concentration the transition at the A-point is very sharp-the domains must be pretty un~orm, but as the concentration and the number of domains increase, inhomogeneities in distribution and size are setting in causing bumps in the high temperature tails for irradiated samples, and the rounding off of the peak for baked carbons. We believe the domains to be antiferromagnetic, not only because for all peaks the decay on the low temperature side is cubic (after all the magnon dispersion relations might not be the same for random spin systems, as they are for ordered systems), but on ground of more general considerations. There are no constraints of a geometrical nature for randomly distributed spins in any space to form a single ferromagnetic domain, nor are there constraints for a one-dimensional system (filament) to be wholly ant~e~omagnetic. But when in a two or tridimensional space one starts from a single spin and proceeds inverting spins of nearest neighbors, the system very quickly comes into conflict with itself, if and when the spins are distributed at random. Thus the growth of antiferromagnetic domains is halted by boundaries full of conflicting alignments. Since one can expect that antiferromagnetic domains can condense only when the local density of spins is sufficiently high, the lowering of the fraction of the total spin concentration responsible for the peak with decrease of the total concentration is a simple
2.2
8.4 x 1OlL
< 1x 10” 0
Being limited from above and from below, the spin density inside of the domains does not vary greatly. This is probably why the peak shifts in position with increase of average concentration not very much. A plot of the temperature T,’ vs the height of the peak ((AC/T’), = (C/T), - y - aZ”) gives roughly a relation T,* = A + BV((AC/T),), which indicates a tendency toward saturation at concentrations approaching the limiting one. But this relation beinga very rough one, the increasingly steep variation at low concentrations makes the exact value of A, the low concentration limit not only highly indefinite, but its existence questionable. The difference in position between the heattreatment series and the AS irradiated of about 0.065”Kmust be due to differences in the material itself transmitting the interaction, or in this case rather to differences in distribution of localized spin centers as they are created in heattreatment vs a more random distribution in irradiation. One has also to remember that the nature of spin centers in these two cases might be different: the centers formed in irradiation are annealed out at 3OO”C,whereas in the heattreatment series they need graphitization temperatures to be annihilated. The influence of the type of material on the strength of interac~on is dramatically exemplified by the large shift of the peak to lower temperature occurring in the case of Glassy Carbon (this might be connected with the lower concentration of conduction electrons and/or lower concentration of localized spins) [5].
218
S.
MROZOWSKI and
An explained in our previous publication[8] there are good reasons to expect that there is in soft carbons another peak present at lower temperature, analogous to the one found in Glassy Carbon[4]. This second, presumably also of a A-type, occurs when the temperature is lowered sufficiently for the conflict areas to be bypassed and for the rest of the field to freeze into an antiferromagnetic phase, with the conflict areas left behind in the form of islands (which continue to contribute to the linear effect). Naturally it is up to the experiments now in progress to test this hypothesis.? Since one does not know how far above 4S”K the anomalous linear term extends, one cannot determine by integration of the corresponding area on the C/T vs T graph the fraction of spins contributing to this effect. Not knowing also the possible contribution of the second peak, one can only hope that the entropy of both peaks and of the linear term will give a total concentration closely approximating the value obtained from the ESR measurements. It seems imperative then, that the studies of the specific heat be extended in both directions, that is, into temperature ranges below 0.4”K and above 4S”K. The striking difference in behavior of the linear effect at high concentrations between the HTT and the AS series, consisting in the linear coefficient y becoming about constant in the baking range 600-800°C might be due to the completely different nature of the spins in the two cases. In the baking range, the carbon is still an organic system and the spins are organic radicals, what is shown by their air sensitivity, and the material is very poorly conducting, if not at all. The fact that in spite of that the peak is so eminent, shows that the exchange via the conduction carriers is here of no importance. Also the smaller linear term would mean that a larger fraction of spins condenses into the antiferromagnetic phase. The response of the carbon material to neutron irradiation, consisting of a decrease in the cubic term aT’ is perplexing. The reduction of aT” is in some way connected with the presence of electronic spins, maybe a result of the gradual disappearance of the extra linear term at higher temperature. If the anneal of the spins at or above 300°C would modify only the low temperature part lWhile this paper was being prepared for publication, a second peak actually has been found by us at around 0.32”Kfor the NCC 1250 carbon, and reported at the 12th Carbon Conference in Pittsburgh (Abstract # 22, Carbon 13, 545, 1975).
A. S.
VAGH
of the specific heat curve, then one would have a reference curve for determination of the contribution of the spin defects to the entropy. Unfortunately, the Kimura-Suzuki results show that anneal wipes out this reference curve by modifying greatly the lattice contribution, that is by increasing the cyT3well above the value for unirradiated as well as irradiated material (note the crossing of curves irradiated and annealed 700” at around 6°K in Fig. 7). This change might be due to formation of interlayer C.-complexes by the diffusion of carbon atoms, or to other restructuring processes occurring in such anneal. All in all it seems that a clarification of the relationships in the higher temperature range (well above 4°K) is needed, particularly in relation to the annealing processes of damaged carbon materials. Acknowledgements-The authors express their thanks to Dr. G. Arnold, who has carried out a number of independent ESR intensity determinations to cross-check our data on localized spin concentrations, and to Dr. .I. Woollam of the NASA Lewis Laboratories in Cleveland, who has been instrumental in obtaining the impurity analyses on our samples.
REFERENCES
1. P. Delhaes and Y. Hishiyama, Carbon 8,31(1970). 2. K. Kamiya, S. Mrozowski and A. S. Vagh, Carbon 10, 267 (1972). 3. A. S. Vagh, B. Carton and S. Mrozowski, Carbon 12, 645 (1974). 4. S. Mrozowski, S. Orzeszko and A. S. Vagh, Carbon 12, 651 (1974). 5. S. Orzeszko and K. T. Yang, Carbon 12, 493 (1974). 6. P. Delhaes, M. Lemerle and G. Blondet-Gonte, C. R. Acad. Sci. Paris 272, 1285(1972). 7. G. Blondet-Gonte, P. Delhaes and M. Daurel, Solid State Comm. 10, 819 (1972). 8. A. S. Vagh and S. Mrozowski, Carbon 13, 301 (1975). 9. E. S. R. Gopal, Specific Heats at Low Temperature. Plenum Press, New York (1966). 10. P. W. Anderson, B. L. Halperin and C. M. Varma, Phil. Msg. 25, 1 (1972). 11. T. A. Kaplan, S. D. Mahanti and W. M. Hartman, Phys. Rev. Lett. 27, 1756 (1971). 12. S. Mrozowski, paper in Industrial Carbon and Graphite. Sot. of Chem. Industry, London (1958).p. 7. 13. Y. Hishiyama, S. Mrozowski and A. S. Vagh, Carbon 9,367 (1971). 14. A. S. Vagh and S. Mrozowski, Carbon 11, 151(1973). 15. 0. Kimura and H. Suzuki, Symposium on Carbon, Tokyo (1964), Abstract VI-l. 16. S. Mrozowski, Carbon 3,305 (1965);Ibid. 6,841 (1%8); Ibid. 9, 97 (1971).
Pergamon Press.
Printed in Great Britain
SPECIFIC HEAT OF SOFT CARBONS BETWEEN 0.4 AND 4S°K-III* S. MROZOWW and A. S. VAGH Carbon Research Laboratory, State University of New Yorkat Buffaloand Departmentof Physicsand Astronomy, BallStateUniversity,Muncie, IN 47306,U.S.A. (Received 25 February 1976) Abstract-A more extensive and thorough investigation of the specific heat of two series of soft carbons heattreated to various temperatures from 600to 3OOO’C and of a series of samples of an AS graphite neutron irradiated to various doses, was carried out. In particular, efforts were concentrated on mapping out the exact shape and position of the low temperature peak. A spectroscopic analysis of the impurity content of several of the investigated samples was made and the concentrations of localized spins were determined for all samples by means of the ESR technique. The most important result of this study is, that as the temperature is lowered, a fraction of all localized spins condenses at around 0.65”Kinto an antiferromagnetic phase, the fraction varying from about 2% for lowest up to 20% or more for the highest spin concentrations. An interpretation of the results is suggested and some other questions and difficulties brought out by this work are discussed.
1. INTRODUCllON
Whereas the theory of lattice vibrations and of the electronic band structure of a perfect graphite crystal has been developed to a pretty high degree of perfection, the nature of defects introduced by various means and their influence on various properties of graphite is much less understood. Still less so are the nature and peculiarities of the disorder in carbons on their way to graphitization. A partial disorder is composed of the sum of many defects of various kinds, and any technique which permits to study the influence and behavior of selected type of defects becomes a valuable tool in the quest to unravel the secrets of the disordered state. In two earlier papers under the same title (Part I [ 1] and Part 11[2])we have reported our findings on the anomalies observed in the specilic heat of soft carbons in the temperature range 0.6-4.2”K. When defects are present in the lattice, due either to the disorder resulting in the process of carbonization, or to lattice damage inflicted upon a graphitic structure by neutron irradiation a formation of a specific heat peak at around 0.6-0.7”K and an appearance of a large linear term of noncarrier origin were observed. Similar anomalies have been found by us to show up in Glassy Carbon, with a peak being located at temperature below our reach ( < 0.4”K)[3,4]. However, the observation of the tail of the peak (above 0.4”K) has supported the earlier suspicions that the development of the peak goes in parallel with the linear term, and that both these anomalies are directly related to the presence in the material of localized free electronic spins. The absence of a tail and the small value of the linear term for Glassy Carbon heattreated to 3OOO”C, which still remains in a highly disordered state and thus possesses many defects of various kinds, but for which the localized free spins are annealed out by such heattreatment [5], serves as a case in point. Extending the magnetic field dependence study of *Researchsupportedby the National Science Foundation.
Delhaes, Lemerle and Blondet-Gonte [6] and of BlondetGonte, Delhaes and Daure1[7] to sufficiently low temperature, so as to observe the behavior of the peak itself, we have found[8] that the peak is affected by the magnetic field in a general manner indicating its nature to be of a cooperative magnetic origin. Whereas the linear term might find an explanation analogous to the one of a linear term observed for some metal alloys and believed to be connected with presence of randomly distributed spins (for older literature on the subject see Gopal[9], pp. 71 and 82. In the newer literature a name of “spin glasses” was introduced by Anderson [ lo], see also Ref. [ 1l]), no magnetic phase transition has been found to occur in such disordered spin systems. To obtain more information about the transition observed in carbons (which we believe to be antiferromagnetic) a more detailed and precise study of the peak’s shape than in the exploratory work carried out previously[2], was undertaken for soft carbons. The results of this new series of measurements are presented below. 2. EXPERIMENTAL 2.1 Apparatus and measuring techniques The same ‘He cryostat built by Janis Research Co. was used in this work as previously [1,2,8]. However, after having finished the magnetic field dependence studies [8], the wide tail was reinstalled, so as to accommodate all the samples, of which some were of a larger size. AU measurements at temperature below 2°K were made with the sample in contact with the cooling block. The sample was held against the block by strings and springs, and was surrounded by a radiation shield attached to the block. The heat pulses were applied to the sample after its temperature equilibrated with that of the block in their very slow warming up process. To avoid any possible small differences in standardization of the thermometers, one and the same Germanium thermometer was used for all the series of measurements reported in this paper. A few series of measurements were carried out in the 211
212
S.
MROZOWSKI and
temperature range l.S-45°K using our regular He4 apparatus, some of the individual points being obtained with the sample in contact, and some others after separation, in order to check the reliability of both procedures. Good agreement was always found. The electronics was further improved and interferences reduced. The evaluation of data, and corrections for the heat capacity of the thermometer glue and strings were introduced the same way as previously.
2.2 Materials In these studies of the heattreatment dependence of the specific heat, we have investigated two sets of samples of soft carbons. They were the same as used in our previous work[2]. National Carbon Company commercial baked carbon rods (here designated NCC) were heattreated to various temperatures in a graphite tube electric furnace. The NCC carbon is a material composed mostly of calcined petroleum coke with some addition of carbonized coal tar binder (about 15% of total weight), the material having been baked to a temperature of about 900°C. Since the petroleum coke previous to baking was calcined in a commercial operation to about 1250°C to avoid inhomogeneities the NCC carbon was heattreated to no less than 1250°C. The second set of samples was made in our laboratory entirely from Resin C pitch. The Resin C is a pitch obtained from coal tar by distillation and thus does not contain the so-called second phase of colloidal benzol-insoluble particles. We have prepared a raw coke from it (at about 600°C) and then made carbon rods by extruding the finely ground raw coke with Resin C pitch as binder. These RC rods were baked to various temperatures up to 900°C in our laboratory baking furnace, and then higher in the graphite tube furnace. The kinetics of the carbonization and graphitization process is such that the properties of the material depend strongly on heattreatment temperature and on residence time at the top temperature. In all graphite tube furnace runs the residence time was 15 min (this happens to be about equal to the duration of the calcination in commercial operations). In baking, however, the residence time had to be necessarily much longer, being of an order of no less than 6 hr in case of our laboratory baking furnace. Such an increase in residence time by a factor of 25 is known to be roughly equivalent to an increase in the heattreatment temperature by about 100°C. In order to assign a common HTT scale to all samples of the series, we have determined the equivalent 15min heattreatment temperature for the samples baked to 500,600 and 700°C by establishing the temperature above which the ESR intensity begins to change when the sample is submitted to a sequence of increasing 15min heattreatments. The equivalent temperatures so obtained and recently rechecked of 600, 680 and 800°C are accurate to about * 10°C. Although both types of carbon (NCC and RC) are of the soft variety, the fact that the Resin C coke was ground at the raw stage and also that the binder was introduced at that stage, causes some small differences in response to heattreatment, in particular at higher temperatures, where
A. S. VAGH
the graphitization process is somewhat hindered by the structural deformation introduced into the raw coke [ 121. The composition of the two groups of samples was given here in detail to emphasize the differences in their origin. Whereas the petroleum coke contains little of inorganic impurities incorporated into the structure (metals, sulfur, etc.), the Resin C possesses some impurities characteristic to coal, of which only those which are chemically bonded to organic molecular systems are transported into the Resin C in the distillation process. But the two groups of impurities coming from petroleum and from coal have a very different distribution in concentration (some of the impurities contained in one are entirely absent in the other). Thus when concordant results are obtained from both series of carbons, this indicates strongly that the effects observed are not caused by impurities, but are due to the carbon structure itself. In order to satisfy our curiosity as to the degree of purity of the commercial product, we have submitted a sample of the NCC 1250carbon to a spectrographic check at the NASA analytical laboratory. The following impurities were found in ppm: Al, 50; Ca, 30; Co, 10; Cr, 10; Cu, 10; Fe, 60; Mg, 20; Ni, 50; Si, 75; Ti, 15; all of the others being below the limits of detection. All of these impurities are known to be characteristic to the nonpurified calcined petroleum cokes. Apparently very little or no iron oxide was added in the manufacturing process. Since both materials retain some impurities even after highest heattreatments, a study of a very pure carbon was considered imperative. For the study of the influence of neutron irradiation, a so-called high purity nuclear polycrystalline graphite made by the Airco Speer Company was used. This is a material very similar in composition to the NCC carbon, heattreated to about 2800°C and subjected during the heattreatment to the F-process high temperature purification (chlorinefluorine). Such material is pure as far as inorganic impurities are concerned down to millionth parts per weight of carbon, the only larger impurity concentration corresponding to gases adsorbed on the surfaces of pores and to dust picked up while the material is handled in air. The AS graphite samples were subjected to neutron irradiation in Western New York Reactor facility for various lengths of time, by placing the samples in sealed aluminum capsules. In the case of the hole used by us, the total flux of neutrons with energies above 10KV was 3.6 x lOI nv, the thermal flux being considerably lower (around 2 x 10” nv). But the exact energy distribution of neutrons causing the damage (and their effectiveness) being unknown for this and many other reactors, comparisons based on the total dose applied are not very meaningful. We have found in our work that it is much better to compare the doses by their effectiveness in damaging the lattice, the damage being evaluated by measurements of the Hall coefficient[l3]. In the case of the AS graphite (and other polycrystalline graphites) the Hall coefficient measured at 78°K reaches its positive maximum after a 12hr exposure in the WNY reactor (1.5 x lOI*nvt dose of fast neutrons), and this figure should be used in comparing our results to others. In the case of all irradiations, with the exception of the
Specific heat of soft carbons between 0.4 and 4S”K-III
heaviest one, the radioactivity of the samples decayed in few weeks to a level at which we were permitted to use them in our laboratory. This was a good proof of the high purity of the AS graphite. In the case of the heaviest dose (1250hr), the cool-off period extended, however, over several months. Although the impurities can be easily identified by the decay periods involved, and their concentrations estimated, to remove all doubts of those less acquainted with the purity levels achieved in nuclear graphites, we have taken small slices from the ends of our rods, and subjected them to a spectrographic check at the NASA analytical laboratory. The sample of unirradiated Airco-Speer graphite was found to contain only measurable amounts of Al (10 ppm) and Mg (2 ppm) and some Cu (< 1 ppm), all the other elements being below detection limits, whereas the same material after the heaviest irradiation (1250hr = 1.6 x 102’ fast neutron dose) was found to contain less Al (4ppm) and Mg (< 1 ppm), but more Cu (1.5 ppm), with all other elements being again below the limits of detection. The small amounts of aluminum found are probably due to the Al-foil in which samples were kept and of the copper to the contact with the copper He3 condensing container in the specific heat experiments (slices of the outside surface of rods end were submitted to the analysis!). Thus, whereas the total concentration of impurities in carbons is of the same order as the concentration of defects responsible for the specific heat peak, the impurity level in AS graphite is by at least two orders of magnitude lower, removing all doubts as to the origin of the anomalies observed being due to defects in the carbon lattice. 3. RESULTS
3.1 The heattreatment series The results of the detailed mapping out of the specific heat peak for the two series of variously heattreated soft carbons are shown in Fig. 1 on a C/T vs T2 graph. The thin straight lines drawn indicate the combined cubic
T2.
OK’
Fig. 1. Specific heat data obtained in the temperature range
0.4-2°Kfor two series of soft carbons RCand NCC heattreated to various temperatures. The curve for RC 1000is taken from older data[Z]. The thin lines indicate the linear and cubic components extrapolated down from higher temperature.
213
(oT’) and linear (yT) contributions to the specific heat, and were obtained by extrapolation of the straight line portions of the curves at temperatures well above the peak taken from Fig. 2. Figure 2 shows the results plotted on a compressed scale, with all earlier results [ 1,2] added to the new ones. In order not to crowd the graphs, the
5
IO
15
20
TZ. OK2
Fig. 2. Specific heat data for the two series of soft carbons RC and NCC over a wider temperature range (0.4-4S”K), combining the results of Fig. 1witholder data[l, 21.
individual experimental points are omitted in this case. A number of regularities are right away noticeable in perusing the Figs. 1 and 2: (1) The concentration of defects responsible for the peak itself decreases continuously with increasing temperature of heattreatment (HIT). The peak disappears when the material is heattreated to or above 2800°C. (2) The position of the peak is not constant, but shifts gradually to lower temperature as the HTT increases and the height of the peak diminishes (see Table 1). (3) On the low temperature side of the peak the specific heat variation with temperature is cubic (/3T’) with a linear component (ST) which varies from high positive to negative values as the HTT increases. The coefficient /3 of the cubic term varies only little with heattreatment. The data are collected in Table 1. The meaning of a negative linear term is obscure. It seems, however, that probably the cubic relationship does not extend much farther into the lower temperatures anyway. When we happened to reach temperatures below 0.45”K in case of the NCC 1250 sample, the cubic decrease was found to terminate, the curve indicating possibly a turnaround (which seems quite definite, in spite of the low reliability of the extrapolation of the thermometer calibration below 0.45”K). (4) On the high temperature side of the peak, the specific heat falls off very steeply for higher HTT’s and much less so for the lower HTT’s but in any case the decrease is too rapid (and the peak too sharp) to be consistent with a Schottky type of anomaly. Clearly the peak must be due to some kind of cooperative effect.
214
S. MROZOWSKI
and A. S.
VAGH
Table 1. Low temperaturespecificheatdatafor the heattreatmentseries of soft carbons Sample RC 600 RC 680 RC 800 RC 1000 RC 1250 NCC 1250 NCC 1600 RC 1700 NCC 2000 NCC 2400 NCC 3100
Height of peak alone
S
B (relat.)
2900 1900 1100
3.4 4.6 4.3
T,‘eK’)
T,(OK)
0.53 0.50 0.47
0.726 0.707 0.686
3300 2840 2OOtJ
0.405
0.637
515
-200
3.4
0.38 0.357
0.610 0.598
285 140 110
- 320 -560
3.1 3.9
(5) The coefficient y of the linear term increases greatly with decrease in heattreatment temperature (and increase in concentration of defects) down to HlT 800°C and stays about constant below that. (6) The cubic part aT3 increases greatly with decrease in HTT and with increase in lattice disorder, particularly so for heattreatments below 1000°Cwhere the carbon is essentially still a kind of organic polymer. It was shown that this increase in (Yresults directly from a decrease in the Debye temperature 8[14]. (7) The quadratic deviation, caused by the twodimensionality of the benzene ring planes being held mutually by weak Van der Waals forces, and evidenced in Fig. 2 by the curving of the lines (above T*= 3), is greatest for HZT between 2000 and 24OO”C,and completely disappears (in the temperature range investigated) for HTT 1250°Cand lower. (8) As expected, only small differences between the two series are observable on Fig. 2. Whereas the RC carbon seems to be slightly ahead of the NCC at HTT 125O”C,it begins to lag behind at higher heattreatment, so that RC at HTT 1700°Cis not much ahead of NCC 1600. This is explainable by the slight retardation in crystallite growth observed for carbons prepared from the raw coke[l2]. 3.2 Neutron damage series Whereas in our exploratory work[2] we concentrated on the similarities between the anomalies observed in the carbonization-graphitization ordering process and in the inverse process of destruction of order by neutron irradiation (something like degraphitization), the present more precise study has revealed interesting differences in detailed behavior. The results of the mapping out of the specific heat peak for the neutron irradiated Airco-Speer polycrystalline graphite are presented in Fig. 3 on a C/T vs T graph. Figure 4 shows the same on a compressed temperature scale, with the earlier results [2] added to the new ones in drawing all curves. The data for the 125Ohr irradiation dose in the range 1.S4S”K in Fig. 4 are new, and were obtained using our old He4 cryostat. The thin lines on Fig. 3 are the extrapolations obtained from Fig. 4. On Figs. 3 and 4 a number of regularities are noticeable: (1) The concentration of defects responsible for the peak increases with the irradiation dose, the rate of
0.5.
2,
05
a (relat.)
490 420 445 260 170 145 100 120 95 55 25
11.6 7.7 3.9 3.3 2.5 2.6 2.2 1.85 1.85 1.2 1.0
sin50
___*zL
As
"O-
y
-
~~
ml0 IO
15
20 25 T',OK2
3.0 35
4.0
Fig. 3. Specific heat data obtained in the temperature range 0.4-2°K for the Airco-Speer graphite neutron irradiated to various doses. The thin lines indicate the linear and cubic components extrapolated down from higher temperatures.
Fii. 4. Specitic heat data for the series of AS samples over a wider temperature range (0.4-45°K). combining the results of Fig. 3 with older data[f]. The data for AS 1250hr from 1.5to 45°K are new, and were obtained in a He4cryostat.
215
Specific heat of soft carbons between 0.4 and 4.5”K-III increase of the height of the peak decreasing at higher
doses indicating incipient saturation at higher doses. (2) The position of the peak shifts gradually to higher temperature with increase of the dose. In relation to the carbonization peaks (Fig. 1) of comparable height all the irradiation peaks are located at temperatures higher by about 0.06S”K (see Table 2). (3) On the low temperature side of the peak the specific heat varies with cube of temperature (/.X3), with a linear component ST changing from a negative to a large positive as the dose increases. The data are collected in Table 2. The coefficient /3 of the cubic term varies strongly with the height of the peak, a behavior remarkably different from the behavior observed in the carbonizationgraphitization series. (4) On the high temperature side of the peak the specific heat falls off steeply for the lowest dose, but for the 50 hr dose some kind of high temperature tail builds up, which then moves away from the peak to higher temperature as the dose increases, as shown by the breaks in the two upper curves. (5) The extrapolated linear coefficient y increases greatly with the dose and the height of the peak, and does not show the saturation effect at and around y = 0.5, as observed for the carbonization series. Although it might be argued that in case of the 1250hr dose our y is too high, because we have not extended our measurements to sufficiently high temperature so as to obtain a reliable extrapolation, such correction could not lower y so much as to wipe out this difference in behavior. It seems that the y saturation effect in the case of the carbonization series must be in some way connected with the presence of the organic groups on the peripheries of the carbon structure and/or with the disappearance of the electronic conductivity (see discussion, Section 4). (6) In the range of higher temperatures the cubic term crT’ decreases with increase of the dose and with increase of the disorder, a behavior opposite to the one observed in the carbonization-graphitization series. This decrease is, however, not reflected in any change in the Debye temperature [ 141,so that this must be an effect limited to a narrow range of the low temperatures. 3.3 Analysis of the data The curves Fig. 1 were replotted on a C/T vs T plot and the areas corresponding to the peaks, that is areas above the extrapolated linear and the cubic terms (AC = C - yT - aT3), were determined using a planimeter. To have closed areas, the C/T curves were extrapolated to lower temperatures following the dependence ST + :$T3 down to 0°K when S > y, or to the crossing
point with the yT + aT’ curve in case of S < y. The concentration of the defects responsible for the peak obtained from integration of such areas, assuming two space alignments possible for each defect, are given below in Table 3. The specific heat curves corresponding to the peaks alone, that is AC = C - yT - aT3, are presented in Fig. 5. For low concentrations, the tips of the peaks are very sharp and so on the figure they were left open, since with our equipment the presence of a phase discontinuity, if present, could not be ascertained. For the two highest concentrations, the relatively slow cubic decay on the high temperature side in Fig. 1, causes the peaks to round off and AC to reach a maximum above and beyond the location of the peak in Fig. 1, the AC/T peak showing up only as a break in the AC vs T curve. The locations of the AC/T peaks are indicated on Fig. 5 by downward pointing
T, “K
Fig. 5. Plots of the contribution of the specific heat peak alone for the heattreatment series, obtained from Fig. 1 after subtracting the extrapolated linear and cubic terms. The positions of the peaks from Fig. I are indicated by downward pointing arrows.
Table 2. Low temperature specific heat data for the AS graphite neutron irradiated series Sample dose (hr)
T,,,*(“K*)
2-m(“K)
Height of peak alone
0.44 0.50 0.55 0.62
0.662 0.706 0.742 0.775
85 560 2110 2920
0
IO 50 250 1250
CAR Vol. 14, No. 4-C
S
P (relat.)
Y
a (relat.)
-130 50 950 2020
1.0 2.2 4.5 6.0
25 55 260 425 1550
1.1 1.1 0.57 0.57 0.65
0
S. MROZOWSKI and A. S. VAGH
216
arrows. We were wondering if the effect of rounding off is possibly due to some deficiencies in our equipment or in our procedures, but this does not look probable; the peculiarity seems to be real and corresponds to some kind of nonhomogeneity among the various domains occurring at high spin concentrations. The curves Fig. 3 were also replotted on a C/T vs T plot and the areas AC/T for the peaks alone determined similarly as in the case of the carbonization peaks, except that in the cases of S < y (the two lower doses) no extrapolation was necessary. Both experimental curves cross the extrapolated yT f aT’ curves, possibly showing that a yT t aT’ curve is not the real asymptotic relation for T + 0°K. The concentrations of the defects responsible for the peak obtained by such integration are given below in Table 3. The specific heat curves corresponding to the peaks themselves, are presented in Fig. 6. The downward pointing arrows indicate the location of each peak taken from Fig. 3, whereas the upward pointing arrows focus the attention on breaks in the curves. At the tip of the uppermost curve an incipient effect of rounding off of the peak is seen, analogous to the effect observed on Fig. 3 for RC 680 and RC 600. Not wanting to destroy our samples, we have not yet
2.:
50 c
I
K-S irr.dose 7~10~ I-& B irr.dose6 xlOI nvtinterpolated L500hrsv/
-I J -L =U
Fig. 7. Plot of specific heat data obtained by Kimura and Suzuki[lS] for a neutron irradiated polycrystalline graphite in the temperature range 1.7-12°Kand for the same graphite after it was annealed at 700 and 1750°C.A low temperature curve B, for our AS graphite irradiated to a dose of 5OOhr calculated by interpolation between the curves of Fig. 3, is inserted to emphasize the influence of anneal on the low temperature part of the curve.
shows the data of Kimura and Suzuki combined with a hypothetical curve which would be obtained by us, if we would have had irradiated the AS graphite for about 500 hr (curve calculated by interpolation between the 250 and 1250hr doses). The Fig. 7 shows quite convincingly that: (a) The anneal to 700°C cuts down the anomalously large value of the linear term yT, at the same time increasing the cubic component aT3 (as it looks, most probably wipes out also the anomalous peak). (b) Further anneal to 175O”C,which almost completely reverts the polycrystalline graphite from the partially disordered 700°C state to its original well ordered state, brings a decrease in the cubic component.
2c
T
performed experiments on annealing the defects by re-heattreatment of the irradiated material, but work done by Kimura and Suzuki[lS] some years ago, when combined with our results, furnishes some important insight into the nature of the effects in question. Figure 7
15
F ? s E -z 3 IO
4. DISCUSSION 05
J
0
T. OK Fig. 6. Plots of the contribution of the specific heat peak alone for the irradiation series, obtained from Fig. 3 after subtracting the extrapolated linear and cubic terms. The position of the peaks from Fig. 3 are indicated by downward pointing arrows. The upward pointing arrows direct the attention to breaks in the high temperature tails, evidencing some kind of structure in these tails.
As stressed in the introduction and discussed in more detail in our recent publication[8], it seems pretty certain now that the two anomalies, that is the appearance of the peak and of the linear term are both caused by the presence in the material of localized free spin centers. We believe that the peak corresponds to a A-phase transition of an antiferromagnetic type. As it was found, however [8], only a small fraction of all spins takes part in this transition. With the new data available from this work, a broader view and better understanding of the reasons involved in this can be obtained. In Table 3 are presented all the data obtained (Section 3.3) for the concentrations of spins taking part in the A-transition (peak alone) and below of each of these values is given the
Specificheat of soft carbons between 0.4 and 4.5”K-III
217
consequence of the statistics of density flu~t~tions in local distribution of spins. One has to bear in mind that even for the highest spin concentrations obtainable in carbons (KIT - 65O”C,or for heaviest neutron dose) the spin systems are still quite diluted, the average distance between spins being not less than 6 atomic distances. Somehow the spins pair off by an unknown but very effective mechanism, when they find themselves at a closer distance than that. As the average concentration of spins increases, this pairing off process d~inishes greatly the effectiveness of the statistical fluctuations and, consequently, the density of the spins tends to become more and more uniform throughout the material.
corresponding concentration of the localized spins as determined by us by the use of the ESR technique[X]. The values for the irradiated AS samples and for the two RC 600 and RC 680 should be quite reliable. However, for the heattreatment series starting from RC 800 up all the ESR estimates are pretty rough, because for these types of soft carbons the ESR line is wide and unsymmetric, the shape and width changing with temperature. Thus all the concentrations of localized spins found by us were lower than those measured for equally heattreated P33 carbon black, this agreeing with observations of others on other soft carbons. The Table 3 shows clearly a very interesting trend of an increasing percentagewise contribution of the localized
Table 3. Concentrations of defects responsible for the specific heat alone compared with localized Spin concentrations as determined by the ESR technique Sample Spec. H. Peak (cone. per g) ESR (cont. per g) Ratio (%) Sample Spec. H. Peak (cont. per g) ESR (cont. per g) Ratio (%)
NCC 2000
RC 680
RC 800
2.5 x IOi9
2.0 x lOI
8.4 x 10”
1.4x lo’*
3.0 x 10”
2.5-5 x 1o’9
2-3 x lOI
4.2-8.4 x 10”
1.65-4.2x lo’* s-2
1.05x IOZD 1.25x to**
NCC 1250
RC 1700
RC 600
23
16
33-16
7-5
7-3.6
AS 1250
AS 250
AS 50
AS 10
AS0 0
2 x lOi
1.45x lOi
2.5 x 1o’s
8.4 x lO’=
9.5 x 10’9
7.8 x lOi
2.5 x 1019
3.7 x 1018
21
18.5
10
spins to the antiferromagnetic phase as the total concentration of localized spins increases. At low concentration the transition at the A-point is very sharp-the domains must be pretty un~orm, but as the concentration and the number of domains increase, inhomogeneities in distribution and size are setting in causing bumps in the high temperature tails for irradiated samples, and the rounding off of the peak for baked carbons. We believe the domains to be antiferromagnetic, not only because for all peaks the decay on the low temperature side is cubic (after all the magnon dispersion relations might not be the same for random spin systems, as they are for ordered systems), but on ground of more general considerations. There are no constraints of a geometrical nature for randomly distributed spins in any space to form a single ferromagnetic domain, nor are there constraints for a one-dimensional system (filament) to be wholly ant~e~omagnetic. But when in a two or tridimensional space one starts from a single spin and proceeds inverting spins of nearest neighbors, the system very quickly comes into conflict with itself, if and when the spins are distributed at random. Thus the growth of antiferromagnetic domains is halted by boundaries full of conflicting alignments. Since one can expect that antiferromagnetic domains can condense only when the local density of spins is sufficiently high, the lowering of the fraction of the total spin concentration responsible for the peak with decrease of the total concentration is a simple
2.2
8.4 x 1OlL
< 1x 10” 0
Being limited from above and from below, the spin density inside of the domains does not vary greatly. This is probably why the peak shifts in position with increase of average concentration not very much. A plot of the temperature T,’ vs the height of the peak ((AC/T’), = (C/T), - y - aZ”) gives roughly a relation T,* = A + BV((AC/T),), which indicates a tendency toward saturation at concentrations approaching the limiting one. But this relation beinga very rough one, the increasingly steep variation at low concentrations makes the exact value of A, the low concentration limit not only highly indefinite, but its existence questionable. The difference in position between the heattreatment series and the AS irradiated of about 0.065”Kmust be due to differences in the material itself transmitting the interaction, or in this case rather to differences in distribution of localized spin centers as they are created in heattreatment vs a more random distribution in irradiation. One has also to remember that the nature of spin centers in these two cases might be different: the centers formed in irradiation are annealed out at 3OO”C,whereas in the heattreatment series they need graphitization temperatures to be annihilated. The influence of the type of material on the strength of interac~on is dramatically exemplified by the large shift of the peak to lower temperature occurring in the case of Glassy Carbon (this might be connected with the lower concentration of conduction electrons and/or lower concentration of localized spins) [5].
218
S.
MROZOWSKI and
An explained in our previous publication[8] there are good reasons to expect that there is in soft carbons another peak present at lower temperature, analogous to the one found in Glassy Carbon[4]. This second, presumably also of a A-type, occurs when the temperature is lowered sufficiently for the conflict areas to be bypassed and for the rest of the field to freeze into an antiferromagnetic phase, with the conflict areas left behind in the form of islands (which continue to contribute to the linear effect). Naturally it is up to the experiments now in progress to test this hypothesis.? Since one does not know how far above 4S”K the anomalous linear term extends, one cannot determine by integration of the corresponding area on the C/T vs T graph the fraction of spins contributing to this effect. Not knowing also the possible contribution of the second peak, one can only hope that the entropy of both peaks and of the linear term will give a total concentration closely approximating the value obtained from the ESR measurements. It seems imperative then, that the studies of the specific heat be extended in both directions, that is, into temperature ranges below 0.4”K and above 4S”K. The striking difference in behavior of the linear effect at high concentrations between the HTT and the AS series, consisting in the linear coefficient y becoming about constant in the baking range 600-800°C might be due to the completely different nature of the spins in the two cases. In the baking range, the carbon is still an organic system and the spins are organic radicals, what is shown by their air sensitivity, and the material is very poorly conducting, if not at all. The fact that in spite of that the peak is so eminent, shows that the exchange via the conduction carriers is here of no importance. Also the smaller linear term would mean that a larger fraction of spins condenses into the antiferromagnetic phase. The response of the carbon material to neutron irradiation, consisting of a decrease in the cubic term aT’ is perplexing. The reduction of aT” is in some way connected with the presence of electronic spins, maybe a result of the gradual disappearance of the extra linear term at higher temperature. If the anneal of the spins at or above 300°C would modify only the low temperature part lWhile this paper was being prepared for publication, a second peak actually has been found by us at around 0.32”Kfor the NCC 1250 carbon, and reported at the 12th Carbon Conference in Pittsburgh (Abstract # 22, Carbon 13, 545, 1975).
A. S.
VAGH
of the specific heat curve, then one would have a reference curve for determination of the contribution of the spin defects to the entropy. Unfortunately, the Kimura-Suzuki results show that anneal wipes out this reference curve by modifying greatly the lattice contribution, that is by increasing the cyT3well above the value for unirradiated as well as irradiated material (note the crossing of curves irradiated and annealed 700” at around 6°K in Fig. 7). This change might be due to formation of interlayer C.-complexes by the diffusion of carbon atoms, or to other restructuring processes occurring in such anneal. All in all it seems that a clarification of the relationships in the higher temperature range (well above 4°K) is needed, particularly in relation to the annealing processes of damaged carbon materials. Acknowledgements-The authors express their thanks to Dr. G. Arnold, who has carried out a number of independent ESR intensity determinations to cross-check our data on localized spin concentrations, and to Dr. .I. Woollam of the NASA Lewis Laboratories in Cleveland, who has been instrumental in obtaining the impurity analyses on our samples.
REFERENCES
1. P. Delhaes and Y. Hishiyama, Carbon 8,31(1970). 2. K. Kamiya, S. Mrozowski and A. S. Vagh, Carbon 10, 267 (1972). 3. A. S. Vagh, B. Carton and S. Mrozowski, Carbon 12, 645 (1974). 4. S. Mrozowski, S. Orzeszko and A. S. Vagh, Carbon 12, 651 (1974). 5. S. Orzeszko and K. T. Yang, Carbon 12, 493 (1974). 6. P. Delhaes, M. Lemerle and G. Blondet-Gonte, C. R. Acad. Sci. Paris 272, 1285(1972). 7. G. Blondet-Gonte, P. Delhaes and M. Daurel, Solid State Comm. 10, 819 (1972). 8. A. S. Vagh and S. Mrozowski, Carbon 13, 301 (1975). 9. E. S. R. Gopal, Specific Heats at Low Temperature. Plenum Press, New York (1966). 10. P. W. Anderson, B. L. Halperin and C. M. Varma, Phil. Msg. 25, 1 (1972). 11. T. A. Kaplan, S. D. Mahanti and W. M. Hartman, Phys. Rev. Lett. 27, 1756 (1971). 12. S. Mrozowski, paper in Industrial Carbon and Graphite. Sot. of Chem. Industry, London (1958).p. 7. 13. Y. Hishiyama, S. Mrozowski and A. S. Vagh, Carbon 9,367 (1971). 14. A. S. Vagh and S. Mrozowski, Carbon 11, 151(1973). 15. 0. Kimura and H. Suzuki, Symposium on Carbon, Tokyo (1964), Abstract VI-l. 16. S. Mrozowski, Carbon 3,305 (1965);Ibid. 6,841 (1%8); Ibid. 9, 97 (1971).