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Electron spin resonance in neutron irradiated and in doped polycrystalline graphite—Part I
Carbon
1965, Vol. 3, pp. 305320.
Pergamon Press Ltd.
Printed in Great Britain
ELECTRON SPIN RESONANCE IN NEUTRON
IRRADIATED
DOPED POLYCRYSTALLINE
AND IN
GRAPHITE-PART
I”
s. MRozowsKI Carbon Research Laboratory and Department of Physics, State University of New York at Buffalo, Buffilo, New York (Received 29 July 1965)
Abstract-The
electron spin resonance of neutron irradiated and lamellar compound doped, incompletely graphitized, P33 carbon black was investigated. An improved temperature arrangement operating from room temperature down to liquid nitrogen was constructed which permits one to perform speedy measurements with a minimum of corrections involved. It is shown that the intensity vs. temperature curves for P33 can be split into a sum of contributions of localized spin centers and conduction carriers; the irradiation producing mainly localized spins and the doping changing only the carrier concentration. The two kinds of spin centers interact by exchange so that they produce a single line with a g-value intermediate between that for localized spin centers gfne and for the conduction carriers g,. The g-value can be calculated using a simple mix formula, each type of spin contributing in proportion to its absorption intensity. The g, value for conduction carriers varies according to irradiation dose or amount of doping and is always lower than the directionally averaged graphite value due to a combined effect of displacement of the Fermi level and of the spreading apart of the layers, both causing a change in spin-orbit interaction. Extensive studies of variation in ESR parameters with irradiation dose, amount of doping (Li, Na, K, Rb, HIS04 and ammonia), temperature of anneal and ambient temperature permitted one, among other things, to observe the transition of the Fermi level across the center of the band overlap (with Na and Li).
1. INTRODUCTION NOT long ago WAGONER(~) and
in more detail, MULLER(‘) investigated the electron spin resonance in neutron-irradiated single crystals of graphite as a function of the irradiation dose. MULLET has shown that the intensity of resonance increases linearly with irradiation dose for doses smaller than 6~ 10’s nvt; from the slope of this line and the magnitude of the intensity at zero dose, MULLER calculated that about 30 spins per cm3 are created by each nvt. A considerably lower number was obtained by WAGONER(~)by comparing the effect of irradiation with boron doping of single crystals. With increasing irradiation dose the g-value and the g-anisotropy, as well as the line width, decrease gradually towards limiting values (gfree and width 1.3 G), thus suggesting to them that the nature of the spins created by neutron irradiation is the same as that of the spins *Supported by the U.S. Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. 305
responsible for the ESR absorption in pure graphite crystals (which have been shown earlier to be the charge carriers by WAGONER(~)), the changes in g-value and width being just the result of the shift of the Fermi level. Thus both MULLER and WAGONERconcluded that there is no evidence of formation of spin centers of a new kind at irradiation of single crystals and that therefore the early interpretation of the paramagnetic resonance of neutron-irradiated polycrystalline graphites as being due to carbon interstitial atoms suggested by HENNIC and HOVE(~) is incorrect. As well known, studies of the temperature dependence are most informative in determination of the nature of spin centers. Both WAGONERand MULLER have not performed temperature studies and in reaching their conclusion have not paid attention to a remark in HENNIG and Hovs’s paper concerning the temperature dependence of the resonance intensity, which according to approximate measurements carried out at two temperatures, was reported to be roughly of the Curie
306
S. MROZOWSKI
character. This strong temperature dependence of the ESR of heavily irradiated polycrystalline graphite was also observed by the author, who together with Y. YOKOZAWA, using a simple apparatus, performed some measurements on this substance.(‘) It was demonstrated by comparing the intensity of the ESR line with the intensity of a reference substance (DPP+H) that, whereas the intensity for unirradiated graphite is almost temperature independent, irradiated graphite shows quite closely inverse temperature dependence from room down to liquid nitrogen temperature. It has been later shown by NECHTSCHEINand ILESTER that the Curie dependence is obeyed by the irradiated graphite even down to the temperature of liquid helium. Thus as the irradiation proceeds localized spin centers must be created at a higher rate than any traps effecting an increase in conduction carrier concentration (holes). The process of irradiation seems to be opposite to what is observed when a carbon is graphitized. As ANTONOWICZ(‘)first observed and YOKO~AWA@) later checked more precisely, the temperature dependence changes gradually from partial Curie type for carbons heat treated in the range 12002000 to a pure carrier type with a slightly positive slope for well graphitized samples. As SINGER and WAGONER(~)have shown earlier, the ESR in well graphitized polyc~stalline graphites is due entirely to charge carriers, the observedg-value being a result of an averaging of g-values by conduction electrons in their travel across variously arranged microcrystallites. Adding the results of observation of ESR on doped carbons and graphites(“) it seemed evident that the variation in total intensity and in the g shift with temperature, with irradiation and with doping are each the result of an overlap of several different effects. The work reported here was undertaken in an effort to disentangle these effects; the material selected for this study was an incompletely graphitized carbon black, showing an intermediate temperature dependence of the intensity of ESR, so that induced changes towards more localized as well as towards more conduction type behavior could be observed.
frequency (17 kc/s) magnetic field sweep and phase sensitive detection system. The cavity is just a section of the waveguide located between the klystron and the detector and was operated in a rectangular TEroa mode. Since it was expected that in this work the dependence of the ESR intensity on temperature will have to be determined for a great number of samples, a variable temperature arrangement had to be constructed which would combine speed with sufficient accuracy. It was found that the arrangement shown in Fig. 1 satisfies these requirements. A small quartz double wall evacuated tube (Dewar) was inserted through the cavity (as shown in scale) and nitrogen gas flown through it. The gas came from a cylinder and was separated into two paths-one directly going to the Dewar, the other indirectly going first through a copper coil immersed in liquid nitrogen. By controlling the flow in each of the two branches any desired temperature from room down to 80°K can be obtained very rapidly and held reasonably constant. The samples were always in fine powder form, either powder being dispersed in par&in and attached to a quartz rod holder, or the powder SAMPLE
OUARTZ
HOLDER
OEWAR
CAVITY
2. EXPERIMENTAL The microwave spectrometer used in this work was an absorption type instrument (3 cm) built by D. C. Wobschall some time ago with a high
l?ro. 1. Variable temperature cavity Dewar and sample holders.
ELECTRON
SPIN
RESONANCE
IN POLYCRYSTALLINE
laying in loose form on the bottom of a well evacuated quartz tube. A fine thermocouple was attached directly to the sample or to the sample tube by means of a white tape. It was noticed that the blackbody absorption of radiation coming from the rest of the cavity prevented the attainment of the lowest temperature, especially in the case of the loose powders in vacuum, if the powder was not surrounded by such a shield. The ends of the cavity wave guide section were closed with mica windows and the cavity kept under vacuum. As a result of all these precautions the temperature of the cavity changed during the experiments very little. When the gas flow was suddenly changed from cold to warm, the temperature of a sample in paraflin could be changed from 80°K to 300°K in a matter of 15 set and although it took somewhat longer for loose powders, no change in the Q of the cavity could be observed,
INVERSE
TEMPERATURE
(OK)
FIG. 2. ESR absorption intensity vs. temperature for samples of DPPH and for heavily irradiated commercial nuclear graphite. P
GRAPHITE
307
not only in any of these cases, but also for much longer periods. It is believed that no correction for Q is needed in our case and therefore the readings as taken directly from the oscilloscope were recorded and plotted in graphs. The necessity of having to compare the readings to a standard substance with a known temperature dependence in the usual arrangements is time-consuming and the results only as precise as the knowledge of the standard. Figure 2 shows the results as obtained with this apparatus for a sample of DPPH and for a heavily irradiated polycrystalline graphite (commercial material of a soft type). What is plotted on the graph are the peak to peak heights of the signal, h, since with the exception of one point (circle) the peak to peak width w stays constant in both cases throughout the temperature range investigated. When a sample of graphite is finely ground and some air is present in the sample tube, the line broadens slightly at the lowest temperatures, presumably due to condensation (adsorption) of oxygen on the surface of and in the pores of the grains. This effect, which is much stronger for finely divided carbons such as carbon blacks,* does not prevent getting correct values for the total intensity, however. It was found that it is not necessary to integrate the curve but it is sufficient to plot I=h.w’ to correct for the variation of the width. The point marked with a circle, after such a correction, coincides with the value obtained when the sample was in high vacuum or dispersed in paraffin (cross). Neither is an overmodulation in case of weak lines a problem-the intensity still comes out right using the formula, although the width is excessive. The only danger lay in saturation which was carefully avoided by using a sufficiently low microwave power in all experiments. With a great number of intensity determinations in this work the avoidance of time consuming integrations and the use of a simplified formula was a necessity. *SINGER and WAGONER@) have found that the line width for well graphitized lampblack base graphite (carbon black with some binder) varies about as 1 /T and below 100°K broadens even faster. Actually, one tinds roughly a 1 /T’ln dependence down to 80°K. SINGERand WAGONER'S results are probably due to strong oxygen adsorption, which seems to start broadening the line as early as 2OO”K, the large amounts of oxygen coming from the surface of silica gel used as dispersant.
308
S. MROZOWSKI
Figure 2 shows that DPPH, as well as strongly irradiated polycrystalline graphite, follow almost exactly the Curie law. A deviation of the type reported for DPPH by DuFFY(~~)with a negative paramagnetic Curie point of -20°K is definitely out of the question. When our heavily irradiated graphite was annealed (heat treated) in vacuum the g-value remained close to gh and the width and intensity varied as indicated in Fig. 3. Comparison of this figure with Fig. 12 of HENNIGand HOVE(~)shows that our sample received an irradiation dose of about 700 Mwd. Even after anneal at 800°C the sample still shows a Curie behavior and g=gp As we will see later an anneal changes the temperature dependence as well as the g-value in case of low irradiation doses, when the number of introduced defects does not greatly exceed the number of originally present spin centers. The material selected for this study was the P33 carbon black in solid form (made without use of binder(12)), heat treated at 2600°C so that it will 1 -6
-6
I
I
250
600 TEMPERATURE
750 OF ANNEAL
I
1000
1 0 I-C
FIG. 3. Variation of intensity and width (measured at room temperature) with temperature of anneal for heavily irradiated commercial nuclear graphite.
show an intermediate temperature dependence. Not only was it more convenient to handle solid pieces in all preparatory operations, but for unknown reasons when P33 in powder form is heat treated the resulting ESR line is much broader and as a result the ESR data less precise. Most of the neutron irradiations were performed in the Brookhaven Reactor but some of them also in the Western New York Nuclear Center facility, both reactors having about the same fast neutron flux intensity. For irradiation the grains of solid P33 were put into small spectroscopic pure graphite containers and then inserted into the proper capsules. Doping experiments were performed with HaSO as acceptors and alkali metals as donors. Graphite-bisulfate compound was prepared as previously c1‘) by putting P33 in warm sulfuric acid with a few drops of nitric acid, keeping it there for various lengths of time and washing it in water afterwards. Evidently only a residual compound was obtained in this fashion. Introduction of alkali metals was performed under high vacuum in glass containers. The metal was brought into a side tube (the operation being performed with nitrogen blowing through the apparatus in case of Rb and Cs), the entrance sealed off, apparatus evacuated and some of the alkali metal slowly distilled into the main chamber where the reaction was performed.(“) Since molten Li reacts very strongly on contact with glass (even more so with quartz) the metal had to be placed in a stainless steel cup ; fortunately the distilled thin layer of metal on glass evaporates easily and does not damage the glass during the reaction. The reaction was performed by heating the main chamber with the P33 black and the metal present to about 150-250°C depending on the kind of alkali used. After the reaction the graphite compound was transferred under vacuum to a quartz tube with a capillary stem (like the one shown on Fig. 1) for ESR measurements. In those cases when ESR measurements of intensity before and after introduction of alkali were wanted, the capillary sample holder was sealed to the main chamber by means of a graded seal and the original sample of carbon black after an intensity determination was transferred from the holder to the main chamber for reacting and then back into the sample holder. In these cases it was essential
ELECTRON
SPIN RESONANCE
IN POLYCRYSTALLINE
not to lose any part of the sample in this operation-an overabundance of metal led to some of it after the reaction being left in the main chamber and caused sticking and loss of some powder. On the other hand, an insufficient amount of metal results in part of the sample absorbing all of it, the rest of the sample remaining in the original state (no compound formed), thus leading to a double line in ESR.(“) In case of the less stable compounds (Li, Na) by subsequent heating of an inhomogeneous sample a homogeneous sample with an intermediate g-value can be obtained. The dosage fitting into the proper limits was determined by trial and error in the course of a large number of operations. 3. NEUTRON
IRRADIATION
Figure 4 presents the results of measurement of the total intensity I, of peak to peak width w and of the excess in the g-value over gee. for the main
GRAPHITE
309
series of irradiations of the P33 carbon black. The irradiations 1,2,3, and 4 were performed all in the N-8 hole of the Brookhaven Reactor for increasing lengths of time. When it became evident by the measurements of ESR that samples with greater doses were needed, two samples, one of unirradiated material and the other a part of the sample 4, were irradiated in an adjacent reactor hole (N-10) for a considerably longer time (samples 5 and 6). Since the fast neutron flux in the latter hole was not known (for N-8 the fast flux is about 2-4x 10” nv) no exact figure for the ratio of effectivities on graphite in the two holes was available. The experimental points were therefore shifted for samples 5 and 6 to higher doses up until the intensity line 5-6 would form a continuation of the line O-4, the slopes of both lines being the same. The shift then gives the ratio of the effects of fast neutron flux damage in graphite as equal to 1.25 for these two reactor holes.
FIG. 4. Dependence of intensity, width and g-value on irradiation dose for P33 carbon black heat treated to 2600°C.
S. MROZOWSKI
I
0
I
250
I
500
I
750
I
1000
0
I
250 500 TEMPERATURE
I
OF
750 1000 ANNEAL
01 0
250
500
FIG. 5. Variation of (A) intensity (B) width and (C) g-value (all measured at room temperature) anneal for irradiated P33 carbon black heat treated originally to 2600°C.
Figure 5 (A, B and C) gives the variation of the intensity I, width w and g-value with temperature of vacuum anneal. The heat treatments were performed by heating the sample gradually up to the maximum temperature, at which it was held for 3 min. It is evident from Fig. 5 (A and C) that most of the damage is annealed in the temperature range 150-300°C. The initial increase in intensity I in the range 0-150°C is due to outgassing of the samples; Fig. 5 (C) shows that the damage begins to be annealed starting at about 100°C. This was evidently the temperature at which the samples were irradiated in the reactor. A considerable amount of damage remains even after heat treatment to SOO”,some of it having been gradually annealed out throughout the range 300400°C. The decrease of intensity above 800°C is believed to be not representing a fast anneal [which would have to be visible on Fig. 5 (C)] but the general effect of unknown origin of decrease of intensity and increase in width occurring above 800°C for all carbons and graphites. In Fig. 6 the results of the temperature dependence of intensity are presented for the samples O-4. The increasingly localized character of the
750
I
1000-c
with temperature
of
spin centers with irradiation dose is evident. Actually the localized character of most of the spin centers created by irradiation could have been inferred already from the strict linearity of the intensity vs. irradiation dose from zero dose up over a wide range of irradiations.* If it is assumed that both the conduction carriers and the localized spin centers contribute to the ESR line intensity independently, the individual contributions can be obtained by splitting the I vs. T curve into two parts: a purely Curie part with I=C/T and a conduction part, for which a temperature dependence such as calculated by MCCLURE and observed by SINGER and WAGONER(~) for well graphitized material is assumed (a slightly positive linear temperature dependence in the range 80-300°C of the type I,=A+BT; the intensity decreasing at *For charge carriers the spin resonance intensity should be proportional to the density of levels at the Fermi surface, and for n(E)gE as for graphite, if the total number of hole carriers is proportional to the dose D (Dg @(E). E) then the spin resonance intensity would have to vary as a square root of the dose n(E)= ~@D+E). E is added to take care of the presence of charge carriers in the unirradiated material.
ELECTRON
SPIN RESONANCE
IN POLYCRYSTALLINE
311
GRAPHITE
intensities at 80°K and 293°K samples, using the mix formula R=0.88
4 0 t
cmi.cmim
I
I
I
60
160
120
TEMPERATURE
RT a
240
200
I
T
260
t-K1
FIG. 6. Temperature dependence of absorption intensity for a serie of irradiated P33 (H’M’ 2600°C) carbon blacks. 80°K
to 88% of the 300°K value). With this assumption the fraction X of the total intensity at the room temperature due to conduction carriers can be easily calculated just from the ratio R of
TABLE
1. VARIATION
X+3.65
for each of the
(1-X).
(I)
The splitting of the intensity into two independent contributions is not an arbitrary assumption however, because for a given X the exact shape of the curve can be calculated and compared with the experimentally obtained curves. The close agreement of all the curves O-6 throughout the whole range 80-300°K can be taken as evidence that such a decomposition into localized and conduction spin contributions is fully justified. Table 1 gives the results of such an analysis carried out on samples O-6. It can be seen that at room temperature 81.5% of the ESR intensity of the original P33 carbon black is due to carriers and 18.5% to localized spins. As irradiation proceeds the total intensity grows rapidly but the contribution of carriers increases only very slowly -in fact less than 11% of the total intensity increase for sample 6 is due to new conduction carriers created by irradiation. The total carrier concentration having been increased only by 45%, one concludes that most of the ESR absorption created by neutron bombardment is due to localized spin centers. The concentration of localized spin centers created by irradiation increases within experimental errors exactly in proportion to the dose (numbers in brackets are calculated for a strict proportionality), while the increase in concentration of conduction electrons does increase at first
OF ESRWITH
IRRADIATION DOSE
Breakdown of absorption at room temperature Sample number
l
Irradiation dose NVT total ( x 3.5 . 10'8)
Intensity ratio
R = I&IRT
Carrier contribution Xin %*
IRT
Total amount Carriers Localized
Irradiation effect Carriers Localized
0
0
1.40
81.5
100
81.5
18.5
1
l/4
1.50
77
112
85
27
3.5 (1.4)
2
l/2
1.66
71
122
86
36
4.5 (2.7)
17.5 (20)
3
1
2.00
60
145
87
58
5.5 (5.5)
39.5 (40)
4
2
2.30
49
190
92
98
10.5 (11)
5
5 l/6
2.75
32.5
340
110
230
28.5 (28.4)
211.5 (206)
6
7 l/6
2.90
27.2
430
117
313
35.5 (39.4)
294.5 (286)
X calculated from R----O.88 X+
3.65 (1-X).
-
8.5 (10)
79.5 (80)
S. MROZOWSKI
312
faster and later slower than proportional to the dose. In view of the smallness of the latter deviations it is difficult to be sure that they are definitely outside experimental errors. Tables 2 and 3 give a similar analysis for the sample 5 at different stages of anneal and a comparison for various samples after heat treatment to 700°C. The comparison of the data shows that in the lower range of heat treatment (lOO-300°C) mainly the localized spin centers are being annealed, the extra conduction carriers being due to some defects which anneal with greater difficulty. It seems thus possible that the localized spin centers are displaced carbon ions, vacancies playing the role of traps for conduction electrons. 4. DOPING
WITH ALKALI METALS AND WITH HPSO,
Previous experiments with introduction of potassium (lo) have shown that in vacuum a compound with g=gf is formed for which upon exposure to air the ESR line slightly shifts to higher g-value. Subsequent driving out of K by heat treatment in vacua does shift the line further to the original untreated position but the process
does not occur smoothly, the line at the lower gvalue gradually disappearing and a new line building up at a higher value of g, this making it difficult to determine the exact temperature dependence of each component. Furthermore, vigorous jumping of the sample during the driving out of potassium made the reproducibility and exact intensity comparisons questionable. It is for this reason that all the other alkali metals were tested. Rubidium does produce a line at g=gf but the line is pretty broad and the compound very stable. Introduction of Cesium broadens the line beyond observation. The results agree with the findings of MULLER and KLEINER(‘~). Sodium turned out to be the best for our studies; when first prepared in vacuum the compound shows ggf and is like all the other alkali compounds perfectly stable. If however it is opened to air for a short while, no matter if it is later well evacuated or if it is imbedded in pa&in-its g-value begins slowly to change with time and the process continues with a decreasing speed as shown in the graph Fig. 7. One can speed up the process at
TAFU 2. VARIATIONOF ESR WITH ANNEALFOR A FIXED IRRADIATION DOSE Breakdown of absorption at room temperature Intensity ratio
SamDle number (Temp. anneal)
R =ILN/IRT
Carrier contribution
IRT
Xin%
Total amount Carriers Localized
Irradiation effect Carriers Localized
5
2.75
32.5
340
110
230
28.5
211.5
5 (150)
2.70
34.5
325
112
213
30.5
194.5
5 (200)
2.35
47
235
110
125
28.5
106.5
5 (300)
2.10
56
160
90
70
8.5
51.5
5 (700)
1.64
72
128
92
36
10.5
17.5
TABLE 3. VARIATIONOF ESR WITH IRRADIATION DOSEAFTERANNEALAT 700°C Breakdown of absorption at room temperature Sample number
Relative irradiation dose
Intensity ratio R=ILN/IRT
Carrier contribution Xin %
IRT
Total amount Carriers Localized
Irradiation effect Carriers Localized
0 (700)
0
1.28
85
90
76
14
-
4 (700) 5 (700)
1 2.6
1.43 1.64
80 72
110 128
88 92
22 36
12 16
8 (8) 22 (21)
-
6 (700)
3.6
1.75
68
140
96
44
20
30 (29)
ELECTRON I 0
SPIN RESONANCE IN POLYCRYSTALLINE I
I
GRAPHITE
I
313
I
r
30hr.
SOhr
1
w
20-‘x\x, *040; “\\ FSO-
xLX
,P Ia \X.,
4 SO-
IOmin
I hr.
3hr. TIME
FIG. 7. Variation of the g-value with time for a P33 carbon black (HTT 2600°C) sample doped with Na, then opened to air and kept under nitrogen atmosphere (the same curve is obtained for the sample imbedded in par&). various stages by proper heating and obtain an ESR line located anywhere between gf and the original position gp for pure P33, but under no condition is a compound obtained with a g-value higher than the original gp, this observation agreeing with the results reported previously with potassium.(’ O) Lithium does go into the graphite and produces a shift of the line to g=gf. Like other alkali compounds the Li compound is very stable as long as it is not exposed to air but for dopings just sufficient to shift the line to gf even traces of oxygen in an atmosphere of nitrogen are sufficient to cause an almost complete decomposition. When air is admitted to the sample the line at gf decays and a new line close to gp builds up instead, all in a matter of seconds. For heavier dopings the decay is much slower and occurs in several steps: at first the intensity of the ESR line diminishes without change in g (about l-2 min), then the line shifts by gradual disappearance of the gf+O0IO6 and a simultaneous buildup of a line at gff0.0055 (about l/2 hr), finally the line moves slowly to higher g’s (it takes about 5 hr to reach gff0.0080. Similarly the transition from gff0.0025 to gi+ 0.0055 in case of Na seems to be representing a double line structure with one line gaining gradual intensity at the expense of the other. Table 4 shows the gradual increase in width of the ESR line with increasing atomic number of the
TABLE 4.
&XATIVE
INCREASE DOPING
Doping 0 (Li)
0 0 0 0
(Na) (IQ (Rb) (Cs)
IN
WIDTH
AS A RBULT
OF
TO grgfrre @“doped
/%htT
0.8-1.2 1.1-1.8 1.2-1.4 3.0-up very large
alkali. The width of the line increases also with the amount of doping, in the indicated range. For all alkalis the intensity of the line increases and the temperature dependence becomes more metallic as the alkali is introduced. However, no reliable quantitative data could be obtained as far as total intensity is concerned except for sodium and potassium. The results are presented in Table 5. The analysis of the data into the two types of spin centers reveals that no new localized spin centers are formed in this treatment-all that occurs when lamellar (or residual) compounds are formed is an imease in concentration of conduction carriers. Since it is very probable that this is generally true and not only in the case of Na and K, such assumption was made in the case of Li and the change in the carrier concentration calculated. The result-a negative change in concentration seems to indicate that here just a proper amount of Li is present which shifted the Fermi level up-
314
S. MROZOWSKI
TABLE5. VARIATION OF ESRWITH
Sample (doping)
O(Li) o(Likf
Intensity rati0 R=ILNJIRT 1.45
DOPING
Breakdown of absorption at room temperature Carriers contribution Xin%
IRT
79
(87)
Total amount Carriera Localized (68.5)
(18.5)
Doping eiIect Carriers Localized (-13)
(0 ass)
-1.03
O(Ndd
1.2s
87
-140
122
O(NG
1.1
92
-220
202
18 18
40.5 120
0
95.5
-450
430
20
350
0
o@Jab OUQy O(Rb)u
0
4.97 1.0 4.96
0
1.40
81.5
O(Ivw
1.22
88
100 (155)
81.5 (136)
185 (18.5)
(54.5)
3(IGSOJ
1.7
70.5
(197)
(1391
(580
(52%
4(Ih%)
2.05
58
(235)
(137)
(4Si?
S@I,S03
2.50
41
(390)
(160)
(983 (230”)
wt)
*See Table 1. tobrained by subtracting the carrier value Table 1 from carrier value in Table 5.
wards into the center of the band overlap (the original carbon black material possessing an excess of holes, as indicated by its positive Hall effect).(r4’ In an effort to observe the transition of the Fermi level across the band overlap acceptors were in~oduced into a strongly decayed sodium compound (Fig. 7). Following a suggestion of Professor R. Setton, ammonia gas was admitted which enters readily into graphite doped with sodium. Unfortunately, when ammonia enters, it shifts the line all the way to a and no adjusting the pressure or driving out of ammonia could help in obtaining a continuous change in g-value from the graphitesodium to the mixed graphite-sodium-ammonia compound with g=gf. Although the number of HSO,’ ions introduced in our treatment was not sufficient to shift the line to g=gr it could not be varied. Analysis of the data using the assumption of “no localized spin centers formed” leads to the result (see Table 5) that no matter if the carbon black wss or was not irradiated the HzS04 treatment changes the Fermi level about equally, thus showing the well known additivity of effects of irradiation and doping. The dependence of the width w on temperature for nontreated P33 carbon black is almost of an in-
verse square root type (w Y l/T”‘). When the material is irradiated or doped, it gradually becomes less and less temperature dependent, and
FIG. 8. Relation between the width ratio (wrwidth at liquid nitrogen temperature, wRr_width at xmm ternperatnre) and g-value for variously irradiated and doped samples of P33 (HTT 2600°C).
ELECTRON
SPIN RESONANCE
IN POLYCRYSTALLINE
315
GRAPHITE
x ITT. d HtSO*
\
0 No.K(, o
Li,No
i
I
40
60 Ag.g-g,(x104)
120
160
FIG.9. ESR intensity of equal amounts of P33 (I-ITT 26WC)
variously irradiatedand doped in relation to the measured g-value.
in many cases reaches a stage beyond which the dependence is reversed and the line narrows as the temperature is lowered. To show this gradual change the dependence of the ratio r of the width at 80°K to the width at room temperature is plotted in Fig. 8 in relation to the g-value. In case of Na-doping an anomalous serie was observed, which shows a more complicated behavior but it is suspected that this was due to the non-homogeneous (composite) structure of the line occurring during decomposition for this sample. Figure 9 shows the observed ESR intensity in relation to the g-value. There is a monotonic increase of intensity as the line shifts towards gf for irradiated samples, as well as for acceptor treated samples (as calculated for I&S04). There is an initial dip and then monotonic increase as the line shifts to lower g-values in case of donors, the existence of the dip being not measured
directly, but inferred from the higher value of R (see Table 5 ; small changes in intensity are more difficult to be determined due to possible losses of material, in driving out the donors) and is supported by other observations (see Section 5). No dip should be present in the case of acceptors, the Fermi level moving away from the center of the band overlap. 5. STUDY OF THE G-SHIFT WITH DOPING AND IR&XDIATION
For an ideal carbon black particle composed of graphite crystallites arranged with c-axes passing through the center of the polyhedron, an electron in its motion across the particle would average out the g-anisotropy so that the g-value would be gG=lj3
811+2f3 g,=k!i+1/3
&Ii ---@I
(2)
since only the 811value along the c-axis differs from the free electron value. SINGERand WAGONER(~)
316
S. MROZOWSKI
k
0.63
_ .
,,“2S04,
4
Ok493t-Y
46 ~
6700 _~lqm~20~6yJw
:E
0.40 049. ~70*3/4700t5~ 0.44
21 II 0
I
40
60 bg=g-g‘
0.56 I 120
c I
I 160
1 200
cx 1041
FIG. 10. Room temperature g-values and extent of their change with cooling to liquid nitrogen temperature for variously irradiated and doped P33 (HTT 2600°C) carbon black samples.
found that the g-value for their lampblack base graphite was below the value predicted from data for a single graphite crystal.c3) This is also what is found for the P33 carbon black. Since carbon blacks do possess some excess of holes, the deviation might be due to the depression of the Fermi level which brings it into a region of a decreased spin-orbit interaction (actually as one will see later, this explains only a part of the deviation in question). One could expect that raising the Fermi level by addition of donors up into the band overlap will cause the g-value to increase above the original value for undoped material. In all experiments with driving out Li, Na and K however, in no case was a larger g-value obtained. The intensity minimum (maximum in R) occurring at already decreased g-value indicates that the change in g-value with interlayer doping is due to a decrease
in spin-orbit interaction resulting rather jbm spreading of layers (S-effect) than jknn a shift of the Fermi level (F-e#ect).(’ ‘) The presence of a third effect causing variation in g-value is revealed when one plots the variation of the g-value with temperature for variously
doped and irradiated samples. This is shown graphically on Fig. 10 where the horizontal black lines indicate the regions through which the gvalue moves as the temperature changes from room to liquid nitrogen (end of the arrow). A straight line means an almost linear temperature dependence. In case of irradiated samples turnaround points are observed at the temperature indicated. The numbers above the lines give the ratio of (gLN_gRr)/(gRT-gf) which will be designated by 6 and called temperature shift. A glance at Fig. 10 shows that doping and irradiation produce two basically different effects. In lamellar compound doping the result is a change in g-value toward gf without essential change in 6 and in temperature dependence, when in irradiation as the g-value tends toward gf the temperature shift 6 becomes inverted. The approximate independence of the 6 shift from degree of doping is very interesting, and as we will see later, is due to a partial compensation of several effects. One can notice however right away the presence of a minimum in 6 shift in the Na-serie at a position corresponding to the intensity minimum in Fig. 9
ELECTRON
SPIN
RESONANCE
IN POLYCRYSTALLINE
317
GRAPHITE
IOO-
IOOX
LIMIT
FIG. 11. Relation between the fraction of total absorption due to conduction carriers and the g-value for a serie of irradiated samples of P33 (HTT 2600°C) ?.s measured at room and at liquid nitrogen temperature.
-such a minimum being not present in case of the HaSO4 series. All these problems can be understood only after the nature of the third effect is pinpointed. Since in irradiation mostly localized spins are formed and only a small shift of the Fermi level is present (Section 3) to explain the shift of the gvalue one has to look elsewhere. Revealing is the fact that the turnaround points in g occur always when the ratio of absorption intensity of ESR due to localized and to conduction spins is about 2:l. Doping with HzS04 increases the concentration of conduction carriers, and as a result the turnaround point is shifted to lower temperature (see sample 4 on Fig. 10). It is therefore this ratio which is the controlling factor-and consequently in Fig. 11 the fraction X of carrier absorption is plotted against the g-value for two temperatures
(RT and LN). In both cases all experimental points line up approximately along straight lines which by virtue of the experimentally tested separability of the absorption into two parts (Fig. 6 and Table 1) means that at any temperature (inside of the investigated temperature limits) g-gL=X(gC-_gL)
org=XgC+(l-X)gL
(3)
where gC is the g-value when there are no localized spin centers and gL is the g-value for the localized spin centers in absence of conduction carriers. The second form of equation (3) shows that the effect is a simple mixing of the g-values fur the two kinds of spin centers, the conduction carriers exchanging the spin with localized ones during their travels across the material. The sharpness of the ESR line indicates a sufficiently slow relaxation mechanism and frequent exchanges leading to such a good mixing
318
S. MROZOWSKI
of the g-values. The extrapolated room temperature value of g,=gr+O.O149 is smaller than the expected value for well graphitized materialgo=gf +0.0157 (calculated from WAGONER’S data(3’). This is to be expected because for such carbon black the Fermi level is depressed from the center of the overlap region and thus must cause a depression in the gc value by the F-effect. However, the nice round number obtained by extrapolation to X=0 for gL=gf- 0.0023=2.0000 is most probably just a result of coincidence. Since even under heavy irradiation when a purely Curie behavior is observed the g-value does not decrease below gf, it is believed that actually gL=gf and that the mixing does occur according to g=X.gc+(l
--q
g_f
(4)
the straight line going through the origin (Fig. 11).
For the unirradiated sample 0 the extrapolated room temperature value for X=1 is gc=gr+ 0.0145=&0.0012. 420
\
360
\ I\
\
4; - 24055
it L . also-
100
200 IS0 TEMPERATuRE*X
250
300
FIG. 12. Dependence of the g-value on temperature for a serie of irradiated samples of P33 (HTT 2600%) with the reduced 0 curve and the curves predicted according to the mix formula (4) assuming the g, obtained from the reduced 0 curve.
Starting with the curve of g vs. temperature for sample 0 (straight line) and using the results for X obtained from the separation of curves into the two components at various temperatures, one can determine for the P33 carbon black the curve ge as it would look like if there were no localized centers. Such a curve of extrapolated values to X=1 is presented in Fig. 12. It does not coincide with the curve calculated from WAGONER’S data(‘) for a perfectly graphitic material but is slightly depressed downwards as previously explained by the F-effect. Now using the gc curve and the data for irradiated samples derived from the temperature curves Fig. 6 all the other g-curves can be calculated by use of equation (4). They are given in Fig. 12 in form of dashed curves which can be compared with the actually measured g-values (continuous curves). The two sets of curves are very similar but deviate (percentagewise) increasingly with increasing irradiation dose, which is not surprising since irradiation not only depresses further the Fermi level, but also puts C atoms and Cz molecules between the layers (s-effect). Conversely, one can start from the experimental g curves and from data extracted from Fig. 6 calculate the g, curves for each irradiated sample-a series of curves similar to the unirradiated gc curve but depressed more and more downwards is obtained. Such curves show the combined effect of the depression of the Fermi level (F) and of spreading the layers (S), with the effect of mixing of the gvalues of localized centers (M-effect) eliminated. The comparison of such curves with predictions for the F-effect(“) shows that in neutron irradiation the spreading of layers is the most important factor causing the depression of the gc value. The procedure in separating out the M-effect from the combined F and S-effects is best illustrated on plot of X vs. g (Fig. 13) for the HzS04 doping. When the carbon black is doped by formation of a lamellar compound the resulting shift in the g-value is due to the simultaneous change of two parameters in equation (4): the g,-gf for the given sample decreases mainly due to the spreading of layers by a factor u commensurate with doping and approximately independent of temperature and the X point shifts to the left by a definite amount X (gc-gf) (1 -a). On the other hand, the increase in conduction carrier absorption in doping which as Table 5 shows is about the same for all
ELECTRON
SPIN RESONANCE
I
I
60
I
I
IN POLYCRYSTALLINE
I
I
120
Ag=g-g,
I
I
180
319
GRAPHITE
k
I
I
240
ix104 f
FIG. 13. Graph demonstrating the analysis of the changes occurring in doping into two effects: (1) decrease in g, as a result of the combined F and 5’ effects and (2) increase in fraction X as a result of increase in number of carriers.
samples, shifts the point upwards along the new to a new higher ValueOfXD. This second shift occurs in opposite direction in g and partly (or even completely) compensates the first one-as a result, for samples with high concentration of localized spin centers doping can produce a shift toward higher g-value I The lame&r compound doping factor c1becomes temperature dependent for heavier dopings as is iliustrated in Fig. 13 by the two experimental points for the Na compound : the a factor decreases somewhat when the temperature goes down (this is probably due to the F-effect). This decrease of the factor a just about makes the temperature shift factor constant for all dopings (see Fig. 11) since it counteracts the increase in 6 due to the increase in carrier fraction (with c1 constant 6
lineg -g_f =xff(g,-gf)
should increase toward a limiting 6 which for graphite is (410- 157)/157=1.6). The a factor for irradiated samples shows the same behavior for heavier doses (5 and 6): u is considerably lower at L.N. than at room temperature. However, a(gC-gf) at lower temperature has the larger value, thus indicating that the crossover in F-effect is not yet reached (depression of Fermi level not s&iciently large for that). The temperature shift factor 6 decreaseswhen the concentration of localized spin center increases (at higher concentration even becoming negative). Thus the minimum in 6 for low Na dopings (observed also for Li) is understandably the result of the passage of the Fermi level through the center of the band overlap with the minimum carrier density.
S. MROZOWSKI
320 6. CONCLUSIONS
It has been shown in this paper that by studying the intensity of the ESR and its temperature dependence in polycrystalline graphite the ESR absorption can be separated into two parts, one IL giving the information about the concentration of localized spins as existing in not fully graphitized carbons or as created in great numbers by neutron irradiation, and the other I, giving the density of electronic conduction levels at the Fermi surface and its changes with doping and irradiation. As a result of mixing of g-values (M-effect) a single line is observed with a g-value intermediate between the value for localized spin centers (gr) and the one for conduction carriers (gc) according to the formula (4) with X=I,/I being the fraction of absorption due to conduction carriers as obtained from an independent set of experiments. The gc value is shifted down from the graphitic value gG (equation 1) to gc=&+&G-gf)
(5)
a being factor taking care of the decrease in the spin-orbit interaction. The latter is caused either by a shift of the Fermi level (F-effect) and/or by spreading of layers occurring with insertion of ions, atoms or molecules between the layers (S-effect). In principle the two effects F and S could be separated if the band structure of incompletely graphitized carbon blacks was known, since then the depth of the Fermi level could be directly estimated from the absorption intensity I,. As it is, one might try to use the graphite band structure as an approximation; unfortunately, the band theoretical predictions of MCCLURE and YAFET(’ 5, do not agree with experimental data on boron doped graphite crystals. It was felt therefore that the work reported here should be supplemented by studies of boron doping (which presumably shifts the Fermi level without spreading the layers apart) in order to have a better picture of the problems involved. The results of such studies will be published in the nearest future. As to the nature of the localized spin centers, the majority of centers formed in irradiation must have a pretty mobile character. They might be carbon ions wedged in between layers or between crystallites which can jump easily back into vacancies, combine into less mobile Cz molecules or diffuse out and hook to the periphery of
crystallites. As a result of the latter processes some vacancies will be left unfilled-these are the defects which are much harder to be annealed out and which possibly contribute only to the shift in the Fermi level, but might not constitute by themselves localized spin centers. It can be visualized that the vacancy is a trap for one electron which pairs off with the three a-electrons of the neighboring carbon atoms, thus each vacancy contributing two holes to the conduction band. The presence of localized spin centers in carbons heat treated to temperature above 2000°C shows however that there are also localized spin centers of great stability. If their nature is identical with those formed in irradiation and which survive high anneals cannot be answered at this time. Acknowledgement-The
sincere thanks to Dr.
author wishes to express his
DONALD G. SCHWBIT~ER of Brookhaven National Laboratory for his kind help in irradiating the carbon samples.
REFERENCES WAGON= G., Bull. Am. Phys. Sot. 6,129 MULLFZRK. A., Phys. Rev. Phys. Actu 35, 617 (1962).
(1961).
123, 1550 (1961); Helv.
WAGONER G., Proceedings of the Fourth Carbon Conference, p. 197. Pergamon Press, Oxford (1960). HENNIG G. R. and HOVB J. E., Proceedings of the First Internotional Conference on the Peaceful Uses of Atomic Energy, Gene&, Vol. 7, p. 472. Unitei
Nations, New York (1956). 5. YOKOZAWAY. and MROZOWSKIS., Bull. Am. Phys. Sot. 7, 354 (1962). 6. NECHTXHBIN M. and KESTER T., Carbon 1, 143 (1964). 7. ANTONOWICZ K., Proceedings of the Fifth Carbon Conference, Vol. 1, p. 56. Pergamon Press, Oxford
(1962).
8. YOKOZAWAY., 3. Chem. Phys. 37, 204 (1962). 9. SINGER L. S. and WAGONER G., Proceedings of the Fifth Carbon Conference. Vol. 2. P. 65. Pernamon
%ess, Oxford (1963). ’ 10. MROZOWSKIS., Proceedings of the Fifth Carbon Cimference, Vol. 2, p. 79. Pergamon Press, Oxford (1963).
11. DUFFY W. Jr., 3. Chem. Phys. 36,490 (1962). 12. MROZOWSKIS., U.S. Patent 2,682,686 (1954). 13. MULLJIR K. A. and KLEINER R., Phys. Letters 1, 98 (1962). 14. MROZOWSKIS., CHASERSKIA., LOEBNER E. E. and PINNICK H. T., Proceedings of the Third Curbon Conference, p. 211. Pergamon Press, London (1959).
15. MCCLUREJ. W. and YAFETY., Proceedings Fifth Carbon Confe+znce, Press, Oxford (1962).
of the Vol. 1, p. 22. Pergamon
1965, Vol. 3, pp. 305320.
Pergamon Press Ltd.
Printed in Great Britain
ELECTRON SPIN RESONANCE IN NEUTRON
IRRADIATED
DOPED POLYCRYSTALLINE
AND IN
GRAPHITE-PART
I”
s. MRozowsKI Carbon Research Laboratory and Department of Physics, State University of New York at Buffalo, Buffilo, New York (Received 29 July 1965)
Abstract-The
electron spin resonance of neutron irradiated and lamellar compound doped, incompletely graphitized, P33 carbon black was investigated. An improved temperature arrangement operating from room temperature down to liquid nitrogen was constructed which permits one to perform speedy measurements with a minimum of corrections involved. It is shown that the intensity vs. temperature curves for P33 can be split into a sum of contributions of localized spin centers and conduction carriers; the irradiation producing mainly localized spins and the doping changing only the carrier concentration. The two kinds of spin centers interact by exchange so that they produce a single line with a g-value intermediate between that for localized spin centers gfne and for the conduction carriers g,. The g-value can be calculated using a simple mix formula, each type of spin contributing in proportion to its absorption intensity. The g, value for conduction carriers varies according to irradiation dose or amount of doping and is always lower than the directionally averaged graphite value due to a combined effect of displacement of the Fermi level and of the spreading apart of the layers, both causing a change in spin-orbit interaction. Extensive studies of variation in ESR parameters with irradiation dose, amount of doping (Li, Na, K, Rb, HIS04 and ammonia), temperature of anneal and ambient temperature permitted one, among other things, to observe the transition of the Fermi level across the center of the band overlap (with Na and Li).
1. INTRODUCTION NOT long ago WAGONER(~) and
in more detail, MULLER(‘) investigated the electron spin resonance in neutron-irradiated single crystals of graphite as a function of the irradiation dose. MULLET has shown that the intensity of resonance increases linearly with irradiation dose for doses smaller than 6~ 10’s nvt; from the slope of this line and the magnitude of the intensity at zero dose, MULLER calculated that about 30 spins per cm3 are created by each nvt. A considerably lower number was obtained by WAGONER(~)by comparing the effect of irradiation with boron doping of single crystals. With increasing irradiation dose the g-value and the g-anisotropy, as well as the line width, decrease gradually towards limiting values (gfree and width 1.3 G), thus suggesting to them that the nature of the spins created by neutron irradiation is the same as that of the spins *Supported by the U.S. Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. 305
responsible for the ESR absorption in pure graphite crystals (which have been shown earlier to be the charge carriers by WAGONER(~)), the changes in g-value and width being just the result of the shift of the Fermi level. Thus both MULLER and WAGONERconcluded that there is no evidence of formation of spin centers of a new kind at irradiation of single crystals and that therefore the early interpretation of the paramagnetic resonance of neutron-irradiated polycrystalline graphites as being due to carbon interstitial atoms suggested by HENNIC and HOVE(~) is incorrect. As well known, studies of the temperature dependence are most informative in determination of the nature of spin centers. Both WAGONERand MULLER have not performed temperature studies and in reaching their conclusion have not paid attention to a remark in HENNIG and Hovs’s paper concerning the temperature dependence of the resonance intensity, which according to approximate measurements carried out at two temperatures, was reported to be roughly of the Curie
306
S. MROZOWSKI
character. This strong temperature dependence of the ESR of heavily irradiated polycrystalline graphite was also observed by the author, who together with Y. YOKOZAWA, using a simple apparatus, performed some measurements on this substance.(‘) It was demonstrated by comparing the intensity of the ESR line with the intensity of a reference substance (DPP+H) that, whereas the intensity for unirradiated graphite is almost temperature independent, irradiated graphite shows quite closely inverse temperature dependence from room down to liquid nitrogen temperature. It has been later shown by NECHTSCHEINand ILESTER that the Curie dependence is obeyed by the irradiated graphite even down to the temperature of liquid helium. Thus as the irradiation proceeds localized spin centers must be created at a higher rate than any traps effecting an increase in conduction carrier concentration (holes). The process of irradiation seems to be opposite to what is observed when a carbon is graphitized. As ANTONOWICZ(‘)first observed and YOKO~AWA@) later checked more precisely, the temperature dependence changes gradually from partial Curie type for carbons heat treated in the range 12002000 to a pure carrier type with a slightly positive slope for well graphitized samples. As SINGER and WAGONER(~)have shown earlier, the ESR in well graphitized polyc~stalline graphites is due entirely to charge carriers, the observedg-value being a result of an averaging of g-values by conduction electrons in their travel across variously arranged microcrystallites. Adding the results of observation of ESR on doped carbons and graphites(“) it seemed evident that the variation in total intensity and in the g shift with temperature, with irradiation and with doping are each the result of an overlap of several different effects. The work reported here was undertaken in an effort to disentangle these effects; the material selected for this study was an incompletely graphitized carbon black, showing an intermediate temperature dependence of the intensity of ESR, so that induced changes towards more localized as well as towards more conduction type behavior could be observed.
frequency (17 kc/s) magnetic field sweep and phase sensitive detection system. The cavity is just a section of the waveguide located between the klystron and the detector and was operated in a rectangular TEroa mode. Since it was expected that in this work the dependence of the ESR intensity on temperature will have to be determined for a great number of samples, a variable temperature arrangement had to be constructed which would combine speed with sufficient accuracy. It was found that the arrangement shown in Fig. 1 satisfies these requirements. A small quartz double wall evacuated tube (Dewar) was inserted through the cavity (as shown in scale) and nitrogen gas flown through it. The gas came from a cylinder and was separated into two paths-one directly going to the Dewar, the other indirectly going first through a copper coil immersed in liquid nitrogen. By controlling the flow in each of the two branches any desired temperature from room down to 80°K can be obtained very rapidly and held reasonably constant. The samples were always in fine powder form, either powder being dispersed in par&in and attached to a quartz rod holder, or the powder SAMPLE
OUARTZ
HOLDER
OEWAR
CAVITY
2. EXPERIMENTAL The microwave spectrometer used in this work was an absorption type instrument (3 cm) built by D. C. Wobschall some time ago with a high
l?ro. 1. Variable temperature cavity Dewar and sample holders.
ELECTRON
SPIN
RESONANCE
IN POLYCRYSTALLINE
laying in loose form on the bottom of a well evacuated quartz tube. A fine thermocouple was attached directly to the sample or to the sample tube by means of a white tape. It was noticed that the blackbody absorption of radiation coming from the rest of the cavity prevented the attainment of the lowest temperature, especially in the case of the loose powders in vacuum, if the powder was not surrounded by such a shield. The ends of the cavity wave guide section were closed with mica windows and the cavity kept under vacuum. As a result of all these precautions the temperature of the cavity changed during the experiments very little. When the gas flow was suddenly changed from cold to warm, the temperature of a sample in paraflin could be changed from 80°K to 300°K in a matter of 15 set and although it took somewhat longer for loose powders, no change in the Q of the cavity could be observed,
INVERSE
TEMPERATURE
(OK)
FIG. 2. ESR absorption intensity vs. temperature for samples of DPPH and for heavily irradiated commercial nuclear graphite. P
GRAPHITE
307
not only in any of these cases, but also for much longer periods. It is believed that no correction for Q is needed in our case and therefore the readings as taken directly from the oscilloscope were recorded and plotted in graphs. The necessity of having to compare the readings to a standard substance with a known temperature dependence in the usual arrangements is time-consuming and the results only as precise as the knowledge of the standard. Figure 2 shows the results as obtained with this apparatus for a sample of DPPH and for a heavily irradiated polycrystalline graphite (commercial material of a soft type). What is plotted on the graph are the peak to peak heights of the signal, h, since with the exception of one point (circle) the peak to peak width w stays constant in both cases throughout the temperature range investigated. When a sample of graphite is finely ground and some air is present in the sample tube, the line broadens slightly at the lowest temperatures, presumably due to condensation (adsorption) of oxygen on the surface of and in the pores of the grains. This effect, which is much stronger for finely divided carbons such as carbon blacks,* does not prevent getting correct values for the total intensity, however. It was found that it is not necessary to integrate the curve but it is sufficient to plot I=h.w’ to correct for the variation of the width. The point marked with a circle, after such a correction, coincides with the value obtained when the sample was in high vacuum or dispersed in paraffin (cross). Neither is an overmodulation in case of weak lines a problem-the intensity still comes out right using the formula, although the width is excessive. The only danger lay in saturation which was carefully avoided by using a sufficiently low microwave power in all experiments. With a great number of intensity determinations in this work the avoidance of time consuming integrations and the use of a simplified formula was a necessity. *SINGER and WAGONER@) have found that the line width for well graphitized lampblack base graphite (carbon black with some binder) varies about as 1 /T and below 100°K broadens even faster. Actually, one tinds roughly a 1 /T’ln dependence down to 80°K. SINGERand WAGONER'S results are probably due to strong oxygen adsorption, which seems to start broadening the line as early as 2OO”K, the large amounts of oxygen coming from the surface of silica gel used as dispersant.
308
S. MROZOWSKI
Figure 2 shows that DPPH, as well as strongly irradiated polycrystalline graphite, follow almost exactly the Curie law. A deviation of the type reported for DPPH by DuFFY(~~)with a negative paramagnetic Curie point of -20°K is definitely out of the question. When our heavily irradiated graphite was annealed (heat treated) in vacuum the g-value remained close to gh and the width and intensity varied as indicated in Fig. 3. Comparison of this figure with Fig. 12 of HENNIGand HOVE(~)shows that our sample received an irradiation dose of about 700 Mwd. Even after anneal at 800°C the sample still shows a Curie behavior and g=gp As we will see later an anneal changes the temperature dependence as well as the g-value in case of low irradiation doses, when the number of introduced defects does not greatly exceed the number of originally present spin centers. The material selected for this study was the P33 carbon black in solid form (made without use of binder(12)), heat treated at 2600°C so that it will 1 -6
-6
I
I
250
600 TEMPERATURE
750 OF ANNEAL
I
1000
1 0 I-C
FIG. 3. Variation of intensity and width (measured at room temperature) with temperature of anneal for heavily irradiated commercial nuclear graphite.
show an intermediate temperature dependence. Not only was it more convenient to handle solid pieces in all preparatory operations, but for unknown reasons when P33 in powder form is heat treated the resulting ESR line is much broader and as a result the ESR data less precise. Most of the neutron irradiations were performed in the Brookhaven Reactor but some of them also in the Western New York Nuclear Center facility, both reactors having about the same fast neutron flux intensity. For irradiation the grains of solid P33 were put into small spectroscopic pure graphite containers and then inserted into the proper capsules. Doping experiments were performed with HaSO as acceptors and alkali metals as donors. Graphite-bisulfate compound was prepared as previously c1‘) by putting P33 in warm sulfuric acid with a few drops of nitric acid, keeping it there for various lengths of time and washing it in water afterwards. Evidently only a residual compound was obtained in this fashion. Introduction of alkali metals was performed under high vacuum in glass containers. The metal was brought into a side tube (the operation being performed with nitrogen blowing through the apparatus in case of Rb and Cs), the entrance sealed off, apparatus evacuated and some of the alkali metal slowly distilled into the main chamber where the reaction was performed.(“) Since molten Li reacts very strongly on contact with glass (even more so with quartz) the metal had to be placed in a stainless steel cup ; fortunately the distilled thin layer of metal on glass evaporates easily and does not damage the glass during the reaction. The reaction was performed by heating the main chamber with the P33 black and the metal present to about 150-250°C depending on the kind of alkali used. After the reaction the graphite compound was transferred under vacuum to a quartz tube with a capillary stem (like the one shown on Fig. 1) for ESR measurements. In those cases when ESR measurements of intensity before and after introduction of alkali were wanted, the capillary sample holder was sealed to the main chamber by means of a graded seal and the original sample of carbon black after an intensity determination was transferred from the holder to the main chamber for reacting and then back into the sample holder. In these cases it was essential
ELECTRON
SPIN RESONANCE
IN POLYCRYSTALLINE
not to lose any part of the sample in this operation-an overabundance of metal led to some of it after the reaction being left in the main chamber and caused sticking and loss of some powder. On the other hand, an insufficient amount of metal results in part of the sample absorbing all of it, the rest of the sample remaining in the original state (no compound formed), thus leading to a double line in ESR.(“) In case of the less stable compounds (Li, Na) by subsequent heating of an inhomogeneous sample a homogeneous sample with an intermediate g-value can be obtained. The dosage fitting into the proper limits was determined by trial and error in the course of a large number of operations. 3. NEUTRON
IRRADIATION
Figure 4 presents the results of measurement of the total intensity I, of peak to peak width w and of the excess in the g-value over gee. for the main
GRAPHITE
309
series of irradiations of the P33 carbon black. The irradiations 1,2,3, and 4 were performed all in the N-8 hole of the Brookhaven Reactor for increasing lengths of time. When it became evident by the measurements of ESR that samples with greater doses were needed, two samples, one of unirradiated material and the other a part of the sample 4, were irradiated in an adjacent reactor hole (N-10) for a considerably longer time (samples 5 and 6). Since the fast neutron flux in the latter hole was not known (for N-8 the fast flux is about 2-4x 10” nv) no exact figure for the ratio of effectivities on graphite in the two holes was available. The experimental points were therefore shifted for samples 5 and 6 to higher doses up until the intensity line 5-6 would form a continuation of the line O-4, the slopes of both lines being the same. The shift then gives the ratio of the effects of fast neutron flux damage in graphite as equal to 1.25 for these two reactor holes.
FIG. 4. Dependence of intensity, width and g-value on irradiation dose for P33 carbon black heat treated to 2600°C.
S. MROZOWSKI
I
0
I
250
I
500
I
750
I
1000
0
I
250 500 TEMPERATURE
I
OF
750 1000 ANNEAL
01 0
250
500
FIG. 5. Variation of (A) intensity (B) width and (C) g-value (all measured at room temperature) anneal for irradiated P33 carbon black heat treated originally to 2600°C.
Figure 5 (A, B and C) gives the variation of the intensity I, width w and g-value with temperature of vacuum anneal. The heat treatments were performed by heating the sample gradually up to the maximum temperature, at which it was held for 3 min. It is evident from Fig. 5 (A and C) that most of the damage is annealed in the temperature range 150-300°C. The initial increase in intensity I in the range 0-150°C is due to outgassing of the samples; Fig. 5 (C) shows that the damage begins to be annealed starting at about 100°C. This was evidently the temperature at which the samples were irradiated in the reactor. A considerable amount of damage remains even after heat treatment to SOO”,some of it having been gradually annealed out throughout the range 300400°C. The decrease of intensity above 800°C is believed to be not representing a fast anneal [which would have to be visible on Fig. 5 (C)] but the general effect of unknown origin of decrease of intensity and increase in width occurring above 800°C for all carbons and graphites. In Fig. 6 the results of the temperature dependence of intensity are presented for the samples O-4. The increasingly localized character of the
750
I
1000-c
with temperature
of
spin centers with irradiation dose is evident. Actually the localized character of most of the spin centers created by irradiation could have been inferred already from the strict linearity of the intensity vs. irradiation dose from zero dose up over a wide range of irradiations.* If it is assumed that both the conduction carriers and the localized spin centers contribute to the ESR line intensity independently, the individual contributions can be obtained by splitting the I vs. T curve into two parts: a purely Curie part with I=C/T and a conduction part, for which a temperature dependence such as calculated by MCCLURE and observed by SINGER and WAGONER(~) for well graphitized material is assumed (a slightly positive linear temperature dependence in the range 80-300°C of the type I,=A+BT; the intensity decreasing at *For charge carriers the spin resonance intensity should be proportional to the density of levels at the Fermi surface, and for n(E)gE as for graphite, if the total number of hole carriers is proportional to the dose D (Dg @(E). E) then the spin resonance intensity would have to vary as a square root of the dose n(E)= ~@D+E). E is added to take care of the presence of charge carriers in the unirradiated material.
ELECTRON
SPIN RESONANCE
IN POLYCRYSTALLINE
311
GRAPHITE
intensities at 80°K and 293°K samples, using the mix formula R=0.88
4 0 t
cmi.cmim
I
I
I
60
160
120
TEMPERATURE
RT a
240
200
I
T
260
t-K1
FIG. 6. Temperature dependence of absorption intensity for a serie of irradiated P33 (H’M’ 2600°C) carbon blacks. 80°K
to 88% of the 300°K value). With this assumption the fraction X of the total intensity at the room temperature due to conduction carriers can be easily calculated just from the ratio R of
TABLE
1. VARIATION
X+3.65
for each of the
(1-X).
(I)
The splitting of the intensity into two independent contributions is not an arbitrary assumption however, because for a given X the exact shape of the curve can be calculated and compared with the experimentally obtained curves. The close agreement of all the curves O-6 throughout the whole range 80-300°K can be taken as evidence that such a decomposition into localized and conduction spin contributions is fully justified. Table 1 gives the results of such an analysis carried out on samples O-6. It can be seen that at room temperature 81.5% of the ESR intensity of the original P33 carbon black is due to carriers and 18.5% to localized spins. As irradiation proceeds the total intensity grows rapidly but the contribution of carriers increases only very slowly -in fact less than 11% of the total intensity increase for sample 6 is due to new conduction carriers created by irradiation. The total carrier concentration having been increased only by 45%, one concludes that most of the ESR absorption created by neutron bombardment is due to localized spin centers. The concentration of localized spin centers created by irradiation increases within experimental errors exactly in proportion to the dose (numbers in brackets are calculated for a strict proportionality), while the increase in concentration of conduction electrons does increase at first
OF ESRWITH
IRRADIATION DOSE
Breakdown of absorption at room temperature Sample number
l
Irradiation dose NVT total ( x 3.5 . 10'8)
Intensity ratio
R = I&IRT
Carrier contribution Xin %*
IRT
Total amount Carriers Localized
Irradiation effect Carriers Localized
0
0
1.40
81.5
100
81.5
18.5
1
l/4
1.50
77
112
85
27
3.5 (1.4)
2
l/2
1.66
71
122
86
36
4.5 (2.7)
17.5 (20)
3
1
2.00
60
145
87
58
5.5 (5.5)
39.5 (40)
4
2
2.30
49
190
92
98
10.5 (11)
5
5 l/6
2.75
32.5
340
110
230
28.5 (28.4)
211.5 (206)
6
7 l/6
2.90
27.2
430
117
313
35.5 (39.4)
294.5 (286)
X calculated from R----O.88 X+
3.65 (1-X).
-
8.5 (10)
79.5 (80)
S. MROZOWSKI
312
faster and later slower than proportional to the dose. In view of the smallness of the latter deviations it is difficult to be sure that they are definitely outside experimental errors. Tables 2 and 3 give a similar analysis for the sample 5 at different stages of anneal and a comparison for various samples after heat treatment to 700°C. The comparison of the data shows that in the lower range of heat treatment (lOO-300°C) mainly the localized spin centers are being annealed, the extra conduction carriers being due to some defects which anneal with greater difficulty. It seems thus possible that the localized spin centers are displaced carbon ions, vacancies playing the role of traps for conduction electrons. 4. DOPING
WITH ALKALI METALS AND WITH HPSO,
Previous experiments with introduction of potassium (lo) have shown that in vacuum a compound with g=gf is formed for which upon exposure to air the ESR line slightly shifts to higher g-value. Subsequent driving out of K by heat treatment in vacua does shift the line further to the original untreated position but the process
does not occur smoothly, the line at the lower gvalue gradually disappearing and a new line building up at a higher value of g, this making it difficult to determine the exact temperature dependence of each component. Furthermore, vigorous jumping of the sample during the driving out of potassium made the reproducibility and exact intensity comparisons questionable. It is for this reason that all the other alkali metals were tested. Rubidium does produce a line at g=gf but the line is pretty broad and the compound very stable. Introduction of Cesium broadens the line beyond observation. The results agree with the findings of MULLER and KLEINER(‘~). Sodium turned out to be the best for our studies; when first prepared in vacuum the compound shows ggf and is like all the other alkali compounds perfectly stable. If however it is opened to air for a short while, no matter if it is later well evacuated or if it is imbedded in pa&in-its g-value begins slowly to change with time and the process continues with a decreasing speed as shown in the graph Fig. 7. One can speed up the process at
TAFU 2. VARIATIONOF ESR WITH ANNEALFOR A FIXED IRRADIATION DOSE Breakdown of absorption at room temperature Intensity ratio
SamDle number (Temp. anneal)
R =ILN/IRT
Carrier contribution
IRT
Xin%
Total amount Carriers Localized
Irradiation effect Carriers Localized
5
2.75
32.5
340
110
230
28.5
211.5
5 (150)
2.70
34.5
325
112
213
30.5
194.5
5 (200)
2.35
47
235
110
125
28.5
106.5
5 (300)
2.10
56
160
90
70
8.5
51.5
5 (700)
1.64
72
128
92
36
10.5
17.5
TABLE 3. VARIATIONOF ESR WITH IRRADIATION DOSEAFTERANNEALAT 700°C Breakdown of absorption at room temperature Sample number
Relative irradiation dose
Intensity ratio R=ILN/IRT
Carrier contribution Xin %
IRT
Total amount Carriers Localized
Irradiation effect Carriers Localized
0 (700)
0
1.28
85
90
76
14
-
4 (700) 5 (700)
1 2.6
1.43 1.64
80 72
110 128
88 92
22 36
12 16
8 (8) 22 (21)
-
6 (700)
3.6
1.75
68
140
96
44
20
30 (29)
ELECTRON I 0
SPIN RESONANCE IN POLYCRYSTALLINE I
I
GRAPHITE
I
313
I
r
30hr.
SOhr
1
w
20-‘x\x, *040; “\\ FSO-
xLX
,P Ia \X.,
4 SO-
IOmin
I hr.
3hr. TIME
FIG. 7. Variation of the g-value with time for a P33 carbon black (HTT 2600°C) sample doped with Na, then opened to air and kept under nitrogen atmosphere (the same curve is obtained for the sample imbedded in par&). various stages by proper heating and obtain an ESR line located anywhere between gf and the original position gp for pure P33, but under no condition is a compound obtained with a g-value higher than the original gp, this observation agreeing with the results reported previously with potassium.(’ O) Lithium does go into the graphite and produces a shift of the line to g=gf. Like other alkali compounds the Li compound is very stable as long as it is not exposed to air but for dopings just sufficient to shift the line to gf even traces of oxygen in an atmosphere of nitrogen are sufficient to cause an almost complete decomposition. When air is admitted to the sample the line at gf decays and a new line close to gp builds up instead, all in a matter of seconds. For heavier dopings the decay is much slower and occurs in several steps: at first the intensity of the ESR line diminishes without change in g (about l-2 min), then the line shifts by gradual disappearance of the gf+O0IO6 and a simultaneous buildup of a line at gff0.0055 (about l/2 hr), finally the line moves slowly to higher g’s (it takes about 5 hr to reach gff0.0080. Similarly the transition from gff0.0025 to gi+ 0.0055 in case of Na seems to be representing a double line structure with one line gaining gradual intensity at the expense of the other. Table 4 shows the gradual increase in width of the ESR line with increasing atomic number of the
TABLE 4.
&XATIVE
INCREASE DOPING
Doping 0 (Li)
0 0 0 0
(Na) (IQ (Rb) (Cs)
IN
WIDTH
AS A RBULT
OF
TO grgfrre @“doped
/%htT
0.8-1.2 1.1-1.8 1.2-1.4 3.0-up very large
alkali. The width of the line increases also with the amount of doping, in the indicated range. For all alkalis the intensity of the line increases and the temperature dependence becomes more metallic as the alkali is introduced. However, no reliable quantitative data could be obtained as far as total intensity is concerned except for sodium and potassium. The results are presented in Table 5. The analysis of the data into the two types of spin centers reveals that no new localized spin centers are formed in this treatment-all that occurs when lamellar (or residual) compounds are formed is an imease in concentration of conduction carriers. Since it is very probable that this is generally true and not only in the case of Na and K, such assumption was made in the case of Li and the change in the carrier concentration calculated. The result-a negative change in concentration seems to indicate that here just a proper amount of Li is present which shifted the Fermi level up-
314
S. MROZOWSKI
TABLE5. VARIATION OF ESRWITH
Sample (doping)
O(Li) o(Likf
Intensity rati0 R=ILNJIRT 1.45
DOPING
Breakdown of absorption at room temperature Carriers contribution Xin%
IRT
79
(87)
Total amount Carriera Localized (68.5)
(18.5)
Doping eiIect Carriers Localized (-13)
(0 ass)
-1.03
O(Ndd
1.2s
87
-140
122
O(NG
1.1
92
-220
202
18 18
40.5 120
0
95.5
-450
430
20
350
0
o@Jab OUQy O(Rb)u
0
4.97 1.0 4.96
0
1.40
81.5
O(Ivw
1.22
88
100 (155)
81.5 (136)
185 (18.5)
(54.5)
3(IGSOJ
1.7
70.5
(197)
(1391
(580
(52%
4(Ih%)
2.05
58
(235)
(137)
(4Si?
S@I,S03
2.50
41
(390)
(160)
(983 (230”)
wt)
*See Table 1. tobrained by subtracting the carrier value Table 1 from carrier value in Table 5.
wards into the center of the band overlap (the original carbon black material possessing an excess of holes, as indicated by its positive Hall effect).(r4’ In an effort to observe the transition of the Fermi level across the band overlap acceptors were in~oduced into a strongly decayed sodium compound (Fig. 7). Following a suggestion of Professor R. Setton, ammonia gas was admitted which enters readily into graphite doped with sodium. Unfortunately, when ammonia enters, it shifts the line all the way to a and no adjusting the pressure or driving out of ammonia could help in obtaining a continuous change in g-value from the graphitesodium to the mixed graphite-sodium-ammonia compound with g=gf. Although the number of HSO,’ ions introduced in our treatment was not sufficient to shift the line to g=gr it could not be varied. Analysis of the data using the assumption of “no localized spin centers formed” leads to the result (see Table 5) that no matter if the carbon black wss or was not irradiated the HzS04 treatment changes the Fermi level about equally, thus showing the well known additivity of effects of irradiation and doping. The dependence of the width w on temperature for nontreated P33 carbon black is almost of an in-
verse square root type (w Y l/T”‘). When the material is irradiated or doped, it gradually becomes less and less temperature dependent, and
FIG. 8. Relation between the width ratio (wrwidth at liquid nitrogen temperature, wRr_width at xmm ternperatnre) and g-value for variously irradiated and doped samples of P33 (HTT 2600°C).
ELECTRON
SPIN RESONANCE
IN POLYCRYSTALLINE
315
GRAPHITE
x ITT. d HtSO*
\
0 No.K(, o
Li,No
i
I
40
60 Ag.g-g,(x104)
120
160
FIG.9. ESR intensity of equal amounts of P33 (I-ITT 26WC)
variously irradiatedand doped in relation to the measured g-value.
in many cases reaches a stage beyond which the dependence is reversed and the line narrows as the temperature is lowered. To show this gradual change the dependence of the ratio r of the width at 80°K to the width at room temperature is plotted in Fig. 8 in relation to the g-value. In case of Na-doping an anomalous serie was observed, which shows a more complicated behavior but it is suspected that this was due to the non-homogeneous (composite) structure of the line occurring during decomposition for this sample. Figure 9 shows the observed ESR intensity in relation to the g-value. There is a monotonic increase of intensity as the line shifts towards gf for irradiated samples, as well as for acceptor treated samples (as calculated for I&S04). There is an initial dip and then monotonic increase as the line shifts to lower g-values in case of donors, the existence of the dip being not measured
directly, but inferred from the higher value of R (see Table 5 ; small changes in intensity are more difficult to be determined due to possible losses of material, in driving out the donors) and is supported by other observations (see Section 5). No dip should be present in the case of acceptors, the Fermi level moving away from the center of the band overlap. 5. STUDY OF THE G-SHIFT WITH DOPING AND IR&XDIATION
For an ideal carbon black particle composed of graphite crystallites arranged with c-axes passing through the center of the polyhedron, an electron in its motion across the particle would average out the g-anisotropy so that the g-value would be gG=lj3
811+2f3 g,=k!i+1/3
&Ii ---@I
(2)
since only the 811value along the c-axis differs from the free electron value. SINGERand WAGONER(~)
316
S. MROZOWSKI
k
0.63
_ .
,,“2S04,
4
Ok493t-Y
46 ~
6700 _~lqm~20~6yJw
:E
0.40 049. ~70*3/4700t5~ 0.44
21 II 0
I
40
60 bg=g-g‘
0.56 I 120
c I
I 160
1 200
cx 1041
FIG. 10. Room temperature g-values and extent of their change with cooling to liquid nitrogen temperature for variously irradiated and doped P33 (HTT 2600°C) carbon black samples.
found that the g-value for their lampblack base graphite was below the value predicted from data for a single graphite crystal.c3) This is also what is found for the P33 carbon black. Since carbon blacks do possess some excess of holes, the deviation might be due to the depression of the Fermi level which brings it into a region of a decreased spin-orbit interaction (actually as one will see later, this explains only a part of the deviation in question). One could expect that raising the Fermi level by addition of donors up into the band overlap will cause the g-value to increase above the original value for undoped material. In all experiments with driving out Li, Na and K however, in no case was a larger g-value obtained. The intensity minimum (maximum in R) occurring at already decreased g-value indicates that the change in g-value with interlayer doping is due to a decrease
in spin-orbit interaction resulting rather jbm spreading of layers (S-effect) than jknn a shift of the Fermi level (F-e#ect).(’ ‘) The presence of a third effect causing variation in g-value is revealed when one plots the variation of the g-value with temperature for variously
doped and irradiated samples. This is shown graphically on Fig. 10 where the horizontal black lines indicate the regions through which the gvalue moves as the temperature changes from room to liquid nitrogen (end of the arrow). A straight line means an almost linear temperature dependence. In case of irradiated samples turnaround points are observed at the temperature indicated. The numbers above the lines give the ratio of (gLN_gRr)/(gRT-gf) which will be designated by 6 and called temperature shift. A glance at Fig. 10 shows that doping and irradiation produce two basically different effects. In lamellar compound doping the result is a change in g-value toward gf without essential change in 6 and in temperature dependence, when in irradiation as the g-value tends toward gf the temperature shift 6 becomes inverted. The approximate independence of the 6 shift from degree of doping is very interesting, and as we will see later, is due to a partial compensation of several effects. One can notice however right away the presence of a minimum in 6 shift in the Na-serie at a position corresponding to the intensity minimum in Fig. 9
ELECTRON
SPIN
RESONANCE
IN POLYCRYSTALLINE
317
GRAPHITE
IOO-
IOOX
LIMIT
FIG. 11. Relation between the fraction of total absorption due to conduction carriers and the g-value for a serie of irradiated samples of P33 (HTT 2600°C) ?.s measured at room and at liquid nitrogen temperature.
-such a minimum being not present in case of the HaSO4 series. All these problems can be understood only after the nature of the third effect is pinpointed. Since in irradiation mostly localized spins are formed and only a small shift of the Fermi level is present (Section 3) to explain the shift of the gvalue one has to look elsewhere. Revealing is the fact that the turnaround points in g occur always when the ratio of absorption intensity of ESR due to localized and to conduction spins is about 2:l. Doping with HzS04 increases the concentration of conduction carriers, and as a result the turnaround point is shifted to lower temperature (see sample 4 on Fig. 10). It is therefore this ratio which is the controlling factor-and consequently in Fig. 11 the fraction X of carrier absorption is plotted against the g-value for two temperatures
(RT and LN). In both cases all experimental points line up approximately along straight lines which by virtue of the experimentally tested separability of the absorption into two parts (Fig. 6 and Table 1) means that at any temperature (inside of the investigated temperature limits) g-gL=X(gC-_gL)
org=XgC+(l-X)gL
(3)
where gC is the g-value when there are no localized spin centers and gL is the g-value for the localized spin centers in absence of conduction carriers. The second form of equation (3) shows that the effect is a simple mixing of the g-values fur the two kinds of spin centers, the conduction carriers exchanging the spin with localized ones during their travels across the material. The sharpness of the ESR line indicates a sufficiently slow relaxation mechanism and frequent exchanges leading to such a good mixing
318
S. MROZOWSKI
of the g-values. The extrapolated room temperature value of g,=gr+O.O149 is smaller than the expected value for well graphitized materialgo=gf +0.0157 (calculated from WAGONER’S data(3’). This is to be expected because for such carbon black the Fermi level is depressed from the center of the overlap region and thus must cause a depression in the gc value by the F-effect. However, the nice round number obtained by extrapolation to X=0 for gL=gf- 0.0023=2.0000 is most probably just a result of coincidence. Since even under heavy irradiation when a purely Curie behavior is observed the g-value does not decrease below gf, it is believed that actually gL=gf and that the mixing does occur according to g=X.gc+(l
--q
g_f
(4)
the straight line going through the origin (Fig. 11).
For the unirradiated sample 0 the extrapolated room temperature value for X=1 is gc=gr+ 0.0145=&0.0012. 420
\
360
\ I\
\
4; - 24055
it L . also-
100
200 IS0 TEMPERATuRE*X
250
300
FIG. 12. Dependence of the g-value on temperature for a serie of irradiated samples of P33 (HTT 2600%) with the reduced 0 curve and the curves predicted according to the mix formula (4) assuming the g, obtained from the reduced 0 curve.
Starting with the curve of g vs. temperature for sample 0 (straight line) and using the results for X obtained from the separation of curves into the two components at various temperatures, one can determine for the P33 carbon black the curve ge as it would look like if there were no localized centers. Such a curve of extrapolated values to X=1 is presented in Fig. 12. It does not coincide with the curve calculated from WAGONER’S data(‘) for a perfectly graphitic material but is slightly depressed downwards as previously explained by the F-effect. Now using the gc curve and the data for irradiated samples derived from the temperature curves Fig. 6 all the other g-curves can be calculated by use of equation (4). They are given in Fig. 12 in form of dashed curves which can be compared with the actually measured g-values (continuous curves). The two sets of curves are very similar but deviate (percentagewise) increasingly with increasing irradiation dose, which is not surprising since irradiation not only depresses further the Fermi level, but also puts C atoms and Cz molecules between the layers (s-effect). Conversely, one can start from the experimental g curves and from data extracted from Fig. 6 calculate the g, curves for each irradiated sample-a series of curves similar to the unirradiated gc curve but depressed more and more downwards is obtained. Such curves show the combined effect of the depression of the Fermi level (F) and of spreading the layers (S), with the effect of mixing of the gvalues of localized centers (M-effect) eliminated. The comparison of such curves with predictions for the F-effect(“) shows that in neutron irradiation the spreading of layers is the most important factor causing the depression of the gc value. The procedure in separating out the M-effect from the combined F and S-effects is best illustrated on plot of X vs. g (Fig. 13) for the HzS04 doping. When the carbon black is doped by formation of a lamellar compound the resulting shift in the g-value is due to the simultaneous change of two parameters in equation (4): the g,-gf for the given sample decreases mainly due to the spreading of layers by a factor u commensurate with doping and approximately independent of temperature and the X point shifts to the left by a definite amount X (gc-gf) (1 -a). On the other hand, the increase in conduction carrier absorption in doping which as Table 5 shows is about the same for all
ELECTRON
SPIN RESONANCE
I
I
60
I
I
IN POLYCRYSTALLINE
I
I
120
Ag=g-g,
I
I
180
319
GRAPHITE
k
I
I
240
ix104 f
FIG. 13. Graph demonstrating the analysis of the changes occurring in doping into two effects: (1) decrease in g, as a result of the combined F and 5’ effects and (2) increase in fraction X as a result of increase in number of carriers.
samples, shifts the point upwards along the new to a new higher ValueOfXD. This second shift occurs in opposite direction in g and partly (or even completely) compensates the first one-as a result, for samples with high concentration of localized spin centers doping can produce a shift toward higher g-value I The lame&r compound doping factor c1becomes temperature dependent for heavier dopings as is iliustrated in Fig. 13 by the two experimental points for the Na compound : the a factor decreases somewhat when the temperature goes down (this is probably due to the F-effect). This decrease of the factor a just about makes the temperature shift factor constant for all dopings (see Fig. 11) since it counteracts the increase in 6 due to the increase in carrier fraction (with c1 constant 6
lineg -g_f =xff(g,-gf)
should increase toward a limiting 6 which for graphite is (410- 157)/157=1.6). The a factor for irradiated samples shows the same behavior for heavier doses (5 and 6): u is considerably lower at L.N. than at room temperature. However, a(gC-gf) at lower temperature has the larger value, thus indicating that the crossover in F-effect is not yet reached (depression of Fermi level not s&iciently large for that). The temperature shift factor 6 decreaseswhen the concentration of localized spin center increases (at higher concentration even becoming negative). Thus the minimum in 6 for low Na dopings (observed also for Li) is understandably the result of the passage of the Fermi level through the center of the band overlap with the minimum carrier density.
S. MROZOWSKI
320 6. CONCLUSIONS
It has been shown in this paper that by studying the intensity of the ESR and its temperature dependence in polycrystalline graphite the ESR absorption can be separated into two parts, one IL giving the information about the concentration of localized spins as existing in not fully graphitized carbons or as created in great numbers by neutron irradiation, and the other I, giving the density of electronic conduction levels at the Fermi surface and its changes with doping and irradiation. As a result of mixing of g-values (M-effect) a single line is observed with a g-value intermediate between the value for localized spin centers (gr) and the one for conduction carriers (gc) according to the formula (4) with X=I,/I being the fraction of absorption due to conduction carriers as obtained from an independent set of experiments. The gc value is shifted down from the graphitic value gG (equation 1) to gc=&+&G-gf)
(5)
a being factor taking care of the decrease in the spin-orbit interaction. The latter is caused either by a shift of the Fermi level (F-effect) and/or by spreading of layers occurring with insertion of ions, atoms or molecules between the layers (S-effect). In principle the two effects F and S could be separated if the band structure of incompletely graphitized carbon blacks was known, since then the depth of the Fermi level could be directly estimated from the absorption intensity I,. As it is, one might try to use the graphite band structure as an approximation; unfortunately, the band theoretical predictions of MCCLURE and YAFET(’ 5, do not agree with experimental data on boron doped graphite crystals. It was felt therefore that the work reported here should be supplemented by studies of boron doping (which presumably shifts the Fermi level without spreading the layers apart) in order to have a better picture of the problems involved. The results of such studies will be published in the nearest future. As to the nature of the localized spin centers, the majority of centers formed in irradiation must have a pretty mobile character. They might be carbon ions wedged in between layers or between crystallites which can jump easily back into vacancies, combine into less mobile Cz molecules or diffuse out and hook to the periphery of
crystallites. As a result of the latter processes some vacancies will be left unfilled-these are the defects which are much harder to be annealed out and which possibly contribute only to the shift in the Fermi level, but might not constitute by themselves localized spin centers. It can be visualized that the vacancy is a trap for one electron which pairs off with the three a-electrons of the neighboring carbon atoms, thus each vacancy contributing two holes to the conduction band. The presence of localized spin centers in carbons heat treated to temperature above 2000°C shows however that there are also localized spin centers of great stability. If their nature is identical with those formed in irradiation and which survive high anneals cannot be answered at this time. Acknowledgement-The
sincere thanks to Dr.
author wishes to express his
DONALD G. SCHWBIT~ER of Brookhaven National Laboratory for his kind help in irradiating the carbon samples.
REFERENCES WAGON= G., Bull. Am. Phys. Sot. 6,129 MULLFZRK. A., Phys. Rev. Phys. Actu 35, 617 (1962).
(1961).
123, 1550 (1961); Helv.
WAGONER G., Proceedings of the Fourth Carbon Conference, p. 197. Pergamon Press, Oxford (1960). HENNIG G. R. and HOVB J. E., Proceedings of the First Internotional Conference on the Peaceful Uses of Atomic Energy, Gene&, Vol. 7, p. 472. Unitei
Nations, New York (1956). 5. YOKOZAWAY. and MROZOWSKIS., Bull. Am. Phys. Sot. 7, 354 (1962). 6. NECHTXHBIN M. and KESTER T., Carbon 1, 143 (1964). 7. ANTONOWICZ K., Proceedings of the Fifth Carbon Conference, Vol. 1, p. 56. Pergamon Press, Oxford
(1962).
8. YOKOZAWAY., 3. Chem. Phys. 37, 204 (1962). 9. SINGER L. S. and WAGONER G., Proceedings of the Fifth Carbon Conference. Vol. 2. P. 65. Pernamon
%ess, Oxford (1963). ’ 10. MROZOWSKIS., Proceedings of the Fifth Carbon Cimference, Vol. 2, p. 79. Pergamon Press, Oxford (1963).
11. DUFFY W. Jr., 3. Chem. Phys. 36,490 (1962). 12. MROZOWSKIS., U.S. Patent 2,682,686 (1954). 13. MULLJIR K. A. and KLEINER R., Phys. Letters 1, 98 (1962). 14. MROZOWSKIS., CHASERSKIA., LOEBNER E. E. and PINNICK H. T., Proceedings of the Third Curbon Conference, p. 211. Pergamon Press, London (1959).
15. MCCLUREJ. W. and YAFETY., Proceedings Fifth Carbon Confe+znce, Press, Oxford (1962).
of the Vol. 1, p. 22. Pergamon