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Activation energies for crystallite growth and ordering in graphistising carbons
Journal of Crystal Growth 34 (1976) 325—331 © North-Holland Publishing Company
ACTIVATION ENERGIES FOR CRYSTALLITE GROWTH AND ORDERING IN GRAPHITISING CARBONS I. Crystallite growth* B.P. RICHARDS The General Electric Co. Ltd., Central Research Laboratories, Hirst Research Centre, h’embley, England Received 15 June 1975; revised manuscript received 16 January 1976
The activation energy for crystallite growth in a variety of graphitising carbons has been investigated using X-ray diffraction techniques. The values Ea and Ec for crystallite growth in the a-direction and c-direction respectively are essent respectively) and are the same for all the materials examined, and are tially single values 300 and —‘ 210 kcal molr independent of the(“Sextent of the transformation of carbon towards the graphite structure. These values imply that in the absence of other restraints, crystallite growth is potentially easiest in the c-direction. In the temperature range 2000— 3000°Cthe activation energy for crystallite growth, especially in the a-direction, is different from that for the “ordering of the stacking sequence”, i.e. crystallite growth is essentially independent of three-dimensional ordering. The results are discussed in terms ofa mosaic model of graphitisation and it is suggested that the processes of crystallite growth are controlled by interstitial migration mechanisms.
1. Introduction
dependent, decreased rapidly with increasing heattreatment time and the degree of graphitisation appeared to approach a limiting value at any heat-treatment temperature (HTT) which increased with HTT. However, in general a zero rate of change was not attamed in the total treatment time (HTt) used. These authors explained their results by assuming a broad distribution of appropriate activation energies for the process with higher activation energies associated with a higher degree of graphitisation, that is the activation energy is a function of the extent of transformation. Mizushima [5] found apparent activation energy values which increased from “—100 kcal mole—1 at 1400°Cto “-220 kcal mole—1 at 2200°C.These values were considerably lower than those obtained by Fair and Collins. In contrast, Fischbach [2] using a conventional coke found that the activation energy for the process was single valued and that graphitisation was adequately described by a super position of many first-order rate processes with a broad distribution of rate constants for which he assumed large differences in preexponential factors. Neither the significance of these differences nor their origin were made clear. An acti-
The processes by which graphitisation and crystallite growth occur are complex and information on the kinetics of these processes should be useful in determining detailed mechanisms. Only relatively recently, however, has attention been paid to the possible rate controlling processes by observing the changes which occur under different heat-treatment conditions in properties such as crystallite parameters [1—4]and conductivity [5]. These studies have been usefully reviewed by Fischbach [6]. There does exist in the literature, however, a diversity of opinion and a number of apparent inconsistencies, and it is the purpose of these papers to provide further data in an attempt to resolve some of these difficulties. Time—temperature studies by Fair and Collins [1] on a conventional composite pitch/coke carbon, and by Mazza et al. [7] on a coked pitch indicated that the rate of graphitisation, which was strongly temperature *
The work described in this paper constituted part of a Ph.D. Thesis submitted to London University, March 1974. 325
326
/
B.P. Richards Activation energies for crystallite growth in graphitising carbons. I
vation energy of 250 kcal mole—1 was found, in agreement with the value observed by the same worker for pyrolytic carbon [8] suggesting that “the graphitisation process was the same in the two types of material, even though they exhibited different time—temperature behaviours”. This value, however, was appreciably larger than the experimental values [91for layer plane self-diffusion (163 kcal mole—1) attributed to a vacancy mechanism [10], and the heat of sublimation of single carbon atoms [9] (170 kcal mole1). It agreed well with Dienes’ theoretical value [11] for vacancy diffusion, as corrected by Kanter [9] (263 kcal mole—1) and with recent experimental values for a vacancy mechanism in the range [12,13] 220—240 kcal mole—1. Murty and his colleagues [3,4] attempted to resolve some of these inconsistencies using a new interpretation of results on the studies of the graphitisation process as a continuous function of the extent of transformation. They showed that for all the materials studied the activation energy was the same (230 kcal mole~),but that the rates of graphitisation were different (due to differences in the so-called pre-exponential or frequency factors) and characteristic, reflecting the “structural configuration” in particular the anisotropy of the starting material the calcined coke itself. It was suggested that the rate controlling mechanism for graphitisation is most probably a vacancy mechanism, but other authors [14] have suggested an
Moreover, the value of G will depend intimately on the physical significance of terms such as “ordering of the stacking sequence” and the ways in which these are expressed mathematically. In an attempt to explore these possibilities, crystallite parameters obtained as a result of the present investigation and those obtained previously in these Laboratories [15—19]have been re-analysed to provide relevant data on activation energies for crystallite growth and graphitisation. It is the purpose of this paper to discuss the activation energy for crystallite growth whilst discussion of the activation energy for three-dimensional ordering will be the subject of Part II.
2. Experimental IfL is the crystallite size (either La or L~)after a treatment at temperature T for a time t, then the value of L at any temperature can be represented by an empirical equation of the type: L
=
(1)
,
—
alternative interstitial mechanism with an activation energy of 190 kcal mole—1. The majority of the values for the activation energy of graphitisation reported in the literature have been based on measurements of the interlayer spacing, it being assumed that only a single process (i.e. ordering of the stacking sequence) is operative during graphitisation. Other energy of graphitisation” authors simply irrespective refer to an of “activation the method of obtaining their data, or of the parameters investigated, and consequently many invalid comparisons have been made of the various (and different) values of the activation energy measured. However, since there appears to be no explicit relationship [15] between stacking order and crystallite growth, it might be speculated that the activation energy for crystallite growth (E) would have a different value(s) from that for the ordering of the stacking sequence (G). Further it is possible that values of E and G would vary from one carbon mataial to another,
2700°C 68
2500°C
-
T ~ 66
-
64
-
62
-
2700°C
—_
2500°C 2700°C
In i
6•O
2700°C 2300°C
— -
2500°C
_____—
2300°C 2500 °C
5~8 -
—
5~6 -
_~~A
,___—
—+-- —-——--—i
2300°C
I
-
‘0
30
34
38
In t
S
I
42
—
46
I 50
Fig. 1. Plots of in L versus in t for petroleum cokes and pitch cokes. Pitch coke: (+) La, (~) L~,Petroleum coke: (x) La, (•) L~.The error bars shown on the left hand side apply to all data points.
B.F. Richards /Activation energies for crystallite growth in graphitising carbons. I T (‘Cl (For dotted curves) 2600 2400 2200 2000 I
56
I
I
I
327
a single value, although the value Ea, for growth in may differ from Ec, for growth in Lc. If a obeys the relation
La,
I
I
%>‘.,
.
N,.
-
.5
~
aa
(2)
0e_Q/i’?T,
...e..
_t._*
where T is the HTT and R the gas constant, this can 1 for values and a petroleum coke-pitch binder artefact [16]. The be confirmed by plotting lna against T— of La and Lc see fig. 2 for data on a petroleum coke —
C
—
4•6
\
straight lines observed over the large temperature range (1800—2700°C)indicate that eq. (2) can be used to relate a, Tand Q. Moreover, the same data do not give straight lines when ln a is plotted [20] as a function From of eqs.T (1)see andbroken (2) lines, fig. 2.
+%
62
—
58
La
‘4’
0eQIRTt~~
‘‘I,””
.2 ~
\\~
.
and
I’
I
s.o
-
4’6
-
I
“*\,~
“.‘
_____________________________________ I I 34
35
+x
4-2
o~(For
(3)
4-6
5~O
1)— Q/RT. lnL = ln(a0t’ For a given material and a given HTt (30 mm for the majority of the present data) this equation can be written
foil curves)
Fig. 2. Plots of in a versus T5 and in a versus T for petroleum cokes and a petroleum coke/pitch binder artefact (smoothed values — see ref. (261): (s) artefact; (+) petroleum coke,
where a and n are constants. The suitability of this equation was confirmed by plotting the relevant isothermal data for petroleum cokes and pitch cokes for different HTT see fig. 1. The methods used to obtam these crystallite data have been described in detail elsewhere [16]. The family of straight parallel lines demonstrates that eq. (1) can be used to describe the relationship between L and t for these types of material —
lnL const. —Q/RT. (4) It has been shown [3,20] that the activation energy E, is given by =
E Q/n (5) As pointed out [3,4] for similar equations involving the interlayer spacing, only when the kinetic relationship given in eq. (1) is linear, is Q = E. Some variations in the value of E reported in the literature arise through this oversight. Differentiating eq. (3) =
.
dL/dt
=
a 0nt’~~ e
at least. The parallelism of the families of petroleum coke lines and pitch coke lines, however, may be fortuitous, and were data available for artefacts, etc., the resulting family of lines might possibly show some divergence from those of fig. 1. It is evident that for these samples n (given by the slopes of the lines) is constant with a value of 0.1, and shows no regular or continuous temperature dependence. This suggests that in these temperature ranges the activation energy for crystallite growth in the a- and c-directions does not have a spectrum of values but can be described by
Q/RT
which is similar to an empirical one proposed by Mizushima [5] dL/dt =fe_Q/RT, where f was an unknown function but thought to involve L. Eqs. (4) and (5) give: lnL const. —En/RT. =
Hence by plotting lnL (where L is either La or Lc) as
328
B.P. Richards /Activation energies for crystallite growth in graphitising carbons. I 2700
bOG
2300 I
2000 I
1800 I
1500 I
T
(°c)
Table 1 Activation energies for crystallite growth from plots of ln L
assuming n
1 ; values obtained from figs. 3—5
versus T— (see text)
Q
•_..i ~
bOO-
La
I 1
1000
Lc
-
=
0.1
(eV)
EQ/n (kcal mole—1)
petroleum coke petroleum coke—tar binder petroleum coke—pitch binder pitch coke pitch coke—pitch binder
1.34 1.22 1.26 1.35 1.34
308 281 291 311 308
±
petroleum coke petroleum coke—tar binder
0.90 0.87
206 199
±15 ±25
petroleum coke—pitch binder pitch coke pitch coke—pitch binder
0.87 0.94 0.94
199 ±15 216 ±15 216 ±15
15
±25 ±15 ±15 ±15
L 0
(n 1
00-
2700
bOOC
3~5
40
4-5
50
2300
2000 I
1500
800 I
I
1
(°c)
5-5
+
~ 1 for petroleum cokes and peFig. 3. Plots of La,c versus T troleum coke/tar binder artefacts: (.) petroleum coke; (+) petroleum coke/tar artefacts.
(A) 00
-
~“-~r—
—
1200°C
a function of T1, it is possible to determine the activation energies Ea and Ec from the slopes of the resulting straight lines and using the value n 0.1 obtamed above. For the purpose of this analysis the value of n for the artefacts was assumed to be the same as those for the cokes. The crystallite size data for petroleum cokes, pitch cokes and various artefacts are plotted as functions of T~ in figs. 3—5 and the activation energies so determined are shown in table 1. In the temperature range above ~‘-‘2000°Cthe following salient conclusions may be drawn: (i) the activation energy Ea for growth Of La appears to be the same for all the (graphitic) materials examined (=300 kcal mole~); (ii) the activation energy Ec for growth of Le appears to be the same for all the (graphitic) materials exammed (‘-‘210 kcal mole1); (iii) since Ea > Ec, in the absence of other effects =
-
1000 ~.
°
() +
-
‘—z~—
—
—
“
IC
35
4-0
4-5
+
50
—
-.52A IZOO°C
5-5
60
io4
Fig. 4. Plots of La c versus T’ for pitch cokes and pitch coke! pitch binder artef~cts:(.) pitch coke; (+) pitch coke/pitch artefact.
B.P. Richards IA ctivation energies for crystallite growth in graphitising carbons. I
2300
2700 I
:
•
(A)
00
-
000
-
If
2000 I
1800 I
1500
T
(‘c)
-.~
-j
•
‘~-.j
•
(~) 00
-
~34A I200’C
IC
30
3-5
40
4-5
4
,o~
Fig. 5. Plots ofLa,c versus T’ for petroleum coke—pitch binder artefacts.
crystallite growth in the c-direction is accomplished more easily than in the a-direction, In those instances where data are available for temperatures below —2000°C(i.e. pitch coke-pitch binder and petroleum coke-pitch binder artefacts), there are sharp discontinuities in the slopes (for both La and L~)at a HTT of ‘-2000°C.The activation energies this lower temperature pear toassociated be at leastwith an order of magnitude less range than apthose for the upper temperature range.
3. Discussion The analysis of the present crystallite size data has indicated that in the temperature range above —2000°C the two activation energies for crystallite growth in the a- and c-directions are different. In addition Ea (and probably E~as well) is different from that (“—230 kcal molel) obtained by other workers for three-
329
dimensional ordering of the layer planes. In other of words, crystallite growth is essentially independent the layer plane ordering process. Moreover, since Ea > E~,growth in L~is potentially accomplished more easily than the growth in La. The values for Ea and E~appear to be constant for all the (graphitic) materials examined, and are again independent of the extent of the transformation of carbon to a graphite, i.e. the “energy barrier” for transformation (i.e. crystallite growth) is independent of the extent of transformation. Franklin [21] suggested that since crystallite growth occurs at measurable rate in the temperature range 1000—3000°Cthe activation energy (for crystallite growth) increases continuously as the crystallite size increases. Graphitisation was pictured as involving rotation and re-orientation of whole layer planes or even groups of layers. However, these ideas bear little relation to the physical and chemical properties of graphitising carbons or to any concept based on the act~,’ationenergy data of the present work, in particular to the discrete values of Ea and E~. Maire and Mering [22] abandoned the hypothesis of the invariance of elementary atomic layers which was implicit in Franklin’s ideas, and suggested that the essential process in crystallite growth and graphitisation lies in the internal transformation of the structures of individual atomic layers. This was accompushed not by the rotation of whole layer planes but by the removal of interstitial carbon atoms initially distributed at random on the two faces of the layers, and then rearrangement on definite structural sites. The atomic migration would be associated with the movement of the interstitial atoms between the layer planes involving an activation energy E~a~ which lies 1 between the theoretical value [23] of 3.2 kcal and 9.2 kcal mole—’ determined experimentallymole— [24]. This very low value implies that this process would be initiated at quite a modest HTT. In the absence of other effects, such as constraints on interstitial diffusion, such a process would result in an easier growth in Lc than in La, as implied by the present data. Following a suggestion by Steward and Cook [25] the present author has developed [26] a Mosaic Model of graphitisation. For convenience, however, and in an attempt to interpret the present results the relevant points of this theory are recapitulated here. There are three main stages involved in the forma-
330
B.P. Richards /Activation energies for crystallite growth in graphitising carbons. I
tion of a graphitic carbon, namely: (i) carbonisation (at temperatures <1000°C); (ii) a first or preliminary stage of graphitisation proper (<2000°C); (iii) a second or final stage of graphitisation proper (>2000°C). It is in the carbonisation stage that the factors which pre-determine the graphitisability of a given material have their maximum effect, and in which the mosaic units (essentially invariant with HTT) and potential long-range order are established. The two stages proper pf graphitisation serve mainly to perfect the graphite structure within these mosaics (however large or small) and do not intrinsically influence the ability of a particular carbon material to graphitise or not. During graphitisation at least two mechanisms operate. At temperatures <2000°Cthe predominant influence is the presence of defects and interstitial atoms (“grafted” to the layer planes consistent with the ideas of Maire and Mering) the removal of which corresponds to preferential growth in L~and slight reorientation and rearrangement of the graphite-like layerlets. On the other hand, at temperatures >2000°C the principal mechanism is the reduction of the interlayer spacing brought about by the availability of sufficient thermal energy to break the intra-lamellar carbon bonds, especially at mobile mosaic sub-boundaries thus promoting boundary movement. In this way the continual movement of crystallite boundaries, if unrestricted, will ultimately yield a single three-dimensional crystallite having the normal graphitic stacking. However the boundaries of the mosaic units, established during carbonisation and which are extremely stable, effectively control the size which the crystallites may ultimately achieve and hence the degree of graphitisation which is possible. The growth in La would in part be accomplished by recombination of the individual migrated interstitial carbon atoms at the peripheries of the layer planes, and in part by the separate process of coalescence of neighbouring, similarly-oriented individual crystallites. Although the two processes are separate they may occur simultaneously. Further, coalescence may occasionally be consequent upon the arrival of interstitials at the boundaries of the layer planes if the crystallites are in favourable orientation/alignment. By its very nature the process of coalescence cannot begin until a significant amount of graphitisation has occurred in —
—
order that well-defined crystallites do exist by which time the majority of interstitial migrations will have taken place. Subsequently the two processes occur simultaneously, coalescence becoming the predominant (and eventually the sole) influence at the higher graphitising temperatures. The activation energy required for the former of these two processes, E~,would be the summation of that for the ‘ungrafting’ or formation of an interstitial, Ef’, and that for interstitial diffusion, E~a~ Assuming either the theoretical value [23] of 225 kcal mole~1 or the experimental value [14] of 204—215 kcal mole—1 for E, we have E1 + Ei ~ 210—225 kcal mole1 —
=
f
ma
The latter of the two processes would involve a high (and slightly variable) activation energy, E~’,implicit in the peculiar atomic configuration, favourable layer alignment and orientation required for such coalescence to occur. The total activation energy for crystallite growth in the a-direction, Ea, would therefore be significantly greater than E~consistent with the present values (-‘-300 kcal mole—1). Crystallite growth in the c-direction would be governed by the mutual “uncrinkling” process associated with the loss of interstitials originally “grafted” on to the layer planes which would constitute an increase in the two-dimensional order (i.e. crystallinity) within the layer planes. Such a process would result from the diffusion and emission of single interstitial atoms (or degenerated groups) from the spacing between the layer planes and allow the crystallite size, Lc, to reach at least the value of the “crinkled” regions. The possibility of the build-up of the new planes (within the mosaic units) on existing, fairly substantial interstitial groups (i.e. those which are energetically stable with respect to the surrounding layer planes), cannot be excluded. The author prefers the view, however, that diffusion and emission of interstitials would be the dominant processes. Hence the activation energy for growth in Lc would be the same as that, E~,for the first constituent process involved in the growth of La, or E~ E’f + Eima ~ 210—225 kcal mole~ =
a value which is in good agreement with that of the present work. At temperatures less than 2000°C, E~’
B. P. Richards / Activation energies for crystallite growth in graphitising carbons. 1
would be small and hence La and Lc would be very similar as previously reported [161. At temperatures greater than 2000°C, the number of interstitials still available for migration would rapidly decrease and hence La would steadily exceed Lc as observed [16—18].It is evident, therefore, that an interstitial mechanism is probably the rate controlling process for crystallite growth, but may not be so for three-dimensional ordering of the stacking sequence. That crystallite growth in general occurs by an interstitial mechanism was again concluded [14] from experiments on the stress-annealing of pyrolytic graphite. A vacancy mechanism was rejected on the grounds that, it would necessitate a model for diffusion in which the activation energy required would be far larger than any of the observed values. Instead these authors suggested two discrete mechanisms an “interstitial mechanism” and a “dynamic interchange mechanism” in addition to the processes responsible for crystallite alignment. —
—
33!
[4] H.N. Murty, D.L. Beiderman and E.A. Heintz, Carbon 7 (1969) 683. [5] S. Mizushima, in: Proc. 5th Carbon Conf., 1963, p. 439. [61 D.B. Fischbach, Chemistry and Physics of Carbon, Vol. 9 Ed. P.L. Walker (Dekker, New York, 1972) pp. 1—104. [7] M. Mazza, A. Marchand and A. Pacault, J. Chim. Phys. 59(1962) 657. (81 D.B. Fischbach, AppI. Phys. Letters 3 (1963) 168. [9] MA. Kanter, Phys. Rev. i07 (1957) 655. [10] C. Baker and A. Kelly, Nature 193 (1962) 235. [111 G.J. Dieries, J. AppI. Phys. 23 (1952) 1194. [12] R.W. Henson and W.N. Reynolds, Carbon 3 (1965) 277. [13] J.A. Turnbull and M.S. Stagg, Phil. Mag. 14 (1966) 1049. [14] C. Roscoe and J. Baker, J. App!. Phys. 40(1969)1665. [15] B.P. Richards, J. App!. Cryst. 1(1968) 35. [16] lB. Mason, E.A. Kellett and B.P. Richards, in: md. Carbon Conf., S.C.!. 1966, p. 159. [17] B.P. Richards, E.A. Kellett and lB. Mason, J. AppL Chem. 17 (1967) 298. [181 E.A. Kellett and B.P. Richards, J. Appi. Chem. 18
55. and E.A. Kellett, J. Appl. Chem. 20 [19] (1968) B.P. Richards
(1970) 240. [20] H.N. Murty, D.L. Beiderman and E.A. Heintz, J. Phys. Chem. 72 (1969) 683. [21] R.E. Franklin, Proc. Roy. Soc. (London) A209 (1951)
References [1] F.V. Fair and F.M. Collins, in: Proc. 5th Carbon Conf., 1962, p. 503. [2] D.B. Fischbach, Nature 200 (1963) 1281. [3] H.N. Murty, D.L. Beiderman and E.A. l-leintz, Carbon 7 (1969) 667.
196. [22] J. Maire and J. Mering, J. Chim. Phys. 57 (1960) 803. [231 CA. Coulson, S. Sennet, M.A. Herraez, M. Lea! and E. Santos, Carbon 3 (1966) 445. [24] P.R. Goggin and W.N. Reynolds, Phil. Mag. 8 (1963) 265. [25] E.G. Steward and B.P. Cook, Z. Krist. 114 (1960) 245. [26] B.P. Richards, Ph.D. Thesis, London (1974).
ACTIVATION ENERGIES FOR CRYSTALLITE GROWTH AND ORDERING IN GRAPHITISING CARBONS I. Crystallite growth* B.P. RICHARDS The General Electric Co. Ltd., Central Research Laboratories, Hirst Research Centre, h’embley, England Received 15 June 1975; revised manuscript received 16 January 1976
The activation energy for crystallite growth in a variety of graphitising carbons has been investigated using X-ray diffraction techniques. The values Ea and Ec for crystallite growth in the a-direction and c-direction respectively are essent respectively) and are the same for all the materials examined, and are tially single values 300 and —‘ 210 kcal molr independent of the(“Sextent of the transformation of carbon towards the graphite structure. These values imply that in the absence of other restraints, crystallite growth is potentially easiest in the c-direction. In the temperature range 2000— 3000°Cthe activation energy for crystallite growth, especially in the a-direction, is different from that for the “ordering of the stacking sequence”, i.e. crystallite growth is essentially independent of three-dimensional ordering. The results are discussed in terms ofa mosaic model of graphitisation and it is suggested that the processes of crystallite growth are controlled by interstitial migration mechanisms.
1. Introduction
dependent, decreased rapidly with increasing heattreatment time and the degree of graphitisation appeared to approach a limiting value at any heat-treatment temperature (HTT) which increased with HTT. However, in general a zero rate of change was not attamed in the total treatment time (HTt) used. These authors explained their results by assuming a broad distribution of appropriate activation energies for the process with higher activation energies associated with a higher degree of graphitisation, that is the activation energy is a function of the extent of transformation. Mizushima [5] found apparent activation energy values which increased from “—100 kcal mole—1 at 1400°Cto “-220 kcal mole—1 at 2200°C.These values were considerably lower than those obtained by Fair and Collins. In contrast, Fischbach [2] using a conventional coke found that the activation energy for the process was single valued and that graphitisation was adequately described by a super position of many first-order rate processes with a broad distribution of rate constants for which he assumed large differences in preexponential factors. Neither the significance of these differences nor their origin were made clear. An acti-
The processes by which graphitisation and crystallite growth occur are complex and information on the kinetics of these processes should be useful in determining detailed mechanisms. Only relatively recently, however, has attention been paid to the possible rate controlling processes by observing the changes which occur under different heat-treatment conditions in properties such as crystallite parameters [1—4]and conductivity [5]. These studies have been usefully reviewed by Fischbach [6]. There does exist in the literature, however, a diversity of opinion and a number of apparent inconsistencies, and it is the purpose of these papers to provide further data in an attempt to resolve some of these difficulties. Time—temperature studies by Fair and Collins [1] on a conventional composite pitch/coke carbon, and by Mazza et al. [7] on a coked pitch indicated that the rate of graphitisation, which was strongly temperature *
The work described in this paper constituted part of a Ph.D. Thesis submitted to London University, March 1974. 325
326
/
B.P. Richards Activation energies for crystallite growth in graphitising carbons. I
vation energy of 250 kcal mole—1 was found, in agreement with the value observed by the same worker for pyrolytic carbon [8] suggesting that “the graphitisation process was the same in the two types of material, even though they exhibited different time—temperature behaviours”. This value, however, was appreciably larger than the experimental values [91for layer plane self-diffusion (163 kcal mole—1) attributed to a vacancy mechanism [10], and the heat of sublimation of single carbon atoms [9] (170 kcal mole1). It agreed well with Dienes’ theoretical value [11] for vacancy diffusion, as corrected by Kanter [9] (263 kcal mole—1) and with recent experimental values for a vacancy mechanism in the range [12,13] 220—240 kcal mole—1. Murty and his colleagues [3,4] attempted to resolve some of these inconsistencies using a new interpretation of results on the studies of the graphitisation process as a continuous function of the extent of transformation. They showed that for all the materials studied the activation energy was the same (230 kcal mole~),but that the rates of graphitisation were different (due to differences in the so-called pre-exponential or frequency factors) and characteristic, reflecting the “structural configuration” in particular the anisotropy of the starting material the calcined coke itself. It was suggested that the rate controlling mechanism for graphitisation is most probably a vacancy mechanism, but other authors [14] have suggested an
Moreover, the value of G will depend intimately on the physical significance of terms such as “ordering of the stacking sequence” and the ways in which these are expressed mathematically. In an attempt to explore these possibilities, crystallite parameters obtained as a result of the present investigation and those obtained previously in these Laboratories [15—19]have been re-analysed to provide relevant data on activation energies for crystallite growth and graphitisation. It is the purpose of this paper to discuss the activation energy for crystallite growth whilst discussion of the activation energy for three-dimensional ordering will be the subject of Part II.
2. Experimental IfL is the crystallite size (either La or L~)after a treatment at temperature T for a time t, then the value of L at any temperature can be represented by an empirical equation of the type: L
=
(1)
,
—
alternative interstitial mechanism with an activation energy of 190 kcal mole—1. The majority of the values for the activation energy of graphitisation reported in the literature have been based on measurements of the interlayer spacing, it being assumed that only a single process (i.e. ordering of the stacking sequence) is operative during graphitisation. Other energy of graphitisation” authors simply irrespective refer to an of “activation the method of obtaining their data, or of the parameters investigated, and consequently many invalid comparisons have been made of the various (and different) values of the activation energy measured. However, since there appears to be no explicit relationship [15] between stacking order and crystallite growth, it might be speculated that the activation energy for crystallite growth (E) would have a different value(s) from that for the ordering of the stacking sequence (G). Further it is possible that values of E and G would vary from one carbon mataial to another,
2700°C 68
2500°C
-
T ~ 66
-
64
-
62
-
2700°C
—_
2500°C 2700°C
In i
6•O
2700°C 2300°C
— -
2500°C
_____—
2300°C 2500 °C
5~8 -
—
5~6 -
_~~A
,___—
—+-- —-——--—i
2300°C
I
-
‘0
30
34
38
In t
S
I
42
—
46
I 50
Fig. 1. Plots of in L versus in t for petroleum cokes and pitch cokes. Pitch coke: (+) La, (~) L~,Petroleum coke: (x) La, (•) L~.The error bars shown on the left hand side apply to all data points.
B.F. Richards /Activation energies for crystallite growth in graphitising carbons. I T (‘Cl (For dotted curves) 2600 2400 2200 2000 I
56
I
I
I
327
a single value, although the value Ea, for growth in may differ from Ec, for growth in Lc. If a obeys the relation
La,
I
I
%>‘.,
.
N,.
-
.5
~
aa
(2)
0e_Q/i’?T,
...e..
_t._*
where T is the HTT and R the gas constant, this can 1 for values and a petroleum coke-pitch binder artefact [16]. The be confirmed by plotting lna against T— of La and Lc see fig. 2 for data on a petroleum coke —
C
—
4•6
\
straight lines observed over the large temperature range (1800—2700°C)indicate that eq. (2) can be used to relate a, Tand Q. Moreover, the same data do not give straight lines when ln a is plotted [20] as a function From of eqs.T (1)see andbroken (2) lines, fig. 2.
+%
62
—
58
La
‘4’
0eQIRTt~~
‘‘I,””
.2 ~
\\~
.
and
I’
I
s.o
-
4’6
-
I
“*\,~
“.‘
_____________________________________ I I 34
35
+x
4-2
o~(For
(3)
4-6
5~O
1)— Q/RT. lnL = ln(a0t’ For a given material and a given HTt (30 mm for the majority of the present data) this equation can be written
foil curves)
Fig. 2. Plots of in a versus T5 and in a versus T for petroleum cokes and a petroleum coke/pitch binder artefact (smoothed values — see ref. (261): (s) artefact; (+) petroleum coke,
where a and n are constants. The suitability of this equation was confirmed by plotting the relevant isothermal data for petroleum cokes and pitch cokes for different HTT see fig. 1. The methods used to obtam these crystallite data have been described in detail elsewhere [16]. The family of straight parallel lines demonstrates that eq. (1) can be used to describe the relationship between L and t for these types of material —
lnL const. —Q/RT. (4) It has been shown [3,20] that the activation energy E, is given by =
E Q/n (5) As pointed out [3,4] for similar equations involving the interlayer spacing, only when the kinetic relationship given in eq. (1) is linear, is Q = E. Some variations in the value of E reported in the literature arise through this oversight. Differentiating eq. (3) =
.
dL/dt
=
a 0nt’~~ e
at least. The parallelism of the families of petroleum coke lines and pitch coke lines, however, may be fortuitous, and were data available for artefacts, etc., the resulting family of lines might possibly show some divergence from those of fig. 1. It is evident that for these samples n (given by the slopes of the lines) is constant with a value of 0.1, and shows no regular or continuous temperature dependence. This suggests that in these temperature ranges the activation energy for crystallite growth in the a- and c-directions does not have a spectrum of values but can be described by
Q/RT
which is similar to an empirical one proposed by Mizushima [5] dL/dt =fe_Q/RT, where f was an unknown function but thought to involve L. Eqs. (4) and (5) give: lnL const. —En/RT. =
Hence by plotting lnL (where L is either La or Lc) as
328
B.P. Richards /Activation energies for crystallite growth in graphitising carbons. I 2700
bOG
2300 I
2000 I
1800 I
1500 I
T
(°c)
Table 1 Activation energies for crystallite growth from plots of ln L
assuming n
1 ; values obtained from figs. 3—5
versus T— (see text)
Q
•_..i ~
bOO-
La
I 1
1000
Lc
-
=
0.1
(eV)
EQ/n (kcal mole—1)
petroleum coke petroleum coke—tar binder petroleum coke—pitch binder pitch coke pitch coke—pitch binder
1.34 1.22 1.26 1.35 1.34
308 281 291 311 308
±
petroleum coke petroleum coke—tar binder
0.90 0.87
206 199
±15 ±25
petroleum coke—pitch binder pitch coke pitch coke—pitch binder
0.87 0.94 0.94
199 ±15 216 ±15 216 ±15
15
±25 ±15 ±15 ±15
L 0
(n 1
00-
2700
bOOC
3~5
40
4-5
50
2300
2000 I
1500
800 I
I
1
(°c)
5-5
+
~ 1 for petroleum cokes and peFig. 3. Plots of La,c versus T troleum coke/tar binder artefacts: (.) petroleum coke; (+) petroleum coke/tar artefacts.
(A) 00
-
~“-~r—
—
1200°C
a function of T1, it is possible to determine the activation energies Ea and Ec from the slopes of the resulting straight lines and using the value n 0.1 obtamed above. For the purpose of this analysis the value of n for the artefacts was assumed to be the same as those for the cokes. The crystallite size data for petroleum cokes, pitch cokes and various artefacts are plotted as functions of T~ in figs. 3—5 and the activation energies so determined are shown in table 1. In the temperature range above ~‘-‘2000°Cthe following salient conclusions may be drawn: (i) the activation energy Ea for growth Of La appears to be the same for all the (graphitic) materials examined (=300 kcal mole~); (ii) the activation energy Ec for growth of Le appears to be the same for all the (graphitic) materials exammed (‘-‘210 kcal mole1); (iii) since Ea > Ec, in the absence of other effects =
-
1000 ~.
°
() +
-
‘—z~—
—
—
“
IC
35
4-0
4-5
+
50
—
-.52A IZOO°C
5-5
60
io4
Fig. 4. Plots of La c versus T’ for pitch cokes and pitch coke! pitch binder artef~cts:(.) pitch coke; (+) pitch coke/pitch artefact.
B.P. Richards IA ctivation energies for crystallite growth in graphitising carbons. I
2300
2700 I
:
•
(A)
00
-
000
-
If
2000 I
1800 I
1500
T
(‘c)
-.~
-j
•
‘~-.j
•
(~) 00
-
~34A I200’C
IC
30
3-5
40
4-5
4
,o~
Fig. 5. Plots ofLa,c versus T’ for petroleum coke—pitch binder artefacts.
crystallite growth in the c-direction is accomplished more easily than in the a-direction, In those instances where data are available for temperatures below —2000°C(i.e. pitch coke-pitch binder and petroleum coke-pitch binder artefacts), there are sharp discontinuities in the slopes (for both La and L~)at a HTT of ‘-2000°C.The activation energies this lower temperature pear toassociated be at leastwith an order of magnitude less range than apthose for the upper temperature range.
3. Discussion The analysis of the present crystallite size data has indicated that in the temperature range above —2000°C the two activation energies for crystallite growth in the a- and c-directions are different. In addition Ea (and probably E~as well) is different from that (“—230 kcal molel) obtained by other workers for three-
329
dimensional ordering of the layer planes. In other of words, crystallite growth is essentially independent the layer plane ordering process. Moreover, since Ea > E~,growth in L~is potentially accomplished more easily than the growth in La. The values for Ea and E~appear to be constant for all the (graphitic) materials examined, and are again independent of the extent of the transformation of carbon to a graphite, i.e. the “energy barrier” for transformation (i.e. crystallite growth) is independent of the extent of transformation. Franklin [21] suggested that since crystallite growth occurs at measurable rate in the temperature range 1000—3000°Cthe activation energy (for crystallite growth) increases continuously as the crystallite size increases. Graphitisation was pictured as involving rotation and re-orientation of whole layer planes or even groups of layers. However, these ideas bear little relation to the physical and chemical properties of graphitising carbons or to any concept based on the act~,’ationenergy data of the present work, in particular to the discrete values of Ea and E~. Maire and Mering [22] abandoned the hypothesis of the invariance of elementary atomic layers which was implicit in Franklin’s ideas, and suggested that the essential process in crystallite growth and graphitisation lies in the internal transformation of the structures of individual atomic layers. This was accompushed not by the rotation of whole layer planes but by the removal of interstitial carbon atoms initially distributed at random on the two faces of the layers, and then rearrangement on definite structural sites. The atomic migration would be associated with the movement of the interstitial atoms between the layer planes involving an activation energy E~a~ which lies 1 between the theoretical value [23] of 3.2 kcal and 9.2 kcal mole—’ determined experimentallymole— [24]. This very low value implies that this process would be initiated at quite a modest HTT. In the absence of other effects, such as constraints on interstitial diffusion, such a process would result in an easier growth in Lc than in La, as implied by the present data. Following a suggestion by Steward and Cook [25] the present author has developed [26] a Mosaic Model of graphitisation. For convenience, however, and in an attempt to interpret the present results the relevant points of this theory are recapitulated here. There are three main stages involved in the forma-
330
B.P. Richards /Activation energies for crystallite growth in graphitising carbons. I
tion of a graphitic carbon, namely: (i) carbonisation (at temperatures <1000°C); (ii) a first or preliminary stage of graphitisation proper (<2000°C); (iii) a second or final stage of graphitisation proper (>2000°C). It is in the carbonisation stage that the factors which pre-determine the graphitisability of a given material have their maximum effect, and in which the mosaic units (essentially invariant with HTT) and potential long-range order are established. The two stages proper pf graphitisation serve mainly to perfect the graphite structure within these mosaics (however large or small) and do not intrinsically influence the ability of a particular carbon material to graphitise or not. During graphitisation at least two mechanisms operate. At temperatures <2000°Cthe predominant influence is the presence of defects and interstitial atoms (“grafted” to the layer planes consistent with the ideas of Maire and Mering) the removal of which corresponds to preferential growth in L~and slight reorientation and rearrangement of the graphite-like layerlets. On the other hand, at temperatures >2000°C the principal mechanism is the reduction of the interlayer spacing brought about by the availability of sufficient thermal energy to break the intra-lamellar carbon bonds, especially at mobile mosaic sub-boundaries thus promoting boundary movement. In this way the continual movement of crystallite boundaries, if unrestricted, will ultimately yield a single three-dimensional crystallite having the normal graphitic stacking. However the boundaries of the mosaic units, established during carbonisation and which are extremely stable, effectively control the size which the crystallites may ultimately achieve and hence the degree of graphitisation which is possible. The growth in La would in part be accomplished by recombination of the individual migrated interstitial carbon atoms at the peripheries of the layer planes, and in part by the separate process of coalescence of neighbouring, similarly-oriented individual crystallites. Although the two processes are separate they may occur simultaneously. Further, coalescence may occasionally be consequent upon the arrival of interstitials at the boundaries of the layer planes if the crystallites are in favourable orientation/alignment. By its very nature the process of coalescence cannot begin until a significant amount of graphitisation has occurred in —
—
order that well-defined crystallites do exist by which time the majority of interstitial migrations will have taken place. Subsequently the two processes occur simultaneously, coalescence becoming the predominant (and eventually the sole) influence at the higher graphitising temperatures. The activation energy required for the former of these two processes, E~,would be the summation of that for the ‘ungrafting’ or formation of an interstitial, Ef’, and that for interstitial diffusion, E~a~ Assuming either the theoretical value [23] of 225 kcal mole~1 or the experimental value [14] of 204—215 kcal mole—1 for E, we have E1 + Ei ~ 210—225 kcal mole1 —
=
f
ma
The latter of the two processes would involve a high (and slightly variable) activation energy, E~’,implicit in the peculiar atomic configuration, favourable layer alignment and orientation required for such coalescence to occur. The total activation energy for crystallite growth in the a-direction, Ea, would therefore be significantly greater than E~consistent with the present values (-‘-300 kcal mole—1). Crystallite growth in the c-direction would be governed by the mutual “uncrinkling” process associated with the loss of interstitials originally “grafted” on to the layer planes which would constitute an increase in the two-dimensional order (i.e. crystallinity) within the layer planes. Such a process would result from the diffusion and emission of single interstitial atoms (or degenerated groups) from the spacing between the layer planes and allow the crystallite size, Lc, to reach at least the value of the “crinkled” regions. The possibility of the build-up of the new planes (within the mosaic units) on existing, fairly substantial interstitial groups (i.e. those which are energetically stable with respect to the surrounding layer planes), cannot be excluded. The author prefers the view, however, that diffusion and emission of interstitials would be the dominant processes. Hence the activation energy for growth in Lc would be the same as that, E~,for the first constituent process involved in the growth of La, or E~ E’f + Eima ~ 210—225 kcal mole~ =
a value which is in good agreement with that of the present work. At temperatures less than 2000°C, E~’
B. P. Richards / Activation energies for crystallite growth in graphitising carbons. 1
would be small and hence La and Lc would be very similar as previously reported [161. At temperatures greater than 2000°C, the number of interstitials still available for migration would rapidly decrease and hence La would steadily exceed Lc as observed [16—18].It is evident, therefore, that an interstitial mechanism is probably the rate controlling process for crystallite growth, but may not be so for three-dimensional ordering of the stacking sequence. That crystallite growth in general occurs by an interstitial mechanism was again concluded [14] from experiments on the stress-annealing of pyrolytic graphite. A vacancy mechanism was rejected on the grounds that, it would necessitate a model for diffusion in which the activation energy required would be far larger than any of the observed values. Instead these authors suggested two discrete mechanisms an “interstitial mechanism” and a “dynamic interchange mechanism” in addition to the processes responsible for crystallite alignment. —
—
33!
[4] H.N. Murty, D.L. Beiderman and E.A. Heintz, Carbon 7 (1969) 683. [5] S. Mizushima, in: Proc. 5th Carbon Conf., 1963, p. 439. [61 D.B. Fischbach, Chemistry and Physics of Carbon, Vol. 9 Ed. P.L. Walker (Dekker, New York, 1972) pp. 1—104. [7] M. Mazza, A. Marchand and A. Pacault, J. Chim. Phys. 59(1962) 657. (81 D.B. Fischbach, AppI. Phys. Letters 3 (1963) 168. [9] MA. Kanter, Phys. Rev. i07 (1957) 655. [10] C. Baker and A. Kelly, Nature 193 (1962) 235. [111 G.J. Dieries, J. AppI. Phys. 23 (1952) 1194. [12] R.W. Henson and W.N. Reynolds, Carbon 3 (1965) 277. [13] J.A. Turnbull and M.S. Stagg, Phil. Mag. 14 (1966) 1049. [14] C. Roscoe and J. Baker, J. App!. Phys. 40(1969)1665. [15] B.P. Richards, J. App!. Cryst. 1(1968) 35. [16] lB. Mason, E.A. Kellett and B.P. Richards, in: md. Carbon Conf., S.C.!. 1966, p. 159. [17] B.P. Richards, E.A. Kellett and lB. Mason, J. AppL Chem. 17 (1967) 298. [181 E.A. Kellett and B.P. Richards, J. Appi. Chem. 18
55. and E.A. Kellett, J. Appl. Chem. 20 [19] (1968) B.P. Richards
(1970) 240. [20] H.N. Murty, D.L. Beiderman and E.A. Heintz, J. Phys. Chem. 72 (1969) 683. [21] R.E. Franklin, Proc. Roy. Soc. (London) A209 (1951)
References [1] F.V. Fair and F.M. Collins, in: Proc. 5th Carbon Conf., 1962, p. 503. [2] D.B. Fischbach, Nature 200 (1963) 1281. [3] H.N. Murty, D.L. Beiderman and E.A. l-leintz, Carbon 7 (1969) 667.
196. [22] J. Maire and J. Mering, J. Chim. Phys. 57 (1960) 803. [231 CA. Coulson, S. Sennet, M.A. Herraez, M. Lea! and E. Santos, Carbon 3 (1966) 445. [24] P.R. Goggin and W.N. Reynolds, Phil. Mag. 8 (1963) 265. [25] E.G. Steward and B.P. Cook, Z. Krist. 114 (1960) 245. [26] B.P. Richards, Ph.D. Thesis, London (1974).