- Email: [email protected]
Kinetics of the deposition of pyrolytic carbon on nickel
Corhrm.
1975. Vol. il, pp 1X9-19?
Pergamon Prex
Printed in Great Bntain
KINETICS OF THE DEPOSITION OF PYROLYTIC CARBON ON NICKEL F. J. DERBYSHIRE*and D. L. TRIMM Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7,England (Received 30 August 1974) Abstract-The kinetics of the deposition of laminar graphite on nickel by the pyrolysis of methane, ethane and ethylene at temperatures from 700-1000”has been studied. Two types of graphitic deposit are identified. Continuous films of laminar graphite are formed at higher temperatures, to a weight limit corresponding to the solubility of carbon in nickel at that temperature. It is concluded that such deposits are formed only as a result of a dissolution-precipitation mechanism. Deposits consisting of islands of graphite in a uniform graphite matrix are formed at lower temperatures. The kinetics of deposition are complex, but qualitative agreement is obtained with a model based on the surface aggregation of carbon atoms to account for island nucleation.
3. RESULTS
1. INTRODUCTION
The formation of graphitic carbon on the surface of transition metals by the pyrolysis of hydrocarbons has been closely studied on a qualitative basis [ l-81. On the other hand, comparatively few quantitative studies of the kinetics of the process have been reported[9-131 and the present studies were initiated to investigate the kinetics of carbon deposition on nickel. Previous studies have shown that the pyrolysis of hydrocarbons over nickel can result in the formation of continuous films of laminar graphite, of non-oriented graphite and of carbon fibres, depending on the reaction conditions[7], and evidence has been obtained to indicate that the formation of laminar graphite might involve the dissolution of carbon in nickel, followed by precipitation of the carbon as well ordered graphite[l4]. The present investigation has been focused on the kinetics of carbon deposition on nickel by the pyrolysis of methane, ethane and ethylene under conditions favourable to the formation of laminar graphite.
Studies have been made of the deposition of carbon
from the pyrolysis of methane, ethane and ethylene at temperatures from 700-lOoo”, and pressures from 4-60 Torr. Two types of laminar graphitic deposits were formed. Continuous films of uniformly thick material were produced at high temperatures and low pressures, and islands of thicker graphite located in a matrix of continuous thinner graphitic film were produced at lower temperatures and higher pressures[7]. The continuous film of graphite appeared to be the same in both cases. Both the islands and the film were found to be graphitic, with an interlayer spacing of 3.354A as measured by X-ray diffraction. Transmission electron microscopy of the deposits showed that the graphite was oriented with the basal plane parallel to the substrate surface, and that there was a variation in thickness between islands. In some cases the thickness of the islands was comparable to the surrounding film while, on the same substrate sample, some islands were thick enough to prevent the transmission of 100kV electrons. The edges of some islands were 2. EXPERIMENTAL found to consist of a series of steps and terraces, as The apparatus and the techniques used to prepare though the islands were composed of overlapping plates. samples have been described previously[7]. Thin, poly- Photo microscopy revealed that the islands were often crystalline foils of high purity nickel were suspended from located adjacent to a substrate metal grain boundary, as one arm of a C.I. Mark 2b microbalance in a stream of has been previously reported [2,7]. hydrocarbon and were heated by radiation in order to The formation of continuous films was investigated as a minimise the production of gas phase carbon. function of temperature and pressure of reagent: typical Temperature-time curves were obtained in duplicate results are shown in Fig. 1. The rate of deposition was experiments using a chromel-alumel thermocouple fixed to found to be initially high but to fall rapidly to zero. the foil centre: repeatability was good to i3”. The The amount of carbon finally deposited was found to be temperature of the foil was found to change by up to 30” temperature dependent and, if the temperature was during the course of reaction, as a result of changes in the increased after attaining zero rate, then further carbon emissivity of the surface caused by carbon deposition. The deposition occurred until the amount deposited equalled effect on rates of carbon formation was noted and, where that which would have been deposited on heating a clean foil to the new temperature. The final deposited weight necessary, corrections were made. The deposits were examined by optical microscopy, by was independent of the nature and pressure of the starting transmission and scanning electron microscopy and by gas. The kinetics of the formation of island deposits were electron diffraction, either in situ or after removal from the foil. found to parallel those for continuous deposits but no reduction to zero rate was observed (Fig. 2). When the *Syncryst Limited, Molesey Avenue, East Molesey, Surrey. area of substrate covered by islands was about 50 per 189
190
F. J.
DERBYSHIREand
(1221 K) (117210 (1116K) (1053K) (1035K)
I 10
0
I
I
I
20
I
I
30 Tame,
I
I
40
50
men
Fig. 1. The change in substrate weight with time for the formation of continuous laminar films.
(dM245K)
D. L.
TRIMM
temperatures the rate decreased with increasing temperature to the limit where continuous films were formed and no further deposition was observed. The number of islands per area of foil was observed to decrease with decreasing rate at higher temperatures. In some cases, the foils were annealed in hydrogen before pyrolysis. This pre-treatment inhibited or suppressed island formation, although it did not appear to affect the formation of continuous films. The effect of the rate of cooling after pyrolysis was examined. Rapid cooling (approximately 10 set for the temperature to drop to 500”) produced a very thin continuous film, whereas slower cooling (10 min for the temperature to drop to SW) produced a much thicker film. The thickness of the islands, where these were present, was unaffected by the rate of cooling. 4.
I 10
0
/
I 20 Ttme.
I
I 30
1
I 40
I
man
Fig. 2. The change in substrate weight with time for the formation of continuous film and islands of carbon. Island formation, curves a-d. Continuous film formation, curve e. 100
DISCUSSION
Studies of the formation of continuous graphite films on nickel show that carbon deposition ceases at a weight which is dependent on the deposition temperature. The amount of carbon deposited in various systems is compared with the solubility of carbon in nickel at various temperatures[E] in Fig. 4. The results show close agreement at all temperatures.
F
+ N,-CH9, 4 0 NI-Ctia ,I5 e NI- CHq .30 0 NI-CHs .60 .NI-CK. c 5 O.
.
N,-&H,.
9
E-N,-C,H,.9 XNt-CZH6. 9 AN,-C&, 4 AN,-CH. . IO
)-
I 8.0
I/T,
Tow Torr Torr Torr Torr
rorr Torr Torr Torr Torr
I
I
8.5 K-‘, x104
90
Fig. 4. Comparison of experimental data with recorded values of the solubility of carbon in nickel (15)--literature values. I/T.
K’, ~16~
Fig. 3. Arrhenius type plot for island formation. Apparent activation energies: curve 1, -44.2 kcal mole-‘: curve 2, -41.3 kcal melee’: curve 3, -42.9 kcal mole-‘: curve 4, 32.0kcal mole-‘. 0: 9 Torr C&HI;q: 18Torr C,H,; 0: 4 Torr C,R.
cent, the rate of deposition was falling, although zero rate was never achieved. At low coverages (10 per cent or less) a constant deposition rate was established, and these constant rates showed a temperature dependency summarised in Figs. 2 and 3. Both these curves are based on results obtained with all three hydrocarbons. At higher
Previous studies of the formation of continuous films of graphite on nickel have suggested that the process involves dissolution of carbon in the metal followed by precipitation of well-ordered graphite films [7,14]. The present results provide quantitative proof of this suggestion and show that the thickness of the film is limited by the solubility of carbon in nickel at any given temperature. They indicate that the dissolution-precipitation mechanism is the only major route to the formation of continuous laminar films of graphite on nickel over the temperature range 7OtLlOW. The fact that the actual thickness of the film depends on the rate of cooling of the sample indicates
191
Kinetics of the deposition of pyrolytic carbon on nickel
that dissolution of carbon in nickel occurs at the beginning of an experiment (Fig. l), while precipitation of the film occurs mainly at the end of an experiment, when the foil is cooled. In the case of the island deposits, the experimental evidence supports the suggestion that the thin continuous graphite matrix is formed by a dissolution-precipitation mechanism. The formation of the islands is more complex, however, and would appear to involve surface nucleation and growth, rather than a dissolutionprecipitation mechanism, for the following reasons. (i) If the continuous graphite film is precipitated on cooling the foil, island formation occurs on an essentially free substrate surface. (ii) Island formation corresponds to a weight increase beyond the solubility limit and a constant growth rate is often established (Figs. 2, 3). (iii) The islands are thicker than the surrounding film and show some thickness variation between themselves. (iv) The thickness of the islands is unaffected by the rate of cooling of the substrate. (v) The islands are usually located at preferred surface nucleation sites such as grain boundaries[7]. (vi) Pre-treatment of the foil with hydrogen inhibits island formation, while not affecting the production of continuous films. The kinetics of island formation were found to be complex (Fig. 3). At low temperatures, the reaction was zero order and the constant rate increased with temperature (apparent activation energy 32.0 K cal mole-‘). At high temperatures, the rate decreased with increasing temperature (apparent activation energy ca -42 K cal mole-‘), the island number density decreased and the island size increased. The rate approximated to first order in hydrocarbon pressure and was apparently independent of the nature of the hydrocarbon. At low temperatures, the results are consistent with island growth by diffusion of carbon through nickel to the nucleation sites. The reaction is zero order in hydrocarbon and the observed activation energy of 32.0 K cal mole-’ IS in close agreement with the value reported for the diffusion of carbon in nickel and differs from the value reported for surface diffusion of carbon on nickel (about 20 K cal mole-‘). At higher temperatures, the decreasing rate with increasing temperature is more characteristic of a surface reaction in that the rates are first order in hydrocarbon. If island formation is dependent on surface nucleation and growth, the rate of uptake of carbon will be related to the number of islands nucleated and to their subsequent growth. The fact that both of these factors are important in the present system is shown by the variation of island number density, n,, and of average island area, a, with reaction conditions. Considering, first, the steady-state growth of stable islands, the deposition rate, C, can be related to the average island area and number density by the equation C = an,w
(1)
where w is the frequency with which carbon atoms attach
themselves to the islands. However, the island number density will obviously be related (although not necessarily by a simple relationship) to the initial rate of nucleation, J. Consequently, it is useful to examine the factors which can be expected to affect both J and n,. The problem may be considered by analogy with the deposition and growth of thin films by vapour deposition, where the process has been describedI in terms of (i) atoms impinging on the substrate being either adsorbed or reacted, (ii) adatoms moving over the substrate by jumping from site to site, (iii) adatoms clustering to form islands, (iv) islands growing mainly by the addition of single atoms, to the pdint where the islands coalesce. For this type of process, an expression may be derived for small aggregates of atoms[l7] which relates the nucleation rate, J, with the rate of deposition of atoms, RI, at the substrate temperature, T. R
I,,*-,)
J,* = (NV)” exp
(i*+ 1)AGa tAGi*-AGtl RT
-.
(,) L
Where ix is the number of atoms in a critical size nucleus such that the probability of growth by the gain of an atom is equal to the probability of decay by the loss of an atom. In a pyrolytic system, the rate of carbon formation would be expected to increase with temperature, following a power rate law (3) and substitution of equation (3) in equation (2) leads to A”‘_”
J,* = (NV)” P
.,,*~,,exp(i*+I)(AGa-~)l~Gi*--SG~ RT
(4) The effect of increasing temperature, if R’ were constant, would be to reduce the supersaturation and to result at some point in an increase of the critical nucleus size from i* to (i* t 1) atoms, since the larger cluster will have a greater binding energy and will be more stable. Since R’ does, in fact, increase with temperature, the supersaturation will increase and will oppose this effect. Provided that the value of E is not too large and remains constant, then the exponent in equation (4) will be positive and J will decrease with increasing temperature. Hence the value of n, will also decrease with temperature, and cause the deposition rate, C, also to decrease (equation I). The experimental observations are generally in agreement with this model. The island density and the rate of carbon formation both decrease with increasing temperature and are dependent on the hydrocarbon pressure. If. as suggested by Presland and Walker[2], the products of dehydrogenation are single carbon atoms (or atom pairs) which are mobile on the metal surface, and the process is limited by diffusion, this would account for the lack of dependence on the structure of the parent hydrocarbon. The model thus provides a reasonable qualitative explanation of the observed effects, although quantitative proof is difficult in the absence of values for some of the constants in equation (3).
F. .I. DERBYSHIREand D. L.
192 NOMENCLATURE
A” c E
AGa AGd AGi* i* J n n, N P R R’ T V w
average island area pre-exponential factor experimental rate of carbon deposition energy of activation energy of activation of adsorption energy of activation of surface diffusion binding energy of a critical nucleus number of atoms in a critical size nucleus rate of nucleation order of reaction island number density number of surface adsorption sites hydrocarbon pressure universal gas constant rate of deposition of atoms temperature adatom vibrational frequency freauencv . , with which carbon atoms attach themselves to islands REFERENCES
1. Karu A. E. and Beer M., J. Appl. Phys. 37, 2179 (1%6). 2. Presland A. E. B. and Walker Jr., P. L., Carbon 7,1 (1969). 3. Blau G. and Presland A. E. B., Third Conf. Indust. Carbon and Graphite, (London: Society of Chemical Industry) (1970). 4. Presland A. E. B., Roscoe C. and Walker Jr. P. L., Third Conf.
GRIMM
Indust. Carbon and Graphite, (London: Society of Chemical Industry) (1970). 5. Robertson S. D., Carbon 8, 365 (1970). 6. Baird T., Fryer J. R. and Grant B., Nature 233, 329 (1971). 7. Derbyshire F. J. and Trimm D. L., Preprint. Fourth Conf. Indust. Carbon and Graphite, (London: Society of Chemical Industry) (1974). 8. Baker R. T. K., Barber M. A., Harris P. S., Feates F. S. and Waite R. J., J. Catalysis 26, 51 (1972). 9. Tamai Y., Nishiyama Y. and Takahashi M., Carbon 6, 593 (1968). 10. Lafitau H. and Jacque L., Bull. Sot. Chim. France 4779 (1968). 11. Tamai Y., Nishiyama Y. and Takahashi M., Carbon 7, 209 (1969). 12. Tomita A., Yoshida K., Nishiyama Y. and Tamai Y., Carbon 10, 601 (1972). 13. Lobo L. F. G., Ph.D. Thesis, University of London (1971). 14. Derbyshire F. J., Presland A. E. B. and Trimm D. L., Carbon 10, li4 (1972). 15. Lander J. J., Kern H. E. and Beach A. L., J. Appl. Phys. 23, 1305(1952). 16. Pashley D. W., Aduan. Phys. 14, 327 (1965). 17. Lane G. E., Ph.D. Thesis, University of London (1972). 18. Derbyshire F. J., Presland A. E. B. and Trimm D. L., Carbon 13, Ill (1975).
1975. Vol. il, pp 1X9-19?
Pergamon Prex
Printed in Great Bntain
KINETICS OF THE DEPOSITION OF PYROLYTIC CARBON ON NICKEL F. J. DERBYSHIRE*and D. L. TRIMM Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7,England (Received 30 August 1974) Abstract-The kinetics of the deposition of laminar graphite on nickel by the pyrolysis of methane, ethane and ethylene at temperatures from 700-1000”has been studied. Two types of graphitic deposit are identified. Continuous films of laminar graphite are formed at higher temperatures, to a weight limit corresponding to the solubility of carbon in nickel at that temperature. It is concluded that such deposits are formed only as a result of a dissolution-precipitation mechanism. Deposits consisting of islands of graphite in a uniform graphite matrix are formed at lower temperatures. The kinetics of deposition are complex, but qualitative agreement is obtained with a model based on the surface aggregation of carbon atoms to account for island nucleation.
3. RESULTS
1. INTRODUCTION
The formation of graphitic carbon on the surface of transition metals by the pyrolysis of hydrocarbons has been closely studied on a qualitative basis [ l-81. On the other hand, comparatively few quantitative studies of the kinetics of the process have been reported[9-131 and the present studies were initiated to investigate the kinetics of carbon deposition on nickel. Previous studies have shown that the pyrolysis of hydrocarbons over nickel can result in the formation of continuous films of laminar graphite, of non-oriented graphite and of carbon fibres, depending on the reaction conditions[7], and evidence has been obtained to indicate that the formation of laminar graphite might involve the dissolution of carbon in nickel, followed by precipitation of the carbon as well ordered graphite[l4]. The present investigation has been focused on the kinetics of carbon deposition on nickel by the pyrolysis of methane, ethane and ethylene under conditions favourable to the formation of laminar graphite.
Studies have been made of the deposition of carbon
from the pyrolysis of methane, ethane and ethylene at temperatures from 700-lOoo”, and pressures from 4-60 Torr. Two types of laminar graphitic deposits were formed. Continuous films of uniformly thick material were produced at high temperatures and low pressures, and islands of thicker graphite located in a matrix of continuous thinner graphitic film were produced at lower temperatures and higher pressures[7]. The continuous film of graphite appeared to be the same in both cases. Both the islands and the film were found to be graphitic, with an interlayer spacing of 3.354A as measured by X-ray diffraction. Transmission electron microscopy of the deposits showed that the graphite was oriented with the basal plane parallel to the substrate surface, and that there was a variation in thickness between islands. In some cases the thickness of the islands was comparable to the surrounding film while, on the same substrate sample, some islands were thick enough to prevent the transmission of 100kV electrons. The edges of some islands were 2. EXPERIMENTAL found to consist of a series of steps and terraces, as The apparatus and the techniques used to prepare though the islands were composed of overlapping plates. samples have been described previously[7]. Thin, poly- Photo microscopy revealed that the islands were often crystalline foils of high purity nickel were suspended from located adjacent to a substrate metal grain boundary, as one arm of a C.I. Mark 2b microbalance in a stream of has been previously reported [2,7]. hydrocarbon and were heated by radiation in order to The formation of continuous films was investigated as a minimise the production of gas phase carbon. function of temperature and pressure of reagent: typical Temperature-time curves were obtained in duplicate results are shown in Fig. 1. The rate of deposition was experiments using a chromel-alumel thermocouple fixed to found to be initially high but to fall rapidly to zero. the foil centre: repeatability was good to i3”. The The amount of carbon finally deposited was found to be temperature of the foil was found to change by up to 30” temperature dependent and, if the temperature was during the course of reaction, as a result of changes in the increased after attaining zero rate, then further carbon emissivity of the surface caused by carbon deposition. The deposition occurred until the amount deposited equalled effect on rates of carbon formation was noted and, where that which would have been deposited on heating a clean foil to the new temperature. The final deposited weight necessary, corrections were made. The deposits were examined by optical microscopy, by was independent of the nature and pressure of the starting transmission and scanning electron microscopy and by gas. The kinetics of the formation of island deposits were electron diffraction, either in situ or after removal from the foil. found to parallel those for continuous deposits but no reduction to zero rate was observed (Fig. 2). When the *Syncryst Limited, Molesey Avenue, East Molesey, Surrey. area of substrate covered by islands was about 50 per 189
190
F. J.
DERBYSHIREand
(1221 K) (117210 (1116K) (1053K) (1035K)
I 10
0
I
I
I
20
I
I
30 Tame,
I
I
40
50
men
Fig. 1. The change in substrate weight with time for the formation of continuous laminar films.
(dM245K)
D. L.
TRIMM
temperatures the rate decreased with increasing temperature to the limit where continuous films were formed and no further deposition was observed. The number of islands per area of foil was observed to decrease with decreasing rate at higher temperatures. In some cases, the foils were annealed in hydrogen before pyrolysis. This pre-treatment inhibited or suppressed island formation, although it did not appear to affect the formation of continuous films. The effect of the rate of cooling after pyrolysis was examined. Rapid cooling (approximately 10 set for the temperature to drop to 500”) produced a very thin continuous film, whereas slower cooling (10 min for the temperature to drop to SW) produced a much thicker film. The thickness of the islands, where these were present, was unaffected by the rate of cooling. 4.
I 10
0
/
I 20 Ttme.
I
I 30
1
I 40
I
man
Fig. 2. The change in substrate weight with time for the formation of continuous film and islands of carbon. Island formation, curves a-d. Continuous film formation, curve e. 100
DISCUSSION
Studies of the formation of continuous graphite films on nickel show that carbon deposition ceases at a weight which is dependent on the deposition temperature. The amount of carbon deposited in various systems is compared with the solubility of carbon in nickel at various temperatures[E] in Fig. 4. The results show close agreement at all temperatures.
F
+ N,-CH9, 4 0 NI-Ctia ,I5 e NI- CHq .30 0 NI-CHs .60 .NI-CK. c 5 O.
.
N,-&H,.
9
E-N,-C,H,.9 XNt-CZH6. 9 AN,-C&, 4 AN,-CH. . IO
)-
I 8.0
I/T,
Tow Torr Torr Torr Torr
rorr Torr Torr Torr Torr
I
I
8.5 K-‘, x104
90
Fig. 4. Comparison of experimental data with recorded values of the solubility of carbon in nickel (15)--literature values. I/T.
K’, ~16~
Fig. 3. Arrhenius type plot for island formation. Apparent activation energies: curve 1, -44.2 kcal mole-‘: curve 2, -41.3 kcal melee’: curve 3, -42.9 kcal mole-‘: curve 4, 32.0kcal mole-‘. 0: 9 Torr C&HI;q: 18Torr C,H,; 0: 4 Torr C,R.
cent, the rate of deposition was falling, although zero rate was never achieved. At low coverages (10 per cent or less) a constant deposition rate was established, and these constant rates showed a temperature dependency summarised in Figs. 2 and 3. Both these curves are based on results obtained with all three hydrocarbons. At higher
Previous studies of the formation of continuous films of graphite on nickel have suggested that the process involves dissolution of carbon in the metal followed by precipitation of well-ordered graphite films [7,14]. The present results provide quantitative proof of this suggestion and show that the thickness of the film is limited by the solubility of carbon in nickel at any given temperature. They indicate that the dissolution-precipitation mechanism is the only major route to the formation of continuous laminar films of graphite on nickel over the temperature range 7OtLlOW. The fact that the actual thickness of the film depends on the rate of cooling of the sample indicates
191
Kinetics of the deposition of pyrolytic carbon on nickel
that dissolution of carbon in nickel occurs at the beginning of an experiment (Fig. l), while precipitation of the film occurs mainly at the end of an experiment, when the foil is cooled. In the case of the island deposits, the experimental evidence supports the suggestion that the thin continuous graphite matrix is formed by a dissolution-precipitation mechanism. The formation of the islands is more complex, however, and would appear to involve surface nucleation and growth, rather than a dissolutionprecipitation mechanism, for the following reasons. (i) If the continuous graphite film is precipitated on cooling the foil, island formation occurs on an essentially free substrate surface. (ii) Island formation corresponds to a weight increase beyond the solubility limit and a constant growth rate is often established (Figs. 2, 3). (iii) The islands are thicker than the surrounding film and show some thickness variation between themselves. (iv) The thickness of the islands is unaffected by the rate of cooling of the substrate. (v) The islands are usually located at preferred surface nucleation sites such as grain boundaries[7]. (vi) Pre-treatment of the foil with hydrogen inhibits island formation, while not affecting the production of continuous films. The kinetics of island formation were found to be complex (Fig. 3). At low temperatures, the reaction was zero order and the constant rate increased with temperature (apparent activation energy 32.0 K cal mole-‘). At high temperatures, the rate decreased with increasing temperature (apparent activation energy ca -42 K cal mole-‘), the island number density decreased and the island size increased. The rate approximated to first order in hydrocarbon pressure and was apparently independent of the nature of the hydrocarbon. At low temperatures, the results are consistent with island growth by diffusion of carbon through nickel to the nucleation sites. The reaction is zero order in hydrocarbon and the observed activation energy of 32.0 K cal mole-’ IS in close agreement with the value reported for the diffusion of carbon in nickel and differs from the value reported for surface diffusion of carbon on nickel (about 20 K cal mole-‘). At higher temperatures, the decreasing rate with increasing temperature is more characteristic of a surface reaction in that the rates are first order in hydrocarbon. If island formation is dependent on surface nucleation and growth, the rate of uptake of carbon will be related to the number of islands nucleated and to their subsequent growth. The fact that both of these factors are important in the present system is shown by the variation of island number density, n,, and of average island area, a, with reaction conditions. Considering, first, the steady-state growth of stable islands, the deposition rate, C, can be related to the average island area and number density by the equation C = an,w
(1)
where w is the frequency with which carbon atoms attach
themselves to the islands. However, the island number density will obviously be related (although not necessarily by a simple relationship) to the initial rate of nucleation, J. Consequently, it is useful to examine the factors which can be expected to affect both J and n,. The problem may be considered by analogy with the deposition and growth of thin films by vapour deposition, where the process has been describedI in terms of (i) atoms impinging on the substrate being either adsorbed or reacted, (ii) adatoms moving over the substrate by jumping from site to site, (iii) adatoms clustering to form islands, (iv) islands growing mainly by the addition of single atoms, to the pdint where the islands coalesce. For this type of process, an expression may be derived for small aggregates of atoms[l7] which relates the nucleation rate, J, with the rate of deposition of atoms, RI, at the substrate temperature, T. R
I,,*-,)
J,* = (NV)” exp
(i*+ 1)AGa tAGi*-AGtl RT
-.
(,) L
Where ix is the number of atoms in a critical size nucleus such that the probability of growth by the gain of an atom is equal to the probability of decay by the loss of an atom. In a pyrolytic system, the rate of carbon formation would be expected to increase with temperature, following a power rate law (3) and substitution of equation (3) in equation (2) leads to A”‘_”
J,* = (NV)” P
.,,*~,,exp(i*+I)(AGa-~)l~Gi*--SG~ RT
(4) The effect of increasing temperature, if R’ were constant, would be to reduce the supersaturation and to result at some point in an increase of the critical nucleus size from i* to (i* t 1) atoms, since the larger cluster will have a greater binding energy and will be more stable. Since R’ does, in fact, increase with temperature, the supersaturation will increase and will oppose this effect. Provided that the value of E is not too large and remains constant, then the exponent in equation (4) will be positive and J will decrease with increasing temperature. Hence the value of n, will also decrease with temperature, and cause the deposition rate, C, also to decrease (equation I). The experimental observations are generally in agreement with this model. The island density and the rate of carbon formation both decrease with increasing temperature and are dependent on the hydrocarbon pressure. If. as suggested by Presland and Walker[2], the products of dehydrogenation are single carbon atoms (or atom pairs) which are mobile on the metal surface, and the process is limited by diffusion, this would account for the lack of dependence on the structure of the parent hydrocarbon. The model thus provides a reasonable qualitative explanation of the observed effects, although quantitative proof is difficult in the absence of values for some of the constants in equation (3).
F. .I. DERBYSHIREand D. L.
192 NOMENCLATURE
A” c E
AGa AGd AGi* i* J n n, N P R R’ T V w
average island area pre-exponential factor experimental rate of carbon deposition energy of activation energy of activation of adsorption energy of activation of surface diffusion binding energy of a critical nucleus number of atoms in a critical size nucleus rate of nucleation order of reaction island number density number of surface adsorption sites hydrocarbon pressure universal gas constant rate of deposition of atoms temperature adatom vibrational frequency freauencv . , with which carbon atoms attach themselves to islands REFERENCES
1. Karu A. E. and Beer M., J. Appl. Phys. 37, 2179 (1%6). 2. Presland A. E. B. and Walker Jr., P. L., Carbon 7,1 (1969). 3. Blau G. and Presland A. E. B., Third Conf. Indust. Carbon and Graphite, (London: Society of Chemical Industry) (1970). 4. Presland A. E. B., Roscoe C. and Walker Jr. P. L., Third Conf.
GRIMM
Indust. Carbon and Graphite, (London: Society of Chemical Industry) (1970). 5. Robertson S. D., Carbon 8, 365 (1970). 6. Baird T., Fryer J. R. and Grant B., Nature 233, 329 (1971). 7. Derbyshire F. J. and Trimm D. L., Preprint. Fourth Conf. Indust. Carbon and Graphite, (London: Society of Chemical Industry) (1974). 8. Baker R. T. K., Barber M. A., Harris P. S., Feates F. S. and Waite R. J., J. Catalysis 26, 51 (1972). 9. Tamai Y., Nishiyama Y. and Takahashi M., Carbon 6, 593 (1968). 10. Lafitau H. and Jacque L., Bull. Sot. Chim. France 4779 (1968). 11. Tamai Y., Nishiyama Y. and Takahashi M., Carbon 7, 209 (1969). 12. Tomita A., Yoshida K., Nishiyama Y. and Tamai Y., Carbon 10, 601 (1972). 13. Lobo L. F. G., Ph.D. Thesis, University of London (1971). 14. Derbyshire F. J., Presland A. E. B. and Trimm D. L., Carbon 10, li4 (1972). 15. Lander J. J., Kern H. E. and Beach A. L., J. Appl. Phys. 23, 1305(1952). 16. Pashley D. W., Aduan. Phys. 14, 327 (1965). 17. Lane G. E., Ph.D. Thesis, University of London (1972). 18. Derbyshire F. J., Presland A. E. B. and Trimm D. L., Carbon 13, Ill (1975).