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Comment on “bulk-to-surface precipitation and surface diffusion of carbon on polycrystalline nickel” by J.F. Mojica and L.L. Levenson
Surface Science 0 North-llolland
71 (1978) 174-177 Publishing Cornpan)
LETTERS TO THE EDITOR
COMMENT ON “BULK-TO-SURFACE PRECIPITATION AND SURFACE DIFFUSION OF CARBON ON POLYCRYSTALLINE NICKEL” BY J.F. MOJICA AND L.L. LEVENSON Received
29 August
1977; manuscript
received
in final form 3 October
1977
In a recent publication Mojica and Levenson [I] reported on the surface diffusion and bulk-to-surface precipitation of carbon on polycrystalline nickel, using Auger electron spectroscopy as a probe for the surface carbon concentration. They interpreted their results in terms of two processes, the first being the diffusion of carbon to the surface, the second the surface diffusion of C-atoms to form graphite. While we agree with this general description, we feel that the treatment of the actual data is open to criticism. Fig. 1 shows some results obtained by Mojica and Levenson as taken from their paper. The carbon Auger peak (272 eV) increases with time, whereas the nickel peak (65 eV) decreases steadily. The ratio of these two signals at any time is taken by the authors in the analysis of the time dependence of the carbon surface concentration “in order to minimise experimental errors”. We feel that this is an incorrect procedure, if one assumes that the continuous decrease in the nickel signal is actually caused by the growing surface layer of carbon (cf. ref. [2]). Secondly, since in region B of fig. 1 graphite is formed, also the growth of graphite islands could influ-
Fig. 1. Nickel (0) and carbon (m) Auger peak heights in arbitrary 345°C. The nickel signal is shit‘ted downwards by 2 units. 174
units as a function
of time at
. . L;;_;/..0. L.J. Gijzeman et
al. / Comment
175
3
I
*
.
.
-
.
. l2
--:.., 1000
2000
3000
LOO0
iisec)
Fig. 2. Carbon Auger peak heights (arbitrary units) as ti function of time at 370°C (*) and 425°C (m).
ence the kinetics. This possibility is neglected in ref. [I]. In this letter we wish to present an alternative explanation of the experimental results shown in figs. 1 and 2. Firstly, we will use the peak heights as recorded, normalising only to the initial value of the nickel Auger peak. Secondly, we will ascribe the time dependence of the carbon concentration in region B to the growth of graphite islands only. The kinetics of nucleation and growth have been treated extensively by Avrami [3]. A somewhat heuristic derivation of equations valid for linear and two-dimensional growth only can be given as follows. Assuming all nucleation to have occurred at t = 0, the dimension of a single, linear, domain (I) will increase with time according to dljdt is constant, provided that no overlap of different domains takes. place. In order to take this into account we assume the rate of change of the total occupied length (dL.,ldt} to be proportional to (L:,,, -L,), which leads to t = J&,,, 11-
ev(-at)1 ,
where cy will be proportions to the supply of active species. For two-dimensional growth we expect that initially both dimensions will increase linearly with time. Thus the area occupied by a single domain (a) will grow as t2, whence daldt Q:t. Accounting, as before, for overlap of different patches we obtain for the total occupied surface (A): Uldt
= @(A,,,,, -A)
t .
Thus, upon integration, A = A,,,
{l .-. exp(-$3t2)}
,
176
1 Parameters values t = ___ _ T (“C)
0.L.f.
in the
(SW) 1200
370 425
200
Gijzernan
curves in
et al. / Comment
1 and
peak heights
scaled with
nickel
12
!I?
h&
(3 (xc--*)
0.32 0.32 0.10
0.7 I 0.74
0.37 0.42 0.45
3.3 lK7 8.3 x 10-7 8.5 x 10-7
where fl will be proportional to the square of the supply of active species. This Avrami type of equation seems more appropriate to use than a diffusional type of equation in region B of fig. 1, since the carbon concentration at the surface is kept constant and uniform by the continuing supply from the bulk, as suggested by the experimental results [ 11. Also saturation, which is evident in figs. 1 and 2 is automatically accounted for. The drawn lines in figs. 1 and 2 have been fitted with the equation
choosing, as did Mojica and Levenson, values for to, the time at which growth starts, and peak values for the saturation concentration h;. The surface background carbon concentration, h:., was held constant, in the absence of detailed information as to its specific form. The tit is seen to be quite satisfactory for curves at the three different temperatures for which data were presented. The parameters obtained are listed in table 1, as well as the normalised values for the carbon and nickel Auger signals at t = 0 and r = m, where presumably a complete layer of graphite has been formed, as shown in ref. [ 11. As can be seen the values of to, the time at which the growth process starts, as well as the carbon content hz decreases with increasing temperature, indicating a decrease in induction time for the growth process. The final surface carbon concentration, h:, (i.e. carbon plus graphite) increases somewhat with temperature, parallel to a slight decrease in the nickel Auger peaks. Taking 0 a(hz)‘, as the constant surface carbon concentration provides the supply for the growing graphite islands, we expect a plot of log /3/(/z:)* against l/T to yield the activation energy for the process. This is found to be 34 f 1 kcal/mol. The present analysis provides in our opinion an alternative interpretation of the data reported by Mojica and Levenson. O.L.J.
GIJZEMAN,
Van ‘t Hoff Laboratory, University of Utrecht, Padualaan 8, Utrecht, The Netherlands
I:.C. SCHOUTEN
and G.A. BOOTSMA
O.L.J.
Gijzeman
et al. / Comment
References [l] J.F. Mojica and L.L. Levenson, Surface Sci. 59 (1976) 447. [2] J.H. Shelton, H.R. Patil and J.M. Blakely, Surface Sci. 43 (1974) 493. [3] M. Avrami, J. Chem. Phys. 7 (1939) 1103; 8 (1940) 212; 9 (1941) 177.
177
71 (1978) 174-177 Publishing Cornpan)
LETTERS TO THE EDITOR
COMMENT ON “BULK-TO-SURFACE PRECIPITATION AND SURFACE DIFFUSION OF CARBON ON POLYCRYSTALLINE NICKEL” BY J.F. MOJICA AND L.L. LEVENSON Received
29 August
1977; manuscript
received
in final form 3 October
1977
In a recent publication Mojica and Levenson [I] reported on the surface diffusion and bulk-to-surface precipitation of carbon on polycrystalline nickel, using Auger electron spectroscopy as a probe for the surface carbon concentration. They interpreted their results in terms of two processes, the first being the diffusion of carbon to the surface, the second the surface diffusion of C-atoms to form graphite. While we agree with this general description, we feel that the treatment of the actual data is open to criticism. Fig. 1 shows some results obtained by Mojica and Levenson as taken from their paper. The carbon Auger peak (272 eV) increases with time, whereas the nickel peak (65 eV) decreases steadily. The ratio of these two signals at any time is taken by the authors in the analysis of the time dependence of the carbon surface concentration “in order to minimise experimental errors”. We feel that this is an incorrect procedure, if one assumes that the continuous decrease in the nickel signal is actually caused by the growing surface layer of carbon (cf. ref. [2]). Secondly, since in region B of fig. 1 graphite is formed, also the growth of graphite islands could influ-
Fig. 1. Nickel (0) and carbon (m) Auger peak heights in arbitrary 345°C. The nickel signal is shit‘ted downwards by 2 units. 174
units as a function
of time at
. . L;;_;/..0. L.J. Gijzeman et
al. / Comment
175
3
I
*
.
.
-
.
. l2
--:.., 1000
2000
3000
LOO0
iisec)
Fig. 2. Carbon Auger peak heights (arbitrary units) as ti function of time at 370°C (*) and 425°C (m).
ence the kinetics. This possibility is neglected in ref. [I]. In this letter we wish to present an alternative explanation of the experimental results shown in figs. 1 and 2. Firstly, we will use the peak heights as recorded, normalising only to the initial value of the nickel Auger peak. Secondly, we will ascribe the time dependence of the carbon concentration in region B to the growth of graphite islands only. The kinetics of nucleation and growth have been treated extensively by Avrami [3]. A somewhat heuristic derivation of equations valid for linear and two-dimensional growth only can be given as follows. Assuming all nucleation to have occurred at t = 0, the dimension of a single, linear, domain (I) will increase with time according to dljdt is constant, provided that no overlap of different domains takes. place. In order to take this into account we assume the rate of change of the total occupied length (dL.,ldt} to be proportional to (L:,,, -L,), which leads to t = J&,,, 11-
ev(-at)1 ,
where cy will be proportions to the supply of active species. For two-dimensional growth we expect that initially both dimensions will increase linearly with time. Thus the area occupied by a single domain (a) will grow as t2, whence daldt Q:t. Accounting, as before, for overlap of different patches we obtain for the total occupied surface (A): Uldt
= @(A,,,,, -A)
t .
Thus, upon integration, A = A,,,
{l .-. exp(-$3t2)}
,
176
1 Parameters values t = ___ _ T (“C)
0.L.f.
in the
(SW) 1200
370 425
200
Gijzernan
curves in
et al. / Comment
1 and
peak heights
scaled with
nickel
12
!I?
h&
(3 (xc--*)
0.32 0.32 0.10
0.7 I 0.74
0.37 0.42 0.45
3.3 lK7 8.3 x 10-7 8.5 x 10-7
where fl will be proportional to the square of the supply of active species. This Avrami type of equation seems more appropriate to use than a diffusional type of equation in region B of fig. 1, since the carbon concentration at the surface is kept constant and uniform by the continuing supply from the bulk, as suggested by the experimental results [ 11. Also saturation, which is evident in figs. 1 and 2 is automatically accounted for. The drawn lines in figs. 1 and 2 have been fitted with the equation
choosing, as did Mojica and Levenson, values for to, the time at which growth starts, and peak values for the saturation concentration h;. The surface background carbon concentration, h:., was held constant, in the absence of detailed information as to its specific form. The tit is seen to be quite satisfactory for curves at the three different temperatures for which data were presented. The parameters obtained are listed in table 1, as well as the normalised values for the carbon and nickel Auger signals at t = 0 and r = m, where presumably a complete layer of graphite has been formed, as shown in ref. [ 11. As can be seen the values of to, the time at which the growth process starts, as well as the carbon content hz decreases with increasing temperature, indicating a decrease in induction time for the growth process. The final surface carbon concentration, h:, (i.e. carbon plus graphite) increases somewhat with temperature, parallel to a slight decrease in the nickel Auger peaks. Taking 0 a(hz)‘, as the constant surface carbon concentration provides the supply for the growing graphite islands, we expect a plot of log /3/(/z:)* against l/T to yield the activation energy for the process. This is found to be 34 f 1 kcal/mol. The present analysis provides in our opinion an alternative interpretation of the data reported by Mojica and Levenson. O.L.J.
GIJZEMAN,
Van ‘t Hoff Laboratory, University of Utrecht, Padualaan 8, Utrecht, The Netherlands
I:.C. SCHOUTEN
and G.A. BOOTSMA
O.L.J.
Gijzeman
et al. / Comment
References [l] J.F. Mojica and L.L. Levenson, Surface Sci. 59 (1976) 447. [2] J.H. Shelton, H.R. Patil and J.M. Blakely, Surface Sci. 43 (1974) 493. [3] M. Avrami, J. Chem. Phys. 7 (1939) 1103; 8 (1940) 212; 9 (1941) 177.
177