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Segregation of carbon to the (100) surface of Ni3Fe and its effect on oxygen adsorption
Applied Surface Science 31 (1988) 413-419 North-Holland, Amsterdam
413
SEGREGATION OF CARBON TO THE (100) SURFACE AND ITS EFFECT ON OXYGEN ADSORPTION R.A. BOUCARUT
*, H. SAIJO
Department
Science, Cornell University, Ithaca, NY 14853, USA
Received
of Materials
8 September
1987; accepted
OF Ni,Fe
* * and J.M. BLAKELY
for publication
6 December
1987
The equilibrium segregation of carbon to the (100) surface of Ni,Fe shows unusual features. The surface carbon concentration is a maximum in the vicinity of the order-disorder transition temperature of the alloy. The effect of segregating carbon on the initial adsorption of oxygen and oxidation of the alloy surface is also reported.
1. Introduction The segregation of C to the (100) and other surfaces of Fe [1,2] and Ni [3-51 has previously been studied. For dilute interstitial solutions of C in these metals the concentrations of C on the (100) surface vary smoothly over a broad range of temperature and have been described by Langmuir-type models [6]. In this paper we describe some observations on the segregation of carbon to the (100) surface of Ni,Fe and the effect of the carbon overlayer on the initial stages of oxygen adsorption. This work is part of a broader program on overlayer effects on oxidation. Ni,Fe is fee and undergoes an order-disorder transition [7] at - 775 K, The transition is believed to be similar to that observed in Cu,Au [8,9], but it is difficult to detect by X-ray or electron scattering methods because of the similarities in atomic scattering factors of Ni and Fe. The solubility of carbon in Ni-Fe alloys has been measured [lo]; at temperatures > 1000 K the heat of solution of C in Ni,Fe is - 30% greater than in Ni and the solubility a factor of 3-5 less, but solubility data does not seem to be available for temperatures down to the order-disorder transition. As described below, the surface concentration of carbon on Ni,Fe(lOO) in equilibrium with the bulk does not vary monotonically with temperature but shows a maximum in the vicinity of the order-disorder temperature. The * Present address: Goddard Space Flight Center, * * Present address: Department of Photographic Matsugasaki, Sakyo-ku, Kyoto 606, Japan.
Code 717.1, Greenbelt, MD 20771, USA. Technology, Kyoto Institute of Technology,
0169-4332/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
effect of the carbon overlayer on O2 uptake is greatest diminishes both at higher and lower temperatures.
around
500 K and
2. Materials and methods Ni 3Fe crystals of (100) surface orientation ( iO.5’) were cut from melt grown single crystals. The crystals were heated directly by resistive heating using electron beam welded polycrystalline Ni ,Fe rods as contacts; a blanking arrangement as described previously [II] was used to observe LEED patterns and Auger spectra with the crystal at the temperature of interest. The Auger spectra were obtained with a double-pass CMA and the LEED patterns observed on a standard set of 4-grid optics. The sample was cleaned by a combination of argon ion bombardment (5 keV). heating in vacuum, and heating to - 1000 K following oxygen exposure at - 425 K.
3. Results and discussion 3.1. Curhon segregation The variation of surface carbon concentration with temperature was monitored both during heating and cooling to test for reversibility. Only when such reversibility is demonstrated can a meaningful thermodynamic analysis of the data be attempted. Fig. la shows the observed variation with temperature of the magnitude of the carbon Auger peak at 272 eV normalized against the Ni 843 eV peak. During heating the spectra were recorded after each increment of 25 K at an average heating rate of 2 K/min. The cooling data were obtained by holding the sample at 1000 K for a few minutes before cooling to the observation temperature and holding for a time At. Values of At used were 3, 30, and 120 min; as can be seen from fig. 1. there is very little dependence on the holding time, At. except in the vicinity of 750 K and that the cooling and heating data are in good agreement. At temperatures below 600 K kinetic limitations are observed. Surface structure observations were made by monitoring LEED patterns as a function of temperature under conditions similar to those for the data in fig. 1. Below - 800 K a c(2 X 2) was detected while above this temperature the surface was always p(1 x 1). Throughout all of these observations the carbon Auger lineshape was of the carbide form as indicated in fig. 2; no detectable changes occurred in the relative magnitudes of the sub-peaks. The relative surface concentrations of Ni and Fe showed little variation with temperature; the ratio of peak-to-peak heights of the Ni 61 eV and Fe 47 Auger signals is shown in fig. lb. The ratio goes through a maximum near that of the carbon signal but it is difficult to
R.A. Boucarut et al. / Segregation
of carbonto (100) surface of NijFe
415
X heating 01 0 cooling
X
---+;
-C(2x2)
II
IL
600
01
----p(lxll-
IIIIII
I
700
800
2.8
(b)
2.7
1
;
2.6
I?
2.5~
2 z
2.4 i 2.3
2
2.2
.
.
l
1
fi
900
TEMPERATURE
> w
II
1
II 1000
(K)
n n
m
n l
l
2.1
1 600
I
,
700
1
I
800 TEMPERATURE
I
900
I
1000
(K)
Fig. 1. (a) Observed variation of the carbon Auger signal (normalized against the Ni 843 eV peak) with temperature. (x) Data taken during heating at 2 K/mm. The other data points were taken during cooling; the sample was held at 1000 K, cooled to the observation temperature and held for a time of - 3 min (o), 30 min (0) and 120 mm (0). Below - 800 K a c(2 x 2) LEED pattern was observed. (b) Variation in the ratio of Ni and Fe Auger peak heights with temperature. The data shown were obtained during heating. Similar data were obtained using the cooling procedure described in (a).
draw conclusions about the surface composition variation since the formation of the carbon overlayer is expected to strongly influence these Auger peaks. It is possible that the surface carbon preferentially associates with Fe atoms. This would be consistent with the greater free energy of formation of Fe,C and with the similarity of the carbide peak shape to that observed on iron [12]. In the ordered state of the alloy (100) planes are alternately of composition 50%Fee60%Ni and O%Fe-lOO%Ni. There may be a preference for the 50 : 50 type termination in the presence of surface carbon. The occurrence of a peak in the temperature variation of the surface concentration of the segregating element is unusual. The maximum occurs
I 200
I
220
I
240
I
260 Energy
I
280
I
300
I
320
I 340
(eV)
Fig. 2. Derivatwe spectra comparing the observed “carbide” peal\ shape. a. for Ni : l:e(100) with that for Ni. b. and Fe. c. The Fe carbide spectrum ia reproduced from ref. [ 171.
near the Ni,Fe ordering temperature and may he associated with rapid changes in carbon chemical potential as a function of the order parameter. Sharp changes in hydrogen solubility in Ni,Fe near the ordering temperature have been reported [13] with the ordered phase exhibiting higher solubility. If such an effect occurs with C it may be responsible for the reduced surface concentration below the ordering temperature. Further studies with different carbon doping levels would be useful in testing this hypothesis. The variation of surface carbon concentration *’ with temperature in the high temperature (800-1000 K) dilute carbon region is more rapid than that observed previously with pure Ni(lOO) [3] an d 1s in fact closer to that reported for pure Fe(lOO) [l], an observation which supports the idea that carbon associates preferentially with surface Fe. 3.2. Effect of the curhon layer on oxygen udsorption Previous work on Ni-Fe alloy surfaces has shown that adsorbed sulfur can have a dramatic effect both on the kinetics of oxide formation [ 14,151 and on the stability of continuous oxide overlayers [16]. In the present work we have investigated the corresponding effect of carbon on 0 adsorption and oxide =’ Using an analyss similar to that for Ni(lOO) [3] the effective Langmuir segregation energy for for Ni(lOO) the value obtained [3] ~a:, carbon to Ni,Fe(lOO) is found to be - 26 kcal/mol: - 10 kcal/mol and for Fe(100) the value reported [1.2] was - 20 kcal/mol (see also ref. 161).
R.A. Boucarut et al. / Segregation
of carbon to (100) surface of Ni3 Fe
411
po,= I x IO-’ torr
0
I Fig. 3. Decrease
2
3
in surface carbon
4 5 EXPOSURE
0
6 7 (Langmulrs)
8
9
Auger signal with oxygen exposure
IO
II
I2
at several temperatures.
formation on Ni,Fe(lOO). The energetics of the coadsorption of C and 0 on this and other transition metal surfaces seem to differ from that of S and 0 in several ways. The binding energy of C on the surface is of order 7 eV/atom while that of 0 is in the region of 4.5 eV/atom. However the CO molecule, dissociation energy - 11 eV, is bound to the surface by - 1 eV/atom. The energy balance is in fact such that surface C and 0 have in most cases a tendency to combine to form CO which in turn is desorbed at relatively low temperatures [17]. Previous work with S and 0 on Ni,,Fe,(lOO) has shown that S displaces 0 from the surface and that a S overlayer dramatically reduces the sticking coefficient of oxygen. A sulfur overlayer is apparently stable in the presence of the other component. Fig. 3 shows the rate of decrease of surface carbon Auger signal in the presence of oxygen for several temperatures between room temperature and 800 K. The rate of removal of surface carbon by 0, increases significantly above 500 K and is very rapid at 800 K. The corresponding increase in surface oxygen signal with exposure is illustrated in fig. 4. The average rate of oxygen uptake over the first 500 L or so actually goes through a minimum around 500 K. The rate at 310 K is affected very little by the presence of the initial segregated carbon layer while at high temperatures the carbon layer is removed during the first few langmuirs of exposure. The series of reactions responsible for reducing the surface carbon are probably adsorption and dissociation of O,, diffusion of C to the surface, formation of CO and desorption to the gas phase. At high temperatures the desorption rate is so rapid that the surface remains essentially carbon free. For the particular conditions used in these experiments it is likely that at - 500 K the initial rate of replenishing of surface carbon by diffusion from the bulk is comparable to the CO desorption rate so that the corresponding surface carbon and CO
TIME
(set) 2000
1000
I
200
400
I
600
EXPOSURE
000
IO00
12c
(Langmulrs)
Fig. 4. Variation in surface oxygen signal ah a function of OL exposurr. Note that the rate c>f increase in surface oxygen coverage is lower at 500 K than at either 310 or X00 K.
concentrations are significant. As the near-surface region becomes depleted the carbon diffusive flux to the surface will diminish and the surface carbon level correspondingly decrease. The sequence of LEED patterns observed with oxygen exposure was similar to that reported previously for Ni,,, Fe,,>(lOO) [15,19]. A c(2 X 2) structure is the first ordered 0 overlayer observed at low temperature and at 800 K domains of the (111) type epitaxial oxide overlayer develop. The effect of carbon segregation to the surface on oxygen adsorption and subsequent oxide formation appears to be rather small except for initial effects in the intermediate temperature range. As noted already this is due to the efficient removal of carbon as the strongly bound CO molecule. The effects of segregating carbon may be much more important for oxidation at internal boundaries where CO removal rates are likely to be much lower.
Acknowledgements This work was supported by the Department of Energy. Contract No. DE-AC02-79ER10501 and by the NSF through the Materials Science Center at Cornell University.
References [l] H.J. Grabke, [2] H.J. Grabke,
G. Tauber and H. Viefhaus. Scripta Met. 9 (1975) 1181. W. Paulitschke, G. Tauber and H. Viefhaus. Surface Sci. 63 (1977) 377.
R.A. Boucarut et al. / Segregatron of carbon to (100) surface of Ni,Fe [3] [4] [5] [6] [7] [8] [9] [lo] [ll] [12] [13] [14] [15] [16] [17] [18] [19]
419
L.C. Isett and J.M. Blakely, Surface Sci. 47 (1975) 645. L.C. Isett and J.M. Blakely, J. Vacuum Sci. Technol. 12 (1975) 232. M. Eizenberg and J.M. Blakely, Surface Sci. 82 (1979) 228. J.M. Blakely and H.V. Thapliyal, in: Interfacial Segregation, Eds. W.C. Johnson and J.M. Blakely (ASM, Metals Park, OH, 1979). F.C. Nix and H.G. Beyer, Phys. Rev. 58 (1940) 1031. L. Guttman, Progr. Solid State Phys. 3 (1956) 145. J.W. Christian, The Theory of Transformations in Metal and Alloys (Pergamon, New York, 1965). T. Wada, H. Wada, J.F. Elliot and J. Chipman, Met. Trans. 2 (1971) 2199. Yung-Yi Tu and J.M. Blakely, Rev. Sci. Instr. 47 (1976) 12. H.P. Bonzel and H.J. Krebs, Surface Sci. 91 (1980) 48. V.A. Goltsov, P.V. Geld, Y.P. Simakov, M.M. Shteinberg and V.B. Vykhodets, Metals Abstr. 3A (1970) 34. P. Marcus, A. Tessier and J. Oudar, Surface Sci. 129 (1983) 432. R.J. Lad and J.M. Blakely, Surface Sci. 179 (1987) 467. R.J. Lad and J.M. Blakely, Appl. Surface Sci. 27 (1987) 318. F.A. List and J.M. Blakely, Surface Sci. 152 (1985) 463. R.J. McClelland, MS Thesis, Cornell University (1986). S.E. Greco, J.P. Roux and J.M. Blakely, Surface Sci. 120 (1982) 203.
413
SEGREGATION OF CARBON TO THE (100) SURFACE AND ITS EFFECT ON OXYGEN ADSORPTION R.A. BOUCARUT
*, H. SAIJO
Department
Science, Cornell University, Ithaca, NY 14853, USA
Received
of Materials
8 September
1987; accepted
OF Ni,Fe
* * and J.M. BLAKELY
for publication
6 December
1987
The equilibrium segregation of carbon to the (100) surface of Ni,Fe shows unusual features. The surface carbon concentration is a maximum in the vicinity of the order-disorder transition temperature of the alloy. The effect of segregating carbon on the initial adsorption of oxygen and oxidation of the alloy surface is also reported.
1. Introduction The segregation of C to the (100) and other surfaces of Fe [1,2] and Ni [3-51 has previously been studied. For dilute interstitial solutions of C in these metals the concentrations of C on the (100) surface vary smoothly over a broad range of temperature and have been described by Langmuir-type models [6]. In this paper we describe some observations on the segregation of carbon to the (100) surface of Ni,Fe and the effect of the carbon overlayer on the initial stages of oxygen adsorption. This work is part of a broader program on overlayer effects on oxidation. Ni,Fe is fee and undergoes an order-disorder transition [7] at - 775 K, The transition is believed to be similar to that observed in Cu,Au [8,9], but it is difficult to detect by X-ray or electron scattering methods because of the similarities in atomic scattering factors of Ni and Fe. The solubility of carbon in Ni-Fe alloys has been measured [lo]; at temperatures > 1000 K the heat of solution of C in Ni,Fe is - 30% greater than in Ni and the solubility a factor of 3-5 less, but solubility data does not seem to be available for temperatures down to the order-disorder transition. As described below, the surface concentration of carbon on Ni,Fe(lOO) in equilibrium with the bulk does not vary monotonically with temperature but shows a maximum in the vicinity of the order-disorder temperature. The * Present address: Goddard Space Flight Center, * * Present address: Department of Photographic Matsugasaki, Sakyo-ku, Kyoto 606, Japan.
Code 717.1, Greenbelt, MD 20771, USA. Technology, Kyoto Institute of Technology,
0169-4332/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
effect of the carbon overlayer on O2 uptake is greatest diminishes both at higher and lower temperatures.
around
500 K and
2. Materials and methods Ni 3Fe crystals of (100) surface orientation ( iO.5’) were cut from melt grown single crystals. The crystals were heated directly by resistive heating using electron beam welded polycrystalline Ni ,Fe rods as contacts; a blanking arrangement as described previously [II] was used to observe LEED patterns and Auger spectra with the crystal at the temperature of interest. The Auger spectra were obtained with a double-pass CMA and the LEED patterns observed on a standard set of 4-grid optics. The sample was cleaned by a combination of argon ion bombardment (5 keV). heating in vacuum, and heating to - 1000 K following oxygen exposure at - 425 K.
3. Results and discussion 3.1. Curhon segregation The variation of surface carbon concentration with temperature was monitored both during heating and cooling to test for reversibility. Only when such reversibility is demonstrated can a meaningful thermodynamic analysis of the data be attempted. Fig. la shows the observed variation with temperature of the magnitude of the carbon Auger peak at 272 eV normalized against the Ni 843 eV peak. During heating the spectra were recorded after each increment of 25 K at an average heating rate of 2 K/min. The cooling data were obtained by holding the sample at 1000 K for a few minutes before cooling to the observation temperature and holding for a time At. Values of At used were 3, 30, and 120 min; as can be seen from fig. 1. there is very little dependence on the holding time, At. except in the vicinity of 750 K and that the cooling and heating data are in good agreement. At temperatures below 600 K kinetic limitations are observed. Surface structure observations were made by monitoring LEED patterns as a function of temperature under conditions similar to those for the data in fig. 1. Below - 800 K a c(2 X 2) was detected while above this temperature the surface was always p(1 x 1). Throughout all of these observations the carbon Auger lineshape was of the carbide form as indicated in fig. 2; no detectable changes occurred in the relative magnitudes of the sub-peaks. The relative surface concentrations of Ni and Fe showed little variation with temperature; the ratio of peak-to-peak heights of the Ni 61 eV and Fe 47 Auger signals is shown in fig. lb. The ratio goes through a maximum near that of the carbon signal but it is difficult to
R.A. Boucarut et al. / Segregation
of carbonto (100) surface of NijFe
415
X heating 01 0 cooling
X
---+;
-C(2x2)
II
IL
600
01
----p(lxll-
IIIIII
I
700
800
2.8
(b)
2.7
1
;
2.6
I?
2.5~
2 z
2.4 i 2.3
2
2.2
.
.
l
1
fi
900
TEMPERATURE
> w
II
1
II 1000
(K)
n n
m
n l
l
2.1
1 600
I
,
700
1
I
800 TEMPERATURE
I
900
I
1000
(K)
Fig. 1. (a) Observed variation of the carbon Auger signal (normalized against the Ni 843 eV peak) with temperature. (x) Data taken during heating at 2 K/mm. The other data points were taken during cooling; the sample was held at 1000 K, cooled to the observation temperature and held for a time of - 3 min (o), 30 min (0) and 120 mm (0). Below - 800 K a c(2 x 2) LEED pattern was observed. (b) Variation in the ratio of Ni and Fe Auger peak heights with temperature. The data shown were obtained during heating. Similar data were obtained using the cooling procedure described in (a).
draw conclusions about the surface composition variation since the formation of the carbon overlayer is expected to strongly influence these Auger peaks. It is possible that the surface carbon preferentially associates with Fe atoms. This would be consistent with the greater free energy of formation of Fe,C and with the similarity of the carbide peak shape to that observed on iron [12]. In the ordered state of the alloy (100) planes are alternately of composition 50%Fee60%Ni and O%Fe-lOO%Ni. There may be a preference for the 50 : 50 type termination in the presence of surface carbon. The occurrence of a peak in the temperature variation of the surface concentration of the segregating element is unusual. The maximum occurs
I 200
I
220
I
240
I
260 Energy
I
280
I
300
I
320
I 340
(eV)
Fig. 2. Derivatwe spectra comparing the observed “carbide” peal\ shape. a. for Ni : l:e(100) with that for Ni. b. and Fe. c. The Fe carbide spectrum ia reproduced from ref. [ 171.
near the Ni,Fe ordering temperature and may he associated with rapid changes in carbon chemical potential as a function of the order parameter. Sharp changes in hydrogen solubility in Ni,Fe near the ordering temperature have been reported [13] with the ordered phase exhibiting higher solubility. If such an effect occurs with C it may be responsible for the reduced surface concentration below the ordering temperature. Further studies with different carbon doping levels would be useful in testing this hypothesis. The variation of surface carbon concentration *’ with temperature in the high temperature (800-1000 K) dilute carbon region is more rapid than that observed previously with pure Ni(lOO) [3] an d 1s in fact closer to that reported for pure Fe(lOO) [l], an observation which supports the idea that carbon associates preferentially with surface Fe. 3.2. Effect of the curhon layer on oxygen udsorption Previous work on Ni-Fe alloy surfaces has shown that adsorbed sulfur can have a dramatic effect both on the kinetics of oxide formation [ 14,151 and on the stability of continuous oxide overlayers [16]. In the present work we have investigated the corresponding effect of carbon on 0 adsorption and oxide =’ Using an analyss similar to that for Ni(lOO) [3] the effective Langmuir segregation energy for for Ni(lOO) the value obtained [3] ~a:, carbon to Ni,Fe(lOO) is found to be - 26 kcal/mol: - 10 kcal/mol and for Fe(100) the value reported [1.2] was - 20 kcal/mol (see also ref. 161).
R.A. Boucarut et al. / Segregation
of carbon to (100) surface of Ni3 Fe
411
po,= I x IO-’ torr
0
I Fig. 3. Decrease
2
3
in surface carbon
4 5 EXPOSURE
0
6 7 (Langmulrs)
8
9
Auger signal with oxygen exposure
IO
II
I2
at several temperatures.
formation on Ni,Fe(lOO). The energetics of the coadsorption of C and 0 on this and other transition metal surfaces seem to differ from that of S and 0 in several ways. The binding energy of C on the surface is of order 7 eV/atom while that of 0 is in the region of 4.5 eV/atom. However the CO molecule, dissociation energy - 11 eV, is bound to the surface by - 1 eV/atom. The energy balance is in fact such that surface C and 0 have in most cases a tendency to combine to form CO which in turn is desorbed at relatively low temperatures [17]. Previous work with S and 0 on Ni,,Fe,(lOO) has shown that S displaces 0 from the surface and that a S overlayer dramatically reduces the sticking coefficient of oxygen. A sulfur overlayer is apparently stable in the presence of the other component. Fig. 3 shows the rate of decrease of surface carbon Auger signal in the presence of oxygen for several temperatures between room temperature and 800 K. The rate of removal of surface carbon by 0, increases significantly above 500 K and is very rapid at 800 K. The corresponding increase in surface oxygen signal with exposure is illustrated in fig. 4. The average rate of oxygen uptake over the first 500 L or so actually goes through a minimum around 500 K. The rate at 310 K is affected very little by the presence of the initial segregated carbon layer while at high temperatures the carbon layer is removed during the first few langmuirs of exposure. The series of reactions responsible for reducing the surface carbon are probably adsorption and dissociation of O,, diffusion of C to the surface, formation of CO and desorption to the gas phase. At high temperatures the desorption rate is so rapid that the surface remains essentially carbon free. For the particular conditions used in these experiments it is likely that at - 500 K the initial rate of replenishing of surface carbon by diffusion from the bulk is comparable to the CO desorption rate so that the corresponding surface carbon and CO
TIME
(set) 2000
1000
I
200
400
I
600
EXPOSURE
000
IO00
12c
(Langmulrs)
Fig. 4. Variation in surface oxygen signal ah a function of OL exposurr. Note that the rate c>f increase in surface oxygen coverage is lower at 500 K than at either 310 or X00 K.
concentrations are significant. As the near-surface region becomes depleted the carbon diffusive flux to the surface will diminish and the surface carbon level correspondingly decrease. The sequence of LEED patterns observed with oxygen exposure was similar to that reported previously for Ni,,, Fe,,>(lOO) [15,19]. A c(2 X 2) structure is the first ordered 0 overlayer observed at low temperature and at 800 K domains of the (111) type epitaxial oxide overlayer develop. The effect of carbon segregation to the surface on oxygen adsorption and subsequent oxide formation appears to be rather small except for initial effects in the intermediate temperature range. As noted already this is due to the efficient removal of carbon as the strongly bound CO molecule. The effects of segregating carbon may be much more important for oxidation at internal boundaries where CO removal rates are likely to be much lower.
Acknowledgements This work was supported by the Department of Energy. Contract No. DE-AC02-79ER10501 and by the NSF through the Materials Science Center at Cornell University.
References [l] H.J. Grabke, [2] H.J. Grabke,
G. Tauber and H. Viefhaus. Scripta Met. 9 (1975) 1181. W. Paulitschke, G. Tauber and H. Viefhaus. Surface Sci. 63 (1977) 377.
R.A. Boucarut et al. / Segregatron of carbon to (100) surface of Ni,Fe [3] [4] [5] [6] [7] [8] [9] [lo] [ll] [12] [13] [14] [15] [16] [17] [18] [19]
419
L.C. Isett and J.M. Blakely, Surface Sci. 47 (1975) 645. L.C. Isett and J.M. Blakely, J. Vacuum Sci. Technol. 12 (1975) 232. M. Eizenberg and J.M. Blakely, Surface Sci. 82 (1979) 228. J.M. Blakely and H.V. Thapliyal, in: Interfacial Segregation, Eds. W.C. Johnson and J.M. Blakely (ASM, Metals Park, OH, 1979). F.C. Nix and H.G. Beyer, Phys. Rev. 58 (1940) 1031. L. Guttman, Progr. Solid State Phys. 3 (1956) 145. J.W. Christian, The Theory of Transformations in Metal and Alloys (Pergamon, New York, 1965). T. Wada, H. Wada, J.F. Elliot and J. Chipman, Met. Trans. 2 (1971) 2199. Yung-Yi Tu and J.M. Blakely, Rev. Sci. Instr. 47 (1976) 12. H.P. Bonzel and H.J. Krebs, Surface Sci. 91 (1980) 48. V.A. Goltsov, P.V. Geld, Y.P. Simakov, M.M. Shteinberg and V.B. Vykhodets, Metals Abstr. 3A (1970) 34. P. Marcus, A. Tessier and J. Oudar, Surface Sci. 129 (1983) 432. R.J. Lad and J.M. Blakely, Surface Sci. 179 (1987) 467. R.J. Lad and J.M. Blakely, Appl. Surface Sci. 27 (1987) 318. F.A. List and J.M. Blakely, Surface Sci. 152 (1985) 463. R.J. McClelland, MS Thesis, Cornell University (1986). S.E. Greco, J.P. Roux and J.M. Blakely, Surface Sci. 120 (1982) 203.