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The equilibrium surface composition of some indium-lead and indium-tin alloys
595
Surface Science 125 (1983) 595-603 North-Holland Publishing Company
THE EQUILIBRIUM SURFACE COMPOSITION INDIUM-LEAD AND INDIUM-TIN ALLOYS R.P. FRANKENTHAL Bell Laboratories, Received
OF SOME
and D.J. SICONOLFI
Murray Hill, New Jersey 07974, USA
19 November
1982
Auger electron spectra have been obtained from the near surface region of six equilibrated, solid, single-phase alloys - four in the In-Pb system and two in the In-Sn system - at temperatures ranging from 2O’C to near the melting point of each. For dilute solutions, the surface is enriched in the solute, the amount increasing with decreasing temperature. As the bulk solute concentration is increased, the relative enrichment in the surface decreases, and at a sufficiently high solute concentration the surface becomes depleted in the solute. These results are consistent with an earlier study of the tin-lead alloy system and with the thermodynamics of non-ideal solutions. Together with the results from the tin-lead system, they represent the first systematic study of the equilibrium surface composition of a series of non-ideal solutions covering several alloy systems.
1. Introduction The equilibrium surface composition of solid binary alloys has been the subject of numerous investigations. Most of the systems that have been studied consist of transition metal alloys that can be treated as either ideal or regular solutions. Few studies exist of surface segregation in non-transition metal alloys, many of which are non-ideal solutions. Recently, we reported the results of a study of the equilibrium surface composition of two tin-lead alloys, one from each end of the phase diagram [l]. From the intensities of the relevant peaks in their Auger electron spectra and assuming that any segregation is limited to the outer monolayer, we obtained the composition of that monolayer. For the Pb-rich alloy, the surface was enriched in tin at temperatures below 170°C but depleted in tin at higher temperatures. For the Sn-rich alloy, the surface was enriched in lead at all temperatures, the quantity increasing to about one monolayer as the temperature decreased to 25’C. Since the alloys exhibit neither ideal nor regular solution behavior, each was treated as a non-ideal solution in terms of the standard and excess free energies of its surface and bulk phases. The excess free energy of the bulk phase was related not only to the chemical binding energy and the strain energy but also to the crystallographic transformation 0039~6028/83/0000-0000/$03.00
0 1983 North-Holland
596
R.P. Frankenthaf,
D.J. Siconolfi / Equilibrium
surface composition
energy, which may be significant when the ahoy consists of metals with different crystallographic structures. We have now extended these studies to two refated alloy systems that exhibit non-ideal solution behavior, namely, indium-lead and indium-tin. Combined with the earlier study of the Sn-Pb alloy system, this represents the first systematic study of the equilibrium surface composition of a set of non-ideal solutions encompassing all the single phase regions of three related alloy systems. Roth alloy systems consist of several phases. In the In-Pb system, lead is soluble in the tetragonal indium phase up to about 13 at%, and indium is soluble in the face-centered cubic lead phase up to about 65 at% at 20°C [2]. In the In-Sn system, tin is soluble in indium up to about 11 at% and indium is soluble in tin up to roughly 7 at% at room temperature [2,3J. In the tin-rich phase, the solubihty of indium decreases with increasing temperature and approaches 0 at% at the melting point of tin (232*C) [3]. Indium has a distorted cubic close packing, being elongated along one of the cube edges, while tin (T > 13 “C) is tetragonal in structure [4], We discuss here the study of equilibrium surface segregation in four single phase In-Pb alloys, PbO.,sInO.,S, PbO,&O.n, Pb,,,,In,,,, and In,,,sPb,.,,,, and in two single phase I&n alloys, In0.g7Sn0,03 and Sn0.981n0,02, at temperatures from 25’C to near the melting point of each.
2. Experimental Single phase binary alloys were prepared from 99.999% indium, 99.9999% tin, and 99.9999% lead in an alumina crucible under an atmosphere of purified argon in an RF-heated furnace. Their compositions, as determined by wet chemical analysis, are given in table 1. Each ingot was cold reduced to half its original thickness, vacuum annealed for one week, cold rolled to 0.8 mm
Table 1 Alloy composition Nominal
Pb~,,&_.~, Pbcuw*no.,, Pbo.slh,, In wxPbo.oo~ In 0.97Sn0.0, Sn0.981n0.0z
and annealing
temperature
In
Pb
Sn
(at%)
(at%)
(at%)
4.56 10.86 49.29 99.83 97.41 2.38
95.44 89.14 50.7 I 0.17 _ _
_
Anneal
_
235 235 140
2.59 91.62
135 135
110
(“C)
R. F. Frankenthal,
D.J. Siconorfi / Equilibrium
surface composition
597
thickness, and vacuum annealed for another week. The annealing temperatures are given in table 1. Examination under an optical microscope at 750 X detected no second phase particles. Prior to introduction into the vacuum system, specimens were degreased. High purity indium, tin, and lead foils were used as standards. The composition of the near surface region was determined by Auger electron spectroscopy (AES). All spectra in the d E. N( E)/d E mode were obtained with a Physical Electronics Industries Thin Film Analyzer system. Normal operating conditions were 5 kV electron gun voltage, 10 PA beam current, and 2 eV modulation amplitude. For sputtering, argon gas was used at a pressure of 7 mPa (5 X 10d5 Torr); the ion beam voltage and emission current were 2 kV and 30 mA, respectively. The residual gas pressure in the vacuum system was less than 100 nPa. Trends were followed on a multiplexer that recorded directly the intensities of the In 404 eV peak, the Sn 430 and 437 eV peaks, the Pb 90/94 eV doublet, and the 0 5 10 eV peak, while a strip chart recorder traced the complete peaks. For quantitative measurements, intensities were obtained from the recorded spectra. Samples were mounted on a heatable probe, so that they could be heated in situ while spectra were being obtained. Chilled water was passed through the probe at all times. This was particularly important for experiments at or near room temperature at which the specimen would otherwise be heated by the ion beam or by the electron beam. The temperature was regulated by a PHI Model 20-028 specimen heater control and was monitored by a thermocouple inside the probe.
3. Results and discussion Each alloy was sputter etched at the temperature of the experiment until no trace of any impurity element was detected. Sputter etching depletes the surface region of the In-Pb alloys of lead and the surface region of the In-Sn alloys of indium [5]. Similar to the Pb-Sn alloy system [l], when sputtering of each alloy is stopped, the surface region relaxes by diffusional processes, and the final steady state represents the equilibrium surface composition at the given temperature. The intensity ratio, Isolute/lsolvent, is plotted as a function of temperature for each alloy in fig. 1. For the PbO,s,In,,,, alloy, indium is considered to be the solute because the alloy has the cy-Pb structure. The spectral peaks measured were the Pb 90/94 eV doublet, the In 404 eV peak and the Sn 430 eV peak; for the In o.WSn0.03 alloy, the Sn 437 eV peak was used in place of the 430 eV peak because of interference with the latter by the indium peaks. Since the Auger electron signal comes from a depth of several atomic layers, the composition of the segregation zone cannot be calculated from the inten-
598
R. P. Frankenthal, D. J. Siconolfi / Equilibrium surface composition T,T 200
100
I
1Ok
25
I
I
“bo.i+“o.ri
0.001’
1.8
I
2.0
I
2.2
I
2.4
1
I
2.6
2.8
I
3.0
_
I
3.2
J 3.4
T-‘, K-‘(x IO31 Fig. 1. Effect of temperature
on the equilibrium
intensity
ratio.
sity ratios without assuming a model for that zone. We calculate the composition of the outermost monolayer using two models: (1) Solute enrichment or depletion exists only in the outermost atomic layer, and the composition of subsequent layers corresponds to the bulk. (2) Solute enrichment or depletion extends over several atomic layers, decaying in an exponential manner to the bulk. The equation that relates the measured intensity ratio to composition for the monolayer model, i.e., for the first model, is [l] I,
I,OCyk,{ X,S [ 1 - exp( -d&I,)]
-Fr= IPC,Ok,{ Xf[ 1 - exp( -d,/X,)]
+ X2” exp( - d”/X,)} + Xp exp( -P/X,)}
’
(1)
T,“C 200
10
1.0
2.0
25
100
2.2
2.4 T-l,
2.6
20
3.0
3.2
3.4
K-‘fX103)
Fig. 2. Effect of temperature on the normalized surface mole fraction ratio. Open points are far monolayer model In = 1); closed points are for exponential decay model with n = 4 (Y = 0.8).
in which X5 and Xb are the mole fractious of components 1 and 2 in the surface and bulk, 1 and 2 being the solvent and solute, respectively, I$‘/Ip is the intensity ratio obtained from the pure metal standards, C” is the molar concentration of the pure metal, k is the backscattering coefficient [6f, d is the atomic diameter, h is the electron escape depth, and d” is the thickness of the monolayer defined by dS= d,X,” + d2X;.
(2)
The terms in X” express the intensity from the surface phase, and the terms in
Xb give the intensity from the bulk phase. With the exception of backscattering, matrix effects are assumed to be minimal, which is a good assumption for the dilute alloys. When solute enrichment or depletion extends over N atomic layers, eq. (I) becomes
600
R. P. Frankenthnl, D.J. Siconolfi / Equilibrium surface composition T,“C
100
150
100
I
25
I
I
II
I
I
I
I
2.2
2.4
2.6
2.6
3.0
I
3.2
I
3.4
T“, K-‘(x 103) Fig. 3. Effect of temperature on the normalized surface mole fraction ratio. Open points are for monolayer model (n = I); closed points are for exponential decay model with n = 4 (Y = 0.8).
in which L = 1 for the surface monolayer, d is the average atomic diameter over the N layers, and the composition of layer N + 1 is that of the bulk alloy. Eq. (3) reduces to eq. (1) for N = 1. When the enrichment or depletion decays in an exponential manner, XL=Xb+(X’-Xb)exp[-(L-
1)/v],
in which v is a constant that determines and, thus, the effective value of N. The intensity ratios for the standards metals side by side on the probe, sputter and obtaining their spectra individually the probe slightly to position each metal ratios were Zgb/ZFn = 0.44, Z~n/Z&;430j were independent of temperature within The normalized surface compositions
(4) how rapidly
the exponential
decays
the two were obtained by mounting etching their surfaces simultaneously, under identical conditions by moving in front of the analyzer. The measured = 1.14, and Z&C,,,,/Zpn = 0.66. They experimental error. of the outer monolayer (L = l),
R. P. Frankenthaf, D.J. Siconolji / Equilibrium surjace composition
601
T, OC
lOOr
2.2
I
,
I
2.4
25
100
150
2.6
2.8
3.0
3.2
3.4
T-‘, K-‘(X 103) Fig. 4. Effect of temperature on the normalized surface mole fraction ratio. Open points are for monolayer model (n = 1); closed points are for exponential decay model with n = 4 (Y = 0.8).
RS/Rb,have been calculated from the monolayer model (eq. (1) or eq. (3) with N = I) and from the exponential decay model using eqs. (3) and (4) with Y = 0.8 and are plotted in figs. 2-4. Here RS is XS~,ute/XS~,vent, and Rb is Xsbol”te/Xsbot”e”t* For v = 0.8, segregation is limited to the first four monolayers, that is, N = 4, the composition of the fifth layer being 0.99Xb. The values of the constants used in the calculations are as follows: Cf, = 0.0637 mol/cm3, c&, = 0.0550 mol/cm3, c& = 0.0616 mol/cm3, d,,, = 0.33 nm [7], dpb = 0.35 nm [7], ds, = 0.32 nm [7], A,, = 0.7 nm [8), A,, = 0.5 nm [9], and As, = 0.8 nm [S]. The values of k,/k, calculated according to ref. [6], are 0.967 for the Pb-rich alloys, 0.968 for Pb0.5,1n0.49r 1.031 for In~.~~*Pb~.~~~, and 1.00 for both In-& alloys. From figs. 2-4, we note the following: (1) For each alloy, the mole fraction ratios in the outer monolayer, as calculated from the two models, differ by only 30-40%. (2) For dilute alloys, the surface is enriched in the solute. (3) For
R. P. Frankenthal,
602
D.J. Siconolfi / Equilibrium
surface composition
the In-Pb alloy system, not only does the relative amount of solute segregation to the surface decrease with increasing bulk solute content (fig. 2), but the surface composition changes from being enriched in indium to being depleted in indium as the bulk concentration of indium increases. For the alloy of intermediate composition, Pbo,ssIno.,,, indium segregates to the surface at temperatures below 205°C but is depleted at the surface at higher temperatures. The same phenomenon was observed for a Pb,,,,Sn,,, alloy [l]. Thus, in the previously studied Sn-Pb alloy system [l] and in the In-Pb and In-Sn alloy systems discussed here, the surface layer is always enriched in the solute when its concentration in the bulk is sufficiently small. Based on the data from the In-Pb alloy system, there is a progression from solute enrichment of the surface at one end of the phase diagram to enrichment of the surface by the other solute at the other end of the phase diagram. This behavior has not been observed in other alloys systems. But most that have been studied consist of transition metals and are either ideal or regular solutions. No systematic study of a set of non-ideal solutions has previously been reported. For any single phase solution, we have [l]
x;
x2”
(y*A2-y1A,)+
>=xpexp 1
(i7;s.s- c-;s*“)- (p*sRT
G;“.b) 3 i
(5)
in which y is the specific surface free energy, A is the molar surface area, and es is the partial molar excess free energy of the indicated phase. When expressed in this manner, the strain energy and the crystallographic transformation energy are included in the @s.b terms. For the In-Pb and In-Sn systems, insufficient thermodynamic data exist to evaluate the terms in eq. (5). However, it should be noted that the results from the Sn-Pb alloy system were consistent with eq. (5), and reasonable values for cl:” and G&7,‘bwere obtained. The results of the present study should be explicable in a similar manner when sufficient thermodynamic data become available. It should be remembered that the crystallograp~c transfo~ation energy may make a significant contribution to the total energy and may account for a major portion of the observed change from surface solute enrichment to surface solute depletion with change in bulk composition and with change in temperature, as was shown for the Sn-Pb alloy system ]I].
4. Conclusions (1) We have obtained Auger electron spectra from the surfaces of four solid, single phase In-Pb alloys and two solid, single phase In-Sn alloys equilibrated at temperatures from 20°C to near the melting point of each and
R.P. Frankenthal,
l3.J. Siconolfi / Equilibrium
surface composition
603
have related the composition of the outer monolayer to the intensities of the spectral peaks. (2) For sufficiently dilute solutions, the surface is enriched in the solute. As the bulk solute concentration is increased, the relative enrichment of the solute in the surface is decreased. At sufficiently high bulk solute concentration, the surface becomes depleted in the solute. (3) These results are consistent with those from an earlier study of the Sn-Pb alloy system [I]. (4) The results must be explained by the thermodynamics of non-ideal solutions, taking into consideration the free energies of chemical binding, crystallographic transformation, and strain. The cryst~lo~ap~c transformation energy, which may be a significant contribution to the total energy, must be included because the two metals that make up each alloy have different structures.
We thank Mr. P.C. Milner for numerous J.E. Bernardini for preparing the alloys.
stimulating
discussions
and Mr.
References [l] R.P. Frankenthal and D.J. Siconolfi, Surface Sci. 119 (1982) 331. [2] R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser and K.K. Kelley, Selected Values of the Thermodynamic Properties of Binary Alloys (American Society for Metals, Metals Park, OH, 1973). [3] T. Heumann and 0. Alpaut, J. Less Common Metals 6 (1964) 108. ]4] R.W.G. Wyckoff, Crystal Structures, 2nd ed., Vol. 1 (~nterscien~e, New York, NY, 1963). [5] R.P. Frankenthai and D.J. Siconolfi, Surface Sci. I.1 I (1981) 317. [6] P.M. Hall and J.M. Morabito, Surface Sci. 83 (1979) 391. [7] L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cornell University Press, Ithaca, NY, 1960) p. 393. [8] D.R. Penn, J. Electron Spectrosc. 9 (1976) 29. [9] C.R. Brundle, J. Vacuum Sci. Technol. 11(1974) 212.
Surface Science 125 (1983) 595-603 North-Holland Publishing Company
THE EQUILIBRIUM SURFACE COMPOSITION INDIUM-LEAD AND INDIUM-TIN ALLOYS R.P. FRANKENTHAL Bell Laboratories, Received
OF SOME
and D.J. SICONOLFI
Murray Hill, New Jersey 07974, USA
19 November
1982
Auger electron spectra have been obtained from the near surface region of six equilibrated, solid, single-phase alloys - four in the In-Pb system and two in the In-Sn system - at temperatures ranging from 2O’C to near the melting point of each. For dilute solutions, the surface is enriched in the solute, the amount increasing with decreasing temperature. As the bulk solute concentration is increased, the relative enrichment in the surface decreases, and at a sufficiently high solute concentration the surface becomes depleted in the solute. These results are consistent with an earlier study of the tin-lead alloy system and with the thermodynamics of non-ideal solutions. Together with the results from the tin-lead system, they represent the first systematic study of the equilibrium surface composition of a series of non-ideal solutions covering several alloy systems.
1. Introduction The equilibrium surface composition of solid binary alloys has been the subject of numerous investigations. Most of the systems that have been studied consist of transition metal alloys that can be treated as either ideal or regular solutions. Few studies exist of surface segregation in non-transition metal alloys, many of which are non-ideal solutions. Recently, we reported the results of a study of the equilibrium surface composition of two tin-lead alloys, one from each end of the phase diagram [l]. From the intensities of the relevant peaks in their Auger electron spectra and assuming that any segregation is limited to the outer monolayer, we obtained the composition of that monolayer. For the Pb-rich alloy, the surface was enriched in tin at temperatures below 170°C but depleted in tin at higher temperatures. For the Sn-rich alloy, the surface was enriched in lead at all temperatures, the quantity increasing to about one monolayer as the temperature decreased to 25’C. Since the alloys exhibit neither ideal nor regular solution behavior, each was treated as a non-ideal solution in terms of the standard and excess free energies of its surface and bulk phases. The excess free energy of the bulk phase was related not only to the chemical binding energy and the strain energy but also to the crystallographic transformation 0039~6028/83/0000-0000/$03.00
0 1983 North-Holland
596
R.P. Frankenthaf,
D.J. Siconolfi / Equilibrium
surface composition
energy, which may be significant when the ahoy consists of metals with different crystallographic structures. We have now extended these studies to two refated alloy systems that exhibit non-ideal solution behavior, namely, indium-lead and indium-tin. Combined with the earlier study of the Sn-Pb alloy system, this represents the first systematic study of the equilibrium surface composition of a set of non-ideal solutions encompassing all the single phase regions of three related alloy systems. Roth alloy systems consist of several phases. In the In-Pb system, lead is soluble in the tetragonal indium phase up to about 13 at%, and indium is soluble in the face-centered cubic lead phase up to about 65 at% at 20°C [2]. In the In-Sn system, tin is soluble in indium up to about 11 at% and indium is soluble in tin up to roughly 7 at% at room temperature [2,3J. In the tin-rich phase, the solubihty of indium decreases with increasing temperature and approaches 0 at% at the melting point of tin (232*C) [3]. Indium has a distorted cubic close packing, being elongated along one of the cube edges, while tin (T > 13 “C) is tetragonal in structure [4], We discuss here the study of equilibrium surface segregation in four single phase In-Pb alloys, PbO.,sInO.,S, PbO,&O.n, Pb,,,,In,,,, and In,,,sPb,.,,,, and in two single phase I&n alloys, In0.g7Sn0,03 and Sn0.981n0,02, at temperatures from 25’C to near the melting point of each.
2. Experimental Single phase binary alloys were prepared from 99.999% indium, 99.9999% tin, and 99.9999% lead in an alumina crucible under an atmosphere of purified argon in an RF-heated furnace. Their compositions, as determined by wet chemical analysis, are given in table 1. Each ingot was cold reduced to half its original thickness, vacuum annealed for one week, cold rolled to 0.8 mm
Table 1 Alloy composition Nominal
Pb~,,&_.~, Pbcuw*no.,, Pbo.slh,, In wxPbo.oo~ In 0.97Sn0.0, Sn0.981n0.0z
and annealing
temperature
In
Pb
Sn
(at%)
(at%)
(at%)
4.56 10.86 49.29 99.83 97.41 2.38
95.44 89.14 50.7 I 0.17 _ _
_
Anneal
_
235 235 140
2.59 91.62
135 135
110
(“C)
R. F. Frankenthal,
D.J. Siconorfi / Equilibrium
surface composition
597
thickness, and vacuum annealed for another week. The annealing temperatures are given in table 1. Examination under an optical microscope at 750 X detected no second phase particles. Prior to introduction into the vacuum system, specimens were degreased. High purity indium, tin, and lead foils were used as standards. The composition of the near surface region was determined by Auger electron spectroscopy (AES). All spectra in the d E. N( E)/d E mode were obtained with a Physical Electronics Industries Thin Film Analyzer system. Normal operating conditions were 5 kV electron gun voltage, 10 PA beam current, and 2 eV modulation amplitude. For sputtering, argon gas was used at a pressure of 7 mPa (5 X 10d5 Torr); the ion beam voltage and emission current were 2 kV and 30 mA, respectively. The residual gas pressure in the vacuum system was less than 100 nPa. Trends were followed on a multiplexer that recorded directly the intensities of the In 404 eV peak, the Sn 430 and 437 eV peaks, the Pb 90/94 eV doublet, and the 0 5 10 eV peak, while a strip chart recorder traced the complete peaks. For quantitative measurements, intensities were obtained from the recorded spectra. Samples were mounted on a heatable probe, so that they could be heated in situ while spectra were being obtained. Chilled water was passed through the probe at all times. This was particularly important for experiments at or near room temperature at which the specimen would otherwise be heated by the ion beam or by the electron beam. The temperature was regulated by a PHI Model 20-028 specimen heater control and was monitored by a thermocouple inside the probe.
3. Results and discussion Each alloy was sputter etched at the temperature of the experiment until no trace of any impurity element was detected. Sputter etching depletes the surface region of the In-Pb alloys of lead and the surface region of the In-Sn alloys of indium [5]. Similar to the Pb-Sn alloy system [l], when sputtering of each alloy is stopped, the surface region relaxes by diffusional processes, and the final steady state represents the equilibrium surface composition at the given temperature. The intensity ratio, Isolute/lsolvent, is plotted as a function of temperature for each alloy in fig. 1. For the PbO,s,In,,,, alloy, indium is considered to be the solute because the alloy has the cy-Pb structure. The spectral peaks measured were the Pb 90/94 eV doublet, the In 404 eV peak and the Sn 430 eV peak; for the In o.WSn0.03 alloy, the Sn 437 eV peak was used in place of the 430 eV peak because of interference with the latter by the indium peaks. Since the Auger electron signal comes from a depth of several atomic layers, the composition of the segregation zone cannot be calculated from the inten-
598
R. P. Frankenthal, D. J. Siconolfi / Equilibrium surface composition T,T 200
100
I
1Ok
25
I
I
“bo.i+“o.ri
0.001’
1.8
I
2.0
I
2.2
I
2.4
1
I
2.6
2.8
I
3.0
_
I
3.2
J 3.4
T-‘, K-‘(x IO31 Fig. 1. Effect of temperature
on the equilibrium
intensity
ratio.
sity ratios without assuming a model for that zone. We calculate the composition of the outermost monolayer using two models: (1) Solute enrichment or depletion exists only in the outermost atomic layer, and the composition of subsequent layers corresponds to the bulk. (2) Solute enrichment or depletion extends over several atomic layers, decaying in an exponential manner to the bulk. The equation that relates the measured intensity ratio to composition for the monolayer model, i.e., for the first model, is [l] I,
I,OCyk,{ X,S [ 1 - exp( -d&I,)]
-Fr= IPC,Ok,{ Xf[ 1 - exp( -d,/X,)]
+ X2” exp( - d”/X,)} + Xp exp( -P/X,)}
’
(1)
T,“C 200
10
1.0
2.0
25
100
2.2
2.4 T-l,
2.6
20
3.0
3.2
3.4
K-‘fX103)
Fig. 2. Effect of temperature on the normalized surface mole fraction ratio. Open points are far monolayer model In = 1); closed points are for exponential decay model with n = 4 (Y = 0.8).
in which X5 and Xb are the mole fractious of components 1 and 2 in the surface and bulk, 1 and 2 being the solvent and solute, respectively, I$‘/Ip is the intensity ratio obtained from the pure metal standards, C” is the molar concentration of the pure metal, k is the backscattering coefficient [6f, d is the atomic diameter, h is the electron escape depth, and d” is the thickness of the monolayer defined by dS= d,X,” + d2X;.
(2)
The terms in X” express the intensity from the surface phase, and the terms in
Xb give the intensity from the bulk phase. With the exception of backscattering, matrix effects are assumed to be minimal, which is a good assumption for the dilute alloys. When solute enrichment or depletion extends over N atomic layers, eq. (I) becomes
600
R. P. Frankenthnl, D.J. Siconolfi / Equilibrium surface composition T,“C
100
150
100
I
25
I
I
II
I
I
I
I
2.2
2.4
2.6
2.6
3.0
I
3.2
I
3.4
T“, K-‘(x 103) Fig. 3. Effect of temperature on the normalized surface mole fraction ratio. Open points are for monolayer model (n = I); closed points are for exponential decay model with n = 4 (Y = 0.8).
in which L = 1 for the surface monolayer, d is the average atomic diameter over the N layers, and the composition of layer N + 1 is that of the bulk alloy. Eq. (3) reduces to eq. (1) for N = 1. When the enrichment or depletion decays in an exponential manner, XL=Xb+(X’-Xb)exp[-(L-
1)/v],
in which v is a constant that determines and, thus, the effective value of N. The intensity ratios for the standards metals side by side on the probe, sputter and obtaining their spectra individually the probe slightly to position each metal ratios were Zgb/ZFn = 0.44, Z~n/Z&;430j were independent of temperature within The normalized surface compositions
(4) how rapidly
the exponential
decays
the two were obtained by mounting etching their surfaces simultaneously, under identical conditions by moving in front of the analyzer. The measured = 1.14, and Z&C,,,,/Zpn = 0.66. They experimental error. of the outer monolayer (L = l),
R. P. Frankenthaf, D.J. Siconolji / Equilibrium surjace composition
601
T, OC
lOOr
2.2
I
,
I
2.4
25
100
150
2.6
2.8
3.0
3.2
3.4
T-‘, K-‘(X 103) Fig. 4. Effect of temperature on the normalized surface mole fraction ratio. Open points are for monolayer model (n = 1); closed points are for exponential decay model with n = 4 (Y = 0.8).
RS/Rb,have been calculated from the monolayer model (eq. (1) or eq. (3) with N = I) and from the exponential decay model using eqs. (3) and (4) with Y = 0.8 and are plotted in figs. 2-4. Here RS is XS~,ute/XS~,vent, and Rb is Xsbol”te/Xsbot”e”t* For v = 0.8, segregation is limited to the first four monolayers, that is, N = 4, the composition of the fifth layer being 0.99Xb. The values of the constants used in the calculations are as follows: Cf, = 0.0637 mol/cm3, c&, = 0.0550 mol/cm3, c& = 0.0616 mol/cm3, d,,, = 0.33 nm [7], dpb = 0.35 nm [7], ds, = 0.32 nm [7], A,, = 0.7 nm [8), A,, = 0.5 nm [9], and As, = 0.8 nm [S]. The values of k,/k, calculated according to ref. [6], are 0.967 for the Pb-rich alloys, 0.968 for Pb0.5,1n0.49r 1.031 for In~.~~*Pb~.~~~, and 1.00 for both In-& alloys. From figs. 2-4, we note the following: (1) For each alloy, the mole fraction ratios in the outer monolayer, as calculated from the two models, differ by only 30-40%. (2) For dilute alloys, the surface is enriched in the solute. (3) For
R. P. Frankenthal,
602
D.J. Siconolfi / Equilibrium
surface composition
the In-Pb alloy system, not only does the relative amount of solute segregation to the surface decrease with increasing bulk solute content (fig. 2), but the surface composition changes from being enriched in indium to being depleted in indium as the bulk concentration of indium increases. For the alloy of intermediate composition, Pbo,ssIno.,,, indium segregates to the surface at temperatures below 205°C but is depleted at the surface at higher temperatures. The same phenomenon was observed for a Pb,,,,Sn,,, alloy [l]. Thus, in the previously studied Sn-Pb alloy system [l] and in the In-Pb and In-Sn alloy systems discussed here, the surface layer is always enriched in the solute when its concentration in the bulk is sufficiently small. Based on the data from the In-Pb alloy system, there is a progression from solute enrichment of the surface at one end of the phase diagram to enrichment of the surface by the other solute at the other end of the phase diagram. This behavior has not been observed in other alloys systems. But most that have been studied consist of transition metals and are either ideal or regular solutions. No systematic study of a set of non-ideal solutions has previously been reported. For any single phase solution, we have [l]
x;
x2”
(y*A2-y1A,)+
>=xpexp 1
(i7;s.s- c-;s*“)- (p*sRT
G;“.b) 3 i
(5)
in which y is the specific surface free energy, A is the molar surface area, and es is the partial molar excess free energy of the indicated phase. When expressed in this manner, the strain energy and the crystallographic transformation energy are included in the @s.b terms. For the In-Pb and In-Sn systems, insufficient thermodynamic data exist to evaluate the terms in eq. (5). However, it should be noted that the results from the Sn-Pb alloy system were consistent with eq. (5), and reasonable values for cl:” and G&7,‘bwere obtained. The results of the present study should be explicable in a similar manner when sufficient thermodynamic data become available. It should be remembered that the crystallograp~c transfo~ation energy may make a significant contribution to the total energy and may account for a major portion of the observed change from surface solute enrichment to surface solute depletion with change in bulk composition and with change in temperature, as was shown for the Sn-Pb alloy system ]I].
4. Conclusions (1) We have obtained Auger electron spectra from the surfaces of four solid, single phase In-Pb alloys and two solid, single phase In-Sn alloys equilibrated at temperatures from 20°C to near the melting point of each and
R.P. Frankenthal,
l3.J. Siconolfi / Equilibrium
surface composition
603
have related the composition of the outer monolayer to the intensities of the spectral peaks. (2) For sufficiently dilute solutions, the surface is enriched in the solute. As the bulk solute concentration is increased, the relative enrichment of the solute in the surface is decreased. At sufficiently high bulk solute concentration, the surface becomes depleted in the solute. (3) These results are consistent with those from an earlier study of the Sn-Pb alloy system [I]. (4) The results must be explained by the thermodynamics of non-ideal solutions, taking into consideration the free energies of chemical binding, crystallographic transformation, and strain. The cryst~lo~ap~c transformation energy, which may be a significant contribution to the total energy, must be included because the two metals that make up each alloy have different structures.
We thank Mr. P.C. Milner for numerous J.E. Bernardini for preparing the alloys.
stimulating
discussions
and Mr.
References [l] R.P. Frankenthal and D.J. Siconolfi, Surface Sci. 119 (1982) 331. [2] R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser and K.K. Kelley, Selected Values of the Thermodynamic Properties of Binary Alloys (American Society for Metals, Metals Park, OH, 1973). [3] T. Heumann and 0. Alpaut, J. Less Common Metals 6 (1964) 108. ]4] R.W.G. Wyckoff, Crystal Structures, 2nd ed., Vol. 1 (~nterscien~e, New York, NY, 1963). [5] R.P. Frankenthai and D.J. Siconolfi, Surface Sci. I.1 I (1981) 317. [6] P.M. Hall and J.M. Morabito, Surface Sci. 83 (1979) 391. [7] L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cornell University Press, Ithaca, NY, 1960) p. 393. [8] D.R. Penn, J. Electron Spectrosc. 9 (1976) 29. [9] C.R. Brundle, J. Vacuum Sci. Technol. 11(1974) 212.