- Email: [email protected]
Surface composition of Pt10Ni90(110)
NIUMI B
Nuclear Instruments and Methods in Physics Research B 85 (1994) 424-428 North-Holland
Beam Interactions with Materials & Atoms
Surface composition of Pt IONi,( 110) P. Weigand, institut
B. Jelinek, W. Hofer, P. Varga *
fti Allgemeine
Physik, TU Wwn, Wiedner Hauptstr. S-10,
A-1040 Henna, Austria
Low energy ion scattering spectroscopy results are presented which allow to derive the first and second layer’s composition of the Pt,,Ni,(llO) single crystal. After annealing at 970 K the topmost layer is found to be nearly pure Ni, whereas the second layer shows a strong enrichment in Pt. After bombarding the surface with ions a similar depth profile is preserved with a slight Ni enrichment in the first monolayer. Thermal treatment of the sputtered surface induces site changes at low temperatures between the first and second layer and at high temperatures equilibration between surface and bulk. Only very few theoretical models successfully describe the oscillating segregation profile and the orientation dependent segregating component of the PtNi system in the ~uilibrium state. A thorough thermodynamic description (previously applied in a monolayer appro~mation) will be used here in mul~ayer calculations to study the influence of the different effects on the com~sition profile. Pt and Ni differ ne~igibly in the surface free energies giving way to a competition between an ordering effect and a size effect. Good agreement between measurement and calculation is found,
1. Introduction Detailed information on the surface composition and other surface properties is essential for understanding processes such as heterogeneous catalysis. The chemical composition of an alloy’s surface which can be quite different from its bulk value depends on various parameters, such as the temperature, the chemical imposition of the bulk, the chemical reactions on the surface and last but not least, the structure and orientation of the surface. Due to the orientation dependent behaviour of some systems, the latest research has been devoted especially to single crystal alloys 111. The PtNi system, which is taken here as an example, shows an alternating segregation profile. For Pt,Ni,_,(llO) Ni enrichment in the first layer and Pt enrichment in the second has been reported from quantitative low energy electron diffraction (LEED) measurements [2,3]. In addition, an orientation dependent change in the se~egating wmponent, giving Ni segregation for the (110) surface and Pt segregation for (lOO} and (111) surfaces has been found [4,5]. Only very few calculational methods succeed in predicting this segregation hehaviour [6,7]. One of them is a thorough thermodynamic description. Already in a first calculational approximation using a “monolayer” approach it has been applied successfully to PtNi alloys [7]. In this
* Corresponding author, phone + 43 15880155891, fax + 43 1 564203, e-mail: varga~eapv38.tu~en.ac.at.
paper a “multilayer” approach will be presented to describe the alternating depth profile as well. Furthermore, the multilayer calculations will be used here to discuss the influence of different effects on the composition profile of Pt,,Ni,,(llO).
2. Ex~~rnen~l
results
Ion scattering spectroscopy (ISS) measurements have been performed for different PtNi single crystals (see references in refs. 14,811.Due to its high surface sensitivity (caused by the high neutralization probability of the rare gas ions scattered at the target atoms), ISS spectra contain information of the topmost atomic layer only. In the case of the open (110) surface different scattering geometries allow to derive the second layer’s composition as well. The experiments were done with He+ ions with an energy of 1 keV. Further details on the experimental conditions (as well as on the data evaluation) are given in ref. [9]. At a scattering angle of 120” only a slight variation in the measured Pt concentration is found for different azimuthal angles of incidence, and a higher Pt concentration as compared to the data obtained at a scattering angle of 60”, which in return show a pronounced minimum for scattering along [liZI (see Fig. 11. This behaviour can be explained by the different scattering geometries resulting in different contributions of the second monolayer atoms to the detected signal (the minimum, for instance, is due to a complete shadowing of the second monolayer atoms by those of the first layer). For an-
0168-583X/94/$07.~ 0 1994 - Elsevier Science B.V. All rights reserved SSDI 0168-583X(93)E0491-X
P. Weigandet al. /Nucl. Instr. and Me&. in Phys. Res. B 8.5 (1994) 424-428
s’ B f
10 _ bulk c--q 8 - . <’
‘b.
6 4 2 0’ -20
6 Ic I 0
20
40
60
80
100
120
azimuthal angle
Fig. 1. Measured Pt ~ncentration versus azimuthal angle for Pt,~Ni~(llO) after anneaiing at 970 K, obtained by 1 keV He+ with scattering angles 0 of 60” and 120”.
425
In this general MTCIP theory (modern thermodynamic calculation of interface properties) the interface, which separates two homogeneous bodies (1) and (2), consists of atomic sublayers I = 1, 2,. . . , m. The system contains atoms of kind i = 1, 2,. . . , K. The thermodynamic equilibrium state of the totally open system (consisting of the two bodies and the interface region) is obtained by looking for the minimum in the free enthalpy under auxiliary conditions reflecting the necessary existence of the interface. In addition to the known equilibrium conditions for the chemical potentials of the two bodies (1) and (2), &) =#), the equilibrium conditions for the interface, ~~-fi$i)-yi~f=O
(1=1,2
,,.., m;i=l,Z
,,.., K), (1)
nealing temperatures of 970 K about 1 at.% Pt has been found in the first and 51 at.% Pt in the second layer. After bombarding the Pt,,Ni,,(llO) surface with 500 eV At-+ ions the measured Pt concentration from ISS at 60” scattering angle shows (as well as the wellannealed surface) a strong variation with the azimuthal angle. This indicates that the crystalline structure of the target after ion bombardement is rather preserved, which allows to extract information about the first and second monolayer composition. Though Ni atoms are removed preferentially during the sputtering process, a slight Ni enrichment in the first monolayer is found. The second monolayer of the sputtered surface shows a strong enrichment in Pt. This indicates that the effects of preferential sputtering and segregation of Ni atoms into the first monolayer are superposed. Different cycles of sputtering and annealing at unique temperatures have been performed to study the annealing behaviour of the sputtered surface. The results show that rather low annealing temperatures up to 570 K do not affect the bulk but rather induce site changes between Pt atoms in the first with Ni atoms of the second monolayer. At higher annealing temperatures the sputter and segregation induced Pt enrichment of the second layer starts to decrease. This indicates that the equilibration is determined by the bulk diffusion which sets in at higher annealing temperatures. Therefore thermodynamic equilibrium will be found only for annealing temperatures of at least 970 K.
3. Th~~ti~al
desc~ption
The thermodynamic basis of this multilayer description is a new thermodynamic theory proposed several years ago for any number of surface sublayers and components, first for free surfaces [lo], and then generalized to interfaces (including grain boundaries) [ll].
are obtained, with the chemical potentials ps and the partial molar surface areas 4; for component i in layer I, and the Lagrange multiplier y’ (which is the sublayer contribution to the free enthalpy of the interface). With the chemical potential &’ of the pure component i, the atomic fraction Xi and the expression RTlnX, connected with the ideal entropy of mixing, the usual de~nition of the excess chemical potential & is given by pi=&+RT
In Xi+$,
(2)
where the excess chemical potential accounts for deviations from the ideal mixture behaviour due to real mixture effects. Introducing the notation A’ for the difference of the sublayer 1 and the respective bulk quantity (including as well contributions due to “broken bonds” in case of a free surface), the index (1) denoting the bulk values and the notation qi,j = &/c#$, we obtain the equations of segregation for the MTCIP theory (given here in a more general form as in ref. 1111):
(I= 1, 2,...,
m;i,
j=l,Z
,..., K).
(3)
The following considerations will be restricted to free surfaces (body (2) replaced by vacuum) and binary systems (only two components, Pt and Ni). The composition of layer b is completely described by XL, the atomic fraction of Pt, and that for Ni is given by X& = 1 -XL. The ratio of the ~mponent partial molar surface areas is given by q = ~~/#~i. Since the interface region is inhomogeneous, consisting of m different layers, the chemical potential in layer 1 depends not only on the concentration of the respective layer, but on that of all the others as well. Therefore a nonlinear system of m equations of the form X1= VII. SCATTERING
P. Weigandet al./Nucl. Instr. and Meth. in Phys.Res. B 85 (1994) 424-428
426
Table 1 Experimental and calculated surface compositions for Pt,,Ni,(llO). The surface compositions are given in at.% Pt and refer to the topmost three surface layers 1st layer TKl
[at.% Pt]
970 1070 1070 1120 1120 1200 1200 970 1070 1120 1200
lf2 6+4 5+5 11 54 53 8 4.0 4.6 4.8 5.0
2nd layer [at.% Ptl
3rd layer [at.% Ptl
51+10 52+2 45*10
lo& 10
48 9 0 14 45.1 38.0 35.0 30.9
2
10 8.0 9.0 9.4 9.9
Method ISS LEED [31 IDEAS [15] TEHM-APM TEJIM [41 a EAM 141a EAh4 [17] a MTCIP-ML MTCIP-ML MTCIP-ML MTCIP-ML
[16] a
pT(TY xj) =al)(T)(l a = a a
a Theoretical results.
f(. . . ,Xt-‘,
X’, Xl+‘, . . .) for the layers 1= 1,. . . , m has to be solved. The surface free energy values of Pt and Ni are rather close [7]: with average values extracted from different experimental results yPt = 2.10 J/m2 and -yNi = 1.99 J/m* is obtained for (110) surfaces at 1070 K. These values will cause a slight increase in the Ni concentration on the surface. However, the individual experimental values for the surface free energies vary considerably (see Table 1 of ref. [12]), and comparing the results of previous MTCIP-1A (monolayer approximation) calculations with the experimentally determined surface compositions for the (100) and (111) surfaces (see ref. [S]), one might find that the effect of the surface free energy difference has been overestimated. Therefore this effect will be neglected in the following considerations. A nearest neighbour approximation will be used to describe the quantity A’& An atom in layer 1 of a (110) plane in a fee structure has 12 nearest neighbours, from which 2 will be found in the same layer, 4 in each of the adjacent layers I+ 1 and 1 - 1, and one in each of the layers l+ 2 and I- 2. Therefore the fraction of nearest neighbours of an atom of layer 1 found in layer 1, 1 f 1 and 1 f 2 is given by (Y’= &, (Y’= $ and C? = &, respectively. Thus the quantity A’&, which represents the change in the component i excess chemical potential for layer 1 compared with the bulk value is given by:
Alp; &[
cL~.‘-2(X’-2) +&+*(X’+*)] ++;‘~-i(X~-*)
+cL;“+i(X’+i)]
+ (Y”[/Q’( X’)] - /.Q”‘( X(i)), with the excess chemical potential
&‘(X’)
at composition X’. The different parts of Eq. (4) represent the interactions with the layers l+ 2, I+ 1 and inside the same layer 1, and the bulk reference value (1). A special notation is used to distinguish between the excess chemical potential functions p:(X) for the different layers because in general they may be different due to a different microstructure (e.g. relaxation in the surface layer). A “quasi-regular” description will be used for the excess chemical potential functions:
(4) for layer 1
-xi)2,
(5)
the same as used in the MTCIP-1A calculations [12] for dilute binary solutions. The determination of the parameter a,(T), using the data given in ref. [13], is described there as well. With the same excess chemical potential function (that one of the bulk) for all of the layers, we get Ni enrichment for the first layer and a (damped) oscillating concentration profile, reaching the bulk value within a few layers. The oscillation is due to the ordering tendency found in PtNi alloys, which can be explained by the preference for unlike bonds (~7 < 0, cf. the data given in ref. [13]), allowing for oscillations of the concentration profile (for the (100) and {110) faces more nearest neighbours are found in the adjacent atomic layers than in the actual one, thus increasing the number of unlike bonds in the case of an alternating profile). In addition, the preference for unlike bonds increases the solvent on the surface (Ni in the case of Pt,,Ni,), since the missing contribution of the excess chemical potential due to missing neighbours at the surface is less unfavourable in this case. This effect is most pronounced for (110) with the most nearest neighbours in the adjacent layers. But using just the bulk excess chemical potential function for all the layers does not suffice to correctly describe the segregational behaviour of PtNi alloys, since that way we would obtain Ni enrichment for all orientations. Although more pronounced for {llO], it is still Ni enrichment for {loo] and (ill], which is in contradiction to the experimental results showing Pt enrichment for (100) and (11 l] (see the collected data in ref. [4,8]). Therefore surface relaxation and reconstruction processes have to be accounted for, leading to an excess chemical potential function for the surface different from that of the bulk. There is a size effect due to the larger Pt atoms favouring Pt enrichment on the surface for Ni rich alloys, as it has been shown by an atomistic treatment, including a relaxation process to minimize the strain energy [14]. According to the excess chemical potential in the bulk [13] for the respective dilute limit, solving Pt in Ni is energetically preferable over solving Ni in Pt (&I < &$ < 0). Taking into account that there is a positive quantity included in &i due to the elastic strain (size mismatch) which will be
P. We&and et al. /Nucl.
427
Instr. and Meth. in Phys. Rex B 85 (1994) 424-428
relaxed at the surface, an even smaller value & is to be expected at the surface: &r < &,‘. Thus a value a,(T) different from the bulk one has to be used to describe the excess chemical potential inside the surface layer 1= 1 (e.g. the one proposed in ref. [12]), which will give rise now to a Pt enrichment for the (111) and (100) faces 181,but Ni enrichment will remain for the more open (110) plane. For the (110) surface the relaxation process will influence the second layer as well, which will be accounted for in the calculations using the surface excess chemical potential function to characterize the interactions between layer I = 1 and 1= 2 (further increasing the Pt concentration in the second layer). The numerical results of these multilayer calculations (“MTCIP-ML”) for the (110) surface are given in Table 1.
4. Discussion Surface segregation phenomena have been investigated with different surface analysis techniques, such as ISS (ion scattering spectroscopy), LEED (low energy electron diffraction) or IDEAS (incidence dependent excitation for auger spectroscopy) [15] and others. The main numerical results reporting an oscillating depth profile for Pt,,Ni,,(llO) after annealing at temperatures of 970-1200 K are collected in Table 1 (showing both experimental and theoretical results). General agreement has been found in the literature on the experimental results of PtNi alloys (cf. the summary in ref. [8]): Pt enrichment for (100) and (111) surfaces, and Ni enrichment for (110). An alternating segregation profile (reaching bulk concentration after a few layers) has been found for all orientations [3,4,15]. For the Pt,,Ni,(llO) surface, the alternating segregation profile has been confirmed by 155 measurements (in this special case different scattering geometries allow to derive the second layer’s composition as well). The ISS measurements further indicate that the effects of preferential sputtering and segregation are superposed. This leads to a slight Ni enrichment in the first and a strong Pt enrichment in the second layer. The segregation of the Ni atoms into the first monolayer occurs at rather low annealing temperatures, whereas only after annealing at rather high temperatures the Pt enrichment in the second layer starts to decrease by bulk diffusion indicating the thermodynamic equilibration. In Table 1 various experimental and theoretical results are given for Pt,,Ni,(llO). To help comparing data given at different temperatures, the results of the thermodynamic multilayer description (MTCIP-ML) are given for several temperatures. The general tendency is less surface enrichment and a less pronounced oscillating composition profile with increasing temperature. At the given annealing temperatures for the
experimental results there should be no problem reaching the thermodynamic equilibrium and no influence left from preferential sputtering (since the altered layer already disappeared by diffusion). The quite different results of the theoretical descriptions show, that only few methods can be used successfully for describing the orientation dependent segregation behaviour of PtNi alloys. This is due to the fact, that the generally dominating factor of the difference in the surface free energies is rather small and negligible in this case, thus giving way to a competition between an ordering effect (a preference for unlike bonds allowing for oscillations of the concentration profile and also depleting the solute on the surface if there were no counteracting effect) and a size effect (strongly asymmetric: favouring Pt enrichment on the surface for Ni rich alloys, and little influence in the other case). This delicate balance has to be accounted for in the calculations. In the MTCIP approach these effects are included in a proper description of the excess chemical potential (being different for the bulk and the surface, thus allowing for relaxation effects, and depending on orientation and concentration). Among the few successful calculations (the results of which are included in Table 1) are more refined electronic theories, such as the tight-binding Ising model (TBIM) [14,16] and a Monte Carlo approach using the embedded atom method (EAM) [6,17,18], as well as the MTCIP description. In general, these segregation models correctly describe the experimental resurface composition [at% Pt] 0
10
20
30
40
50
6C
MTCIP-ML
LEED [3]
MTCIP-ML LEED [3]
Fig. 2. The surface composition of the first three layers of Pt,,Ni,(llOI as obtained by the thermodynamic multilayer calculations (MTCIP-ML), in comparison with experimental results (ISS and LEED). Annealing temperatures are 970 K (ISS and MTCIP-ML) and 1070 K (LEED). The LEED data have been taken from ref. [3].
VII. SCATTERING
428
P. Weigand et al. /Nucl.
Instr. and Meth. in Phys. Rex B 85 (1994) 424-428
sults, although the oscillating behaviour is less pronounced in all the calculations, and for the (110) face, for which two or more solutions might be found for EAM and TBIM (ref. [16]), sometimes a metastable solution (in contradiction to experimental results) has been obtained. Including an APM (area-preserving map) technique in the TBIM calculations allows to find all possible solutions [16]. In Fig. 2 the main results of this paper are illustrated, graphically comparing thermodynamic multilayer calculations with experimental 1% results. To confirm our experimental data, LEED results taken from ref. [3] are included. Good agreement is found between the different experimental data, as well as between theoretical and experimental results. Acknowledgements
This work has been supported by the Austrian Fonds zur Forderung der wissenschaftlichen Forschung, Projekt Nr. P8147 and S6204. We would also like to thank L.Z. Mezey for many helpful discussions on thermodynamic problems. References [l] P.A. Dowben and A. Miller (eds.1 Surface segregation phenomena (CRC, Boca Raton, 1990).
[2] Y. Gauthier, R. Baudoing, M. Lundberg and J. Rundgren, Phys. Rev. B 35/15 (1987) 7867. [3] Y. Gauthier, R. Baudoing and J. Jupille, Phys. Rev. B 40 (19891 1500. [4] Y. Gauthier and R. Baudoing, in: ch. 7 of ref. [l], p. 169. [5] P. Weigand, P. Novacek, G. van Husen, T. Neidhart and P. Varga, Surf. Sci 269/270 (1992) 1129. 161 M. Lundberg, Phys. Rev. B 36 (1987) 4692. [7] L.Z. Mezey and W. Hofer, Surf. Interf. Anal. 19 (1992) 618. [S] W. Hofer, Fres. J. Anal. Chem. 346 (1993) 246. [9] P. Weigand, B. Jelinek, W. Hofer and P. Varga, Surf. Sci (1993) 295 (1993) 57. [lo] L.Z. Mezey and J. Giber, Proc. IVCS-ICSS4 (Sept 1980, Cannes, France) vol. I, p. 28. [ll] L.Z. Mezey, Surf. Sci. 162 (1985) 510. [12] L.Z. Mezey and W. Hofer, Surf. Sci. 269/270 (1992) 1135. [13] R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser and K.K. Kelley, Selected Values of Thermodynamic Properties of Binary Alloys (American Society for Metals, Metals Park, 1973). [14] G. Treglia and B. Legrand, Phys. Rev. B 35 (1987) 4338. [15] D. Dufayard, R. Baudoing and Y. Gauthier, Surf. Sci. 233 (1990) 223. [16] B. Legrand, G. Treglia and F. Ducastelle, Phys. Rev. B 41 (1990) 4422. [17] H. Stadler, W. Hofer, M. Schmid and P. Varga, Surf. Sci. 287/288 (19921366. [18] SM. Foiles, Phys. Rev. B 32 (198517685.
Nuclear Instruments and Methods in Physics Research B 85 (1994) 424-428 North-Holland
Beam Interactions with Materials & Atoms
Surface composition of Pt IONi,( 110) P. Weigand, institut
B. Jelinek, W. Hofer, P. Varga *
fti Allgemeine
Physik, TU Wwn, Wiedner Hauptstr. S-10,
A-1040 Henna, Austria
Low energy ion scattering spectroscopy results are presented which allow to derive the first and second layer’s composition of the Pt,,Ni,(llO) single crystal. After annealing at 970 K the topmost layer is found to be nearly pure Ni, whereas the second layer shows a strong enrichment in Pt. After bombarding the surface with ions a similar depth profile is preserved with a slight Ni enrichment in the first monolayer. Thermal treatment of the sputtered surface induces site changes at low temperatures between the first and second layer and at high temperatures equilibration between surface and bulk. Only very few theoretical models successfully describe the oscillating segregation profile and the orientation dependent segregating component of the PtNi system in the ~uilibrium state. A thorough thermodynamic description (previously applied in a monolayer appro~mation) will be used here in mul~ayer calculations to study the influence of the different effects on the com~sition profile. Pt and Ni differ ne~igibly in the surface free energies giving way to a competition between an ordering effect and a size effect. Good agreement between measurement and calculation is found,
1. Introduction Detailed information on the surface composition and other surface properties is essential for understanding processes such as heterogeneous catalysis. The chemical composition of an alloy’s surface which can be quite different from its bulk value depends on various parameters, such as the temperature, the chemical imposition of the bulk, the chemical reactions on the surface and last but not least, the structure and orientation of the surface. Due to the orientation dependent behaviour of some systems, the latest research has been devoted especially to single crystal alloys 111. The PtNi system, which is taken here as an example, shows an alternating segregation profile. For Pt,Ni,_,(llO) Ni enrichment in the first layer and Pt enrichment in the second has been reported from quantitative low energy electron diffraction (LEED) measurements [2,3]. In addition, an orientation dependent change in the se~egating wmponent, giving Ni segregation for the (110) surface and Pt segregation for (lOO} and (111) surfaces has been found [4,5]. Only very few calculational methods succeed in predicting this segregation hehaviour [6,7]. One of them is a thorough thermodynamic description. Already in a first calculational approximation using a “monolayer” approach it has been applied successfully to PtNi alloys [7]. In this
* Corresponding author, phone + 43 15880155891, fax + 43 1 564203, e-mail: varga~eapv38.tu~en.ac.at.
paper a “multilayer” approach will be presented to describe the alternating depth profile as well. Furthermore, the multilayer calculations will be used here to discuss the influence of different effects on the composition profile of Pt,,Ni,,(llO).
2. Ex~~rnen~l
results
Ion scattering spectroscopy (ISS) measurements have been performed for different PtNi single crystals (see references in refs. 14,811.Due to its high surface sensitivity (caused by the high neutralization probability of the rare gas ions scattered at the target atoms), ISS spectra contain information of the topmost atomic layer only. In the case of the open (110) surface different scattering geometries allow to derive the second layer’s composition as well. The experiments were done with He+ ions with an energy of 1 keV. Further details on the experimental conditions (as well as on the data evaluation) are given in ref. [9]. At a scattering angle of 120” only a slight variation in the measured Pt concentration is found for different azimuthal angles of incidence, and a higher Pt concentration as compared to the data obtained at a scattering angle of 60”, which in return show a pronounced minimum for scattering along [liZI (see Fig. 11. This behaviour can be explained by the different scattering geometries resulting in different contributions of the second monolayer atoms to the detected signal (the minimum, for instance, is due to a complete shadowing of the second monolayer atoms by those of the first layer). For an-
0168-583X/94/$07.~ 0 1994 - Elsevier Science B.V. All rights reserved SSDI 0168-583X(93)E0491-X
P. Weigandet al. /Nucl. Instr. and Me&. in Phys. Res. B 8.5 (1994) 424-428
s’ B f
10 _ bulk c--q 8 - . <’
‘b.
6 4 2 0’ -20
6 Ic I 0
20
40
60
80
100
120
azimuthal angle
Fig. 1. Measured Pt ~ncentration versus azimuthal angle for Pt,~Ni~(llO) after anneaiing at 970 K, obtained by 1 keV He+ with scattering angles 0 of 60” and 120”.
425
In this general MTCIP theory (modern thermodynamic calculation of interface properties) the interface, which separates two homogeneous bodies (1) and (2), consists of atomic sublayers I = 1, 2,. . . , m. The system contains atoms of kind i = 1, 2,. . . , K. The thermodynamic equilibrium state of the totally open system (consisting of the two bodies and the interface region) is obtained by looking for the minimum in the free enthalpy under auxiliary conditions reflecting the necessary existence of the interface. In addition to the known equilibrium conditions for the chemical potentials of the two bodies (1) and (2), &) =#), the equilibrium conditions for the interface, ~~-fi$i)-yi~f=O
(1=1,2
,,.., m;i=l,Z
,,.., K), (1)
nealing temperatures of 970 K about 1 at.% Pt has been found in the first and 51 at.% Pt in the second layer. After bombarding the Pt,,Ni,,(llO) surface with 500 eV At-+ ions the measured Pt concentration from ISS at 60” scattering angle shows (as well as the wellannealed surface) a strong variation with the azimuthal angle. This indicates that the crystalline structure of the target after ion bombardement is rather preserved, which allows to extract information about the first and second monolayer composition. Though Ni atoms are removed preferentially during the sputtering process, a slight Ni enrichment in the first monolayer is found. The second monolayer of the sputtered surface shows a strong enrichment in Pt. This indicates that the effects of preferential sputtering and segregation of Ni atoms into the first monolayer are superposed. Different cycles of sputtering and annealing at unique temperatures have been performed to study the annealing behaviour of the sputtered surface. The results show that rather low annealing temperatures up to 570 K do not affect the bulk but rather induce site changes between Pt atoms in the first with Ni atoms of the second monolayer. At higher annealing temperatures the sputter and segregation induced Pt enrichment of the second layer starts to decrease. This indicates that the equilibration is determined by the bulk diffusion which sets in at higher annealing temperatures. Therefore thermodynamic equilibrium will be found only for annealing temperatures of at least 970 K.
3. Th~~ti~al
desc~ption
The thermodynamic basis of this multilayer description is a new thermodynamic theory proposed several years ago for any number of surface sublayers and components, first for free surfaces [lo], and then generalized to interfaces (including grain boundaries) [ll].
are obtained, with the chemical potentials ps and the partial molar surface areas 4; for component i in layer I, and the Lagrange multiplier y’ (which is the sublayer contribution to the free enthalpy of the interface). With the chemical potential &’ of the pure component i, the atomic fraction Xi and the expression RTlnX, connected with the ideal entropy of mixing, the usual de~nition of the excess chemical potential & is given by pi=&+RT
In Xi+$,
(2)
where the excess chemical potential accounts for deviations from the ideal mixture behaviour due to real mixture effects. Introducing the notation A’ for the difference of the sublayer 1 and the respective bulk quantity (including as well contributions due to “broken bonds” in case of a free surface), the index (1) denoting the bulk values and the notation qi,j = &/c#$, we obtain the equations of segregation for the MTCIP theory (given here in a more general form as in ref. 1111):
(I= 1, 2,...,
m;i,
j=l,Z
,..., K).
(3)
The following considerations will be restricted to free surfaces (body (2) replaced by vacuum) and binary systems (only two components, Pt and Ni). The composition of layer b is completely described by XL, the atomic fraction of Pt, and that for Ni is given by X& = 1 -XL. The ratio of the ~mponent partial molar surface areas is given by q = ~~/#~i. Since the interface region is inhomogeneous, consisting of m different layers, the chemical potential in layer 1 depends not only on the concentration of the respective layer, but on that of all the others as well. Therefore a nonlinear system of m equations of the form X1= VII. SCATTERING
P. Weigandet al./Nucl. Instr. and Meth. in Phys.Res. B 85 (1994) 424-428
426
Table 1 Experimental and calculated surface compositions for Pt,,Ni,(llO). The surface compositions are given in at.% Pt and refer to the topmost three surface layers 1st layer TKl
[at.% Pt]
970 1070 1070 1120 1120 1200 1200 970 1070 1120 1200
lf2 6+4 5+5 11 54 53 8 4.0 4.6 4.8 5.0
2nd layer [at.% Ptl
3rd layer [at.% Ptl
51+10 52+2 45*10
lo& 10
48 9 0 14 45.1 38.0 35.0 30.9
2
10 8.0 9.0 9.4 9.9
Method ISS LEED [31 IDEAS [15] TEHM-APM TEJIM [41 a EAM 141a EAh4 [17] a MTCIP-ML MTCIP-ML MTCIP-ML MTCIP-ML
[16] a
pT(TY xj) =al)(T)(l a = a a
a Theoretical results.
f(. . . ,Xt-‘,
X’, Xl+‘, . . .) for the layers 1= 1,. . . , m has to be solved. The surface free energy values of Pt and Ni are rather close [7]: with average values extracted from different experimental results yPt = 2.10 J/m2 and -yNi = 1.99 J/m* is obtained for (110) surfaces at 1070 K. These values will cause a slight increase in the Ni concentration on the surface. However, the individual experimental values for the surface free energies vary considerably (see Table 1 of ref. [12]), and comparing the results of previous MTCIP-1A (monolayer approximation) calculations with the experimentally determined surface compositions for the (100) and (111) surfaces (see ref. [S]), one might find that the effect of the surface free energy difference has been overestimated. Therefore this effect will be neglected in the following considerations. A nearest neighbour approximation will be used to describe the quantity A’& An atom in layer 1 of a (110) plane in a fee structure has 12 nearest neighbours, from which 2 will be found in the same layer, 4 in each of the adjacent layers I+ 1 and 1 - 1, and one in each of the layers l+ 2 and I- 2. Therefore the fraction of nearest neighbours of an atom of layer 1 found in layer 1, 1 f 1 and 1 f 2 is given by (Y’= &, (Y’= $ and C? = &, respectively. Thus the quantity A’&, which represents the change in the component i excess chemical potential for layer 1 compared with the bulk value is given by:
Alp; &[
cL~.‘-2(X’-2) +&+*(X’+*)] ++;‘~-i(X~-*)
+cL;“+i(X’+i)]
+ (Y”[/Q’( X’)] - /.Q”‘( X(i)), with the excess chemical potential
&‘(X’)
at composition X’. The different parts of Eq. (4) represent the interactions with the layers l+ 2, I+ 1 and inside the same layer 1, and the bulk reference value (1). A special notation is used to distinguish between the excess chemical potential functions p:(X) for the different layers because in general they may be different due to a different microstructure (e.g. relaxation in the surface layer). A “quasi-regular” description will be used for the excess chemical potential functions:
(4) for layer 1
-xi)2,
(5)
the same as used in the MTCIP-1A calculations [12] for dilute binary solutions. The determination of the parameter a,(T), using the data given in ref. [13], is described there as well. With the same excess chemical potential function (that one of the bulk) for all of the layers, we get Ni enrichment for the first layer and a (damped) oscillating concentration profile, reaching the bulk value within a few layers. The oscillation is due to the ordering tendency found in PtNi alloys, which can be explained by the preference for unlike bonds (~7 < 0, cf. the data given in ref. [13]), allowing for oscillations of the concentration profile (for the (100) and {110) faces more nearest neighbours are found in the adjacent atomic layers than in the actual one, thus increasing the number of unlike bonds in the case of an alternating profile). In addition, the preference for unlike bonds increases the solvent on the surface (Ni in the case of Pt,,Ni,), since the missing contribution of the excess chemical potential due to missing neighbours at the surface is less unfavourable in this case. This effect is most pronounced for (110) with the most nearest neighbours in the adjacent layers. But using just the bulk excess chemical potential function for all the layers does not suffice to correctly describe the segregational behaviour of PtNi alloys, since that way we would obtain Ni enrichment for all orientations. Although more pronounced for {llO], it is still Ni enrichment for {loo] and (ill], which is in contradiction to the experimental results showing Pt enrichment for (100) and (11 l] (see the collected data in ref. [4,8]). Therefore surface relaxation and reconstruction processes have to be accounted for, leading to an excess chemical potential function for the surface different from that of the bulk. There is a size effect due to the larger Pt atoms favouring Pt enrichment on the surface for Ni rich alloys, as it has been shown by an atomistic treatment, including a relaxation process to minimize the strain energy [14]. According to the excess chemical potential in the bulk [13] for the respective dilute limit, solving Pt in Ni is energetically preferable over solving Ni in Pt (&I < &$ < 0). Taking into account that there is a positive quantity included in &i due to the elastic strain (size mismatch) which will be
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relaxed at the surface, an even smaller value & is to be expected at the surface: &r < &,‘. Thus a value a,(T) different from the bulk one has to be used to describe the excess chemical potential inside the surface layer 1= 1 (e.g. the one proposed in ref. [12]), which will give rise now to a Pt enrichment for the (111) and (100) faces 181,but Ni enrichment will remain for the more open (110) plane. For the (110) surface the relaxation process will influence the second layer as well, which will be accounted for in the calculations using the surface excess chemical potential function to characterize the interactions between layer I = 1 and 1= 2 (further increasing the Pt concentration in the second layer). The numerical results of these multilayer calculations (“MTCIP-ML”) for the (110) surface are given in Table 1.
4. Discussion Surface segregation phenomena have been investigated with different surface analysis techniques, such as ISS (ion scattering spectroscopy), LEED (low energy electron diffraction) or IDEAS (incidence dependent excitation for auger spectroscopy) [15] and others. The main numerical results reporting an oscillating depth profile for Pt,,Ni,,(llO) after annealing at temperatures of 970-1200 K are collected in Table 1 (showing both experimental and theoretical results). General agreement has been found in the literature on the experimental results of PtNi alloys (cf. the summary in ref. [8]): Pt enrichment for (100) and (111) surfaces, and Ni enrichment for (110). An alternating segregation profile (reaching bulk concentration after a few layers) has been found for all orientations [3,4,15]. For the Pt,,Ni,(llO) surface, the alternating segregation profile has been confirmed by 155 measurements (in this special case different scattering geometries allow to derive the second layer’s composition as well). The ISS measurements further indicate that the effects of preferential sputtering and segregation are superposed. This leads to a slight Ni enrichment in the first and a strong Pt enrichment in the second layer. The segregation of the Ni atoms into the first monolayer occurs at rather low annealing temperatures, whereas only after annealing at rather high temperatures the Pt enrichment in the second layer starts to decrease by bulk diffusion indicating the thermodynamic equilibration. In Table 1 various experimental and theoretical results are given for Pt,,Ni,(llO). To help comparing data given at different temperatures, the results of the thermodynamic multilayer description (MTCIP-ML) are given for several temperatures. The general tendency is less surface enrichment and a less pronounced oscillating composition profile with increasing temperature. At the given annealing temperatures for the
experimental results there should be no problem reaching the thermodynamic equilibrium and no influence left from preferential sputtering (since the altered layer already disappeared by diffusion). The quite different results of the theoretical descriptions show, that only few methods can be used successfully for describing the orientation dependent segregation behaviour of PtNi alloys. This is due to the fact, that the generally dominating factor of the difference in the surface free energies is rather small and negligible in this case, thus giving way to a competition between an ordering effect (a preference for unlike bonds allowing for oscillations of the concentration profile and also depleting the solute on the surface if there were no counteracting effect) and a size effect (strongly asymmetric: favouring Pt enrichment on the surface for Ni rich alloys, and little influence in the other case). This delicate balance has to be accounted for in the calculations. In the MTCIP approach these effects are included in a proper description of the excess chemical potential (being different for the bulk and the surface, thus allowing for relaxation effects, and depending on orientation and concentration). Among the few successful calculations (the results of which are included in Table 1) are more refined electronic theories, such as the tight-binding Ising model (TBIM) [14,16] and a Monte Carlo approach using the embedded atom method (EAM) [6,17,18], as well as the MTCIP description. In general, these segregation models correctly describe the experimental resurface composition [at% Pt] 0
10
20
30
40
50
6C
MTCIP-ML
LEED [3]
MTCIP-ML LEED [3]
Fig. 2. The surface composition of the first three layers of Pt,,Ni,(llOI as obtained by the thermodynamic multilayer calculations (MTCIP-ML), in comparison with experimental results (ISS and LEED). Annealing temperatures are 970 K (ISS and MTCIP-ML) and 1070 K (LEED). The LEED data have been taken from ref. [3].
VII. SCATTERING
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sults, although the oscillating behaviour is less pronounced in all the calculations, and for the (110) face, for which two or more solutions might be found for EAM and TBIM (ref. [16]), sometimes a metastable solution (in contradiction to experimental results) has been obtained. Including an APM (area-preserving map) technique in the TBIM calculations allows to find all possible solutions [16]. In Fig. 2 the main results of this paper are illustrated, graphically comparing thermodynamic multilayer calculations with experimental 1% results. To confirm our experimental data, LEED results taken from ref. [3] are included. Good agreement is found between the different experimental data, as well as between theoretical and experimental results. Acknowledgements
This work has been supported by the Austrian Fonds zur Forderung der wissenschaftlichen Forschung, Projekt Nr. P8147 and S6204. We would also like to thank L.Z. Mezey for many helpful discussions on thermodynamic problems. References [l] P.A. Dowben and A. Miller (eds.1 Surface segregation phenomena (CRC, Boca Raton, 1990).
[2] Y. Gauthier, R. Baudoing, M. Lundberg and J. Rundgren, Phys. Rev. B 35/15 (1987) 7867. [3] Y. Gauthier, R. Baudoing and J. Jupille, Phys. Rev. B 40 (19891 1500. [4] Y. Gauthier and R. Baudoing, in: ch. 7 of ref. [l], p. 169. [5] P. Weigand, P. Novacek, G. van Husen, T. Neidhart and P. Varga, Surf. Sci 269/270 (1992) 1129. 161 M. Lundberg, Phys. Rev. B 36 (1987) 4692. [7] L.Z. Mezey and W. Hofer, Surf. Interf. Anal. 19 (1992) 618. [S] W. Hofer, Fres. J. Anal. Chem. 346 (1993) 246. [9] P. Weigand, B. Jelinek, W. Hofer and P. Varga, Surf. Sci (1993) 295 (1993) 57. [lo] L.Z. Mezey and J. Giber, Proc. IVCS-ICSS4 (Sept 1980, Cannes, France) vol. I, p. 28. [ll] L.Z. Mezey, Surf. Sci. 162 (1985) 510. [12] L.Z. Mezey and W. Hofer, Surf. Sci. 269/270 (1992) 1135. [13] R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser and K.K. Kelley, Selected Values of Thermodynamic Properties of Binary Alloys (American Society for Metals, Metals Park, 1973). [14] G. Treglia and B. Legrand, Phys. Rev. B 35 (1987) 4338. [15] D. Dufayard, R. Baudoing and Y. Gauthier, Surf. Sci. 233 (1990) 223. [16] B. Legrand, G. Treglia and F. Ducastelle, Phys. Rev. B 41 (1990) 4422. [17] H. Stadler, W. Hofer, M. Schmid and P. Varga, Surf. Sci. 287/288 (19921366. [18] SM. Foiles, Phys. Rev. B 32 (198517685.