- Email: [email protected]
Segregation behaviour in PtxNi1−x(110) and (111) surfaces
Solid State Commumcatlons, Prmted m Great Bntam
Vol 79, No 9, pp 759-761, 1991
SEGREGATION
BEHAVIOUR
S Gangopadhyay,
IN Pt,Nl,_,(l
0038-1098/91 %3.00 + 00 Pergamon Press plc
10) AND (111) SURFACES
S Modak and B C Khanra’
Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bldhannagar, Calcutta-700064, India and J C Bertolml Instltut de Recherches sur la Catalyse, 2, Avenue Albert Emstem, 69626 Vllleurbanne Cedex, France (Received 4 May 1991 by C N R Rao) A three layer model m the tight bmdmg scheme has been used to study the segregation behavlour of Pt,Ni,-,(I 10) and (1 1 1) surfaces The role of relaxation has been taken into account through the modlficatlon of the hopping parameter For Pt, 5NI, 5(1 10) surface we find a composition osclllatlon m agreement with the observed experimental findings, I e , NI and Pt atoms enriching the first and second layer respectively For the (1 1 1) onentatlon, on the other hand, the reverse segregation behavlour, namely Pt and NI atoms ennchmg the top two layers respectively, 1s found only for very large relaxation The results are crltlcally analysed and discussed 1 INTRODUCTION Pt-NI ALLOYS are known to exhlblt exceptionally irregular behavlour m their segregation properties [l-8] While the (I 1 1) surface shows composltlon osclllatlon with Pt. NI, Pt atoms enriching the first, second and third layer respectively, the (1 10) surface shows a segregation reversal with NI, Pt, NI atoms enriching the first, second and third layer respectively (see [2] and references therein) Attempts have been made to interpret this behavlour with various models but without total success [l, 9-l 11 A particular model named “Tight bmdmg Ismg model” by Legrand and Tregha [2] seems to interpret the results with some success This model rehes on some drastic modlfications of the pair interaction m the surface layer compared to their values m the bulk For example, for (1 10) surface the authors assumed that the surface pair interaction y = 24, where V, IS the bulk pair interaction Slmllarly for the (1 1 I) and (10 0) surfaces they assumed y = 1 SV, These modlficatlons are due to the broken bonds m the surface The aim of the present commumcatlon IS to present the results of our mvestlgatlons on the segregation behavlour of Pt, 5Nl, 5( 1 10) and (1 1 1) surfaces m which we speaally considered the role of relaxation m the segregation phenomenon We have used three layer model using a tight bmdmg scheme with experimental results
* To whom all correspondence
should be addressed
on relaxation duly incorporated m the calculations The results are m good agreement with expenmental results for the (1 10) surface For the (1 1 1) surface the agreement IS good only for large relaxation m surface layers In Section 2 we briefly discuss the theoretical model In Section 3 we present our results and cntltally discuss them 2 THEORETICAL
MODEL
The model used for calculatmg the segregation properties 1s essentially based on mmlmlsmg the free x) with respect to x,, x2 and energy F(x, ,x2, x3, x7which are the concent;atlons of A component metal m the first, second and third layer respectively m the alloy A,B,_,, x being the bulk concentration Due to computational restrictions we assume that the concentration from the fourth layer onward 1s the same as that of the bulk In the tight bmdmg scheme, Fmay be expressed as [I21 F
=
f i’Ep,(E)dE ,=I -@.
*=I
- TS
*=I
(1)
where ~1and v (= &) are the Lagrange multlphers coming from the constraints that the total number of atoms and electrons m the whole system are conserved p, and EF are the density of states of the Ith layer and the Fermi energy respectively T and S denote the
759
760
Pt,Nl,_,(
1 10) AND (1 1 1) SURFACES
temperature and entropy respectively For any partlcular value of bulk concentration x we have found the composltlon m the first three layers by calculatmg and comparing the free energy F for various values of Y,, x2 and x:3 In calculating the density of states p,(E) from Green’s function we use the Hamlltoman of the form
Vol
79, No
9
first layer 1s nickel enriched, and the second layer IS Pt enriched at an arbitrary temperature 400 K We have noticed however, that the contrlbutlon of the entropy term to the total free energy of the system 1s very small In the absence of the experimental relaxation results for other concentration we could not calculate the precise surface concentration for those concentrations For the (1 1 1) surface we calculate the segregation with both experlmental and theoretical relaxation values [2. IO] With experimental relaxation where 11s the site Index, and E, and I$ are respectively values for (1 I 1) surface the segregation reversal was the site energy and hopping energy between the zth not found In fact the relaxation for (1 1 1) surface IS and thelth site We use the mixed Bethe lattice scheme very small leading to very minor modlficatlon m the to get p, [12] It IS experimentally well known that the hopping parameters For the (I 1 1) surface, for (1 10) surface of f c c systems is an open surface so example, we obtained l’,* = I 02 V,. V& = 1 05 Vh that there IS significant relaxation of top few layers By For Pt,,Ni,,(l 1 1) surface we thus obtained Y, = 0 2, this relaxation the mterlayer spacmgs differ from Y? = 0 8. Y? = 0 5 slgmfymg the same surface comthose m the bulk and hence the hopping mteractlons posltlon oscillation as for (1 10) surface However, between atoms m top layer and the second layer are with higher value of mteractlon terms V,z and Vzx we modified from their bulk values Slmllarly, mtermay find the top layer Pt-ennched as found experactions between atoms m the second and third and imentally Higher values of V,? and K3 would imply between third and fourth layer are also modified We large relaxation m (I I 1) orlentatlon which has experhave incorporated m our calculations these modlfiimentally not yet been found In view of the complexlcations as follows ties of the problem we consider these results quite Sayers [13] has shown that the nearest nelghbour significant What all these results indicate IS that the hopping integrals vary with distance R as surface segregation m both the (1 1 1) and the (1 10) surface of Pt-Ni alloy can be explained by higher V cc eeyR (3) relaxation in surface layers At the bulk mteratomlc spacing &, qRo z 3 for tranIt IS true that an electromc theory of multilayer sition metals so that we have segregation IS a formidable task to formulate the -qR,,ll+A) electronic parameters like the mean energy of the V,oce . (4) component metals, the number of delectrons and their where A 1s the change m the mteratomlc distance due band widths are to be taken accurately to give creto relaxation If there 1s contraction between the dence to the calculated results It IS found that the adjacent layers V increases with respect to the bulk segregdtlon behavlour IS quite sensitive to all these hopping parameter In calculatmg the segregation values Let us see how these parameters affect the properties of the system we take this modification mto segregation behavlour conslderatlon through y, m equation (2) It has been shown by Kerker et af [16] that depending upon the value of 6, the difference m mean 3 RESULTS AND DISCUSSIONS energy of the constituent metals, segregation reversal can be caused m CuNl alloy They observed that for The various parameters required for these calcularge 6 the usual Cu segregation that takes place for all lations are as follows the number of d electrons m Pt bulk composltlons IS modified and Nl segregates at and a NI atom m the alloy were taken to be 9 7 and 9 4 higher bulk Cu concentration Very recently, Modak respectively [14] The Pt and NI band wldt hs are taken and Gangopadhyay [17] used a Hubbard model to as 7 3 and 3 7 eV respectively [15] the mean energy calculate accurately the mean energies of Pt and NI m difference, 6 of Pt 5d and NI 3d IS taken to be 2 3 eV Pt-Ni alloy and thus calculated the modified 6 These [ 151 The calculations are done with the experimental calculations were done to study surface segregation in value of A for the (1 10) surface of Pt [3, lo] For model There dgam, It was found that Pt, gN1O5 (I 10) surface we found that V,? = 1 13 b’b monolayer while the mean energy values of [ 151 lead to Nl segreand V2, = 0 92 Vhr where V,, and V,, are the hopping gation m the surface layer of (1 1 1) surface, the mean parameters for the mteractlons between first and energies calculated by Hubbard scheme lead to Pt second, and between second and third layer atoms segregation in thdt surface This suggests the importrespectively For Pt,,Nl, 5(1 10) surface we thus find ance of the mean energy values x, = 0 05, x2 = 0 95 and x1 = 0 7 slgmfymg that the
Vol
79, No
9
Pt,NI,_,(I
10) AND
Secondly, it has also been checked that the number of d electrons also plays slgmficant role m the segregation behavlour For example, for Pt-Nl (1 1 I) surface m the monolayer model calculation, If n,(Pt) IS very low (e g 8 2 as calculated by Norlander et al [ 151) instead of 9 7 as determmed by Shevchlk et al [14], one gets the surface layer Pt enriched In view of the fact that the segregation behavlour 1s sensltlve to N,,, very accurate values of N,, must be chosen for the calculations Finally, the mterslte hoppmg mteractlon, which creeps m the tight bmdmg scheme, IS usually known from the band width However, that has to be modified m view of surface relaxation rn top few layers In the present calculation we have, thus, taken mto conslderatlon the best values of these electromc parameters available for the system For the (1 1 0) surface we find that the experlmental relaxation values lead to the observed composrtlon reversal m top two layers In the (1 1 1) surface only large relaxation may lead to the experlmental composltlon Besldes reliable values of band width, Nd and 6 an accurate knowledge of surface relaxation m top few layers IS Important m understandmg the segregation behavlour m this complex system In this context. It will also be of enormous Importance to study both theoretlcally and experimentally the alloy composltlon - dependence of the relaxation m this system and slmllar complex systems like Pt-Fe etc This ~111 help us to have a better understanding of the segregation behavlour m alloys Acknowledgements - B C Khanra and J C Bertolml acknowledge receipt of financial assistance from the Indo-French Centre for the promotlon of Advanced Research/(Centre France-Indlen pour la Promotion de la Recherche Avancee) under the ProJect No 106-O 1
761
(1 1 1) SURFACES REFERENCES
4
8 9 10 11
12 13 14 15 16 17
A R Mledema, 2 Metallk 69, 455 (1969) B Legrand, G Tregha & F Ducastelle, Phys Rev B41, 4422 (1990) Y Gauthler, Y Joly, R Baudomg & J Rundgren, Whys Rev B31,6216 (1985), R Baudomg, Y Gauthler, M Lundberg & J Rundgren, J Phys C19, 2825 (1986) Y Gauthler, R Baudomg, Y Joly, J Rundgren, J C Bertolrm & J Massandler, Surf Scz 162, 342 (1985) Y Gauthler, R Baudomg, M Lundberg & J Rundgren, Phys Rev B35,7867 (1987) G Tregha, B Legrand & F Ducastelle, Europhys Lett 7, 575 (1988) J C Bertohm, J Massardler, P Dehchere, B Tardy, B Imehk & Y Jugnet, Tran Mmh Due, L De Temmerman, C Creemers, H Van Hove & A Neyens, Surf Scz 119, 95 (1982) L de Temmerman & J Massardler, Surf Scz 178, 888 (1986) L de Temmerman, C Creemers, H Van Hove & A Neyens, Surf Scz 183, 565 (1987) M Lundberg, Phys Rev B36, 4692 (1987) B Legrand & G Tregha, The Structure of Surfaces II (Edlted by J F Van der Veen & M A Van Hove), p 167, Springer (1987) S MukherJee, J L Moran-Lopez, V Kumar & K H Benneman, Phys Rev B25, 730 (1982) C M Sayers, J Phys C12, 4333 (1979) NJ Shevchlk & D Bloch, J Phys F7, 543 (1977) P Norlander, S Holloway & J K Norskov, Surf Scz 136, 59 (1984) G Kerker, J L Moran-Lopez & K H Bennemann, Phys Rev B15, 638 (1977) S Modak & S Gangopadhyay, Solzd St Commun 78, 429 (1991)
Vol 79, No 9, pp 759-761, 1991
SEGREGATION
BEHAVIOUR
S Gangopadhyay,
IN Pt,Nl,_,(l
0038-1098/91 %3.00 + 00 Pergamon Press plc
10) AND (111) SURFACES
S Modak and B C Khanra’
Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bldhannagar, Calcutta-700064, India and J C Bertolml Instltut de Recherches sur la Catalyse, 2, Avenue Albert Emstem, 69626 Vllleurbanne Cedex, France (Received 4 May 1991 by C N R Rao) A three layer model m the tight bmdmg scheme has been used to study the segregation behavlour of Pt,Ni,-,(I 10) and (1 1 1) surfaces The role of relaxation has been taken into account through the modlficatlon of the hopping parameter For Pt, 5NI, 5(1 10) surface we find a composition osclllatlon m agreement with the observed experimental findings, I e , NI and Pt atoms enriching the first and second layer respectively For the (1 1 1) onentatlon, on the other hand, the reverse segregation behavlour, namely Pt and NI atoms ennchmg the top two layers respectively, 1s found only for very large relaxation The results are crltlcally analysed and discussed 1 INTRODUCTION Pt-NI ALLOYS are known to exhlblt exceptionally irregular behavlour m their segregation properties [l-8] While the (I 1 1) surface shows composltlon osclllatlon with Pt. NI, Pt atoms enriching the first, second and third layer respectively, the (1 10) surface shows a segregation reversal with NI, Pt, NI atoms enriching the first, second and third layer respectively (see [2] and references therein) Attempts have been made to interpret this behavlour with various models but without total success [l, 9-l 11 A particular model named “Tight bmdmg Ismg model” by Legrand and Tregha [2] seems to interpret the results with some success This model rehes on some drastic modlfications of the pair interaction m the surface layer compared to their values m the bulk For example, for (1 10) surface the authors assumed that the surface pair interaction y = 24, where V, IS the bulk pair interaction Slmllarly for the (1 1 I) and (10 0) surfaces they assumed y = 1 SV, These modlficatlons are due to the broken bonds m the surface The aim of the present commumcatlon IS to present the results of our mvestlgatlons on the segregation behavlour of Pt, 5Nl, 5( 1 10) and (1 1 1) surfaces m which we speaally considered the role of relaxation m the segregation phenomenon We have used three layer model using a tight bmdmg scheme with experimental results
* To whom all correspondence
should be addressed
on relaxation duly incorporated m the calculations The results are m good agreement with expenmental results for the (1 10) surface For the (1 1 1) surface the agreement IS good only for large relaxation m surface layers In Section 2 we briefly discuss the theoretical model In Section 3 we present our results and cntltally discuss them 2 THEORETICAL
MODEL
The model used for calculatmg the segregation properties 1s essentially based on mmlmlsmg the free x) with respect to x,, x2 and energy F(x, ,x2, x3, x7which are the concent;atlons of A component metal m the first, second and third layer respectively m the alloy A,B,_,, x being the bulk concentration Due to computational restrictions we assume that the concentration from the fourth layer onward 1s the same as that of the bulk In the tight bmdmg scheme, Fmay be expressed as [I21 F
=
f i’Ep,(E)dE ,=I -@.
*=I
- TS
*=I
(1)
where ~1and v (= &) are the Lagrange multlphers coming from the constraints that the total number of atoms and electrons m the whole system are conserved p, and EF are the density of states of the Ith layer and the Fermi energy respectively T and S denote the
759
760
Pt,Nl,_,(
1 10) AND (1 1 1) SURFACES
temperature and entropy respectively For any partlcular value of bulk concentration x we have found the composltlon m the first three layers by calculatmg and comparing the free energy F for various values of Y,, x2 and x:3 In calculating the density of states p,(E) from Green’s function we use the Hamlltoman of the form
Vol
79, No
9
first layer 1s nickel enriched, and the second layer IS Pt enriched at an arbitrary temperature 400 K We have noticed however, that the contrlbutlon of the entropy term to the total free energy of the system 1s very small In the absence of the experimental relaxation results for other concentration we could not calculate the precise surface concentration for those concentrations For the (1 1 1) surface we calculate the segregation with both experlmental and theoretical relaxation values [2. IO] With experimental relaxation where 11s the site Index, and E, and I$ are respectively values for (1 I 1) surface the segregation reversal was the site energy and hopping energy between the zth not found In fact the relaxation for (1 1 1) surface IS and thelth site We use the mixed Bethe lattice scheme very small leading to very minor modlficatlon m the to get p, [12] It IS experimentally well known that the hopping parameters For the (I 1 1) surface, for (1 10) surface of f c c systems is an open surface so example, we obtained l’,* = I 02 V,. V& = 1 05 Vh that there IS significant relaxation of top few layers By For Pt,,Ni,,(l 1 1) surface we thus obtained Y, = 0 2, this relaxation the mterlayer spacmgs differ from Y? = 0 8. Y? = 0 5 slgmfymg the same surface comthose m the bulk and hence the hopping mteractlons posltlon oscillation as for (1 10) surface However, between atoms m top layer and the second layer are with higher value of mteractlon terms V,z and Vzx we modified from their bulk values Slmllarly, mtermay find the top layer Pt-ennched as found experactions between atoms m the second and third and imentally Higher values of V,? and K3 would imply between third and fourth layer are also modified We large relaxation m (I I 1) orlentatlon which has experhave incorporated m our calculations these modlfiimentally not yet been found In view of the complexlcations as follows ties of the problem we consider these results quite Sayers [13] has shown that the nearest nelghbour significant What all these results indicate IS that the hopping integrals vary with distance R as surface segregation m both the (1 1 1) and the (1 10) surface of Pt-Ni alloy can be explained by higher V cc eeyR (3) relaxation in surface layers At the bulk mteratomlc spacing &, qRo z 3 for tranIt IS true that an electromc theory of multilayer sition metals so that we have segregation IS a formidable task to formulate the -qR,,ll+A) electronic parameters like the mean energy of the V,oce . (4) component metals, the number of delectrons and their where A 1s the change m the mteratomlc distance due band widths are to be taken accurately to give creto relaxation If there 1s contraction between the dence to the calculated results It IS found that the adjacent layers V increases with respect to the bulk segregdtlon behavlour IS quite sensitive to all these hopping parameter In calculatmg the segregation values Let us see how these parameters affect the properties of the system we take this modification mto segregation behavlour conslderatlon through y, m equation (2) It has been shown by Kerker et af [16] that depending upon the value of 6, the difference m mean 3 RESULTS AND DISCUSSIONS energy of the constituent metals, segregation reversal can be caused m CuNl alloy They observed that for The various parameters required for these calcularge 6 the usual Cu segregation that takes place for all lations are as follows the number of d electrons m Pt bulk composltlons IS modified and Nl segregates at and a NI atom m the alloy were taken to be 9 7 and 9 4 higher bulk Cu concentration Very recently, Modak respectively [14] The Pt and NI band wldt hs are taken and Gangopadhyay [17] used a Hubbard model to as 7 3 and 3 7 eV respectively [15] the mean energy calculate accurately the mean energies of Pt and NI m difference, 6 of Pt 5d and NI 3d IS taken to be 2 3 eV Pt-Ni alloy and thus calculated the modified 6 These [ 151 The calculations are done with the experimental calculations were done to study surface segregation in value of A for the (1 10) surface of Pt [3, lo] For model There dgam, It was found that Pt, gN1O5 (I 10) surface we found that V,? = 1 13 b’b monolayer while the mean energy values of [ 151 lead to Nl segreand V2, = 0 92 Vhr where V,, and V,, are the hopping gation m the surface layer of (1 1 1) surface, the mean parameters for the mteractlons between first and energies calculated by Hubbard scheme lead to Pt second, and between second and third layer atoms segregation in thdt surface This suggests the importrespectively For Pt,,Nl, 5(1 10) surface we thus find ance of the mean energy values x, = 0 05, x2 = 0 95 and x1 = 0 7 slgmfymg that the
Vol
79, No
9
Pt,NI,_,(I
10) AND
Secondly, it has also been checked that the number of d electrons also plays slgmficant role m the segregation behavlour For example, for Pt-Nl (1 1 I) surface m the monolayer model calculation, If n,(Pt) IS very low (e g 8 2 as calculated by Norlander et al [ 151) instead of 9 7 as determmed by Shevchlk et al [14], one gets the surface layer Pt enriched In view of the fact that the segregation behavlour 1s sensltlve to N,,, very accurate values of N,, must be chosen for the calculations Finally, the mterslte hoppmg mteractlon, which creeps m the tight bmdmg scheme, IS usually known from the band width However, that has to be modified m view of surface relaxation rn top few layers In the present calculation we have, thus, taken mto conslderatlon the best values of these electromc parameters available for the system For the (1 1 0) surface we find that the experlmental relaxation values lead to the observed composrtlon reversal m top two layers In the (1 1 1) surface only large relaxation may lead to the experlmental composltlon Besldes reliable values of band width, Nd and 6 an accurate knowledge of surface relaxation m top few layers IS Important m understandmg the segregation behavlour m this complex system In this context. It will also be of enormous Importance to study both theoretlcally and experimentally the alloy composltlon - dependence of the relaxation m this system and slmllar complex systems like Pt-Fe etc This ~111 help us to have a better understanding of the segregation behavlour m alloys Acknowledgements - B C Khanra and J C Bertolml acknowledge receipt of financial assistance from the Indo-French Centre for the promotlon of Advanced Research/(Centre France-Indlen pour la Promotion de la Recherche Avancee) under the ProJect No 106-O 1
761
(1 1 1) SURFACES REFERENCES
4
8 9 10 11
12 13 14 15 16 17
A R Mledema, 2 Metallk 69, 455 (1969) B Legrand, G Tregha & F Ducastelle, Phys Rev B41, 4422 (1990) Y Gauthler, Y Joly, R Baudomg & J Rundgren, Whys Rev B31,6216 (1985), R Baudomg, Y Gauthler, M Lundberg & J Rundgren, J Phys C19, 2825 (1986) Y Gauthler, R Baudomg, Y Joly, J Rundgren, J C Bertolrm & J Massandler, Surf Scz 162, 342 (1985) Y Gauthler, R Baudomg, M Lundberg & J Rundgren, Phys Rev B35,7867 (1987) G Tregha, B Legrand & F Ducastelle, Europhys Lett 7, 575 (1988) J C Bertohm, J Massardler, P Dehchere, B Tardy, B Imehk & Y Jugnet, Tran Mmh Due, L De Temmerman, C Creemers, H Van Hove & A Neyens, Surf Scz 119, 95 (1982) L de Temmerman & J Massardler, Surf Scz 178, 888 (1986) L de Temmerman, C Creemers, H Van Hove & A Neyens, Surf Scz 183, 565 (1987) M Lundberg, Phys Rev B36, 4692 (1987) B Legrand & G Tregha, The Structure of Surfaces II (Edlted by J F Van der Veen & M A Van Hove), p 167, Springer (1987) S MukherJee, J L Moran-Lopez, V Kumar & K H Benneman, Phys Rev B25, 730 (1982) C M Sayers, J Phys C12, 4333 (1979) NJ Shevchlk & D Bloch, J Phys F7, 543 (1977) P Norlander, S Holloway & J K Norskov, Surf Scz 136, 59 (1984) G Kerker, J L Moran-Lopez & K H Bennemann, Phys Rev B15, 638 (1977) S Modak & S Gangopadhyay, Solzd St Commun 78, 429 (1991)