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High-temperature surface faceting
Surface Science North-Holland
Letters
258 ClYYl) L676-L678
Surface Science Letters
High-temperature G. Bilalbegovik
surface faceting
‘,“, F. Ercolessi
a and E. Tosatti
“J’
” International School ,for Adanced Studies. Vu Brim/ 4, l-34014 Tries/e. Itu!\ ’ International Centre for Theoreticul Physics, P.O. Box M6, I-34014 Trievte. Ita!\ Received
22 March
1991; accepted
for publication
22 August
1YYl
We have performed molecular dynamics simulations which illustrate how a vicinal surtucr close to a non-melting tact will undergo high-temperature faceting. Specifically, we demonstrated the phenomenon for the Au(423) vicinal. close to the non-melting (111) face of gold. Interatomic forces are obtained from the many-body “glue” Hamiltonian. Our results show that the near the bulk melting temperature this vicinal becomes unstable and facet9 into the flat Au(l11) surface and tilted surface-melted region.
Faceting, that is the spontaneous decay of a crystal face into portions (facets) of other faces, is a phenomenon which occurs quite commonly for many vicinal surfaces, most notably for metals [ 11. The microscopic mechanisms leading to surface faceting may however be diverse, so long as they produce a dip in the specific surface free energy of a crystal, which should be important enough to generate an unstable region. Here we wish to address the question of what kind of faceting is to be expected on a crystal surface at high temperature, particularly in the neighbourhood of the melting point. We present molecular dynamics (MD) simulation results for the case of gold which demonstrate that a high-temperature faceting mechanism is provided by the onset of surface melting for vicinals of a non-melting face, such as Au(ll1). Faceting is due to the fact that the specific surface free energy f(P>/cos /? is in general not a convex function of tan /3, (where p is the face orientation angle), as it should be for thermodynamic stability of that face [2]. If initially prepared, an unstable surface orientation will undergo phase separation into two (or more) stable facets, very much in the same way a supersaturated fluid separates into stable liquid and vapour regions. The step density I tan p I of the stable facets is determined by the well-known “Herring 0039-6028/Y
l/$03.50 0 1991
Elsevier
Science
Publishers
construction” [2], analogous to the classic Maxwell double-tangent construction for the supersaturated fluid. Usually, faceting is a low-temperature phenomenon, and the dip is generated by the particularly favourable energy of certain special facets. A phenomenon which is instead typical of high temperature is surface melting [?I]. It consists of preferential thermal breakdown of crystalline rigidity with onset of liquid-like mobility and diffusion near the surface. When present, this phenomenon leads eventually to the formation of a stable “quasi-liquid layer”. which coats the crystal surface, and whose thickness may diverge when the melting point T,, is approached from below. Surface melting has been shown to take place on a large variety of well-characterized crystal faces [4]. Generally speaking, surface melting is common for weakly bonded crystals (such as van der Waals crystals), and for the poorly packed faces of any given crystal. On the contrary, the wellpacked surfaces of strongly bounded metals arc more stable and less prone to surface melting, which has been shown not to occur (surface “non-melting”) for Cd(OOO1) [S], Cut 111) [6], Au(ll1) [7], Pb(ll1) [g], and Al(111) [‘,I. Recently, using scanning electron microscopy, studies of the equilibrium crystal shapes for lead in the surface melting temperature region have been
B.V. All rights
reserved
G. Bilalbegod
et d. / High--temperature surface faceting
performed [l&11]. In connection with these results Nozi&res [12] proposed some ideas about the competing free energies of a melted and nonmelted face, which imply a sharp angle between the two. In experiments it was indeed found that the junction between the non-melting Pb(lll) face and the curved, surface-melted part of the crystal becomes sharp at ,w20 K below the bulk melting point. Similar, although Iess detailed, results have long been available for gold and copper [6,71. We observe there that sharp edges on crystals imply high-temperature faceting close to the melting point for a range of vicinal orientations near a non-melting face. Suppose at fi = 0 the flat face is stable against melting. Analogy between the Maxwell double-tangent construction and the Herring construction implies that no uniform surface is stable between p = 0 and a critical angle p = p,. Any vicinal surface in this range must undergo phase separation, that is faceting into two neighbouring stable phases, namely fl = 0 (the flat, solid phase) and /3 = p, (the stable melted phase). In order to study and ilfustrate a case of hightemperature faceting we have performed MD computer simulation for the vicinal surface close to Au(ll1). We used a many-body potential of the “glue” type [ 131.The same method and model Hamiltonian was used in the work of Carnevali et al. [14], who demonstrated microscopically the non-melting of the flat Au(ll1). Fig. la shows particle trajectories at low temperature for the surface configuration chosen, in this particular case a (423) vicinal, with fl G 15.2 o and rec~nstrueted terraces. The MD box, periodically repiicated, contains 1080 particies. Our MD box consists of six steps and six terraces of width 3n/ v%, where a is the lattice parameter. The length of the simulation box along the (11% direction is 2ma. Bringing this surface in thermal equilibrium close ta the bulk melting temperature, produces the result shown in fig. lb. The steps have merged, or collapsed together to form a liquid “drop” whose surface is slanted at an angle p, N 30 o with respect to the (111) direction. Elsewhere, the surface has become a fiat (111). The size of this slanted facet is related to the size of
Fig. 1. Molecular dynamics particle trajectories for the Auu(423) surface, observed along (11%. fa) at T = 0.3?T,. Our MD box cant&s six monoatomic steps and six terraces. lb) about 10 K below the bulk melting point. Four (I@ atomic planes are averlapped in the picture. The trajectories refer to a time span of - 7 ps, after a typical equilibration time of several hundreds of ps. Note the spontaneous evolution (faceting) from the stepped surface into coexisting (111) facet and a surface melted region.
the simulation box. In particular, the facet occupies a fraction tan p/tan p, of the sample (Ill&projected area, as a result of the condition that the average orientation must be fl as imposed by the slab geometry. Our result clearly indicates that Au(423) belongs to a range of orientations which are unstable near T,, and facet into tilted, surface-melted regions and the flat, non-melted surface. It is well known that stepped surfaces are an important subject for a wide ranges of fields, from fundamental statistical mechanics to catalysis. Surface faceting is a process where unstable vicinal orientations spontaneously evoke into hill-and-valley structures. We have described a
G. Bilalbegotk? et al. / High-temperature surface faceting
high-temperature faceting mechanism and have demonstrated it for a vicinal surface close to Au(ll1). Thermal step collapsing observed on Pb(l11) [ 15] is very likely also due to high-temperature faceting. This mechanism should be of relevance to many other vicinals of non-melting surfaces, and to other kinds of experimental studies, such as scanning tunneling microscopy. It suggests an easy way to “sweep” a surface, pro~kfed it is non-melting, clean of all steps, by simply bringing it up close enough (of a few percent) to the melting temperature r,,.
References and L.D. Schmidt, Prog. Ill M. Flytzani-Stephanopoulos Surf. Sci. 9 (1979) 83. 121M. Wortis, in: Chemistry and Physics of Solid Surfaces, Vol. 7, Eds. R. Vanselow and R. Howe (Springer, Berlin, 1988) p. 367. [31 E. Tosatti, in: The Structure of Surfaces II, Eds. J.F. van der Veen and M.A. van Hove (Springer, Berlin, 1988) p. 535.
[41 J.F. van der Veen, B. Pluis and A.W. Denier van der Gon, in: Chemistry and Physics of Solid Surfaces, Vol. 7. Eds. R. Vanselow and R. Howe (Springer, Berlin, 198X) p. 455. and J. Zell, Surf. Sci. 12 (1968) 317. [51 B. Mutaftschiev I61 K.D. Stock, Surf. Sci. 91 (1980) 655. [71 K.D. Stock and B. Grosser. J. Cryst. Growth SO (1980) 485. 181 B. Pluis, A.W. Denier van der Gon, J.W.M. Frenken and J.F. van der Veen, Phys. Rev. Lett. 59 (1987) 2678. [91 A.W. Denier van der Gon, R.J. Smith, J.M. Gay. D.J. O’Connor and J.F. van der Veen, Surf. Sci. 227 (1990) 143. I101 J.C. Heyraud, J.J. MCtois and J.M. Bermond, J. C‘ryst. Growth 98 (1989) 355. K. Faulian and E. Bauer, Surf. Sci. 221 [ill A. Pavlovska, (1989) 233. 1121P. Nozigres, J. Phys. 50 (1989) 2541. and E. Tosatti, Philos Mag. A [131 F. Ercolessi, M. Parrinello, 58 (1988) 213. [141 P. Carnevali, F. Ercolessi and E. Tosatti, Phys. Rev. B 36 (1987) 6701. (151 H.N. Yang, T.M. Lu and G.C. Wang, Phys. Rev. Lett. 62 (1989) 2148.
Letters
258 ClYYl) L676-L678
Surface Science Letters
High-temperature G. Bilalbegovik
surface faceting
‘,“, F. Ercolessi
a and E. Tosatti
“J’
” International School ,for Adanced Studies. Vu Brim/ 4, l-34014 Tries/e. Itu!\ ’ International Centre for Theoreticul Physics, P.O. Box M6, I-34014 Trievte. Ita!\ Received
22 March
1991; accepted
for publication
22 August
1YYl
We have performed molecular dynamics simulations which illustrate how a vicinal surtucr close to a non-melting tact will undergo high-temperature faceting. Specifically, we demonstrated the phenomenon for the Au(423) vicinal. close to the non-melting (111) face of gold. Interatomic forces are obtained from the many-body “glue” Hamiltonian. Our results show that the near the bulk melting temperature this vicinal becomes unstable and facet9 into the flat Au(l11) surface and tilted surface-melted region.
Faceting, that is the spontaneous decay of a crystal face into portions (facets) of other faces, is a phenomenon which occurs quite commonly for many vicinal surfaces, most notably for metals [ 11. The microscopic mechanisms leading to surface faceting may however be diverse, so long as they produce a dip in the specific surface free energy of a crystal, which should be important enough to generate an unstable region. Here we wish to address the question of what kind of faceting is to be expected on a crystal surface at high temperature, particularly in the neighbourhood of the melting point. We present molecular dynamics (MD) simulation results for the case of gold which demonstrate that a high-temperature faceting mechanism is provided by the onset of surface melting for vicinals of a non-melting face, such as Au(ll1). Faceting is due to the fact that the specific surface free energy f(P>/cos /? is in general not a convex function of tan /3, (where p is the face orientation angle), as it should be for thermodynamic stability of that face [2]. If initially prepared, an unstable surface orientation will undergo phase separation into two (or more) stable facets, very much in the same way a supersaturated fluid separates into stable liquid and vapour regions. The step density I tan p I of the stable facets is determined by the well-known “Herring 0039-6028/Y
l/$03.50 0 1991
Elsevier
Science
Publishers
construction” [2], analogous to the classic Maxwell double-tangent construction for the supersaturated fluid. Usually, faceting is a low-temperature phenomenon, and the dip is generated by the particularly favourable energy of certain special facets. A phenomenon which is instead typical of high temperature is surface melting [?I]. It consists of preferential thermal breakdown of crystalline rigidity with onset of liquid-like mobility and diffusion near the surface. When present, this phenomenon leads eventually to the formation of a stable “quasi-liquid layer”. which coats the crystal surface, and whose thickness may diverge when the melting point T,, is approached from below. Surface melting has been shown to take place on a large variety of well-characterized crystal faces [4]. Generally speaking, surface melting is common for weakly bonded crystals (such as van der Waals crystals), and for the poorly packed faces of any given crystal. On the contrary, the wellpacked surfaces of strongly bounded metals arc more stable and less prone to surface melting, which has been shown not to occur (surface “non-melting”) for Cd(OOO1) [S], Cut 111) [6], Au(ll1) [7], Pb(ll1) [g], and Al(111) [‘,I. Recently, using scanning electron microscopy, studies of the equilibrium crystal shapes for lead in the surface melting temperature region have been
B.V. All rights
reserved
G. Bilalbegod
et d. / High--temperature surface faceting
performed [l&11]. In connection with these results Nozi&res [12] proposed some ideas about the competing free energies of a melted and nonmelted face, which imply a sharp angle between the two. In experiments it was indeed found that the junction between the non-melting Pb(lll) face and the curved, surface-melted part of the crystal becomes sharp at ,w20 K below the bulk melting point. Similar, although Iess detailed, results have long been available for gold and copper [6,71. We observe there that sharp edges on crystals imply high-temperature faceting close to the melting point for a range of vicinal orientations near a non-melting face. Suppose at fi = 0 the flat face is stable against melting. Analogy between the Maxwell double-tangent construction and the Herring construction implies that no uniform surface is stable between p = 0 and a critical angle p = p,. Any vicinal surface in this range must undergo phase separation, that is faceting into two neighbouring stable phases, namely fl = 0 (the flat, solid phase) and /3 = p, (the stable melted phase). In order to study and ilfustrate a case of hightemperature faceting we have performed MD computer simulation for the vicinal surface close to Au(ll1). We used a many-body potential of the “glue” type [ 131.The same method and model Hamiltonian was used in the work of Carnevali et al. [14], who demonstrated microscopically the non-melting of the flat Au(ll1). Fig. la shows particle trajectories at low temperature for the surface configuration chosen, in this particular case a (423) vicinal, with fl G 15.2 o and rec~nstrueted terraces. The MD box, periodically repiicated, contains 1080 particies. Our MD box consists of six steps and six terraces of width 3n/ v%, where a is the lattice parameter. The length of the simulation box along the (11% direction is 2ma. Bringing this surface in thermal equilibrium close ta the bulk melting temperature, produces the result shown in fig. lb. The steps have merged, or collapsed together to form a liquid “drop” whose surface is slanted at an angle p, N 30 o with respect to the (111) direction. Elsewhere, the surface has become a fiat (111). The size of this slanted facet is related to the size of
Fig. 1. Molecular dynamics particle trajectories for the Auu(423) surface, observed along (11%. fa) at T = 0.3?T,. Our MD box cant&s six monoatomic steps and six terraces. lb) about 10 K below the bulk melting point. Four (I@ atomic planes are averlapped in the picture. The trajectories refer to a time span of - 7 ps, after a typical equilibration time of several hundreds of ps. Note the spontaneous evolution (faceting) from the stepped surface into coexisting (111) facet and a surface melted region.
the simulation box. In particular, the facet occupies a fraction tan p/tan p, of the sample (Ill&projected area, as a result of the condition that the average orientation must be fl as imposed by the slab geometry. Our result clearly indicates that Au(423) belongs to a range of orientations which are unstable near T,, and facet into tilted, surface-melted regions and the flat, non-melted surface. It is well known that stepped surfaces are an important subject for a wide ranges of fields, from fundamental statistical mechanics to catalysis. Surface faceting is a process where unstable vicinal orientations spontaneously evoke into hill-and-valley structures. We have described a
G. Bilalbegotk? et al. / High-temperature surface faceting
high-temperature faceting mechanism and have demonstrated it for a vicinal surface close to Au(ll1). Thermal step collapsing observed on Pb(l11) [ 15] is very likely also due to high-temperature faceting. This mechanism should be of relevance to many other vicinals of non-melting surfaces, and to other kinds of experimental studies, such as scanning tunneling microscopy. It suggests an easy way to “sweep” a surface, pro~kfed it is non-melting, clean of all steps, by simply bringing it up close enough (of a few percent) to the melting temperature r,,.
References and L.D. Schmidt, Prog. Ill M. Flytzani-Stephanopoulos Surf. Sci. 9 (1979) 83. 121M. Wortis, in: Chemistry and Physics of Solid Surfaces, Vol. 7, Eds. R. Vanselow and R. Howe (Springer, Berlin, 1988) p. 367. [31 E. Tosatti, in: The Structure of Surfaces II, Eds. J.F. van der Veen and M.A. van Hove (Springer, Berlin, 1988) p. 535.
[41 J.F. van der Veen, B. Pluis and A.W. Denier van der Gon, in: Chemistry and Physics of Solid Surfaces, Vol. 7. Eds. R. Vanselow and R. Howe (Springer, Berlin, 198X) p. 455. and J. Zell, Surf. Sci. 12 (1968) 317. [51 B. Mutaftschiev I61 K.D. Stock, Surf. Sci. 91 (1980) 655. [71 K.D. Stock and B. Grosser. J. Cryst. Growth SO (1980) 485. 181 B. Pluis, A.W. Denier van der Gon, J.W.M. Frenken and J.F. van der Veen, Phys. Rev. Lett. 59 (1987) 2678. [91 A.W. Denier van der Gon, R.J. Smith, J.M. Gay. D.J. O’Connor and J.F. van der Veen, Surf. Sci. 227 (1990) 143. I101 J.C. Heyraud, J.J. MCtois and J.M. Bermond, J. C‘ryst. Growth 98 (1989) 355. K. Faulian and E. Bauer, Surf. Sci. 221 [ill A. Pavlovska, (1989) 233. 1121P. Nozigres, J. Phys. 50 (1989) 2541. and E. Tosatti, Philos Mag. A [131 F. Ercolessi, M. Parrinello, 58 (1988) 213. [141 P. Carnevali, F. Ercolessi and E. Tosatti, Phys. Rev. B 36 (1987) 6701. (151 H.N. Yang, T.M. Lu and G.C. Wang, Phys. Rev. Lett. 62 (1989) 2148.