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Structural and dynamical properties of van der Waals clusters with impurities
CHEMICALPHYSICS LETTERS
Volume 158, number 6
23 June 1989
STRUCTURAL AND DYNAMICAL PROPERTIES OF VAN DER WAALS CLUSTERS WITH IMPURITIES I.L. GARZON
’ , X.P. LONG, R. KAWAI and J.H. WEARE
Department of Chemistry. B-040, University of CaliSornia, San &ego, La Joiia. CA 92093, USA Received 22 June 1988; in final form 10 April 1989
Mixed clusters of Lennard-Jones atoms have been studied using molecular dynamic simulations. For sufficiently high impurityhost interaction energy, the structure is significantlydistorted from those found for pure clusters, and the three-dimensional solidliquid-like transition identified in pure system simulations is absent. Instead, at very low temperatures, structures may be characterxed as having two-dimensional solid-like salvation shells formed by the host atoms surrounding the impurity. When these solvatinn shells are incomplete, well-defined two-dimensional solid-liquid transitions corresponding to the appearance of disorder in the solvatinn shells (two-dimensional melting) are observed as the temperature is increased. Studies ofA,,R,,-type clusters are also reported. For the parameters studied, a clear segregation of species within the cluster is observed.
1. Introduction Recently there has been considerable interest in the physics and chemistry of clusters [ 11. One area of special emphasis in theoretical research is the study of the structure and dynamics of pure clusters bound by van der Waals interactions. For these systems the forces between atoms are well described by simple two-body interactions using for example the LennardJones (LJ) potential. Three-body contributions to the many-body potential appear to bc unimportant for most calculations [2]. The simulation of these systems has led to the observation that some systems with particularly stable structures (e.g. the t3-atom icosahedral structure) display an abrupt change in dynamical behavior as a function of temperature (average kinetic energy per internal degree of freedom) in a constant energy simulation [ 31. This transition has received a great deal of attention because of its possible relation to the melting transition in macroscopic systems. While the theoretical evidence for such a transition in some pure clusters is well established, experimental vali’ Permanent address: lnstituto de Fisica, Universidad Autonoma de Mexico, Apartado nada, Baja California, Mexico.
National Postal 2681, 22800 Ense-
0 009-26 14/89/s 03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division )
dation of these results is difficult because of the weak interaction of radiation with the interspecies vibrational modes of the van der Waals systems modeled theoretically. Recently, in an effort to provide experimental information about van der Waals clusters, Stoles and coworkers [4] and others [ 5,6] have initiated experimental studies of similarly bound systems with photoactive impurities. In these experiments, the shifts and widths of the impurity vibrational levels arc intcrpretcd in terms of the host-impurity interactions and the dynamical state of the clusters [ 571. However, while the bonding in these impure systems is of similar character to the pure clusters [ 31, the differences in bond strengths between host-impurity and host-host interactions is usually substantial. This implies that there may be significant differences in the structures and dynamics of the pure and impure systems [ 71. The objective of this article is to describe some of our efforts to address these questions by direct simulation of mixed cluster systems. Similar calculations have recently been reported by Shelley et al. [ 81. The systems consisted of n atoms A and m atoms B interacting through LJ potentials with parameters a,, eA and c8, cB respectively. The A-B interaction is also modeled by a LJ potential with parameters B.V.
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Volume 158,number 6
CHEMICAL PHYSICS LETTERS
given by u,~= 1 (o,+ 0~8) and tAB. For systems with only one B atom, results are given for various values oEthe ratio tR= tAB/tA and uK=~~B/~~ For systems with more than one B atom, fAB= (~,,t~)“’ and CR= tB/Ca. Starting from an initial condition, the equations of motion were integrated with a Verlet algorithm [91 with a time step of 0.01 r, where I= (M,a~/s,)“” is a number characteristic of the period of vibration of a Lennard-Jones diatomic with parameters ~7and t. 7 therefore scales approximately with the relaxation times in the pure host system. Energy was added to or removed from the system (temperature raised or lowered) by scaling the velocities [ 10 1. The cluster temperature was defined in the usual way as proportional to the mean kinetic energy divided by the number of internal degrees of freedom. It is given in reduced units of tA/kB, where kB is the Boltzmann constant.
2. Low-temperature
structures
23 June 1989
is strongly dependent on the oR and the cR value. Results are summarized in table 1. For ~~~0.4 the R atom is always inside the host cluster, independently of the tR values used in the simulations. In this case the A atoms from a slightly distorted icosahedron with the B atom interstitially packed inside. When C~ = 1.O and Ed= 1.O (pure system) our simulations always place the B atom in the surface. In this situation, all sites are equivalent. However, in the time of the simulation the atoms arc not rcarrangcd. When oR = 1.O and tR r 1.O, the B atom accommodates the center of the cluster surrounded by the A atoms in an icosahedral configuration. For oK= 1.0 and + < 1.O, the B atom sits on the surface of a essentially undistorted icosahedral cluster. When both aR and tR have reached fairly large values, the low-temperature cluster structure is changed qualitatively. For these clusters the large B atom provides a sulfate upon which the host A atoms form a two-dimensional layer. At low temperatures this solvation layer is a well-ordered two-dimensional solid. The solvation layer structure is illustrated in fig. 1, giving the polar positions of the atoms in the
2. I. AiJB clusrer The minimum energy structures for this system were obtained by repeatedly heating and cooling the clusters. The simulation was initiated by placing the impurity atom in a fixed position with zero momentum and letting the host cluster move around the impurity until the whole system equilibrated. At this point, the system was usually at a high temperature. After the first equilibration, the system was cooled, then repeatedly heated and cooled by scaling the final velocities of the cluster atoms. For strongly bound clusters (see below), the highest temperatures reached were well above the pure system melting temperature [ 3 1. The cooling rates were chosen such that the caloric curve on the cooling cycle closely followed the heating curve. (There is always a small discrepancy between the heating and cooling curve in the liquid-solid transition region.) This process was carried out many times to insure that the fully annealed low-temperature structure was obtained. For temperatures well into the liquid region the equilibration times at high temperature were limited by evaporation. The low-temperature structure of the A, 1B cluster 526
Table I Low-temperature
structure
of the A ,,B clusters a)
0.4
1.0
2.0
icosahedron
icosahedron with B atom adsorbed
icosahedron
icosahedron with B atom inside
icosahedron with B atom
distorted icosahedr-on with B atom adsorbed
icosahedron with B atom inside
icosahedron with B atom
2.0
icosahedron with B atom inside
icoyahedron with B atom at the center
partially solvated B atom ‘I
3.0
icosahedron with B atom inside
icosahedron with B atom at the center
partially solvated B atom hi
0.7
with B atom inside 1.0
1.5
in the surface
al the center
with B atom adsorbed
very disroned lcosahedron with B atom adsorbed
Volume 158, number 6
CHEMICAL
PHYSICS LETTERS Table 2 Low-temperature CH
structure
of the A,,B clusters”’
OK 0.4
1.0
2.0
icosahedron with B atom inside
icosahedron with B atom
icosahedron with B atom
adsorbed
adsorbed
1.0
icosahedron with B atom inside
icosahedron with B atom in the surface
icosahedron with B atom adsorbed
1.5
icosahedron with B atom inside
icosahedron with B atom at the center
distorted icosahedron with B atom adsorbed
0.1
6270"
23 June 1989
2.0
Fig. 1. Polar diagram of atomic positions in the salvation she11 of the impurity B arom. LT~=1.5, cR= 3.0. The origin of spherical coordinates is the center of the impurity. The polar diagram shows the polar (0) and azimuthal (@) angles for the A atoms.
icosahedron with B atom inside
icosahedron with B atom at the center
completely solvated B atom with incomplete second salvation shell
3.0
solvation shell relative to the center of mass of the solvation shell. The parameters of the system leading to the figure, I&= 1.5 and +,=3.0, are Similar” to those expected in the systems studied experimentally by Stoles and coworkers [ 41 and Hahn and Whetten [ 61. As illustrated by fig. 1 these systems are quite different from the icosahedrally symmetric 13-pureatom systems studied by Berry and coworkers [ 31. Therefore the behavior measured in these experiments may not be easily related to the properties of pure systems.
icosahedron with B atom inside
icosahedron with B atom at the center
completely solvated B atom with incomplete second salvation shell
ature configurations in which the impurity is adsorbed on surface on a distorted icosahedral cluster ( cR= 0.7, 1.O and 1.5 ) or solvated inside ordered shell ( eR= 2.0 and 3.0). In the latter case the structure may be characterized as a B atom with a fully saturated first solvation shell and a partially completed second solvation shell.
2.2. A>,% cluster
2.3. A,3i3,3 cluster
The results obtained for this cluster are similar to those obtained for the A13B system and are summarized in table 2. In this case, however, there are mare than enough host atoms to fill the first solvation shell. For uR = 0.4 the B atom is always inside the cluster between their first and second shells independent of the cR value chosen. For oR = 1.O and ~~~0.7 the impurity adsorbs on the cluster surface. When tR increases it is solvated by the cluster. For bigger impurities ( nR = 2.0) we obtain low-temper-
Two types of 26-atom compound clusters were studied, in the first one we combined atoms of the same atomic size and different interaction energy (a*=~~ and ca= 1.5~~). In the second case atoms of different size but equal interaction energy (a, = 1.5~~ and Q,= Q,) were mixed. Fig. 2a shows the low-temperature structure for compound clusters with atoms of equal size but different interaction energy. As expected we found that the stronger interacting particles are inside the compound cluster, forming an icosahedral shape cluster core, while the weaker interacting particles are outside forming a partial cluster surface following the fivefold icosahedral sym-
*’ The SF6-Ar interaction has been modeled with a LennardJones potential by Porter and Grosser [ I 11.
527
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23 June 1989
CHEMICALPHYSICSLETTERS 3. Behavior as a function of temperature 3.1. A12B cluster
This system was simulated in order to study the effect of the impurity interaction energy in the melting and freezing transition as a function of impurity parameters. Fig. 3 shows the total energy of the A, 2B cluster as a function of the temperature for OR= 1.O andt,=0.5, 1.0, 1.5,2.0,and2.5. Theaveragingtime in all these simulations was 50000 steps or approximately 1 ns. The case tR= 1.O and OR= 1.0 corresponds to the pure cluster, which has been widely studied [ 31. For this system a transition from solidlike to liquid-like behavior takes place at T=0.31. The abrupt change in the distribution of total energy, from kinetic to potential energy in going from the solid-like to the liquid-like states at this temperature, results in a sharp change in the caloric curve. The evidence for the transition in the caloric curves is less evident for fR= 1.5. Forweakly interacting (cR=0.5) and strongly interacting impurities ( tR = 2.0 and 3.0) the feature corresponding to the transition is not present. Instead at sufficiently high temperatures evaporation takes place before any significant disorder in the solvation shell occurs. The behavior of the strongly interacting system changes as the size of the impurity atom is increased. As the radius of the B atom is increased, the solva-
a
b Fig. 2. (a) Low-temperaturestructure for the A,,B,, cluster with u,=u~ and t,=l.%,. z,+=cR.
(b) Same as in (a) but u,,= ISa,
and
metry. A different situation is found in the other case of clusters of equally interacting atoms and unlike size. Fig. 2b shows that the low-temperature configuration is a cluster in which the smaller atoms form an internal disordered subcluster surrounded by the bigger surface atoms. 528
0
0.1
0.2
0.3
0.4
temperature Fig. 3. Caloric curves for the A,*B cluster. All cwves were ob-
tained with Us= 1.O.
Volume 158, number 6
CHEMICAL
PHYSICS LETTERS
tion shell around the B atom develops vacancies. Now low-energ? configurations in which bonds arc broken in the two-dimensional solvation layer are possible. For these systems, a two-dimensional solidliquid-like phase transition corresponding to the abrupt appearance of disorder in the solvation shell occurs at low temperatures. Evidence for this transition is apparent in the mean square displacement (MSD) calculations reported in fig, 4. The open circles correspond to the MSD of bond lengths from the impurity to the solvating cluster atoms. As temperature is increased this average bond length remains almost constant indicating solidlike vibration in the radial direction perpendicular to the solvation shell. On the other hand the filled circles correspond to the MSD of the positions of atoms within the solvation layer. In this case there is a sharp change in behavior at T= 0.11. This corresponds to the appearance of disordered solvation structures in the simulation and appears to be analogous to the three-dimensional solid-liquid transition studied in pure cluster simulations. This behavior is similar to that reported by Shelley et al. [ 81. However, we have not seen evidence for a second sharp three-dimensional transition at higher temperature as is reported in this paper. These workers used different two-body potentials in their simulations.
l
I
23 June 1989
Also in the simulations reported in ref. [ 81 a Longlived solid-like droplet structure was observed in the simulation for a small temperature range above the two-dimensional liquid transition temperature. Similar structures were observed in our simulations. However, they were very short lived. In order to investigate further the question of the appearance of a sharp three-dimensional transition we simulated clusters with a filled first solvation shell. For [TV= 1.5 and Ed= 3.0 this corresponds to a cluster with 30 host atoms. For this system no sharp changes in MSD at low temperatures were observed, as is consistent with the quenching of the two-dimensional melting behavior because of the filled solvation shell. Again higher temperature simulations showed no feature corresponding to three-dimensional melting contrary to the results of ref. [ 8 1. Simulations as a function of temperature were also carried out for the A5,B cluster with CUR=1.5 and +=3.0. For this system there is a complete first solvation and an incomplete second shell. In this case we again found evidence for a two-dimensional transition in the second solvation shell, but no evidence for a three-dimensional transition.
Acknowledgement We wish to acknowledge the support of the SDIO/ TA/USAF (ONR-NO00 14-87-K-0675) for this project. We thank the San Diego Supercomputing Center for the use of their computing facilities. One of us (ILG) wishes to thank the Consejo National de Ciencia y Tecnologia (Mexico) for the partial support.
References
0.1
0.2
0.3
temperature Fig. 4. Mean square displacements after au interval of 500 time steps for A,,B cluster with CJ~= 1.5and en= 3.0. Total time in the simulation 50000 steps. 100time origins were used.
[ I] Proceedings of the Fourth International Symposium on Small Particles and Inorganic Clusters, Z. Physik D, to be published; G. Stoles, ed., The chemical physics of atomic and molecular clusters (Ndrth-Holland, Amsterdam), to be published, G. Benedek, T.P. Martin and G. Paccioni, eds., Monographs on materiais science, Vol. 6. Elemental and molecular clusters (Springer, Berlin, 1988);
529
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P. Jena, B.K. Rao and S.N. Khana, eds., Proceedings of the International Symposium on the Physics and Chemistry of Small Clusters, NATO ASI Ser. (Plenum Press, New York, 1987). [2 ] IL. Garzon and E. Blaisten-Barojas, Chem. Phys. Letters 124 (1986) 84; H. Jonsson and J.H. Weare, Phys. Rev. Letters 57 (1986) 412. ]3 ] D.J. McGmty, J. Chem. Phys. 58 (1973) 4733; CL. Briant and J.J. Burton, J. Chcm. Phys. 63 ( 1975) 2045; J. Jellinek, T.L. Beck and R.S. Berry, J. Chem. Phys. 84 (1986) 2783; R.S. Berry, T.L. Beck, H.L. Davis and J. Jellinek, Advan. Chem. Phys. 70 ( 1988), in press. [ 41 T.E. Cough, D.G. Knight and G. Stoles, Chem. Phys. Letters 97 (1983) 155; T.E. Gough, M. Mengel, P.A. Rowntree and C. Stoles, J. Chem. Phys. 83 (1985) 4958; D.J. Levandter and G. Stoles, to be published.
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PHYSICS LETTERS
23 June 1989
[5] J. Bosiger and S. Leutwyler, Phys. Rev. Letters 59 ( 1987) 1895. [6] M.V. Hahn and R.L. Whetten, Phys. Rev. Letters 61 (I 988) 1190. [7]D. Eichenauer and R.J. Le Roy, Phys. Rev. Letters 57 (1986) 2920; J. Chem. Phys. 88 (1988) 2898. [8] J.C. Shelley, R.J. Le Roy and F.G. Amar, Chem. Phys. Letters 152 (198X) 14. 191 L. Verlet, Phys. Rev. 159 ( 1964) 98. [ IO]I.L. Garzdn. M. Avalos and E. Blaisten-Barojas, in: Proceedings ofthe International Symposium on the Physics and Chemistry of Small Clusters, NATO ASI Ser., eds. P. Jena, B.K. Rao and S.N. Khana (Plenum Press, New York, 1987) p. 193; E. Blaisten-Earojas, I.L. Ganon and M. Avalos-Borja, Phys. Rev.B36(1987)8447. [ 1 I ] A. Porter and A.E. Grosser, Mol. Phys. 38 ( 1979) 6 I I.
Volume 158, number 6
23 June 1989
STRUCTURAL AND DYNAMICAL PROPERTIES OF VAN DER WAALS CLUSTERS WITH IMPURITIES I.L. GARZON
’ , X.P. LONG, R. KAWAI and J.H. WEARE
Department of Chemistry. B-040, University of CaliSornia, San &ego, La Joiia. CA 92093, USA Received 22 June 1988; in final form 10 April 1989
Mixed clusters of Lennard-Jones atoms have been studied using molecular dynamic simulations. For sufficiently high impurityhost interaction energy, the structure is significantlydistorted from those found for pure clusters, and the three-dimensional solidliquid-like transition identified in pure system simulations is absent. Instead, at very low temperatures, structures may be characterxed as having two-dimensional solid-like salvation shells formed by the host atoms surrounding the impurity. When these solvatinn shells are incomplete, well-defined two-dimensional solid-liquid transitions corresponding to the appearance of disorder in the solvatinn shells (two-dimensional melting) are observed as the temperature is increased. Studies ofA,,R,,-type clusters are also reported. For the parameters studied, a clear segregation of species within the cluster is observed.
1. Introduction Recently there has been considerable interest in the physics and chemistry of clusters [ 11. One area of special emphasis in theoretical research is the study of the structure and dynamics of pure clusters bound by van der Waals interactions. For these systems the forces between atoms are well described by simple two-body interactions using for example the LennardJones (LJ) potential. Three-body contributions to the many-body potential appear to bc unimportant for most calculations [2]. The simulation of these systems has led to the observation that some systems with particularly stable structures (e.g. the t3-atom icosahedral structure) display an abrupt change in dynamical behavior as a function of temperature (average kinetic energy per internal degree of freedom) in a constant energy simulation [ 31. This transition has received a great deal of attention because of its possible relation to the melting transition in macroscopic systems. While the theoretical evidence for such a transition in some pure clusters is well established, experimental vali’ Permanent address: lnstituto de Fisica, Universidad Autonoma de Mexico, Apartado nada, Baja California, Mexico.
National Postal 2681, 22800 Ense-
0 009-26 14/89/s 03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division )
dation of these results is difficult because of the weak interaction of radiation with the interspecies vibrational modes of the van der Waals systems modeled theoretically. Recently, in an effort to provide experimental information about van der Waals clusters, Stoles and coworkers [4] and others [ 5,6] have initiated experimental studies of similarly bound systems with photoactive impurities. In these experiments, the shifts and widths of the impurity vibrational levels arc intcrpretcd in terms of the host-impurity interactions and the dynamical state of the clusters [ 571. However, while the bonding in these impure systems is of similar character to the pure clusters [ 31, the differences in bond strengths between host-impurity and host-host interactions is usually substantial. This implies that there may be significant differences in the structures and dynamics of the pure and impure systems [ 71. The objective of this article is to describe some of our efforts to address these questions by direct simulation of mixed cluster systems. Similar calculations have recently been reported by Shelley et al. [ 81. The systems consisted of n atoms A and m atoms B interacting through LJ potentials with parameters a,, eA and c8, cB respectively. The A-B interaction is also modeled by a LJ potential with parameters B.V.
525
Volume 158,number 6
CHEMICAL PHYSICS LETTERS
given by u,~= 1 (o,+ 0~8) and tAB. For systems with only one B atom, results are given for various values oEthe ratio tR= tAB/tA and uK=~~B/~~ For systems with more than one B atom, fAB= (~,,t~)“’ and CR= tB/Ca. Starting from an initial condition, the equations of motion were integrated with a Verlet algorithm [91 with a time step of 0.01 r, where I= (M,a~/s,)“” is a number characteristic of the period of vibration of a Lennard-Jones diatomic with parameters ~7and t. 7 therefore scales approximately with the relaxation times in the pure host system. Energy was added to or removed from the system (temperature raised or lowered) by scaling the velocities [ 10 1. The cluster temperature was defined in the usual way as proportional to the mean kinetic energy divided by the number of internal degrees of freedom. It is given in reduced units of tA/kB, where kB is the Boltzmann constant.
2. Low-temperature
structures
23 June 1989
is strongly dependent on the oR and the cR value. Results are summarized in table 1. For ~~~0.4 the R atom is always inside the host cluster, independently of the tR values used in the simulations. In this case the A atoms from a slightly distorted icosahedron with the B atom interstitially packed inside. When C~ = 1.O and Ed= 1.O (pure system) our simulations always place the B atom in the surface. In this situation, all sites are equivalent. However, in the time of the simulation the atoms arc not rcarrangcd. When oR = 1.O and tR r 1.O, the B atom accommodates the center of the cluster surrounded by the A atoms in an icosahedral configuration. For oK= 1.0 and + < 1.O, the B atom sits on the surface of a essentially undistorted icosahedral cluster. When both aR and tR have reached fairly large values, the low-temperature cluster structure is changed qualitatively. For these clusters the large B atom provides a sulfate upon which the host A atoms form a two-dimensional layer. At low temperatures this solvation layer is a well-ordered two-dimensional solid. The solvation layer structure is illustrated in fig. 1, giving the polar positions of the atoms in the
2. I. AiJB clusrer The minimum energy structures for this system were obtained by repeatedly heating and cooling the clusters. The simulation was initiated by placing the impurity atom in a fixed position with zero momentum and letting the host cluster move around the impurity until the whole system equilibrated. At this point, the system was usually at a high temperature. After the first equilibration, the system was cooled, then repeatedly heated and cooled by scaling the final velocities of the cluster atoms. For strongly bound clusters (see below), the highest temperatures reached were well above the pure system melting temperature [ 3 1. The cooling rates were chosen such that the caloric curve on the cooling cycle closely followed the heating curve. (There is always a small discrepancy between the heating and cooling curve in the liquid-solid transition region.) This process was carried out many times to insure that the fully annealed low-temperature structure was obtained. For temperatures well into the liquid region the equilibration times at high temperature were limited by evaporation. The low-temperature structure of the A, 1B cluster 526
Table I Low-temperature
structure
of the A ,,B clusters a)
0.4
1.0
2.0
icosahedron
icosahedron with B atom adsorbed
icosahedron
icosahedron with B atom inside
icosahedron with B atom
distorted icosahedr-on with B atom adsorbed
icosahedron with B atom inside
icosahedron with B atom
2.0
icosahedron with B atom inside
icoyahedron with B atom at the center
partially solvated B atom ‘I
3.0
icosahedron with B atom inside
icosahedron with B atom at the center
partially solvated B atom hi
0.7
with B atom inside 1.0
1.5
in the surface
al the center
with B atom adsorbed
very disroned lcosahedron with B atom adsorbed
Volume 158, number 6
CHEMICAL
PHYSICS LETTERS Table 2 Low-temperature CH
structure
of the A,,B clusters”’
OK 0.4
1.0
2.0
icosahedron with B atom inside
icosahedron with B atom
icosahedron with B atom
adsorbed
adsorbed
1.0
icosahedron with B atom inside
icosahedron with B atom in the surface
icosahedron with B atom adsorbed
1.5
icosahedron with B atom inside
icosahedron with B atom at the center
distorted icosahedron with B atom adsorbed
0.1
6270"
23 June 1989
2.0
Fig. 1. Polar diagram of atomic positions in the salvation she11 of the impurity B arom. LT~=1.5, cR= 3.0. The origin of spherical coordinates is the center of the impurity. The polar diagram shows the polar (0) and azimuthal (@) angles for the A atoms.
icosahedron with B atom inside
icosahedron with B atom at the center
completely solvated B atom with incomplete second salvation shell
3.0
solvation shell relative to the center of mass of the solvation shell. The parameters of the system leading to the figure, I&= 1.5 and +,=3.0, are Similar” to those expected in the systems studied experimentally by Stoles and coworkers [ 41 and Hahn and Whetten [ 61. As illustrated by fig. 1 these systems are quite different from the icosahedrally symmetric 13-pureatom systems studied by Berry and coworkers [ 31. Therefore the behavior measured in these experiments may not be easily related to the properties of pure systems.
icosahedron with B atom inside
icosahedron with B atom at the center
completely solvated B atom with incomplete second salvation shell
ature configurations in which the impurity is adsorbed on surface on a distorted icosahedral cluster ( cR= 0.7, 1.O and 1.5 ) or solvated inside ordered shell ( eR= 2.0 and 3.0). In the latter case the structure may be characterized as a B atom with a fully saturated first solvation shell and a partially completed second solvation shell.
2.2. A>,% cluster
2.3. A,3i3,3 cluster
The results obtained for this cluster are similar to those obtained for the A13B system and are summarized in table 2. In this case, however, there are mare than enough host atoms to fill the first solvation shell. For uR = 0.4 the B atom is always inside the cluster between their first and second shells independent of the cR value chosen. For oR = 1.O and ~~~0.7 the impurity adsorbs on the cluster surface. When tR increases it is solvated by the cluster. For bigger impurities ( nR = 2.0) we obtain low-temper-
Two types of 26-atom compound clusters were studied, in the first one we combined atoms of the same atomic size and different interaction energy (a*=~~ and ca= 1.5~~). In the second case atoms of different size but equal interaction energy (a, = 1.5~~ and Q,= Q,) were mixed. Fig. 2a shows the low-temperature structure for compound clusters with atoms of equal size but different interaction energy. As expected we found that the stronger interacting particles are inside the compound cluster, forming an icosahedral shape cluster core, while the weaker interacting particles are outside forming a partial cluster surface following the fivefold icosahedral sym-
*’ The SF6-Ar interaction has been modeled with a LennardJones potential by Porter and Grosser [ I 11.
527
Volume
15X,number 6
23 June 1989
CHEMICALPHYSICSLETTERS 3. Behavior as a function of temperature 3.1. A12B cluster
This system was simulated in order to study the effect of the impurity interaction energy in the melting and freezing transition as a function of impurity parameters. Fig. 3 shows the total energy of the A, 2B cluster as a function of the temperature for OR= 1.O andt,=0.5, 1.0, 1.5,2.0,and2.5. Theaveragingtime in all these simulations was 50000 steps or approximately 1 ns. The case tR= 1.O and OR= 1.0 corresponds to the pure cluster, which has been widely studied [ 31. For this system a transition from solidlike to liquid-like behavior takes place at T=0.31. The abrupt change in the distribution of total energy, from kinetic to potential energy in going from the solid-like to the liquid-like states at this temperature, results in a sharp change in the caloric curve. The evidence for the transition in the caloric curves is less evident for fR= 1.5. Forweakly interacting (cR=0.5) and strongly interacting impurities ( tR = 2.0 and 3.0) the feature corresponding to the transition is not present. Instead at sufficiently high temperatures evaporation takes place before any significant disorder in the solvation shell occurs. The behavior of the strongly interacting system changes as the size of the impurity atom is increased. As the radius of the B atom is increased, the solva-
a
b Fig. 2. (a) Low-temperaturestructure for the A,,B,, cluster with u,=u~ and t,=l.%,. z,+=cR.
(b) Same as in (a) but u,,= ISa,
and
metry. A different situation is found in the other case of clusters of equally interacting atoms and unlike size. Fig. 2b shows that the low-temperature configuration is a cluster in which the smaller atoms form an internal disordered subcluster surrounded by the bigger surface atoms. 528
0
0.1
0.2
0.3
0.4
temperature Fig. 3. Caloric curves for the A,*B cluster. All cwves were ob-
tained with Us= 1.O.
Volume 158, number 6
CHEMICAL
PHYSICS LETTERS
tion shell around the B atom develops vacancies. Now low-energ? configurations in which bonds arc broken in the two-dimensional solvation layer are possible. For these systems, a two-dimensional solidliquid-like phase transition corresponding to the abrupt appearance of disorder in the solvation shell occurs at low temperatures. Evidence for this transition is apparent in the mean square displacement (MSD) calculations reported in fig, 4. The open circles correspond to the MSD of bond lengths from the impurity to the solvating cluster atoms. As temperature is increased this average bond length remains almost constant indicating solidlike vibration in the radial direction perpendicular to the solvation shell. On the other hand the filled circles correspond to the MSD of the positions of atoms within the solvation layer. In this case there is a sharp change in behavior at T= 0.11. This corresponds to the appearance of disordered solvation structures in the simulation and appears to be analogous to the three-dimensional solid-liquid transition studied in pure cluster simulations. This behavior is similar to that reported by Shelley et al. [ 81. However, we have not seen evidence for a second sharp three-dimensional transition at higher temperature as is reported in this paper. These workers used different two-body potentials in their simulations.
l
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Also in the simulations reported in ref. [ 81 a Longlived solid-like droplet structure was observed in the simulation for a small temperature range above the two-dimensional liquid transition temperature. Similar structures were observed in our simulations. However, they were very short lived. In order to investigate further the question of the appearance of a sharp three-dimensional transition we simulated clusters with a filled first solvation shell. For [TV= 1.5 and Ed= 3.0 this corresponds to a cluster with 30 host atoms. For this system no sharp changes in MSD at low temperatures were observed, as is consistent with the quenching of the two-dimensional melting behavior because of the filled solvation shell. Again higher temperature simulations showed no feature corresponding to three-dimensional melting contrary to the results of ref. [ 8 1. Simulations as a function of temperature were also carried out for the A5,B cluster with CUR=1.5 and +=3.0. For this system there is a complete first solvation and an incomplete second shell. In this case we again found evidence for a two-dimensional transition in the second solvation shell, but no evidence for a three-dimensional transition.
Acknowledgement We wish to acknowledge the support of the SDIO/ TA/USAF (ONR-NO00 14-87-K-0675) for this project. We thank the San Diego Supercomputing Center for the use of their computing facilities. One of us (ILG) wishes to thank the Consejo National de Ciencia y Tecnologia (Mexico) for the partial support.
References
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temperature Fig. 4. Mean square displacements after au interval of 500 time steps for A,,B cluster with CJ~= 1.5and en= 3.0. Total time in the simulation 50000 steps. 100time origins were used.
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