ARTICLE pubs.acs.org/JPCA
Thermodynamic Properties of Ga27Si3 Cluster Using Density Functional Molecular Dynamics Seyed Mohammad Ghazi*,†,z and D. G. Kanhere*,‡ †
Department of Physics, University of Pune, Pune 411 007, India Department of Physics, Central University of Rajasthan, Kishangarh, India z Ministry of Science, Research and Technology, Tehran, Iran ‡
ABSTRACT: Density functional molecular dynamical calculations have been carried out to explore the effect of silicon impurities on thermodynamic properties of Ga30. We have obtained 500 distinct low energy equilibrium geometries of Ga27Si3 in order to obtain reliable ground state geometry. The specific heat has been calculated using multiple histogram techniques and compared with that of Ga30. We demonstrate that silicon impurities have a dramatic effect on the thermodynamic properties of the host cluster. In contrast to Ga30, the specific heat of Ga27Si3 shows a clear melting peak at ≈500 K, changing the character of Ga30 from a nonmelter to a melter.
’ INTRODUCTION During the past decade finite temperature properties of small clusters in the size range of N = 20150, where N is the number of atoms, have shown rather intriguing behavior. In one of the first series of experiments on sodium clusters Haberland and co-workers17 observed a large size dependent fluctuation in their melting temperatures (of the order of ≈90 K). On the basis of ionic mobility measurement, Jarrold and co-workers8 demonstrated that the melting temperatures of small clusters of tin are higher than that of bulk tin. They also measured the heat capa cities of clusters of gallium in the size range of 3055 atoms.9 These measurements revealed two interesting features: higher than the bulk melting points for all clusters and the extreme size sensitivity of the shape of their specific heat curves. For example, the specific heat of Ga30 showed no recognizable peak, but an addition of just one atom changed the nature from nonmelter to what has been called magic melter.10 In other words, the heat capacity of Ga31 has a well-defined melting temperature. A similar size-sensitive nature of the heat capacity has been observed in the experimental measurements on aluminum clusters1114 in a similar size range. In this case the melting points are less than their bulk counterpart. A number of experimental works dealing with thermal properties of heterogeneous clusters have been reported.9,11,1525 Haberland and co-workers15 showed that the oxidization of sodium clusters with 135192 atoms by a single oxygen molecule reduces both the melting points and the latent heats. Their calculations revealed that the interaction between the pure and oxidized part of the cluster is responsible for the effect. However, a combined experimental and theoretical study of Jarrold and co-workers16 have shown that the above conclusion is not valid r 2011 American Chemical Society
for Al44(()N2 clusters. They concluded that the qualitative thermal behavior of the doped systems is unpredictable in general for small clusters. They also measured heat capacities for Aln1Cu clusters (n = 4962) and compared the results for pure Aln+ clusters.17 They observed that Cu impurity can either increase or decrease the melting points of the doped clusters as well as change the size and the width of the peaks of their specific heat curves. However, it turns out that when Al+ is doped in gallium clusters, there is no noticeable change in the melting temperatures.18 There has been a lot of interest in the theoretical studies of thermodynamics properties of homogeneous clusters.8,10,2637 By and large the estimated melting temperatures for the clusters of sodium, gallium, and tin are in excellent agreement with the experimental reports. A good deal of progress has been made in understanding the size sensitive nature of their specific heat curves.814,26,27,38 Specifically the density functional simulations have established a clear correlation between the nature of the ground state geometry and the shape of the heat capacity curve. A cluster having an ordered ground state geometry shows a recognizable peak in its heat capacity, while a cluster having an amorphous ground state tends to have a rather flat heat capacity. Most of the thermodynamic studies reported so far are on homogeneous clusters. Theoretical treatment of heterogeneous clusters is challenging because of the need to span a much larger configuration space for geometry optimization. A cluster with a small number of impurities is a simpler version of heterogeneous Received: April 13, 2011 Revised: November 6, 2011 Published: November 30, 2011 11
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systems and is of considerable interest, one of the issues being the effect of dopants on the thermodynamic properties.3944 Some simulations based on Density Functional Molecular Dynamics (DFMD) or classical potentials have been reported in this area.4548 Joshi and Kanhere have studied a representative system of Li6Sn where a competition between ionic and covalent bonding makes its finite temperature behavior very different from that seen in the Li7 cluster.46 Lee et al. have presented the equilibrium geometries, electronic structure, and the nature of bonding in LiSn, and thermodynamic properties of Al-doped Li clusters.49,50 They found that the geometries of Li-rich clusters change significantly by a few Sn impurities.49 Chandrachud et al.51 have studied thermodynamics of carbon doped aluminum and gallium clusters. Their studies show that upon doping there is a substantial reduction in the melting temperature of the host clusters, and, in the case of gallium, the carbon atom changes the geometry from decahedral to icosahedral. The results of the work by Krishnamurty et al.52 indicate that the small clusters of Sin (n = 15 and 20) become unstable and fragment when heated up to approximately 1500 K. However, Kumar et al.5356 found that it is possible to stabilize a caged structure of Si cluster using a certain class of dopants. Specifically, they showed that a single impurity of transition metal atoms such as Ti, Zr, and Hf enhances the binding energy of Si16 and changes the structure to a caged one, similar to carbon cages. Zorriasatein et al.57 have shown that the fragmentation process in Si16 can be suppressed by doping with a Ti atom. Liu et al.58 observed that on heating, the bimetallic clusters of AuPt transform to the most stable Pt-core/Au-shell structure from other structural forms at certain temperatures. An interesting work of Ferrando and co-workers48 based on classical interatomic potentials showed that a single impurity of Ni or Cu can considerably shift the melting temperature of icosahedral silver clusters of several tens or hundreds of atoms. They observed that a small central impurity causes a better relaxation of the strained icosahedral structure, which becomes more stable against thermal disordering. All the theoretical studies show a strong correlation between the geometric structure and the shape of the heat capacity. Recently, Calvo and co-workers59 investigated the heat capacity of pure and heterogeneous water clusters by means of exchange Monte Carlo simulations with different intermolecular potentials. They also observed that a single impurity tends to shift the melting point to a higher temperature in the small cluster containing 21 molecules, but the effect is already much reduced in the larger system having 50 molecules. The work of Lyalin et al.60 shows that the addition of a carbon impurity in Ni147 lowers its melting temperature by 30 K. This is mainly due to excessive stress produced on the cluster lattice. The distortion of the system lattice leads to the change in energetics as well as entropy of the cluster. The reduction of the melting temperature of magic Lennard-Jones clusters due to a single impurity has also been observed.61 Quite clearly the effect of a few impurities on the properties of host cluster can be quite dramatic. In the present work we focus on the thermodynamic properties of silicon doped Ga30 cluster. This work is motivated by the extreme size sensitivity observed in the measured specific heat curves of Ga30 and Ga31. The specific heat for Ga30 does not show recognizable melting peak, while Ga31 shows a sharp melting peak at ≈440 K.9,10 It turns out there is a subtle difference in the nature of the ordering in the ground state geometries of these two clusters. The interesting question is as follows: Can we change the finite temperature behavior of this
nonmelter by doping with suitable impurities. Clearly, there are many interdependent factors such as geometry, electronic structure, and the nature of the bonding between impurity and the host. Small clusters of gallium are known to be covalent.10 Hence in this work we chose silicon, having covalent bonding. Moreover, the electronegativity on the Pauling scale for Si (1.90) is almost the same as that of Ga (1.81) and has a smaller ionic radius (1.11 Å) as compared to another covalent element, germanium (1.22 Å). The binding energy of GaSi dimer turns out to be larger than the binding energy of GeGa dimer by about 0.14 eV.62 Thus silicon is a likely choice for doping to make small structural changes in Ga30, thereby affecting the melting behavior. Therefore we doped the host with three silicon atoms substitutionally. The number of the electrons then equals those of Ga31, without changing the total number of atoms in the host. As we shall see, the doped cluster turns out to be relatively more ordered and develops a well recognizable melting peak. Finally we mention that the choice of doping element is not unique.
’ COMPUTATIONAL DETAILS All the calculations have been carried out using density functional formalism within the Generalized Gradient Approximations (GGA). We have used a plane wave basis set together with Vanderbilt’s ultrasoft pseudopotentials63 as implemented in the VASP package.64 We have optimized about 800 geometries for the studied system and have found 500 distinct isomers. These 800 initial geometries were chosen from a series of molecular dynamical runs (density functional theory based) carried out at seven different temperatures between 200 and 1500 K. The starting configurations for these runs were chosen as randomly substituted geometries obtained from Ga30 and Ga31 ground state geometries (after removing one gallium atom). All the molecular dynamical runs were of 45 ps duration. These generate about 100000 configurations. Out of these, about 800 configurations were chosen for geometry optimization after examining the potential energy curves. These 800 geometries were minimized and analyzed for removing the duplicates. The isomers differing in energy and bond length by 0.005 eV and 0.01 Å respectively were considered distinct. All such isomers were carefully examined visually before deciding to discard them. We have used cubic super cell of length 20 Å and have ensured the convergence of the results with respect to the energy cutoff and size of the simulation box. We note that it is possible to take another starting configuration such as Si27 plus randomly placed three silicon atoms and carry out similar exercise. We believe that we have spanned reasonable large configuration space, especially because of the MD run at 1500K, and are confident that we have obtained the ground state or a state very close to the true ground state. We note that we did not find any lowering of potential energy upon heating the lowest energy structure. The thermodynamic data are extracted from the molecular dynamical trajectories at constant temperature using Nose-Hoover thermostat.65 We have used 17 temperatures in the range of 175 K e T e 1100 K, chosen so as to give overlapping histograms. For each temperature the trajectory data was collected for period of at least 240 ps. We have discarded first 30 ps for the thermalization. The resulting ionic trajectory data has been used to obtain multiple histograms. We have also analyzed various thermodynamic indicators such as Lindemann criteria (δrms) and mean square displacements (MSDs). 12
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The shape of the ground state geometry plays an important role in understanding the thermodynamics properties of cluster. We have used a shape deformation parameter, β, to analyze the shapes of the isomers. The deformation parameter, β, is defined as β¼
2Qz Qx þ Qy
ð1Þ
where Qz g Qy g Qx are the eigenvalues, in descending order, of the quadrupole tensor
∑I RIiRIj
Qij ¼
ð2Þ
Here i and j run from 1 to 3, I runs over the number of ions, and RIi is the ith coordinate of ion I relative to the cluster center of mass. We note that β will be unity for a spherical cluster (Qx = Qy = Qz) while β > 1.0 indicates a deformation. The shape is said to be prolate when Qz . Qy ≈ Qx and oblate when Qz ≈ Qy . Qx. A general completely asymmetric distribution of atoms is signaled by Qx 6¼ Qy 6¼ Qz. We have analyzed the nature of bonding via the electron localization function (ELF).66 The ELF is defined as " 2 #1 D χELF ¼ 1 þ ð3Þ Dh
Figure 1. The multiple histogram showing the potential energy distribution. At higher temperatures the histograms are much wider, indicating the liquid-like behavior.
A typical multiple histogram, i.e. the potential energy distribution spanned by the cluster at all the temperatures, is shown in Figure 1. The temperatures range from 175 to 1100 K and have been chosen so as to have a substantial overlap in the distributions. The upper temperature has been chosen to be well above the melting temperature in order to have reliable heat capacity above the melting temperature. It may be noted from the figure that the normalized potential energy distribution for low temperatures is narrow. Indeed, at low temperature the atoms exhibit low amplitude oscillatory motion around their equilibrium positions. At higher temperatures the bonds begin to break and the clusters span a much wider potential energy landscape, leading to a broad distribution. Such a broad potential energy distribution seen above 600 K is suggestive of the liquid-like nature of the cluster in this range of temperatures. The Lindemann criteria δrms is defined as
where 1 D¼ 2 Dh ¼
∑i
1 ∇F 2 j∇ψi j 8 F 2
3 ð3π2 Þ5=3 F5=3 10
ð4Þ
ð5Þ
Here F F(r) is the valence electron density. The χELF is 1.0 for perfect localized function and 0.5 for homogeneous electron gas. The topological features of the (ELF) surface are analyzed by using the concepts of attractors and their basins.67 The locations of the maxima of χELF are called attractors. In this case the attractors are located at the ionic sites, the ELF being maximum there. A set of atoms which can be connected to these attractors by maximum gradient paths is called their basin. For large values of ELF, there are as many basins as number of ions. As the value of the ELF is decreased, the basins get connected, and finally at some low value we get a single basin. The value of the ELF at which the basins get connected is a measure of the strength of interaction between the different atoms. In other words, the number of atoms in the single basin are bonded to each other with similar strength depending upon the value of the ELF. The ionic specific heat is calculated by using the Multiple Histogram (MH) technique.51,68,69 We extract the classical ionic density of states (Ω(E)) of the system, or equivalently the classical ionic entropy, S(E) = kB ln Ω(E). In the canonical ensemble, the specific R heat is defined as usual by C(T) = ∂U(T)/∂T, where U(T) = Ep(E,T)dE is the average total energy. The probability of observing an energy E at a temperature T is given by the Gibbs distribution p(E,T) = Ω(E) exp(E/kBT)/Z(T), with Z(T) being normalizing partition function. We normalize the calculated specific heat by the zero-temperature classical limit of the rotational plus vibrational specific heat, i.e., C0 = (3N 9/2)kB.
δrms
2 1=2
ðÆrij æt Ærij æt Þ 2 ¼ NðN 1Þ i > j Ærij æt
∑
2
ð6Þ
where N is the number of atoms in the system, rij is the distance between atoms i and j, and Æ...æt denotes a time average over the entire trajectory. It is convenient to define MSDs for individual atoms as Ær2I ðtÞæ ¼
1 M ½R I ðt0m þ tÞ R I ðt0m Þ2 M m¼1
∑
ð7Þ
where RI is the position of the Ith atom, and we average over M different time origins t0m spanning over the entire trajectory. The interval between the consecutive t0m for the average was taken to be 1.5 ps. The MSDs of a cluster is indicative of the extent of displacements of atoms as a function of time.
’ RESULTS AND DISCUSSION Geometries. The ground state geometries of Ga30 and Ga27Si3 are shown from three different perspectives in Figure 2(a)Figure 2(c) and Figure 2(d)-Figure 2(f) respectively. In Figure 2(g)Figure 2(i) the two lowest energy isomers and a typical high energy isomer are presented. We begin the discussion by 13
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Figure 3. The distance from the center of mass ordered in the increasing fashion for the ground states of Ga30 and Ga27Si3 clusters. The x-axis enumerates all the atoms. The steps seen in the impurity doped cluster indicate more order.
Figure 2. (a), (b), (c), (d), (e), and (f) represent the ground state geometries of Ga30 and Ga27Si3 respectively from different perspectives. (g) and (h) depict the two lowest energy isomers, while (i) shows a typical high energy isomer. In all the cases the silicon atoms form a triangle inside. ΔE represents the energy difference with respect to the ground state. The shape parameter β and the symmetry group for each of the clusters are also noted.
recalling the structural differences in the ground state geometry of Ga30 and Ga31 as discussed in the reference.10 Their analysis shows that the Ga31 has well-ordered planes. On the basis of detailed analysis of the electron localization function and coordination numbers of all the atoms of these two clusters, they designate Ga31 as relatively more ordered than Ga30. This turns Ga31 into a magic melter. Upon doping by three silicon atoms, the structure of Ga30 becomes more symmetric. It changes from C1 symmetry to C2v. It may be noted that three silicon atoms form an equilateral triangle at the core of the structure, the SiSi distance being 3.46 Å. The presence of well-ordered vertical layers can also be seen in Figure 2(d) very clearly. In Figure 3, we show distances of all the atoms from the center of mass, ordered in the increasing way for Ga30 and Ga27Si3. A formation of step-like structures for Ga27Si3 (dark line) is clearly evident. The difference between these two clusters for this indicator is subtle but significant. Figure 4 shows the isosurface of the electron localization function (ELF) at the value χELF = 0.66 for Ga27Si3. A closer examination shows the existence of two basins. The first one consists of five atoms (three core silicon atoms and two nearest gallium atoms) as shown by dark lines in Figure 4. The remaining 25 gallium atoms form a separate basin. These two basins merged
Figure 4. The ELF of Ga27Si3 at the value of χELF = 0.66. Atoms shown by the black line form a basin (three silicon and two gallium atoms) and the rest of the atoms form another basin.
at a lower value of χELF = 0.60. We recall that this is very similar to the large basin seen in Ga31 consisting of 26 gallium atoms at χELF = 0.68. For the same isosurface value the basin structure of Ga30 is more fragmented.10 The above analysis shows that Ga27Si3 is more ordered and its basin structure is similar to the basin of Ga31. Therefore, the specific heat of Ga27Si3 is expected to resemble that of Ga31, i.e. it is expected to show a recognizable peak. Indeed, as we shall see the melting behavior of doped system is dramatically different than that of Ga30. Figure 2(g) and Figure 2(h) show the geometries of the first and second low lying isomers. The first isomer can be viewed as a rearrangement of a single atom by moving it from one of the bottom layers to the top one. Interestingly, the high energy isomer (Figure 2(i)) has a lower β than the low energy isomers. 14
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Figure 7. The Lindemann criteria δrms for Ga27Si3. It may be noted that δrms is dominated by the motion of gallium atoms and is not sensitive to a rather small number of silicon atoms.
interatomic distance of Ga30 by 0.022 Å and the longest interatomic distance by 0.068 Å. As we shall see, these differences lead to a significantly different finite temperature behavior of Ga27Si3 with respect to Ga30. Thermodynamics. The calculated normalized heat capacities for Ga27Si3 and Ga30 are shown in Figure 5. The melting temperature is identified by the temperature at which the first peak is located. Quite clearly the three silicon atoms induce dramatic change in the thermal behavior of Ga30. Unlike Ga30, a recognizable melting behavior is seen at a temperature of the order of 500 K. A detailed analysis of the ionic motion reveals that the melting is a two stage process. The first melting peak, seen around 500 K, is due to the melting of gallium atoms, and the second stage around 660 K is due to the melting of silicon core atoms. To support the above claim we show the mean square displacements of silicon and gallium atoms separately at relevant temperatures. It can be noted from Figure 6 that the contrast in the response of silicon and gallium atoms to temperatures is evident. The gallium atoms do not show any diffusive motion up to 475 K (MSDs e 2 Å2) indicating a solid-like phase of the cluster. The sudden increase in the value of MSDs (20 Å2) at 500 K clearly signals the melting. Remarkably the displacements of silicon atoms are rather small even at 550 K. They show a significant mean square displacement only above 600 K. This gives rise to a small broad peak at 660 K. This is also reflected in the Lindemann criteria (δrms) shown in Figure 7. As can be seen, the value of δrms is quite low up to 500 K, and then we encounter a sudden increase in its value signifying the melting. A detailed analysis of the ionic motion reveals an interesting feature of the motion of silicon. The triangular cluster of the silicon remains intact and moves as a whole unit up to 550600 K. In other words there is a diffusive motion of the silicon triangle as a whole. The breaking of SiSi bonds is observed only at temperatures above 600 K. It is interesting to compare the changes in the Radial Distribution Function (RDF) i.e. the number of atoms between r and r+dr (spherical shell) from the center of mass. Figure 8 presents the results of RDF calculations for some representative temperatures. Two peaks near the origin (one large, followed by a small one) seen at low temperatures are due to the silicon atoms and the rest are due to gallium atoms. The width of peak of silicon atoms remains almost the same up to 500 K. However at 500 K the gallium atoms show a rather broad peak with width of about 2 Å. The diffusing motion appears to be complete, and the cluster is completely liquid-like at 700 K.
Figure 5. The normalized heat capacity curves for Ga27Si3 and Ga30. The main melting peak for silicon doped cluster is due to the melting of Ga (at about 500 K). The second peak occurs when core silicon atoms ‘melt’. In contrast, the curve for the host (Ga30) is rather broad over a temperature range of 200 K.
Figure 6. The MSD for Ga and Si atoms for five different temperatures. Note the difference in the values of MSDs at 550 K for the two species.
This is a reflection of a rather strong bond between Si and Ga, making low energy isomers elongated. This high energy isomer is visible at about 1000 K. Finally, we mentioned that the gap between the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) is slightly reduced from 0.72 eV (for Ga30) to 0.63 eV (for Ga27Si3), and the binding energy per atom increases from 2.62 eV (for Ga30) to 2.85 eV (for Ga27Si3). The impurities also decrease the shortest 15
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’ ACKNOWLEDGMENT S. M. Ghazi acknowledges financial support from the Indian Council for Cultural Relations (ICCR). D. G. Kanhere acknowledges the CSIR Emeritus Fellowship awarded by CSIR India. We acknowledge CDAC India, for providing us HPC facilities. ’ REFERENCES (1) Schmidt, M.; Haberland, H. C. R. Physique 2002, 3, 327. (2) Schmidt, M.; Donges, J.; Hippler, T.; Haberland, H. Phys. Rev. Lett. 2003, 90, 103401. (3) Haberland, H.; Hippler, T.; Donges, J.; Kostko, O.; Schmidt, M.; Issendroff, B. V. Phys. Rev. Lett. 2005, 94, 035701. (4) Schmidt, M.; Kusche, R.; Issendorff, B. V.; Haberland, H. Nature (London) 1998, 393, 238. (5) Kusche, R.; Hippler, T.; Schmidt, M.; Issendorff, B. V.; Haberland, H. Eur. Phys. J. D 1999, 9, 1. (6) Schmidt, M.; Kusche, R.; Hippler, T.; Donges, J.; Kronm€uller, W.; Issendorff, B. V.; Haberland, H. Phys. Rev. Lett. 2001, 86, 1191. (7) Schmidt, M.; Kusche, R.; Kronm€uller, W.; Issendorff, B. V.; Haberland, H. Phys. Rev. Lett. 1997, 79, 99. (8) Shvartsburg, A. A.; Jarrold, M. F. Phys. Rev. Lett. 2000, 85, 2530. (9) Breaux, G. A.; Hillman, D. A.; Neal, C. M.; Benirschke, R. C.; Jarrold, M. F. J. Am. Chem. Soc. 2004, 126, 8628. (10) Joshi, K.; Krishnamurty, S.; Kanhere, D. G. Phys. Rev. Lett. 2006, 96, 135703. (11) Breaux, G. A.; Neal, C. M.; Cao, B.; Jarrold, M. F. Phys. Rev. Lett. 2005, 94, 173401. (12) Starace, A. K.; Neal, C. M.; Cao, B.; Jarrold, M. F.; Aguado, A.; Lopez, J. M. J. Chem. Phys. 2009, 131, 044307. (13) Cao, B.; Starace, A. N.; Judd, O. H.; Bhattacharyya, I.; Jarrold, M. F. J. Chem. Phys. 2009, 131, 124305. (14) Starace, A. N.; Cao, B.; Judd, O. H.; Bhattacharyya, I.; Jarrold, M. F. J. Chem. Phys. 2010, 132, 034302. (15) Hock, C.; Strassburg, S.; Haberland, H.; Issendorff, B. V.; Aguado, A.; Schmidt, M. Phys. Rev. Lett. 2008, 101, 023401. (16) Cao, B.; Strace, A. K.; Judd, O. H.; Bhattacharyya, I.; Jarrold, M. F.; Lopez, J. M.; Aguado, A. J. Am. Chem. Soc. 2010, 132, 12906. (17) Cao, B.; Strace, A. K.; Neal, C. M.; Jarrold, M. F.; N o~ nez, S.; Lopez, J. M.; Aguado, A. J. Chem. Phys. 2008, 129, 124709. (18) Neal, C. M.; Strace, A. K.; Jarrold, M. F. J. Phys. Chem A 2007, 111, 8056. (19) Breaux, G. A.; Neal, C. M.; Cao, B.; Jarrold, M. F. Phys. Rev. B 2005, 71, 073410. (20) Breaux, G. A.; Benirschke, R. C; Sugai, T.; Kinnear, B. S.; Jarrold, M. F. Phys. Rev. Lett. 2003, 91, 215508. (21) Breaux, G. A.; Cao, B.; Jarrold, M. F. J. Phys. Chem. 2005, 109, 16575. (22) Li, R.; Owen, J. H. G.; Kusano, S.; Miki, K. Appl. Phys. Lett. 2006, 89, 073116. (23) Krishnamurty, S.; Chacko, S.; Kanhere, D. G.; Breaux, G. A.; Neal, C. M.; Jarrold, M. F. Phys. Rev. B 2006, 73, 045406. (24) Breaux, G. A.; Benirschke, R. C; Jarrold, M. F. J. Chem. Phys. 2004, 121, 6502. (25) Neal, C. M.; Starace, A. K.; Jarrold, M. F. J. Am. Soc. Mass Spectrom. 2007, 18, 74. (26) Zorriasatein, S.; Lee, M.-S.; Kanhere, D. G. Phys. Rev. B 2007, 76, 165414. (27) Ghazi, S. M.; Lee, M.-S.; Kanhere, D. G. J. Chem. Phys. 2008, 128, 104701. (28) Chacko, S.; Joshi, K.; Kanhere, D. G. Phys. Rev. Lett. 2004, 92, 135506. (29) Neal, C. M.; Starace, A. K.; Jarrold, M. F.; Joshi, K.; Krishnamurti, S.; Kanhere, D. G. J. Phys. Chem. C 2007, 111, 17788. (30) Ding, F.; Rosen, A.; Bolton, K. Phys. Rev. B 2004, 70, 075416. € g€ut, S.; Chelikowsky, J. R.; Ho, K. M. (31) Chuang, F.; Wang, C. Z.; O Phys. Rev. B 2004, 69, 165408.
Figure 8. The radial distribution function calculated for Ga27Si3 for five different temperatures. The evolution from a (mainly) three peaked structure to a featureless single peak one is clearly evident. The cluster is completely liquid-like at about 700 K.
’ SUMMARY AND CONCLUSION We have presented the ground state geometry, a few low energy isomers, and finite temperature properties of Ga27Si3 using density functional molecular dynamics. The results clearly show the effect of doped silicon atoms on the specific heat of Ga30. In contrast to the pure gallium cluster (Ga30), the doped cluster Ga27Si3 undergoes a solid-like to liquid-like transition at 500 K, identified by a clear peak in the specific heat. The melting occurs in two steps. In the first step the gallium atoms melt at around 500 K. This is followed by the second step where silicon atoms melt around 660 K. The impurity induces more order in the ground state geometry. The structure of Ga30 changes from C1 symmetry to C2v in Ga27Si3. The ELF analysis reveals formation of a large basin of gallium atoms at a high value of ELF. The present work brings out two facts. First, if the dopant changes the geometry of the host to a more ordered one, then the resulting cluster will have a well-defined melting peak. Second, if after doping, the binding energy per atom increases, as is the case here, then it is likely to lead to a higher melting temperature. It must be noted that these preliminary conclusions need to be made more definitive by systematic investigations on more impurity-host systems. The present work has been carried out within the framework of density functional molecular dynamics. In the present context it may be noted that the specific heat curve for Ga30 shows a weak peak, not seen in the experimental data. However, the method has successfully brought out the dramatic size sensitive effect (and the underlaying physics) on the specific heat curves of Ga30 when one atom is added to it.10 The present work is a step toward the desired objective to have a predictive power for tuning the melting temperature by use of suitable dopants. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (S.M.G.);
[email protected] (D.G.K.). 16
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dx.doi.org/10.1021/jp2034505 |J. Phys. Chem. A 2012, 116, 11–17
