J. Phys. Chem. B 2005, 109, 2703-2709
2703
Structure and Properties of ZnS Nanoclusters Said Hamad* and C. Richard A. Catlow DaVy Faraday Research Laboratory, The Royal Institution of Great Britain, 21 Albemarle Street, London W1S 4BS, United Kingdom
Eleonora Spano´ UniVersita´ de Milano Bicocca, Departamento di Scienza dei Materiali, Via R. Cozzi 53, 120125 Milano, Italy
Jon M. Matxain and Jesus M. Ugalde Kimika Fakultatea, Euskal Herriko Unibertsitatea, P. K. 1072, 20080 Donostia, Euskadi, Spain ReceiVed: July 30, 2004; In Final Form: October 20, 2004
Earlier studies have shown that the most stable structures for (ZnS)n clusters with n = 10-47 are hollow polyhedral clusters (“bubbles”). We report a detailed study of larger clusters, where n ) 50, 60, 70, and 80, for which onionlike or “double bubble” structures are predicted. We report calculations of the vibrational spectra and the electronic structure of bubble and double bubble clusters, which may assist in their experimental identification.
1. Introduction In recent years both II-VI and III-V semiconductors have been extensively studied because of their wide range of applications,1-3 deriving from the optical, electrical, and mechanical properties of the materials. There is, moreover, growing interest in the study of small clusters of these compounds.4-6 It is well-known that the transition from bulk systems to small clusters leads to substantial changes in physical and chemical properties,7,8 giving rise to unusual properties (such as the size quantization effect) that can lead to promising applications; but the understanding of these phenomena remains incomplete. More generally, since the discovery of fullerenes9 and carbon nanotubes,10 the exploration of the chemistry of nanoclusters with different chemical compositions has expanded rapidly; in particular, several studies have focused on the search for noncarbon nanotubes11 and fullerene-like structures.12,13 Boron nitride is one of the most widely investigated systems, since, owing to the similarity between B-N bonds and C-C bonds, BN can assume almost all the structures adopted by carbon: both diamond-like and graphite-like structures as well as BN nanotubes can be routinely synthesized.11,14 Fullerene-like BN cages have also been studied experimentally, revealing that they form onion structures, in which a small cage in the center in usually surrounded by three or more other cages,15 or isolated hollow cages as in the case of B24N24,16 B28N28,17 and B36N36.18 These fullerene-like structures show a B/N stoichiometry of ∼1; they are thought to be formed by an arrangement of hexagons and squares. Theoretical studies19 have also discussed the possibility of forming nonstoichiometric clusters, such as BxNx+4. These simulations stimulate the search for analogues in the II-VI and III-V compounds, although we note that the nature of the bonding in the latter differs from that in the C-C and B-N systems. ZnS nanocrystals have also been studied both theoretically and experimentally,20,21 showing an interesting range of phase transformations. * Corresponding author: fax (+44) 20-7629-3569; e-mail
[email protected].
ZnS is observed in nature in two polymorphs, zinc blende and wurzite, with cubic and hexagonal lattice structures, respectively, with atoms in the bulk of both polymorphs being four-coordinated, having tetrahedral coordination. Although the zinc blende phase is more stable than wurzite, it is common to find both in the same sample, and it is not clear what factors control which phase predominates. A variety of techniques have been used in order to understand the processes of nucleation and crystal growth,17,22 but up to now, only big clusters with bulklike structures have been found, which are far away from the initial stages of nucleation. Our study aims to throw light onto these interesting problems by examining a range of smaller clusters. We have therefore carried out a theoretical analysis with the aim of predicting the structure and stability of (ZnS)n nanoclusters with n ) 10-47, 50, 60, 70, and 80 ZnS units. The cluster structures are generated by a simulated annealing procedure employing classical molecular dynamics techniques, following which ab initio calculations have been used to refine the resulting models. We find that the previously reported tendency23 for small (ZnO)n and (ZnS)n clusters (n ) 10-15) to aggregate in open, hollow structures (subsequently denoted as “bubbles”) is also followed by the larger clusters (with n e 47). These clusters are formed by the spatial arrangement of 4-, 6-, and 8-atom rings. For clusters with n g 50 we have found onionlike structures, in which one bubble encloses another, which we denote as “double bubbles”. This paper therefore reports detailed models for the structures, stabilities, and properties of these clusters. 2. Computational Details Our calculations aimed to find the global minimum energy structures for the clusters studied, although no global optimization technique (Monte Carlo, fast annealing, genetic algorithm) is able unambiguously to discriminate between global and local minima. In the present work we employ a simulated annealing
10.1021/jp0465940 CCC: $30.25 © 2005 American Chemical Society Published on Web 01/22/2005
2704 J. Phys. Chem. B, Vol. 109, No. 7, 2005 technique, based on classical molecular dynamics. The molecular dynamics calculations have been performed with DL_POLY code,24 using the Born model interatomic potential developed in ref 25. We start the procedure by choosing randomly an initial configuration of the cluster we wish to minimize. The initial structure of the cluster is heated to a high temperature (3000 K). Regardless of the initial configuration, after 50 ps of dynamics, the Zn and S atoms adopt an irregular and very disordered arrangement; some ZnS units are isolated, while others form linear structures, similar to wires. As a result, there is no influence of the initial on the final structure. Following this initial 50 ps simulation, the temperature of the system is decreased by 10 K, and the system is allowed to evolve for another 50 ps, which is repeated until the temperature reaches the value of 300 K. As with any global optimization procedure, we cannot ensure that the final structure of the cluster is the global minimum configuration; it is possible that the system is trapped in a local minimum. We try to minimize the possibility of the latter by performing three different simulated annealing processes for each cluster. In some cases the final cluster structure is the same, regardless of the process, but in others cases each simulated annealing gives distinct, although very similar, final structures. In these cases we choose the most stable cluster configuration. Once the structure of a (ZnS)n cluster is determined by simulated annealing, two energy minimization techniques are employed to give an accurate value of the cluster energy. Optimization of the geometries by use of interatomic potentials is carried out with the GULP code,26 using the same interatomic potentials as employed in the molecular dynamics. The second technique employed is density functional theory (DFT), with the PW91exchange-correlation functional,27,28 as implemented in the DMol3 code.29,30 Effective core potentials model the 10 core electrons and a double numerical plus polarization basis set describes the valence electrons. We denote this calculation PW91/ecp-dnp. In a previous paper31 we showed that this level of theory gives the same results as B3LYP calculations. 3. Results and Discussion We have carried out an analysis of the structural, vibrational and energetic properties of the (ZnS)n clusters (for n ) 10-47, 50, 60, 70, and 80) obtained by the simulated annealing technique. 3.1.1. Structural Analysis: Cluster Structures. One of the most striking results of our study is the finding that ZnS clusters have a tendency to form very open bubble structures where all the atoms are three-coordinated. The bubble clusters are formed by 4-, 6-, and 8-atom rings with a shell-like arrangement, leaving a big hollow interior. The rings are nonplanar, nor are they regular polygons: bond angles and bond distances in the same ring differ from each other. The number of rings appearing in the different cluster structures can be predicted by the simple rules obtained from Euler’s law:
N6-ring ) n - 4 - 2N8-ring
N4-ring ) 6 + N8-ring (1)
which states that in a closed structure formed by polyhedra, the number of vertexes plus the number of faces will always equal the number of edges plus two. We note that these simple rules are more general than the previously described squarehexagon route, which is obtained for the cases where N8-ring ) 0. As the two equations contain three variables (the number of 4-, 6-, and 8-rings), the number of 8-rings could be regarded as a degree of freedom of the structures, and indeed, in some cases,
Hamad et al. we obtained different structures for a (ZnS)n cluster, which contained a different number of 8-rings. We usually find, however, that for a given (ZnS)n cluster, the lower the number of octagons, the more stable the structure. Figure 1 shows the structures of some representative bubble clusters. We reported the onionlike structure of (ZnS)60 in a previous paper.32 We now report three other new onionlike structures, denoted double bubbles: (ZnS)50, (ZnS)70, and (ZnS)80 (see Figure 2). They are the first ZnS structures obtained in which four-coordinated atoms appear, and there are bonds between the atoms of the inner and outer bubbles. (ZnS)50 is the smallest ZnS cluster in which an onionlike structure is found. The innermost cluster adopts the same structure as the configuration of the (ZnS)6 cluster found in vacuo, consisting of two 6-atom rings one on top of the other. The outer structure is a bubble with 44 ZnS units. The next double bubble found is the highly symmetric (ZnS)60, with an innermost (ZnS)12 cluster with the structure of a sodalite cage, which is the most stable in vacuo for that size. (ZnS)70 has the same cluster inside, but the outside bubble is larger, and we do not find the perfect matching between the two shells found in the (ZnS)60 cluster. The structure of the (ZnS)80 cluster shows a larger bubble inside, which is the same as that obtained for (ZnS)17. The outermost bubble is the largest found so far, with 63 ZnS units. 3.1.2. Structural Analysis: Radial Distribution Functions. The radial distribution function (RDF) gives us more detailed information on the geometrical properties of clusters. Analyses of the calculated RDFs are therefore reported for selected clusters, and comparisons are made with the RDFs of the bulk polymorphs. The Zn-S RDF in Figure 3 shows that the first neighbor Zn-S bond distances in the bubble clusters (≈2.25 Å) are shorter than in both bulk polymorphs ()2.34 Å), which is primarily a consequence of the lower coordination numbers in the clusters compared to the bulk. The Zn-S bond distances seem to be independent of the size of the bubbles, as there is no significant shift in the first neighbor peak with size. The double bubbles are the first clusters in which there are tetracoordinated atoms, which makes the atomic surroundings more similar to those found in the bulk structures. Note, however, that the Zn-S-Zn and S-Zn-S angles in the double bubbles vary between 100° and 125°, far away from the 109.5° corresponding to a tetrahedral arrangement. The network of four coordinated atoms clearly still needs to undergo substantial structural transformation in order to resemble either of the bulklike phases. Figure 3 also shows the Zn-Zn RDF of the same set of clusters. There is a peak at 3.75 Å, associated with the Zn-Zn distance in a 6-ring for both polymorphs, because both are formed by three-dimensional stacking of 6-rings. Since single and double bubble clusters have 6-rings in their structures, they also show a similar peak in the RDF. Double bubbles also have at least six 4-rings beside the 6-rings. These 4-rings contribute to the RDF with the first peak observed, at a distance of 3.15 Å. While the intensity of the second Zn-Zn peak seems to be constant for all the clusters, the first peak tends to decrease as the cluster size increases, since the ratio (number of 4-rings)/ (number of 6-rings) decreases with the cluster size. The Zn-Zn RDF of the (ZnS)12 cluster is quite different from the others, since (ZnS)12 is an unusual structure, in which all the Zn atoms are part of 4-rings as well as 6-rings, hence generating a shift of the first peak to a larger distance and the second to a shorter distance.
Structure and Properties of ZnS Nanoclusters
J. Phys. Chem. B, Vol. 109, No. 7, 2005 2705
Figure 1. Structures of selected bubble clusters. Light gray spheres refer to sulfide atoms and dark gray spheres to zinc atoms.
The Zn-Zn RDF of the (ZnS)60 cluster is similar to those of the other double bubbles and is shown in Figure 3. Remarkably, however, there is no sharp peak associated with the first neighbor. The first peak is very broad, spreading significantly in the range 3.4-3.7 Å, for which there are two reasons: (i) the structures are less spherical; they have more protuberances, which lead to some bent 6-rings in which the Zn-Zn distance decreases from 3.75 Å to the range previously noted; and (ii) the Zn atoms of the innermost bubbles do not necessarily form 4- or 6-rings with the atoms of the outermost bubbles; they form the bonding structure that minimizes the global energy, which results in the Zn-Zn distances between atoms in the two bubbles varying within the described range. It is interesting to note that, unlike the disorder associated with the first Zn-Zn neighbors, the second, third, and fourth neighbors show peaks that are similar to those found in the two bulk phases. 3.2. Vibrational Analysis. Here we present a vibrational analysis of the bubble structures and related bulklike clusters, by calculating harmonic frequencies at the PW91/ecp-dnp level of theory using the DMol3 code. These harmonic frequencies have been fitted with Lorentzian transformations in order to obtain theoretical IR spectra, which are comparable to the experimental IR spectrum. In Figure 4, the calculated spectra of the bubble clusters are displayed, showing the existence of a dominant peak at around 360 cm-1, the only significant peak
observed, which can be assigned to the motion of threecoordinated S atoms. The calculated spectra of selected bulklike clusters are also presented in Figure 4, showing clear differences with respect to the bubble structures, of which the main is that the spectra are much broader, with several peaks giving significant intensities. There is a peak with the same frequency as the dominant one for the bubble clusters (360 cm-1), which arises from the three-coordinated atoms that the clusters have in the outer regions. There is another prominent peak at around 320-330 cm-1, which is assigned to the vibrations of the four-coordinated atoms in the inner regions of the bulklike clusters. There are also some two-coordinated atoms that contribute to the broadening of the spectra in the region from 220 to 360 cm-1. Clearly, if clusters of this size can be synthesized, the vibrational spectra could help to determine the structures. In particular, if the lower frequency features in the range 200360 cm-1 were observed, bulklike structures would be indicated. The IR spectrum of the (ZnS)60 double bubble is shown in Figure 4. It has the same dominant peak associated with the vibrations of three-coordinated atoms that the bubble clusters have, at 360 cm-1, but also shows the peak associated with the vibrations of four-coordinated atoms, at 330 cm-1. The result is a spectrum that is more similar to the bulklike clusters than
2706 J. Phys. Chem. B, Vol. 109, No. 7, 2005
Hamad et al.
Figure 3. Zn-S and Zn-Zn radial distribution functions of representative single and double bubble clusters. For comparison, the RDFs of the two ZnS bulk phases are also plotted; the continuous vertical lines correspond to wurtzite and the discontinuous vertical lines to sphalerite.
energy, Enuc(n), defined as
Enuc(n) ) E(n) - E(n - 1) - EZnSbulk
(2)
where E(n) is the total energy of the (ZnS)n cluster and EZnSbulk is the energy per ZnS unit in the bulk sphalerite polymorph bulk. The nucleation energy gives information about the cluster growth. The more negative the nucleation energy for a given cluster, the more thermodynamically favorable is the addition of a ZnS unit. Figure 5 shows the variation of the nucleation energy as a function of the cluster size, calculated with two methods, pure DFT and interatomic potentials (IP) based calculations. Both methods give similar results. At the bottom of Figure 5 we can see the difference between the nucleation energies calculated with both methods:
∆Enuc(n) ) {Enuc(n)}IP - {Enuc(n)}pureDFT
Figure 2. Structures of the four bubble clusters studied. The complete structures are shown in the center of each panel, while the innermost and outermost clusters are shown below them.
to bubble clusters, which is not surprising, since this cluster has a network of four-coordinated atoms. 3.3. Relative Stability of the Bubble Clusters. To study the stability of clusters, we calculate the evolution of the nucleation
(3)
Two features are evident. The first is that the maximum difference in energy between both methods is smaller than 0.4 eV. The second is more significant: the plot of ∆Enuc(n) resembles the behavior of Enuc(n) itself. It is then possible to scale the values of {Enuc(n)}IP in order to give values closer to {Enuc(n)}pureDFT. The scaled nucleation energies are calculated by
{Enuc(n)}scaledIP ) A{Enuc(n)}IP + B
(4)
Structure and Properties of ZnS Nanoclusters
Figure 4. IR spectra of selected ZnS clusters. The top panel shows the spectra of three single bubbles and one double bubble. There is no trend followed as the cluster size increases; all clusters show a prominent peak at 360 cm-1. The main difference comes with the appearance of a second peak for the (ZnS)60 double bubble, due to the network of four coordinated atoms. The bottom panel presents the spectra of bulklike clusters.
where A and B are fitted constants, calculated by requiring that there are two points at which {Enuc(n)}IP ) {Enuc(n)}pureDFT. The election of these two points is almost irrelevant, so we chose n ) 10 and 12, which give the following values for the constants: A ) 0.66 and B ) 0.05. Figure 5 also shows the close similarity between the two curves: {Enuc(n)}scaledIP and {Enuc(n)}pureDFT are for all clusters; the difference is now less than 0.16 eV, which is small compared to the absolute values of the nucleation energies. The point of this analysis is that we may now use only interatomic potentials methods in order to calculate the nucleation energies for the bigger clusters, with an accuracy similar to that of the more time-consuming pure DFT calculations. Scaled nucleation energies of all the clusters are reported in Figure 6. The main characteristic is the oscillatory behavior with increasing size, rather than a constant trend. For example, the addition of a ZnS unit to the (ZnS)11 cluster is a thermodynamically favored process, as it leads to the highly symmetric and stable (ZnS)12 cluster. But the addition of a further ZnS unit to this cluster reduces its stability; there is a big change in the geometry, and the (ZnS)13 cluster is much less symmetric than (ZnS)12 (see Figure 1). This difference in stability is reflected in the high positive nucleation energy of (ZnS)13. Interestingly the highest peak in experimental mass spectra33,34 corresponds to the (ZnS)13 cluster, which our calculations predict to be one of the less stable clusters. This discrepancy could be the result
J. Phys. Chem. B, Vol. 109, No. 7, 2005 2707
Figure 5. (Top panel) Values of the nucleation energies for (ZnS)n clusters (n ) 11-20), calculated from eq 2. The difference between the values obtained with interatomic potentials (IP) and with pure density functional theory (DFT) is shown in the bottom panel. Note that that difference has a similar behavior to the nucleation energies, which allows us to scale the IP values to make them closer to the DFT ones, making use of the linear dependence expressed in eq 4. The top panel also shows the nucleation energies calculated after scaling of the IP values, which are now very close to the DFT ones.
Figure 6. Nucleation energies of (ZnS)n clusters (n ) 11-47) calculated with IP, after application of the scaling factors to correct them.
of not having identified the global minimum for the (ZnS)13 cluster. We therefore, carried out a more detailed investigation of this cluster, performing several simulated annealing calculations, which all generated the structure shown in Figure 1. As a final check, we also performed DFT calculations on several clusters, chosen by our chemical intuition (bulklike clusters, other bubble clusters, new mixtures), to investigate further the stability of clusters, and in all cases the low symmetry structure of Figure 1 was the most stable. An independent study
2708 J. Phys. Chem. B, Vol. 109, No. 7, 2005
Figure 7. Band gap energies of bubble, double bubble, and bulklike clusters, obtained with DFT calculations. The band gap energy of the bulk ZnS (3.6 eV) is set as the reference level. Bulklike clusters have smaller band gaps compared to bubble clusters, whose band gaps vary from 4.4 to 4.8 eV. As observed in other properties, the appearance of a network of four coordinated atoms in double bubble clusters induces a change in the band gap, making it lower and more stable with respect to the cluster size.
using genetic algorithms has also found the same cluster to be the most stable.35 A core-cage structure34 has been suggested for that cluster to explain its high stability in thermodynamic terms, but recent DFT calculations35 show that that structure is indeed less stable than the bubble cluster. All these facts suggest that kinetic factors might be responsible for the apparent discrepancy. Another interesting feature to note from Figure 6 is the parity of the maxima and minima. Most of the maxima correspond to (ZnS)n odd-numbered clusters, whereas the minima correspond to even values of n. The latter are more stable owing to their more symmetric structures. 3.4. Calculated Band Gaps. Many electrical and optical properties are directly related to the band gap. We have thus calculated their energies by use of PW91/ecp-dnp procedure, as the difference in energy between the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals. Although there are more elaborate definitions of the band gap, this simple formulation allows us to compute qualitatively the trend in band gap energy with cluster size. The experimental value for bulk ZnS is 3.6 eV, while our pure DFT calculations give an energy of 2.1 eV, a difference between calculated and experimental values that falls within the usual DFT errors when calculating band gap energies.36,37 We assume that this shift in the band gap energy is constant for any cluster, so we add a correction of 1.5 eV to all the calculated band gaps. Support for this procedure is provided by calculations of the smaller clusters by use of B3LYP functionals; the values of the calculated band gaps fall within 0.15 eV of those obtained from the PW91/ecp-dnp calculations plus energy shift, corroborating the validity of adding the energy correction. Figure 7 shows the band gap energies of some bubble, double bubble, and bulklike clusters as a function of the cluster size (including the 1.5 eV correction). The so-called quantum size effect results in the band gap of nanoparticles of many systems decreasing as the particle size increases. Of all the clusters, (ZnS)12 has the highest band gap, while (ZnS)80 has the lowest with a difference of 0.55 eV. With the exception of (ZnS)12, the band gap energies of the bubble clusters oscillate between 4.4 and 4.7 eV, and there is no clear
Hamad et al. trend with increasing cluster size, which suggests that the electronic structure of all the clusters is similar, with its characteristics being governed not by the cluster size but by the geometrical structure, which is the same in all: hollow clusters with three-coordinated atoms forming 4- and 6-rings. The band gap of the double bubble clusters is smaller than the band gap of the single bubble clusters, suggesting a change in the electronic structures of the clusters. The presence of a network of tetracoordinated atoms changes the electronic structure. Since there is not a clear trend of the band gap with respect to the cluster size, we can conclude that the small band gap of the double bubble clusters is due not to the quantum size effect but to the presence of the network of four-coordinated atoms. The band gap energies of some bulklike clusters are also shown in Figure 7. The most important feature observed is that bulklike clusters have smaller band gap energies than the bubble clusters, typically between 3.6 and 4 eV, with the exception of the bulklike (ZnS)13 cluster, whose band gap is similar to that of the (ZnS)13 bubble cluster of 4.43 eV. All these results suggest that the band gap would be another useful quantity indicative of the structure of these nanoclusters. 4. Conclusion The most important findings of our computational study are as follows: (i) The stability of bubblelike clusters for (ZnS)n is confirmed for n ) 10-80; double bubble structures predominate for the larger clusters. (ii) Experiments aiming to detect the presence of bubble clusters can use the Zn-Zn and Zn-S RDFs as evidence. A peak at the usual Zn-Zn first neighbors distance (3.75 Å), and an additional one at a shorter distance (around 3.15 Å) would suggest that small bubble clusters have been found. (iii) Measurements of the vibrational spectra may be able to distinguish between bubbles and bulklike clusters. There will be a strong peak at around 360 cm-1 in both cases, but the appearance of another peak at around 320 cm-1 would strongly suggest that four-coordinated atoms are present, as is the case of bulklike clusters or double bubbles. (iv) The nucleation energy changes with the cluster size, with no definite trend. Some clusters have much higher nucleation energies, which will have faster growth and therefore will be the predominant species. Clusters with even numbers of ZnS units tend to be more stable than odd-numbered clusters. (v) The band gap energy of the bubble clusters does not change significantly with the cluster size, as it appears to be dominated by the local coordination. The band gaps of the double bubbles are smaller than those of the single bubbles. Overall, our study reveals a fascinating and rich nanochemistry of these clusters, which would reward detailed experimental investigation. Acknowledgment. We thank Alexei Sokol for his invaluable help throughout this work. We are grateful to the European Union, framework 5, for supporting this work under the NUCLEUS project. We also thank EPSRC for provision of computational resources at the Royal Institution. References and Notes (1) O’Regan, B.; Graztel, M. Nature 1991, 353, 737. (2) Ishibashi, A. J. Crystal Growth 1996, 159, 555. (3) Hoffman, A. J.; Mills, G.; Yee, H.; Hoffmann, M. R. J. Phys. Chem. 1992, 96, 5546. (4) Matxain, J. M.; Mercero, J. M.; Fowler, J. E.; Ugalde, J. M. Phys. ReV. A 2001, 64, 053201.
Structure and Properties of ZnS Nanoclusters (5) Sa´nchez-Lo´pez, J. C.; Justo, A.; Fe´rnandez, A. Langmuir 1999, 15, 7822. (6) Albe, V.; Jouanim, C.; Bertho, D. J. Crystal Growth 1998, 184/ 185, 388. (7) Yoffe, A. D. AdV. Phys. 2001, 50, 1. (8) Hartke, B. Angew. Chem., Int. Ed. 2002, 41, 1468. (9) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (10) Iijima, S. Nature (London) 1991, 354, 51. (11) Chopra, N. G.; Luyken, R. J.; Cherrey, K.; Crespi, V. H.; Cohen, M. L.; Louie, S. G.; Zetti, A. Science 1995, 269, 966. (12) Parrilla, P. A.; Dillan, A. C.; Jones, K. M.; Riker, G.; Schulz, D. L.; Ginley, D. S.; Heben, M. J. Nature 1999, 397, 114. (13) Wootton, A.; Harrowell, P. J. Phys. Chem. B 2004, 108, 8412. (14) Golberg, D.; Bando, Y.; Eremets, M.; Takemura, K.; Kurashima, K.; Yusa, H. Appl. Phys. Lett. 1996, 69, 2045. (15) Golberg, D.; Bando, Y.; Sthe´phan, O.; Kurashima, K. Appl. Phys. Lett. 1998, 73, 2441. (16) Oku, T.; Nishiwaki, A.; Narita, I.; Gonda, M. Chem. Phys. Lett. 2003, 380, 620. (17) Luther, G. W.; Theberge, S. M.; Rickard, D. T. Geochim. Cosmochim. Acta 1999, 63, 3159. (18) Oku, T.; Narita, I.; Nishiwaki, A. J. Phys. Chem. Solids 2004, 65, 369. (19) Fowler, P. W.; Rogers, K. M.; Seifert, G.; Terrones, M.; Terrones, H. Chem. Phys. Lett. 1999, 299, 359. (20) Zhang, H.; Gilbert, B.; Huang, F.; Banfield, J. F. Nature 2003, 424, 1025.
J. Phys. Chem. B, Vol. 109, No. 7, 2005 2709 (21) Zhang, H.; Banfield, J. F. Nano Lett. 2004, 4, 713. (22) Eshuis, A.; Elderen, G. R. A. v.; Koning, C. A. J. Colloids Surf. A 1999, 151, 505. (23) Tozzini, V.; Buda, F.; Fasolino, A. Phys. ReV. Lett. 2000, 85, 4554. (24) Smith, W.; Forester, T. R. J. Mol. Graphics 1996, 14, 136. (25) Hamad, S.; Cristol, S.; Catlow, C. R. A. J. Phys. Chem. B 2002, 106, 11002. (26) Gale, J. D. J. Chem. Soc., Faraday Trans. 1997, 93, 629. (27) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (28) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (29) Delley, B. J. Chem. Phys. 1990, 92, 508. (30) Delley, B. J. Chem. Phys. 2000, 113, 7756. (31) Spano´, E.; Hamad, S.; Catlow, C. R. A. J. Phys. Chem. B 2003, 107, 10337. (32) Spano´, E.; Hamad, S.; Catlow, C. R. A. Chem. Commun. 2004, 864. (33) Burnin, A.; Belbruno, J. J. Chem. Phys. Lett. 2002, 362, 341. (34) Nirasawa, T.; Romanyuk, V. R.; Kumar, V.; Mamykin, S. V.; Tohji, K.; Jeyadevan, B.; Shinoda, K.; Kudo, T.; Terasaki, O.; Liu, Z.; Belosludov, R. V.; Sundararajan, V.; Kawazoe, Y. Nature 2004, 3, 99. (35) Woodley, S.; Sokol, A.; Catlow, C. R. A. Z. Anorg. Allg. Chem. 2004, 630, 2343. (36) Godby, R. W.; Schluter, M.; Sham, L. J. Phys. ReV. Lett. 1986, 56, 2415. (37) Godby, R. W.; Schluter, M.; Sham, L. J. Phys. ReV. Lett. 1988, 37, 10159.
