Dendritic Crystals - American Chemical Society

Nov 14, 2008 - Jingjing Ma,† Hua Jin,† Xiaoyang Liu,*,† Michael E. Fleet,‡ Jixue Li,† ... Jilin UniVersity, 2699 Qianjin Street, Changchun, ...
1 downloads 0 Views 2MB Size
CRYSTAL GROWTH & DESIGN

Selective Synthesis and Formation Mechanism of TiS2 Dendritic Crystals Jingjing Ma,† Hua Jin,† Xiaoyang Liu,*,† Michael E. Fleet,‡ Jixue Li,† Xuejing Cao,† and Shouhua Feng†

2008 VOL. 8, NO. 12 4460–4464

State Key Laboratory of Inorganic Synthesis and PreparatiVe Chemistry, College of Chemistry, Jilin UniVersity, 2699 Qianjin Street, Changchun, 130012, People’s Republic of China, and Department of Earth Sciences, UniVersity of Western Ontario, London, Ontario N6A 5B7, Canada ReceiVed April 4, 2008; ReVised Manuscript ReceiVed August 28, 2008

ABSTRACT: High-purity TiS2 dendritic crystals have been selectively synthesized via an easy and simple CVT (chemical vapor transport) process using only inorganic reagents. Reaction temperature and duration are the most important factors controlling the morphologies of TiS2 dendrites. Instead of using organic reagents as templates to induce the self-assembly of inorganic molecules, a simple CVT process was adopted to realize the hierarchical self-assembly of inorganic molecules via transport in a sulfur-rich atmosphere far from thermodynamic equilibrium conditions. The phase structures and morphologies of the TiS2 products were characterized by XRD, polarized-light microscopy, SEM, and TEM. All microscopic observations not only indicate a dendritic morphology but also provide direct evidence for the growth process of TiS2 dendrites. The formation mechanism for TiS2 fractals is further investigated and discussed on the basis of the experimental results. Introduction One of the active research topics of the past few years has been the investigation of the synthesis and formation mechanism of fractal crystals. Fractal structures are common in nature across all length scales, from self-assembled molecules, to the shapes of coastlines, to the distribution of galaxies, and even to the three-dimensional shapes of clouds. On the nanoscale, dendritic fractals are one type of hyperbranched structure which are generally formed by hierarchical self-assembly under nonequilibrium conditions.1,2 Hierarchical self-assembly of nanoscale building blocks (nanoparticles, nanoclusters, nanowires, etc.) is a technique for building functional electronic and photonic nanodevices.3,4 Investigation of hierarchically self-assembled fractal patterns in chemical systems has shown that the distinct size, shape, and chemical functionality of such structures make them promising candidates for the design and fabrication of new functional nanomaterials.5,6 As a result, various fractal structures have been obtained based on Ag dendrites.6-17 Also, organic reagents are widely used in dendrite synthesis because their molecular configurations are ready templates for the formation of fractal structures. On the other hand, various sulfide nanomaterials such as nanowires, nanobelts, and nanotubes have been synthesized in the past two decades because of their low dimensionality and high aspect ratio, as well as their unusual physical properties.15-31 However, it is still challenging to develop simple and novel synthetic approaches for building hierarchically self-assembled fractal architectures of sulfide nanomaterials, and only a few successful examples have been reported. For instance, PbS dendritic nanostructures were first synthesized through a hydrothermal process in the presence of N-cetyl-N,N,N-trimethylammonium bromide (CTAB) as a surfactant.15 In addition, rodbased PbS dendrites with different morphologies have been obtained via a solvothermal process.16 Single-crystal Sb2S3 dendrite-like superstructures have also been successfully syn* Corresponding author. Telephone/fax: +86-431-8516-8316. E-mail: [email protected]. † Jilin University. ‡ University of Western Ontario.

thesized through a precursor-solvothermal-pyrolysis route at ∼160 °C.17 Note that organic reagents or solvents have been widely used to assist growth of sulfide dendrites in all these reports. To the best of our knowledge, the preparation of sulfide dendrites using only inorganic reagents remains poorly studied and no successful example has been reported. Layered titanium disulfide TiS2 is of interest to us because TiS2 compounds have a high energy of formation for the intercalation compounds, and show potential low-cost, highcapacity, good-reversibility properties as the cathode materials of Mg ion batteries32 and high energy lithium rechargeable batteries.33,34 Also, TiS2 is more electron beam sensitive than other analogous metal sulfides such as HfS2 and ZrS2.35 However, the specific applications of such nanomaterials in fractal structures is still under research. Some synthetic methods for preparing TiS2 have been developed. Thin films of TiS2 were first obtained by thermal chemical vapor deposition (CVD), by reacting TiCl4 and a series of sulfur sources,36 and they were also obtained from metal-organic precursors.37 TiS2 nanotubes have been synthesized via reaction of TiCl4, H2, and H2S at 450 °C.38 Furthermore, Wu and Seo synthesized TiS2 compounds with TiO2 powder and mixtures of boron and sulfur as starting materials through a solid-gas metathetical reaction,39 but the morphology of these compounds was not reported. However, to the best of our knowledge, TiS2 fractal nanocrystals have not been synthesized. Herein we report the spontaneous hierarchical self-assembly of high-purity TiS2 dendrites via a simple CVT (chemical vapor transport) process using only inorganic reagents, yielding product dendrites large enough to be used directly in electrical and electronic applications, and we discuss the growth mechanism of the TiS2 dendrites, combining diffusion limited aggregation (DLA)40 and nucleation limited aggregation (NLA)41 models for the first time. Experimental Section TiS2 dendritic crystals were prepared by direct reaction of titanium and sulfur within evacuated sealed quartz-glass tubes with a diameter of 10 mm and a length of 170 mm. Titanium sponge (99.7%; Alfa Aesar) and sulfur sublimate (99.99%; Aldrich) were used as the titanium and sulfur sources, respectively. Charges, consisting of about 1 g of

10.1021/cg800348y CCC: $40.75  2008 American Chemical Society Published on Web 11/14/2008

Synthesis of TiS2 Dendritic Crystals

Crystal Growth & Design, Vol. 8, No. 12, 2008 4461

Figure 2. EDX analysis of TiS2 fractals.

Figure 1. XRD patterns of Ti-S products obtained at different reaction temperatures. (a) Monoclinic TiS3 nanobelts synthesized at 600 °C. (b) TiS2 powder obtained at 700 °C. (c) Hexagonal TiS2 dendritic crystals synthesized at 800 °C confirming formation of a pure TiS2 phase. starting composition in the stoichiometric proportion of TiS2, were loaded in a quartz-glass tube closed at one end using a long-stemmed funnel. Then the tube with starting materials was evacuated and sealed, and heated in a horizontal tube furnace. The synthesis was achieved by establishing a temperature gradient of 80-100 °C along the tube with the starting mixture at the hot end. TiS2 dendrites formed at the cool end when charges were heated at 800 °C. The TiS2 dendrites began to form after being heated at 800 °C for 48 h, but the optimum reaction time was around 15 days. When the temperature was set below 800 °C but above 700 °C, a powder of poorly crystallized TiS2 was synthesized at the hot end. Temperatures above 600 °C but below 700 °C tended to produce a mixture of TiS2 powder and crystals of TiS2. TiS3 fibers formed at the cool end when charges were heated at 600 °C with excess sulfur: TiS3 undergoes peritectic decomposition (to TiS2 + native sulfur) at 632 °C, 8.95 atm. In addition, high temperature (>800 °C) frequently led to explosive tube failure.

Results and Discussion The products were characterized by X-ray diffraction (XRD; using a SIEMENS D5005 diffractometer with a graphite monochromator), scanning electron microscopy (SEM; JEOL Ltd. JSM-6700F), transmission electron microscopy (TEM; JEOL Ltd. JEM-3010), and polarized-light microscopy (Olympus BX51). The XRD pattern of the product (Figure 1c) is consistent with pure TiS2 (JCPDS No. 15-0853), with hexagonal unit cell parameters a ) 3.3961(5) Å and c ) 5.6964(9) Å. The diffraction peaks are sharp and strong, confirming that the products are pure phases and well crystallized. The XRD pattern also indicates that the [001] direction should be the preferred direction of growth for the TiS2 dendrites. In order to further demonstrate the purity and perfect crystallization of the products, the XRD patterns of two other samples obtained at different temperatures via the same CVT process are given (Figure 1a,b). The products synthesized at 600 °C (Figure 1a) were confirmed to be pure TiS3 nanobelts,42 while 700 °C tended to produce TiS2 powder of inferior crystal quality (Figure 1b). Therefore, the optimum reaction temperature for TiS2 dendrites appears to be about 800 °C. EDX (energy dispersive X-ray spectroscopy) was performed on samples during high-resolution TEM measurements. The EDX spectrum for the dendrite fractals is shown in Figure 2,

Figure 3. Appearance of TiS2 fractals in polarized-light microscopy. (a, b) TiS2 dendrites synthesized at 800 °C and 2 days duration showing their relatively symmetric structure. (c) Section of quartz tube used for synthesizing TiS2 dendrites in an experiment of 2 days duration revealing that the TiS2 golden crystal laminae were grown with crystallographic c-axis perpendicular to the inside wall of the quartz tube at the cool end. (d-f) TiS2 crystal laminae obtained at 800 °C and 2 days indicating their random morphology and sufficient size for direct use in applications.

and yielded a composition very close to the stoichiometric 1:2 proportion for TiS2. Using polarized-light microscopy, the TiS2 crystals synthesized at 800 °C for 48 h are golden with a metallic luster and dendritic habit (Figure 3a,b). A typical image taken at the tip of the dendrite (Figure 3b) reveals both the symmetrical dendritic modality and a layered structure, in agreement with the strong preferred orientation indicated by the bulk XRD pattern (Figure 1c). Figure 3c shows part of a quartz tube used for synthesizing TiS2 dendrites; the TiS2 golden crystal laminae grow preferentially with the crystallographic c-axis perpendicular to the inside wall of the quartz tube at the cool end for heating at 800 °C and 48 h, consistent with the XRD result. In order to understand the growth mechanisms of TiS2 dendrites, control experiments of differing duration were conducted. Figure 3d-f shows the

4462 Crystal Growth & Design, Vol. 8, No. 12, 2008

Ma et al.

Figure 4. Low-magnification SEM images of TiS2 products synthesized via a simple CVT process of Ti and S at 800 °C. (a) Tip of TiS2 dendrites showing both the smooth laminar crystal faces and a layered structure with average thickness of 20 nm. (b) TiS2 powder obtained at 700 °C showing porous and pockmarked laminar faces. (c-f) Typical TiS2 dendritic crystals grown at 800 °C and 15 days providing direct evidence for their growth process.

morphology of TiS2 crystal laminae obtained at 800 °C for 15 days. TiS2 crystal laminae with rounded edges and without symmetrical structures are evidently cumulated layer by layer as shown in Figure 3d. The TiS2 crystal lamina in Figure 3e is close to 0.5 × 0.5 mm2 in surface area and, thus, is apparently suitable without further treatment as a functional material in electrical devices. By magnifying the selected area of Figure 3e, the clear junction and some growth marks of TiS2 crystal laminae are revealed (Figure 3f). With the evolution of the morphology of TiS2 crystals through the patterns (Figure 3a,d,e), we speculate that TiS2 dendrites may tend to associate with each other to form TiS2 crystal laminae, with area increasing with increase in reaction time (from 2 to 15 days). The morphology of TiS2 dendritic crystals obtained by heating at 800 °C for 15 days was further investigated by SEM. The SEM image taken at the tip of the TiS2 dendrites (Figure 4a) indicates both the smooth laminar crystal faces and the layered structure of the crystal; the average thickness of these layers is around 20 nm. Compared with the smooth laminar crystal faces of TiS2 dendrites, the crystal faces of TiS2 powder are porous and pockmarked (Figure 4b), consistent with the XRD evidence. Figure 4c shows a clear and typical fractal structure of TiS2 dendritic crystals. By magnifying the selected area of the TiS2 dendrite in Figure 4c, some TiS2 monomers which were not crystallized completely can be found aggregating on the branches of the TiS2 dendrite in a common direction (Figure

Figure 5. TEM images of TiS2 dendrites synthesized at 800 °C with differing reaction duration also indicating the formation process of TiS2 fractal structures. (a, b) TiS2 dendrites obtained with reaction duration of 2 days revealing clear and well-defined dendritic fractal structures. (inset) The corresponding electron diffraction pattern confirms the single-crystal nature of the sample and can be indexed to a hexagonal structure consistent with the XRD result presented above. (c-f) TiS2 dendrites obtained with reaction duration of 15 days showing a more massive and random habit. (inset) The SAED pattern taken from these TiS2 nuclei showing that they are not single crystals related to fractal structures.

4d). Figure 4e is a representative image of the colonial dendrite structure. Many TiS2 dendritic crystals originate from a common point and grow outward to form TiS2 crystal laminae. An individual TiS2 dendrite (Figure 4f) reveals a more massive habit and a more random edge for TiS2 fractal structures. TEM images (Figure 5) provide further insight into the morphology of the TiS2 dendritic crystals. Samples obtained

Synthesis of TiS2 Dendritic Crystals

by heating at 800 °C for 2 days are shown in Figure 5a,b. Figure 5a reveals a clear and well-defined dendritic fractal structure with a pronounced trunk and highly symmetrical branches distributed on both sides of the trunk. The selected-area electron diffraction (SAED) pattern (inset) taken from the highly ordered TiS2 dendrites confirms the single-crystal nature of local areas of the samples and can be indexed on a wurtzite-structure lattice, consistent with the powder XRD result presented above. The diffraction pattern combined with the results of XRD and polarized-light microscopy also indicate that the dendrite is oriented parallel to (001), with the three branches along [100], [11j0], and [01j0]; the growth along the two lateral directions is much slower than along [11j0] because of spatial confinement. A single, incompletely developed TiS2 dendrite (Figure 5b) supports this presumption. Figure 5c-f shows the morphology of TiS2 dendrites synthesized at 800 °C for 15 days. Compared with the dendritic crystals heated for 2 days, TiS2 dendrites heated for 15 days have a more random morphology without highly symmetrical branches (Figure 5c). Note that globular particles aggregate on or around the branches of TiS2 dendrites, as is clearly shown by the images of Figure 5d,e; these appear to be poorly crystallized TiS2 monomers. Figure 5f shows that some of these globular particles nucleate dendrites. The SAED pattern (inset) taken from these particles demonstrates that they are not single-crystal dendrites and, therefore, do not represent fractal structures. The evolution from Figure 5b, Figure 5a, Figure 5c, to Figure 5d provides further evidence relating to the formation mechanism of TiS2 dendritic crystals. It is generally accepted that fractal aggregation arises in situations far from thermodynamic equilibrium where high driving forces lead to the generation of rough crystallites and random association.10 In recent decades, diffusion limited aggregation (DLA)40 and nucleation limited aggregation (NLA)41 models have been widely used to interpret various fractal phenomena. DLA43 is a deceptively simple process for growing clusters by capturing randomly diffusing particles. The underlying dynamics are as follows: initial seed particles (or row of particles) are placed on a lattice; additional particles are then injected, one at a time, at remote random locations, and allowed to wander randomly over the lattice nodes until a site adjacent to one already occupied is reached. When this happens, the particle joins the growing cluster. To accelerate growth rate without biasing cluster shape, either particles can be allowed to take larger steps when far from the cluster, or the injection points can be brought closer to the current cluster boundary.44 In contrast, Hu and Wang first described a new growth process in which fast growth along six crystallographically equivalent directions forms single-crystal dendrites or snowflake-like structures.6 In the present system, the formation of TiS2 dendritic crystals can be interpreted completely by neither the DLA model nor the new growth process. Instead, a combination of these two kinds of interpretation is the best explanation according to the results obtained from polarized-light microscopy, SEM, and TEM. Figure 6 is a schematic drawing revealing the formation of TiS2 dendrites, and this process should be divided into two steps. The first step is similar to that described in ref 6, and the correlated orientations of TiS2 dendritic crystals seem to play an important role in this step. As shown, for reasons of spatial confinement, the growth along one of the directions, for instance, [11j0], is much faster than along the other directions, and as a result, a needle is formed (Figure 6a). Subsequent growth along the other two crystallographically equivalent directions, [100] and [01j0], leads to the formation of main and symmetric

Crystal Growth & Design, Vol. 8, No. 12, 2008 4463

Figure 6. Proposed formation process of TiS2 dendritic crystals, which is best described by the combination of oriented growth (Ι) and DLA model (Π) according to the results obtained from polarized-light microscopy, SEM, and TEM.

branches on both sides (Figure 6b). As growth continues, each side branch can initiate growth along ([01j0] and ([100] to form minibranches (Figure 6c). With prolonged reaction (from 2 to 15 days duration), the correlated orientations of TiS2 dendrites seem to become weaker, accompanied by the strengthening of the nucleation-controlled aggregation process to form fractals (Figure 6d-g). At first, some TiS2 nuclei aggregate at the tips of TiS2 dendrites with highly ordered structure to form a much more random fractal instead of highly symmetrical branches (Figure 6d). With increase in the mobility and range of TiS2 monomers, more nuclei will be formed at dendrite tips. These random moving nuclei accumulate with each other to accelerate the growth of TiS2 dendrites with random morphology (Figure 6e), as in the DLA model. Then, the associated TiS2 dendrites reveal a more massive habit and a more random structure when large-scale TiS2 nuclei aggregate around them (Figure 6f). Finally, a whole TiS2 crystal lamina with random edge will be obtained via the further association and overlay of the associated TiS2 dendrites (Figure 6g). The TiS2 crystal lamina can surely be larger with prolonged reaction, and some of them are large enough (0.5 × 0.5 mm2) to be used directly in electrical and electronic applications. The random shape of each TiS2 crystal lamina has a fractal dimension which can be described by a Koch curve similar to that of coastlines. These

4464 Crystal Growth & Design, Vol. 8, No. 12, 2008

TiS2 crystal laminae are held together in the resulting fractal structure only by van der Waals forces. Conclusions In the past few years, various fractal structures had been obtained using organic reagents as templates to induce the selfassembly of inorganic molecules.6-17 In this study, instead of using organic reagents, we adopted a simple CVT method to realize the hierarchical self-assembly of inorganic molecules by transport in a sulfur-rich atmosphere, under conditions far from thermodynamic equilibrium. High-purity TiS2 dendritic crystals have been selectively synthesized via an easy and simple CVT process using only inorganic reagents. For the synthetic process, reaction temperature and duration are the most important factors controlling the morphologies of TiS2 dendrites. Therefore, establishing these parameters and the relationship between them are key points for the synthesis of metal sulfides with fractal structures via this simple CVT method. Moreover, this general approach could be adapted to the large-scale, high-purity growth of dendritic fractal structures of a wide range of materials because of its high yield, simple reaction apparatus, and favorable atmosphere for forming fractals. The resulting TiS2 golden crystal laminae are large enough (≈0.5 × 0.5 mm2 in surface area) to be used directly in electrical and electronic applications. Also, they are expected to present more novel physical properties and applications in practice, and further research is now in progress in our laboratory. Acknowledgment. This work was supported by the Natural Sciences Foundation of China (Nos. 20471022, 40673051, and 20121103) and NCET.

References (1) (a) Lisiecki, I.; Albouy, P. A.; Pileni, M. P. AdV. Mater. 2003, 15, 712. (b) Witten, T. A., Jr.; Sander, L. M. Phys. ReV. Lett. 1981, 47, 1400. (2) Meakin, P. Phys. ReV. Lett. 1983, 51, 1119. (3) Whetten, R. L.; Khoury, J. T.; Alvarez, M. M.; Murthy, S.; Vezmar, I.; Wang, Z. L.; Cleveland, C. C.; Luedtke, W. D.; Landman, U. AdV. Mater. 1996, 8, 428. (4) Sun, S.; Murray, C. B.; Weller, D.; Folks, L.; Moser, A. Science 2000, 287, 1989. (5) Yang, P. D.; Deng, T.; Zhao, D. Y.; Feng, P. Y.; Pine, D.; Chmelka, B. F.; Whitesides, G. M.; Stucky, G. D. Science 1998, 282, 2244. (6) Cao, M. H.; Liu, T. F.; Gao, S.; Sun, G. B.; Wu, X. L.; Hu, C. W.; Wang, Z. L. Angew. Chem., Int. Ed. 2005, 44, 4197. (7) (a) Selvan, S. T. Chem. Commun. 1998, 351. (b) Wang, X. Q.; Naka, K.; Itoh, H.; Park, S.; Chujo, Y. Chem. Commun. 2002, 1300. (8) (a) Xiao, J. P.; Xie, Y.; Tang, R.; Chen, M.; Tian, X. B. AdV. Mater. 2001, 13, 1887. (b) Zhou, Y.; Yu, S. H.; Wang, C. Y.; Li, X. G.; Zhu, Y. R.; Chen, Z. Y. AdV. Mater. 1999, 11, 850. (9) Wang, M.; Zhong, S.; Yin, X. B.; Zhu, J. M.; Peng, R. W.; Wang, Y.; Zhang, K. Q.; Ming, N. B. Phys. ReV. Lett. 2001, 86, 3827.

Ma et al. (10) Wang, M.; Liu, X. Y.; Strom, C. S.; Bennema, P.; Enckevort, W.; Ming, N. B. Phys. ReV. Lett. 1998, 80, 3089. (11) Zhu, J.; Liu, S.; Palchik, O.; Koltypin, Y.; Gedanken, A. Langmuir 2000, 16, 6396. (12) (a) Tian, Z. G. R.; Liu, J.; Voigt, J. A.; Xu, H. F.; Mcdermott, M. J. Nano Lett. 2003, 3, 89. (b) Parfenov, A.; Gryczynski, I.; Malicka, J.; Geddes, C. D.; Lakowicz, J. R. J. Phys. Chem. B 2003, 107, 8829. (13) Peng, Q.; Dong, Y. J.; Deng, Z. X.; Li, Y. D. Inorg. Chem. 2002, 41, 5249. (14) Xie, S. H.; Zhou, W. Z.; Zhu, Y. Q. J. Phys. Chem. B 2004, 108, 11561. (15) Kuang, D. B.; Xu, A. W.; Fang, Y. P.; Liu, H. Q.; Frommen, C.; Fenske, D. AdV. Mater. 2003, 15, 1747. (16) Wang, D. B.; Yu, D. B.; Shao, M. W.; Liu, X. M.; Yu, W. C.; Qian, Y. T. J. Cryst. Growth 2003, 257, 384. (17) Mo, M. S.; Zhu, Z. Y.; Yang, X. G.; Liu, X. Y.; Zhang, S. Y.; Gao, J.; Qian, Y. T. J. Cryst. Growth 2003, 256, 377. (18) Duan, X.; Huang, Y.; Agarwal, R.; Lieber, C. M. Nature 2003, 421, 241. (19) Ye, C. H.; Meng, G. W.; Jiang, Z.; Wang, Y. H.; Wang, G. Z.; Zhang, L. D. J. Am. Chem. Soc. 2002, 124, 15180. (20) Chen, C.; Gao, W.; Qi, Z.; Hu, W.; Qu, M. J. Appl. Phys. 1991, 70, 6277. (21) Chen, C.; Qu, M.; Hu, W.; Zhang, X.; Lin, F.; Hu, H. J. Appl. Phys. 1991, 69, 6114. (22) Pasquariello, D. M.; Kershaw, R.; Passaretti, J. D.; Dwight, K.; Wold, A. Inorg. Chem. 1984, 23, 872. (23) Li, Y. D.; Li, X. L.; He, R. R. J. Am. Chem. Soc. 2002, 124, 1411. (24) Margolin, A.; Rosentsveig, R.; Albu-Yaron, A.; Popovitz-Biro, R.; Tenne, R. J. Mater. Chem. 2004, 14, 617. (25) Oshima, K.; Yokoyama, M.; Hinode, H.; Wakihara, M.; Taniguchi, M. J. Solid State Chem. 1986, 65, 392. (26) Sourisseau, C.; Gwet, S. P.; Gard, P.; Mathey, Y. J. Solid State Chem. 1988, 72, 257. (27) Gard, P.; Cruege, F.; Sourisseau, C.; Gorochov, O. J. Raman Spectrosc. 1986, 17, 283. (28) Li, Y. D.; Ge, J. P. Chem. Commun. 2003, 2498. (29) Cao, X. B.; Li, L. Y.; Xie, Y. J. Colloid Interface Sci. 2004, 273, 175. (30) Liang, H.; Shimizu, Y.; Sasaki, T.; Umehara, H.; Koshizaki, N. J. Phys. Chem. B 2004, 108, 9728. (31) Zhou, S. M.; Zhang, X. H.; Meng, X. M.; Fan, X.; Lee, S. T.; Wu, S. K. J. Solid State Chem. 2005, 178, 399. (32) Tao, Z. L.; Xu, L. N.; Gou, X. L.; Chen, J.; Yuan, H. T. Chem. Commun. 2004, 2080. (33) Whittingham, M. S. Science 1972, 192, 1126. (34) Chen, J.; Tao, Z. L.; Li, S. L. Angew. Chem., Int. Ed. 2003, 42, 2147. (35) Nath, M.; Rao, C. N. R. Angew. Chem., Int. Ed. 2002, 41, 3457. (36) Chang, H. S. W.; Schleich, D. M. J. Solid State Chem. 1992, 100, 62. (37) Cheon, J.; Gozum, J. E.; Girolami, G. S. Chem. Mater. 1997, 9, 1847. (38) Chen, J.; Li, S. L.; Tao, Z. L.; Gao, F. Chem. Commun. 2003, 980. (39) Wu, L. M.; Seo, D. K. J. Am. Chem. Soc. 2004, 126, 4676. (40) Halsey, T. C.; Duplantier, B.; Honda, K. Phys. ReV. Lett. 1997, 78, 1719. (41) Ming, N. B.; Wang, M.; Peng, R. W. Phys. ReV. B 1993, 48, 621. (42) Ma, J. J.; Liu, X. Y.; Cao, X. J.; Feng, S. H.; Fleet, M. E. Eur. J. Inorg. Chem. 2006, 3, 519. (43) (a) Gould, H.; Tobochnik, J. An Introduction to Computer Simulation Methods; Addison-Wesley: Reading MA, 1988. (b) Vicserk, T. Fractal Growth Phenomena; World Scientific: Singapore, 1989. (44) Bundle, A.; Havlin, S. Fractals in Science; Springer-Verlag: New York, 1991.

CG800348Y