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Thermodynamic and kinetic competition in silver dendrite growth
Chemical Physics Letters 439 (2007) 204–208 www.elsevier.com/locate/cplett
Thermodynamic and kinetic competition in silver dendrite growth Jixiang Fang *, Hongjun You, Chao Zhu, Peng Kong, Miao Shi, Xiaoping Song, Bingjun Ding School of Science, State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Shann Xi 710049, People’s Republic of China Received 15 December 2006; in final form 1 February 2007 Available online 21 March 2007
Abstract An interesting morphological evolution process driven by a competition between the thermodynamic and kinetic factors is first experimentally observed in a replacement reaction. At relatively short reaction time, a kinetic factor driven by concentration gradient dominates the growth process and contributes to the formation of silver dendrite due to a non-equilibrium and anisotropic growth. While at longer reaction time, the small grains may have sufficient time to relax and transfer to the minimum energy position thus obtain a thermodynamically stable hexagonal plate-like silver nanostructures. The observation here provides a theoretical study system for a better understanding of the microscopic origin and morphological transition. 2007 Published by Elsevier B.V.
1. Introduction Fractal or dendritic patterns in an electrochemical deposition (ECD) has attracted much attention in physics and materials community since 1984, when Matsushita et al. observed that the patterns of electrodeposit look quite similar to those generated by a computer model known as diffusion-limited aggregation (DLA) [1,2]. Up to now, much effort has especially been devoted to establishing the relationship between cluster morphology and the growth mechanism from theoretical and experimental studies using different system such as ultra-high vacuum (UHV) chamber and ECD. Although, the DLA and the sequent noise reduction and curvature dependent sticking probabilities models are quite successful to interpret the growth mechanism, some apparent drawbacks such as failure on some realistic systems still exist [3–5]. The experimental exploration in ECD system on the point of the growth conditions influence on morphologies and their corresponding explanations also achieved some significant results [6–10]. However, most studies have focused on the large-scale structure of the deposits [11]. Therefore, many of questions concern*
Corresponding author. E-mail address: [email protected] (J. Fang).
0009-2614/$ - see front matter 2007 Published by Elsevier B.V. doi:10.1016/j.cplett.2007.03.046
ing the structure formation and transition between different growth morphologies and whether the transitions are driven by thermodynamic or kinetic factors have not so far been satisfactorily answered. To gain deep insights into these fundamental issues, an atomic-scale or nanoscale study is another opportunity. Recently, a series of important experiments were conducted at a highly ideal systemultra-high vacuum (UHV) chamber with in site scanning tunneling microscopy (STM) observation [12–15], which provides a better understanding for the microscopic origin of morphology transition and how this microscopic detail is transferred to the overall pattern shape. Recently, we observed, in the ECD system, a transition from fractal pattern to dendrite driven by a suggested oriented attachment mechanism, involving a grains rotation and realignment process that contribute to the formation of the final prefect single crystal silver nanostructures [16]. In this Letter, we demonstrate, at the nanoscale, the other interesting morphological evolution process driven by the competition between the thermodynamic and kinetic factors. 2. Experimental We have used an electrochemical cell that is similar to the literature reported [17]. The experiment experiences a
J. Fang et al. / Chemical Physics Letters 439 (2007) 204–208
two-dimensional deposition of Ag trees from a silver nitride water solution on a linear edge of a thin zinc plate. The detailed growth process could be found elsewhere [16]. Briefly, the replacement reaction was carried out on an electrochemical cell consisted of two glass plates separated by 1.5 mm and placed horizontally for CCD monitoring. The zinc plate is first treated by hydrochloric acid to remove surface contamination and rinsed by distilled water. Then the zinc plate is fixed at the bottom-center position on the glass and reacted with 200 Mm silver nitrate solution for different reaction time. The reaction time varies from 10 s to 200 s. The products remain on the substrate after cell rinsing, and can be used for further analysis. The morphologies and structures of the products are investigated by a FEI Sirion 200 FEG filed-emission scanning electron microscope (FE-SEM) and a Philips CM200 transmission electron microscopy (TEM). 3. Results and discussion The optical micrographs of fractal silver trees are shown in Fig. 1a, which corresponding silver ion concentrations are 200 mM. The deposits are standard fractal styles, which consist of a splitting tip and non-obvious backbones with a considerable number of irregular side branches. Fig. 1b presents a results of simulation by Monte Carlo method, which has great similarity to those observed in Fig. 1a.
Fig. 1. (a) The optical micrograph of fractal silver trees grown from zinc plate at 200 mM silver ion concentration. (b) The aggregation in the Monte Carlo simulation.
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One can found that some small trees at the bottom of silver trees do not grow forever when their neighbors flourish. This could be related with supply and diffusion of silver ions. The flourished dendrites always grow quickly and continuously contact the region of high silver ions concentration. While around small trees, there is not enough silver ions supply. Thus it cannot grow continuously. Fig. 2a demonstrates a typical SEM image of silver dendrites, exhibiting a single morphology with uniform feather-like branches. The individual dendrite length is about 5–10 lm and composed of symmetrical branches and leaves. Fig. 2b is an X-ray diffraction (XRD) pattern of silver dendrites synthesized at 200 mM silver nitrite (aq), indicating that the dendrites are of high crystallinity. The five diffraction peaks can be indexed to diffraction from the (1 1 1), (200), (2 2 0), (3 1 1) and (2 2 2) of face-centered cubic (fcc) silver (JCPDS Card File, 4-783). The refined lattice parameters a = 2.3588 is extracted from the XRD data, which is in good agreement with the literature ˚ [18]. value of a = 2.359 A The growth of the dendritic nanostructure is carefully followed by time-dependent process. As the replacement reaction proceeds, the initial silver dendrites will experience a morphological evolution and convert to some hexagon nanoplates. The TEM images of Fig. 3a–d detail the morphological evolution of silver dendrites that were prepared
Fig. 2. (a) Silver dendrites obtained from 200 mM silver nitrate (aq). (b) X-ray diffraction (XRD) pattern of sample (a).
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Fig. 3. The observed morphological evolution of silver dendrite prepared at 200 mM silver nitrate (aq): (a) 10 s, (b) 50 s, (c) 100 s and (d) 200 s.
at 200 mM silver nitrate (aq) for 10 s, 50 s, 100 s and 200 s reaction time, respectively. In the first 10 s, the branch tip presents round shape as shown in Fig. 3a. As the reaction time increases to about 50 s, the tips of silver dendrite partly convert their shape from round to hexagonal (Fig. 3b). When the reaction time reaches 100 s, nearly all the tips become hexagon as shown in Fig. 3c. One can found that the spacing of different branches obviously decreases as prolonging the reaction time according to the images of Fig. 3a–c. However, for the sample of 200 s reaction time, an interesting phenomenon that the sub-dendrite grows again from the corners of silver hexagonal plates as shown in Fig. 3d can be observed. We believe that the observations here imply a competition between thermodynamic and kinetic factors. For Step 1, defined as the evolution process that the dendrite with round tips convert to hexagonal pattern (Fig. 4a), the reaction system spontaneously engage in a transition from nonequilibrium to equilibrium as the reaction proceeds. At the early stage (e.g., within 10 s), the reaction process is dominated by a non-equilibrium condition, and a dendritic morphology is always formed. As the replacement reaction proceeds, the monomer concentration in some areas is consumed by the continuously growth of silver trees. If the reaction time is long enough, the monomer concentration could drop to such a level that the reaction process is dominated by quasi-equilibrium or equilibrium conditions. From a view of thermodynamics, the silver dendrite, by virtue of its extended surface, has a considerably increased surface energy in contrast to the equilibrium shape [17]. Therefore, the aggregation process of the dendritic silver, in a growth situation far from equilibrium, may be much faster than the relaxation process of the small grains [19], so the branch tip of silver dendrite presents a round shape.
Fig. 4. (a) The schematic morphology evolution process. (b) A silver dendrite with a hexagonal plate-like shape. (c) HRTEM image of silver hexagonal nanoplate. The inset is the SAED pattern of the blue circled area in Fig. 2b. The circled and boxed spots in the SAED pattern are indexed as {2 2 0} and formally forbidden 1/3 {4 2 2} Bragg reflections. (d) SEM images of hexagonal nanoplate viewed form the top-flat and side face. (e) Profile view and top view of a truncated tetrahedral crystal (1 1 1) oriented on the substrate.
As the reaction proceeds, the silver ion concentration around previous grains drops to a certain level, the small grains may have sufficient time to relax and transfer to the minimum energy position by the proposed oriented attachment mechanism [16], and thus the product exhibits the transition from dendrite to a more compact hexagonal structure. Therefore, a thermodynamically stable hexagonal structure is formed. In fact, the shape conversion for silver or gold reaction system has been observed by other groups [20–23]. For example, using a photoinduced method or Plasmon excitation, the silver nanospheres are prone to converting into triangular or truncated triangular (hexagonal) shapes [20,21]. Wang et al. well explains the nature of shape conversion of polyhedral nanocrystals and believes the shape conversion results from the ratio of the growth rate in the Æ1 0 0æ to that of the Æ1 1 1æ[22,23]. Xia et al. presents that, for a face-centered cubic (fcc) noble metal, the
J. Fang et al. / Chemical Physics Letters 439 (2007) 204–208
thermodynamically favorable shapes are truncated nanocubes and multiple twinned particles (MTPs) [24]. Crystalline structure and shape of the silver hexagonal nanoplates are studied further and shown in Fig. 4. A silver dendrite with a hexagonal plate-like shape is shown in Fig. 4b, and the corresponding SAED pattern from the blue circled area in Fig. 4b is shown in Fig. 4c. The electron beam is perpendicular to the flat surface of the nanoplate laying on the TEM grid. The circled and boxed spots in the SAED pattern are indexed as {2 2 0} and formally forbidden 1/3 {4 2 2} Bragg reflections, indicating that the flat surface of the disks is parallel to the (1 1 1) habit plane, the most stable crystal plane of silver. Fig. 4d shows an HRTEM image of the [1 1 1] orientated disk with the lattice ˚ and its flat (1 1 1) plane lying on TEM spacing of 2.498 A grid, which is consistent with the diffraction pattern given in Fig. 4c. Fig. 4e shows the SEM images of hexagonal nanoplate viewed form the top-flat and side face. One may find that the lateral faces of the hexagonal nanoplate are not perpendicular to the top and bottom faces. In previous work [25], the crystallography of the similar nanodisk is described as a flat nanocrystals sitting on (1 1 1) face, truncated by an extended (1 1 1) face on top and probably by three straight (1 1 1) faces at the edges and by three more or less extended (1 0 0) faces at the corners (top inset in Fig. 4f). Their outside shape then appears in top view as hexagonal or pseudo hexagonal with an aspect ratio between 4 and 5.5, as drawn in the bottom inset of Fig. 4f. For the Step 2, defined as the evolution process that the sub-dendrite grows out from the corners of the silver hexagonal plates, one may suggest that a kinetic process resume dominating the reaction. As the reaction proceeds, the growing region of the hexagonal plates has an opportunity to grain silver ions again due to concentration field oscillation or fluctuation caused by surface tension, eletroconvection or other factors. Once the hexagonal plate contact enough silver ions from the bulk solution of silver nitrate, the sub-dendrite may grow out from the corners of the silver hexagonal plates, because the concentration gradient at the corners of a faceted pattern is higher than that in the middle of the straight edge [26,27]. In the experiment, in order to generate an obvious concentration fluctuation, we add more 10 ml silver nitrate (aq) with same silver ion concentration (200 mM) into the reaction system which has experienced about 5 min and completely consumed silver ions. In the products obtained from above experimental design, the sub-dendrite is easy to be observed. Fig. 5a shows a significant result, where many of sub-dendrite grow out from the hexagonal silver plates. The magnified TEM images shown in Fig. 5b– e are the different areas in Fig. 5a. In Fig. 5b (red boxed area in a) and c (blue circled area in a) demonstrate two symmetrical side-branches which have the same distance to the tip of the silver dendrite. The circle area in Fig. 5b shows a bump at the corner of a hexagonal plate, implying the formation of sub-sprout. While some sub-sprouts have formed and grown up for the area as shown in Fig. 5c due
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Fig. 5. (a) TEM image of a silver dendrite with hexagonal structure and sub-dendrites. (b–e) The different areas of the silver dendrite shown in Fig. 3a, (f) the schematic diagram of fluid flow and the mass motion based on Refs. [27,28].
to the greater supply of silver ions comparing to the red boxed area in Fig. 5b. Comparing to the areas shown in Fig. 5b,c for a tip of silver dendrite as shown in Fig. 5d, the sub-dendrite has been developed at the corners of silver hexagonal plate due to the most opportunity to contact the silver ions from bulk solution. In addition, although the corners grow more rapidly than the center region of the hexagonal plate, we still can observe that some sub-sprouts grow out from the center region of hexagonal plate as shown in Fig. 5e. Fig. 5f presents a schematic diagram of fluid flow and the mass motion that have been reported by previous papers [28–31]. For a pattern as shown in Fig. 5f–I, the stream lines of the vortices are prone to converging to the corners of the hexagonal plate, so the region on the corners has more chance to grow. Consequently, the sub-sprouts grow out from the corners of hexagonal plate (Fig. 5f-II). In addition, a protrusion growth mode also contributes to finally formation of sub-dendrites [32]. To conclude, an interesting competition between the thermodynamic and kinetic factors in a replacement reaction is experimentally observed. At relatively short reaction time, a non-equilibrium and anisotropic growth controlled by a kinetic factor dominates the growth process and contributes to the formation of silver dendrite. By an experimental design of generating an obvious concentration
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fluctuation, the sub-dendrite can easy to obtain, which provide obvious evidence that the sub-dendrite growth is controlled by a kinetic factor. While at longer reaction time, the small grains may have sufficient time to relax and transfer to the minimum energy position thus obtain a thermodynamically stable hexagonal plate-like silver nanostructures. In these regard, the observation here provides a theoretical study system for a better understanding of the microscopic origin and morphological transition, and also clarifies the dominated factor between kinetic and thermodynamic for different reaction stages within a replacement reaction. This study also has a potential application on artificially fabricating multiple-functional complex three-dimensional nanostructures [33]. Acknowledgements This work was supported by the National Science Foundation of China (No. 50471033), and the Doctoral Foundation of Xi’an Jiaotong University (No. DFXJTU200512). References [1] J.S. Langer, Science 243 (3) (1989) 1150. [2] Vincent Fleury, Wesley A. Watters, Nature 416 (18) (2002) 716. [3] Vladislav A. Bogoyavlenskiy, Natasha A. Chernova, Phys. Rev. E 1629 (2000) 61. [4] Harald Burne, Surf. Sci. Rep. 121 (1998) 31. [5] M. Tasinkevych, J.M. Tavares, F. de los Santos, J. Chem. Phys. 064706 (2006) 124. [6] Mu Wang, Sheng Zhong, Xiaobo Yin, et al., Phys. Rev. Lett. 3827 (2001) 86. [7] Bin Sun, Xianwu Zou, Zhunzhi Jin, Phys. Rev. E 067202 (2004) 69. [8] Mu Wang, Naiben Ming, Phys. Rev. A R7898 (1991) 44. [9] Chang He Shang, Phys. Rev. B 13579 (1996) 53.
[10] C.M. Cronemberger, L.C. Sampaio, Phys. Rev. E 041403 (2006) 73. [11] F.A. Moller, J. Kintrup, A. Lachenwitzer, O.M. Magnussen, R.J. Behm, Phys. Rev. B 12506 (1997) 56. [12] K. Bromann, H. Brune, H. Roder, K. Kern, Phys. Rev. Lett. 677 (1995) 75. [13] J.H. Kang, X.Y. Zhang, Chem. Mater. 1318 (2006) 18. [14] S. Blerkamp, A. Thoma, C. Polop, G. Pirgy, U. Linke, T. Michely, Phys. Rev. Lett. 115503 (2006) 96. [15] S. Ogura, K. Fukutani, M. Matsumoto, T. Okano, M. Okada, T. Kawamura, Phys. Rev. B 125442-1 (2006) 73. [16] Jixiang Fang, Xiaoni Ma, Hanhui Cai, Xiaoping Song, Bingjun Ding, Yong Guo, Appl. Phys. Lett. 173104 (2006) 89. [17] Vincent Fleury, Nature 390 (1997) 145. [18] JCPDS, No. 40783. [19] Mu Wang, G. Wildburg, J.H. van Esch, P. Bennema, R.J.M. Nolte, H. Rinsdorf, Phys. Rev. Lett. 4003 (1993) 71. [20] Jin Rongchao, Cao Yunwei, Chad A. Mirkin, K.L. Kelly, Gerorge C. Schatz, J.G. Zheng, Science 1901 (2001) 294. [21] Rongchao Jin, Y. Charles Cao, Encai Hai, Gabridlla S. Metraux, George C. Schatz, Chad A. Mirkin, Nature 487 (2003) 425. [22] Z.L. Wang, J. Phys. Chem. B 1153 (2000) 104. [23] V. Germain, Jing Li, D. Ingert, Z.L. Wang, M.P. Pileni, J. Phys. Chem. B 8717 (2003) 107. [24] I. Whshio, Y.J. Xiong, Y.D. Yin, Y.N. Xia, Adv. Mater. 18 (2006) 1745. [25] Mathieu Maillard, Suzanne Giorgio, Marie-Paule Pileni, Ada. Mater. 1084 (2002) 14. [26] R.F. Xiao, J.I.D. Alexander, R. Rosenberger, Phys. Rev. A 1447 (1988) 38. [27] Jean-Marc Flesselles, Marcelo O. Magnasco, Albert Libchaber, Phys. Rev. Lett. 2489 (1991) 67. [28] V. Fleury, J.H. Kaufman, D.B. Hibbert, Nature 435 (1994) 367. [29] Mu Wang, Willem J.P. van Enchevort, Nai-ben Ming, Piet Bennema, Nature 438 (1994) 367. [30] Cheng Suan et al., Phys. Lett. A 237 (1998) 247. [31] Mu wang, Ru-Wen Peng, P. Bennema, Phil. May. A 71 (1995) 409. [32] A.R. Despic, J. Diggle, J.O.M. Bockris, J. Electrochem. Soc. 508 (1968) 5. [33] Kimberly A. Dick, Knut Deppert, Magnus W. Larsson, Thomas Martensson, Werner Seifert, L. Reine Wallenberg, Lars Samuelson, Nat. Mater. 3 (2004) 380.
Thermodynamic and kinetic competition in silver dendrite growth Jixiang Fang *, Hongjun You, Chao Zhu, Peng Kong, Miao Shi, Xiaoping Song, Bingjun Ding School of Science, State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Shann Xi 710049, People’s Republic of China Received 15 December 2006; in final form 1 February 2007 Available online 21 March 2007
Abstract An interesting morphological evolution process driven by a competition between the thermodynamic and kinetic factors is first experimentally observed in a replacement reaction. At relatively short reaction time, a kinetic factor driven by concentration gradient dominates the growth process and contributes to the formation of silver dendrite due to a non-equilibrium and anisotropic growth. While at longer reaction time, the small grains may have sufficient time to relax and transfer to the minimum energy position thus obtain a thermodynamically stable hexagonal plate-like silver nanostructures. The observation here provides a theoretical study system for a better understanding of the microscopic origin and morphological transition. 2007 Published by Elsevier B.V.
1. Introduction Fractal or dendritic patterns in an electrochemical deposition (ECD) has attracted much attention in physics and materials community since 1984, when Matsushita et al. observed that the patterns of electrodeposit look quite similar to those generated by a computer model known as diffusion-limited aggregation (DLA) [1,2]. Up to now, much effort has especially been devoted to establishing the relationship between cluster morphology and the growth mechanism from theoretical and experimental studies using different system such as ultra-high vacuum (UHV) chamber and ECD. Although, the DLA and the sequent noise reduction and curvature dependent sticking probabilities models are quite successful to interpret the growth mechanism, some apparent drawbacks such as failure on some realistic systems still exist [3–5]. The experimental exploration in ECD system on the point of the growth conditions influence on morphologies and their corresponding explanations also achieved some significant results [6–10]. However, most studies have focused on the large-scale structure of the deposits [11]. Therefore, many of questions concern*
Corresponding author. E-mail address: [email protected] (J. Fang).
0009-2614/$ - see front matter 2007 Published by Elsevier B.V. doi:10.1016/j.cplett.2007.03.046
ing the structure formation and transition between different growth morphologies and whether the transitions are driven by thermodynamic or kinetic factors have not so far been satisfactorily answered. To gain deep insights into these fundamental issues, an atomic-scale or nanoscale study is another opportunity. Recently, a series of important experiments were conducted at a highly ideal systemultra-high vacuum (UHV) chamber with in site scanning tunneling microscopy (STM) observation [12–15], which provides a better understanding for the microscopic origin of morphology transition and how this microscopic detail is transferred to the overall pattern shape. Recently, we observed, in the ECD system, a transition from fractal pattern to dendrite driven by a suggested oriented attachment mechanism, involving a grains rotation and realignment process that contribute to the formation of the final prefect single crystal silver nanostructures [16]. In this Letter, we demonstrate, at the nanoscale, the other interesting morphological evolution process driven by the competition between the thermodynamic and kinetic factors. 2. Experimental We have used an electrochemical cell that is similar to the literature reported [17]. The experiment experiences a
J. Fang et al. / Chemical Physics Letters 439 (2007) 204–208
two-dimensional deposition of Ag trees from a silver nitride water solution on a linear edge of a thin zinc plate. The detailed growth process could be found elsewhere [16]. Briefly, the replacement reaction was carried out on an electrochemical cell consisted of two glass plates separated by 1.5 mm and placed horizontally for CCD monitoring. The zinc plate is first treated by hydrochloric acid to remove surface contamination and rinsed by distilled water. Then the zinc plate is fixed at the bottom-center position on the glass and reacted with 200 Mm silver nitrate solution for different reaction time. The reaction time varies from 10 s to 200 s. The products remain on the substrate after cell rinsing, and can be used for further analysis. The morphologies and structures of the products are investigated by a FEI Sirion 200 FEG filed-emission scanning electron microscope (FE-SEM) and a Philips CM200 transmission electron microscopy (TEM). 3. Results and discussion The optical micrographs of fractal silver trees are shown in Fig. 1a, which corresponding silver ion concentrations are 200 mM. The deposits are standard fractal styles, which consist of a splitting tip and non-obvious backbones with a considerable number of irregular side branches. Fig. 1b presents a results of simulation by Monte Carlo method, which has great similarity to those observed in Fig. 1a.
Fig. 1. (a) The optical micrograph of fractal silver trees grown from zinc plate at 200 mM silver ion concentration. (b) The aggregation in the Monte Carlo simulation.
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One can found that some small trees at the bottom of silver trees do not grow forever when their neighbors flourish. This could be related with supply and diffusion of silver ions. The flourished dendrites always grow quickly and continuously contact the region of high silver ions concentration. While around small trees, there is not enough silver ions supply. Thus it cannot grow continuously. Fig. 2a demonstrates a typical SEM image of silver dendrites, exhibiting a single morphology with uniform feather-like branches. The individual dendrite length is about 5–10 lm and composed of symmetrical branches and leaves. Fig. 2b is an X-ray diffraction (XRD) pattern of silver dendrites synthesized at 200 mM silver nitrite (aq), indicating that the dendrites are of high crystallinity. The five diffraction peaks can be indexed to diffraction from the (1 1 1), (200), (2 2 0), (3 1 1) and (2 2 2) of face-centered cubic (fcc) silver (JCPDS Card File, 4-783). The refined lattice parameters a = 2.3588 is extracted from the XRD data, which is in good agreement with the literature ˚ [18]. value of a = 2.359 A The growth of the dendritic nanostructure is carefully followed by time-dependent process. As the replacement reaction proceeds, the initial silver dendrites will experience a morphological evolution and convert to some hexagon nanoplates. The TEM images of Fig. 3a–d detail the morphological evolution of silver dendrites that were prepared
Fig. 2. (a) Silver dendrites obtained from 200 mM silver nitrate (aq). (b) X-ray diffraction (XRD) pattern of sample (a).
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Fig. 3. The observed morphological evolution of silver dendrite prepared at 200 mM silver nitrate (aq): (a) 10 s, (b) 50 s, (c) 100 s and (d) 200 s.
at 200 mM silver nitrate (aq) for 10 s, 50 s, 100 s and 200 s reaction time, respectively. In the first 10 s, the branch tip presents round shape as shown in Fig. 3a. As the reaction time increases to about 50 s, the tips of silver dendrite partly convert their shape from round to hexagonal (Fig. 3b). When the reaction time reaches 100 s, nearly all the tips become hexagon as shown in Fig. 3c. One can found that the spacing of different branches obviously decreases as prolonging the reaction time according to the images of Fig. 3a–c. However, for the sample of 200 s reaction time, an interesting phenomenon that the sub-dendrite grows again from the corners of silver hexagonal plates as shown in Fig. 3d can be observed. We believe that the observations here imply a competition between thermodynamic and kinetic factors. For Step 1, defined as the evolution process that the dendrite with round tips convert to hexagonal pattern (Fig. 4a), the reaction system spontaneously engage in a transition from nonequilibrium to equilibrium as the reaction proceeds. At the early stage (e.g., within 10 s), the reaction process is dominated by a non-equilibrium condition, and a dendritic morphology is always formed. As the replacement reaction proceeds, the monomer concentration in some areas is consumed by the continuously growth of silver trees. If the reaction time is long enough, the monomer concentration could drop to such a level that the reaction process is dominated by quasi-equilibrium or equilibrium conditions. From a view of thermodynamics, the silver dendrite, by virtue of its extended surface, has a considerably increased surface energy in contrast to the equilibrium shape [17]. Therefore, the aggregation process of the dendritic silver, in a growth situation far from equilibrium, may be much faster than the relaxation process of the small grains [19], so the branch tip of silver dendrite presents a round shape.
Fig. 4. (a) The schematic morphology evolution process. (b) A silver dendrite with a hexagonal plate-like shape. (c) HRTEM image of silver hexagonal nanoplate. The inset is the SAED pattern of the blue circled area in Fig. 2b. The circled and boxed spots in the SAED pattern are indexed as {2 2 0} and formally forbidden 1/3 {4 2 2} Bragg reflections. (d) SEM images of hexagonal nanoplate viewed form the top-flat and side face. (e) Profile view and top view of a truncated tetrahedral crystal (1 1 1) oriented on the substrate.
As the reaction proceeds, the silver ion concentration around previous grains drops to a certain level, the small grains may have sufficient time to relax and transfer to the minimum energy position by the proposed oriented attachment mechanism [16], and thus the product exhibits the transition from dendrite to a more compact hexagonal structure. Therefore, a thermodynamically stable hexagonal structure is formed. In fact, the shape conversion for silver or gold reaction system has been observed by other groups [20–23]. For example, using a photoinduced method or Plasmon excitation, the silver nanospheres are prone to converting into triangular or truncated triangular (hexagonal) shapes [20,21]. Wang et al. well explains the nature of shape conversion of polyhedral nanocrystals and believes the shape conversion results from the ratio of the growth rate in the Æ1 0 0æ to that of the Æ1 1 1æ[22,23]. Xia et al. presents that, for a face-centered cubic (fcc) noble metal, the
J. Fang et al. / Chemical Physics Letters 439 (2007) 204–208
thermodynamically favorable shapes are truncated nanocubes and multiple twinned particles (MTPs) [24]. Crystalline structure and shape of the silver hexagonal nanoplates are studied further and shown in Fig. 4. A silver dendrite with a hexagonal plate-like shape is shown in Fig. 4b, and the corresponding SAED pattern from the blue circled area in Fig. 4b is shown in Fig. 4c. The electron beam is perpendicular to the flat surface of the nanoplate laying on the TEM grid. The circled and boxed spots in the SAED pattern are indexed as {2 2 0} and formally forbidden 1/3 {4 2 2} Bragg reflections, indicating that the flat surface of the disks is parallel to the (1 1 1) habit plane, the most stable crystal plane of silver. Fig. 4d shows an HRTEM image of the [1 1 1] orientated disk with the lattice ˚ and its flat (1 1 1) plane lying on TEM spacing of 2.498 A grid, which is consistent with the diffraction pattern given in Fig. 4c. Fig. 4e shows the SEM images of hexagonal nanoplate viewed form the top-flat and side face. One may find that the lateral faces of the hexagonal nanoplate are not perpendicular to the top and bottom faces. In previous work [25], the crystallography of the similar nanodisk is described as a flat nanocrystals sitting on (1 1 1) face, truncated by an extended (1 1 1) face on top and probably by three straight (1 1 1) faces at the edges and by three more or less extended (1 0 0) faces at the corners (top inset in Fig. 4f). Their outside shape then appears in top view as hexagonal or pseudo hexagonal with an aspect ratio between 4 and 5.5, as drawn in the bottom inset of Fig. 4f. For the Step 2, defined as the evolution process that the sub-dendrite grows out from the corners of the silver hexagonal plates, one may suggest that a kinetic process resume dominating the reaction. As the reaction proceeds, the growing region of the hexagonal plates has an opportunity to grain silver ions again due to concentration field oscillation or fluctuation caused by surface tension, eletroconvection or other factors. Once the hexagonal plate contact enough silver ions from the bulk solution of silver nitrate, the sub-dendrite may grow out from the corners of the silver hexagonal plates, because the concentration gradient at the corners of a faceted pattern is higher than that in the middle of the straight edge [26,27]. In the experiment, in order to generate an obvious concentration fluctuation, we add more 10 ml silver nitrate (aq) with same silver ion concentration (200 mM) into the reaction system which has experienced about 5 min and completely consumed silver ions. In the products obtained from above experimental design, the sub-dendrite is easy to be observed. Fig. 5a shows a significant result, where many of sub-dendrite grow out from the hexagonal silver plates. The magnified TEM images shown in Fig. 5b– e are the different areas in Fig. 5a. In Fig. 5b (red boxed area in a) and c (blue circled area in a) demonstrate two symmetrical side-branches which have the same distance to the tip of the silver dendrite. The circle area in Fig. 5b shows a bump at the corner of a hexagonal plate, implying the formation of sub-sprout. While some sub-sprouts have formed and grown up for the area as shown in Fig. 5c due
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Fig. 5. (a) TEM image of a silver dendrite with hexagonal structure and sub-dendrites. (b–e) The different areas of the silver dendrite shown in Fig. 3a, (f) the schematic diagram of fluid flow and the mass motion based on Refs. [27,28].
to the greater supply of silver ions comparing to the red boxed area in Fig. 5b. Comparing to the areas shown in Fig. 5b,c for a tip of silver dendrite as shown in Fig. 5d, the sub-dendrite has been developed at the corners of silver hexagonal plate due to the most opportunity to contact the silver ions from bulk solution. In addition, although the corners grow more rapidly than the center region of the hexagonal plate, we still can observe that some sub-sprouts grow out from the center region of hexagonal plate as shown in Fig. 5e. Fig. 5f presents a schematic diagram of fluid flow and the mass motion that have been reported by previous papers [28–31]. For a pattern as shown in Fig. 5f–I, the stream lines of the vortices are prone to converging to the corners of the hexagonal plate, so the region on the corners has more chance to grow. Consequently, the sub-sprouts grow out from the corners of hexagonal plate (Fig. 5f-II). In addition, a protrusion growth mode also contributes to finally formation of sub-dendrites [32]. To conclude, an interesting competition between the thermodynamic and kinetic factors in a replacement reaction is experimentally observed. At relatively short reaction time, a non-equilibrium and anisotropic growth controlled by a kinetic factor dominates the growth process and contributes to the formation of silver dendrite. By an experimental design of generating an obvious concentration
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fluctuation, the sub-dendrite can easy to obtain, which provide obvious evidence that the sub-dendrite growth is controlled by a kinetic factor. While at longer reaction time, the small grains may have sufficient time to relax and transfer to the minimum energy position thus obtain a thermodynamically stable hexagonal plate-like silver nanostructures. In these regard, the observation here provides a theoretical study system for a better understanding of the microscopic origin and morphological transition, and also clarifies the dominated factor between kinetic and thermodynamic for different reaction stages within a replacement reaction. This study also has a potential application on artificially fabricating multiple-functional complex three-dimensional nanostructures [33]. Acknowledgements This work was supported by the National Science Foundation of China (No. 50471033), and the Doctoral Foundation of Xi’an Jiaotong University (No. DFXJTU200512). References [1] J.S. Langer, Science 243 (3) (1989) 1150. [2] Vincent Fleury, Wesley A. Watters, Nature 416 (18) (2002) 716. [3] Vladislav A. Bogoyavlenskiy, Natasha A. Chernova, Phys. Rev. E 1629 (2000) 61. [4] Harald Burne, Surf. Sci. Rep. 121 (1998) 31. [5] M. Tasinkevych, J.M. Tavares, F. de los Santos, J. Chem. Phys. 064706 (2006) 124. [6] Mu Wang, Sheng Zhong, Xiaobo Yin, et al., Phys. Rev. Lett. 3827 (2001) 86. [7] Bin Sun, Xianwu Zou, Zhunzhi Jin, Phys. Rev. E 067202 (2004) 69. [8] Mu Wang, Naiben Ming, Phys. Rev. A R7898 (1991) 44. [9] Chang He Shang, Phys. Rev. B 13579 (1996) 53.
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