APPLIED PHYSICS LETTERS 93, 153115 共2008兲

Single crystal growth via a grain rotation mechanism within amorphous matrix Jixiang Fang,1,3,a兲 Peng Kong,1 Bingjun Ding,1 Xiaoping Song,1 Yong Han,2 Horst Hahn,3 and Herbert Gleiter3 1

School of Science, State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Shann Xi 710049, People’s Republic of China 2 Institute of Physical Research and Technology and Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA 3 Forschungszentrum Karlsruhe, Institut für Nanotechnologie, Karlsruhe 76021, Germany

共Received 27 April 2008; accepted 15 September 2008; published online 17 October 2008兲 The molecular dynamics simulations were applied to study the crystallization of Ag from an amorphous matrix. The results show that the spontaneously crystallized nuclei interact with the amorphous phase, undergoing a rotation and realignment process, promote the crystallization of amorphous phase, and finally form a single crystalline nanostructure. Our results not only provide a system for the theoretical study on the amorphous formation and its function in the crystal growth but also break a path for producing single crystals. © 2008 American Institute of Physics. 关DOI: 10.1063/1.3001576兴 Since Prof. Gleiter and Banfield presented the crystal growth mechanism,1,2 “oriented attachment” 共OA兲, which describes the self-organization of adjacent particles, has attracted increasing interest as a route in the fabrication and self-organization of nanocrystalline materials.3 To date, a great number of structures, such as nanowires, nanorods, and nanoplates through self-organization, were experimentally observed.4 At the same time, several growth kinetic models have been developed by considering the nanoparticle collision to study the driving force in the OA growth mechanism.5,6 Recently, a type of crystal growth mode has been experimentally observed in different systems such as the sea urchin spine calcite formation,7 anatase phase crystallization from amorphous titania,8 single crystal ZnWO4 nanorods directed epitaxial growth from amorphous nanoparticulates,9 and the Ag single crystal growth.10 It seems the single crystal growth from an amorphous matrix is a common phenomenon, and the difference in free energy for different systems mentioned above is the driving force of crystallization process. For the titania system, the anatase even the rutile can be obtained by increasing the applied energy on amorphous precursor.8 The single crystal calcite formation only requires a spontaneous crystallization process within 3 weeks.7 The transition from Ag amorphous phase to single crystal is a transient process.10 However, so far, the growth mechanism within this type of crystal growth mode, such as how the amorphous precursor phase crystallizes and grows to be a single crystal, remains unclear. In this paper, we present the results of the crystallization of Ag from the amorphous matrix. The studies are performed by molecular dynamics 共MD兲 simulations. Such investigation, as a most fundamental knowledge, is very necessary and important not only in studying the thermodynamic stability of amorphous precursor phase but also in providing a deep insight into the role of amorphous precursor and crystal growth mechanism. a兲

Author to whom correspondence should be addressed. Electronic mail: [email protected].

0003-6951/2008/93共15兲/153115/3/$23.00

MD simulations are performed at constant pressure to investigate the rotation and realignment of the crystalline nuclei behavior of nuclei in amorphous surrounding. The second nearest-neighbor modified embedded atom method 共2NN MEAM兲11 has proved a feasible and effective method in calculating various thermodynamic and kinetic properties of metals.12,13 Therefore, we choose the 2NN MEAM in this work. The initial configurations of Ag atoms are prepared by a similar method reported in Ref. 14. The calculation model uses a liquidlike cluster structure.14 In the first step of the simulation, the system is heated from room temperature 共300 K兲 to 1800 K and relaxed for 100 ps at 1800 K to guarantee that an equilibrium liquid state is achieved before the system is cooled to 300 K. Then, the system is quenched to room temperature at the rate of 8 K / ps. During the above processes, the two nuclei are fixed. After that, all atoms in

FIG. 1. 共Color online兲 Two clusters 共134 atoms for each兲 relaxed at vacuum 共a兲 potential energy evolution and simulation time. Different snapshots at simulation time: 共b兲 0 ps, 共c兲 18 ps, 共d兲 40 ps, and 共e兲 200 ps, respectively.

93, 153115-1

© 2008 American Institute of Physics

Downloaded 19 Oct 2008 to 129.186.11.23. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp

153115-2

Fang et al.

FIG. 2. 共Color online兲 Two nuclei 共134 atoms for each兲 relaxed in the amorphous surrounding 共totally, 1240 atoms兲. 关共a兲 and 共b兲兴 Initial and final 共200 ps兲 configurations, 共c兲 potential energy evolution and simulation time, 关共d兲–共g兲兴 side-view snapshots at simulation time: 共d兲 0 ps, 共e兲 20 ps, 共f兲 30 ps, and 共g兲 200 ps, respectively.

the system are relaxed at room temperature for a long time to observe the interaction between two nuclei and amorphous phase and the simulated structure details. To obtain a stable and lowest energy configuration, the simulated annealing and simulated quenching methods are applied to the optimization of final configurations.15 The time step is 0.5 fs for all the MD simulation. In this paper, as a comparison, the relaxation of Ag clusters under vacuum condition was investigated. The evolution of the potential energy is shown in Fig. 1共a兲. According to Fig. 1共a兲, the system has quickly reached an equilibrium state after a MD time of 80 ps, undergoing a four-step potential energy decrease. Figures 1共b兲–1共e兲 show the evolution process with interval snapshots at various simulation times. Figure 1共b兲 is the initial configuration of the MD simulation with 134 atoms for each cluster and 20° angle for both of them. At the beginning of the relaxation, the two clusters stick each other after ⬃15 ps 关Fig. 1共c兲兴, which associates with the significant decrease in the potential energy 关step I in Fig. 1共a兲兴. Subsequently, the two clusters start to adjust their crystallographic orientation by means of the rotation and realignment. The potential energy further decreases 关steps II–IV in Fig. 1共a兲兴 to a stable value, and the corresponding Ag configurations demonstrate a single crystal gradually as shown in Figs. 1共d兲 and 1共e兲 after 40 and 80 ps MD time, respectively. Our previous observations show that the crystallized nuclei can be spontaneously formed from amorphous matrix10 based on a size-dependent structural transformation process.16 After the formation of nuclei, a self-assembling process involving the rotation and realignment movements is used to describe the final formation of Ag single crystalline structure.10 In the present work, we use MD simulation to study how the rotation and realignment proceed for the crystallized nuclei within amorphous surrounding. The angles from 10° to 90° for two nuclei are evaluated and the results are shown in Figs. 2 and 3, respectively. To illustrate the

Appl. Phys. Lett. 93, 153115 共2008兲

FIG. 3. 共Color online兲 Final configurations 关共a兲–共c兲兴 and potential energy curves 关共d兲–共f兲兴 for the system with each nucleus of 134 atoms and totally 1240 atoms, corresponding to angles of 共a兲 20°, 共b兲 40°, and 共c兲 60°. 共g兲 Required simulation time 共picoseconds兲 of forming single crystal as a function of misorientation angles of two nuclei.

rotation and realignment processes, various interval simulation steps are detailed for the case of 20° angle and the results are shown in Fig. 2. For the safety of clear clarification, the nuclei are shown by the coordinated style and two different colors 共orange and green兲 are used for the left and right parts of the model. It is observed that the two nuclei with initial 20° angle 关Fig. 2共a兲兴 have rotated and realigned 关Fig. 2共b兲兴 after MD time of 160 ps 关Fig. 2共c兲兴. Meanwhile, the amorphous phase has also crystallized and shared the same crystallographic orientation as the realigned nuclei. Figure 2共c兲 shows the potential energy evolution during relaxation, where the curve presents two obvious potential energy decreasing processes at MD times of ⬃30 and 160 ps. Figure 2共d兲 is the side view of the initial configuration. Figures 2共e兲–2共g兲 describe what happen during the decrease in potential energy. At ⬃20 ps, the two nuclei have rotated in the same orientation, as shown in Fig. 2共e兲, where the nucleus marked gradually by orange is hidden behind the green one. Subsequently, a quick structural relaxation 共20– 30 ps兲 causes the crystallization of the surrounding amorphous matrix 关Fig. 2共f兲兴. It is noticed that the most orange-colored atoms have been hidden by the front green atoms, which implies the progress of the rotation and realignment processes. At 30 ps, only a few misorientation regions may be observed. After a relatively longer relaxation of 30– 160 ps, the misorientated orange-colored atoms will progressively disappear and finally from a perfect single crystal 关Fig. 2共g兲兴. Comparing the case of relaxation under vacuum 共Fig. 1兲, the nuclei within the amorphous surrounding do not walk a longer distance. This could result from the bondage of the surrounding atoms. When the two nuclei are surrounded and restricted by amorphous phase, they relax only around the initial positions and interact with amorphous atoms and themselves. Therefore, the two nuclei could only relax around their original positions. In fact, even a single nucleus that starts growing already has the ability to arrange surrounding amorphous atoms into crystalline order, as shown in Fig. S1 共Ref. 17兲. Undergoing

Downloaded 19 Oct 2008 to 129.186.11.23. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp

153115-3

Appl. Phys. Lett. 93, 153115 共2008兲

Fang et al.

FIG. 4. 共Color online兲 HRTEM images of 共a兲 interface region of three grains and 共b兲 the bulk region of a silver monocrystal.

a relatively short relaxation 共⬃10 ps兲, the system may transform to be a perfect single crystalline structure. To evaluate the influence of initial misorientation angles on the final crystal structures, different initial misorientation angles for two nuclei from 10° to 90° are simulated and the results are shown in Fig. 3. Typically, in Figs. 3共a兲–3共c兲 and Figs. 3共d兲–3共f兲, we present the final configurations and the corresponding potential energy curves for initial misorientation angles of 20°, 40°, and 60°, respectively. From Figs. 3共a兲–3共c兲, one can find that the prefect single crystal can be formed for the angles of 20° and 60°. In the case of 40°, although the surrounding amorphous phase may be crystallized, the initial two misoriented grains cannot rotate in the same direction definitely even after a considerably long relaxation time 共⬎10 000 ps兲, as shown in Fig. 3共e兲. In contrast to the case of 20°, a relatively longer crystallization process is required for the case of 60°, where about 160 ps of relaxation time for the case of 20° and 750 ps for 60° are used to form a single crystal structure, respectively. Here, by comparing the required relaxation time of forming a single crystal under different initial misorientation angles, we obtain an approximate estimate, as shown in Fig. 3共g兲. With increasing misorientation angles from 0° to 40°, a longer relaxation time is requested to form the single crystal structure. At the range of 60°–90°, a reverse rule is found. The shadow region indicates that the two grains with the initial misorientation angles in the region of 40°–50° could not rotate to be the single crystal during this simulation. The current curve demonstrates a similar tendency to the grain growth in nanocrystalline fcc metals,18 implying that the crystallization process in this growth mode could not be governed by the conventional curvature-driven grain-boundary migration, but the grain rotations play an equally important

role, at least during the early stages of grain growth.18 The current simulation results were well confirmed from the experiments by the high resolution transmission electron microscopy 共HRTEM兲 observation. In Fig. 4, we present a typical rotation and realignment pictures. Figure 4共a兲 is an interface area where three crystallized grains 共marked by white, red and blue dashed lines兲 approach together. The D1–D4 共the blue, red, and white arrows兲 represents different crystallographic orientations for the marked areas, which demonstrate the deviation of atomic positions from the crystalline perfection. For the clear comparison, the D1–D4 are put into one box marked by black dashed line in Fig. 4共a兲. It is noticed that the three grains demonstrate initially different crystallographic orientations 共D1–D4兲. However, they show a small initial misorientation angles 共⬍30° 兲. Thus undergoing a rotation and realignment process, they have the opportunity to finally form the single crystal or imperfect single crystal 关Fig. 4共b兲兴 with some crystalline defects such as dislocation, twins 共T兲 and stacking faults 共SF兲 as marked in Figs. 4共a兲 and 4共b兲. It is worth noting that not only twins and/or dislocations can always be found in the configurations from simulation as shown in Figs. 3共a兲 and 3共c兲, but may also be frequently observed from the experiment, as shown in Fig. 4. The crystalline defects formed at self-assembling interfaces are typical characteristic of the rotation and realignment crystallization processes, which is also in agreement with the crystallization process of amorphous silicon powders,19 the crystallization process of Pd-Si amorphous alloy as shown in Fig. S2 共Ref. 17兲, and the terms OA reported by Penn and Banfield.2 The authors thank Dr. Byeong-Joo Lee for his help in the MEAM code. 1

G. Herrmann, H. Gleiter, and G. Baro, Acta Geophys. Pol. 24, 353 共1976兲. 2 R. L. Penn and J. F. Banfield, Science 281, 969 共1998兲. 3 Z. Y. Tang, N. A. Kotov, and M. Giersig, Science 297, 237 共2002兲. 4 J. X. Fang, X. N. Ma, H. H. Cai, X. P. Song, and B. J. Ding, Nanotechnology 17, 5841 共2006兲. 5 H. Z. Zhang and J. F. Banfield, Nano Lett. 4, 713 共2004兲. 6 C. Ribeiro, E. J. H. Lee, E. Longo, and E. R. Leite, ChemPhysChem 6, 690 共2005兲. 7 Y. Politi, T. Arad, E. Klein, S. Weiner, and L. Addadi, Science 306, 1161 共2004兲. 8 H. Z. Zhang, M. Finnegan, and J. F. Bandield, Nano Lett. 1, 81 共2001兲. 9 B. Liu, S. H. Yu, L. J. Li, F. Zhang, Q. Zhang, M. Yoshimura, and P. K. Shen, J. Phys. Chem. B 108, 2788 共2004兲. 10 J. X. Fang, X. N. Ma, H. H. Cai, X. P. Song, and B. J. Ding, Appl. Phys. Lett. 89, 173104 共2006兲. 11 B.-J. Lee and M. I. Baskes, Phys. Rev. B 62, 8564 共2000兲. 12 B.-J. Lee, J.-H. Shim, and M. I. Baskes, Phys. Rev. B 68, 144112 共2003兲. 13 Y. Han, F. Liu, S.-C. Li, J.-F. Jia, Q.-K. Xue, and B.-J. Lee, Appl. Phys. Lett. 92, 021909 共2008兲. 14 E. Apra, F. Baletto, R. Ferrando, and A. Fortunelli, Phys. Rev. Lett. 93, 065502 共2004兲. 15 I. L. Garzon, K. Michaelian, M. R. Beltran, A. P. Amarillas, P. Ordejon, E. Artacho, D. Sanchez-Portal, and J. M. Soler, Phys. Rev. Lett. 81, 1600 共1998兲. 16 J. X. Fang, H. J. You, P. Kong, B. J. Ding, and X. P. Song, Appl. Phys. Lett. 92, 143111 共2008兲. 17 See EPAPS Document No. E-APPLAB-93-033842 for the crystallizations of single Ag nucleus and Pd-Si system. For more information on EPAPs, see http://www.aip.org/pubservs/epaps.html. 18 A. J. Haslam, S. R. Phillpot, D. Wolf, D. Moldovan, and H. Gleiter, Mater. Sci. Eng., A 318, 293 共2001兲. 19 H. Hofmeister, J. Dutta, and H. Hofmann, Phys. Rev. B 54, 2856 共1996兲.

Downloaded 19 Oct 2008 to 129.186.11.23. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp