Aggregation, Coarsening, and Phase Transformation in ZnS

NANO LETTERS

Aggregation, Coarsening, and Phase Transformation in ZnS Nanoparticles Studied by Molecular Dynamics Simulations

2004 Vol. 4, No. 4 713-718

Hengzhong Zhang* and Jillian F. Banfield Department of Earth and Planetary Science, UniVersity of California, Berkeley, 307 McCone Hall, Berkeley, California 94720 Received December 26, 2003; Revised Manuscript Received February 11, 2004

ABSTRACT Molecular dynamics simulations at 300 K in vacuum were used to study nanoparticle motion and structural changes during aggregation and coarsening of 3 nm sphalerite (ZnS) particles and atomic diffusion during the subsequent phase transformation. Interaction forces between atoms in different nanoparticles can induce translational and rotational movements of the nanoparticles, driving them to find appropriate locations and orientations for aggregation. Following aggregation, the coarsened particle adopts a near-amorphous structure that transforms rapidly to wurtzite. Atomic diffusion is faster on the surface than in the bulk. Transient episodes of very fast atomic diffusion occur locally on the surface. Diffusion plays significant roles in nanoparticle structural change, aggregation, coarsening, and surface nucleation.

Molecular dynamics (MD) simulation is a computational technique used to study the motions of atoms in a given system (e.g., a solid material or a solid solution) in order to understand and predict the structural, dynamic, kinetic, and/ or equilibrium properties at the chosen conditions (e.g., compositions, temperatures, and pressures). Usually atomic motions are described by Newton’s equations of motion, and the interactions between atoms are described using forcefields or interatomic potential functions. MD simulations are invaluable tools in investigation of materials at extreme conditions such as at very high temperatures and pressures, and for nanometer-scale systems. MD permits studies of atomic motion that cannot yet be documented experimentally. For instance, Gribb and Banfield found that the rate of the phase transformation from nanocrystalline anatase (TiO2) to rutile is almost linearly correlated with the coarsening rate of the anatase nanoparticles.1 However, direct observation of atomic motions in the two processes is impossible. Nanocrystals can grow via oriented attachment2 in many systems under very diverse conditions.3-7 The driving force and mechanism are yet to be elucidated at the atomic level. MD simulations may provide insights into the pathways of processes such as these. Zhu and Averback used MD simulations to study the sintering of Cu nanoparticles and found that misaligned nanoparticles rotate to form low energy interfaces during sintering.8 MD simulations of sintering of two anatase nano* Corresponding author. E-mail: [email protected]. 10.1021/nl035238a CCC: $27.50 Published on Web 02/27/2004

© 2004 American Chemical Society

particles by Ogata et al. revealed that neck formation was promoted by surface diffusion at high temperatures.9 Using MD simulations, Latapie and Farkas found the stress-induced phase transformation in nanocrystalline iron started at the crack tip.10 Wilson et al. created MD potential functions to study the mechanisms of pressure-induced phase transformations in model bulk metal halides.11 From their simulations, they found a structure similar to that of β-Sn may be the transition phase for the transformation. We studied the phase stability of ZnS nanoparticles in vacuum and in the presence of water using combined MD simulations, thermodynamic analysis, and experiments.12 It was found that wurtzite (ZnS) nanoparticles smaller than 7 nm are more stable than sphalerite nanoparticles in vacuum at 300 K. However, adsorption of water onto the ZnS nanoparticle surface stabilizes the sphalerite structure. Our MD simulations also predicted that very fine (∼3 nm) anhydrous ZnS nanoparticles have a highly distorted structure, and that adsorption of water onto the nanoparticle surfaces results in the formation of a relatively crystalline core.13 These predictions were confirmed by wide-angle X-ray scattering analysis.13 In the present work we used MD simulations to study the structure, nanoparticle motion, and transformation kinetics in 3 nm sphalerite nanoparticles undergoing aggregation, coarsening, and phase transformation in vacuum at 300 K. The nanoparticle aggregation state depends on the sample preparation conditions. Nanoparticles not in direct contact must move toward each other to aggregate. One way to simulate nanoparticle interactions is to use an initial con-

Figure 2. Snapshots of the MD system at different MD times: 0 ps (a), 13.8 ps (b), 16.3 ps (c), 28.8 ps (d), 41.3 ps (e), 78.9 ps (f), 167.0 ps (g), 479.5 ps (h), and 1100.0 ps (i). The translational and the rotational directions of nanoparticle #5 are depicted in (c), (d), and (e).

An angle-bending form of three-body interactions is considered for nearest S-Zn-S atoms: 1 uijk ) kijk(θ - θijk)2 2 Figure 1. (a) Initial configuration for the MD simulation, and (b) evolution of the potential energy of the MD system with MD time. Stage I: rearrangement of surface atoms; stage II: aggregation; stage III: coarsening; and stage IV: phase transformation.

figuration of five nanoparticles in a closest packed arrangement. The disadvantage of this configuration is that it allows for only limited analysis of nanoparticle movement during aggregation. Thus, 3 nm diameter unrelaxed sphalerite nanoparticles (each containing 360 ZnS molecular units with a diameter of 28.8 Å) were placed at the four corners of a tetrahedron, and another was placed at the center (Figure 1). The distance between the centers of nanoparticles placed in the center of the tetrahedron and at its corners is 30.5 Å. The five nanoparticles were randomly oriented with respect to each other. A few interatomic potential functions have been developed for ZnS.14-16 In this work, we adopted the shell model17 of ZnS by Wright and Jackson.15 With this model, a Zn or S atom is treated as a core and a massless (or, very light) shell that are connected by a spring, accounting for ionic polarity induced under a local electric field. The Zn and S atoms have the electrical charges of +2 and -2, respectively. The short-range non-Coulombic interaction between two atoms i and j is described using the following Buckingham equation:

( )

uij(short-range) ) Aij exp -

Rij Cij - 6 Fij Rij

(1)

where uij is the interaction potential, Rij the distance between atoms i and j, and Aij, Fij, and Cij are three model parameters. 714

(2)

where uijk is the interaction potential, kijk a model parameter, θ the angle formed by atoms i (S), j (Zn, center), and k (S), and θijk the equilibrium value of the angle (109.4°). Detailed values of the model parameters can be found from ref 15. The MD simulation code DL-Poly18 was used in this work. The MD simulation was done in a canonical ensemble at 300 K and ambient pressure using a time step of 0.5 fs. The energy evolution of the MD simulation is illustrated in Figure 1b. Though the system has not reached an equilibrium state after an MD time of ∼1.1 ns, it has already undergone the processes of structural relaxation (∼0-10 ps), particle aggregation (∼10-235 ps), particle coarsening (∼235-480 ps), and is in an ongoing phase transformation to nanocrystalline wurtzite (after ∼480 ps). Figure 2 shows snapshots from the system at various simulation times. After ∼10 ps, the five nanoparticles reach a local energy minimum (Figure 1b), mainly by rearrangement of surface atoms, which reduces the number of dangling bonds on the nanoparticle surfaces. Aggregation occurs simultaneously with rearrangement of surface atoms. The nanoparticles undergo translational and/or rotational movements, as demonstrated in Figure 2a-g (also see the animation in Figure S.1 in Supporting Information). At 13.8 ps (Figure 2b), sphalerite nanoparticles were relaxed and nanoparticle #4 moved toward nanoparticles #1-2-3. At 16.3 ps (Figure 2c), #4 docked over #1-2-3, and #5 was undergoing translational and rotational movements toward #1-2-3-4. The directions of the movements are shown in the box in Figure 2c. At 28.8 ps, #5 collided with #4, causing a change in the rotational direction of #5 (see the box in Figure 2d). Nanoparticle #5 continued to Nano Lett., Vol. 4, No. 4, 2004

move and passed over #4 and then moved to the right of #1-2-3 at 41.3 ps (Figure 2e). Aggregation continued, accompanied by change in shape and fusion of pairs of adjacent nanoparticles (Figure 2e-g). There is an energy maximum located at ∼80 ps (Figure 1b). This corresponds to an activation energy for aggregation of ∼10 kJ/mol ZnS. This value should depend on the spatial distribution of the nanoparticles and thus will vary with the nanoparticle synthesis conditions in a real system. Given the relatively small value of the aggregation energy, it should be possible to disaggregate the nanoparticles by applying an external force. This should be even easier if there are surface-adsorbed molecules that inhibit coarsening. In fact, Huang et al. experimentally realized reversible aggregation-disaggregation in 3 nm ZnS nanoparticles.19 Disaggregation was achieved via ultrasonic agitation. To determine whether the extent of nanoparticle movement depended upon the initial structural state of the nanoparticles, a second simulation (up to 70 ps) was carried out using nanoparticles that had already undergone structural relaxation (Figure S.2 in Supporting Information). The simulation predicts translational and rotational motions that are similar to those in the simulation using unrelaxed nanoparticles. The simulations provide insight into the driving forces for nanoparticle movement during aggregation. Interactions between nanoparticles involve electrostatic Coulombic and non-Coulombic forces between atoms within the nanoparticles. In an assembly of nanoparticles with random orientations, the particles are subjected to anisotropic forces from their neighbors. Depending on the distribution of the nanoparticles in space, the nonzero vector forces can lead to either attractive or repulsive interactions and can cause translational and/or rotational movements. The observation of comparable motion in simulations using unrelaxed and relaxed nanoparticles indicates that the energy used in aggregation comes primarily from the potential energy released when nanoparticles interact to achieve lower energy arrangements, and not from energy released during surface relaxation. In the simulation, the loss of potential energy of the system is compensated by addition of energy from the constant temperature environment. Our simulations showed nanoparticle translations and rotations over much longer distances than observed by Zhu and Averback.8 The motions that enable particles to find appropriate positions for aggregation could be important in the early stages of crystal growth via oriented attachment.2-7 After the aggregation stage (up to 235 ps), nanoparticles started to coarsen via crystallization upon each other via atomic diffusion (diagram not shown). If there were physically adsorbed or chemically bound organic molecules on the nanoparticle surfaces, coarsening should be retarded (or even prohibited), since these exotic molecules could prevent atomic diffusion. After coarsening, the particle is ∼5 nm in diameter. At 479.5 ps, a periodic layer has formed on the nanoparticle surface (Figure 2h). The S-Zn-S layer is near-close packed (Figures 3a and b) and subsequently propagates into the nanoparticle as wurtzite. This is consistent with previous Nano Lett., Vol. 4, No. 4, 2004

work, which showed that at 300 K in vacuum wurtzite is more stable than sphalerite if the nanoparticles are less than 7 nm in diameter.12 The wurtzite domain within the coarsened particle is bounded by a (001) surface. Formation of a wurtzite (001) surface is interesting, as the surface energy of (001) wurtzite (1.52 J/m2) is higher than those of (100) and (110) wurtzite (1.00 and 0.28 J/m2, respectively).12 The (001) orientation may be favored because it minimizes interfacial energy with underlying untransformed ZnS. Experimentally, the formation of wurtzite (001) caps on sphalerite nanoparticles (with [001] wurtzite parallel to 〈111〉 sphalerite) was observed under hydrothermal conditions.20 The snapshot taken at 1.1 ns (Figure 2i) shows that a large portion of the coarsened particle has transformed to wurtzite (Figure 3c). When the wurtzite regions are viewed from the perpendicular [001], [110], and [11h0] directions (Figures 3df) it is apparent that the structure is distorted (e.g., especially see Figure 3f). A phase transformation in a nanoparticle may begin at an interface, on the surface, or within the bulk, depending on particle structure, size, aggregation state, and the temperature and pressure.21 Our previous MD simulation of the phase transformation in an isolated 3-nm sphalerite nanoparticle in vacuum suggested that conversion from nanocrystalline sphalerite to wurtzite occurs via surface nucleation.12 The present work shows that the phase transformation from 3 nm nanocrystalline sphalerite to wurtzite accompanying nanoparticle aggregation and coarsening also occurs via surface nucleation. Theoretical X-ray diffraction (XRD) patterns of the MD system at various MD times were calculated for Cu KR radiation (X-ray wavelength ) 1.5418 Å) using the DebyeFourier analysis (DFA)22 and are shown in Figure 4. After structure relaxation (0-13.8 ps in Figure 4), XRD peaks broaden and decrease in intensity due to the decrease in size of the coherently scattering regions within the nanoparticles following rearrangement of surface atoms. Further aggregation and subsequent coarsening in the aggregate lead to broadening and overlapping of the original (220) and (311) sphalerite peaks (16.3-167.0 ps in Figure 4). Loss of resolution of peaks in the theoretical XRD patterns indicates that a transient (a few hundred ps), near-amorphous state occurs during coarsening. If the nanoparticles were larger, or if their surfaces were passivated by adsorbed molecules, some crystallinity might be retained. Following wurtzite nucleation (479.5 ps in Figure 4), the overlapping wurtzite (110) and (112) peaks become more resolved and the characteristic (102) and (103) wurtzite peaks appear. The peak positions differ slightly from those in bulk wurtzite due to strain and distortion (see Figure 3e and f). Figure 5 shows the bond length distribution between Zn and S atoms, as well as the S-Zn-S bond angle distribution in the particle at 1.1 ns. The average length of the Zn-S bond is 2.33 Å, close to that in bulk wurtzite (2.34 Å). However, most Zn-S bonds are 2.31 Å (Figure 5a) and the distribution of bond lengths is asymmetric. Bond shortening is due to compressive surface stress.23 Most S-Zn-S angles 715

Figure 3. Structures of the particle at different MD times: 479.5 ps (a, b) and 1100 ps (c-f). Formation of the wurtzite structure (balls and sticks) starts by formation of the wurtzite (001) face on the nanoparticle surface (a). Structure (b) is a close-up of the wurtzite nuclei. At 1100 ps, the nanoparticle is dominated by the wurtzite structure (c). Structures (d), (e), and (f) are views of a wurtzite region viewed along three perpendicular directions, the wurtzite [001], [110], and [11h0], respectively. Insets show the bulk wurtzite structure in each orientation.

are distributed around 109.4°, the equilibrium value in sphalerite or wurtzite (Figure 5b). However, quite a few bond angles are distributed around 90°. Analysis of the MD trajectory showed that the angles of ∼90° are associated with atoms in the process of bond breakage during wurtzite formation. Atomic diffusion is important for nanoparticle coarsening and structural transformation. Atoms on the surface and in the interior of the particle are subject to different forces and thus possess different mobility. Figure 6 shows the mobility 716

distribution of atoms in the particle at 1.1 ns. Most Zn or S atoms moved ∼2.3 Å in the last 1 ps of the simulation (Figure 6a). The atoms that moved more than 3.5 Å are shown as balls in Figure 6b. It is clear that these fast moving atoms are all located in specific areas on the surface of the particle. Clearly, surface diffusion is faster than bulk diffusion. Areas with high diffusion rates occur at different regions on the particle surface at different times. Results of this study are generally consistent with the findings of prior experimental investigations, which have Nano Lett., Vol. 4, No. 4, 2004

Figure 4. Calculated XRD patterns of the MD system at various MD times. Curves from top to bottom are, respectively, for MD time 0, 13.8, 16.3, 28.8, 41.3, 78.9, 167.0, 479.5, 604.5, 713.5, 1032.0, 1042.0, 1052.0, 1062.0, 1072.0, 1082.0, and 1100.0 ps. The XRD peaks from the JCPDS cards for bulk sphalerite (squares) and wurtzite (diamonds) are also plotted for comparison.

Figure 6. Mobility distribution of atoms at 1100 ps (a). The distance is that moved by each atom in the last 1 ps of the simulation. The atoms with higher mobility (distance moved g3.5 Å) are all on the nanoparticle surface (shown as balls) (b).

of Energy (grant # DE-FG03-01ER15218 and # LBNL LDRD 36615) and the National Science Foundation (grant # EAR-0123967). This research was performed in part using the U.S. Department of Energy funded Molecular Science Computing Facility located at Pacific Northwest National Laboratory. Drs. Feng Huang, Jim Rustad, and an anonymous reviewer are thanked for helpful comments. Supporting Information Available: Animated GIF diagrams showing the movements of the ZnS nanoparticles in the aggregation stage of the MD simulations. This material is available free of charge via the Internet at http:// pubs.acs.org. References

Figure 5. Bond length distribution of Zn-S (a) and bond angle distribution of S-Zn-S (b) in the particle at 1100 ps.

documented size-dependent coarsening, phase stability, and phase transformation processes.2-7,12,13,19-21,23 Thus, the MD simulations provide insights into factors governing aggregation, coarsening, and phase transformation in nanoparticulate ZnS.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Acknowledgment. We thank Dr. W. Smith and Dr. T. R. Forester for providing the MD simulation code. Financial support for this work was provided by the U.S. Department Nano Lett., Vol. 4, No. 4, 2004

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