VOLUME 76, NUMBER 26 PHYSICAL REVIEW LETTERS 24 JUNE 1996 Dimer Shearing as a Novel Mechanism for Cluster Diffusion and Dissociation on Metal (100) Surfaces Zhu-Pei Shi, Zhenyu Zhang, Anna K. Swan, and John F. Wendelken Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6032 (Received 15 February 1996) Using bond-counting arguments and embedded-atom calculations, we establish the crucial importance of dimer shearing in metal (100) submonolayer epitaxy. This process provides the easiest pathway for diffusion of compact clusters of sizes 4, 6, and 8, and introduces a rich variety of localized cluster dynamics. A combination of the dimer shear motion and the traditional mechanism of sequential motion of individual atoms provides a better interpretation of the oscillatory behavior of cluster mobility with cluster size. This combination also defines a new set of critical cluster sizes that are likely to be selected in epitaxial growth. [S0031-9007(96)00442-5] PACS numbers: 68.35.Fx, 68.55.–a, 82.20.Mj Many recent studies have been aimed at providing mi- croscopic mechanisms of crystal growth, whose nonequi- librium nature is usually characterized by growth kinet- ics. The phrase growth kinetics encompasses all atomic processes taking place during growth. Examples include adatom diffusion on terraces and over steps, as well as nucleation, aggregation, migration, and dissociation of un- stable and/or stable clusters. These are among the ele- mental and crucially important rate processes determining the growth mode of a given system. Of particular note is metal-on-metal systems. In such systems, recent studies have shown that even very large clusters can have signif- icant mobility at moderate temperatures [1–3]. Smaller clusters are expected to move even faster; therefore their mobility could play a more important role in influencing the growth characteristics of such systems. The focus of this work is on the migration and disso- ciation of relatively small metal clusters on metal (100) surfaces. We notice that essentially all microscopic mod- els developed in extensive previous studies of cluster dif- fusion and dissociation in metal (100) epitaxy have been based on the central assumption that cluster dynamics re- sults from sequential motion of individual adatoms [4 – 13]. Here we show that this prevailing assumption is in fact in- correct or at least incomplete in many cases. Specifically, we use simple bond-counting arguments and detailed quan- titative calculations to establish the importance of a col- lective atomic process, shear motion of a dimer belonging to a compact cluster. This previously overlooked process turns out to provide the most effective pathway for diffu- sion and dissociation of some clusters, as shown on several fcc (100) surfaces. Besides diffusion and dissociation, this process also introduces a rich variety of localized cluster dynamics. A combination of the dimer shear motion and the traditional mechanism of sequential motion of individ- ual atoms provides a better interpretation of the oscillatory behavior of cluster mobility with cluster size. This com- bination also defines a new set of critical cluster sizes that are likely to be selected in epitaxial growth. We first present a qualitative description of the dimer shear motion, and the corresponding bond-counting argu- ments favoring this process. In the traditional mechanism of sequential motion of individual atoms, diffusion of a compact tetramer shown in Fig. 1(a) must be initiated by first placing atom 1 one step ahead, involving the break- age of two nearest-neighbor (nn) bonds [see Fig. 1( b)]. The activation energy E 2b for this process is relatively high. After this rate-limiting step, if the rest of the clus- ter follows the motion of atom 1, then the event leads to diffusion of the tetramer. Alternatively, we should expect the process from Figs. 1(c) and 1(d), induced by a shear motion of the two dimers that constitute the tetramer, to be considerably easier than that from Figs. 1(a) to 1(b), because in reaching Fig. 1(d) only one net nn bond needs to be broken. The activation barrier E s for this collective process can be significantly lower than E 2b if the bond switching (breaking of the 2-3 bond and reforming of the 2-4 bond) happens simultaneously near or right at the tran- sition state. Similarly, dimer shearing cold be an impor- tant process contributing to the diffusion and dissociation of any other cluster which has a lone dimer along its edge. FIG. 1. A comparison of two competing mechanisms leading to the diffusion or diffusion of a tetramer (a),(b) by double bond scission: (c),(d) by a shear motion of a dimer. The solid and dashed lines represent nearest-neighbor and next-nearest- neighbor bonds, respectively. 0031-9007 96 76(26) 4927(4)$10.00 © 1996 The American Physical Society 4927