Mechanisms of the Wurtzite to Rocksalt Transformation in CdSe Nanocrystals Michael Gru ¨nwald, 1 Eran Rabani, 2 and Christoph Dellago 1 1 Faculty of Physics and Center for Computational Materials Science, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria 2 School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel (Received 7 March 2006; published 27 June 2006) We study the pressure-driven phase transition from the four-coordinate wurtzite to the six-coordinate rocksalt structure in CdSe nanocrystals with molecular dynamics computer simulations. With an ideal gas as the pressure medium, we apply hydrostatic pressure to spherical and faceted nanocrystals ranging in diameter from 25 to 62 A ˚ . In spherical crystals, the main mechanism of the transformation involves the sliding of (100) planes, but depending on the specific surface structure we also observe a second mechanism proceeding through the flattening of (100) planes. In faceted crystals, the transition proceeds via a five-coordinated hexagonal structure, which is stabilized at intermediate pressures due to dominant surface energetics. DOI: 10.1103/PhysRevLett.96.255701 PACS numbers: 64.70.Nd, 61.46.Df, 71.15.Pd The thermodynamic properties of nanosized particles can differ significantly from those of the corresponding bulk materials due to the large surface to volume ratio. In particular, the kinetics and the mechanism of first order phase transitions are strongly affected by the surface free energetics of such systems. In a series of recent experi- ments, Alivisatos and co-workers [1–6] have demonstrated that the pressure-induced transition from the four- coordinate wurtzite structure to the six-coordinate rocksalt structure in CdSe is strongly influenced by crystal size. The transition pressure increases by about a factor of 2 as the size of the sample is decreased from macroscopic dimen- sions to the nanometer scale [1], and also the kinetics of this highly activated process change markedly as a function of size [2,4]. A considerable amount of work has been concerned with the wurtzite to rocksalt transition and possible intermediate structures in the bulk [7–15] where, for CdSe, the trans- formation occurs at approximately 2.5 GPa [16,17]. In a recent molecular dynamics study of bulk CdSe, Shimojo et al. identified two main mechanisms [12]. The first mechanism was previously proposed by Tolbert and Alivisatos and involves the flattening out of parallel (100) planes [1], the second mechanism is realized through sliding of parallel (100) planes along the 010 direction. Using transition path sampling methods [18], Zahn, Grin, and Leoni recently showed that the second mechanism is highly preferred and the transition does not involve a concerted motion of atoms, but occurs via nucleation and growth [15]. In the nanocrystal, surface effects may significantly alter the transition mechanism. In this Letter, we use molecular dynamics simulation to study the structural transformation of CdSe nanocrystals of various shapes and sizes. Our simulations reveal that transition mechanisms are strongly shape dependent: Most spherical nanocrystals transform through the bulk mechanism of sliding (100) planes [15], but the other mechanism, unfavored in the bulk, also occurs. For faceted nanocrystals the transformation pro- ceeds through an intermediate five-coordinate structure, that is unstable in the bulk but is stabilized by surface effects in the nanoparticle. In all our simulations we use the empirical pair potential for CdSe developed by Rabani [17], designed to reproduce the lattice and elastic constants of bulk CdSe as well as the bulk wurtzite to rocksalt transition pressure of 2.5 GPa [15,17]. A crucial point in the simulation of nanoparticles under pressure is the choice of pressure medium. As such we use an ideal gas of noninteracting particles that interact with the crystal atoms through the soft-sphere pair potential ur =r 12 . As the equation of state of the ideal gas is known analytically, the pressure can be easily tuned by controlling the density of the pressure bath. We set   1 kJ=mol and   3:0  A, large enough to prevent infiltra- tion of gas particles into the nanocrystal. For an efficient calculation of the forces needed in the molecular dynamics simulation, we use cell lists [19] and a cutoff of 2 for the interactions between ideal gas particles and the crystal atoms. To reduce the number of ideal gas particles required to exert a given pressure, these particles fill only a thin layer around the crystal. The volume that is occupied by the gas consists of all cells, already defined for the cell lists, that can hold possible interaction partners of the crystal atoms. This minimal volume of cells is updated every time step and particles leaving the volume are no longer con- sidered. The loss of gas particles is compensated by ran- domly introducing new gas particles on the cell walls confining the volume, with statistics appropriate for an ideal gas at temperature T and pressure P. When, by movement of crystal atoms, a new cell is added to the gas atmosphere, it is filled with a number of particles drawn from an appropriate Poisson distribution; when a cell is removed from the gas atmosphere, the particles in this cell are no longer considered. In this method, the gas serves as a barostat as well as a thermostat. The exerted pressure is hydrostatic (we have numerically verified that in our simulations the forces tangential to the crystal PRL 96, 255701 (2006) PHYSICAL REVIEW LETTERS week ending 30 JUNE 2006 0031-9007= 06=96(25)=255701(4) 255701-1  2006 The American Physical Society