VOLUME 74, NUMBER 20 PHYSICAL REVIEW LETTERS 15 MAv 1995 Pressure-Induced Transformation Path of Graphite to Diamond S. Scandolo, M. Bernasconi, * G. L. Chiarotti, P. Focher, and E. Tosatti International School for Advanced StudiesV, ia Beirut 4, I 340-14 Trieste, Italy (Received 13 December 1994) Using constant-pressure ab initio molecular dynamics we have simulated the conversion of carbon from graphite to diamond under high pressure. We found that the transformation path proceeds through sliding of graphite planes into an unusual orthorhombic stacking, from which an abrupt collapse and buckling of the planes leads to both cubic and hexagonal forms of diamond in comparable proportions. The mutual orientation of the initial and final phases is in agreement with that of shock- wave experiments. PACS numbers: 62.50. +p, 64.70.Kb, 81. 30. Hd Understanding the dense phases of carbon, and the mechanisms which underlie their mutual transformations, is a long-standing problem of great practical and funda- mental importance. Although hexagonal graphite (hex-g) is known to be the most stable phase of carbon at am- bient conditions, a large activation barrier prevents cubic diamond (cub-d) from transforming, even on a geologi- cal time scale, to graphite. Since the high-pressure region of the carbon phase diagram is instead dominated by di- amond [1], methods devised to convert graphite into dia- mond rely on the use of high pressure [2]. After the first report [3] on the shock-wave conversion of graphite to diamond without catalyst, there is now general agreement that the conversion takes place even statically at a pressure of — 15 GPa and at temperatures exceeding 1000 K [2]. Instead, agreement is far from complete on the conversion mechanism. In particular, the role of hexagonal diamond (Lonsdaleite), first synthesized under similar experimental conditions [4], is not clear. A number of reports indicate that, although metastable with respect to cub-d, hexagonal diamond (hex-d) may be produced through rapid quench- ing of shocked samples [2], or even in static high-pressure conditions [5]. However, recent attempts to reproduce the graphite to hex-d conversion under static conditions failed [6]. The relevance of hex-d in the graphite to cub-d con- version appears to be twofold. First, the mutual orienta- tion of graphite and cub-d before and after the conversion process is consistent with the presence of hex-d as an in- termediate phase [2]. Secondly, hex-d was observed in situ in a recent x-ray diffraction experiment at high pres- sure [7], but after heating and quenching to room condi- tions, only cub-d could be retrieved. More generally, the existence of an intermediate phase has often been invoked [5,8,9], but never been substantiated. From the theoretical side, only the highly symmetric path from rhombohedral graphite (rho-g) (Fig. 1) to cub-d has been considered [10, 11]. This path leads to a final [111] diamond orientation parallel to the original graphite c axis [Fig. 2(a)]. This is at variance with shock-wave experiments, where the final [112] is instead found to be parallel to the c axis [12] [Fig. 2(b)]. The relative 0- Hexagonal Orthorhombic Rhombohedral 0. O. B B 0 -4------O--0 B FIG. 1. Hexagonal, orthorhombic, and rhombohedral phases of graphite. The different stackings of the hexagonal planes are viewed along the c axis (above) and sideways (below). crystal-axes orientation is a particularly revealing feature of the transformation path which has not been addressed theoretically so far. In this Letter we present the results of an ab initio molecular dynamics (MD) simulation of the graphite to diamond conversion. They have been obtained by using a recently developed ab initio constant-pressure simula- tion method [13], where the lack of symmetry constraints is crucial in allowing for possible low-symmetry transfor- mation paths. We find that pressure eventually causes a sliding of graphite planes towards an orthorhombic stack- ing, from which a fast transformation to both hexagonal and/or cubic diamond takes place. A Car — von Barth atomic pseudopotential for carbon in the Kleinman-Bylander form was used [14], and the sam- pling of the Brillouin zone was restricted to the I point. Because of the hardness of carbon pseudopotential and the large volume reduction expected in the compression of graphite, a corrected version of the kinetic energy func- tional was introduced in order to mimic a constant energy cutoff of 35 Ry in the plane-wave expansion of the ground state at different volumes [15]. Although full convergence cannot be claimed at 35 Ry, the basic chemistry and crys- tal binding is quite well described. For example, with this choice bond lengths in carbon clusters are accurate within a few percent [14]. The equations of motion have been 0031-9007/95/74(20)/4015(4)$06. 00 1995 The American Physical Society 4015