MAGIC NUMBER AND QUASI-MELTING TEMPERATURE DISCOVERED IN CRYSTAL-GROWTH AND SURFACE PHASE-TRANSITIONS

For crystal growth and surface phase transitions, we discovered a simp le rule in the relationship between surface structure and temperature. This rule states that changes in crystal growth modes and those in su rface structures occur at temperatures that are simple fractions, such as 1/2, 2/3, and 3/4, of the melting temperature, T-m, of the materia l. Here, we first show our experimental results of transition temperat ures for Si-MBE (molecular beam epitaxy) on Si(111) and Si(001) substr ates and for structure changes on Si(lll) surface. We then discuss the m for other materials from the literature, having fee (face centered c ubic) or diamond structures, which are similar crystal structures to S i We found that the transition temperatures were the same, regardless of material, depending on crystal surface orientation. That is, transi tions take place at the temperatures of 2/6, 3/6, 4/6, 5/6 T-m for (11 1) surfaces, and 1/4, 2/4, 3/4 T-m for (001) surfaces, when transition temperatures are normalized to the melting temperature of each materi al. We discuss the origin of these fraction temperatures by considerat ion of surface atom energy based on the geometry of atom arrangement o n a crystal surface. We think that the reason why transition temperatu res were same is due to the same coordination numbers of the respectiv e surface atoms if material has similar crystal structure even if mate rials differ. We consider these fractions are one kind of magic number s, and also call these temperatures as quasi-melting temperatures, fro m the analogy of the melting for bulk crystal. For example, at 1/2 T-m , atoms bound at kink sites become free, i.e. kink melting occurs, sin ce kink-site atoms have half the coordination number of bulk atoms. Fi nally, we point out that it is important for understanding various sur face phenomena to consider the role of surface-defects such as terrace s, ledges, and kinks.