Ring-diffusion mediated homogeneous melting in the superheating regime Xian-Ming Bai* and Mo Li † School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0245, USA Received 11 January 2008; revised manuscript received 3 March 2008; published 18 April 2008 Homogeneous melting in the superheating regime is investigated by using molecular dynamics simulation of a Lennard-Jones model system. We show that the commonly observed catastrophic melting at the superheating limit is caused by fast heating rate. By keeping the system isothermally at temperatures below the superheating limit, we observe intense self-diffusion motions as the precursor of melting. The highly correlated atomic motions are related to the self-diffusion loops or rings. Two types of loops are observed, closed loop and open loop, where the latter is directly related to the homogeneous nucleation of the liquid phase. Homogeneous melting occurs when the number density of diffusion loops reaches a critical value. Our results suggest that homogeneous melting in the superheating regime is a first-order thermodynamic phase transition triggered by the self-diffusion loops when the kinetic constraint imposed by heating rate is lessened. DOI: 10.1103/PhysRevB.77.134109 PACS numbers: 64.70.D-, 61.72.Bb, 66.10.C-, 87.10.Tf I. INTRODUCTION Melting is commonly observed but also one of the least understood phenomena in nature. When the temperature reaches the melting point, heterogeneous melting usually oc- curs at defect sites in solids, such as surfaces, grain bound- aries, and interfaces. 1 The heterogeneous melting can be ex- plained satisfactorily through the thermodynamic relation among the interface energies. Namely, the sum of the newly formed solid-liquid and liquid-vapor interface energies is less than or equal to the solid-vapor interface energy, or  sv   sl +  lv , where s, l, v represent solid, liquid, and vapor phases, respectively. 1 The decrease in the total interfacial free energies is the cause for the heterogeneous melting. However, how a liquid nucleates in a perfect i.e., surface- free and defect-free crystal remains an open question to date. Specifically, the detailed microscopic mechanisms and the thermodynamic relations of this seemingly simple phe- nomenon still remain unanswered, despite extensive studies made in the past century. 2–21 The difficulties originated mainly from the presence of surfaces. Since all materials have surfaces and the preemp- tive heterogeneous surface melting is always dominant, ho- mogeneous melting could not occur without superheating the solids. 4,7,8 Nevertheless, in several cases, superheating was indeed achieved when special techniques were used to sup- press the surface melting. For example, Daeges et al. 9 coated a silver sphere with a thin layer of gold. Since the lattice constants of gold and silver are very close, coating or pref- erably epitaxially growing gold is tantamount to removing the free surface of the silver particle. Because the melting temperature of gold is higher than that of silver, the coated silver core would melt earlier than the gold shell. As a result, up to 25 K of superheating above the normal melting point in the silver was observed for a time period of about 1 min. Superheating can also be achieved by using picosecond pulsed laser irradiation techniques. 10–14 The laser irradiation heats the materials internally and therefore can initiate melt- ing from the bulk, or homogeneously. Substantial superheat- ing about 20% above the normal melting point has been observed from these experiments. However, melting is ex- tremely fast in these experiments, typically, in just a few nanoseconds. Thus, many kinetic and thermodynamic param- eters could not be precisely measured or controlled. Conse- quently, it is difficult to investigate the detailed microscopic mechanisms of homogeneous melting in the superheating regime from these experiments. Recently, computer simulations 15–19,21 have been used for investigating homoge- neous melting. By employing periodic boundary conditions, one can “remove” surfaces, so superheating can be achieved easily. However, the heating rates are extremely high in most simulations, 15–19,21 usually on the order of 10 11 –10 13 K / s. Under such high heating rates, melting is always observed to occur catastrophically. Due to the short time window e.g., a few hundred femptoseconds available in the catastrophic melting, many vital kinetic and thermodynamic properties are suppressed. As a result, the detailed microscopic mecha- nism and kinetic behavior related to homogeneous melting are either missed or only partially accessible. 15–19,21 In this paper, we investigate the microscopic mechanism of homogeneous melting in the superheating regime by using molecular dynamics simulation. The baseline of this study begins at the heating rate effects on melting. We show that while the fast heating rate leads to catastrophic melting at the superheating limit, slow heating rate can lead to more detailed observations of the thermodynamic and, in particu- lar, the kinetic processes at temperatures below the super- heating limit. To this end, an isothermal heating method is implemented see Sec II A for the explanation. Detailed in- formation will be examined at fixed temperatures before and after melting occurs by monitoring various structural and defect characterization quantities, thermodynamic properties, kinetic behaviors, and atomic movements. In particular, we focus on the correlated atomic motions under the isothermal heating condition and their relation to local disorder or liquid nucleus formation. Our results reveal that strong diffusive atomic motions occur in a quiescent period before melting occurs, which have been missed in the fast heating process. The highly correlated motions consist of both closed and open loops of self-diffusing atoms. It is the open loops that eventually lead to the formation of liquid nuclei. The ther- modynamic and kinetic properties obtained from this work allow us to probe into the atomic mechanisms of homoge- PHYSICAL REVIEW B 77, 134109 2008 1098-0121/2008/7713/13410913 ©2008 The American Physical Society 134109-1