molecular dynamics simulation of heat transfer and phase change during

1 Copyright © 2001 by ASME Proceedings of NHTC'01 35th National Heat Transfer Conference Anaheim, California, June 10-12, 2001 NHTC2001-20070 MOLECULAR DYNAMICS SIMULATION OF HEAT TRANSFER AND PHASE CHANGE DURING LASER MATERIAL INTERACTION Xinwei Wang, Xianfan Xu * School of Mechanical Engineering Purdue University West Lafayette, IN 47907 * To whom correspondence should be addressed ABSTRACT In this work, heat transfer and phase change of an argon crystal illuminated with a picosecond pulsed laser are investigated using molecular dynamics simulations. The result reveals no clear interface when phase change occurs, but a transition region where the crystal structure and the liquid structure co-exist between the solid and the liquid. Superheating is observed during the melting process. The solid-liquid and liquid-vapor interfaces are found to move with a velocity of hundreds of meters per second. In addition, the vapor is found to be ejected from the surface with a velocity close to a thousand meters per second. Keywords: heat transfer, phase change, MD simulation, laser- material interaction, ablation threshold NOMENCLATURE F force I laser intensity k thermal conductivity B k Boltzmann's constant m atomic mass M P probability for atoms moving with a velocity v q ′′ heat flux applied to the surface of the target for thermal conductivity calculation r atomic position c r cut off distance s r the nearest neighbor distance t time T t preset time constant in velocity scaling t δ time step T temperature T δ initial temperature increase for calculating the specific heat T ∆ final temperature increase for calculating the specific heat v velocity x coordinate in x direction y coordinate in y direction z coordinate in z direction Greek Symbols χ velocity scaling factor ε LJ well depth parameter φ potential σ equilibrium separation parameter ξ current kinetic temperature in velocity scaling Subscripts i atomic index Superscripts * no-dimensionalized I. INTRODUCTION In recent years, ultrashort pulsed lasers have been rapidly developed and used in materials processing. Due to the extremely short pulse duration, many difficulties exist in experimental investigation of laser material interaction such as measuring the transient surface temperature, the velocity of the solid-liquid interface, and the material ablation rate. Ultrashort laser material interaction involves several coupled, non-linear, and non-equilibrium processes inducing an extremely high 2 Copyright © 2001 by ASME heating rate (10 16 K/s) and a high temperature gradient (10 11 K/m). The continuum approach of solving the heat transfer problem becomes questionable under these extreme situations. On the other hand, the molecular dynamics (MD) simulation, which solves the movement of atoms or molecules directly, is suitable for investigating the ultrashort laser material interaction process. One aim of this work is to use the MD simulation to investigate heat transfer occurring in ultrashort laser-material interaction and to compare the results with those obtained with the continuum approach. A large amount of work has been dedicated to studying laser material interaction using MD simulations. Due to the limitation of computer resources, most work was restricted to systems with a small number of atoms, thus only qualitative results such as the structural change due to heating were obtained. For instance, using quantum MD simulations, Shibahara and Kotake studied the interaction between metallic atoms and the laser beam in a system consisting of 13 atoms or less [1, 2]. Their work was focused on the structural change of metallic atoms due to laser beam absorption. Häkkinen and Landman [3] studied dynamics of superheating, melting, and annealing at the Cu surface induced by laser beam irradiation using the two-step heat transfer model developed by Anisimov [4]. This model describes the laser metal interaction in two steps including photon energy absorption in electrons and lattice heating through interaction with electrons. A large body of the MD simulation of laser material interaction was to study the laser induced ablation in various systems. Kotake and Kuroki [5] studied laser ablation of a small dielectric system consisting of 4851 atoms. Laser beam absorption was simulated by exciting the potential energy of atoms. Applying the same laser beam absorption approach, Herrmann and Campbell [6] investigated laser ablation of a silicon crystal containing approximately 23000 atoms. Zhigileit et al. [7, 8] studied laser induced ablation of organic solid using the breathing sphere model, which simulated laser irradiation by vibrational excitation of molecules. However, because of the arbitrary properties chosen in the calculation, their calculation results were qualitative, and were restricted to small systems with tens of thousands of atoms. Ohmura et al. [9] attempted to study laser metal interaction with the MD simulation using the Morse potential function for metals [10]. The Morse potential function simplified the potential calculation among the lattice and enabled them to study a larger system with 160,000 atoms. Heat conduction by the electron gas, which dominated heat transfer in metal, could not be predicted by the Morse potential function. Alternatively, heat conduction was simulated using the finite difference method based on the thermal conductivity of metal. Laser material interaction in a large system was recently investigated by Etcheverry and Mesaros [11]. In their work, a crystal argon solid containing about half a million atoms was simulated. For laser induced acoustic waves, a good agreement between the MD simulation and the standard thermoelastic calculation was observed. In this work, MD simulations are conducted to study laser argon interaction. The system under study has 486,000 atoms, which is large enough to suppress statistical uncertainty. Laser heating of argon with different laser fluences is investigated. Laser induced heat transfer, melting, evaporation, material ablation are emphasized in this work. Phase change relevant parameters, such as the velocity of solid-liquid and liquid-vapor interfaces, ablation rate, and ablation threshold fluence are reported. In section II, theories for the MD simulation used in this work are introduced. Calculation results are summarized in section III. II. THEORY OF MD SIMULATION Molecular dynamics simulation is a computational method to investigate the behavior of materials by simulating the atomic motion controlled by a given potential. Argon is overwhelmingly explored in MD simulation due to the meaningful physical constants of the widely-accepted Lennard- Jones 12-6 (LJ) potential and the less computation time required than more complicated potentials involving multi-body interaction or electric static force. In this calculation, an argon crystal at 50 K is assumed to be illuminated with a spatially uniform laser beam. The melting and the boiling temperatures of argon at one atm are 83.8 K and 87.3 K, respectively, while its critical temperature is 150.87 K. The basic problem involves solving Newtonian equations for each atom interacting with its neighbors by means of a pairwise Lennard-Jones force: ∑ = ≠ij ij i i F dt rd m 2 2 (1) where i m and i r are the mass and position of atom i, respectively, ij F is the interaction force between atoms i and j, which is obtained from the Lennard-Jones potential as ijijij rF ∂∂φ /−= . The Lennard-Jones potential ij φ is written as                 −         = 612 4 ijij ij rr σσ εφ (2a) where ε is the LJ well depth parameter, σ is the equilibrium separation parameter, and ijij rrr −= . Therefore, the force ij F can be expressed as ij ijij ij r rr F ⋅         +−= 8 6 14 12 6124 σσ ε (2b) A standard method for solving ordinary differential equations (1) and (2) is the finite difference approach. The general idea is to obtain the atomic positions, velocities, etc. at time tt δ + based on the positions, velocities, and other 3 Copyright © 2001 by ASME dynamic information at time t. The equations are solved on a step-by-step basis, and the time interval t δ is dependent somehow on the method applied. However, t δ is usually much smaller than the typical time taken for an atom to travel its own length. Many different algorithms have been developed to solve Eqs. (1) and (2), of which the Verlet algorithm is widely used due to its numerical stability, convenience, and simplicity [12]. In this calculation, the velocity Verlet algorithm is used, which is expressed as: tttvtrttr ii δδδ )2/()()( ++=+ (3a) ij ij ij r tt ttF ∂ δ∂φ δ )( )( + −=+ (3b) t m ttF ttvttv i ij δ δ δδ )( )2/()2/3( + ++=+ (3c) In the calculation, most time is spent on calculating forces using Eq. (3b). When two atoms are far away enough from each other, the force between them is negligible. The distance between atoms beyond which the interaction force is neglected is called cutoff distance (potential cutoff), c r . In this work, c r is taken as 2.5 σ , which is a cutoff potential widely used in MD simulations using the LJ potential. At this distance, the potential is only about 1.6% of the well depth. In the calculation, the distance between atoms is first compared with c r , and only when the distance is less than c r , the force is calculated. The comparison of the atomic distance with c r is organized by means of the cell structure and the linked list methods [12]. In these methods, the computation domain is divided into many structural cells with a characteristic size of c r . To speed up the calculation, direct evaluation of the force using Eqs. (2) is avoided by looking up a pre-prepared table for the force in the range of 2 ij r from 0.25 2 σ to 2 c r , with an interval of 10 -6 2 σ . Laser energy absorption in the material is simulated by scaling the velocities of all atoms in each structural cell by an appropriate factor. The amount of energy deposited in each cell is calculated assuming the laser beam is exponentially absorbed in the target. In order to prevent undesired amplification of atomic macromotion, the average velocity of atoms in each layer of structural cells is subtracted before velocity scaling. Non-dimensionalized parameters are used, which are listed in Table 1. With non-dimensionalization, Eqs. (1) and (2) become ∑ = ≠ij ij i F td rd * 2* *2 )( (4a) 6*12* * )( 1 )( 1 ijij ij rr −= φ (4b) * 8*14* * )( 6 )( 12 ij ijij ij r rr F ⋅         +−= (4c) The form of Eqs. (3a) and (3b) is preserved, while Eq. (3c) becomes ********** )()2/()2/3( tttFttvttv ij δδδδ +++=+ (5) Table 1. Nondimensionalized parameters Quantity Equation Time )4//( * εσ mtt = Length σ / * rr = Mass 1/ * == mmm Velocity mvv /4/ * ε = Potential εφφ 4/ * = Force )/4/( * σε ijij FF = Temperature ε 4/ * TkT B = Parameters used in the calculation are listed in Table 2. A face-centered cubic (fcc) structure is used to initialize atomic positions. The initial atomic velocities are specified randomly from a Gaussian distribution based on the temperature. III. CALCULATION RESULTS The target studied consists of 90 fcc unit cells in x and y directions, and 15 fcc unit cells in the z direction. Each unit cell contains 4 atoms, and the system consists of 486,000 atoms. In both x and y directions, the computational domain has a size of 48.73 nm. In the z direction, the size of the computation domain is 17.14 nm with the bottom of the target located at 4.51 nm and the top surface (laser irradiated surface ) at 12.63 nm. 4 Copyright © 2001 by ASME Table 2. Values of the parameters used in the calculation Parameter Value ε , LJ well depth parameter 21 10653.1 − × J σ , LJ equilibrium separation 0.3406 nm m , Argon atomic mass 27 103.66 − × kg B k , Boltzmann’s constant 23 1038.1 − × J/K a, Lattice constant 0.5414 nm c r , Cut off distance 0.8515 nm Size of the sample – x 48.726 nm Size of the sample –y 48.726 nm Size of the sample –z 8.121 nm Time step 25 fs Number of atoms 486000 III.1 Thermal Equilibrium Calculation The first step in the calculation is to initialize the system so that it is in thermal equilibrium before laser heating, which is done by a thermal equilibrium calculation. In this calculation, the target is initially constructed based on the fcc lattice structure with the (100) surface facing up. The nearest neighbor distance, s r , in the fcc lattice for argon depends on temperature T, and is calculated using the expression given by Broughton et al. [13], 2 014743.0054792.00964.1)(       +       += εεσ TkTk T r BB s 543 25057.023653.0083484.0       +       −       + εεε TkTkTk BBB (7) Initial velocities of atoms are specified randomly from a Gaussian distribution based on the specified temperature of 50 K using the following formula, Tkvm B i i 2 3 2 1 3 1 2 = ∑ = (8) where B k is the Boltzmann's constant. During the equilibrium calculation, due to the variation of the atomic positions, the temperature of the target may change because of the energy transform between the kinetic and potential energies. In order to allow the target to reach thermal equilibrium at the expected temperature, velocity scaling is necessary to adjust the temperature of the target during the early period of equilibration. The velocity scaling approach proposed by Berendsen et al. [14] is applied in this work. At each time step, velocities are scaled by a factor 2/1 1                 += ξ δ χ T t t T (9) where ξ is the current kinetic temperature, and T t is a preset time constant, which is taken as 0.4 ps in the simulation. This technique forces the system towards the desired temperature at a rate determined by T t , while only slightly perturbing the forces on each atom. After scaling the velocity for 50 ps, the calculation is continued for another 100 ps to reach thermal equilibrium. The final equilibrium temperature of the target is 49.87 K, which is close to the desired temperature of 50 K. When the target reaches the thermal equilibrium status, the atomic velocity distribution should follow the Maxwellian distribution Tk mv B M B e Tk m vP 2 2/3 2 2 2 4 −         = π π (10) where M P is the probability for an atom moving with a velocity, v . The velocity distribution based on the simulation results as well as the Maxwell's distribution, are shown in Fig. 1, which indicates a good agreement between the two. 0 10 0 2 10 -3 4 10 -3 6 10 -3 8 10 -3 0 100 200 300 400 500 MD Simulation Maxwell's Distribution Probability Velocity (m/s) Figure 1. Comparison of the velocity distribution by the MD simulation with the Maxwellian velocity distribution. Figure 2 shows the lattice structure in the x-z plane when the system is in thermal equilibrium. For the purpose of illustration, only the atoms in the range of 120 << x nm and 6.120 << y nm are plotted. It is seen that atoms are located around their equilibrium positions, and the lattice structure is preserved. It is also observed from Fig. 2 that at the top and the 5 Copyright © 2001 by ASME bottom surfaces of the target, a few atoms have escaped due to the free boundary conditions. 4 7 10 13 024681012 z (nm) x (nm) Figure 2. Structure of the target in the x-z plane within the range of 120 << x nm and 6.120 << y nm III.2 Calculation of Thermophysical Properties In order to check the validity of the simulation, thermal physical properties including the specific heat at constant pressure, the specific heat at constant volume, and the thermal conductivity are calculated and compared with published data. To calculate the specific heat at constant pressure, the system is first equilibrated with periodical boundary conditions in x and y directions, and free boundary conditions in the z direction, which simulates a target in vacuum. A kinetic energy of Tk B δ ⋅2/3 with 8=T δ is added to each atom and the system is calculated for about 100 ps to reach a new thermal equilibrium status with a final temperature increase of T ∆ . The specific heat is calculated as )/(2/3 TmTkc Bp ∆δ ⋅⋅= (11) The specific heat at constant pressure (vacuum) is calculated to be 787.8 J/kg·K at 51.476 K. This value is about 24% higher than the literature data, which is 637.5 J/kg·K [15]. This difference is mainly due to the free boundary conditions of vacuum used in the MD simulation, while the experimental results are for samples under atmospheric pressure. Under free boundary conditions, atoms are easier to expand in space when heated. Therefore, more heat is stored in the form of potential energy and resulting in a larger specific heat. The specific heat at constant volume is calculated in the similar way as described above except that free boundary conditions in the z direction are replaced with periodical boundary conditions in order to keep the volume constant. The specific heat at constant volume is calculated to be 576.0 J/kg·K, which is only 6% higher than the literature value of 543.5 J/kg·K [15]. This small difference might be due to the potential function used in the calculation, which is more suitable for argon in liquid state. The thermal conductivity of argon is calculated as follows. The target is first equilibrated with periodical boundary conditions in x and y directions, and free boundary conditions in the z direction. A constant heat flux q ′′ is applied to the surface of the target by scaling velocities of atoms in cells on the top surface, and the same amount of heat flux is dissipated from the bottom of the target by scaling velocities of atoms in cells at the bottom. The heat flux q ′′ is taken as 8 1083216.2 × W/m 2 , which induces a temperature difference of about 5 K across the target. Figure 3 shows the temperature distribution in the target when a heat flux is passing through. It is seen that a linear temperature distribution is established in the target due to the heat flux. The thermal conductivity k is calculated as x T q k ∂∂ / ′′ −= (12) The thermal conductivity of the target is calculated to be 0.304 W/m·K, which is about 34% smaller than the experimental value of 0.468 W/m·K. This large difference could be due to the free boundary conditions used in the calculation and possible errors in the potential function. Further work is necessary to study the effects of boundary conditions and different potential functions. 46 47 48 49 50 51 52 53 54 471013 Temperature (K) z (nm) Figure 3. Temperature distribution in the target subjected to a constant heat flux III.3 Laser Material Interaction In laser material interaction, periodical boundary conditions are assumed on surfaces in x and y directions, and free boundary conditions on surfaces in the z direction. The simulation corresponds to the problem of irradiating a block in vacuum. The laser beam is uniform in space, and has a temporal Gaussian distribution with a 5 ps FWHM centered at 10 ps. The 6 Copyright © 2001 by ASME laser beam energy is absorbed exponentially in the target and expressed as τ /)(zI d z dI −= (13) where I is the laser beam intensity, and τ is the characteristic absorption depth, which is taken as 2.5 nm. Laser Heating The temperature distribution in the target illuminated with a laser pulse of 0.03 J/m 2 is first calculated and compared with finite difference results. With this laser fluence, only a temperature increase is induced, and no phase change occurs. Figure 4 shows the temperature distribution calculated using the MD simulation and the finite difference method. In MD simulations, temperature at different locations is calculated as an ensemble average of a domain with thickness of 2.5 σ in the z direction. In the calculation using the finite difference method, properties of the target obtained with the MD simulation are used. It is observed from Fig. 4 that the results obtained from the MD simulation show proper trends comparing with those by the finite difference method. The difference between them is on the same order of the statistic uncertainty of the MD simulation. In other words, the continuum approach is still capable of predicting the heating process induced by a picosecond laser pulse. Laser Induced Phase Change In this section, various phenomena accompanying phase change in an argon target illuminated with a laser pulse of 0.7 J/m 2 are investigated. The threshold fluence for ablation is also studied. For argon illuminated with a pulsed laser of 0.7 J/m 2 , a series of snapshots of atomic positions at different times is shown in Fig. 5. It is seen that until 10 ps, the lattice structure is still preserved in the target. At about 10 ps, melting starts, and the lattice structure is destroyed in the melted region and is replaced by a random atomic distribution. After 20 ps, the solid liquid interface stops moving into the target, and vaporized atoms are clearly seen. Figure 6 shows the distribution of number density of atoms in space at different times, which demonstrates the variation of solid structure during laser heating. At the early stage of laser heating, the crystal structure is preserved in the target, which is seen as the peak number density of atoms on each lattice layer. Due to the increase of the atomic kinetic energy in laser heating, atoms vibrate more in the crystal region, causing a lower peak of the number density of atoms and a wide distribution. As laser heating progresses, the target is melted from its front surface, and the atomic distribution becomes random. Therefore, the number density of atoms becomes uniform over the melted region. However, no clear interface is observed between the solid and the liquid. Instead, the structure of solid and liquid co-exists within a certain range between the solid and the liquid, which is shown as the co-existence of the peak and the high base of the number density of atoms. Evaporation happens at the surface of the target, which reduces the number density of atoms significantly at the location near the liquid surface. 48 50 52 54 56 MD simulation Finite Difference t=5 ps 50 52 54 56 MD simulation Finite Difference t=10 ps 50 52 54 56 MD simulation Finite Difference t=15 ps Temperature (K) 50 52 54 56 MD simulation Finite Difference t=20 ps 50 52 54 56 MD simulation Finite Difference t=25 ps 50 52 54 56 MD simulation Finite Difference 4 7 10 13 t=30 ps z (nm) Figure 4. Temperature distribution in the target illuminated with a laser pulse of 0.03 J/m 2 . In order to find out the rate of melting and evaporation, criteria are needed to determine the solid-liquid and liquid- vapor interfaces. For solid argon, the average number density of atoms is 28 1052.2 × m -3 with a distribution in space as shown in Fig. 6. Owing to the lattice structure, the number density of atoms is higher than the average value around the lattice layer location. In this work, if the number density of atoms is higher 7 Copyright © 2001 by ASME than 28 1052.2 × m -3 , the material is treated as solid. At the front of the melted region, it is seen from Fig. 6 that when the number density of atoms is below 27 42.8 × m -3 , a relatively sharp decrease of the number density of atoms happens. Therefore, when the number density of atoms is less than 27 1042.8 × m -3 , which is about one third of the number density in solid, the material is assumed to be vapor. Although this criterion for liquid-vapor interface is not quite rigorous due to the large transition range from liquid to vapor, further study of the liquid- vapor interface using radial distribution function shows that the criterion used here gives a good approximation of the liquid- vapor interface. 0 4 8 12 (t=5 ps) 0 4 8 12 (t=10 ps) 0 4 8 12 (t=15 ps) 0 4 8 12 (t=20 ps) 0 4 8 12 (t=25 ps) 0 4 8 12 357911131517 x (nm) (t=30 ps) z (nm) Figure 5. Snapshots of atomic positions in argon illuminated with a laser pulse with a fluence of 0.7 J/m 2 . Applying these criteria, transient locations of the solid- liquid and liquid-vapor interfaces, as well as the velocity of interfaces can be obtained and are shown in Fig. 7. It is observed that melting and evaporation start at 10 ps, while laser heating starts at around 5 ps. It is seen that the solid-liquid interface moves into the solid owing to the melting of the solid, and the liquid-vapor interface moves outward as the melted region expands because liquid is less dense than solid. At about 20 ps, both solid-liquid and liquid-vapor interfaces stop moving. The velocities of the interfaces are shown in Fig. 7b. It is seen that the duration of the interface movement is about 10 ps, which is about the same as the laser pulse width. The highest velocity of the liquid-vapor interface is about 200 m/s, close to the equilibrium velocity (233.5 m/s) of the argon atom at the boiling temperature. The highest velocity of the solid-liquid interface is about 400 m/s, lower than the sound velocity (1501 m/s) in argon. 0.00 0.25 0.50 0.75 1.00 1.25 t=5 ps 0.00 0.25 0.50 0.75 1.00 1.25 t=10 ps /m 3 ) 0.00 0.25 0.50 0.75 1.00 1.25 t=15 ps of Atoms (10 29 0.00 0.25 0.50 0.75 1.00 1.25 t=20 ps Number Density 0.00 0.25 0.50 0.75 1.00 1.25 t=25 ps 0.00 0.25 0.50 0.75 1.00 1.25 3 5 7 9 11 13 15 17 t=30 ps z (nm) Figure 6. Distribution of number density of atoms at different times in argon illuminated with a laser pulse of 0.7 J/m 2 . The temperature distribution in argon at different times is shown in Fig. 8. At 5 ps, laser heating just starts, and the target has a spatially uniform temperature of about 50 K. Note that the initial size of the target extends from 4.5 nm to 12.6 nm. Melting starts at 10 ps as indicated in Fig. 7, and it is clear from Fig. 8 that at this moment, the temperature is higher than the melting and the boiling point in the heated region, and is even close to the critical point. At 15 ps, a flat region in the temperature distribution is observed around the location of 10 8 Copyright © 2001 by ASME nm, which is the melting interface region. The temperature in this flat region is around 90 K, which is higher than the melting point, indicating superheating at the melting front. 9 10 11 12 13 14 15 16 0 5 10 15 20 25 30 Solid-liquid Interface Liquid-vapor Interface z (nm) Time (ps) (a) -500 -250 0 250 500 0 5 10 15 20 25 30 Solid-liquid Interface Liquid-vapor Interface Velocity (m/s) Time (ps) (b) Figure 7. (a) Positions (b) velocities of the solid-liquid interface and the liquid-vapor interface in argon illuminated with a laser pulse of 0.7 J/m 2 . An interesting phenomenon is observed at 20 ps, shortly after melting stops. At this moment, a minimum temperature is observed at 9.5 nm. The reason for this temperature drop is not known yet, and is still under investigation. This minimum temperature disappears gradually due to heat transfer from the surrounding higher temperature regions. It is worth noting that results of superheating, as well as the lack of a sharp solid- liquid interface as mentioned previously, could not be predicted using the continuum approaches without assumptions. 40 60 80 100 120 140 3 5 7 9 11 13 15 17 t=5 ps t=10 ps t=15 ps t=20 ps t=25 ps t=30 ps Temperature (K) z (nm) T m T b Figure 8. Temperature distribution in argon illuminated with a laser pulse of 0.7 J/m 2 . The velocity distribution of vaporized atoms at different times is shown in Fig. 9. At 10 ps, melting just starts, and the average velocity of atoms is close to zero except those on the surface, which have high kinetic energy due to the free boundary condition. At 15 ps, a higher atomic velocity is observed. At the vapor front, the velocity is close to 800 m/s, while at locations near the surface, the vapor velocity is much smaller. At 30 ps, non-zero velocities are only observed at locations of 15 nm or further beyond the liquid-vapor interface as indicated in Fig. 7. This shows evaporation from the liquid surface is weak after laser heating stops. -200 0 200 400 600 800 0 5 10 15 20 t=5 ps t=10 ps t=15 ps t=20 ps t=25 ps t=30 ps Average Velocity (m/s) z (nm) Figure 9. Spatial distribution of the average velocity in the z direction in argon illuminated with a laser pulse of 0.7 J/m 2 . 9 Copyright © 2001 by ASME 0 1 2 3 0 5 10 15 20 25 30 Melting Evaporation Depth (nm) Time (ps) (a) -100 0 100 200 300 400 0 5 10 15 20 25 30 Melting Evaporation Rate of Depth (m/s) Time (ps) (b) Figure 10. (a) Depths of the solid melted and vaporized, and (b) rate of melting and evaporation in argon illuminated with a laser pulse of 0.7 J/m 2 . 0 1 2 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Ablation Depth (nm) Energy Fluence (J/m 2 ) Figure 11. The ablation depth induced by different laser fluences in argon. The depth of melting and vaporization, as well as the melting and evaporation rates are shown in Fig. 10. It is seen that the melting depth is much larger than the vaporization depth. From Fig. 10b it is found that melting happens mostly between 10 and 20 ps, while the evaporation process goes on until 25 ps, then reduces to a lower level corresponding to evaporation of liquid in vacuum. The depths of ablation induced by different laser fluences are shown in Fig. 11. IV. CONCLUSION In this work, laser material interaction is studied using MD simulations. Based on the results, the following conclusions are obtained. First, during picosecond laser heating, the heat transfer process predicted using the continuum approach agrees with the result of the MD simulation. Second, when melting happens, a transition region of about 1 nm, instead of a clear interface is found between the solid and the liquid. During the melting process, the solid-liquid interface moves at almost a constant velocity much lower than the local sound velocity, while the liquid-vapor interface moves with a velocity close to the local equilibrium atomic velocity. At the solid-liquid interface, superheating is observed. Finally, the laser ablated material is found to move out of the target with a velocity of about a thousand meters per second. ACKNOWLEDGMENTS Support to this work by the National Science Foundation (CTS-9624890) is gratefully acknowledged. REFERENCES 1. Shibahara, M., and Kotake, S., 1997, "Quantum Molecular Dynamics Study on Light-to-heat Absorption Mechanism: Two Metallic Atom System," International Journal of Heat and Mass Transfer, 40, pp. 3209-3222. 2. Shibahara, M., and Kotake, S., 1998, "Quantum Molecular Dynamics Study of Light-to-heat Absorption Mechanism in atomic Systems," International Journal of Heat and Mass Transfer, 41, pp. 839-849. 3. Häkkinen, H., and Landman, U., 1993, "Superheating, Melting, and Annealing of Copper Surfaces," Physical Review Letters, 71, pp. 1023-1026. 4. Anisimov, S. I., Kapeliovich, B. L., Perel'man, T. L., 1974, "Electron Emission from Metal Surfaces Exposed to Ultra-short Laser Pulses," Soviet Physics, JETP, 39, pp. 375- 377. 5. Kotake, S., and Kuroki, M., 1993, "Molecular Dynamics Study of Solid Melting and Vaporization by Laser Irradiation," International Journal of Heat and Mass Transfer, 36, pp. 2061- 2067. 6. Herrmann, R. F. W., and Campbell, E. E. B., 1998, "Ultrashort Pulse Laser Ablation of Silicon: an MD Simulation Study," Applied Physics A, 66, pp. 35-42. 10 Copyright © 2001 by ASME 7. Zhigilei, L. V., Kodali, P. B. S., and Garrison, J., 1997, "Molecular Dynamics Model for Laser Ablation and Desorption of Organic Solids," Journal of Physical Chemistry B, 101, pp. 2028-2037. 8. Zhigilei, L. V., Kodali, P. B. S., and Garrison, J., 1998, "A Microscopic View of Laser Ablation," Journal of Physical Chemistry B, 102, pp. 2845-2853. 9. Ohmura, E., Fukumoto, I., and Miyamoto, I., 1999, "Modified Molecular Dynamics Simulation on Ultrafast Laser Ablation of Metal," the International Congress on Applications of Lasers and Electro-Optics, 1999, pp. 219-228. 10. Girifalco, L. A., and Weizer, V. G., 1959, "Application of the Morse Potential Function to Cubic Metals," Physical Review, 114, pp. 687-690. 11. Etcheverry, J. I., and Mesaros, M., 1999, "Molecular Dynamics Simulation of the Production of Acoustic Waves by Pulsed Laser Irradiation," Physical Review B, 60, pp. 9430- 9434. 12. Allen, M. P. and Tildesley, D. J., 1987, Computer Simulation of Liquids, Clarendon Press, Oxford. 13. Broughton, J. Q. and Gilmer, G. H., 1983, "Molecular Dynamics Investigation of the Crystal-fluid Interface. I. Bulk Properties," Journal of Chemical Physics, 79, pp. 5095-5104. 14. Berendsen, H. J. C, Postma, J. P. M, van Gunsteren, W. F., DiNola, A., and Haak, J. R., 1984, "Molecular Dynamics with Coupling to an External Bath," Journal of Chemical Physics, 81, pp. 3684-90. 15. Peterson, O. G., Batchelder, D. N., and Simmons, R. O., 1966, "Measurements of X-Ray Lattice Constant, Thermal Expansivity, and Isothermal Compressibility of Argon Crystals," Physical Review, 150, pp. 703-711 . Proceedings of NHTC'01 35th National Heat Transfer Conference Anaheim, California, June 10-12, 2001 NHTC2001-20070 MOLECULAR DYNAMICS SIMULATION OF HEAT TRANSFER AND PHASE CHANGE DURING. Shibahara, M., and Kotake, S., 1998, "Quantum Molecular Dynamics Study of Light-to -heat Absorption Mechanism in atomic Systems," International Journal of Heat and Mass Transfer, 41,. 375- 377. 5. Kotake, S., and Kuroki, M., 1993, " ;Molecular Dynamics Study of Solid Melting and Vaporization by Laser Irradiation," International Journal of Heat and Mass Transfer, 36, pp.