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ABSTRACT
The rapid melting and resolidification in femtosecond laser interaction with a single nanoparticle are investigated analytically. The dual-hyperbolic two-step (DHTS) model is coupled with the interfacial tracking method to describe the ultrafast melting and resolidification behavior. The optical reflectivity is solved using the Mie theory. Comparisons between the DHTS model and the parabolic two-step (PTS) model are presented. The results show that, for the femtosecond lasers, the melting depth predicted by the DHTS model is much higher than that of the PTS model. In addition, a phase map also presents the due parameters for laser sintering.
Nomenclature
| Ae | = | material constant for electron relaxation time [1/K2 · s] |
| Be | = | coefficient for electronic heat capacity [J/m3 · K2] |
| Bl | = | material constant for lattice relaxation time [1/K2 · s] |
| C | = | heat capacity [J/m3 · K] |
| f | = | liquid fraction |
| F | = | spherical factor |
| G | = | electron-lattice coupling factor [W/m3 · K] |
| GRT | = | electron-lattice coupling factor at room temperature [W/m3 · K] |
| hm | = | latent heat of melting [J/kg] |
| J | = | heat source fluence of laser [J/m2] |
| k | = | thermal conductivity [W/m · K] |
| kB | = | Boltzmann constant [J/K] |
| ksca | = | scattering efficiency |
| kext | = | extinction efficiency |
| m | = | refractive index |
| N | = | number density of atom [m−3] |
| q | = | heat flux [J/m2] |
| R | = | reflectivity of gold film |
| Rg | = | gas constant for gold [J/kg · K] |
| r | = | radius [m] |
| S | = | heat source of unit volume [W/m3] |
| s | = | interfacial location [m] |
| t | = | time [s] |
| tp | = | FWHM (full width at half maximum) pulse width [s] |
| T | = | temperature [K] |
| us | = | interfacial velocity [m/s] |
| V | = | volume [m3] |
| V0 | = | maximum interfacial velocity [m/s] |
| α | = | dimensionless radius |
| ϵr | = | relative dielectric constant |
| δ | = | optical penetration depth [m] |
| δb | = | ballistic range [m] |
| λ | = | wavelength [m] |
| η | = | electron thermal conductivity constant |
| ϑ | = | dimensionless temperature |
| ξ | = | critical coefficient |
| ρ | = | density [kg/m3] |
| τ | = | relaxation time [s] |
| μr | = | relative permeability |
| χ | = | electron thermal conductivity constant [W/m · K] |
| Subscript | = | |
| c | = | critical |
| e | = | electron |
| eq | = | thermal equilibrium state |
| F | = | Fermi |
| i | = | initial |
| I | = | interfacial |
| l | = | lattice |
| ℓ | = | liquid |
| m | = | melting |
| s | = | space |
| v | = | vaporization |
Nomenclature
| Ae | = | material constant for electron relaxation time [1/K2 · s] |
| Be | = | coefficient for electronic heat capacity [J/m3 · K2] |
| Bl | = | material constant for lattice relaxation time [1/K2 · s] |
| C | = | heat capacity [J/m3 · K] |
| f | = | liquid fraction |
| F | = | spherical factor |
| G | = | electron-lattice coupling factor [W/m3 · K] |
| GRT | = | electron-lattice coupling factor at room temperature [W/m3 · K] |
| hm | = | latent heat of melting [J/kg] |
| J | = | heat source fluence of laser [J/m2] |
| k | = | thermal conductivity [W/m · K] |
| kB | = | Boltzmann constant [J/K] |
| ksca | = | scattering efficiency |
| kext | = | extinction efficiency |
| m | = | refractive index |
| N | = | number density of atom [m−3] |
| q | = | heat flux [J/m2] |
| R | = | reflectivity of gold film |
| Rg | = | gas constant for gold [J/kg · K] |
| r | = | radius [m] |
| S | = | heat source of unit volume [W/m3] |
| s | = | interfacial location [m] |
| t | = | time [s] |
| tp | = | FWHM (full width at half maximum) pulse width [s] |
| T | = | temperature [K] |
| us | = | interfacial velocity [m/s] |
| V | = | volume [m3] |
| V0 | = | maximum interfacial velocity [m/s] |
| α | = | dimensionless radius |
| ϵr | = | relative dielectric constant |
| δ | = | optical penetration depth [m] |
| δb | = | ballistic range [m] |
| λ | = | wavelength [m] |
| η | = | electron thermal conductivity constant |
| ϑ | = | dimensionless temperature |
| ξ | = | critical coefficient |
| ρ | = | density [kg/m3] |
| τ | = | relaxation time [s] |
| μr | = | relative permeability |
| χ | = | electron thermal conductivity constant [W/m · K] |
| Subscript | = | |
| c | = | critical |
| e | = | electron |
| eq | = | thermal equilibrium state |
| F | = | Fermi |
| i | = | initial |
| I | = | interfacial |
| l | = | lattice |
| ℓ | = | liquid |
| m | = | melting |
| s | = | space |
| v | = | vaporization |