Multi-material two-temperature model for simulation of ultra-short laser ablation

We investigate the interaction of 100 fs laser pulses with metal targets at moderate intensities (10¹² to 5 × 10¹³ W/cm²). To take into account effects of laser energy absorption and relaxation we develop a multi-material two-temperature model based on a combination of different approaches. The backbone of the numerical model is a high-order multi-material Godunov method in a purely Eulerian form. This formulation includes an interface-tracking algorithm and treats spallation at high strain rates and negative pressures. The model consistently describes the hydrodynamic motion of a two-temperature plasma and accounts for laser energy absorption, electron-phonon/ions coupling and electron heat conductivity. In particular, phase transitions are accurately taken into account by means of a wide-range two-temperature multi-phase equation of state in a tabular form. The dynamics of the phase transitions and the evolution of the heat-affected zone are modeled and analyzed. We have found that a careful treatment of the transport coefficients, as well as consideration of phase transitions is of a great importance in obtaining reliable numerical results. Calculation results are furthermore compared for two metals with different electron-phonon coupling parameters (Au and Al). We have found that the main part of ablated material results from fragmentation of melted phase caused by tensile stresses. A homogeneous nucleation mechanism alone does not explain experimentally observed ablation depth.     

Comparative time-resolved study of solid-state and liquid ablation of polyethylene-glycol 1000: temperature, viscosity and surface tension dependence

Comparative study of solid and liquid phase ablation on the same sample by time-resolved investigations is presented in this paper. Polyethylene-glycol (PEG) 1000 having relatively low melting point (35 °C) was used in our experiments. By varying the sample temperature in the 20–80 °C range we could study the ablation mechanism in both solid and liquid (below and above the melting point) state of matter. An ArF excimer laser (λ=193 nm, FWHM=20 ns) was used for ablation at 1.95 J/cm² fluence. Ablation processes were observed by transmission fast photographic arrangement. It was demonstrated that plasma development and expansion (primer ablation, in 0–50 ns time range), formation and propagation parameters of shock wave and contact front did not depend on sample temperature and state of matter. The secondary material ejection (between 1–100 μs) showed a strong temperature dependence. Material ejection in the case of solid target occurred in the form of dense material cloud, and in the form of splashing for liquid (molten) sample. The ejection velocity of splashed jets depended on the sample temperature, significantly. This can be due to the change of molten PEG 1000 viscosity. Received: 1 November 1999 / Accepted: 17 April 2000 / Published online: 5 July 2000     

The melting behaviors of the Nb(1 1 0) nanofilm: a molecular dynamics study

By using molecular dynamics (MD) and the modified analytic embedded atom method (MAEAM), we have studied the melting point, the melting mechanism and the correspondingly dynamical behaviors of a Nb(1 1 0) nanofilm. Firstly, in accordance to the MD time dependence of the potential energy, the melting point of this nanofilm has been roughly estimated. Then, the melting mechanism of the nanofilm have been analyzed in detail with the application of the structure factor. The results clearly indicate that the melting transition of the 8th, 9th, and 10th atomic layer of the nanofilm has been characterized by the exponential, polynomial and linear sequence respectively when the thickness of the quasiliquid film attains to about 1.3 nm. Thirdly, the dynamical behaviors of the nanofilm melting, such as the melting front propagation velocity and the kinetic coefficient, which have also been analyzed, demonstrate that the melting front propagation velocity has linearly increased with the incremental temperature and the evaluated kinetic coefficient has approximately equaled 1.43m/(sK). Finally, by extrapolating the melting front propagation velocity to zero, we can accurately deduce the melting point of the Nb(1 1 0) nanofilm to 2568.3 K, which is much lower than the counterpart (2740 K) of the bulk niobium.     

Strength properties of an aluminum melt at extremely high tension rates under the action of femtosecond laser pulses

The dynamics of the melting of a surface nanolayer and the formation of thermal and shock waves in metals irradiated by femtosecond laser pulses has been investigated both experimentally and theoretically. A new experimental-computational method has been implemented to determine the parameters of laser-induced shock waves in metallic films. Data on the strength properties of the condensed phase in aluminum films at an extremely high strain rate ($ \dot V $ \dot V /V ∼ 10⁹ s⁻¹)under the action of a laser-induced shock wave have been obtained.     

Thermal conductivities of solid and liquid phases for neopentylglycol, aminomethylpropanediol and their binary alloy

The variations of thermal conductivities of solid phases versus temperature for neopentylglycol (NPG), 2-amino-2-methyl-1,3-propanediol (AMPD) and AMPD-42.2 mol% NPG alloy were measured with a radial heat flow apparatus. From the graphs of the solid phases thermal conductivity variations versus temperature, the thermal conductivities of the solid phases at their melting temperature and temperature coefficients for same materials were also found to be 0.22±0.01, 0.45±0.02 and 0.32±0.02 W/Km and 0.0047, 0.0031 and 0.0043 K⁻¹, respectively. The thermal conductivity ratios of liquid phase to solid phase for the same materials at their melting temperature are found to be 1.07, 1.12 and 0.74 with a Bridgman type directional solidification apparatus, respectively. Thus, the thermal conductivities of liquid phases for pure NPG, pure AMPD and AMPD-42.2 mol% NPG alloy at their melting temperature were evaluated to be 0.24, 0.50 and 0.23 W/Km, respectively, by using the values of solid phase thermal conductivities and the thermal conductivity ratios of liquid phase to solid phase.     

Modeling of femtosecond ablation of aluminum film with single laser pulses

Detailed investigation of pulsed laser ablation dynamics is performed for aluminum target under action of 100 fs pulses with peak intensity 3.95 × 10¹² W/cm² and wavelength 0.8 μm.Non-equilibrium two-temperature model with hydrodynamic Stephan problem was used for modeling. Explicit tracking of moving interphase boundaries permits exact determination of their velocity and amount of removed and evaporated material. Detailed ablation process is analyzed using the study of temperature, pressure and density evolution in the target. High phase front velocities (melting up to 5 km/s and evaporation up to 350 m/s) are caused by strong overheating of solid and liquid phases.     

Metastable phases in Gallium-Indium eutectic alloy particles and their size dependence

In this paper, submicrometer-sized Ga-In eutectic alloy particles were dispersed into polymethylmethacrylate (PMMA) matrix by ultrasonic vibration and sedimentation method. The solidification and melting processes of Ga-In eutectic alloy particles were studied by differential scanning calorimeter (DSC). Four endothermal peaks with the onset temperature located at 16, −11, −22, and −27 °C were observed in DSC heating curves, which corresponded to the melting process of the stable Ga-In phase α-Ga(In) and three metastable phases of β-Ga(In), δ-Ga(In) and γ-Ga(In), respectively. The stable phase α-Ga(In) can only be formed when the size of alloy particle was larger than 0.58 μm. Conversely, metastable phases β-Ga(In), δ-Ga(In) and γ-Ga(In) are mainly formed. The result shows that phase structures in Ga-In eutectic alloy are size dependent.     

Thermal equation of state, and melting and thermoelastic properties of bcc tantalum from molecular dynamics

We performed molecular dynamics simulations with the extended Finnis-Sinclair (EFS) potential to investigate thermal equation of state (EOS), and melting and thermoelastic properties of tantalum. The agreement of the obtained thermal EOS with experiments at ambient conditions is reasonably good. The EFS potential with the two-phase method also reproduced very satisfyingly the high-pressure melting curve, excellently consistent with both the experiments of melting temperature at ambient pressure and shock melting at high pressure. From molecular dynamics simulations, we also obtained the thermoelastic properties of Ta for temperatures up to 3000 K at ambient pressure. Fully including anharmonic effects in molecular dynamics, our calculated elastic constants are in excellent agreement with experimental data. Shear modulus G decreases quickly with increasing temperature.     

Structure of a high temperature phase of potassium dideuteriophosphate (DKDP)

We previously determined the crystal structures of the high temperature phases of KH₂PO₄ [J.A. Subramony, S. Lovell, B. Kahr, Chem. Mater. 10 (1998) 2053. [6]]. These triclinic and monoclinic phases were obtained by heating the room temperature tetragonal form until new crystal phases were identified by polarization microscopy. These samples were subsequently cooled to room temperature thereby preserving the metastable high temperature phases for analysis. KD₂PO₄ is distinct from KH₂PO₄ in that it crystallizes at room temperature in a monoclinic phase unknown for its isotopomer, therefore the question as to whether it would support the corresponding high temperature phases remained open until our report here of the transformation of monoclinic KD₂PO₄ to an isomorphous triclinic high temperature phase: space group P with a=7.475(1) Å, b=7.440(1) Å, c=7.184(1) Å, α=88.53(1) Å, β=86.81(1)°, γ=88.09(1)°, V=398.58 Å³. This is the first known high temperature phase of DKDP, a material coveted at room temperature for its optical properties.     

Features of laser radiation interaction with metals having cryogenic temperature

In this paper we determine the features of the thermophysical processes involved in the interaction of laser radiation with metals that have cryogenic temperature. To do so, we use a one-dimensional model that involves heating a semi-infinite solid by a point thermal source with a constant flux density. Temperature fields, heating and cooling rates in the laser-irradiated zone for iron and titanium at the ambient temperatures of 77 (liquid nitrogen), 293 and 573 K were calculated. The intensity of the laser irradiation enabled the melting temperatures of 1933 K and 1812 K on the Ti and Fe surface, respectively, to be reached. The duration of the laser pulse was 4.5 ms. We show that a drop in ambient temperature from 573 to 77 K leads to a rise in cooling rate from 3.25 × 10³ and 6.4 × 10⁶ K/s to 4.25 × 10³ and 1.3 × 10⁷ K/s in the Ti and Fe targets, respectively. Agreement was good between the calculated depths of melting and phase transformation isotherms and the experimental depths of the interfaces of melting and heat-affected zones.     

Modifications of AISI 1045 steel by picosecond Nd:YAG laser at 266 nm; comparison with 532 and 1064 nm pulses

Interaction of Nd:YAG laser, operating at 266 nm wavelength and a pulse duration of 40 ps, with AISI 1045 steel was studied. Surface damage threshold was estimated to be 0.14 J/cm². The steel surface modification was studied at the laser fluence of ∼1.0 J/cm². The energy absorbed from Nd:YAG laser beam is partially converted to thermal energy, which generates a series of effects, such as melting, vaporization of the molten material, shock waves, etc. The following AISI 1045 steel surface morphological changes and processes were observed: (i) intensive damage of the target in the central zone of irradiated area; (ii) appearance of periodic surface structures at nano-level, with periodicity in agreement with the used wavelength; (iii) reduction of oxygen concentration in irradiated area; and (iv) development of plasma in front of the target. Generally, interaction of laser beam with AISI 1045 steel (at 266 nm) results in a near-instantaneous creation of damage, meaning that large steel surfaces can be modified in short times.     

Surface modifications of AISI 1045 steel created by high intensity 1064 and 532 nm picosecond Nd:YAG laser pulses

Interaction of Nd:YAG laser, operating at 1064 or 532 nm wavelength and a pulse duration of 40 ps, with AISI 1045 steel was studied. Surface damage thresholds were estimated to be 0.30 and 0.16 J/cm² at the wavelengths of 1064 and 532 nm, respectively. The steel surface modification was studied at the laser energy density of 10.3 J/cm² (at 1064 nm) and 5.4 J/cm² (at 532 nm). The energy absorbed from Nd:YAG laser beam is partially converted to thermal energy, which generates a series of effects, such as melting, vaporization of the molten material, shock waves, etc. The following AISI 1045 steel surface morphological changes and processes were observed: (i) both laser wavelengths cause damage of the steel in the central zone of irradiated area; (ii) appearance of a hydrodynamic feature in the form of resolidified droplets of the material in the surrounding outer zone with 1064 nm laser wavelength; (iii) appearance of periodic surface structures, at micro- and nano-level, with the 532 nm wavelength and, (iv) development of plasma in front of the target. Generally, interaction of laser beam with the AISI 1045 steel (at 1064 and 532 nm) results in a near-instantaneous creation of damage, meaning that large steel surfaces can be processed in short time.     

Diagnostics of picosecond laser pulse absorption in preformed plasma

We present results where highly supersonic plasma jets and accelerated plasma fragments are generated by interaction of an intense picosecond laser pulse with a metallic target (Al, Cu, W, and Ta) in gas atmosphere. The formation of jets and well-localized massive plasma fragments occurs when a strong forward shock from a main laser pulse and a reverse shock from a pre-pulse meet to. Interferometric and shadow graphic measurements with high temporal (100 ps) and spatial (1 μm) resolution yield information about the formation and evolution of plasma jets and plasma fragments. The excitation of the electric and self-generated magnetic field by ponderomotive force during propagation of the laser pulse in a gas atmosphere was investigated as well. It had been shown previously that under certain conditions a hollow current channel can be generated in laser-produced plasma. The azimuthal magnetic field in such a micro-channel was determined by Faraday rotation of a probing laser beam to be 7.6 MGauss (MG). Ion acceleration in a pinched annular current channel up to 8 MeV analogous to micro-“plasma focus” conditions, may be realized at lengths of 100 μm. Self-generated magnetic fields of 4-7 MG have also been measured in thin skin layers in front of shock waves, where well-collimated plasma blocks were separated and accelerated away from the plasma body. The velocity of dense plasma blocks reaches values of order of 3 × 10⁸ cm/s and they are stable during acceleration and propagation in gas.     

Molecular dynamics simulation of femtosecond ablation and spallation with different interatomic potentials

Fast heating of target material by femtosecond laser pulse (fsLP) with duration τ_L∼40-100 fs results in the formation of thermomechanically stressed state. Its unloading may cause frontal cavitation of subsurface layer at a depth of 50 nm for Al and 100 nm for Au. The compression wave propagating deep into material hits the rear-side of the target with the formation of rarefaction wave. The last may produce cracks and rear-side spallation. Results of MD simulations of ablation and spallation of Al and Au metals under action fsLP are presented. It is shown that the used EAM potentials (Mishin et al. and our new one) predict the different ablation and spallation thresholds on absorbed fluence in Al: ablation F_a=60{65} mJ/cm²and spallation F_s=120{190} mJ/cm², where numbers in brackets { } show the corresponding values for Mishin potential. The strain rate in spallation zone was 4.3×10⁹ 1/s at spallation threshold. Simulated spall strength of Al is 7.4{8.7} GPa, that is noticeably less than 10.3{14} GPa obtained from acoustic approximation with the use of velocity pullback on velocity profile of free rear surface. The ablation threshold F_a≈120 mJ/cm² and crater depth of 110 nm are obtained in MD simulations of gold with the new EAM potential. They agree well with experiment.     

Diffraction gratings of isotropic negative-phase velocity materials

Diffraction of electromagnetic plane waves by the gratings made by periodically corrugating the exposed planar boundaries of homogeneous, isotropic, linear dielectric-magnetic half-spaces is examined. The phase velocity vector in the diffracting material can be either co-parallel or anti-parallel to the time-averaged Poynting vector, thereby allowing for the material to be classified as of either the positive- or the negative-phase velocity (PPV or NPV) type. Three methods used for analyzing dielectric gratings — the Rayleigh-hypothesis method, a perturbative approach, and the C formalism — are extended here to encompass NPV gratings by a careful consideration of field representation inside the refracting half-space. Corrugations of both symmetric as well as asymmetric shapes are studied, as also the diversity of grating response to the linear polarization states of the incident plane wave. The replacement of PPV grating by its NPV analog affects only nonspecular diffraction efficiencies when the corrugations are shallow, and the effect on specular diffraction efficiencies intensifies as the corrugations deepen. Whether the type of the refracting material is NPV or PPV is shown to affect surface wave propagation as well as resonant excitation of surface waves.     

Direct observation of phase transitions by time-resolved pyro/reflectometry of KrF laser-irradiated metal oxides and metals

New experimental results are obtained by coupling both time-resolved reflectivity and rapid infrared pyrometry under a hemispherical reactor. The heating source KrF laser beam (28 ns, 248 nm) is homogenized and as for probing, a CW He-Ne laser beam (10 mW, 633 nm) is used.Using both methods infrared pyrometry with an IR detector cooled with liquid nitrogen and sensitive in the spectral range 1-12 μm, and time-resolved reflectivity with a rapid photodiode, we were able to study complex thermodynamic transitions with nanosecond time resolution. Three different materials are studied by varying the KrF fluence (energy/surface) from 100 to 2000 mJ/cm²: thin films melting (Au/Ni), the threshold of plasma formation (Ti), and complex liquid phase segregation under semi-conductor state (ZnO). The formation of a liquid Zn film induced by temperature gradient is well evidenced by our signals. Also melting of thin films irradiated by low laser fluences (less than 500 mJ/cm²) translates the typical thermodynamic behavior. Finally, wide fluence dynamic (400-2000 mJ/cm²) is analyzed in the case of Ti surface, and results show two distinguished regimes: first one bellow 1000 mJ/cm² corresponding to the early stage plasma initiation, and second one over 1000 mJ/cm² to the dynamics of plasma expansion.     

Generation of nanospikes via laser ablation of metals in liquid environment and their activity in surface-enhanced Raman scattering of organic molecules

The formation of dense arrays of nanospikes occurs under laser ablation of bulk targets (Ag, Au, Ta, Ti) immersed in liquids such as water or ethanol. The average height of spikes is 50 nm and their density on the target amounts to 10¹⁰ cm⁻². The effect is observed with sufficiently short laser pulses. In particular, either a 350 ps or a 90 ps Nd:YAG lasers are used in their fundamental harmonics. The nanospikes are characterized by UV-Visible reflection spectrometry and atomic force microscopy. The oscillations of electrons within nanospikes result in a permanent coloration of the surface and a modification of the optical reflection spectra of the metal. Scanning the laser beam along the metal surface allows its nanostructuring over extended areas (∼1 cm²). The nanostructured Ag surface shows enhanced Raman scattering of acridine molecules at a concentration of 10⁻⁵ M/l, whereas the initial Ag targets do not show any signal within the accuracy of measurements.     

Substrate temperature influenced structural, electrical and optical properties of dc magnetron sputtered MoO3 films

Molybdenum oxide (MoO₃) films were deposited on glass and (1 1 1) silicon substrates by sputtering of metallic molybdenum target in an oxygen partial pressure of 2 × 10⁻⁴ mbar and different substrate temperatures in the range 303-623 K using dc magnetron sputtering technique. X-ray photoelectron spectrum of the films formed at 303 K showed asymmetric Mo 3d_5/2 and Mo 3d_3/2 peaks due to the presence of mixed oxidation states of Mo⁵⁺ and Mo⁶⁺ while those deposited at substrate temperatures ≥473 K were in Mo⁶⁺ oxidation state of MoO₃. The films formed at substrate temperatures ≥473 K were polycrystalline in nature with orthorhombic α-phase MoO₃. Fourier transform infrared spectra of the films showed an absorption band at 1000 cm⁻¹ correspond to the stretching vibration of MoO, the characteristic of the α-MoO₃ phase. The electrical resistivity increased from 3.3 × 10³ to 8.3 × 10⁴ Ω cm with the increase of substrate temperature from 303 to 473 K respectively due to improvement in the crystallinity of the films. Optical band gap of the films increased from 3.03 to 3.22 eV with the increase of substrate temperature from 303 to 523 K.     

Laser synthesis of nitrides on the surface of refractory metals immersed in liquid nitrogen

In this paper we describe an approach for the formation of composite layers on the surface of refractory metals. We show that laser radiation on refractory metals (Ti, V, Zr, Mo, Hf, Ta, and W) immersed in liquid nitrogen can provide a chemical synthesis of nitride phases on the surface of metals. The metals were subjected to pulsed laser radiation with a wavelength of 1.06 μm. The power density ranged from 10⁴ to 10⁹ W cm⁻². The synthesis of nitrides began with the formation of Me_xN_y (x > y) phases with low contents of nitrogen. When the melting point was reached at the metal surface, the quantity of MeN phases increased sharply. Study of the melting zone showed that it contained a non-uniform distribution of nitride phases. The quantity of nitrides was a maximum on the surface and decreased with the increase of the depth of melting zone. Due to the high-cooling rates, titanium nitride crystallized in the form of columns. Maximum microhardness in the Ti surface layer was up to 20,000 MPa.     

High pressure behaviour of KHSO4 studied by electrical impedance spectroscopy

Measurements of the electrical conductivity were performed in KHSO₄ at pressures between 0.5 and 2.5 GPa and in the temperature range 120-350 °C by the use of the impedance spectroscopy. The temperatures of the α-β phase transition (T_Tr) and of the melting (T_m), determined from the Arrhenius plots ln(σT) vs. 1/T, increase with pressure up to 1.5 GPa having dT/dP∼+45 K/GPa. Above the pressure 1.5 GPa, the pressure dependencies of T_Tr and T_m are negative dT/dP∼−45 K/GPa. At pressures above 0.5 GPa, the reversible decomposition of KHSO₄ into K₃H(SO₄)₂+H₂SO₄ (and probably into K₅H₃(SO₄)₄+H₂SO₄) affects the electrical conductivity of KHSO₄, with the typical values of the protonic electrical conductivity, c. 10⁻¹ S/cm at 2.5 GPa.