Near-critical nanosecond laser-induced phase ...

Appl Phys A DOI 10.1007/s00339-010-5954-z

Near-critical nanosecond laser-induced phase explosion on graphite surface S.I. Kudryashov · A.A. Tikhov · V.D. Zvorykin

Received: 22 January 2010 © Springer-Verlag 2010

Abstract Optical reflectivity, removal rate and ablative recoil pressure magnitudes were measured as a function of laser fluence during high-power UV nanosecond laser ablation of graphite. At low fluences only melting and weak surface vaporization of molten carbon were observed. At moderate fluences there is a very narrow fluence interval where the reflected fluence starts to saturate, while the removal rate and ablative recoil pressure rise drastically in a correlated manner, indicating the onset of a near-critical surface phase explosion. Then, at higher fluences the reflected fluence, removal rate and recoil pressure saturate with an appearance of a luminous plume, altogether indicating negligible specular reflectance and absorbance on the target surface due to its complete screening by the highlyabsorbing laser plume. The overall strong correlation between the removal rate and recoil pressure magnitudes may indicate rather quasi-continuous removal of the near-critical superheated molten carbon layer by a propagating unloading wave in the absence of a crucial sub-surface temperature maximum in the layer.

1 Introduction Basic ablation mechanisms and their multiple material attributes were actively experimentally and theoretically studied during the last few decades in lieu of fundamental research of laser-matter interaction and broad range of various

S.I. Kudryashov () · A.A. Tikhov · V.D. Zvorykin P.N. Lebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia e-mail: [email protected] Fax: +7-499-7833690

applications related to pulsed laser ablative implantation, deposition and structuring of materials surfaces for their new or improved functional catalytic, tribological, medical, microelectronic and photonic characteristics, and laser sampling for microanalysis purposes [1]. Depending on parameters of incident laser radiation, target of interest and ambient atmosphere, various ablation regimes, e.g., surface vaporization, phase explosion or formation of ablative laser plasma, may occur resulting in removal of the target material in vapor, liquid and/or plasma states [1–6]. The first, surface vaporization regime is currently used for laser cleaning or polishing of surfaces, fabrication of shallow craters and slow laser sputtering of target materials in atomic or molecular forms. In contrast, laser-matter interaction regimes with more intense laser irradiation, such as sub-surface phase explosion and formation of ablative plasma, are more efficient for deep laser drilling, or cutting of materials at high removal rates, being accompanied by different vaporization instabilities [1, 3], expulsion of vapor-droplet mixtures [7–9] and plasma ignition in ablative laser plumes with complex spatiotemporal structures [1, 2, 10, 11]. Transitions between the basic laser ablation regimes, occurring in a multi-factor space of optical, thermal and hydrodynamic degrees of freedom, and thus requiring multi-parameter, multi-scale comprehensive experimental and theoretical investigation approaches, are not well understood yet. This strongly limits our current opportunities for monitoring and control of the abovementioned laser ablation regimes in promising technological applications and for advanced understanding of the underlying thermal physics of metastable superheated liquid fluids [12, 13], physics of optical breakdown and mesoscopic laser-matter interactions in mixtures of vapor species and nano- or micro-droplets [14]. In this work we report on a multi-parametric study of laser-induced ablative surface phase explosion in graphite,

S.I. Kudryashov et al.

Fig. 1 Experimental setup for optical reflectance, ultrasonic and mass removal studies during UV nanosecond laser ablation: BS—-beam splitter, PD—fast trigger silicon photodiode, VA—variable energy attenuator, FL—focusing fused silica lens, EM—thermocouple energy

meter, UT—-ultrasonic transducer, CCD—charge-coupled device camera for plume imaging, PC—computer for data acquisition and sample motion control

a key refractory material for walls of nuclear and thermonuclear reactors and a common precursor for mass production of fullerenes, nanotubes, graphenes and other perspective building blocks of new promising optoelectronic and biomedical nanosystems. The high-power nanosecond laser ablation of graphite reveals new important optical, acoustic and thermophysical details of the transition from common surface vaporization of a superheated molten carbon layer to its near-critical surface phase explosion, apparently driven by fast vaporization/unloading wave and accompanied by expulsion of an opaque vapor-droplet mixture.

5-mm thick protective front window of the transducer via a thin lubricating vacuum grease layer. The 1.5-mm wide active front electrode of the transducer was centered relative to the laser focal point on the front surface of the sample. The voltage transients from the transducer were recorded using a 50- input of a digital storage oscilloscope, Tektronix TDS-2024, which was triggered via another 50- input by an electric pulse from a fast photodiode DET-210 (Thorlabs) fed by a weak split laser beam. The relatively thin and highly-oriented quasi-crystalline graphite film was used in the ultrasonic experiments to avoid attenuation of ultrasonic transients in graphite samples due to scattering of sound waves on graphite crystallite boundaries. Also, energies of single specularly reflected laser pulses on fresh surface spots of the optical-quality quasi-crystalline graphite film were measured at a small incidence angle of 100 and variable fluence values, using another thermocouple energy meter, in order to track laser-induced changes of optical constants of graphite. Finally, to monitor ablative mass removal, a number of millimeter-deep multi-shot trenches were fabricated at different laser fluences on the surface of the polycrystalline graphite plate mounted onto a PC-driven motorized three-axis stage, with the corresponding maximum trench depths optically measured at the plate edge under an optical microscope. During the latter studies we did not have sufficiently thick samples of the quasi-crystalline graphite, which is rather exotic and expensive substance, to perform all three—optical, ultrasonic and profilometric—sets of experiments under the same conditions.

2 Experimental setup and techniques We performed laser ablation of a millimeter-thick polycrystalline graphite plate (mass density ρ1 ≈ 1.7 g/cm3 ) and a centimeter-wide, micron-thick high optical-quality film of highly-oriented quasi-crystalline graphite torn off as a separate layer from a large piece of quasi-monocrystalline graphite (trademark UPV-1TMO, ρ2 ≈ 2.18 g/cm3 ) and rolled onto a 1-mm thick silica glass slide. The irradiation source was an excimer KrF laser (LPX-210i) with a laser wavelength λlas ≈ 248 nm, a laser pulse full width at a half maximum (FWHM) τlas ≈ 25 ns, maximum pulse energy E0 ≈ 120 mJ, homogeneous vertical and Gaussian horizontal fluence (F ) distributions with parameters a ≈ 70 µm and b1/e ≈ 30 µm, respectively. The UV laser pulses were focused using a fused silica lens (focal length f ≈ 40 cm) and their energies were monitored by means of a thermocouple energy meter (Fig. 1). To probe instantaneous ablation characteristics, broadband ultrasonic measurements were carried out in a singleshot mode at variable F in the acoustic near-field using a piezoelectric transducer SHAPR-13 (LiNbO3 , bandwidth > 100 MHz, sensitivity of 1 mV/atm) manufactured by UC VINFIN, with the supported graphite film sliding on the

3 Experimental results At low incident laser fluences F > 0.8 J/cm2 the measured energies of specularly reflected single laser pulses increase sub-linearly versus F showing gradually decreasing optical reflectance R (248 nm, 100 ) (Fig. 2), according to expected thermo-optical responses of semi-metallic solid

Near-critical nanosecond laser-induced phase explosion on graphite surface

Fig. 2 (Left axis) Reflectance R (248 nm, 100 ) of the quasimonocrystalline graphite film (dark circles) versus incident laser fluence F with Fmelt ≈ 0.5–1.0 J/cm2 , Fthr ≈ 4–5 J/cm2 and Fcut-off ≈ 6 J/cm2 representing the melting, surface phase explosion and reflectance cut-off thresholds. The Rsolid and Rmelt marks represent the corresponding 248-nm normal-incidence reflectance (≈0.51) of the solid graphite (dashed horizontal line), and the 372-nm normal-incidence reflectance (≈0.25) of the molten carbon;1 (right axis) reflected laser fluence FR versus F with its plateau value FR,sat (dashed horizontal line) for this graphite

graphite [15] probed on the blue side of its π → π ∗ absorption band peaked at 4 eV [16], and of molten carbon.1 This observation is in agreement with the melting threshold of graphite, Fmelt ≈ ΔHmelt (χτlas )1/2 /(1−R248 ) ≈ 0.5– 1.1 J/cm2 , which is estimated accounting for the “thermally thin” optical skin depth in graphite at 248 nm (the skin depth δ248 ≈ 10 nm [χτlas ]1/2 ≈ 70–150 nm for the pre-melting thermal diffusivity χ ≈ (2–10) × 10−3 cm2 /s [17–20]) and using the available optical (zero-angle reflectivity R248 ≈ 51% and δ248 [21]) and thermal (the triplepoint melt enthalpy ΔH (liq) ≈ 2 × 105 J/mole [15]) characteristics of graphite. However, at higher fluences, F > 6 J/cm2 , the reflected laser energies saturate in a thresholdlike manner above the cut-off fluence Fcut-off ≈ 6 J/cm2 , indicating drastically enhanced, complete scattering and/or absorption on the molten graphite surface or in the laser plume for the trailing part of the laser pulse, which begins at the instant during the pulse when the accumulated fluence exceeds Fcut-off . Indeed, the saturating reflected laser fluence (FR,sat ≈ 1.3 J/cm2 ) corresponds to the characteristic reciprocal dependence of the graphite reflectance R (248 nm, 100 ) ∝ 1/F (Fig. 2), observed earlier on graphite surfaces during their normal-incidence, highpower 1064-nm laser irradiation and related to formation of ablative carbon plasma [22]. Then, the acquired acoustic waveforms rose sharply in their amplitude near a similar threshold fluence F thr ≈ 4–5 J/cm2 (Fig. 3), showing presumably unipolar compressive pressure transients of ablative character [23] (with the 1 Our

unpublished results on 372-nm reflectivity (≈0.25) of acoustically relaxed, molten carbon produced on a picosecond timescale (20–100 ps) via heating of highly-oriented pyrolitic graphite by 744-nm, 50-fs laser pulses.

Fig. 3 Compressive pressure amplitude Pcomp (dark circles) and removal rate X (light squares) with its plateau value Xplat (horizontal dashed line) versus F for the quasi-monocrystalline and polycrystalline graphite samples, respectively. The Fmelt , Fthr and Fcut-off marks show the corresponding melting, surface phase explosion and reflectance cut-off thresholds

compressive pressure amplitude Pcomp rarefaction pressure amplitude Prare , i.e., Prare ≈ 0). This sharp increase of Pcomp slightly precedes the abovementioned saturation of the reflected laser fluence at Fcut-off , apparently indicating the onset of strongly enhanced material removal and a possible change of its ablation mechanism, and may result in the increased surface screening by the laser plume; alternative explanations of the pressure rise—due to either stronger pressure generation in the surface molten carbon layer due to its enhanced absorbance (see the decreasing reflectance in Fig. 2) or another, more efficient pressure generation process in the superheated layer—should be ruled out as typically related to bipolar thermoacoustic pressure transients [24]. Our multi-shot mass removal measurements enable to resolve this ambiguity demonstrating for F ≥ Fthr a simultaneous strong increase of an average ablated depth per pulse, X, and its subsequent saturation at a level Xplat , closely correlating with the Pcomp (F ) trend in Fig. 3. First, this close correlation—even coincidence on the relative scales— between the depth and pressure magnitudes, which were measured in multi- and single-shot modes, respectively, demonstrates the absence of any potential significant memory effects (variation of the target absorbance due to its surface modification, reduced mass removal due to a limited crater aperture or extra-absorption of ablated gas-phase species inside a crater, etc.) during the fabrication of the deep trenches on the graphite surface. Second, this coincidence, appearing both at the rise and saturation stages, represents the concerted character of mass removal and pressure generation during laser ablation for F ≥ Fthr at the rather constant lift-off speeds of ablation products (see Sect. 4 below), as compared, for example, to a pressure generation in an absorbing laser plume above the target surface. Moreover, this coincidence also means that the laser energy deposition, mass removal and pressure generation occur rather smoothly (continuously) during the incident laser pulse, rather than


as a single explosive event. Also, it is also noteworthy that the abovementioned rise of X in Fig. 3 is definitely not related to the previously observed time-delayed melt removal [25], occurring for graphite at much higher 248-nm laser fluences (F ≥ 25 J/cm2 [6]) and resulting from hot plasma-driven “bulk phase explosions” [6, 26], in agreement with the coincidence of the rising X(F ) and P comp (F ) curves. Our plasma formation (optical breakdown) threshold of ≈25 J/cm2 /1 GW/cm2 (248 nm, 25 ns) for the carbon plume is consistent with its theoretical estimates of 1 and 3–4 GW/cm2 obtained using, respectively, a new advanced approach [27] (accounting for continuous high-temperature thermionic and thermal ion emission from eventually dissociating carbon nanodroplets in denser ablative plumes near the critical point of carbon and the ideal-gas equation of state) and (11) in the work [28].

4 Discussion and conclusions The entire set of experimental findings of this work, including observation of the cut-off fluence Fcut-off ≈ 6 J/cm2 in optical reflection, the correlated drastic rise of removal rate and recoil pressure near the similar threshold fluence Fthr ≈ 4–5 J/cm2 and their subsequent saturation enable us to draw a few important conclusions and suggestions. The most obvious one is that the intense mass removal starts during the laser pulse at the instant trem , when the instantaneous accumulated fluence F (t) ≈ Fthr , and continues until the instant tcut-off at F (t) ≈ Fcut-off eventually dropping down the good specular reflection/absorption of the pulse on the target surface because of the almost complete absorption/scattering in the laser plume of the trailing part of the pulse (t > trem ). The existence of the threshold Fcut-off in optical reflectance shows that the instant t rem shifts at increasing F > Fthr to the leading part of the laser pulse. Likewise, the observed saturation of the removal rate X for F > Fthr at the F -independent maximal crater depth Xplat indicates complete screening of the target by the plume of the fixed screening depth (ablated mass screening), rather than by the sparse thermal plasma of this plume. In contrast, dense reflective plasma appears above the 248-nm plasma formation threshold of 25 J/cm2 (see the related discussion in the previous section), via pressure-dependent optical breakdown [27–29] at the corresponding isobar in the plume (ablative plasma screening) and would yield not in the saturated, but in a decreasing dependence X(F ), as at higher F the breakdown and the succeeding plasma screening would appear earlier during the laser pulse [27]. This intense removal regime (F > Fthr ) with Xplat ≈ 1 µm {δ248 ≈ 0.01 µm, [χτlas ]1/2 ≈ 0.07 µm} may be related to a near-critical phase explosion of the superheated molten layer on the graphite surface [5, 6, 30]. For example,

Fig. 4 Schematics of the near-critical laser ablation in the fast surface vaporization (a) and vapor-droplet mixture expulsion (b) regimes (see the text for notations)

from an approximate energy-balance equation (neglecting the eventually increasing plume screening of the graphite surface) (1) εabl X ≈ 1 − R 248 nm, 100 F, one can estimate the enthalpy ΔH ∗ of the molten graphite prior its phase explosion as ΔH ∗ ≈ εabl , using the values Xplat , Fcut-off , R (248 nm, 100 ) ≈ 0.2–0.25 at F ≈ Fcut-off and obtaining the value 2.8 × 105 J/mole, which is close to the previously measured ΔH ∗ ≈ 3.1 × 105 J/mole [30]. Such a phase explosion in the molten surface layer, i.e., surface phase explosion (comparing to similar bulk phase explosions in multi-micron thick melt baths [6, 26]), may appear as very intense near-critical surface vaporization providing very dense, pressurized carbon vapor in a nearsurface layer (Fig. 4a). Using the well-known hydrodynamic continuity (mass and momentum conservation) relations for the liquid-vapor interface [31] ρvap Vvap ≈ ρ1,2 Vev ,

(2a)

2 Prec ≈ ρvap Vvap

(2b)

≈ ρ1,2 Vev Vvap ,

one can exclude the vapor mass density ρvap in (2b), evaluating for the intense removal regime the maximum ablative recoil pressure Prec ∼ 103 bar during the surface phase explosion for the graphite density ρ1,2 ∼ 103 kg/m3 , removal rate Vev ∼ Xplat /τlas ∼ 102 m/s for Xplat ∼ 1 µm and τlas ∼ 10−8 s, and vapor velocity Vvap ∼ (RTcrit /M)1/2 ∼ 103 m/s for the carbon molar mass M = 1.2 × 10−2 kg/mole and the accepted estimate of the critical temperature of carbon Tcrit ≈ 7 × 103 K [32]. This upper pressure estimate is also


consistent with the near-critical equilibrium vapor pressures of carbon ∼102 –103 bar [30, 32], approaching the accepted value of its critical pressure ≈2240 bar [33]. However, it is not clear how vaporized atomic and molecular carbon species (typically, C1 and C3 [33, 34]) with their rather low absorption cross-sections can considerably screen the graphite target. Alternatively, the intense ablation regime may be also related to a surface phase explosion occurring via expulsion of a vapor-nanodroplet mixture of ablation products (Fig. 4b) [9, 30, 35]. In this mechanism, the superheated carbon melt converts via its intensive near-critical homogeneous boiling into a two-phase (liquid-vapor) mesoscopic system with strongly corrugated external and internal surfaces [35]. Under these conditions, the processes of surface vaporization and bulk thermal expansion in the cavitating melt become hardly distinguishable, and a few important features related to its acoustic (hydrodynamic) and optical properties appear. First, the anticipated longitudinal sound velocity in the superheated molten carbon because of its two-phase (vapor/droplet) structure could be rather low—in the range of 10–102 m/s [36] with the lower and upper limits dictated by the longitudinal sound velocities in a cavitating liquid (Ccav ) and a dense vapor with a high component of nanodroplets (Caero ), respectively. The corresponding expressions for Ccav and Caero are found in [37]: Ccav ≈

Caero ≈

MP Vliq Δev H , Cpliq T

Rgas T

M

Rgas T

+

(3a) 2

Δev H

+

Cpvap T Δev H 2

−1 ,

(3b)

where P and T are the pressure and temperature of the twophase system, Cpliq , Cpvap , Rgas and Δev H are the heat capacities of its liquid and vapor components, universal gas constant and evaporation enthalpy of the liquid at the given P and T values. Though (3a, 3b) represent rather simplified extreme cases of a more general, but very cumbersome expression for the longitudinal sound velocity in such twophase system as a function of the corresponding relative vapor (θ ) and liquid (1−θ ) fractions derived in [37], their very preliminary analysis of the equations in the near-critical region shows negligible longitudinal sound speeds both in the cavitating liquid and fogy vapor for Δev H → 0, as expected near the thermodynamic critical point at θ ≤ 2/3 [12, 13]. These estimates illustrate our point regarding the slow expansion of the vapor/droplet mixture of the graphite ablation products for F > Fthr and formation of the dense, pressurized screening carbon plume. Second, for the rather low sonic velocities in the nearcritical vapor/droplet mixture in this ablation regime one can expect for the mass density of the mixture to be comparable to that of the superheated molten graphite. In this context, the maximum, the high overall ablation depth Xplat ∼

1 µm demonstrates the rather transparent (still absorbing) vapor/droplet plume, indicating the rather transparent character of the initial near-critical molten graphite layer at the UV wavelength (the estimated absorption coefficient αliq ∼ 1/Xplat ∼ 104 cm−1 ), as compared to the solid graphite (1/δ248 ∼ 106 cm−1 ) [21], and providing rather smooth temperature profiles in the superheated graphite melt. Such bleaching of the liquid carbon under the near-critical conditions could be explained by a dramatic transformation of the carbon electronic structure upon melting (see the wellknown density-driven Mott-like “conductor-insulator” transitions [38]), which is still subject of multiple controversial views (for a review, see [39–41]). Nevertheless, the UV laser-induced bleaching and the related micrometer-deep melting of graphite suggested in this work does not contradict to previous experimental observations for graphite and other materials (see footnote 1, [30, 39–43]). Interestingly, such laser-induced near-critical surface phase explosions were previously assigned to formation of a pronounced sub-surface temperature maximum with nearcritical [4] or even super-critical [5] peak temperatures, relaxing via an instantaneous single explosion event, at moderate [4] or very high [5] laser fluences, respectively (in the latter case, however, one can talk about bulk phase explosions driven by ultra-deep—multi-micron—heating of solids by short-wavelength radiation of ablative laser plasma [6, 26]). An appearance of such sub-surface temperature maximum is usually related to evaporative surface cooling of bulk absorbing liquids with the off-surface vapor energy flux dominating over the heat flux to the surface from the heated bulk, thus satisfying the criterion αliq χliq /Vev 1 [3, 5, 42], where αliq and χliq are the absorption and thermal diffusivity coefficients of the liquids, and the surface vaporization rate Vev is known to be an intensity-dependent quantity [4], which can tuned (increased) to bring the melt into the sub-surface overheating regime. In this work in the intense removal regime (F > Fthr ) the evaluated magnitudes of the key ablation parameters—αliq ∼ 104 cm−1 , χliq ∼ 10−3 –10−2 cm2 /s, Vev ∼ Xplat /τlas ∼ 102 m/s— support the appearance of a significant sub-surface temperature maximum in the near-critical phase explosion regime (αliq χliq /Vev ≤ 1) [3, 5, 42]. However, this would result in single [5] or multiple [44] sub-surface phase explosions, rather than in the observed quasi-continuous (steadystate) removal of the vapor/droplet mixture during the laser pulse from the “bleached” near-critical superheated surface molten layer with the anticipated rather monotonous temperature field, i.e. in the absence of significant sub-surface overheating. In our opinion, such potential sub-surface temperature maximum can be considerably suppressed by intense homogeneous bulk nucleation of vapor bubbles [6], which is strongly enhanced in the proximity of the critical point prior the surface phase explosion [12, 13] and may


be able to consume the excessive deposited laser energy in the molten carbon layer both in the thermal and hydrodynamic aspects due to the well-known singularities of the heat capacity (Cp ) and thermal expansion (βT ) coefficients [12, 13]. These diverging quantities stabilize internal thermal and pressure fields in the near-critical graphite melt by limiting its superheating and expansion. We believe one can account for these divergences considering, as suggested for such near-critical ablation regimes by Anisimov et al. [45], a hydrodynamic picture of the laser ablation regime. In this picture, for UV nanosecond laser fluences F > Fthr there appears a front of fast homogeneous boiling at the near-critical temperatures (in the proximity of the spinode curve for liquid carbon), which propagates in the superheated molten carbon in the form of a tensile/unloading acoustic wave or a thermal (isotherm) wave with the temperature T ≈ Tspinode [30], converting the weakly absorbing molten material into a weakly vapordroplet mixture. The slowly lifting-off vapor-droplet mixture gradually warms up further and expands locally via absorption of the incident laser radiation, tending, probably, closer toward (or beyond) the spinode curve and eventually converting at its apparent outer surface (position x = 0) into much warmer, but more sparse carbon vapors (Fig. 4b), which rapidly expands into the ambient air providing convective recession of the vapor-droplet mixture surface (x > 0) at a time(intensity)-dependent speed u. As a result, one can write an equation for the energy conservation in the mixture in the general form of a heat conduction equation [46] with the laser absorption source term [6]: T

∂S ∂S ∂S ∂T ∂P =T +T ∂t ∂T P ∂t ∂P T ∂t = Cp∗

∂T ∂P + βT∗ V ∂t ∂t

∂T ∂ 2T + αliq 1 − R(I ) + Cp∗ u 2 ∂x ∂x

t × I exp −αliq x − u dt ,

=κ

−∞

(4)

where Cp∗ and βT∗ represent the diverging magnitudes of the heat capacity and thermal expansion coefficients of the liquid at their near-critical singularity points, while S, V , κ are the entropy, volume and heat conduction coefficient of the liquid. To complete the hydrodynamic picture, the heat conduction equation should be supplied by continuity and Euler equations for the mass and mechanical momentum conservation in the vapor-droplet mixture in some, e.g., linearized forms [47], describing dynamics of the recession speed u and internal pressure P inside the vapor-droplet mixture, re-

spectively. Then, the initial and boundary conditions can be set in the standard form T (0, x) = T∞ , ∂T −κ + Lu(t) = 1 − R(I ) I, ∂x x=0

(5)

where T∞ and L are the initial temperature of the graphite sample and effective extra enthalpy to transform the nearcritical vapor-droplet mixture into its vapor, respectively. Moreover, another heat conduction equation with its own initial and boundary conditions should be added to describe the propagating inner front of the near-critical transformation of the superheated melt into the vapor-droplet mixture (accounting for the suggested low longitudinal sound speed in the mixture, we believe it can be reduced to the standard Stefan problem). While the overall analysis of the nearcritical ablation problem is cumbersome and hardly possible at all, when focused on ablation, one can draw attention to the point that in the vapor-droplet mixture heat conduction should be negligible for the diverging Cp∗ magnitude and the resulting flattened temperature profile. Hence, the boundary condition in (5) simplifies coming to the form similar to (4) for the same ablation regime in [4] Lu(t) = 1 − R(I ) I.

(6)

This expression describes the intense near-critical laser ablation rate in the very simple form, well consistent with the main experimental findings (mainly, the quasi-continuous (steady-state) character of the intense mass removal) of this work. In conclusion, in this multi-parametric study we have employed optical reflectance, contact ultrasonics and optical profilometry to identify and explore the apparent nearcritical phase explosion of the molten layer on the surface graphite, occurring during the heating laser pulses as a quasi-continuous material removal, most probably, in the form of a vapor/droplet mixture. This intense and deep quasi-continuous removal of the material may be explained by dramatic optical bleaching of the near-critical molten carbon phase and the flattening of the internal thermal and pressure fields in the slowly expanding, weakly absorbing micron-thick vapor-droplet mixture due to the near-critical divergence of the heat capacity and thermal expansion coefficients. Acknowledgements The authors acknowledge enlightening discussions with Drs. Alexander and Nadezhda Bulgakov, Institute of Thermal Physics (SB RAS). This work was partially supported by the Russian Foundation for Basic Research (projects Nos. 08-08-00756a and 10-08-00941a).


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