I. Smurov et al- Overheated metastable states in pulsed laser deposition versus laser radiation wavelength

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JOURNAL DE PHYSIQUE IVColloque C4, supplkment au Journal de Physique 111, Volume 4, avril1994

Overheated metastable states in pulsed laser deposition versus laser

radiation wavelength

I. SMUROV,C. SURRY,V.I. MAZHUKIN* and G. FLAMANT*

Ecole Na tionale d'lngknieurs de Saint-Etienne, 58 rue Jean Parot, 42023 Saint-Etienne cedex 2, fiance* Institute of M athematical Modeling, Russian Acade my of Sciences, Miusskaya Square 4,

125047 Moscow, Russia** Znstitut de Science et de Gknie des Matkriaux et Prockdks, CNRS, BI! 5, 66125 Font-Romeu cedex,France

ABSTRACT

The effect of absorption coefficient of laser radiationon temperature distribution in the material and phase frontdynamics is studied by numerical simulation. Overheating ofboth solid and liquid phases is shown and discussed.

1. MATHEMATICAL MODEL

Mathematical description of the processes of laserheating, melting-solidification and evaporation ofsuperconducting ceramics is made within the framework of thecombined version of the Stefan problem including the dynamicsof both phase fronts : melting-solidification and evaporation.The proposed mathematical model is a boundary-value problem forthe thermal conductivity equation with two moving phaseboundaries solid-liquid Tsl(t) and liquid-vapour I',,(t).Volume heating of the solid and liquid phases is taken intoaccount with the help of the term aG/ax in the heat transfer(1) and the radiation transfer (2) equations

aT a aT

C, (T) - - (T)- (1at ax ax

solid phase : x, < x < r s l(t),t > O (3)

liquid phase : rsl(t) x < rl,(t),

aTboundary condition : x = x,, 1- 0

axIn the classical version of the Stefan problem for the

description of melting-solidification phase transitions at theinterphase boundary I',,(t) the differential condition is used

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1994433

http://www.edpsciences.org/

http://dx.doi.org/10.1051/jp4:1994433

http://dx.doi.org/10.1051/jp4:1994433

http://www.edpsciences.org/



JOURNALDE PHYSIQUEIV

from which the velocity of the front movement us, isdetermined.

Intensive evaporation gives rise to a strongly

nonequilibrium Knudsen layer at the interface. In the presentpaper the relations reported in [l] are used. In case of volumeheating of a condensed medium the boundary conditions on thesurface being evaporated have the form :

en = P,T,,/(R T,, 1, P, = pbexp

Nomenclature : a - thermal diffusivity; A ( T , , ) - surface

absorptivity; C, - heat capacity; G - energy density flux;Go - maximum value of incident energy density flux; L, - latentheat of melting: L, - latent heat of evaporation; M - Machnumber; P - pressure; R - universal gas constant; To - initialtemperature; T, - melting point; u - vapor velocity; us, -velocity of solid - liquid interface; ulv - velocity of liquid-vapor interface; y - the ratio of heat capacities; T,, - solid-liquid interface; T,, - liquid-vapor interface; x - coefficientof heat conductivity; Q - density.

Subscripts : b - boiling point; H - saturated vapor;1 - liquid phase; s - condensed phase: v - gas phase; sr -surf ce.



2. Results and Discussion

According to the ~ ( h v ) urve based on experimental data121, the absorption coefficient K ranges from K = 8.105 cm-lfor the radiation wavelength hv = 0.2 Fm to n = lo4 for the

radiation wavelength hv 2 1 pm. Thus, depending on the incidentradiation wavelength hv, superconducting ceramics can absorbeither practically as metals (surface heating) or asdielectrics (volume mechanism of energy release).

The temporal profile of laser pulse was assumed to havethe Gaussian shape with respect to the variable t : G(t) =

Go xp(-(t/t ) 2 ) where - -ctc+-,t is the pulse half -width at thehalf -height, t=40 ns, Go =lo7 W/cm2. In the present simulationG, and z remain the same for all the variations of absorptionlenght

Under the combined action of the processes of meltingand volume heating, the temperature maximum, Fig.1, is formedin subsurface layers of the material. The presence of the sub-

surface temperature maximum indicates that a certain volume ofthe solid phase is overheated with respect to the melting equi-librium temperature T,. Liquid phase heating causes anintensive surface evaporation, which in turn (with allowancefor volume energy release in the depth of the liquid phase)leads to the formation of the second temperature maximum. Whena certain relation between the parameters is respected, bothmaxima can be observed simultaneously, Fig.2.

To show general tendencies of the dynamics of phasetransitions, laser action over a wide range of mean free pathlv - n - I (from lv=O to lv = 5.103 A ) was analysed (Fig.3,4). Inexperiments an explosive decay of the metastable state in solid/liquid phase may lead to an ejection of particles/droplets.

3. CONCLUSION

The numerical simulation shows that pulsed energyevaporation of materials with a volume energy release may leadto volume overheating of the solid and liquid phases. Themaximum values of the overheating of the solid phase may exceeda hundred degrees and those for the liquid phase may exceedseveral hundreds degrees. The times of the metastable statesexistence are tens and hundreds nanoseconds, respectively.Volume energy release leads to the domination of the meltingprocess which, together with a decreased effect of evaporation

and low solidification rates, makes the liquid phase lifetime5-6 times longer than for the surface absorption of radiation.It is shown that the probability of explosive decay of themetastable states in solid phase increaces with laserwavelength, while for the ones in the liquid phase thecorresponding dependencies have the maxima versus laserwavelength.

REFERENCES

1. C.J. Knigt, 1979, AIAA Journal, v.17, pp. 518-523.

2. E. Fouarassy, C. Fuchs. S. de Unamuno. J. Perriere..

F. ~erherve;, 992, ater rials and ~anufacturin~ rocesses;Vol. 7, pp. 31-51.



(3-1.54 JOURNALDE PHYSIQUEIV

X x lo-' (cm)

Fig.3. Maximum values of solid (1) and liquih(2) phase overheating (during thermocycle)

versus absorption length.

x x 10-4 (cm)

Fig.1. Spatia l distribution of temperature Tand absorbed energy intensity G : (a) just

before melting; (b) - illustrating theappearance of solid state overheating short

time after the melting starts (Iv=3000 A) .Fig.4. Life-time of solid (1) and liquid (2 )

phase overheating (during thermocycle)versus absorption length.

X x (cm)

Fig.2. Spatial distribution of temperature Tand absorbed energy intensity G illustrating

the existance of two subsurface

temperature maxima, short time after the

intensive evaporation starts (Iv=3000 A).

Fig. 5. Maximum values of surface tempe-

rature (1 ) and evaporation front velocity (2)

during thermocycle versus absorption length.

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I. Smurov et al- Overheated metastable states in pulsed laser deposition versus laser radiation wavelength