DOI 10.1007/s11018-014-0515-z Measurement Techniques, Vol. 57, No. 6, September, 2014

THERMAL MEASUREMENTS THE BRIGHTNESS TEMPERATURE OF ALUMINUM OXIDE WHEN IT IS HEATED BY CONCENTRATED LASER RADIATION

V. K. Bityukov and V. A. Petrov

UDC 536.52:536.33

The results of a calculation of the temperature fields in a plane layer of aluminum oxide when it is rapidly heated and melted by the radiation of a CO2-laser with different flux densities are presented. The calculations are carried out using a new mathematical model of nonstationary radiation-conduction heat transfer. It is shown that the brightness temperature, measured at a wavelength of 0.65 μm, differs from the surface temperature. Keywords: brightness temperature, aluminum oxide, radiation-conduction heat transfer, two-phase zone.

Rapid heating of different materials by concentrated laser radiation up to temperatures exceeding their melting point is widely used in a number of technological processes. One of the most important parameters in this process, representing the processing of the material by laser radiation, is their surface temperature. Numerous publications exist relating to modeling of these processes, where the surface heating and melting of metals and other nontransparent materials, the energy transfer in which is purely by heat conduction, are mainly considered. In other materials, called semitransparent materials, energy transfer occurs not only by thermal conduction but also by radiation, and the heating laser radiation penetrates a certain distance inside the material. Such materials include all dielectrics, semiconductors and, in particular, practically all refractory oxides. When refractory oxides are heated by laser radiation, the temperature field is formed in a process of combined radiation-conduction heat transfer with volume heat release. To calculate the temperature field in this case, one must know the optical and thermal properties of the materials, determined experimentally. Because of the difficulties in carrying out appropriate experiments, there are practically no data available at the present time on the optical and thermal properties of solid oxides and their melts in the region of the melting point. An exception is aluminum oxide Al2O3, since its melting point (2327 K) is relatively low. There are also data available on the properties of the melt, but the disagreement between the values obtained by different researchers is considerable (particularly as regards the absorption coefficients of the melt and the actual thermal conductivity, unaffected by the radiation). Nevertheless, Al2O3 is unique among high melting-point oxides, for the melt of which the necessary data are available for calculating the radiation-conduction heat transfer. Nevertheless, up to recently (the beginning of the Twenty First Century) the energy transfer when Al2O3 melts has only been considered as a heat conduction problem [1–3]. The first publications on the problem of radiation-conduction heat transfer when semitransparent materials are heated and melted appeared at the end of the 1960s and the beginning of the 1970s; a detailed review of these can be found in [4]. At the same time, the classical model of the phase transition was always used, in which two layers – solid and liquid, separated by a boundary, were considered. The traditional Stefan condition was used to describe this model, but for radiation energy transfer this is mathematically incorrect. A more general model of the melting and solidification for volume sources of Moscow State Technical University of Radio Engineering, Electronics, and Automation (MIREA), Moscow, Russia; e-mail: [email protected]. Translated from Izmeritel’naya Tekhnika, No. 6, pp. 33–37, June, 2014. Original article submitted April 18, 2014.

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0543-1972/14/5706-0658 ©2014 Springer Science+Business Media New York

T, K sec sec

δ, mm

t, sec x·102, mm

X, mm

a

b

Fig. 1. Distribution of the temperature T for heating by laser radiation with a flux density q = 600 W/cm2 at the instant of time t in a plane layer (a) and in the surface layer of Al2O3 (b); the inset shows the dependence of the thickness of the melt δ on the time t.

energy includes the formation of a two-phase zone of definite extent, with a ratio of the solid and liquid phases that is variable along the coordinate. Such a model was formulated in [5], as it applies to semitransparent materials. However, the results of the calculations presented in [5], due to the extremely limited computer facilities available at the time, were not based on the model developed but on its general formulation. No actual materials and boundary conditions were considered in that paper. In order to demonstrate the effect of the formation of a two-phase zone, the results of a calculation of the radiationconduction heat transfer were presented there for three extremely idealized cases of the solidification of a geometrically infinitely extended liquid medium, on the surface of which the temperature decreased abruptly to a temperature below the melting point. A detailed analysis of the results of radiation-conduction heat transfer under conditions in which a two-phase zone is formed was given in [6]. The melting and solidification of a plane layer were considered. It was convincingly shown that it is necessary to take into account the formation of a two-phase zone, but, as in [5], radiation-conduction heat transfer was only analyzed, as in [6], in model media, which considerably simplified the mathematical formulation of the problem and made it easier to carry out the calculations. A generalized rigorous mathematical model of radiation-conduction heat transfer was presented for the first time in [7] for the case of the heating and melting by concentrated laser radiation of selectively radiating and absorbing material and its subsequent cooling and hardening. Some numerical calculations using this model were obtained for Al2O3 as a specific standard material. Due to the small number of calculations carried out, the results presented in [7] are only fragmentary for a single flux density q of the heating radiation. The effect of q on the formation of the temperature field in Al2O3 were later considered in more detail in [8]. However, up to the present time the problem of measuring the surface temperature in the rapid heating of a semitransparent material has not been investigated. The temperature of the surface is the most important technological parameter of laser processing, and, as a rule, in technological processes is measured by monochromatic brightness pyrometers, using a wavelength of λ = 0.65 μm in the majority of cases. Here one must necessarily introduce a correction to the value of the emissivity, which can be done if the radiating layer is isothermal. In the case of rapid heating of semitransparent materials by concentrated laser radiation, isothermal conditions do not exist in the emissive layer. 659

Tsf, Tsr, K

Tsf – Tbf, K

t, sec

a

b

Fig. 2. Change in the temperatures for different flux densities q: a) temperature of the front surface Tsf and of the rear surface Tsr of the layer and the differences Tsf – Tbf of the actual and brightness temperatures; b) the same temperatures at the initial stage of the heating on a greater time scale; 1, 1′, 1″) q = 200 W/cm2; 2, 2′, 2″) q = 400 W/cm2; 3, 3′, 3″) q = 600 W/cm2; 4, 4′, 4″) q = 1200 W/cm2; 5, 5′, 5″) q = 3000 W/cm2.

In Fig. 1a, we show, as an example, the results of a calculation of the temperature fields at different instants of time t in a plane crystal of Al2O3, 5 mm thick when it is heated by the radiation of a CO2 laser with q = 600 W/cm2. A melting temperature of 2327 K is reached on the surface of the crystal at the instant tbh = 0.94 sec from the beginning of heating and after 0.44 sec (see Fig. 1b) it is not changed, whereas in a very thin surface layer a two-phase zone is observed, in which the thickness of the liquid phase is increased. Beginning at the instant tbh = 1.38 sec only a single-phase melt remains in this zone. On further heating, both the thickness of the melt δ and the temperature of its surface increase. At the instant when the heating ceases, which was 20 sec, the temperature of the heated surface Tsf = 2895 K and δ ≈ 0.8 mm, while the temperature of the opposite (rear) surface Tsr = 2164 K. Calculations have shown that the two-phase zone is only formed at the initial stage of the heating. Its maximum thickness is determined to a considerable extent by the absorption coefficient of the heating radiation of the CO2-laser for λ = 10.6 μm. Due to the lack of experimental data for the absorption coefficient of the melt at this wavelength, it is taken to be 1000 cm–1 and is independent of the temperature, which corresponds to the experimental data obtained at room temperature. The time for which the two-phase zone exists during the heating depends on q. Calculations were carried out for q = 200, 400, 600, 1200, and 3000 W/cm2. In Fig. 2a, we show the dependences of the temperatures Tsf and Tsr of the surfaces of a plane layer, corresponding to these densities, and also the difference in the actual and brightness temperatures Tsf – Tbf of the front surface. In Fig. 2b, we also show the initial stage of the heating with a larger time resolution. The results obtained reveal the specific features of the heating of semitransparent materials by concentrated radiation; the overall characteristic features are the rapid heating of condensed media by high-power thermal fluxes, the properties of a specific semitransparent material (Al2O3), the feature of which is the considerable difference (about two orders of magnitude) of the absorption coefficients of the oxide melt and its solid phase close to the melting point [9–12]. A specific feature of a semitransparent material is the formation at the depth of penetration of the heating radiation of the CO2-laser of a two-phase zone, which, due to the assumed absorption coefficient, should only be 0.01 mm, if it was isothermal before the melting begins. However, a considerable temperature gradient before melting begins means that the layer closest to the surface begins to melt slightly earlier, but in all cases it takes much less time from the start of surface melting to the formation of an extended two-phase zone than the melting time of the two-phase zone. The maximum thickness of 660

the two-phase zone is less than the value of the quantity that is the inverse of the absorption coefficient for the wavelength of the heating radiation of the CO2-laser. This is due to the large temperature gradient due to the removal of heat both by conduction and radiation, which is very important, since the Al2O3 crystal has a low absorption coefficient in the region of the spectrum that is electrically important for radiation transfer [9]. It follows from Fig. 2a and b that the melting time of the two-phase zone is determined by the flux density q of the heating laser radiation. As q increases, the relative reduction in the melting time of the two-phase zone becomes much greater than the relative increase in the flux density. The fairly large q = 3000 and 1200 W/cm2 lead to the occurrence of a maximum (a sharp peak) in the surface temperature at the initial heating stage for tbh = 0.18 and 0.9 sec, respectively. For q = 600 W/cm2, this maximum is more spread out and is observed in the region tbh = 12 sec, while for q = 400 W/cm2 and 200 W/cm2, it generally disappears. Calculations showed that the thickness of the melt δ for heating by radiation with q = 3000 W/cm2 at the initial stage of heating, as might have been expected, increases more rapidly than with q = 1200 W/cm2. However, the graphs of δ(t) then merge, and, beginning approximately from 1.2 sec, the melt thickness for these two values of the density differ only slightly. The reason for this is the evaporation of the melt from the surface. For these values of q, up to the instant tbh = 1.2 sec, the temperatures of the heated front surface are identical (see Fig. 2b), and their further monotonic decrease is due to heating of the layer in the solid phase and the increase in its temperature, which leads to an increase in the loss of heat as a result of radiation from the volume of the oxide through the rear surface of the layer. In Fig. 2a, we can follow a situation that is not completely obvious: as the duration of the heating increases, the graphs of the temperature of the rear surface Tsr of the layer begin to approach one another not only for q = 3000 and 1200 W/cm2, where evaporation exists and the temperatures of the heated surfaces are close to one another, but also for q = 600 and 400 W/cm2, where evaporation is insignificant. Here we see a specific feature of Al2O3: since its melt has an absorption coefficient which is very high and in the important energy region of the spectrum exceeds 100 cm–1, the radiation emerging through the cold surface only makes a contribution to the melt at the boundary with the crystal, which has a fixed melting point of 2327 K. Since the melt occupies a small part of the layer thickness, the temperature field of the layer in the solid phase becomes the same as it heats up and transfers to the quasistationary state, which gives the same temperature of the rear surface. The temperature of the front heated surface will then be different. In the results shown in Fig. 2a, for the least q = 200 W/cm2, the temperature of the rear surface is less due to the slower heating, for which, after a time tbh = 20 sec has not yet reached the quasistationary state. Calculations showed that for q = 200 W/cm2 after tbh = 20 sec, the temperature Tsr = 2023 K, where Tsf = 2346 K and the melt thickness δ = 0.05 mm. In additional calculations for this q, we obtained that at the instant of time tbh = 30 sec they were 2126 K, 2353 K, and 0.063 mm, respectively, while at the instant tbh = 40 sec they were 2131 K, 2353 K, and 0.066 mm, and for further heating, up to 100 sec, they did not change. This indicates the following: already at the instant tbh = 40 sec for q = 200 W/cm2 a stationary temperature state is reached. Here the values of Tsf are close for all other flux densities q of the heating radiation. The way in which a temperature field is formed during the heating and the absorption coefficient of the oxide for λ = 0.65 μm determine the ratio between the actual temperature Tsf and the brightness temperature Tbf of the heated surface. The radiation emerging from the front surface during the heating of the solid-phase layer contains a contribution from the whole thickness of the layer of 5 mm due to the smallness of the absorption coefficient of the Al2O3 crystal. This is reflected in Fig. 2a and b, where the value of Tsf – Tbf increases rapidly for all q, and, at the instant when melting begins (the occurrence of a liquid phase in the two-phase zone which is formed) it reaches a maximum. It should be noted that when Tsf > 1800 K, the rate of increase of Tsf – Tbf decreases due to the sharper increase in the absorption coefficient for λ = 0.65 μm in this temperature range [9]. At the instant when melting begins, in view of the appearance of the first portion of the melt in the twophase zone (due to the absorption coefficient of the melt being two orders of magnitude greater than that of the Al2O3 crystal), the thickness of the radiating layer, which makes a contribution to the output radiation, decreases. This is reflected as a sharp reduction in Tsf – Tbf. At the active two-phase zone stage, a reduction in the rate of fall of Tsf – Tbf occurs, which can be seen on the graph of Tsf(t) as a slightly inclined plateau, which is opposite the horizontal ones. After complete melting of the two-phase zone, a second brief reduction of Tsf – Tbf begins, caused by an increase in the thickness δ of the layer of melt and an increase in its absorption coefficient as the temperature increases. Gradually, due 661

TABLE 1. Dependence of the Brightness Temperature Tbf for Different Temperatures of the Surface Tsf When Heating a Layer of Al2O3, 5 mm Thick, Using Radiation of Different Density q of a CO2-Laser Tsf, K

*

Tbf, K, for q, W/cm2 200

400

600

1200

3000

1400

934

909

895

875

–

1600

1042

1015

995

971

948

1800

1186

1146

1123

1094

1070

2000

1369

1316

1283

1248

193

2200

1549

1477

1438

1391

1330

2327

*

1894

1664

1580

1556

1543

2400

–

2240

2182

2099

1944

2600

–

2547

2527

2453

2314

2800

–

–

2762

2706

2591

3000

–

–

2970

2934

2845

3200

–

–

–

–

3076

The data relate to the beginning of melting.

to the effect of both factors, the layer of melt becomes optically infinite, the solid phase ceases to make a contribution to the emerging radiation, the rate of change of Tsf – Tbf decreases and gradually becomes constant. Evaporation from the surface of the melt facilitates this and makes a considerable contribution when heating with radiation of densities q = 1200 and 3000 W/cm2. The data obtained on the temperature dependences of the brightness temperature Tbf on the temperature Tsf for λ = 0.65 µm and for different flux densities q of the heating radiation are presented in Table 1. Conclusions. For all q during the heating of the layer of solid aluminum oxide, there is an enormous difference between the actual temperature Tsf and the brightness temperature Tbf of the surface, and it increases as q increases. However, even for the minimum value of the values considered (q = 200 W/cm2), monochromatic pyrometers with λ = 0.65 μm cannot be used to measure surface temperature. After the melting of the two-phase zone, as the thickness δ of the melt increases, the difference in the actual and brightness temperatures decreases. For certain q and high temperatures, when the melt thickness becomes considerable, and the emerging radiation is determined solely by the temperature field in the melt, the value of Tsf – Tbf becomes small. In this case, to determine the surface temperature from the measured brightness temperature, the use of the calculated correction may give acceptable accuracy in determining Tsf. This situation is observed, for example, for q = 400 W/cm2, when Tsf ≈ 2600 K, and for q = 600 W/cm2 in the range Tsf = 2800–3000 K. However, for higher values of q = 1200 and 3000 W/cm2, when there is a high temperature gradient in the melt layer, the value of Tsf – Tbf remains high, up to intensive evaporation temperatures of 3200 K.

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