ISSN 1054-660X, Laser Physics, 2006, Vol. 16, No. 1, pp. 116–125. © MAIK “Nauka /Interperiodica” (Russia), 2006. Original Text © Astro, Ltd., 2006.
INTERACTION OF RADIATION AND BEAMS OF CHARGED PARTICLES WITH MATTER
Laser Synthesis of Nanopowders V. V. Osipov, Yu. A. Kotov, M. G. Ivanov, O. M. Samatov, V. V. Lisenkov, V. V. Platonov, A. M. Murzakaev, A. I. Medvedev, and E. I. Azarkevich Institute of Electrophysics, Ural Division, Russian Academy of Sciences, ul. Amundsena 106, Yekaterinburg, 620016 Russia e-mail:
[email protected] Received September 1, 2005
Abstract—YSZ, YSZ + Al2O3, Ce0.78Gd0.22O2 – δ, and 5NdY2O3 nanopowders are obtained using target evaporation with a repetitively pulsed CO2 laser and subsequent vapor condensation in the flow of a carrier gas. The design of the laser complex for producing the nanopowder and the block diagram and the characteristics of the repetitively pulsed CO2 laser pumped by a combined discharge are presented. The size distribution of the nanoparticles is studied and the x-ray data are reported. It is demonstrated that a nanopowder output rate of 15– 75 g/h linearly increases with the mean laser power. Under equal conditions, the size distribution of the particles is weakly affected by the type of the target material. The results obtained are interpreted. DOI: 10.1134/S1054660X06010105
1. INTRODUCTION The discovery of self-sustained and non-self-sustained space discharges and the creation of high-power high-pressure gas lasers based on these discharges and exhibiting lasing in the UV and IR spectral ranges with a short pulse duration and a tunable wavelength [1] enabled G.A. Mesyats to formulate a problem regarding the creation of electric-discharge repetitively pulsed technological lasers. By that time, N.G. Basov and coworkers had demonstrated that the repetitively pulsed irradiation of materials is more effective than cw irradiation [2]. However, commercial repetitively pulsed CO2 lasers for action on materials are still unavailable. The primary reason for this is the absence of high-power fast reliable switches and in the intention to pump the entire gas medium that crosses the gas gap. We succeeded in the development of a repetitively pulsed CO2 laser and the corresponding technology for the production of nanopowders with improved parameters. There exist a variety of chemical and physical methods for nanopowder synthesis [3]. The chemical methods exhibit a relatively high efficiency. The synthesized nanopowders are cheap and tend to strong agglomeration. The physical methods make it possible to produce weakly agglomerating nanopowders. However, the efficiency of the physical methods is lower, and the nanopowders are more expensive. The following methods exhibit the highest efficiency: plasma and plasma chemical methods, exploding-wire methods, and laser synthesis. Note that the powders produced using laser synthesis have the narrowest size distribution of particles and the highest price. Therefore, the nanopowder is chosen based on the desired application. The nanopowders produced using laser synthesis should be preferred in the production of nanoceramic
materials whose density is equal or close to the theoretical density and the crystallite size is about 100 nm. Nanopowder synthesis in the laser plume has been demonstrated in [4]. However, only in 1995 did Muller et al. [5] prove the competitiveness of this method in comparison with the alternative techniques. Using a cw CO2 laser with a power of 4 kW, Muller et al. produced ZnO2 nanopowders with a mean particle size of about 60 nm at an output rate of 130 g/h and an energy consumption of 25 W h/g. The laser pulses with a repetition rate of 3.5 kHz, a FWHM of 120 ns, and a peak power of 100 kW were generated using a Q-switched cavity. In this case, the particle size decreases to 15 nm, the output rate decreases to 11 g/h, and the energy consumption sharply increases. Therefore, the Q-switched mode is inappropriate. However, in our opinion, the energy consumption of the nanopowder production should decrease owing to a decrease in the energy loss by heat conduction in the repetitively pulsed mode. 2. EXPERIMENTAL COMPLEX We prove the above assumptions using the experimental setup whose block diagram is shown in Fig. 1. The laser radiation is focused on the target 2 with a lens 8 that also serves as the input window of the evaporation chamber 3. Drive 1 rotates the target 2 and moves it linearly in the horizontal plane, so that the laser beam scans the target surface with a constant linear velocity. This provides for the homogeneous processing of the surface. When the target surface is worked out, the target is axially moved in such a way that the focal spot remains on the target surface. The focal length of the KCl lens 8 is 10 cm, and the focal spot diameter is 0.7 mm. The beam moves along the tar-
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LASER SYNTHESIS OF NANOPOWDERS Laser beam 8
Air
7
4
3
Air
6
5 2 1
Fig. 1. Block diagram of the experimental setup for the synthesis of the nanopowder.
get surface with a velocity of 35 m/s, so that the target moves by 0.7 mm over the interpulse time interval. Fan 4 provides the air flow in the chamber 3. The air flow brings the powder to cyclone 5 and filter 6, which collects the powder. Air returns to the chamber after additional cleaning in filter 7. The gas-flow velocity over the target surface is about 15 m/s. The nanopowders are analyzed using a DRON-4 X-ray diffractometer, a JSM-T220A scanning electron microscope, a GKh-1 chromatograph for the BET method, and a Q-1500 device. Tablets consisting of pressed and partially sintered YSZ powders (ZrO2 stabilized with Y2O3) or a mixture of rough powders (ZrO2 and Y2O3, Al2O3, CeO2, Nd2O3, and Gd2O3) with a particle size of 1–10 µm serve as the targets. The CO2 laser pumped by a combined discharge is the most complicated unit of the complex for nanopowder production. Certain properties of this laser make it possible to obtain small mean sizes at a relatively low energy consumption. Therefore, we present a detailed analysis of this original device. Figure 2 demonstrates the schematic circuit diagram of the repetitively pulsed CO2 laser [6]. On the left-hand side, we show the oscillator that produces short high-voltage pulses. On the right-hand side, we present the dc voltage source for the non-selfsustained discharge. The self-sustained discharge is ignited in the gap with a high-voltage source. The main
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part of the energy is deposited to the gas from the dc voltage source after the termination of the self-sustained discharge at the stage of plasma decay. Figure 3 shows the oscillograms of the currents of the self-sustained and non-self-sustained discharges. It is seen that the duration of the self-sustained discharge is 100 ns, and the duration of the non-self-sustained discharge is 100 µs. The self-sustained discharge is excited when the current decreases to a certain level and the process is repeated. The energy deposited to the gas at the stage of the self-sustained discharge and passing through the thyratron is 1–2% of the energy of the non-self-sustained discharge. This makes it possible to create a technological repetitively pulsed CO2 laser. A variation in the number of pulses in the burst leads to a variation in the duration of the radiation. If the number of pulses in the burst is no greater than three, the radiation duration remains unchanged and we observe only variations in the shape (Fig. 4a). It is seen that, at a mean power of 1 kW, the peak power is 10 kW. For the production of nanopowders, we employ radiation with the second pulse shape. Figure 4b shows the variation in the pulse shape with a delay between the high-voltage pulses. The best results are obtained for a delay of 75 µs. The characteristics of the laser are as follows: wavelength, 10.6 µm; controlled mean power of the radiation, up to 800 W; controlled peak power of the radiation, up to 11 kW; controlled pulse repetition rate, up to 650 Hz; controlled pulse duration, 150–350 µs; and efficiency, 10%.
The above energy characteristics are averaged over 2.5 h of the laser operation in the sealed-off mode. 3. RESULTS AND DISCUSSION Using the laser complex, we produce the nanopowders YSZ, Al2O3 + YSZ, Ce0.78Gd0.22O2 – δ, NdY2O3, etc. For the nanopowders YSZ, Al2O3 + YSZ, and NdY2O3, 12
6
7
16 15
9
8
17 3
1 2
R2
R1
R3
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13
11
14
Y2 Y1 Fig. 2. Schematic circuit diagram of the repetitively pulsed CO2 laser. LASER PHYSICS
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90 60 30 0
(b)
30 20 10 0
0
100
200
300
400
t, µ s
Fig. 3. Oscillograms of the currents of (a) self-sustained and (b) non-self-sustained discharges.
the output rate is 15–25 g/h and the energy consumption is 20–30 W h/g. These values are very close to the best results from [5]. However, the energy needed for the evaporation of ZrO2 is about 2.7 W h/g. Hence, the results obtained in this work and in [5] indicate a relatively low efficiency of laser energy consumption. Therefore, we need additionally to study the reasons for such high loss and to search for methods of decreasing the loss. Analysis of the samples obtained shows that the powders are weakly agglomerated and consist of two fractions differing by size. The first fraction (Fig. 5a)
with a relative content of 3–7 wt % contains spherical particles with a size of 0.2–2 µm. Apparently, this fraction is obtained owing to splattering of the liquid phase, since the composition of the particles is close to the composition of the raw material or is enriched with the component (Y2O3), which has a higher boiling point. Note the deficit of this component in the nanofraction relative to the raw material (Table 1). The second fraction may contain shapeless particles with a size of up to 10 µm that, apparently, represent target debris. The fraction remaining in the suspension (Fig. 5b) exhibits a size distribution of particles (Fig. 5c) that LASER PHYSICS
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Laser power, kW (a) 5
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5 0
0
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300
400
500
Time, µ s
Laser power, kW (b)
10 kW
0
0
Time, µ s
50
Fig. 4. Pulse shape variation with (a) the number of pulses of the self-sustained discharge in the pulse burst and (b) the delay time between the pulses of the self-sustained discharge.
shows that 98% of the particles have a size of less than 40 nm and only 10 in 4000 particles have a size of 65– 100 nm. These particles have a weakly faceted nearspherical shape. LASER PHYSICS
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Normally, the specific surface of the particles decreases by 10% upon sedimentation. This indicates weak agglomeration of the powders. However, the sedimentation results in an order-of-magnitude increase in
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5.130
5.120 10 µm
(‡)
5.110 10087628
~ ~ 4.927 0
2
4
6
8 10 Y2O3, mol %
Fig. 6. Plot of the YSZ lattice parameter vs. the Y2O3 content.
100 nm
(b) 0.10
100
(c)
0.08
80
0.06
60
0.04
40
0.02
20
described well by a linear dependence (Fig. 6) whose initial point coincides with the value obtained in [7] for pure ZrO2 (90% of the tetragonal phase) produced with the plasma chemical method. The data obtained for ZrO2 nanopowders produced with electric explosion and containing from 55 to 65 wt % of the tetragonal phase [8] agree with the range indicated in Fig. 6.
We may assume that the YSZ lattice is impregnated with a part of the liquid Al2O3, so that a solid solution is formed. Assuming a linear variation in the parameter
Q, %
The analysis of the phase compositions and the structure (Table 1) indicates a single-phase character of the YSZ powders. Their mean cell parameter is
Density function
the bulk weight of the powders and, hence, facilitates technological applications.
The analysis of the elemental composition of the mixture powders (Table 2) shows that, in the case of coevaporation, the content of the high-temperature component in these samples decreases to a greater extent than in the YSZ powders. Such a decrease grows with an increase in the content of the low-temperature Al2O3 (the boiling point is Tb = 3800 K and the melting point is Tm = 2320 K). In particular, in the first (second) mixture, the YSZ content decreases by about 2% (25%) and the content of Y2O3 in YSZ decreases by 12% (30%). Thus, the initial equality of the volumes of the components (the first mixture) and the masses of the components (the second mixture) is not satisfied in the resulting powders. These powders exhibit an unusual phase composition. Specifically, in the first mixture, about 40 wt % of 1.45 YSZ are in the cubic phase. In addition, the cell parameter of both the tetragonal and cubic phases is significantly smaller than the cell parameter following from the concentration dependence (Fig. 6). The monoclinic phase is completely absent.
0
20
40 60 Grain size, nm
0
Fig. 5. Typical photographs of (a) the YSZ powder precipitated upon the sedimentation and (b) the nanopowder from the suspension and (c) the size distribution of the nanoparticles.
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Table 1 No.
Characteristic of the target material
Characteristic of the nanopowder after sedimentation
1
Mixture of powders: ZrO2 , S = 20 m2/g; 3.1Y2O3 , S = 4.5 m2/g
2
Mixture of powders: ZrO2 , S = 20 m2/g, T = 45 and M = 55 wt %; 4.5Y2O3 , S = 4.5 m2/g
3
Mixture of powders: ZrO2 , S = 51 m2/g, T = 60 and M = 40 wt %; 9.1Y2O3 , S = 4.5 m2/g
4
Powder: 10.15YSZ, S = 6.1 m2/g, K—a = 5.1448 Å
2.8YSZ: S = 68 m2/g, T—a = 5.106 and c = 5.1638 Å, grain size D = 19 nm, volatile mass m(L) = 2.7 wt % Sediment—3.4YSZ: T: a = 5.1084 and c = 5.1674 Å; D = 26 nm. 6% of the M phase are available. Melted crust of the target—5.2YSZ 4.15YSZ: S = 64.4 m2/g, T—a = 5.115 and c = 5.161 Å, D = 17 nm, m(L) = 2.6 wt % Sediment—4.35YSZ: K—a = 5.13 Å, D = 25 nm. 7% of the M phase are available 8.6YSZ: S = 86 m2/g, K—a = 5.1405 Å D = 17 nm, m(L) = 2.4 wt % Sediment—8.9YSZ: K—a = 5.144 Å, D = 25 nm. 7% of the M phase are available 9.85YSZ: S = 79 m2/g, K—a = 5.1459 Å, D = 18 nm, m(L) = 2.8 wt % Sediment—10.4YSZ: K—a = 5.15 Å, D = 41 nm
Note: In the mixtures, for the raw material, we present the molar percentage of the Y2O3 powder. Letters M, T, and K stand for the monoclinic, tetragonal, and cubic YSZ lattices, respectively.
Table 2 Composition of the target
Characteristic of the target material
Mixture of powders A40 + 1.65YSZ60
Al2O3 , S = 74 m2/g; γ ≈ 20 wt %; δ ≈ 80 wt %. 1.65YSZ, S = 7.76 m2/g; M = 58 and T = 42 wt %. Grain size D = 70 nm
Mixture of powders A85 + 1.65YSZ15
″
of the YSZ lattice from the initial value 5.123 Å, which corresponds to pure 1.45 YSZ, and with allowance for a radius ratio of zirconium and aluminum of 1.2, we can estimate the amount of Al2O3 dissolved in the YSZ lattice. Such estimates show that the Al2O3 contents in the tetragonal and cubic phases are about 0.7 and 19.4 wt %, respectively. It is also seen from the diffractograms that part of the Al2O3 is in the amorphous state. The content of the amorphous Al2O3 in the powder under study is about 21 wt % assuming that the all the 1.45 YSZ is in the crystalline state. It is even more difficult to interpret the results obtained for the A88.8 +1.15YSZ11.1 powder, since the asymmetry of the lines and the background level are relatively high. We may guarantee that an increase in the Al2O3 content does not lead to an increase in the fraction of the cubic modification relative to the tetragonal fraction after the laser synthesis. However, in the case of sedimentation, a significant part of the powder LASER PHYSICS
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Characteristic of the nanopowder after sedimentation A41.1 + 1.45YSZ58.9, S = 80.6 m2/g, m(L) = 4.9 wt %. Composition and structure: 1.45YSZ: T—31 wt %: a = 5.095 and c = 5.156 Å, D = 11 nm. K—28 wt %: a = 4.924 Å, D = 6 nm. γ-Al2O3 – 20 wt %, D = 10 nm Amorphous γ-Al2O3—21 wt % A88.8 + 1.15YSZ11.2, S = 86 m2/g, m(L) = 4.8 wt %. Composition and structure: cubic and tetragonal are available 1.15YSZ, γ-Al2O3 and amorphous Al2O3 , the interpretation of the results of the analysis goes on
in the tetragonal phase precipitates. A strong asymmetry of the lines (especially for the tetragonal phase) leads to a greater error in the determination of the weight composition of the phases and the grain size. This fact and the fact that the tetragonal phase of YSZ with a grain size of 6 nm is virtually completely precipitated make it possible to assume that the aluminum oxide exists on the surface of the tetragonal grains of YSZ and that the real size of these grains is apparently greater. Hence, these grains precipitate in the case of sedimentation. To obtain Ce0.8Gd0.2O2 – δ powders, we use targets made of a mixture of CeO2 and Gd2O3 powders. The original powders were tested using various methods. The original CeO2 powder exhibits a specific surface area of S = (2.8 ± 0.2) m2/g (determined with the BET method on the GKh-1 device) and contains 0.25 wt % of volatile matter, whose desorption is terminated at a temperature of 600°C (determined with thermogravi-
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(a) 30 KU
(c)
× 5.000
5 µm
(b) 30 KU
1 µm
× 10.000
Number of particles 500 (d) 450 400 350 300 250 200 150 50 0 10 20 30 40 25 nm
50
60 70 80 Diameter, nm
Fig. 7. Typical photographs of (a) CeO2 raw material, (b) powder precipitated upon the sedimentation, and (c) Ce0.78Gd0.22O2 – δ nanopowder in the suspension and (d) the size distribution of the nanoparticles.
metric analysis (TGA) on the Q-1500 device). The results of x-ray phase analysis (XPA) on the DRON-4 diffractometer show that the powder exhibits a cubic structure with a lattice parameter of 0.5411 nm, which corresponds to the data from the ASTM library. Impurities were not detected. Raster electron microscopy (JSM-T220A) shows that the powder consists of shapeless particles and their agglomerates (Fig. 7a) with a size of up to 10 µm. Similar tests show that the Gd2O3 powder exhibits S = (2.0 ± 0.2) m2/g and contains 0.97 wt % of volatile matter whose desorption is terminated at a temperature of 700°C. The single-phase powder has a cubic lattice with a parameter of 1.0813 nm. It is seen from the photographs of the powder (Fig. 7b) that its particles are shapeless and strongly agglomerated. The size of the particles and the agglomerates is up to 5 µm. When nanopowders are produced using the evaporation of the CeO2/Gd2O2 targets, the output rate increases to a level of 60–80 g/h, which is three times higher than the output rate for YSZ. In our opinion, the main reasons for this are the decrease in the boiling point from 4310 to 3500°C and a decrease in the energy needed for the evaporation of the mixture. Calculations based on the thermodynamic data from [9, 10] for the
oxides ZrO2, Y2O3, CeO2, and Gd2O3 show that the energy needed for the heating and evaporation of the mixture 0.83ZrO2 + 0.17Y2O3 (corresponding to 10 YSZ) under the adiabatic conditions is W(H + E) ≈ 7.9 kJ/g. For the mixture 0.654CeO2 + 0.346Gd2O3, this energy is W(H + E) ≈ 4.75 kJ/g. The specific surface area of the nanopowder is 57 ± 4 m2/g. Sedimentation analysis in the isopropyl alcohol shows that the powder contains no greater than 8 wt % of particles with a size of greater than 200 nm (Fig. 7b), which represent a mixture of spherical particles with a diameter of up to 1.5 µm related to the splattering of the liquid bath on the target and shapeless particles with a size of up to 5 µm (target debris). Therefore, the sedimentation is used to obtain high-quality ceramics. After sedimentation, the specific surface area remains virtually unchanged (SBET = 56 ± 4 m2/g), since the extraction of large particles is accompanied by a weak agglomeration of the powder. Transmission electron microscopy (JEM-200) shows that the shape of the particles is varied from cubic to spherical (Fig. 7c). The size distribution of 1583 particles (Fig. 7d) is close to the log-normal disLASER PHYSICS
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LASER SYNTHESIS OF NANOPOWDERS Output rate, g/h
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Density function 0.10
70
Y2O3:Nd CeGdO YSZ
0.08
60 50
0.06 40 30
0.04
20 0.02
10 0
100
200
300
400 500 600 Laser power, W
Fig. 8. Plot of the output rate for the Ce0.78Gd0.22O2 – δ nanopowder vs. the mean laser power.
tribution with the geometric mean diameter dg = 9.4 nm and the variance σg = 1.7. In the range d > 40 nm, we find particles with the sizes d = 50, 60, 65, 80, 100, and 200 nm (one particle per size), so that, for more than 99% of the particles, the size is d < 40 nm (as was demonstrated for the YSZ powders). The XPA results show that the powder consists of a single phase and represents a solid solution of Gd in the CeO2 cubic lattice with a parameter of 0.5424 nm and the grain size D = 19 nm determined with the Scherer method. Note that the major contribution to the grain size is related to large particles and D > dg. Hence, the powder contains single-crystal particles. Elemental analysis (Jobin 48 spectrometer) shows that, within the experimental error, the composition of the nanopowder is equal to the desired composition. With allowance for 2.8 wt % of volatile matter, the oxide content on CeO2 (Gd2O3) basis determined with TGA is 0.782 (0.218). This fact needs to be additionally analyzed, since the target contains an excessive amount of Gd2O3. In addition, evaporation should lead to the enrichment of the target with the high-temperature component (i.e., Gd2O3). However, its evaporation is significantly slower than the evaporation of CeO2. In the long experimental series, we studied the effect of the laser radiation parameters on the characteristics of the nanopowder and the output rate. Figure 8 demonstrates the dependence of the efficiency of Ce0.78Gd0.22O2 – δ nanopowder production on the mean radiation power. In the experiments, the mean power is varied owing to a variation in the energy input to the gas at a repetition rate of the pulse bursts of 500 Hz. It is seen that the dependence is linear in the mean power range 400–600 W. The point in the vicinity LASER PHYSICS
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5
10
15
20
25
30
35 40 45 Grain size, nm
Fig. 9. Experimental size distribution functions of the nanoparticles for various materials under equal conditions for the laser synthesis.
of the power axis corresponds to the appearance of the laser plume. In addition, we studied the effect of the peak power of a radiation pulse that is varied due to a variation in the delay time between the pump pulses in the burst on the efficiency of the nanopowder production at a constant mean power and a constant pulse energy. In the peak-power range (5.2–8.2) × 103 W and the corresponding range of the peak power densities averaged over the focal spot (1.3–2.05) × 106 W/cm2, the efficiency of the nanopowder production remains virtually unchanged. In our opinion, the reason for this lies in the fact that the laser radiation energy in the focal spot is significantly higher than the energy needed to increase the temperature of the surface layer to the boiling point. It is expedient to study the dependence of the size distribution of the nanoparticles on the type of material under otherwise equal conditions. In the long experimental series, the mean radiation power is 600 ± 40 W. The pulse repetition rate is constant (500 Hz). In addition to the aforementioned powders, we produce the 5Nd:Y2O3 nanopowders. Thus, nanopowders of the following oxides are processed: 5Nd:Y2O3, Ce0.78Gd0.22O2 – δ, and 9.8 YSZ. Figure 9 demonstrates the results of the processing as a size distribution of the particles after the sedimentation of the powders. Analysis of the results shows that the nanopowders produced using different materials under equal experimental conditions exhibit similar size distributions of the particles. The largest difference is observed for the 5Nd:Y2O3 (curve 1, the mean size of the particles is 10.8 nm) and 9.8 YSZ (curve 2, the mean size of the particles is 9.4 nm) nanopowders.
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This result is unexpected, since the thermophysical characteristics of these powders are similar and substantially differ from the characteristics of the Ce0.78Gd0.22O2 – δ nanopowder. Note that the output rates of the 9.8 YSZ and 5Nd:Y2O3 nanopowders are equal, since the boiling points and the sublimation energies of these materials are virtually identical. The production of the Ce0.78Gd0.22O2 – δ nanopowder exhibits a different efficiency. In particular, the maximum output rates for the 5Nd:Y2O3 and 9.8 YSZ powders are 25 g/h, whereas the maximum output rate for the Ce0.78Gd0.22O2 – δ powder amounts to 80 g/h. The higher the efficiency, the larger the size of the laser plume from the target surface. A possible reason for the difference between the size distributions of the 5Nd:Y2O3 and 9.8 YSZ nanoparticles is the difference between the initial conditions and the errors in the data processing. In our opinion, the closeness of the size distributions of particles made of different materials is related to the equality of the volumes of the evaporated target materials in a unit volume of the laser plume. Indeed, the volume of the laser plume increases up to the moment when the pressure inside the plume becomes equal to the surrounding gas pressure. The gas pressure in the chamber is constant and is equal to the atmospheric pressure. Therefore, at the final stage, the pressures inside different plumes are equal. This makes it possible to interpret the closeness of the size distributions. To estimate the sizes of the nanoparticles, we employ the approach developed in [11, 12] and based on the theory of quasichemical condensation. The mean diameter of the particles is given by 3M 〈 n〉 1/3 〈 d〉 = 2 ⎛ ------------------⎞ , ⎝ 4πN A ρ⎠ where M is the molar mass, ρ is the density, and NA is the Avogadro number. The mean number of molecules 〈n〉 in a particle is represented as 1 4 + 2 〈 n〉 = --- --- k ( N ) /J 0 4 3
3/4
1/4
( n* ) ,
where k+ is the rate of molecular attachment to the cluster, N is the vapor concentration, n* is the number of molecules in the critical nucleus, and J0 is the rate of their formation. We omit the equations for k+, n*, and J0. Note that n* and J0 depend on the quantity ln(p/ps), where p is the pressure and ps is the saturation vapor pressure at the given temperature. The needed parameters N, p, and T are found from the one-dimensional system of the hydrodynamic equations ∂ρ ------ + ∇ ( ρv ) = 0, ∂t
∂ ( ρv ) -------------- + ∇ ( ρv ⋅ v ) = – ∇p, ∂t ∂E ------ + ∇ ( Ev ) = – ∇ ( pv ), ∂t where ρ is the density, v is the velocity, p is the pressure, and E is the total energy of the medium: E = Ein + Ekin, where Ein is the internal (thermal) energy and Ekin is the kinetic energy pf the medium that are represented as i E in = --- nkT , 2 2
E kin
ρv = ---------, 2
p = nkT . Here, i is the number of degrees of freedom, k is the ρ Boltzmann constant, T is temperature, n = ---- is the m number density of molecules, and m is the molecular mass. The boundary conditions are determined by the time dependence of the laser intensity. For each point of the medium, we calculate 〈d〉 and the variance D using the expressions from [12]. We assume that the distribution function of the powder at each point of the medium is the Gaussian function 2
1 ( d – 〈 d〉 ( x ) ) f ( x, d ) = ----------------------- exp ⎛ – --------------------------------⎞ . ⎝ 2D ( x ) ⎠ 2πD ( x ) Figure 10 shows the integral (with respect to the plume volume) distribution function of the powder in terms of the diameter F(d ) =
∫ f ( x, d ) dx.
It is seen that the distribution functions for YSZ, CeGdO, and Y2O3:Nd are close to each other. The reason for this lies in the fact that the molecular concentrations N are virtually equal to the pressure in the plume, which reaches atmospheric pressure, and the temperature differences are compensated for owing to the weak temperature dependence of the initial expressions (k+ ~ T –1). Thus, the results of the calculations qualitatively prove the similarity of the size distributions (obtained under identical experimental conditions) of particles that contain different materials. Note that the similarity of the thermophysical parameters accounts for the closeness of the distributions obtained for the 9.8 YSZ and 5Nd:Y2O3 particles. A quantitative difference between the results of the calculations and the experimental data follows from the approximate character of the model used in the calculations and the fact that we LASER PHYSICS
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LASER SYNTHESIS OF NANOPOWDERS f, arb. units YSZ CeGdO2 Y2O3:Nd
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bution of the majority of the particles with respect to size (2–30 nm). (iii) The nanopowders produced with a repetitively pulsed CO2 laser exhibit low agglomeration and can be easily disintegrated. (iv) For equal parameters of the laser pulses and under otherwise equal conditions, the size distributions of the nanoparticles are close to each other irrespective of the composition of the target material. REFERENCES
1
0
20
40
60
80
100 d, nm
Fig. 10. Calculated size distribution functions of the nanoparticles for various materials.
neglect the carrier gas flow over the target surface, which substantially affects the vapor condensation. 4. CONCLUSIONS (i) The method proposed makes it possible to produce pure nanopowders with a complex composition and a narrow size distribution of particles using both the finished compounds and the mechanical mixtures of various powders. (ii) The advantages of the experimental setup based on a repetitively pulsed CO2 laser are as follows: low energy consumption (10–25 W h/g), mean sizes (9– 15 nm) of the particles smaller than the sizes obtained with cw lasers by a factor of four, and a narrow distri-
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