Nucleation rate surfaces for modeling of nanomaterial generation from crystals under short pulses of energy

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Nucleation rate surfaces for modeling of nanomaterial generation from crystals under short pulses of energy

M.P. Anisimov and A.V. Trilis


Institute of Chemical Kinetics&Combustion, SB RAS, 630090 Novosibirsk, Russia

Keywords: aerosol, nucleation, crystal ablation, fast melting, milling

Nanomaterials can be produced using several wais.  Short pulses of energy impacts which produce aerosol are considered.  As examples can be mentioned aerosols which can be appeared from melted wire under powerful enough electric pulse, a laser ablation or milling of crystals, etc.  Crystal sublimation, liquid boiling, superheating up to the spinodal conditions and aerosol production are investigated experimentally and theoretically, for example [.  Nevertheless one might say that nucleation rate surface topologies for the gas and liquid embryos are not discussed carefully up to now.

Let consider qualitatively the nucleation rate surface topology for vapor embryo-forming from droplets under the short pulses of energy (Fig. 1).

Fig. 1. The simplified PT phase diagram following article by Anisimov et al. (1998).


Fig. 2. The nucleation rate surfaces for droplets (gray colour) and vapor embryos (dark gray one).


Fig. 3. Topology for droplet (dark gray)

and crystal (gray) particles nucleation.


Here P is total pressure, T is temperature, and J is nucleation rate.  Line ct illustrates schematically the vapor-liquid equilibria.  The dotted continuation of that line into the stable crystal conditions is representing unstable equilibria of supercooled liquid and vapor.  The liquid spinodal is represented by line cc1 and its continuation.  Line of the crystal-liquid equilibria is continued by dotted line to the vapor and vacuum conditions. Critical point c1 ends that line. Spinodal for melting crystal is represented by line c1c2 and its continuation to the high pressure side.  Spinodal for crystal-vapor coincides with line с2c1 schematically and is continued to the negative pressures.  That coincidence is not so obvious and needs to be considered more carefully in future. 

In Fig. 2 the nucleation rate surfaces for droplets and vapor embryos are shown schematically.  Surfaces overlap each other between critical points.  Assumptions used for design are such as: nucleation rate along the phase equilibrium lines has zero values and the maximum nucleation rates are achieved at the spinodal conditions.  It is assumed that nucleation rate surface is represented by continuous and monotonous function for one given phase state.  Nucleation rate at the critical points has zero value because these points are representing the second order phase transitions where two different phase coexistence is impossible [3].

When the short pulses of energy become over then vapor gets supercooled and generates mikrocrystals and mikro glasses in the same fashion as Buckle at al. [4] get the amosphous and crystal particles from Zn vapors (Fig. 3).

Non-evaporated droplets should grow under the vapor cooling then freeze to the crystal or glass state.

1. Lu, Q., Mao, S.S., Mao, X., and Russo, R.E. (2002) Appl. Phys. Letters, 80(17), 3072-3074.

2. Martynyuk, M.M. (1977) Phys. Combust. Explosions, 13, 178-184.

3. Anisimov M.P. P.K. Hopke, D.H. Rasmussen, S.D. Shandakov, V.A. Pinaev. (1998) J. Chem. Phys., 109, № 4, 1435-1444.

4. Buckle, E.R., Mawella, K.J.A., Tsakiropolous, P. (1986) J. Colloid Interface Sci., 112, 42-51.

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