Abstract

The nucleation and growth of pure titanium nanoparticles in a low-pressure sputter plasma has been believed to be essentially impossible. The addition of impurities, such as oxygen or water, facilitates this and allows the growth of nanoparticles. However, it seems that this route requires such high oxygen densities that metallic nanoparticles in the hexagonal αTi-phase cannot be synthesized. Here we present a model which explains results for the nucleation and growth of titanium nanoparticles in the absent of reactive impurities. In these experiments, a high partial pressure of helium gas was added which increased the cooling rate of the process gas in the region where nucleation occurred. This is important for two reasons. First, a reduced gas temperature enhances Ti2 dimer formation mainly because a lower gas temperature gives a higher gas density, which reduces the dilution of the Ti vapor through diffusion. The same effect can be achieved by increasing the gas pressure. Second, a reduced gas temperature has a ‘more than exponential’ effect in lowering the rate of atom evaporation from the nanoparticles during their growth from a dimer to size where they are thermodynamically stable, *. We show that this early stage evaporation is not possible to model as a thermodynamical equilibrium. Instead, the single-event nature of the evaporation process has to be considered. This leads, counter intuitively, to an evaporation probability from nanoparticles that is exactly zero below a critical nanoparticle temperature that is size-dependent. Together, the mechanisms described above explain two experimentally found limits for nucleation in an oxygen-free environment. First, there is a lower limit to the pressure for dimer formation. Second, there is an upper limit to the gas temperature above which evaporation makes the further growth to stable nuclei impossible.

Highlights

  • A model is presented for experimentally obtained nucleation of pure titanium nanoparticles, from sputtered titanium vapor, in an ultra-high vacuum system

  • The effect of helium is that it cools the process gas in the region where nucleation occurs, which is important for two reasons

  • A reduced gas temperature enhances Ti2 dimer formation, which is proposed to be dominated by three-body collisions between titanium ions, titanium neutrals and argon atoms

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Summary

Introduction

A cloud of Ti and Ti+ is ejected out of the hollow cathode It is in the region outside the hollow cathode that the nanoparticles are most likely to nucleate and begin to grow, within a range of distances from the cathode where the two necessary conditions for nucleation are met: a sufficiently low gas temperature, and high enough density of growth material. Represents that no nanoparticles are found at zero argon gas flow, i.e. in a pure helium discharge This limit (marked by crosses in figure 1(c)) is only drawn in the pressure range above 530 Pa. The reason is that a process instability makes it impossible to operate the discharge at combinations QAr = 0 and QHe < 530 Pa. We will not be able to make a quantitative theory which explains the specific numerical constants in the equations above.

Process 3: cooling collisions with process gas
Dimer formation
Process 6: atomistic growth
Process 7: titanium atom loss
Discussion
Dimer formation: two alternatives
The growth from dimers to stable size r*
Findings
The role of He
Summary and conclusions

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