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The nucleation and growth of pure titanium nanoparticles in a low-pressuresputter plasma has been believed to be essentially impossible. The addition ofimpurities, such as oxygen or water, facilitates this and allows the growth ofnanoparticles. However, it seems that this route requires so high oxygendensities that metallic nanoparticles in the hexagonal aTi-phase cannot besynthesized. Here we present a model which explains results for the nucleationand growth of titanium nanoparticles in the absent of reactive impurities. Inthese experiments, a high partial pressure of helium gas was added whichincreased the cooling rate of the process gas in the region where nucleationoccurred. This is important for two reasons. First, a reduced gas temperatureenhances Ti2 dimer formation mainly because a lower gas temperature gives ahigher gas density, which reduces the dilution of the Ti vapor throughdiffusion. The same effect can be achieved by increasing the gas pressure.Second, a reduced gas temperature has a "more than exponential" effect inlowering the rate of atom evaporation from the nanoparticles during theirgrowth from a dimer to size where they are thermodynamically stable, r*. Weshow that this early stage evaporation is not possible to model as athermodynamical equilibrium. Instead, the single-event nature of theevaporation process has to be considered. This leads, counter intuitively, toan evaporation probability from nanoparticles that is exactly zero below acritical nanoparticle temperature that is size-dependent. Together, themechanisms described above explain two experimentally found limits fornucleation in an oxygen-free environment. First, there is a lower limit to thepressure for dimer formation. Second, there is an upper limit to the gastemperature above which evaporation makes the further growth to stable nucleiimpossible.

Nucleation of titanium nanoparticles in an oxygen-starved environment, II: Theory