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2142834668
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note
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Because the only degrees of freedom of the metal atoms in these clusters are vibrations, the entropic contributions to the free energy are small and differ very little with cluster size. Thus, Eq. 1 is also often applied to describe the size dependence of internal energy as well as free energy. Generally, γ is assumed to be independent of particle radius at the value for bulk metal (3, 4, 13-15).
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15
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2142840949
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note
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The assumption of a constant number density of islands is probably slightly incorrect in that their number generally increases weakly with coverage in this range for such systems (13, 41). Correcting for this would cause the measured decrease in stability with radius to be even more dramatic than shown.
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19
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2142683039
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note
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2 (42)] gives even poorer agreement with experiment. Using Eq. 1 here neglects the energy of the flat face of the hemisphere, which is equivalent to setting the Pb/MgO adhesion energy at this face equal to the Pb-Pb adhesion energy. [if the Pb/MgO adhesion energy were zero, the factor of 2 in Eq. 1 would instead be 3. In reality, the needed correction is much smaller (16).]
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2142848613
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note
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DePristo estimated that relation empirically by extrapolating between measured energies of: the gaseous dimer (CN = 1), a (111) surface (CN = 9), and the bulk (CN = 12). Furthermore, we used DePristo's relation to estimate the errors in the MBA model of Fig. 1 and found that the errors due to the decrease in bond energy with CN nearly compensate for the errors associated with extrapolating between only the most stable clusters, further justifying its use.
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27
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2142734878
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note
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tot.
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28
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2142723481
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note
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μ(∞)}/kT in Taylor series and neglected all but the first two terms. This is equivalent to assuming that μ(R) - μ(∞) is small compared to kT. Inspection of the heat data in Fig. 1 proves that this is clearly not the case below 1000 K for particles with a radius of a few nanometers.
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31
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2142782896
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note
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2(110) under similar deposition conditions was estimated by scanning tunneling microscopy (13) and high-resolution scanning electron microscopy (33) to be about 1 nm. We used a slightly smaller average size because those techniques could have missed the smallest particles.
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38
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2142731143
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43
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2142793073
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note
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We thank the U.S. Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division, for support of this work. D.E.S. thanks NSF and the University of Washington Center for Nanotechnology for an IGERT Fellowship.
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