Theory of the charged cluster formation in the low pressure synthesis of diamond: Part II. Free energy function and ther
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Theory of the charged cluster formation in the low pressure synthesis of diamond: Part II. Free energy function and thermodynamic stability Hyun M. Janga) Department of Materials Science and Engineering, and Laboratory for Physics/Chemistry of Dielectric Materials, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea
Nong M. Hwang Korea Research Institute of Standards and Science, P.O. Box 102, Daedok Science Town, Daejon 305-600, Republic of Korea (Received 11 August 1997; accepted 3 March 1998)
To account for the dominant formation of diamond over graphite in the gas-activated chemical vapor deposition (CVD) process we have theoretically examined the free energy function of a small carbon-atom cluster as a function of the cluster size. The scalar potential around a charged spherical cluster was derived using the linearized Poisson–Boltzmann equation. It was shown that the repulsive electrostatic energy associated with the growth of the charged diamond cluster was proportional to the fifth power of the cluster size. This suggests the existence of a deep potential-energy-well for the cluster size larger than the critical size corresponding to the free energy barrier for the nucleation. Thus, the growing diamond cluster will be trapped in this potential well before it transforms to the thermodynamically stable graphite. Considering all the relevant thermodynamic driving forces, we have constructed the free energy function in terms of the cluster size. The numerical computation also supports the existence of the potential-energy-well. Therefore, the present theoretical model clearly explains why the charged diamond cluster does not transform to the neutral graphite cluster when the thermodynamic stability is reversed above a certain critical size during the growth.
I. INTRODUCTION 1
In the preceding article, we theoretically examined the thermodynamic driving forces for the charge-induced nucleation in the gas phase and applied this formalism to the nucleation of a charged carbon-atom cluster. It was shown that the short-range ion-induced dipole interaction and the ion-solvation (Born term) were mainly responsible for the charge-induced nucleation of carbon atoms in the gas phase. The effect of the charge-induced nucleation on the enhanced nucleation rate of the carbon-atom cluster was further estimated using the theoretical model developed.1 From the computation, it was clear that the charge-induced nucleation markedly enhanced the rate of the diamond cluster formation by effectively reducing the potential energy barrier for the nucleation in the gas phase. Therefore, it is quite likely that the nanometersized diamond cluster is more stable than the corresponding graphite in the nucleation stage, as was advocated by Badziag and co-workers2 and Hwang et al.3 However, the reduction in the activation free energy does not guarantee the dominant formation of the thermodynamically metastable phase over the stable one. Because graphite is
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