Hydrogen Diffusion in Quartz: A Molecular Dynamics Investigation
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INTRODUCTION Silicon dioxide (Si0 2 ) is an important material for the manifacturing industry, as well as for basic science. Its most natural contaminant, for both the crystalline (quartz) and amorphous (silica) phase, is hydrogen (H). Despite this, there is very little knowledge about the diffusion process of H in SiO 2 . As for the experimental results, the determination of the activation energy E5 for the diffusion process is vague. Values for Ea are scattered in the large 0.07 eV - 0.92 eV interval.[1-6] Furthermore, no experimental determination of the diffusion path and mechanism is present. On the theoretical side, the picture is even less established. Most of the theoretical investigations on impurity diffusion in quartz and silica have been addressed to model the charge transport by interstitial alkali halides. Evidence of anisotropic diffusion along the optical axis (c-axis) is reported.[7,8] The goal of the present work is to derive a complete atomistic description of H diffusion
in a- and #-quartz. To this aim we have performed large-scale simulations based on classical molecular dynamics (MD). MD is an ideal tool for modelling impurity diffusionh
since the complete dynamics of the defect as well as the host matrix is in fact described. The issues that are addressed in this work are: (i) the determinantion of the diffusion coefficient of atomic H versus temperature; (ii) the determination of the diffusion path and diffusion mechanism. In the next Section we briefly describe our computational framework and present the model potential here adopted. Finally, we present and discuss our results. THE COMPUTATIONAL MODEL As for Si0 2 , we adopted the interatomic model by Vashista et al.,[9] consisting in both short range and Coulomb interactions. In particular, the short range contribution is represented as a sum of a two-body steric repulsion, a three-body angular interaction, and a charge-dipole contribution taking into account the electron polarizability effects. This model potential has been widely and successfully applied to a number of Si0 2 -based materials, like: quartz,[9] fused silica,[10] and pressure-amorphized Si0 2 .[11] Although a full description of the model potential can be found elsewhere,[9] we like to remark that the Vashista et al. potential gives a fairly good reproduction of the phonon spectrum of quartz. This, in turn, provides a realistic thermal bath for the diffusing H defect. 515 Mat. Res. Soc. Symp. Proc. Vol. 408 01996 Materials Research Society
The Si-H and O-H interactions have been modeled with a two-body short range potential. We adopted the anharmonic Morse functional to fit a selected set of properties of the Si-H and O-H bonds. In the case of the Si-H pair, we simply fitted the universal binding curve as derived by Rose et al..[12] This procedure has been previously and successfully followed to model Si-H in crystalline silicon.J13] In the case of the O-H pair, we exactly solved the Schr6dinger equation for the Morse oscillator and fitted the first and second energy le
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