Ionic porosity

It has been observed that in some phases, the diffusivity is smaller, and in other phases the diffusivity is larger. One explanation is that the diffusivity is larger if there is more "free" volume in a structure (Dowty, 1980b Fortier and Giletti, 1989). The "free" volume in a structure is quantified by ionic porosity, defined as... 

When comparing ionic porosity of different minerals, for self-consistency, the same set of ionic radii should be used, and the same temperature and pressure should be adopted to calculate the molar volume of the mineral. Table 3-3 lists the ionic porosity of some minerals. It can be seen that among the commonly encountered minerals, garnet and zircon have the lowest ionic porosity, and feldspars and quartz have the highest ionic porosity. More accurate calculation of IP may use actual X-ray data of average inter-ionic distance and determine the ionic radius in each structure. 

Although the correlation between ionic porosity and diffusivity is imperfect, there is a rough trend that oxygen diffusivity in the minerals increases with increasing IP. The trend is useful in qualitative estimation of closure temperature (among other applications). Extending the relation to metallic systems, one prediction is that diffusion in face-centered cubic structure (25.95% free space) is slower that that in body-centered structure (31.98% free space) of the same metal composition. To avoid the issue of anisotropy, it would be worthwhile to reexamine the relations between diffusivity and ionic porosity using only isometric minerals. 

The dependence of diffusivity in silicate melts on composition is related to how melt structure (including degree of polymerization and ionic porosity) depends on composition. One the one hand, as Si02 concentration increases, the melt becomes more polymerized and the viscosity increases. Hence, diffusivity of most structural components, such as Si02 and AI2O3, decreases from basalt to rhyolite. On the other hand, as Si02 content increases, the ionic porosity increases. The increasing He diffusivity from basalt to rhyolite to silica, opposite to the viscosity... 

Table 3-2 Diffusion coefficients of noble gases in aqueous solutions Table 3-3 Ionic porosity of some minerals Table 4-1 Steps for phase transformations Table 4-2 Measured crystal growth rates of substances in their own melt...

Figure 2.5 Correlation between argon solubility (in natural logarithm of the Henry s law constant) in silicate melts and various parameters NBO/Si (no bridging oxygen to silicon ratio), molar volume, ionic porosity, and density. Reproduced from Shibata et al. (1998).

Carroll, M. R., Stolper, E. M. (1993) Noble gas solubility in silicate melts and glasses New experimental results for Ar and the relationship between solubility and ionic porosity. 

Fortier and Giletti (1989) compared oxygen diffusion data from silicates reacted with H2O at 100 MPa with ionic porosities corrected for thermal expansion at 500 and 800°C. The straight-line fits to data at each temperature were reasonably good, from which they proposed an overall empirical equation that describes diffusion in select silicates at 100 MPa given as... 

Carr MH (1999) Retention of an atmosphere on early Mars. J Geophys Res 104 21897-21909 Carroll MR, Stolper EM (1993) Noble gas solubilities in sihcate melts and glasses new experimental results for argon and the relationship between solubihty and ionic porosity. Geochim Cosmochim Acta 57 5039-5051... 

Nnccio PM, Paonita A (2000) Investigation of the noble gas solubility in HjO-COj bearing silicate liquids at moderate pressure II the extended ionic porosity (EIP) model. EarthPlanet Sci Lett 183 499-512 O Nions RK (1987) Relationships between chemical and convective layering in the Earth. J Geol Soc Lond 144 259-274... 

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