Birch's Law and Modeling Hydration in the Earth's Interior
Abstract
Anderson (1969) showed that Birch's Law (1947); "Seismic sound speeds can be plotted as a simple function of density and that curve spreads out according to atomic weight", can be extended to show that bulk modulus has a near linear relationship with reduced density (density divided by mean atomic weight). This potentially useful relationship, however does not apply if hydrogen is included in the mean atomic weight. Hydrogen, however, does not substitute in a normal cation site in either hydrous or nominally anhydrous minerals, but rather finds a position between adjacent oxygen atoms limiting its repulsive potential in the structure. It is therefore reasonable to exclude H from the mean atomic weight calculation. We have found that there is useful relationship that predicts bulk modulus for anhydrous, hydrous and partially hydrated nominally anhydrous minerals. KT = 2747 ( ρ /M) - 308 (GPa) R = 98.5 % where ρ is density, and M is mean atomic weight exclusive of hydrogen. Whereas this requires some knowledge of volumes and mechanisms of hydration to apply to nominally anhydrous minerals that are possible hydration sites in the mantle, such data are forthcoming from laboratory mineral physics.
- Publication:
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AGU Spring Meeting Abstracts
- Pub Date:
- May 2007
- Bibcode:
- 2007AGUSMMR44A..01S
- Keywords:
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- 3620 Mineral and crystal chemistry (1042);
- 3909 Elasticity and anelasticity;
- 3919 Equations of state;
- 3924 High-pressure behavior