The Number Density of Interfaces affects Heat Transfer and Speed of Sound in Mantle Materials
Abstract
We have demonstrated previously that the velocity of sound waves is significantly affected by the grain size of the solid medium through which it propagates (Pollemans and de Jong (1996)). With our advances in thermodynamic and thermo mechanical modeling we are now able to make estimates about the order of magnitude difference in bulk sound wave velocity induced by chemical vis a vis grain size variations. Problem The interaction between surface and deep earth as revealed by mantle tomography is arguably the largest advance in the earth sciences since the discovery of plate tectonics. The interpretation of these tomograms as delineations of variation in seismic velocity is commonly interpreted as being due to variations in temperature, pressure, and composition. We have calculated these bulk sound velocity variations in the (Mg1-xFex)2SiO4 system at different pressures and temperatures. Depending on the Mg number this velocity varies between 6.1 and 5.0 km/sec. The rate of change of the bulk sound velocity with temperature is constant, the bulk sound speed varies 0.2 km/sec per 600oC. This 0.2 km/sec corresponds to a pressure increase of roughly 2GPa, or to roughly a 20 percent change in the mole fraction of Fe2SiO4. As noted earlier (Pollemans & de Jong, 1996) sound wave velocities are also affected significantly by grain size variations as demonstrated for the internally nucleating Li2O.2SiO2 system. This variation in Vp is on the order of 1.4 km/sec depending on the crystallite size which varies between 0.2 and 0.02 mm, the smaller crystallite size, i.e. the largest number density of interfaces having the largest Vp. Calculating the bulk sound velocity from these experimental data shows that this variation in Vp corresponds to about 0.3 km/sec or about 0.002 km/sec per 0.02 mm increment of crystallite size well outside the 0.03 km/sec error margin in seismological bulk sound velocity measurements. We also measure the room temperature phonon dominated thermal conductivity of coarse and fine grained Li2O.2SiO2 ceramics. Our results indicate that fine grained materials, i.e. with a high number density of interfaces has a thermal conductivity of 5.35 W/mK, in contrast to 3.36 W/mK for the coarse grained material. Thus grain size variations, which are reflections of the re-crystallization regime to which a material is subjected by processes such as Zener pinning and Oswald ripening may next to chemical differentiation, be invoked to account for seismic velocity variations as well as mantle plumes.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2012
- Bibcode:
- 2012AGUFM.V51A2760D
- Keywords:
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- 1042 GEOCHEMISTRY / Mineral and crystal chemistry