Clapeyron slope

Figure 4-6 Interface reaction rate as a function of temperature, pressure, and composition. The vertical dashed line indicates the equilibrium condition (growth rate is zero), (a) Diopside growth and melting in its own melt as a function of temperature with the following parameters Te= 1664K at 0.1 MPa, A5m-c = 82.76J mol K , E/R —30000 K, 4 = 12.8 ms K, and AV c l. l x 10 m /mol. The dots are experimental data on diopside melting (Kuo and Kirkpatrick, 1985). (b) Diopside growth and melting in its own melt as a function of pressure at 1810 K (Tg = 1810 K at 1 GPa from the equilibrium temperature at 0.1 MPa and the Clapeyron slope for diopside). (c) Calcite growth and dissolution rate in water at 25 °C as a function of Ca " and CO concentrations.

Perhaps one of the most important consequences of a peridotite composition for the upper mantle is that the phase transitions in olivine that are manifested as seismic discontinuities should exhibit thermally controlled variations in their depth of occurrence that are consistent with the measured Clapeyron slopes (Bina and Helffrich, 1994) of the transitions. In particular, the olivine-wadsleyite transition at 410 km should be deflected upwards in the cold environment of subduction zones while the disproportionation of ringwoodite to silicate perovskite and magnesiowiistite at 660 km should be deflected downwards, thereby locally thickening the transition zone. In anomalously warm regions (such as the environs of mantle plumes as described below), the opposite deflections at 410 and 660 should locally thin the transition zone. The seismically observed topography of 20-60 km on each of the 410 and 660 is consistent with lateral thermal anomalies of 700 K or less (Helffrich, 2000 Helffrich and Wood, 2001). 

Given the opposing signs of the Clapeyron slopes of the primary phase transitions associated with these seismic discontinuities, any elevated mantle temperatures associated with thermal plumes may be expected to yield thinning of the transition zone (Figure 2), via depression of the 410 and uplift of 660 (Shen et al., 1998 Bina, 1998c Lebedev et al., 2002). Some global and... 

Finally, there is yet another possible contributor to the apparent cold 660 puzzle noted above. It is the negative Clapeyron slope of the y —> pv + mw transition that predicts uplift of the 660 in hot plumes. The y pv + mw transition, however, may be replaced by a )8 —> pv + mw transition at high temperatures, the latter exhibiting a positive Clapeyron slope and so allowing 660 depression instead of uplift (Liu, 1994). However, )8 pv + mw appears to succeed y — pv + mw only in pure Mg2Si04 compositions, so this particular mechanism is unlikely to operate in real multicomponent mantle compositions (Bina and Liu, 1995 Niu et al., 2002). 

Bina C. R. and Helflrich G. (1994) Phase transition Clapeyron slopes and transition zone seismic discontinuity topography. J. Geophys. Res. 99, 15853-15860. 

For most materials that expand on melting, the volume expansion is positive, except for covalent or Van der Waals sohds for which the solid is less dense than the liquid (i.e., with a negative Clausius-Clapeyron slope) such as ice and some elements of group IVA(14) (e.g., C, Si, Ge, and Sn). 

Fig. 20 Relationship between pressure and the temperature of the isotropic transition for PEOii4-h-PMA(Az)4o under CO2 closed circles) and N2 (open circles), and for PEOna-h-PMA (Az)2o under Hg (open squares) for comparison. The different lines represent the Clapeyron slopes, depending on the pressure-transmitting fluid. Note the significant shift by CO2 of T-a to a lower temperature...

Remarkably, the transition entropy A5a decreases with increasing pressure when the pressurizing fluid is Hg this is typically the manifestation of a pure hydrostatic effect, which restricts molecular motions under inert Hg. In complete contrast, A5tr increases when the pressure is exerted by N2 and CO2. In this respect, as observed previously, N2 is a neutral fluid as compared to chemically active CO2 and, consequently, the large increase in AS, shows that the organization of nanostructures is easiest the more active is the fluid, in particular when the fluid is in supercritical state [2,59,60], The influence of the pressure-transmitting fluid on the transition temperature 7 is well illustrated (see Fig. 20) in the case of PEOn4- -PMA(Az)4o copolymer by the increase of the Clapeyron slope (dp/d7 tr in the... 

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