Kinetics of high-pressure phase transformations: Implications to the evolution of the olivine → spinel transition in the downgoing lithosphere and its consequences on the dynamics of the mantle

The rate of a high-pressure phase transition increases exponentially with temperature (T) and overpressure or pressure beyond equilibrium (ΔP). It is also greatly promoted by introducing shear stress, diminishing grain size, and adding water or other catalysts to the reactants. For an isothermal and isobaric transition with no compositional change, if steady state of nucleation on grain surfaces is attained, the rate equation can be expressed: (1) before site saturation by: X = 1 − exp(−Kt⁴), where

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and (2) after site saturation by: X = 1 − exp(−K′T), where

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, where X is volume fraction of completion of transformation, t is time, and the C's are characteristic constants. C₁ and C₉ are functions of grain size, C₃ and C₆ are functions of shear stress. All the C's are almost independent of temperature and pressure. Thus, if X as a function of T, ΔP, and t over a narrow P-T range can be experimentally determined, the C's can be calculated and the effect of grain size and shear stress on the rate of transformation can be evaluated. The isothermal and isobaric rate equations for a given composition, shear stress, and grain size are then experimentally determinable. The non-isothermal and non-isobaric rate equation can be calculated from the isothermal and isobaric ones if the rate of penetration into the metastability field is known. The important feature of the kinetics of high-pressure phase transitions predicted by these rate equations is that for a given rate of penetration into the metastability field, there can be defined a characteristic temperature, T_ch, below which the rate of the transition is virtually zero no matter how metastable the material is. For the olivine → spinel transition in the mantle, this characteristic temperature may be as high as 700° C. Thus, in a fast moving downgoing slab, the temperature at its cold center may remain below T_ch even down to depths in excess of 600 km, thereby greatly depressing the olivine—spinel phase boundary.At an early stage in the development of a downgoing slab, the plunging speed is slow. This allows the interior of the slab to heat up and the olivine → spinel transition to proceed rapidly and near equilibrium. As a result, the olivine—spinel phase boundary in the slab will be distorted upwards. The rising of the denser spinel phase then provides an additional driving force which accelerates the plate. Since the upper portion of the slab is pulled from below and the lower portion pushed from above, earthquakes of down-dip extension will occur in the upper mantle while those of down-dip compression will originate in the transition zone. Because the transformation occurs close to equilibrium, there will be an aseismic region separating the two seismic zones. When the plate velocity exceeds a certain limit, the temperature in the cold interior becomes low enough to depress the olivine → spinel transition. The phase boundary is then distorted downwards. The buoyant force thereby created will reduce the driving force, and the plunging speed of the plate will approach a steady state. In addition, the buoyant force will compress the slab from below and result in earthquakes of down-dip compression throughout the length of the slab. Now the olivine → spinel transition is so far from equilibrium that the reaction becomes implosive. A rise in frequency of deep earthquakes towards the implosion region in the lower transition zone is thus predicted. Therefore, as well as stabilizing the plate velocity, the olivine → spinel transition may also control earthquake distributions throughout the downgoing slab.