Subducted oceanic lithosphere appears to have a diversity of interaction with the mantle transition zone, which results in a complex chemical evolution and convective pattern of the Earth's mantle. An important factor that controls the fate of subducted lithosphere is its creep strength, to which grain-size reduction and latent heat release, associated with the olivine-spinel transformation might contribute important effects. The effects due to grain-size reduction can potentially be large because rheological properties of Earth materials are highly sensitive to grain size when grain size becomes sufficiently small [1][2][3].
Earlier studies suggested significant weakening of slabs due to grain-size reduction, based on laboratory observations of small grain sizes after phase transformations [1][2][4][5]. A major limitation of these previous studies, however, is the fact that grain-size reduction was observed at laboratory time scales where large driving forces for phase transformation(s) are applied to achieve a significant transformation within reasonable laboratory times (a few hours). Phase transformations in the Earth, such as in subducting slabs, occur at much longer time scales with either much smaller driving forces or at much lower temperatures. Thus, grain size after transformations in subducting slabs could be significantly different from those observed in high-pressure experiments, and the observation of small grain size in the laboratory does not necessarily imply significant grain-size reduction in the Earth's mantle. The central question then arises of how to estimate likely grain sizes for geologically relevant time scales from laboratory data.
Recently, Riedel and Karato [6] have developed a theoretical model for assessing the scaling laws of grain-size evolution during first-order phase transformations. Here, we apply this theoretical framework to estimate the grain sizes during and after the olivine-spinel transformation in subducting slabs, and, in addition, we estimate the effects of grain-size reduction on the rheological structure of slabs. For this purpose, we have also taken into account the temperature feedback from the latent heat release associated with the transformation. We assume that the rheology of peridotite is controlled either by the rheology of olivine, the weakest and most abundant mineral in the upper mantle [7][8], or by that of its high-pressure polymorphs 
- or 
-spinel. In the two-phase region, we use a phenomenological flow law [9] to estimate the creep strength of mixed aggregates of olivine and spinel. The degree of phase transformation inside the slab is calculated on the basis of the available experimental data on the olivine-spinel transition kinetics (a compilation is given, e.g., in [10]) and the geothermal models of slabs by McKenzie [11][12], and the change in creep strength is calculated on the basis of a representative strain rate of 10-15 s-1.