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Grain-size evolution in a subducting slab

The main process that controls the grain-size of the product phase during a first-order phase transformation is competition between nucleation and growth. Briefly, grain-size is small when nucleation dominates over growth, and vice versa. Theoretical considerations show [11] that the average grain-size is given approximately by the so-called Avrami length, either in 3D ( $\delta_{Av}$ , grain size after completion of the transformation), or in 2D ( $\delta_{Av}^{2D}$ , grain diameter at the formation of continuous films). These scaling parameters are defined as (Y - growth rate; I^V, I^B - homogeneous resp. grain-boundary nucleation rate)

$\begin{displaymath}\delta_{Av} = \bigl[I^V / Y\bigr]^{-1/4} , \quad \quad \delta_{Av}^{2D} = \bigl[I^B / Y\bigr]^{-1/3} . \end{displaymath}$

(1)

In Fig. 2, we have plotted the numerically calculated spinel grain-sizes according to eq. (1) for a slab with varying thickness (60-100 km) on the basis of the thermal model shown in Fig.1. This plot indicates that under subduction zone conditions a dramatic grain-size reduction up to 4 orders in magnitude is possible when slab temperatures reach values well below 900 K, as a result of the metastable persistence of olivine in peridotite.

Figure 2

Dependence of spinel grain-size (logarithmic scale) on slab temperature (reciprocal scale). Above 900 K, there is an Arrhenius dependence with an apparent "activation energy" of about 412 kJ/mol (branch ``A''). Within the metastable wedge, the apparent "activation energy" for spinel grain-size can be negative (branch ``B'').

Upon completion of the olivine-spinel transformation, spinel grain-size will be further controlled by grain-growth. The grain-growth kinetics is also very temperature sensitive: it is slow at low temperatures. Therefore, when a phase transformation occurs in a cold slab, any significant grain-size reduction will be kept for a relatively long time. Thus the cold slab interior will tend to have a weaker strength when a phase transformation affect its rheology through grain-size reduction. In Fig. 3, we illustrate the two main effects of the phase transformation, the thermal feedback due to the release of latent heat [17] and the kinetic grain-size reduction, for the case of a slab of 85 km thickness shown in Fig. 1b.

Figure 3

Spinel grain-size (given in Table 1) and temperatures (in Kelvin) along the cold olivine wedge of a fast subducting slab, Fig. 1b. Arrows indicate large thermal gradients.

**Table 1:**
Spinel grain-size (in $\mu$ m) at the triangle points of Fig. 3
1	2	3	4	5	6	7	8	9	10	11
5.01	2.76	0.43	0.23	0.10	0.08	0.07	0.08	0.12	0.19	0.68

The formation of a continuous film of very fine-grained (sub-micron) spinel around the olivine grains in peridodite is very likely - at a certain stage of the transformation (critical volume fraction of spinel $\sim$ 1% to 10%, depending on the p,T -conditions in the slab) - related to a change of the creep mechanism of the whole slab material. The dominant deformation mechanism of the cold slab core will then change from dislocation creep to diffusion creep, and deformation will occur predominantly at shear zones along the olivine grain boundaries, resulting in considerable rheological weakening of the slab interior of fast subducting slabs. Both the degree of weakening due to grain-size reduction and the extent to which the weakened state lasts depend critically on slab temperatures. Based on the well-known deformation laws for olivine [18,19] and available data on spinel creep [5], we have estimated the resulting strength profile of slabs [20]. Taking into account the two combined effects of latent heat release and grain-size reduction, we found that

(i): the strength of slabs will have unusual temperature dependence through the temperature dependence of grain-size and that
(ii): a subducting slab has a complicated rheological structure containing a weak region near the tip of a cold slab.

Both observations contradict to the conventional picture of cold slabs that they should be mechanically stronger than their surroundings [21,22]. The results cast some doubts on the capability of cold slabs to sustain and transmit higher stresses to greater depth.

Next: Discussion Up: No Title Previous: Thermal slab structure and transformation kinetics

Michael Riedel
1999-01-27