Grain-size evolution in subducted oceanic lithosphere associated with the olivine-spinel transformation and its effects on rheology

Received 6 June 1996; accepted 22 January 1997

Abstract

We investigate the role of grain-size reduction during the olivine-spinel transformation on rheological properties of subducting slabs on the basis of a scaling model for microstructural development during nucleation and growth. In this model, the size of spinel grains nucleating at olivine grain boundaries is controlled by the relative rates of nucleation and growth, taking into account the impingement through the collision of grains due to growth. When the volume fraction of spinel reaches a certain threshold value (critical volume fraction ~1-10%, depending on the P-T conditions in the slab), the new phase will form a continuous film and will significantly reduce the strength of the two-phase aggregate, if spinel grain size is small. The size of spinel grains, ₀, at this stage is calculated and is shown to be highly sensitive to temperature. At relatively high temperatures (T>1000 K), ₀ shows an Arrhenius-type dependence on temperature; that is, ₀~exp(-E^*/RT) with E^*~400 kJ/mol, whereas a more complicated temperature dependence is found at low temperatures (T<900 K), where a grain-size reduction of up to 4 orders in magnitude is possible.

Strength profiles of slabs due to combined effects of temperatures and of grain-size reduction are calculated. It is shown that: (1) the strength of slabs will have an unusual temperature dependence through the temperature dependence of grain size; and (2) a subducting slab has a complicated rheological structure containing a weak region below the tip of a metastable olivine-bearing wedge in a cold slab. Possible implications of these anomalous rheological structures of slabs on the dynamics of subduction are discussed, including the mechanisms of deep earthquakes.

Keywords: subduction zones, rheology, phase transitions, deep-focus earthquakes, grain size, kinetics

Printable version available (780 kB)

Table of contents

1. Introduction
2. Thermal structure of subducted slabs and phase transformation kinetics
3. Grain-size evolution in subducting slabs
4. Rheological structure of subducted slabs
5. Results and discussion
6. Conclusions

• Acknowledgement
• Appendix 1
• References
  • Body of article in one file

  

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  Fig. 1. Slab geometry used for the numerical model. The slab is considered as a rigid body with thickness L and a fixed length of 1000 km. The penetration angle is 45° (upper surface of the slab at the right side). Isotherms (in Kelvin) are calculated using McKenzie's model [11][12], corrected with the latent heat feedback. The bold line shows the phase equilibrium boundary of olivine and -spinel, according to the thermodynamic data of Akaogi et al. [44] Table 1 . (a) v_slab=4 cm/yr, L=85 km, Re=59.30. (b) v_slab=10 cm/yr, L=85 km, Re=148.25. The metastability region of pure olivine (grey) and the region with mixed olivine-spinel aggregates (dark grey) are shown. (to main text)
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  Fig. 2. P-T phase diagram showing the kinetic phase boundaries for 1% and 99% transformation degree (dashed lines). The thick line shows the phase equilibrium of olivine and -spinel, according to the thermodynamic data of Akaogi et al. [44]. The adiabats a-e represent the P-T paths of the coldest portion of a slab (v_slab=10 cm/yr) with different thicknesses: (a) L=100 km; (b) L=90 km; (c) L=80 km; (d) L=70 km; (e) L=60 km; (f) boundary condition of the McKenzie model. (to main text)
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  Fig. 3. Grain-size reduction accompanying the olivine->spinel transformation and subsequent grain growth in the coldest portion of downgoing slabs. The P-T paths and the labelling as in Fig. 2 . Spinel grain growth (not included in the model) would increase again the grain size at greater depth depending on the P-T conditions. (to main text)
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  Fig. 4. Arrhenius plot of spinel grain size (logarithmic scale) vs. temperature (reciprocal scale), both numerically determined at the first kinetic phase boundary (=1%) for different slab thicknesses. The symbols show the values obtained of spinel grain size at =1% for different subducting layers of lithosphere across the slab. Above 900 K, they follow an Arrhenius dependence with an apparent "activation energy" of about 412 kJ/mol (branch A). Shown as a thick solid line is the semi-analytical solution of Eq. A6 , predicting a slightly higher value of 447 kJ/mol. Note that, within the metastable wedge, the apparent "activation energy" for spinel grain size can be negative (branch B). Predicted grain sizes exceeding ~3 mm are not realistic since the presence of secondary phases such as pyroxenes and garnets prevents the formation of larger spinel grains. (to main text)
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  Fig. 5. Calculated metastable overshoot P=P_kin-P_eq of olivine over the equilibrium pressure with -Mg₂SiO₄ (Eq. A6 ) under subduction zone conditions (dashed line). The squares show the numerically calculated onset of transformation at =1% for a slab with thickness L=100 km (integration of the differential Eq. A4 Eq. A5 , thick line=phase equilibrium). For comparison, the isochron _Av=1 h is included, showing the expected location of the kinetic phase boundary at the laboratory time scale (dash-dotted curve). At the geological time-scale, wedge formation sets in at temperatures below 850 K. A compilation of some spinel grain sizes at selected P-T conditions (crosses) is given in Table 3 ; solid diamonds mark the reported P-T conditions of three different high pressure experiments: (1) P=15 GPa, T=1173 K [36], spinel grain size1 µm, Eq. 6 predicts 1.8 µm; (2) P=15.5 GPa, T=1273 K [16], spinel grain size1.8 µm, Eq. 6 predicts 0.4 µm, (3) P=15.5 GPa, T=1473 K [46], spinel grain size not mentioned, Eq. 6 predicts 4.6 µm. (to main text)
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  Fig. 6. Creep strength of the slab shown in Fig. 1 along its coldest part (slab thickness 85 km) below 400 km. The grain size reduction produces a strength drop of several orders in magnitude, in dependence of the relevant spinel creep mechanism. An average strain rate of 10^-15 s^-1 is assumed uniformly across the slab. (to main text)
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  Fig. 7. Calculated strength profile of the slab shown in Fig. 1 on the basis of a Nabarro-Herring creep mechanism for spinel (m=2 and n=1 in Eq. 13 ). The creep strength of spinel is assumed to be bounded by the olivine creep strength within the slab. The grey area shows the slab portions with a creep strength higher than 100 MPa; the dark grey shows the slab portions with a creep strength higher than 200 MPa. Note the dramatic strength drop below the tip of the metastable wedge. Spinel grain growth (not included in the model) would cause a significant decrease in the size of the weak zone below the metastable wedge. The two arrows indicate the possible effect of a sustainable pressure drop in the cold interior of fast slabs (see discussion). (to main text)
  

  

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