Deformation maps

It is convenient to use deformation mechanism maps to illustrate the parameter space (like a grain size) where one mechanism dominates over others.

Based on the formulas of Eqs. (3.16) and (3.21) for diffusion and dislocation creep, respectively, I have constructed stress-temperature deformation mechanism maps for Mg2SiO4 wadsleyite at a pressure of 20 GPa, water contents of 10 and 10000 wt. ppm and grain sizes from 0.01 to 100 mm (Fig.

9.11). The effective diffusion coefficient 𝐷^eff for diffusion creep has been calculated using Eq. (3.15) and the grain-boundary diffusivity reported by (Shimojuku et al, 2009, 2010). The molar volume Ω and constant 𝛼_𝑁𝐻, respectively, are set to be 40.53 cm3/mol and 13.3 (H. J. Frost & Ashby, 1982;

Shimojuku et al., 2009). In the case of dislocation creep, I have adopted the same parameters and formulas as described in the beginning of this section.

Construction was based on the sum of Si and O diffusivity vectors in the a-, b- and c-directions obtained by this study.

The temperature and stress ranges corresponded to the MTZ and subducted slabs are marked as hatched rectangles in Fig. 9.11. The temperature range in the MTZ is chosen from 1800 to 2000 K according to (Katsura et al., 2010). The lowest temperature in slabs is assumed to be 1100 K (“cold” slab), and the highest is 1500 K (“warm” slab). Stress range in the MTZ (purple rectangular) is assumed to be between 1 to 10 MPa based on estimations in the literature (Shimojuku et al., 2009; Vassiliou et al., 1984). A further stress range in the MTZ (green rectangular) is estimated from the assumption that strain rates are from 10^-14 to 10^-16 s^-1 (Billen, 2008). Stresses are assumed by one – two orders of magnitude higher (10 – 100 MPa) in slabs than ambient mantle.

Fig. 9.11 shows that the increasing water content shifts strain rates to lower values at the same applied stresses. Thus, within the same grain size of 0.01 mm, if strain rates were for example 10^-9 – 10^-11 s^-1 at 10 wt. ppm H2O, they would increase to 10^-6 – 10^-8 s^-1 at 10000 wt. ppm H2O. On the other hand, the grain size mostly determines stress conditions of the creep mechanism

9.3. Rheology application

120

transition from dislocation creep to diffusion creep. Namely, at a H2O content of 10 wt. ppm, a grain size increase from 0.01 to 10 mm shifts boundary for the stress condition of the dislocation-diffusion creep from 10² to 10^-1 MPa.

Fig. 9.11 a. A deformation map showing the boundaries between the various deformation mechanisms in stress-temperature space estimated at 20 GPa at 10 wt. ppm H2O and 0.01 mm grain size. Solid blue line is boundary between dislocation and diffusion creep. Levels of some strain rates are noted with numbers. Stress-temperature ranges for slabs and MTZ are shown by hatched rectangular.

121 Fig. 9.11 b. A deformation map showing the boundaries between the various deformation mechanisms in stress-temperature space estimated at 20 GPa at 10 wt. ppm H2O and 0.1 mm grain size. Solid blue line is boundary between dislocation and diffusion creep. Levels of some strain rates are noted with numbers. Stress-temperature ranges for slabs and MTZ are shown by hatched rectangular.

9.3. Rheology application

122

Fig. 9.11 c. A deformation map showing the boundaries between the various deformation mechanisms in stress-temperature space estimated at 20 GPa at 10 wt. ppm H2O and 1 mm grain size. Solid blue line is boundary between dislocation and diffusion creep. Light green lines are strain rate with one order of magnitude step, levels of some strain rates are noted with numbers. Stress-temperature ranges for slabs and MTZ are shown by hatched rectangular.

123 Fig. 9.11 d. A deformation map showing the boundaries between the various deformation mechanisms in stress-temperature space estimated at 20 GPa at 10 wt. ppm H2O and 10 mm grain size. Solid blue line is boundary between dislocation and diffusion creep. Light green lines are strain rate with one order of magnitude step, levels of some strain rates are noted with numbers. Stress-temperature ranges for slabs and MTZ are shown by hatched rectangular.

9.3. Rheology application

124

Fig. 9.11 e. A deformation map showing the boundaries between the various deformation mechanisms in stress-temperature space estimated at 20 GPa at 10000 wt. ppm H2O and 0.01 mm grain size. Solid blue line is boundary between dislocation and diffusion creep. Levels of some strain rates are noted with numbers. Stress-temperature ranges for slabs and MTZ are shown by hatched rectangular.

125 Fig. 9.11 f. A deformation map showing the boundaries between the various deformation mechanisms in stress-temperature space estimated at 20 GPa at 10000 wt. ppm H2O and 0.1 mm grain size. Solid blue line is boundary between dislocation and diffusion creep. Levels of some strain rates are noted with numbers. Stress-temperature ranges for slabs and MTZ are shown by hatched rectangular.

9.3. Rheology application

126

Fig. 9.11 g. A deformation map showing the boundaries between the various deformation mechanisms in stress-temperature space estimated at 20 GPa at 10000 wt. ppm H2O and 1 mm grain size. Solid blue line is boundary between dislocation and diffusion creep. Levels of some strain rates are noted with numbers. Stress-temperature ranges for slabs and MTZ are shown by hatched rectangular.

127 Fig. 9.11 h. A deformation map showing the boundaries between the various deformation mechanisms in stress-temperature space estimated at 20 GPa at 10000 wt. ppm H2O and 10 mm grain size. Solid blue line is boundary between dislocation and diffusion creep. Light green lines are strain rate with one order of magnitude step, levels of some strain rates are noted with numbers. Stress-temperature ranges for slabs and MTZ are shown by hatched rectangular.

9.3. Rheology application

128

Fig. 9.11 i. A deformation map showing the boundaries between the various deformation mechanisms in stress-temperature space estimated at 20 GPa at 10000 wt. ppm H2O and 100 mm grain size. Solid blue line is boundary between dislocation and diffusion creep. Light green lines are strain rate with one order of magnitude step, levels of some strain rates are noted with numbers. Stress-temperature ranges for slabs and MTZ are shown by hatched rectangular.

In the stress range from 1 to 10 MPa (purple rectangular) and at a H2O content of 10 wt. ppm, the MTZ condition leads to the dislocation creep regime as long as grain size is equal to or larger than 1 mm (Fig. 9.11 a – d). However, strain rates corresponding to these stresses range from 10^-11 to 10^-14 s^-1, which

129 is higher than estimations in literature of 10^-14 – 10^-16 s^-1. Assuming previous strain rate estimations, one can conclude that dry MTZ with 10 wt. ppm of H2O is under stresses from 0.01 to 1 MPa and 0.5 – 1 MPa at grain size of 1 and 10 mm, respectively. These ranges are by up to 2 orders of magnitude lower (green rectangular) than previously proposed for MTZ (1 – 10 MPa). Lower stresses enable dry MTZ to deform by diffusion mechanism at grain sizes smaller than 1 mm (Fig. 9.11 c) and by dislocation mechanism as long as grain size is equal or larger than 10 mm (Fig. 9.11 d). Dry slabs with 10 wt. ppm H2O within the stress range from 10 to 100 MPa are in the dislocation creep regime as long as grain size is larger than 0.1 mm. They deform at strain rates of 10^-9 to 10^-14 s^-1 (Fig. 9.11 b – d).

Fig. 9.11 e – i show deformation maps for hydrous wadsleyite of 1 wt.% H2O in the stress–temperature spaces at a pressure of 20 GPa. According to these maps, MTZ in the stress range from 1 to 10 MPa deforms by dislocation-creep mechanism if grain size is equal or larger than 1 mm (Fig. 9.11 g). Strain rates under these stress-temperature conditions are from 10^-8 to 10^-11 s^-1. On the other hand, assuming that strain rates in hydrous MTZ are 10^-14 – 10^-16 s^-1, the stress range shifts to 0.005 – 0.1 MPa and 0.05 – 0.1 MPa with grain sizes of 10 and 100 mm, respectively. Under these stresses and at temperatures of 1800 to 2000 K, hydrous MTZ with 1 wt.% H2O is in the dislocation-creep regime as long as the grain size is equal or larger than 50 mm. Assuming that the stress range is 10 – 100 MPa in slabs, they are in the diffusion-creep regime at a water content of 1 wt.% if the grain size is equal to or smaller than 100 µm at strain rates from 10^-6 to 10^-9 s^-1. Slabs are believed to be hydrous with grain sizes a few orders smaller than in MTZ, and with a strain rate that is higher than in MTZ. Under these assumptions slabs are always in the diffusion-creep regime (Fig. 9.11 e).

The result that the MTZ is in the dislocation-creep regime is consistent with observed seismic anisotropy in the MTZ (Trampert & Van Heistz, 2002; Visser, Trampert, Lebedev, & Kennett, 2008) suggested by the velocity contrast between horizontally-polarized and vertically-polarized S-waves. It is also

9.3. Rheology application

130

consistent with the idea that the seismic anisotropy in MTZ is caused by lattice preferred orientation of wadsleyite. However, MTZ might be in the diffusion-creep regime, in which lattice preferred orientation of wadsleyite does not occur by creep. This argument implies that there must be regions in MTZ where anisotropy is very weak or completely absent.