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2.4.1 Differential Stress Measurements in Lower Mantle Phases

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Radial diffraction experiments can provide information on flow stress of materials. Lattice strains measured during deformation experiments can be used to calculate differential stresses supported by each lattice plane sampled by diffraction. If plastic flow has been achieved, then these stresses represent the flow strength of the material. Note that particularly in DAC experiments, the measured differential stress value is unlikely to correspond to the yield strength/stress at pressure as the material undergoes strain hardening. Thus, if plasticity has occurred, these values are representative of the flow strength as opposed to the yield strength. In some studies, it is not clear that flow stress has been achieved, and thus these measurements can only provide a lower bounds for the flow stress. If significant texture evolution is observed, then one may be able to assume that the flow stress has been reached. However, more sophisticated modeling using, for example, EPSC (Clausen et al., 2008; Neil et al., 2010; Turner & Tomé, 1994) or EVPSC (H. Wang et al., 2010), methods can provide a more robust estimate of the flow strength (Burnley & Zhang, 2008; L. Li et al., 2004; F. Lin et al., 2017; Merkel et al., 2009; Raterron et al., 2013).

Methodologies used to calculate stresses in these types of experiments can result in discrepancies between measurements. Calculation of stresses not only requires knowledge of the elastic properties of the materials but also the assumption of an appropriate micromechanical model. Generally, some sort of Reuss‐Voigt‐Hill approximation is used to calculate stress from individual lattice strains using the method outlined in Singh (1993) and Singh et al. (1998). Alternately, some studies have used the moment pole stress model (Matthies & Humbert, 1993) and the bulk path geometric mean (Matthies et al., 2001) to calculate stress. Generally, elastic properties calculated with a Reuss‐Voigt‐Hill average and the geometric mean are quite close (Mainprice et al., 2000). However, differences can arise between these methodologies because the moment pole stress model typically assigns a single stress value based only on elastic anisotropy. As this does not account for plastic anisotropy, this may result in systematic deviations from the true stress. On the other hand, using the method of Singh (1993) and Singh et al. (1998) allows one to calculate a stress on each plane. This is particularly useful where large plastic anisotropy is observed. However, one is still left with the problem of deciding the appropriate way to average stresses measured on individual planes to get a “bulk stress”. The general practice is to take a simple arithmetic mean of the measured lattice planes on all planes and use the deviation in the values to calculate an error on the measurement. Because limited diffraction planes are sampled in experiments, sampling bias may result in systematically over‐ or underestimating the bulk stress. Again, more sophisticated modeling using the EPSC method (Clausen et al., 2008; Neil et al., 2010; Turner & Tomé, 1994) or EVPSC method (H. Wang et al., 2010) can alleviate issues with sampling bias (e.g., Burnley & Kaboli, 2019; Burnley & Zhang, 2008; Li et al., 2004; Li & Weidner, 2015; F. Lin et al., 2017; Merkel et al., 2009, 2012; Raterron et al., 2013). Another issue with flow strength measurement in the DAC, which is exacerbated at high temperatures is that strain rates are typically unconstrained, which is problematic for minerals that are generally rate sensitive. In the following discussion, the majority of the deformation studies, particularly in the DAC, are at uncontrolled strain rates. Finally, the effects of grain size strengthening (particularly in room temperature experiments) through the well‐known Hall‐Petch effect, where grain boundaries as barriers to dislocation motion, are typically poorly constrained. Frequently, grain size and microstructure are not documented in DAC studies.

Mantle Convection and Surface Expressions

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