Diffusion Creep and Grain Growth in Forsterite +20 vol% Enstatite Aggregates: 1. High‐Resolution Experiments and Their Data Analyses

Abstract

We conducted uniaxial compression and grain growth experiments on fine‐grained (~1 μm) forsterite +20 vol% enstatite aggregates. Based on analyses of the sensitivity of the strain rate as a function of stress, we find power law creep at low stress, Newtonian creep at intermediate stress, and again power law creep at high stress, which correspond to interface‐controlled diffusion creep, grain boundary diffusion (Coble) creep, and a dislocation‐controlled process, respectively. The creep rate of these samples is well expressed by a combination of strain rates of these three mechanisms where interface‐controlled and Coble creep rates are combined as series‐sequential processes, while the rate of the dislocation process is added with them as a parallel‐concurrent process. Mechanical data collected continuously during the application of a constant load but while slowly changing temperature were decomposed into data for every 1 °C, which allowed consideration of >600 mechanical data points from 1054 to 1370 °C. The data were analyzed using Bayesian statistics implementing a Markov chain Monte Carlo method imposed on the above constitutive equation, resulting in the best fit flow law parameters for interface‐controlled and Coble creep. Samples were annealed for 500 hr at various temperatures. A comparison of the final grain sizes as a function of temperature on an Arrhenius plot resulted in an activation energy for grain growth similar to that observed for grain boundary diffusion during Coble creep of these materials.

Grain‐Boundary Diffusion Creep of Olivine: 1. Experiments at 1 atm

“…The observed convex shape of the log σ and relationships (Figure 6), in which the value of n app decreases from ~3 to ~1 with increasing σ (Figure 8), is well described by strain rates determined by a combination of power law creep and Newtonian creep mechanisms (Figure 1), which are connected sequentially (Equation 3). The combined occurrence of these mechanisms is consistent with our previous explanations for the deformation of Fe‐free olivine aggregates at low to intermediate stress (Nakakoji et al, 2018). A similar convex‐shaped log σ and relationship can also be produced by Newtonian creep with a threshold stress ( σ th ), that is, ; however, it predicts n app →∞ with decreasing σ (Nakakoji et al, 2018), which is not supported by our results (Figure 8).…”

“…Since a p app value of 3 is well supported by theoretical models of grain‐boundary diffusion creep (e.g., Coble, 1963), the observation indicates that pyroxene has little effect on the creep rates in our samples. This is the same conclusion reached in our previous studies of creep in olivine aggregates with f px varying from 0 to 0.4 (Nakakoji et al, 2018; Tasaka et al, 2013). As a result, our established reference constitutive equation for olivine creep reproduces the mechanical data of samples with different f px equally well (Figures 6a–6c and 11).…”

“…We can obtain mechanical data by changing one of the factors controlling creep rate, such as temperature in the stepped‐temperature tests, where grain size is essentially kept constant (Figure 7a). This approach differs from our previous Bayesian analysis to determine flow law parameters (Nakakoji et al, 2018) where >600 experimental data points for different grain sizes, stresses, and temperatures were analyzed at the same time. This statistical approach was essential due to variations in multiple creep rate‐controlling factors during the deformation tests.…”

Full Field and Mean Field Modeling of Grain Growth in a Multiphase Material Under Dry Conditions: Application to Peridotites

“…In two recent papers,Nakakoji et al () and Nakakoji and Hiraga () (NH2018) published the results of long‐term (500 hr) experiments for grain growth and deformation in an enstatite‐forsterite synthetic aggregate for a DSP proportion of 20%, at different temperatures. Unfortunately, only the results after 500 hr of annealing are available, but these results allow us to evaluate the performance of our mean field model at large timescales.…”

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

“…The EMC method is able to estimate a probability distribution on each parameter, which could be used for estimating the uncertainty associated with the parameters more efficiently than the MCMC methods [30], without becoming trapped in local minima [31]. In the field of Earth science, the EMC method has been applied to problems pertaining to geophysics [30,32] and rheology [33], and, to the authors' best knowledge, this is the first time that the EMC method has been coupled to equations of a geochemical kinetic model in order to estimate kinetic parameters. The proposed method was tested by examining multiple parameterizations of a synthetized serpentinization system.…”