Fig. 1. Sketch of the change in microstructure anticipated as increases from below to above the RCMF in a texturally equilibrated partially molten rock. With peridotite as an example, olivine is represented by light grey hexagonal grains and basalt by dark grey. Initially, melt is present in three-grain junctions. With an increase in melt fraction, the melt pockets expand to meet the neighboring triple junctions at _RCMF. Modified from [34].

Fig. 2. Log–log plot of ε˙ vs. σ data from creep experiments on five samples of olivine + MORB (PI-1101, PI-1108, PI-1143, PI-1146, and PI-1158) at three different melt fractions,  = 0.15, 0.20, and 0.25. We normalized the strain rate to T = 1523 K and d = 50 μm using Eq. (3) with H = 600 kJ/mol, m = 2, and α = 32 for the GBS regime and H = 375 kJ/mol, m = 3, and α = 21 for the diffusion creep regime. Open symbols are data from samples with d = 50 μm and closed symbols from samples with d = 10 μm. The solid lines represents the constitutive equation (Eq. (3)) composed of the flow laws for diffusion creep and dislocation-accommodated dislocation creep. The dot-dashed line represents the flow law for diffusion creep (n = 1, α = 21) and the dashed line represents the flow law for GBS creep (n = 3.5, α = 32).

Fig. 3. Reflected light optical micrographs of deformed samples of olivine + MORB. Olivine is light grey, and MORB is dark grey. The microstructures of deformed peridotites with high melt fraction are characterized by large melt pockets at grain junctions, with a nearly homogeneous distribution of melt at the sample scale. The maximum principal stress is aligned vertically. Shown are images from the two categories of experiments: samples with fine-grained olivine and melt fractions (a)  = 0.16 and (b)  = 0.25, and samples with coarser-grained olivine (d ≈ 50 μm) and melt fractions (c)  = 0.20 (note: the sample surface has been etched with dilute HF + HCl in order to enhance grain boundaries) and (d)  = 0.25. In (c) and (d), it is evident that the grain size distribution for the coarse grained samples is bimodal.

Fig. 4. Pole figures of crystallographic orientation obtained by EBSD analyses of (a) an undeformed (PI-1153) and (b) a deformed (PI-1158) aggregate of olivine + MORB with  = 0.25. The direction of maximum principal stress, σ₁, is normal to the page through the white circle indicated on the [010] axis pole figure in (b). These pole figures indicate that an alignment of [010] axes was induced during the cold-press and hot-press steps and strengthened by deformation in the dislocation-accommodated GBS creep regime. The measurements were taken by mapping the samples in 50 (PI-1153) and 30 (PI-1158) μm steps. A total of 7882 and 7662 grains were measured in the undeformed and deformed samples, respectively. Points were first clustered in 5° areas and then smoothed with a Gaussian of 10° full width at half maximum. The measurements were carried out on a Leo 1530 Gemini FEG–SEM with an EBSD detector provided by HKL Technology at an accelerating voltage of 30 keV and a beam current of 4 nA. The sample surface was coated with 3.5 nm of carbon to avoid charging.

Fig. 5. Semi-log plots of η vs. at T = 1523 K for samples with: (a) d = 10 μm from data in the diffusion creep regime (n = 1) at low stresses, σ < 30 MPa. Results from both our study and that of [3] are included. A linear least squares fit yields α = 21 ± 1 for  ≤ 0.25. The data point at  = 0.30 is an upper bound on viscosity (see text). (b) d = 50 μm and constant σ = 80 MPa from data in the dislocation-accommodated GBS creep regime with n = 3.5 and m = 2. Plotted are the η vs. results from our study and that of [4], extrapolated to d = 50 μm using n = 3.5 and m = 2. A linear least-squares fit yields α = 32 ± 1 for  ≤ 0.25. The data point at  = 0.30 is an upper bound on viscosity (see text).

Fig. 6. Reflected-light optical micrograph showing the microstructure of a deformed partially molten sample of olivine + MORB with d = 10 μm and  = 0.30 (PI-1111). Some of the grain boundaries that are in contact with neighboring grains are indicated by arrows, some of which are parallel to the maximum principal stress direction (σ₁), which is vertical.

Fig. 7. Semi-log plots of η vs. at T = 1523 K for samples with grain size (a) d = 10 μm for diffusion creep and (b) d = 50 μm and σ = 80 MPa for dislocation-accommodated GBS creep. The sharp drop in viscosity between  = 0.25 and  = 0.30 marks the RCMF. The Einstein–Roscoe equation (Eq. (4)), labeled as E–R, is plotted for two different values of melt viscosity.

Flow law parameters from Hirth and Kohlstedt [26]

Experimental results