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1. Rheology of the lower mantle: a review

   https://doi.org/10.1186/s40645-025-00695-6  

   Karato, Shun-ichiro; Girard, Jennifer; Cho, Heechen_E (March 2025, Progress in Earth and Planetary Science)

   Abstract We review our current understanding of the rheological properties of the lower mantle based both on materials science and geophysics points of view. We assume a simple model of the lower mantle that is made of only two minerals: bridgmanite (Br) (Mg,Fe)SiO₃and ferropericlase (Fp) (Mg,Fe)O, and address a question of (i) which mineral is weaker (lower viscosity), (ii) how does lower mantle viscosity change with depth and location, and (iii) discuss implications for shear localization. We first review plausible mechanisms of deformation based on the deformation mechanism map on the normalized stress and temperature space. We conclude that likely mechanism of deformation in the lower mantle is either diffusion creep or power-law dislocation creep. Based on this review, we discuss recently proposed models by Cordier and his group (Cordier in Nature 481:177–181, 2012; Cordier in Nature 613:303–306 , 2023) where either asthermal creep (i.e., low-temperature plasticity) or pure climb creep (not power-law dislocation creep) would play an important role. We conclude that these models are not acceptable because (1) many aspects of their models are incompatible with experimental observations and theoretical models of deformation of most materials including oxides and metals and (2) these models are not consistent with the distribution of seismic anisotropy. Hence, we focus on power-law dislocation creep and diffusion creep. We review previously published results on deformation (by dislocation creep) and diffusion, we conclude that Fp is weaker than Br. The radial (depth) depth and lateral variation of viscosity is discussed based on the estimated activation volume and estimated variation of grain-size. Geophysical studies suggest only modest depth variation of viscosity that demands relatively small activation volume (V* (< 3$$\times$$ $\times$10^–6m³/mol)). Plausible models to explain small activation volume are discussed including the role of extrinsic diffusion. Grain-size also controls viscosity if deformation is by diffusion creep. Okamoto and Hiraga (J Geophys Res, 2024. 10.1029/2023JB027803), Solomatov et al. (Phys Earth Planet Inter 129:265–282, 2002) estimated the grain-size evolution in the lower mantle based on the kinetics of grain-growth and the role of a phase transformation. In contrast, there are other papers (e.g., Paul et al. in Prog Earth Planet Sci 11:64, 2024; Rozel in Geochem Geophys Geosyst, 2012. 10.1029/2012GC004282) where grain-size distribution is estimated assuming that grain-size is controlled by dynamic recrystallization. The validity of assumption is questionable because dynamic recrystallization occurs due to deformation by dislocation creep but not by diffusion creep and the absence of seismic anisotropy indicates that diffusion creep dominates in most of the lower mantle. Finally, we review the published models of shear localization that would explain the long-term preservation of geochemical reservoirs in the lower mantle. Accepting that two minerals (Fp and Br) in the lower mantle have largely different viscosity, Ballmer et al. (Nat Geosci 10:236–240, 2017) proposed that the presence of regions of compositional difference (difference in Fp/Br ratio) leads to localized deformation (deformation mainly in the weaker regions). However, in addition to the ad hoc nature of this model, there is no strong evidence for the presence of large variation in Fp/Br in the lower mantle that makes the validity of this model questionable. There are some papers where processes of shear localization are explored without invoking the presence of regions of large rheological contrast. Thielmann et al. (Geochem Geophys Geosyst, 2020. 10.1029/2019GC008688) presented the results of theoretical study of deformation of initially homogeneous two-phase mixture (Fp and Br) and showed that deformation causes the elongation of a weak Fp that promotes shear localization. In this model, the rheological contrast between Fp and Br was assumed to be independent of strain. However, Cho and Karato (J Geophys Res 2022. 10.1029/2021JB022673 ; Phys Earth Planet Inter, 2024. 10.1016/j.pepi.2024 ) showed that when deformation is by diffusion creep, the rheological contrast increases with strain due to the evolution of stress concentration caused by grain elongation. They showed that this will promote strain weakening particularly in simple shear that would lead to shear localization. Consequently, the tendency for shear localization is stronger in their model than a model where rheological contrast is assumed to be independent of strain. 

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2. The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law

   https://doi.org/10.5194/tc-15-4589-2021  

   Behn, Mark D.; Goldsby, David L.; Hirth, Greg (January 2021, The Cryosphere)

   Abstract. Viscous flow in ice is often described by the Glen flow law – anon-Newtonian, power-law relationship between stress and strain rate with astress exponent n ∼ 3. The Glen law is attributed tograin-size-insensitive dislocation creep; however, laboratory and fieldstudies demonstrate that deformation in ice can be strongly dependent ongrain size. This has led to the hypothesis that at sufficiently lowstresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain size dependence of ice rheology. Experimental studiesfind that neither dislocation creep (n ∼ 4) nor grain boundarysliding (n ∼ 1.8) have stress exponents that match the value ofn ∼ 3 in the Glen law. Thus, although the Glen law provides anapproximate description of ice flow in glaciers and ice sheets, itsfunctional form is not explained by a single deformation mechanism. Here weseek to understand the origin of the n ∼ 3 dependence of theGlen law by using the “wattmeter” to model grain size evolution in ice.The wattmeter posits that grain size is controlled by a balance between themechanical work required for grain growth and dynamic grain size reduction.Using the wattmeter, we calculate grain size evolution in two end-membercases: (1) a 1-D shear zone and (2) as a function of depth within anice sheet. Calculated grain sizes match both laboratory data and ice coreobservations for the interior of ice sheets. Finally, we show thatvariations in grain size with deformation conditions result in an effectivestress exponent intermediate between grain boundary sliding and dislocationcreep, which is consistent with a value of n = 3 ± 0.5 over the rangeof strain rates found in most natural systems. 

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3. High‐Throughput Growth of Microscale Gold Bicrystals for Single‐Grain‐Boundary Studies

   https://doi.org/10.1002/adma.201902189  

   Gan, Lucia_T; Yang, Rui; Traylor, Rachel; Cai, Wei; Nix, William_D; Fan, Jonathan_A (June 2019, Advanced Materials)

   Abstract The study of grain boundaries is the foundation to understanding many of the intrinsic physical properties of bulk metals. Here, the preparation of microscale thin‐film gold bicrystals, using rapid melt growth, is presented as a model system for studies of single grain boundaries. This material platform utilizes standard fabrication tools and supports the high‐yield growth of thousands of bicrystals per wafer, each containing a grain boundary with a unique <111> tilt character. The crystal growth dynamics of the gold grains in each bicrystal are mediated by platinum gradients, which originate from the gold–platinum seeds responsible for gold crystal nucleation. This crystallization mechanism leads to a decoupling between crystal nucleation and crystal growth, and it ensures that the grain boundaries form at the middle of the gold microstructures and possess a uniform distribution of misorientation angles. It is envisioned that these bicrystals will enable the systematic study of the electrical, optical, chemical, thermal, and mechanical properties of individual grain boundary types. 

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4. Physical limits to meltwater penetration in firn

   https://doi.org/10.1017/jog.2021.44  

   Humphrey, Neil F.; Harper, Joel T.; Meierbachtol, Toby W. (April 2021, Journal of Glaciology)

   null (Ed.)

   Abstract Processes governing meltwater penetration into cold firn remain poorly constrained. Here, in situ experiments are used to develop a grain-scale model to investigate physical limitations on meltwater infiltration in firn. At two sites in Greenland, drilling pumped water into cold firn to >75 m depth, and the thermo-hydrologic evolution of the firn column was measured. Rather than filling all available pore space, the water formed perched aquifers with downward penetration halted by thermal and density conditions. The two sites formed deep aquifers at ~40 m depth and at densities considerably less than the air pore close-off density (~725 kg m −3 at −18°C, and ~750 kg m −3 at −14°C), demonstrating that some pore space at depth remains inaccessible. A geometric grain-scale model of firn is constructed to quantify the limits of a descending fully saturated wetting front in cold firn. Agreement between the model and field data implies the model includes the first-order effects of water and heat flow in a firn lattice. The model constrains the relative importance of firn density, temperature and grain/pore size in inhibiting wetting front migration. Results imply that deep infiltration, including that which leads to firn aquifer formation, does not have access to all available firn pore space. 

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5. A cold laboratory hyperspectral imaging system to map grain size and ice layer distributions in firn cores

   https://doi.org/10.5194/tc-18-1925-2024  

   McDowell, Ian E; Keegan, Kaitlin M; Skiles, S McKenzie; Donahue, Christopher P; Osterberg, Erich C; Hawley, Robert L; Marshall, Hans-Peter (January 2024, The Cryosphere)

   Abstract. The Greenland and Antarctic ice sheets are covered in a layer of porous firn. Knowledge of firn structure improves our understanding of ice sheet mass balance, supra- and englacial hydrology, and ice core paleoclimate records. While macroscale firn properties, such as firn density, are relatively easy to measure in the field or lab, more intensive measurements of microstructural properties are necessary to reduce uncertainty in remote sensing observations of mass balance, model meltwater infiltration, and constrain ice age – gas age differences in ice cores. Additionally, as the duration and extent of surface melting increases, refreezing meltwater will greatly alter firn structure. Field observations of firn grain size and ice layer stratigraphy are required to test and validate physical models that simulate the ice-sheet-wide evolution of the firn layer. However, visually measuring grain size and ice layer distributions is tedious, is time-consuming, and can be subjective depending on the method. Here we demonstrate a method to systematically map firn core grain size and ice layer stratigraphy using a near-infrared hyperspectral imager (NIR-HSI; 900–1700 nm). We scanned 14 firn cores spanning ∼ 1000 km across western Greenland’s percolation zone with the NIR-HSI mounted on a linear translation stage in a cold laboratory. We leverage the relationship between effective grain size, a measure of NIR light absorption by firn grains, and NIR reflectance to produce high-resolution (0.4 mm) maps of effective grain size and ice layer stratigraphy. We show the NIR-HSI reproduces visually identified ice layer stratigraphy and infiltration ice content across all cores. Effective grain sizes change synchronously with traditionally measured grain radii with depth, although effective grains in each core are 1.5× larger on average, which is largely related to the differences in measurement techniques. To demonstrate the utility of the firn stratigraphic maps produced by the NIR-HSI, we track the 2012 melt event across the transect and assess its impact on deep firn structure by quantifying changes to infiltration ice content and grain size. These results indicate that NIR-HSI firn core analysis is a robust technique that can document deep and long-lasting changes to the firn column from meltwater percolation while quickly and accurately providing detailed firn stratigraphy datasets necessary for firn research applications. 

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