Kinematics and Balance Relations for Bidimensional Continua

This work is concerned with the formulation of the kinematics and balance relations for a so-called bidimensional continuum, which can be used in modeling thin layers and interface regions such as phase boundaries. Such a continuum represents a thin, shell-like 3-dimensional region in which the upper and lower surfaces move relative to each other as well as relative to the dividing, non-material interface between them. As such, it is more general than standard interfaces or shells. The standard balance relations of three-dimensional continua are adapted to this dynamic bidimensional geometry using the differential geometric notion of a flow. On this basis, the adapted balance relations are averaged over the dynamic thickness of the bidimensional continuum to obtain reduced 2-dimensional, surface forms of these on the dividing interface. In addition to the usual influence of the surface geometry on their form, the resulting adapted and averaged surface balance relations contain flux terms accounting for the effect of relative motion, i.e., diffusion, on the balances. In the limit that the thickness of the bidimensional continuum goes to zero, the generalized surface balance relations reduce to the classical jump balance relations across an interface

Shock-induced temperatures of MgO

Shock-compressed MgO radiates thermally at temperatures between 2900 and 3700 K in the 170–200 GPa pressure range. A simple energy-transport model of the shocked-MgO-targets distinguishes between different shock-induced radiation sources in these targets and provides estimates of spectral absorption-coefficients, α_(λMgO), for shocked MgO (e.g. at 203 GPa, α_(λMgO) ~ 630, 7500, 4200 and 3800 m^(−1), at 450, 600, 750 and 900 nm, respectively). The experimentally inferred temperatures of the shock-compressed states of MgO are consistent with temperatures calculated for MgO assuming that (1) it deforms as an elastic fluid, (2) has a Dulong-Petit value for specific heat at constant volume in its shocked state, and (3) undergoes no phase transformation below 200 GPa

Dynamic compression of diopside and salite to 200 GPa

New Hugoniot data on single crystal diopside, CaMgSi_2O_6 (Di), suggest that transformation to a high-pressure thermomechanical state begins at ∼50 GPa and is complete above 100 GPa, in agreement with other pyroxenes and silicates of geophysical interest. Comparison of the new high pressure phase (HPP) data for Di and salite, CaMg_(0.82)Fe_(0.18)Si_2O_6 (Sa) with appropriate mixed oxide and perovskite models implies compatibility between either model and the data. Conversely, least-squares fits to the HPP Di data favor lower (3.6 - 3.9 Mg/m³) values of zero-pressure, room-temperature density than the models (4.0 - 4.1 Mg/m³). Similar comments apply to porosity-corrected HPP hedenbergite (Hd) data. The HPP Di, Sa, and Hd data also imply much larger density differences between these compositions in the HPP regime (e.g., ≈0.8 Mg/m³ between Di and Hd) than at STP (0.38 Mg/m³). This may represent the influence of multiple transition processes (e.g., polymorphism and Fe^(2+) high-low spin) as a function of Fe content across the Di-Hd series. The new HPP Sa data closely parallel (≈0.1 Mg/m³ less dense) the lower mantle density profile from ∼90 GPa to 136 GPa. Our results are consistent with the speculations of Jeanloz and Ahrens on the possibility of significant Ca in the lower mantle

Shock-induced temperatures of CaMgSi_2O_6

Optical radiation from CaMgSi_2O_6 crystal (diopside) shock-compressed to 145–170 GPa yields shock-induced temperatures of 3500–4800 K, while that from CaMgSi_2O_6 glass, with a density 86% that of CaMgSi_2O_6 crystal, shock-compressed to 96–98 GPa, yields shock-induced temperatures of 3700–3900 K. The observed radiation histories of of the targets containing CaMgSi_2O_6 crystal and glass imply that the shock-compressed states of both are highly absorptive, with effective absorption coefficients of ≥ 500–1000 m^(−1). Calculated shock-compressed states for both CaMgSi_2O_6 crystal and glass, when compared to experimental results, imply the presence of a high-pressure phase (HPP) along both Hugoniots over the respective pressure ranges. The CaMgSi_2O_6 crystal experimental results are consistent with a standard temperature and pressure (STP) HPP mass density of 4100±100 kg/m^3, a STP HPP bulk modulus of 250±50 GPa, and a difference in specific internal energy (SIE) between (metastable) HPP and the CaMgSi_2O_6 crystal states at STP (“energy of transition”) of 2.2±0.5 MJ/kg. The CaMgSi_2O_6 glass results are “best-fit” by the same (median) values of all three parameters; except for the STP SIE difference between the CaMgSi_2O_6 glass and HPP states, however, they are less sensitive to parameter variations than the crystal results because they are at lower pressure. All these model constraints are insensitive to the range of values (1–2) assumed for the STP HPP Gruneisen's parameter. The relatively high value of the STP SIE difference between HPP and CaMgSi_2O_6 crystal or glass most likely implies that CaMgSi_2O_6 glass and crystal experience both solid-solid and solid-liquid phase transformations along their respective Hugoniots below 96 and 144 GPa, respectively. The HPP CaMgSi_2O_6 Hugoniot constrained by the crystal experimental results lies between 2500–3000 K in the pressure range (110–135 GPa) of the lowermost mantle (D′′)] our results imply that CaMgSi_2O_6 is at least partly molten at these pressures and temperatures. Seismically constrained compositional models for this region of Earth's lower mantle suggest that it could contain a significant amount of Ca (25–30 wt % CaO). If so, our results imply that the temperature of the D′′ region must be below ≈ 3000 K, since the finite S-wave velocity of the D′′ region implies that it must be (at least at seismic frequencies) predominantly solid

Modeling of grain boundary dynamics using amplitude equations

We discuss the modelling of grain boundary dynamics within an amplitude equations description, which is derived from classical density functional theory or the phase field crystal model. The relation between the conditions for periodicity of the system and coincidence site lattices at grain boundaries is investigated. Within the amplitude equations framework we recover predictions of the geometrical model by Cahn and Taylor for coupled grain boundary motion, and find both $\langle100\rangle$ and $\langle110\rangle$ coupling. No spontaneous transition between these modes occurs due to restrictions related to the rotational invariance of the amplitude equations. Grain rotation due to coupled motion is also in agreement with theoretical predictions. Whereas linear elasticity is correctly captured by the amplitude equations model, open questions remain for the case of nonlinear deformations.Comment: 21 pages. We extended the discussion on the geometrical nonlinearities in Section

Shock-induced melting and shear banding in single-crystal NaCl

Radiative color temperatures were measured in single-crystal sodium chloride under shock compression parallel to [100] over a pressure range from 20 to 35 GPa. Color temperatures from 2500 to 4500 K and emittances from 0.003 to 0.3 were determined by fitting observed spectra (450–850 nm) to the Planck greybody radiation law. These data support a heterogeneous shock deformation model of shocked halite in this pressure range. A 2500-K temperature rise, of unknown origin, is observed over the B1–B2 mixed phase region from 25 to 30 GPa. Assuming that shock deformation occurs via yielding in localized planar zones which become melt and the melting temperature at high pressure controls the temperature, we infer that the temperature of the B2 fusion curve from 30 to 35 GPa rises from 3200 to 3300 K. The B1–B2-liquid triple point is predicted to be at a temperature of 2250 K and 23.5 GPa

Phenomenological modeling of anisotropy induced by evolution of the dislocation structure on the macroscopic and microscopic scale \ud

This work focuses on the modeling of the evolution of anisotropy induced by the development of the dislocation microstructure. A model formulated at the engineering scale in the context of classical metal plasticity and a model formulated in the context of crystal plasticity are presented. Images obtained by transmission-electron microscopy (TEM) show the influence of the strain path on the evolution of anisotropy for the case of two common materials used in sheet metal forming, DC06 and AA6016-T4. Both models are capable of accounting for the transient behavior observed after changes in loading path for fcc and bcc metals. The evolution of the internal variables of the models is correlated with the evolution of the dislocation structure observed by TEM investigations