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1. In situ quantitative study of plastic strain-induced phase transformations under high pressure: Example for ultra-pure Zr.

   Pandey, K. K. ; Levitas, V. I. ( February 2020 , ArXivorg)

   The first in situ quantitative synchrotron X-ray diffraction (XRD) study of plastic strain-induced phase transformation (PT) has been performed on $\alpha-\omega$ PT in ultra-pure, strongly plastically predeformed Zr as an example, under different compression-shear pathways in rotational diamond anvil cell (RDAC). Radial distributions of pressure in each phase and in the mixture, and concentration of $\omega$-Zr, all averaged over the sample thickness, as well as thickness profile were measured. The minimum pressure for the strain-induced $\alpha-\omega$ PT, $p^d_{\varepsilon}$=1.2 GPa, is smaller than under hydrostatic loading by a factor of 4.5 and smaller than the phase equilibrium pressure by a factor of 3; it is independent of the compression-shear straining path. The theoretically predicted plastic strain-controlled kinetic equation was verified and quantified; it is independent of the pressure-plastic strain loading path and plastic deformation at pressures below $p^d_{\varepsilon}$. Thus, strain-induced PTs under compression in DAC and torsion in RDAC do not fundamentally differ. The yield strength of both phases is estimated using hardness and x-ray peak broadening; the yield strength in shear is not reached by the contact friction stress and cannot be evaluated using the pressure gradient. Obtained results open a new opportunity for quantitative study of strain-induced PTs andmore »reactions with applications to material synthesis and processing, mechanochemistry, and geophysics.« less
2. Resolving puzzles of the phase-transformation-based mechanism of the strong deep-focus earthquake

   https://doi.org/10.1038/s41467-022-33802-y  

   Levitas, Valery I. ( October 2022 , Nature Communications)

   Deep-focus earthquakes that occur at 350–660 km are assumed to be caused by olivine → spinel phase transformation (PT). However, there are many existing puzzles: (a) What are the mechanisms for jump from geological 10⁻¹⁷ − 10⁻¹⁵ s⁻¹to seismic 10 − 10³ s⁻¹strain rates? Is it possible without PT? (b) How does metastable olivine, which does not completely transform to spinel for over a million years, suddenly transform during seconds? (c) How to connect shear-dominated seismic signals with volume-change-dominated PT strain? Here, we introduce a combination of several novel concepts that resolve the above puzzles quantitatively. We treat the transformation in olivine like plastic strain-induced (instead of pressure/stress-induced) and find an analytical 3D solution for coupled deformation-transformation-heating in a shear band. This solution predicts conditions for severe (singular) transformation-induced plasticity (TRIP) and self-blown-up deformation-transformation-heating process due to positive thermomechanochemical feedback between TRIP and strain-induced transformation. This process leads to temperature in a band, above which the self-blown-up shear-heating process in the shear band occurs after finishing the PT. Our findings change the main concepts in studying the initiation of the deep-focus earthquakes and PTs during plastic flow in geophysics in general.
3. Athermal resistance to phase interface motion due to precipitates: A phase field study

   Javanbakht, Mahdi ; Levitas, Valery I. ( June 2022 , ArXivorg)

   Athermal resistance to the motion of a phase interface due to a precipitate is investigated. The coupled phase field and elasticity equations are solved for the phase transformation (PT). The volumetric misfit strain due to the precipitate is included using the error and rectangular functions. Due to the presence of precipitates, the critical thermal driving forces remarkably differ between the direct and reverse PTs, resulting in a hysteresis behavior. For the precipitate radius small compared to the interface width, the misfit strain does not practically show any effect on the critical thermal driving force. Also, the critical thermal driving force value nonlinearly increases vs. the precipitate concentration for both the direct and reverse PTs. Change in the precipitate surface energy significantly changes the PT morphology and the critical thermal driving forces. The critical thermal driving force shows dependence on the misfit strain for large precipitate sizes compared to the interface width. For both the constant surface energy (CSE) and variable surface energy (VSE) boundary conditions (BCs) at the precipitate surface, the critical thermal driving force linearly increases vs. the misfit strain coefficient for the direct PT while it is almost independent of it for the reverse PT. For larger precipitates,more »the critical thermal driving force nonlinearly increases vs. the precipitate concentration for the direct PT. For the reverse PT, its value for the CSE BCs linearly increases vs. the precipitate concentration while it is independent of the precipitate concentration for the VSE BCs. Also, for any concentration, the VSE BCs result in higher thermal critical driving forces, a smaller hysteresis range, and a larger transformation rate. The critical microstructure and thermal driving forces are validated using the thermodynamic phase equilibrium condition for stationary interfaces.« less
4. Athermal resistance to phase interface motion due to precipitates: A phase field study

   Javanbakht, Mahdi ; Levitas, Valery I. ( June 2022 , ArXivorg)

   Athermal resistance to the motion of a phase interface due to a precipitate is investigated. The coupled phase field and elasticity equations are solved for the phase transformation (PT). The volumetric misfit strain due to the precipitate is included using the error and rectangular functions. Due to the presence of precipitates, the critical thermal driving forces remarkably differ between the direct and reverse PTs, resulting in a hysteresis behavior. For the precipitate radius small compared to the interface width, the misfit strain does not practically show any effect on the critical thermal driving force. Also, the critical thermal driving force value nonlinearly increases vs. the precipitate concentration for both the direct and reverse PTs. Change in the precipitate surface energy significantly changes the PT morphology and the critical thermal driving forces. The critical thermal driving force shows dependence on the misfit strain for large precipitate sizes compared to the interface width. For both the constant surface energy (CSE) and variable surface energy (VSE) boundary conditions (BCs) at the precipitate surface, the critical thermal driving force linearly increases vs. the misfit strain coefficient for the direct PT while it is almost independent of it for the reverse PT. For larger precipitates,more »the critical thermal driving force nonlinearly increases vs. the precipitate concentration for the direct PT. For the reverse PT, its value for the CSE BCs linearly increases vs. the precipitate concentration while it is independent of the precipitate concentration for the VSE BCs. Also, for any concentration, the VSE BCs result in higher thermal critical driving forces, a smaller hysteresis range, and a larger transformation rate. The critical microstructure and thermal driving forces are validated using the thermodynamic phase equilibrium condition for stationary interfaces.« less
5. Resolving puzzles of the phase-transformation-based mechanism of the deep-focus earthquake

   Levitas, Valery I. ( October 2021 , ArXivorg)

   Deep-focus earthquakes that occur at 350–660 km, where pressures p =12-23 GPa and temperature T =1800-2000 K, are generally assumed to be caused by olivine→spinel phase transformation, see pioneering works [1–10]. However, there are many existing puzzles: (a) What are the mechanisms for jump from geological 10−17−10−15 s−1 to seismic 10−103s−1(see [3]) strain rates? Is it possible without phase transformation? (b) How does metastable olivine, which does not completely transform to spinel at high temperature and deeply in the region of stability of spinel for over the million years, suddenly transforms during seconds and generates seismic strain rates 10−103s−1 that produce strong seismic waves? (c) How to connect deviatorically dominated seismic signals with volume-change dominated transformation strain during phase transformations [9,11]? Here we introduce a combination of several novel concepts that allow us to resolve the above puzzles quantitatively. We treat the transformation in olivine like plastic strain-induced (instead of pressure/stress-induced) and find an analytical 3D solution for coupled deformation-transformation-heating processes in a shear band. This solution predicts conditions for severe (singular) transformation-induced plasticity (TRIP) and self-blown-up deformation-transformation-heating process due to positive thermomechanochemical feedback between TRIP and strain-induced transformation. In nature, this process leads to temperature in a band exceedingmore »the unstable stationary temperature, above which the self-blown-up shear-heating process in the shear band occurs after finishing the phase transformation. Without phase transformation and TRIP, significant temperature and strain rate increase is impossible. Due to the much smaller band thickness in the laboratory, heating within the band does not occur, and plastic flow after the transformation is very limited. Our findings change the main concepts in studying the initiation of the deep-focus earthquakes and phase transformations during plastic flow in geophysics in general. The latter may change the interpretation of different geological phenomena, e.g., the possibility of the appearance of microdiamond directly in the cold Earth crust within shear-bands [12] during tectonic activities without subduction to the mantle and uplifting. Developed theory of the self-blown-up transformation-TRIP-heating process is applicable outside geophysics for various processes in materials under pressure and shear, e.g., for new routes of material synthesis [12,13], friction and wear, surface treatment, penetration of the projectiles and meteorites, and severe plastic deformation and mechanochemical technologies.« less