Tensorial stress-plastic strain fields in α - ω Zr mixture, transformation kinetics, and friction in diamond-anvil cell.

Various phenomena (phase transformations (PTs), chemical reactions, microstructure evolution, strength, and friction) under high pressures in diamond-anvil cell are strongly affected by fields of stress and plastic strain tensors. However, they could not be measured. Here, we suggest coupled experimental-analytical-computational approaches utilizing synchrotron X-ray diffraction, to solve an inverse problem and find fields of all components of stress and plastic strain tensors and friction rules before, during, and after α-ω PT in strongly plastically predeformed Zr. Results are in good correspondence with each other and experiments. Due to advanced characterization, the minimum pressure for the strain-induced α-ω PT is changed from 1.36 to 2.7 GPa. It is independent of the plastic strain before PT and compression-shear path. The theoretically predicted plastic strain-controlled kinetic equation is verified and quantified. Obtained results open opportunities for developing quantitative high-pressure/stress science, including mechanochemistry, synthesis of new nanostructured materials, geophysics, astrogeology, and tribology.

Resolving puzzles of the phase-transformation-based mechanism of the strong deep-focus earthquake.

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-1 to seismic 10 - 103 s-1 strain 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.

Nontrivial nanostructure, stress relaxation mechanisms, and crystallography for pressure-induced Si-I → Si-II phase transformation.

Crystallographic theory based on energy minimization suggests austenite-twinned martensite interfaces with specific orientation, which are confirmed experimentally for various materials. Pressure-induced phase transformation (PT) from semiconducting Si-I to metallic Si-II, due to very large and anisotropic transformation strain, may challenge this theory. Here, unexpected nanostructure evolution during Si-I → Si-II PT is revealed by combining molecular dynamics (MD), crystallographic theory, generalized for strained crystals, and in situ real-time Laue X-ray diffraction (XRD). Twinned Si-II, consisting of two martensitic variants, and unexpected nanobands, consisting of alternating strongly deformed and rotated residual Si-I and third variant of Si-II, form [Formula: see text] interface with Si-I and produce almost self-accommodated nanostructure despite the large transformation volumetric strain of [Formula: see text]. The interfacial bands arrest the [Formula: see text] interfaces, leading to repeating nucleation-growth-arrest process and to growth by propagating [Formula: see text] interface, which (as well as [Formula: see text] interface) do not appear in traditional crystallographic theory.

Stress-Measure Dependence of Phase Transformation Criterion under Finite Strains: Hierarchy of Crystal Lattice Instabilities for Homogeneous and Heterogeneous Transformations.

Hierarchy of crystal lattice instabilities leading to a first-order phase transformation (PT) is found, which consists of PT instability described by the order parameter and elastic instabilities under different prescribed stress measures. After PT instability and prior to the elastic instability, an unexpected continuous third-order PT was discovered, which is followed by a first-order PT after the elastic instability. Under prescribed compressive second Piola-Kirchhoff stress, PT is third order until completion; it occurs without hysteresis and dissipation, properties that are ideal for various applications. For heterogeneous perturbations and PT, first-order PT occurs when the first elastic instability criterion (among criteria corresponding to different stress measures) is met inside the volume, surprisingly independent of the stress measure prescribed at the boundary.

Phase field approach for nanoscale interactions between crack propagation and phase transformation.

The phase field approach (PFA) for the interaction of fracture and martensitic phase transformation (PT) is developed, which includes the change in surface energy during PT and the effect of unexplored scale parameters proportional to the ratio of the widths of the crack surface and the phase interface, both at the nanometer scale. The variation of these two parameters causes unexpected qualitative and quantitative effects: shift of PT away from the crack tip, "wetting" of the crack surface by martensite, change in the structure and geometry of the transformed region, crack trajectory, and process of interfacial damage evolution, as well as transformation toughening. The results suggest additional parameters controlling coupled fracture and PTs.

Fatigue-resistant high-performance elastocaloric materials made by additive manufacturing.

Elastocaloric cooling, a solid-state cooling technology, exploits the latent heat released and absorbed by stress-induced phase transformations. Hysteresis associated with transformation, however, is detrimental to efficient energy conversion and functional durability. We have created thermodynamically efficient, low-hysteresis elastocaloric cooling materials by means of additive manufacturing of nickel-titanium. The use of a localized molten environment and near-eutectic mixing of elemental powders has led to the formation of nanocomposite microstructures composed of a nickel-rich intermetallic compound interspersed among a binary alloy matrix. The microstructure allowed extremely small hysteresis in quasi-linear stress-strain behaviors-enhancing the materials efficiency by a factor of four to seven-and repeatable elastocaloric performance over 1 million cycles. Implementing additive manufacturing to elastocaloric cooling materials enables distinct microstructure control of high-performance metallic refrigerants with long fatigue life.

Highly reactive energetic films by pre-stressing nano-aluminum particles.

Energetic films were synthesized using stress altered nano-aluminum particles (nAl). The nAl powder was pre-stressed to examine how modified mechanical properties of the fuel particles influenced film reactivity. Pre-stressing conditions varied by quenching rate. Slow and rapid quenching rates induced elevated dilatational strain within the nAl particles that was measured using synchrotron X-ray diffraction (XRD). An analytical model for stress and strain in a nAl core-Al2O3 shell particle that includes creep in the shell and delamination at the core-shell boundary, was developed and used for interpretation of strain measurements. Results show rapid quenching induced 81% delamination at the particle core-shell interface also observed with Transmission Electron Microscopy (TEM). Slower quenching elevated dilatational strain without delamination. All films were prepared at approximately a 75 : 25 Al : poly(vinylidene fluoride) PVDF weight ratio and were 1 mm thick. A drop weight impact test was performed to assess ignition sensitivity and combustion. Stress altered nAl exhibited greater energy release rates and more complete combustion than untreated nAl, but reaction dynamics and kinetics proceeded in two different ways depending on the nAl quenching rate during pre-stressing.

Scale-Free Modeling of Coupled Evolution of Discrete Dislocation Bands and Multivariant Martensitic Microstructure.

A scale-free model for the coupled evolution of discrete dislocation bands and multivariant martensitic microstructure is developed. In contrast to previous phase field models, which are limited to nanoscale specimens, this model allows for treating the nucleation and evolution of martensite at evolving dislocation pileups, twin tips, and shear bands in a sample of an arbitrary size. The model is applied for finite element simulations of plastic strain-induced phase transformations (PTs) in a polycrystalline sample under compression and shear. The solution explains the one to two orders of magnitude reduction in PT pressure by plastic shear, the existence of incompletely transformed stationary state, and optimal shear strain for the strain-induced synthesis of high pressure phases.

Lattice Instability during Solid-Solid Structural Transformations under a General Applied Stress Tensor: Example of Si I→Si II with Metallization.

The density functional theory was employed to study the stress-strain behavior and elastic instabilities during the solid-solid phase transformation (PT) when subjected to a general stress tensor, as exemplified for semiconducting Si I and metallic Si II, where metallization precedes the PT, so stressed Si I can be a metal. The hydrostatic PT occurs at 76 GPa, while under uniaxial loading it is 11 GPa (3.7 GPa mean pressure), 21 times lower. The Si I→Si II PT is described by a critical value of the phase-field's modified transformation work, and the PT criterion has only two parameters given six independent stress elements. Our findings reveal novel, more practical synthesis routes for new or known high-pressure phases under predictable nonhydrostatic loading, where competition of instabilities can serve for phase selection rather than free energy minima used for equilibrium processing.

High pressure phase transformations revisited.

High pressure phase transformations play an important role in the search for new materials and material synthesis, as well as in geophysics. However, they are poorly characterized, and phase transformation pressure and pressure hysteresis vary drastically in experiments of different researchers, with different pressure transmitting media, and with different material suppliers. Here we review the current state, challenges in studying phase transformations under high pressure, and the possible ways in overcoming the challenges. This field is critically compared with fields of phase transformations under normal pressure in steels and shape memory alloys, as well as plastic deformation of materials. The main reason for the above mentioned discrepancy is the lack of understanding that there is a fundamental difference between pressure-induced transformations under hydrostatic conditions, stress-induced transformations under nonhydrostatic conditions below yield, and strain-induced transformations during plastic flow. Each of these types of transformations has different mechanisms and requires a completely different thermodynamic and kinetic description and experimental characterization. In comparison with other fields the following challenges are indicated for high pressure phase transformation: (a) initial and evolving microstructure is not included in characterization of transformations; (b) continuum theory is poorly developed; (c) heterogeneous stress and strain fields in experiments are not determined, which leads to confusing material transformational properties with a system behavior. Some ways to advance the field of high pressure phase transformations are suggested. The key points are: (a) to take into account plastic deformations and microstructure evolution during transformations; (b) to formulate phase transformation criteria and kinetic equations in terms of stress and plastic strain tensors (instead of pressure alone); (c) to develop multiscale continuum theories, and (d) to couple experimental, theoretical, and computational studies of the behavior of a tested sample to extract information about fields of stress and strain tensors and concentration of high pressure phase, transformation criteria and kinetics. The ideal characterization should contain complete information which is required for simulation of the same experiments.

Pressure Self-focusing Effect and Novel Methods for Increasing the Maximum Pressure in Traditional and Rotational Diamond Anvil Cells.

The main principles of producing a region near the center of a sample, compressed in a diamond anvil cell (DAC), with a very high pressure gradient and, consequently, with high pressure are predicted theoretically. The revealed phenomenon of generating extremely high pressure gradient is called the pressure self-focusing effect. Initial analytical predictions utilized generalization of a simplified equilibrium equation. Then, the results are refined using our recent advanced model for elastoplastic material under high pressures in finite element method (FEM) simulations. The main points in producing the pressure self-focusing effect are to use beveled anvils and reach a very thin sample thickness at the center. We find that the superposition of torsion in a rotational DAC (RDAC) offers drastic enhancement of the pressure self-focusing effect and allows one to reach the same pressure under a much lower force and deformation of anvils.

Triaxial-Stress-Induced Homogeneous Hysteresis-Free First-Order Phase Transformations with Stable Intermediate Phases.

Starting with thermodynamic predictions and following with molecular dynamics simulations, special triaxial compression-tension states were found for which the stresses for the instability of the crystal lattice of silicon (Si) are the same for direct and reverse phase transformations (PTs) between semiconducting Si I and metallic Si II phases. This leads to unique homogeneous and hysteresis-free first-order PTs, for which each intermediate crystal lattice along the transformation path is in indifferent thermodynamic equilibrium and can be arrested and studied by fixing the strain in one direction. By approaching these stress states, a traditional two-phase system continuously transforms to homogenous intermediate phases. Zero hysteresis and homogeneous transformations are the optimal property for various PT applications, which drastically reduce damage and energy dissipation.

Superheating and melting within aluminum core-oxide shell nanoparticles for a broad range of heating rates: multiphysics phase field modeling.

The external surface of metallic particles is usually covered by a thin and strong oxide shell, which significantly affects superheating and melting of particles. The effects of geometric parameters and heating rate on characteristic melting and superheating temperatures and melting behavior of aluminum nanoparticles covered by an oxide shell were studied numerically. For this purpose, the multiphysics model that includes the phase field model for surface melting, a dynamic equation of motion, a mechanical model for stress and strain simulations, interface and surface stresses, and the thermal conduction model including thermoelastic and thermo-phase transformation coupling as well as transformation dissipation rate was formulated. Several nontrivial phenomena were revealed. In comparison with a bare particle, the pressure generated in a core due to different thermal expansions of the core and shell and transformation volumetric expansion during melting, increases melting temperatures with the Clausius-Clapeyron factor of 60 K GPa-1. For the heating rates Q ≤ 109 K s-1, melting temperatures (surface and bulk start and finish melting temperatures, and maximum superheating temperature) are independent of Q. For Q ≥ 1012 K s-1, increasing Q generally increases melting temperatures and temperature for the shell fracture. Unconventional effects start for Q ≥ 1012 K s-1 due to kinetic superheating combined with heterogeneous melting and geometry. The obtained results are applied to shed light on the initial stage of the melt-dispersion-mechanism of the reaction of Al nanoparticles. Various physical phenomena that promote or suppress melting and affect melting temperatures and temperature of the shell fracture for different heating-rate ranges are summarized in the corresponding schemes.

A phase-field approach to nonequilibrium phase transformations in elastic solids via an intermediate phase (melt) allowing for interface stresses.

A phase-field approach for phase transformations (PTs) between three different phases at nonequilibrium temperatures is developed. It includes advanced mechanics, thermodynamically consistent interfacial stresses, and interface interactions. A thermodynamic Landau-Ginzburg potential developed in terms of polar order parameters satisfies the desired instability and equilibrium conditions for homogeneous phases. The interfacial stresses were introduced with some terms from large-strain formulation even though the small-strain assumption was utilized. The developed model is applied to study the PTs between two solid phases via a highly disordered intermediate phase (IP) or an intermediate melt (IM) hundreds of degrees below the melting temperature. In particular, the ß â†” δ PTs in HMX energetic crystals via IM are analyzed. The effects of various parameters (temperature, ratios of widths and energies of solid-solid (SS) to solid-melt (SM) interfaces, elastic energy, and interfacial stresses) on the formation, stability, and structure of the IM within a propagating SS interface are studied. Interfacial and elastic stresses within a SS interphase and their relaxation and redistribution with the appearance of a partial or complete IM are analyzed. The energy and structure of the critical nucleus (CN) of the IM are studied as well. In particular, the interfacial stresses increase the aspect-ratio of the CN. Although including elastic energy can drastically reduce the energy of the CN of the IM, the activation energy of the CN of the IM within the SS interface increases when interfacial tension is taken into account. The developed thermodynamic potential can also be modified to model other multiphase physical phenomena, such as multi-variant martensitic PTs, grain boundary and surface-induced pre-melting and PTs, as well as developing phase diagrams for IPs.

Coupled phase field, heat conduction, and elastodynamic simulations of kinetic superheating and nanoscale melting of aluminum nanolayer irradiated by picosecond laser.

An advanced continuum model for nanoscale melting and kinetic superheating of an aluminum nanolayer irradiated by a picosecond laser is formulated. Barrierless nucleation of surface premelting and melting occurs, followed by a propagation of two solid-melt interfaces toward each other and their collision. For a slow heating rate of Q = 0.015 K ps(-1) melting occurs at the equilibrium melting temperature under uniaxial strain conditions T = 898.1 K (i.e., below equilibrium melting temperature Teq = 933.67 K) and corresponding biaxial stresses, which relax during melting. For a high heating rate of Q = 0.99-84 K ps(-1), melting occurs significantly above Teq. Surprisingly, an increase in heating rate leads to temperature reduction at the 3 nm wide moving interfaces due to fast absorption of the heat of fusion. A significant, rapid temperature drop (100-500 K, even below melting temperature) at the very end of melting is revealed, which is caused by the collision of two finite-width interfaces and accelerated melting in about the 5 nm zone. For Q = 25-84 K ps(-1), standing elastic stress waves are observed in a solid with nodal points at the moving solid-melt interfaces, which, however, do not have a profound effect on melting time or temperatures. When surface melting is suppressed, barrierless bulk melting occurs in the entire sample, and elastodynamic effects are more important. Good correspondence with published, experimentally-determined melting time is found for a broad range of heating rates. Similar approaches can be applied to study various phase transformations in different materials and nanostructures under high heating rates.

The strong influence of internal stresses on the nucleation of a nanosized, deeply undercooled melt at a solid-solid phase interface.

The effect of elastic energy on nucleation and disappearance of a nanometer size intermediate melt (IM) region at a solid-solid (S1S2) phase interface at temperatures 120 K below the melting temperature is studied using a phase-field approach. Results are obtained for broad range of the ratios of S1S2 to solid-melt interface energies, k(E), and widths, k(δ). It is found that internal stresses only slightly promote barrierless IM nucleation but qualitatively alter the system behavior, allowing for the appearance of the IM when k(E) < 2 (thermodynamically impossible without mechanics) and elimination of what we termed the IM-free gap. Remarkably, when mechanics is included within this framework, there is a drastic (16 times for HMX energetic crystals) reduction in the activation energy of IM critical nucleus. After this inclusion, a kinetic nucleation criterion is met, and thermally activated melting occurs under conditions consistent with experiments for HMX, elucidating what had been to date mysterious behavior. Similar effects are expected to occur for other material systems where S1S2 phase transformations via IM take place, including electronic, geological, pharmaceutical, ferroelectric, colloidal, and superhard materials.

Pre-stressing micron-scale aluminum core-shell particles to improve reactivity.

The main direction in increasing reactivity of aluminum (Al) particles for energetic applications is reduction in their size down to nanoscale. However, Al nanoparticles are 30-50 times more expensive than micron scale particles and possess safety and environmental issues. Here, we improved reactivity of Al micron scale particles by synthesizing pre-stressed core-shell structures. Al particles were annealed and quenched to induce compressive stresses in the alumina passivation shell surrounding Al core. This thermal treatment was designed based on predictions of the melt-dispersion mechanism (MDM); a theory describing Al particle reaction under high heating rate. For all anneal treatment temperatures, experimental flame propagation rates for Al combined with nanoscale copper oxide (CuO) are in quantitative agreement with the theoretical predictions based on the MDM. The best treatment increases flame rate by 36% and achieves 68% of that for the best Al nanoparticles.

Phase transformations in nanograin materials under high pressure and plastic shear: nanoscale mechanisms.

There are two main challenges in the discovery of new high pressure phases (HPPs) and transforming this discovery into technologies: finding conditions to synthesize new HPPs and finding ways to reduce the phase transformation (PT) pressure to an economically reasonable level. Based on the results of pressure-shear experiments in the rotational diamond anvil cell (RDAC), superposition of plastic shear on high pressure is a promising way to resolve these problems. However, physical mechanisms behind these phenomena are not yet understood. Here, we elucidate generic mechanisms of coupled nucleation and evolution of dislocation and HPP structures in the nanograin material under pressure and shear utilizing the developed advanced phase field approach (PFA). Dislocations are generated at the grain boundaries and are densely piled up near them, creating a strong concentrator of the stress tensor. Averaged shear stress is essentially larger in the nanograin material due to grain boundary strengthening. This leads to the increase in the local thermodynamic driving force for PT, which allows one to significantly reduce the applied pressure. For all cases, the applied pressure is 3-20 times lower than the PT pressure and 2-12.5 times smaller than the phase equilibrium pressure. Interaction between nuclei leads sometimes to their coalescence and growth of the HPP away from stress concentrators. Plasticity plays a dual role: in addition to creating stress concentrators, it may relax stresses at other concentrators, thus competing with PT. Some ways to optimize the loading parameters have been found that lead to methods for controlling PT. Since such a local stress tensor with high shear stress component cannot be created without plastic deformations, this may lead to new transformation paths and phases, which are hidden during pressure induced PTs.

Mechanochemical mechanism for reaction of aluminium nano- and micrometre-scale particles.

A recently suggested melt-dispersion mechanism (MDM) for fast reaction of aluminium (Al) nano- and a few micrometre-scale particles during fast heating is reviewed. Volume expansion of 6% during Al melting produces pressure of several GPa in a core and tensile hoop stresses of 10 GPa in an oxide shell. Such stresses cause dynamic fracture and spallation of the shell. After spallation, an unloading wave propagates to the centre of the particle and creates a tensile pressure of 3-8 GPa. Such a tensile pressure exceeds the cavitation strength of liquid Al and disperses the melt into small, bare clusters (fragments) that fly at a high velocity. Reaction of the clusters is not limited by diffusion through a pre-existing oxide shell. Some theoretical and experimental results related to the MDM are presented. Various theoretical predictions based on the MDM are in good qualitative and quantitative agreement with experiments, which resolves some basic puzzles in combustion of Al particles. Methods to control and improve reactivity of Al particles are formulated, which are exactly opposite to the current trends based on diffusion mechanism. Some of these suggestions have experimental confirmation.

Anisotropic compositional expansion and chemical potential for amorphous lithiated silicon under stress tensor.

Si is a promising anode material for Li-ion batteries, since it absorbs large amounts of Li. However, insertion of Li leads to 334% of volumetric expansion, huge stresses, and fracture; it can be suppressed by utilizing nanoscale anode structures. Continuum approaches to stress relaxation in LixSi, based on plasticity theory, are unrealistic, because the yield strength of LixSi is much higher than the generated stresses. Here, we suggest that stress relaxation is due to anisotropic (tensorial) compositional straining that occurs during insertion-extraction at any deviatoric stresses. Developed theory describes known experimental and atomistic simulation data. A method to reduce stresses is predicted and confirmed by known experiments. Chemical potential has an additional contribution due to deviatoric stresses, which leads to increases in the driving force both for insertion and extraction. The results have conceptual and general character and are applicable to any material systems.