The Strong Influence of Internal Stresses on the Nucleation of a Nanosized, Deeply Undercooled Melt at a Solid-Solid Phase Interface (original) (raw)
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Journal of Physical Chemistry B, 2006
We theoretically predict a new phenomenon, namely, that a solid-solid phase transformation (PT) with a large transformation strain can occur via internal stress-induced virtual melting along the interface at temperatures significantly (more than 100 K) below the melting temperature. We show that the energy of elastic stresses, induced by transformation strain, increases the driving force for melting and reduces the melting temperature. Immediately after melting, stresses relax and the unstable melt solidifies. Fast solidification in a thin layer leads to nanoscale cracking which does not affect the thermodynamics or kinetics of the solidsolid transformation. Thus, virtual melting represents a new mechanism of solid-solid PT, stress relaxation, and loss of coherence at a moving solid-solid interface. It also removes the athermal interface friction and deletes the thermomechanical memory of preceding cycles of the direct-reverse transformation. It is also found that nonhydrostatic compressive internal stresses promote melting in contrast to hydrostatic pressure. Sixteen theoretical predictions are in qualitative and quantitative agreement with experiments conducted on the PTs in the energetic crystal HMX. In particular, (a) the energy of internal stresses is sufficient to reduce the melting temperature from 551 to 430 K for the δ phase during the f δ PT and from 520 to 400 K for the phase during the δ f PT; (b) predicted activation energies for direct and reverse PTs coincide with corresponding melting energies of the and δ phases and with the experimental values; (c) the temperature dependence of the rate constant is determined by the heat of fusion, for both direct and reverse PTs; results b and c are obtained both for overall kinetics and for interface propagation; (d) considerable nanocracking, homogeneously distributed in the transformed material, accompanies the PT, as predicted by theory; (e) the nanocracking does not change the PT thermodynamics or kinetics appreciably for the first and the second PT T δ cycles, as predicted by theory; (f) T δ PTs start at a very small driving force (in contrast to all known solid-solid transformations with large transformation strain), that is, elastic energy and athermal interface friction must be negligible; (g) f R and R f PTs, which are thermodynamically possible in the temperature range 382.4 < θ < 430 K and below 382.4 K, respectively, do not occur.
Phys. Chem. Chem. Phys., 2016
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 β ↔ 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.
Size and mechanics effects in surface-induced melting of nanoparticles
Nature Communications, 2011
Various melting-related phenomena (like surface melting, size dependence of melting temperature, melting of few nm-size particles and overheating at a very fast heating rate) are of great fundamental and applied interest, although the corresponding theory is still lacking. Here we develop an advanced phase-field theory of melting coupled to mechanics, which resolves numerous existing contradictions and allowed us to reveal exciting features of melting problems. The necessity of introducing an unexpected concept, namely, coherent solid-melt interface with uniaxial transformation strain, is demonstrated. A crossover in temperature dependence of interface energy for radii below 20 nm is found. surface-induced premelting and barrierless melt nucleation for nanoparticles down to 1 nm radius is studied, and the importance of advanced mechanics is demonstrated. our model describes well experimental data on the width of the molten layer versus temperature for the Al plane surface and on melting temperature versus particle radius.
Solid-solid ðSSÞ phase transformations via nanometer-size intermediate melts ðIMsÞ within the SS interface, hundreds of degrees 12 below melting temperature, were predicted thermodynamically and are consistent with experiments for various materials. A necessary 13 condition for the appearance of IMs, using a sharp interface approach, was that the ratio of the energies of SS and solid-melt ðSMÞ 14 interfaces, k E , were >2. Here, an advanced phase-field approach coupled with mechanics is developed that reveals various new scale and interaction effects and phenomena. Various types of IM are found: (i) continuous and reversible premelting and melting; (ii) jump-like barrierless transformation to IMs, which can be kept at much lower temperature even for k E < 2; (iii) unstable IMs, i.e. a crit-17 ical nucleus between the SS interface and the IM. A surprising scale effect related to the ratio of widths of SS and SM interfaces is found: 18 it suppresses barrierless IMs but allows IMs to be kept at much lower temperatures even for k E < 2. Relaxation of elastic stresses strongly promotes IMs, which can appear even at k E < 2 and be retained at k E ¼ 1. The theory developed here can be tailored for diffusive phase 20 transformations, formation of intergranular and interfacial phases, and surface-induced phase transformations.
Physical Review B, 2014
Previously unknown phenomena, scale, and kinetic effects are revealed by introducing the finite width ξ of the particle-exterior interface as the additional scale parameter and thermally activated melting in the phase field approach. In addition to traditional continuous barrierless premelting and melting for ξ = 0, barrierless hysteretic jumplike premelting (melting) and thermally activated premelting (melting) via critical nucleus are revealed. A very rich temperature θξ transformation diagram is found, which includes various barrierless and thermally activated transformations between solid, melt, and surface melt, and complex hysteretic behavior under various temperature and ξ trajectories. Bistable states (i.e., spontaneous thermally activated switching between two states) between solid and melt or surface melt are found for Al particles. Strong dependence of the melting temperature (which, in contrast to previous approaches, is defined for thermally activated premelting and melting) for nanoparticles of various radii on ξ is found. Results are in good agreement with experiments for Al for ξ = 0.8-1.2 nm. They open an unexplored direction of controlling surface melting and melting or solidification by controlling the width of the external surface and utilizing predicted phenomena. They also can be expanded for other phase transformations (e.g., amorphization, solid-solid diffusionless, diffusive, and electromagnetic transformations) and phenomena, imbedded particles, and mechanical effects.
Non-equilibrium solidification of undercooled metallic melts
Advances in Space Research, 1991
If a liquid is undercooled below its equilibrium melting temperature an excess Gibbs free energy is created. This gives access to solidification of metastable solids under non-equilibrium conditions. In the present work, techniques of containerless processing are applied. Electromagnetic and electrostatic levitation enable to freely suspend a liquid drop of a few millimeters in diameter. Heterogeneous nucleation on container walls is completely avoided leading to large undercoolings. The freely suspended drop is accessible for direct observation of rapid solidification under conditions far away from equilibrium by applying proper diagnostic means. Nucleation of metastable crystalline phases is monitored by X-ray diffraction using synchrotron radiation during non-equilibrium solidification. While nucleation preselects the crystallographic phase, subsequent crystal growth controls the microstructure evolution. Metastable microstructures are obtained from deeply undercooled melts as supersaturated solid solutions, disordered superlattice structures of intermetallics. Nucleation and crystal growth take place by heat and mass transport. Comparative experiments in reduced gravity allow for investigations on how forced convection can be used to alter the transport processes and design materials by using undercooling and convection as process parameters.
Solid-Solid Phase Transformation via Virtual Melting Significantly Below the Melting Temperature
Physical Review Letters, 2004
A new phenomenon is theoretically predicted, namely, that solid-solid transformation with a relatively large transformation strain can occur through virtual melting along the interface at temperatures significantly (more than 100 K) below the melting temperature. The energy of elastic stresses, induced by transformation strain, increases the driving force for melting and reduces the melting temperature. Immediately after melting, the stresses relax and the unstable melt solidifies. Fast solidification in a thin layer leads to nanoscale cracking, which does not affect the thermodynamics and kinetics of solid-solid transformation. Seven theoretical predictions are in quantitative agreement with experiments conducted on the ! transformation in the HMX energetic crystal.
A diffuse interface approach to phase transformation via virtual melting
This work represents development of the first phase field models and detailed study solidsolid transformations via intermediate melting within nanometer size interface. Such phase transformations can occur in different materials, including HMX energetic crystals, PbTiO 3 nanowires, complex pharmaceutical substances, electronic and geological materials, as well as colloidal, and superhard materials. A thermodynamically consistent phase field model for three phases is developed using two polar order parameters. It includes the effect of energy and width of solid-solid and solid-melt interfaces, interaction between two solid-melt interfaces, temperature, mechanics, and interface stresses. The derived thermodynamic potential satisfies
Particle-Based Computer Simulation of Crystal Nucleation and Growth Kinetics in Undercooled Melts
HERLACH:UNDERCOOLED MELTS O-BK, 2012
ABSTRACT Crystallization from the melt in Ni and Al50Ni50 is investigated using Monte Carlo (MC) as well as Molecular Dynamics (MD) simulation techniques. Crystal-liquid interfaces in Ni are analyzed in the framework of capillary wave theory (CWT). Anisotropic interfacial stiffnesses and tensions are determined by means of different predictions of CWT with respect to the spectrum, finite-size broadening and different geometries. Free energy barriers G for homogeneous nucleation in Ni are obtained from MC simulations in conjunction with umbrella sampling. These simulations indicate a non-spherical geometry of crystalline clusters, fluctuating between prolate and oblate shape at a given size. Nevertheless, the temperature dependence of G is well described by classical nucleation theory. Finally, the movement of planar solid-liquid interfaces in undercooled Ni is compared to that in the system Al50Ni50. In the latter binary system crystal growth is a factor of about 24 slower than in the one-component metal Ni. We show that this difference is associated with an additional segregation process in the binary system that occurs prior to the formation of a new crystalline layer.