No Arabic abstract
Amorphous solids yield at a critical value of the strain (in strain controlled experiments); for larger strains the average stress can no longer increase - the system displays an elasto-plastic steady state. A long standing riddle in the materials community is what is the difference between the microscopic states of the material before and after yield. Explanations in the literature are material specific, but the universality of the phenomenon begs a universal answer. We argue here that there is no fundamental difference in the states of matter before and after yield, but the yield is a bona-fide first order phase transition between a highly restricted set of possible configurations residing in a small region of phase space to a vastly rich set of configurations which include many marginally stable ones. To show this we employ an order parameter of universal applicability, independent of the microscopic interactions, that is successful in quantifying the transition in an unambiguous manner.
The effect of coordination on transport is investigated theoretically using random networks of springs as model systems. An effective medium approximation is made to compute the density of states of the vibrational modes, their energy diffusivity (a spectral measure of transport) and their spatial correlations as the network coordination $z$ is varied. Critical behaviors are obtained as $zto z_c$ where these networks lose rigidity. A sharp cross-over from a regime where modes are plane-wave-like toward a regime of extended but strongly-scattered modes occurs at some frequency $omega^*sim z-z_c$, which does not correspond to the Ioffe-Regel criterion. Above $omega^*$ both the density of states and the diffusivity are nearly constant. These results agree remarkably with recent numerical observations of repulsive particles near the jamming threshold cite{ning}. The analysis further predicts that the length scale characterizing the correlation of displacements of the scattered modes decays as $1/sqrt{omega}$ with frequency, whereas for $omega<<omega^*$ Rayleigh scattering is found with a scattering length $l_ssim (z-z_c)^3/omega^4$. It is argued that this description applies to silica glass where it compares well with thermal conductivity data, and to transverse ultrasound propagation in granular matter.
The yield of amorphous solids like metallic glasses under external stress was discussed asserting that it is related to the glass transition by increasing temperature, or that it can be understood using statistical theories of various sorts. Here we study the approach to stress-controlled yield and argue that neither assertions can be supported, at least at low temperatures. The yield of amorphous solids at low temperatures is a highly structured phenomenon, characterized by a specific series of mechanical instabilities, and having no similarity at all to fluidization by increased temperature, real or fictive. The series of instabilities followed by stress controlled yield at low but finite temperature protocols can be predicted by analyzing athermal quasi-static strain controlled protocols, making the latter highly relevant for the deep understanding of the mechanical properties of amorphous solids.
First order phase transitions occur discretely from one state to another, however they often display continuous behavior. To understand this nature, it is essential to probe how the emergent phase nucleates, interacts and evolves with the initial phase across the transition at microscopic scales. Here, the prototypical first-order magneto-structural transition in FeRh is used to investigate these phenomena. We find that the temperature evolution of the final phase exhibits critical behavior. Furthermore, a difference between the structure and magnetic transition temperatures reveals a novel intermediate phase created from the interface between the initial and nucleated final states. This emergent phase, characterized by its lack of spin order due to the competition between the antiferromagnetic and ferromagnetic interactions, leads to suppression of the dynamic aspect of the transition, generating a static mixed-phase-morphology. Understanding and controlling the transition process at this spatial scale is critical to optimizing functional device capabilities.
Taking the pseudobinary C15-Laves phase compound Ce(Fe$_{0.96}$Al$_{0.04}$)$_2$ as a paradigm for studying a ferromagnetic(FM) to antiferromagnetic(AFM) phase transition, we present interesting thermomagnetic history effects in magnetotransport measurements across this FM-AFM transition. We argue that these distinctive hysteretic features can be used to identify the exact nature -first order or second order - of this kind of transition in magnetic systems where electrical transport is strongly correlated with the underlying magnetic order. A comparison is made with the similar FM-AFM transitions observed in Nd and Pr-based manganese compounds with perovskite-type structure.
Surface stress and surface energy are fundamental quantities which characterize the interface between two materials. Although these quantities are identical for interfaces involving only fluids, the Shuttleworth effect demonstrates that this is not the case for most interfaces involving solids, since their surface energies change with strain. Crystalline materials are known to have strain dependent surface energies, but in amorphous materials, such as polymeric glasses and elastomers, the strain dependence is debated due to a dearth of direct measurements. Here, we utilize contact angle measurements on strained glassy and elastomeric solids to address this matter. We show conclusively that interfaces involving polymeric glasses exhibit strain dependent surface energies, and give strong evidence for the absence of such a dependence for incompressible elastomers. The results provide fundamental insight into our understanding of the interfaces of amorphous solids and their interaction with contacting liquids.