Unified analysis of topological defects in 2D systems of active and passive disks

We provide a comprehensive quantitative analysis of localized and extended topological defects in the steady state of 2D passive and active repulsive Brownian disk systems. We show that, both in and out-of-equilibrium, the passage from the solid to the hexatic is driven by the unbinding of dislocations, in quantitative agreement with the KTHNY singularity. Instead, extended clusters of defects largely dominate below the solid-hexatic critical line. The latter percolate in the liquid phase very close to the hexatic-liquid transition, both for continuous and discontinuous transitions, in the homogeneous liquid regime. At critical percolation the clusters of defects are fractal with statistical and geometric properties that are independent of the activity and compatible with the universality class of uncorrelated critical percolation. We also characterize the spatial organization of point-like defects and we show that the disclinations are not free, but rather always very near more complex defect structures. At high activity, the bulk of the dense phase generated by Motility-Induced Phase Separation is characterized by a density of point-like defects, and statistics and morphology of defect clusters, set by the amount of activity and not the packing fraction. Hexatic domains within the dense phase are separated by grain-boundaries along which a finite network of topological defects resides, interrupted by gas bubbles in cavitation. This structure is dynamic in the sense that the defect network allows for an unzipping mechanism that leaves free space for gas bubbles to appear, close, and even be released into the dilute phase.

Peritectic solidification of Cu-Sn alloys

Frédéric Kohler

Many commercially important alloys such as Fe-C, Fe-Ni, Cu-Zn, Cu-Sn and Ti-Al exhibit peritectic transitions on solidification. In the two-solid phase region of peritectic metallic systems, a wide spectrum of microstructures has been revealed during directional solidification experiments at low growth rates, where both α- and β-phases would grow independently as planar fronts [1, 2, 12–20]: discrete bands, islands, simultaneous growth of the α- and β-phases in the form of oriented lamellae or fibers and continuous oscillatory tree-like microstructures in highly convective peritectic systems [3, 21, 22]. Recently, Vandyoussefi et al. [27] and Dobler et al. [16] have done extensive solidification experiments on Fe-Ni alloys in the corresponding two-solid phase region. Depending on the growth conditions and local composition, a lamellar eutectic-like structure was observed. Despite recent works, the peritectic solidification at low growth rate is not fully understood. Additionally, coupled growth was observed only for peritectic systems for which the solidification interval of the primary phase ΔΤ 0α is fairly small and with negligible convection; but is it also possible for peritectic alloys with fairly large ΔΤ 0α such as Cu-Sn? If so, what would be the effect of convection? And finally, is the coupled growth front really isothermal? In the present contribution, the peritectic Cu-Sn system has been chosen because of its remarkable properties and technological importance. Indeed, two essential features distinguish Cu-Sn alloys from other peritectic systems: The equilibrium solidification interval of the a-phase decreases with the tin concentration in the hypoperitectic composition range. Additionally, the equilibrium solidification interval of the primary phase is about 25 times larger in the Cu-Sn system than in the Fe-Ni peritectic system. Since only few studies have been made on the detailed solidification of tin bronze alloys, the first goal of this study was to carry out thermal analyses in order to investigate precisely the solidification of Cu-Sn alloys and to measure temperatures of solid-state phase transformations. Therefore, an SPTA assembly has been built and successfully calibrated. Additionally, a heat flow model was developed in this work and coupled with a Cu-Sn thermodynamic database to treat solidification-dependent latent heat. Single pan thermal analyses on three Cu-Sn alloy compositions revealed that the corresponding phase diagram recently re-investigated in Liu et al. review [28] is the most reliable. Directional solidification experiments on Cu-Sn alloys of various compositions have been conducted at different velocities in a high gradient Bridgman furnace. In this context, the set-up already used by Dobler [14] has been modified in order to reduce the size of the samples and, accordingly, natural convection and the associated macrosegregation. During each solidification run, two different geometries were thus tested (3 mm diameter cylinder and 4/6 mm tube), allowing the observation of convection effects on solidifying microstructures. An essential outcome of this project is that α+β lamellar structures have been observed in both sample geometries, even when Vp is above the critical velocity for the α planar front growth, i.e., the α-phase grew with a cellular morphology. With the Cu-Sn phase diagram used in the present work and for positions close to the quenched interface, concentration profiles measured across the lamellar structures revealed that the corresponding operating temperature Τ*(x) seems to be non-isothermal, in contradiction with previous experimental observations in Fe-Ni peritectic alloys [14–16]. But, since the Cu-Sn phase diagram is not assessed accurately, Τ*(x) is still subject to large variations (±10°C). On the other hand, the peritectic transformation after solidification has been evidenced and modifies the compositions and fractions of phases. Additionally, local concentration showed that a partial banding mechanism and an unstable lateral propagation of both solid phases were responsible for the formation of lamellar structures. Various geometrical arrangements were revealed on transverse cuts of lamellar structures: straight α- and β-lamellae, labyrinth-like microstructures, disordered arrays of rods of one phase in the matrix of the other phase and uniform regions of β-phase. The dynamic evolution of lamellar structures was attributed to growth competition mechanisms and instabilities between phases originated from the same nuclei. Finally, it should be noted that the Kurdjumov-Sachs relationship was observed between the primary and the peritectic phases on both the straight lamellae and labyrinth-like microstructure. Finally, all lamellar structures ended by the termination of α-lamellae and the subsequent growth of a β planar front. In this context, the α-lamellae of lamellar structures observed in the 4/6 mm tube exhibited in all cases a "hammer-like" morphology before being overgrown by the peritectic phase. Careful investigations of this morphology revealed that it resulted effectively from growth competition mechanisms, which remain to be fully understood. In a simulated geometry corresponding to the 4/6 mm tube of Cu-Sn samples, 3D macrosegregation modeling revealed that a nearly helical convection pattern existed in the liquid phase ahead of a moving planar α-liquid interface. And between each plume, the fluid flow was mostly oriented parallel to the solid-liquid interface. As a consequence, the lateral propagation of the α- and β-phases during the 3D growth competition was surely affected by these convective motions. Finally, natural convection and the associated solute enrichment were assumed to be responsible for the destabilization of lamellar structures and the subsequent end of α-lamellae. The multi-phase field computations emphasized that the stability of the triple junction between α-, β- and liquid phases is function of the initial alloy concentration C0, of the lamellar spacing λ and of the thermal gradient Gl. In a near future, directional solidification experiments are planned to be conducted onboard of the International Space Station. Then, the obtained peritectic microstructures will have to be compared with the microstructures observed in the present work in order to assess more precisely the effect of natural convection on the formation of lamellar structures.

EPFL2008

Towards the Glass Transition in Vibrated Granular Matter

Alessandro Luigi Sellerio

Granular materials are large sets of macroscopic particles that interact solely via contact forces. The static behavior depends on the contact network and on the surface friction forces between grains; when they are set in motion (typically by vibrations) their dynamics is dominated by inelastic collisions. For these reasons granular media show an extremely rich phenomenology, ranging from fluid-like properties (if strongly vibrated), to "jamming", glassy, behavior (if weakly vibrated), to aging and hysteretical phenomena observed when they become trapped in frozen, amorphous states. The objective of this work is to study these states and transitions, and to characterize the analogies found between the dynamic behavior of vibrated granular media and the glass transition observed in thermal glass-formers. These analogies justify the interest in granular materials, because granular media can be seen as simplified model systems useful in the study of out of equilibrium thermodynamics, and, in general, to the larger framework known as "complexity". The granular materials considered here are composed of spheric, polished glass spheres. Since the surface state plays an important role in the grain-grain interaction, some measurements were also performed with acid etched beads, having different surface roughness. The samples are vertically vibrated to achieve vibrofluidization. Different kinds of vibration are used, to highlight different properties of the system. We first consider the transition between the fluid and the subcooled glassy phase, using different experimental techniques. The most important one is a torsion oscillator, that interacts with the granular media via immersed probes. The torsion oscillator can be used in forced mode. A torque is applied on the probe, and we measure the mechanical response function (complex susceptibility). In general, a relaxation is found and it is interpreted as the signature of the irreversible energy loss (damping) in granular collisions. This relaxation has an intrinsic time scale, and systematic analysis of it shows that a clear parallel can be traced to the behavior of "strong" glasses. In particular, it is found that (i) the relaxation time is a function of a unified control parameter, proportional to the square root of the average vibration, and phenomenologically equivalent to an effective temperature; (ii) the functional form with which the relaxation times approach the final "frozen" state has an Arrhenius, or Vögel-Fulcher-Tamman (VFT) behavior. The same torsion oscillator is employed in free mode. In this case, no external torque is applied, and the probe moves adapting its position under the effect of the continuous rearrangements in the sample. The system is studied by computing the power spectral density of the (angular position) time series. The resulting spectra represent a "configurational noise" as the system randomly hops from one configuration to the following. This allows to define, using a completely different approach, the same intrinsic time scale observed in forced mode measurements. The comparison of the two techniques allows to obtain a more complete and detailed picture of the dynamics in the jamming region. From this comparison, it was inferred that the system is also influenced by an effective vibration frequency, and that the relaxation time has indeed a non-Arrhenius behavior as a function of a control parameter defined as as = √ Γ/ωs. A model was developed combining rheological observations to a statistic approach describing extremal phenomena. This model justifies the appearance of both the control parameter and the VFT evolution of the relaxation. Furthermore, the model is predictive and exposes the effect of a few other rheologic properties of granular system. The effect of surface roughness are considered, showing that the static and dynamic surface friction coefficients are well described by the model. A second relevant part of this work is devoted to an explicit verification that macroscopic probes act as Brownian objects. This fact is often used to interpret experimental data (also in the present work) and to propose theoretical model. However, no explicit evidence has ever been discussed. This is hard to do, using a constrained system such as the torsion oscillator, because the restoring coefficient influences the dynamics of diffusion. To overcome the problem we built a different apparatus, called "Brownian motor", where the probes are mounted on ball bearings, so that they are free to turn without constraint. The properties of the time series of the position of the free turning probe and of the torsionally constrained oscillator can finally be analyzed and compared with simple simulations. The data show an overall diffusion-like behavior, that is influenced by the presence of constraints. Using fractal analysis we estimate the diffusion, or Hurst exponent. This allows to verify that a "macroscopic" object (the probe) immersed in the "microscopic" granular medium indeed behaves as a Brownian object, and that its dynamics can be studied in detail, showing that it undergoes anomalous diffusion. This work is concluded with a discussion on a few possible developments. The most promising idea is a novel approach to the study of the geometrical properties of the contact network of granular assemblies, that is responsible for many of the properties of the granular sample. By using Magnetic Resonance Imaging, the static 3-D structure of granular media can be reconstructed with unprecedented accuracy, resolution and ease of reproducibility. From the spatial information we can extract all the properties of static granular media: the compaction factor, the grain-grain correlation function, the free volume and other observables. Systematic studies could allow experimental confirmations of the many theoretical models that have been proposed in the last years and that still lack a thorough comparison with experiments. This idea does not conclude the perspectives of this work, that are vast and intriguing. A few promising subjects are reviewed more into detail in the corresponding Perspective section. To name a few we cite: measurements of induced aging in non-vibrated samples, the Brownian motor, stick and slip phenomena and their comparison with earthquakes.

EPFL2012

Spatio-temporal observation of dynamical structures in order-disorder phenomena and phase transitions via Ultrafast Electron Diffraction

Francesco Pennacchio

The development of ultrafast time-resolved techniques in the last decades allowed the direct observation of out-of-equilibrium transient states and dynamical processes up to then hidden in many different fields, ranging from chemistry to solid state physics and biology. Amongst them, Ultrafast Electron Diffraction (UED) allows the retrieval of direct information on the structural dynamics of solids, surfaces, nanostructures and molecular crystals with femtosecond (10^-15 s) and atomic (Ã…, 10^-10 m) temporal and spatial resolution. The UED setup implemented at EPFL is characterised by 30 keV, 20 kHz pulses containing up to 105 electrons each and can work in both transmission and reflection geometry. A sub-500 fs time resolution in transmission geometry is achieved by means of a radio frequency compression cavity for electrons. This time resolution, combined with the high transverse coherence of our electrons, allowed the observation of order-disorder phenomena in 2D-supracrystals of functionalised gold nanoparticles. The insurgence of ligand-dependent photo- mechanical stiffness phenomena was observed and characterised in the aforementioned systems. In reflection geometry, the time resolution suffered severe limitations - especially when probing mm2-sized samples - due to the velocity mismatch between the pump and the probe beam. To overcome this limitation, an optimal optical front tilt scheme for the pump pulse was designed, implemented and characterised, thus disclosing a sub-500 fs temporal resolution also in reflection geometry. The newly achieved time resolution allowed the direct visualisa- tion of ultrafast structural dynamics in two systems of current interest: graphite and magnetite. In graphite, the selective excitation via electron-phonon coupling of a subset of phonon modes called Strongly Coupled Optical Phonons - with a characteristic timescale of ~ 500 fs - was experimentally resolved. In magnetite, the photoinduction of the Verwey phase transition was achieved, unveiling phase segregation intermediate states during the transformation and disclosing structural differences between the photoinduced and the thermal phase transition mechanism.

EPFL2018