Direct Observation of Entropic Stabilization of bcc Crystals Near Melting

Fragility and thermal expansion control crystal melting and the glass transition

Analytical relations for the glass transition temperature, Tg, and the crystal melting temperature, Tm, are developed on the basis of nonaffine lattice dynamics. The proposed relations explain the following: (i) the seemingly universal factor of ≈2/3 difference between the glass transition temperature and the melting temperature of the corresponding crystal, and (ii) the recent empirical discovery that both Tg and Tm are proportional to the liquid fragility m divided by the thermal expansion coefficient α of the solid.

Collective motion and its connection to the energy landscape in 2D soft crystals

We examine the collective motion in computational models of a two-dimensional dusty plasma crystal and a charged colloidal suspension as they approach their respective melting transitions. To unambiguously identify rearrangement events in the crystal, we map the trajectory of configurations from an equilibrium molecular dynamics simulation to the corresponding sequence of configurations of local potential energy minima ("inherent structures"). This inherent structure (IS) trajectory eliminates the ambiguity that arises from localized vibrational motion. We find that the evolution of the IS trajectory in the crystal can be split into comparatively longer-lived ground states and shorter-lived discrete excited states. These discrete excited energy levels are a consequence of discrete numbers of defect clusters in the crystal. We find that the collective rearrangement occurs through different mechanisms: (i) small closed-loop motion in the ground states without the facilitation of defects, and (ii) much larger and complex open-ended particle motions in excited states that are facilitated by clusters of defects. In both cases, clusters of displacing particles can be separated into much smaller groups of replacing particles with a loop-like structure. In contrast to glass-forming liquids, the mass of the rearranging groups grows on heating towards the melting temperature rather than cooling. We find that crystal melting in these systems can be anticipated by the merging of the average time the crystal spends in the ground state with the average time in the excited states.

Evolution of liquid phase during homogenous non-equilibrium melting of Ta at superheating temperature

Homogenous melting at superheating temperature is commonly described by classical nucleation theory (CNT), but the atomic mechanism of the formation and development of critical liquid nuclei is still unclear. Molecular dynamics simulations were conducted to analyze the melting process of Ta. It is found that the process of subcritical liquid clusters evolving into critical liquid nucleus occupies most of the melting time, and merging between neighboring liquid clusters is the main path for subcritical liquid clusters to grow in size. Total melting time is strongly affected by the distribution of formation sites of subcritical liquid clusters, which has been considered random in homogenous melting. This work depicts a clear picture of the formation and development of liquid phase during the homogeneous melting process at superheating temperature and suggests an internal factor of melting mechanism.

Induced phase transformation in ionizable colloidal nanoparticles

Acid-base equilibria directly influence the functionality and behavior of particles in a system. Due to the ionizing effects of acid-base functional groups, particles will undergo charge exchange. The degree of ionization and their intermolecular and electrostatic interactions are controlled by varying the pH and salt concentration of the solution in a system. Although the pH can be tuned in experiments, it is hard to model this effect using simulations or theoretical approaches. This is due to the difficulty in treating charge regulation and capturing the cooperative effects in a colloidal suspension with Coulombic interaction. In this work, we analyze a suspension of ionizable colloidal particles via molecular dynamics (MD) simulations, along with Monte Carlo simulations for charge regulation (MC-CR) and derive a phase diagram of the system as a function of pH. It is observed that as pH increases, particles functionalized with acid groups change their arrangement from face-centered cubic (FCC) packing to a disordered state. We attribute these transitions to an increase in the degree of charge polydispersity arising from an increase in pH. Our work shows that charge regulation leads to amorphous solids in colloids when the mean nanoparticle charge is sufficiently high.

The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard-Jones systems

Monolayer and two-dimensional (2D) systems exhibit rich phase behavior, compared with 3D systems, in particular, due to the hexatic phase playing a central role in melting scenarios. The attraction range is known to affect critical gas–liquid behavior (liquid–liquid in protein and colloidal systems), but the effect of attraction on melting in 2D systems remains unstudied systematically. Here, we have revealed how the attraction range affects the phase diagrams and melting scenarios in a 2D system. Using molecular dynamics simulations, we have considered the generalized Lennard-Jones system with a fixed repulsion branch and different power indices of attraction from long-range dipolar to short-range sticky-sphere-like. A drop in the attraction range has been found to reduce the temperature of the gas–liquid critical point, bringing it closer to the gas–liquid–solid triple point. At high temperatures, attraction does not affect the melting scenario that proceeds through the cascade of solid–hexatic (Berezinskii–Kosterlitz–Thouless) and hexatic–liquid (first-order) phase transitions. In the case of dipolar attraction, we have observed two triple points inherent in a 2D system: hexatic–liquid–gas and crystal–hexatic–gas, the temperature of the crystal–hexatic–gas triple point is below the hexatic–liquid–gas triple point. This observation may have far-reaching consequences for future studies, since phase diagrams determine possible routes of self-assembly in molecular, protein, and colloidal systems, whereas the attraction range can be adjusted with complex solvents and external electric or magnetic fields. The results obtained may be widely used in condensed matter, chemical physics, materials science, and soft matter.

Reentrant transitions in a mixture of small and big particles interacting via soft repulsive potential

We report an observation of a temperature-controlled reentrant transition in simulations of mixtures of small and big particles interacting via a soft repulsive potential in two dimensions. As temperature increases, the system passes from a fluid mixture, to a crystal of big particles in a fluid of small particles, and back to a fluid mixture. Solidification is driven by entropy gain of small particles which overcomes the free-energy cost of confining big ones. Melting results from enhanced interpenetration of particles at high temperature which reduces the entropic forces that stabilize the crystal.

Microscopic and Macroscopic Fragmentation Characteristics under Hypervelocity Impact Based on MD and SPH Method

This work investigates the difference in the fragmentation characteristics between the microscopic and macroscopic scales under hypervelocity impact, with the simulations of Molecular Dynamics (MD) and Smoothed Particle Hydrodynamics (SPH) method. Under low shock intensity, the model at microscopic scale exhibits good penetration resistance due to the constraint of strength and surface tension. The bullet is finally embedded into the target, rather than forming a typical debris cloud at macroscopic scale. Under high shock intensity, the occurrence of unloading melting of the sample reduces the strength of the material. The material at the microscopic scale has also been completely penetrated. However, the width of the ejecta veil and external bubble of the debris cloud are narrower. In addition, the residual velocity of bullet, crater diameter and expansion angle of the debris cloud at microscopic scale are all smaller than those at macroscopic scale, especially for low-velocity conditions. The difference can be as much as two times. These characteristics indicate that the degree of conversion of kinetic energy to internal energy at the microscopic scale is much higher than that of the macroscopic results. Furthermore, the MD simulation method can further provide details of the physical characteristics at the micro-scale. As the shock intensity increases, the local melting phenomenon becomes more pronounced, accompanied by a decrease in dislocation atoms and a corresponding increase in disordered atoms. In addition, the fraction of disordered atoms is found to increase exponentially with the increasing incident kinetic energy.

2D colloids in rotating electric fields: A laboratory of strong tunable three-body interactions

Many-body forces play a prominent role in structure and dynamics of matter, but their role is not well understood in many cases due to experimental challenges. Here, we demonstrate that a novel experimental system based on rotating electric fields can be utilised to deliver unprecedented degree of control over many-body interactions between colloidal silica particles in water. We further show that we can decompose interparticle interactions explicitly into the leading terms and study their specific effects on phase behaviour. We found that three-body interactions exert critical influence over the phase diagram domain boundaries, including liquid-gas binodal, critical and triple points. Phase transitions are shown to be reversible and fully controlled by the magnitude of external rotating electric field governing the tunable interactions. Our results demonstrate that colloidal systems in rotating electric fields are a unique laboratory to study the role of many-body interactions in physics of phase transitions and in applications, such as self-assembly, offering exciting opportunities for studying generic phenomena inherent to liquids and solids, from atomic to protein and colloidal systems.

Mean-field model of melting in superheated crystals based on a single experimentally measurable order parameter

Melting is one of the most studied phase transitions important for atomic, molecular, colloidal, and protein systems. However, there is currently no microscopic experimentally accessible criteria that can be used to reliably track a system evolution across the transition, while providing insights into melting nucleation and melting front evolution. To address this, we developed a theoretical mean-field framework with the normalised mean-square displacement between particles in neighbouring Voronoi cells serving as the local order parameter, measurable experimentally. We tested the framework in a number of colloidal and in silico particle-resolved experiments against systems with significantly different (Brownian and Newtonian) dynamic regimes and found that it provides excellent description of system evolution across melting point. This new approach suggests a broad scope for application in diverse areas of science from materials through to biology and beyond. Consequently, the results of this work provide a new guidance for nucleation theory of melting and are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Revealing thermally-activated nucleation pathways of diffusionless solid-to-solid transition

Solid-to-solid transitions usually occur via athermal nucleation pathways on pre-existing defects due to immense strain energy. However, the extent to which athermal nucleation persists under low strain energy comparable to the interface energy, and whether thermally-activated nucleation is still possible are mostly unknown. To address these questions, the microscopic observation of the transformation dynamics is a prerequisite. Using a charged colloidal system that allows the triggering of an fcc-to-bcc transition while enabling in-situ single-particle-level observation, we experimentally find both athermal and thermally-activated pathways controlled by the softness of the parent crystal. In particular, we reveal three new transition pathways: ingrain homogeneous nucleation driven by spontaneous dislocation generation, heterogeneous nucleation assisted by premelting grain boundaries, and wall-assisted growth. Our findings reveal the physical principles behind the system-dependent pathway selection and shed light on the control of solid-to-solid transitions through the parent phase's softness and defect landscape.

Stiffness of the interface between a colloidal body-centered cubic crystal and its liquid

Equilibrium interfaces were established between body-centered cubic (BCC) crystals and their liquid using charged colloidal particles in an electric bottle. By measuring a time series of interfacial positions and computing the average power spectrum, their interfacial stiffness was determined according to the capillary fluctuation method. For the (100) and the (114) interfaces, the stiffnesses were 0.15 and 0.18 [Formula: see text] (σ: particle diameter), respectively, and were isotropic in the plane of the interface. For comparison, similar charged colloids were used to create an interface between a face-centered cubic (FCC) crystal and its liquid. Its stiffness was significantly larger: 0.26 [Formula: see text] This result gives experimental support to the explanations offered for the preferential nucleation of BCC over FCC in metallic alloys.

Colloids in rotating electric and magnetic fields: designing tunable interactions with spatial field hodographs

Opening a way to designing tunable interactions between colloidal particles in rotating electric and magnetic fields provides rich opportunities both for fundamental studies of phase transitions and engineering of soft materials. Spatial hodographs, showing the distribution of the field magnitude and orientation, allow the adjustment of interactions and can be an extremely potent tool for prospective experiments, but remain unstudied systematically. Here, we calculate the tunable interactions between spherical particles in rhodonea, conical, cylindrical, and ellipsoidal field hodographs, as the most experimentally important cases. We discovered that spatial hodographs are reduced to each other, providing a plethora of interactions, e.g., repulsive, attractive, barrier-like, and double-scale repulsive ones. Complementing the "magic" conical angle, the "magic" compression and ellipticity of cylindrical and ellipsoidal hodographs are introduced. In the "magic" hodographs, the interactions become spatially isotropic and attain dispersion-force-like asymptotic (the same for pairwise and many-body energies), being attractive or repulsive, if the particle permittivity is larger or smaller than that of the solvent. With the diagrammatic method and numerical calculations, we obtained physically meaningful fits to the many-body tunable potentials for silica (iron oxide) particles in deionised water in the rotating electric (magnetic) fields. Our results provide essential guidance for future experiments and simulations of colloidal liquids, crystals, gels, and glasses, important for a broad range of problems in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Relaxation and vibrational properties in metal alloys and other disordered systems

The relaxation dynamics and the vibrational spectra of amorphous solids, such as metal alloys, have been intensely investigated as well separated topics in the past. The aim of this review is to summarize recent results in both these areas in an attempt to establish, or unveil, deeper connections between the two phenomena of relaxation and vibration. Theoretical progress in the area of slow relaxation dynamics of liquid and glassy systems and in the area of vibrational spectra of glasses and liquids is reviewed. After laying down a generic modelling framework to connect vibration and relaxation, the physics of metal alloys is considered where the emergence of power-law exponents has been identified both in the vibrational density of states (VDOS) as well as in density correlations. Also, theoretical frameworks which connect the VDOS to the relaxation behaviour and mechanical viscoelastic response in metallic glasses are reviewed. The same generic interpretative framework is then applied to the case of molecular glass formers where the emergence of stretched-exponential relaxation in dielectric relaxation can be put in quantitative relation with the VDOS by means of memory-function approaches. Further connections between relaxation and vibration are provided by the study of phonon linewidths in liquids and glasses, where a natural starting point is given by hydrodynamic theories. Finally, an agenda of outstanding issues including the appearance of compressed exponential relaxation in the intermediate scattering function of experimental and simulated systems (metal alloys, colloidal gels, jammed packings) is presented in light of available (or yet to be developed) mathematical models, and compared to non-exponential behaviour measured with macroscopic means such as mechanical spectroscopy/rheology.

Electroplasticization of Liquid Crystal Polymer Networks

Shape-shifting liquid crystal networks (LCNs) can transform their morphology and properties in response to external stimuli. These active and adaptive polymer materials can have impact in a diversity of fields, including haptic displays, energy harvesting, biomedicine, and soft robotics. Electrically driven transformations in LCN coatings are particularly promising for application in electronic devices, in which electrodes are easily integrated and allow for patterning of the functional response. The morphing of these coatings, which are glassy in the absence of an electric field, relies on a complex interplay between polymer viscoelasticity, liquid crystal order, and electric field properties. Morphological transformations require the material to undergo a glass transition that plasticizes the polymer sufficiently to enable volumetric and shape changes. Understanding how an alternating current can plasticize very stiff, densely cross-linked networks remains an unresolved challenge. Here, we use a nanoscale strain detection method to elucidate this electric-field-induced devitrification of LCNs. We find how a high-frequency alternating field gives rise to pronounced nanomechanical changes at a critical frequency, which signals the electrical glass transition. Across this transition, collective motion of the liquid crystal molecules causes the network to yield from within, leading to network weakening and subsequent nonlinear expansion. These results unambiguously prove the existence of electroplasticization. Fine-tuning the induced emergence of plasticity will not only enhance the surface functionality but also enable more efficient conversion of electrical energy into mechanical work.

Experimental validation of interpolation method for pair correlations in model crystals

Accurate analysis of pair correlations in condensed matter allows us to establish relations between structures and thermodynamic properties and, thus, is of high importance for a wide range of systems, from solids to colloidal suspensions. Recently, the interpolation method (IM) that describes satisfactorily the shape of pair correlation peaks at short and at long distances has been elaborated theoretically and using molecular dynamics simulations, but it has not been verified experimentally as yet. Here, we test the IM by particle-resolved studies with colloidal suspensions and with complex (dusty) plasmas and demonstrate that, owing to its high accuracy, the IM can be used to experimentally measure parameters that describe interaction between particles in these systems. We used three- and two-dimensional colloidal crystals and monolayer complex (dusty) plasma crystals to explore suitability of the IM in systems with soft to hard-sphere-like repulsion between particles. In addition to the systems with pairwise interactions, if many-body interactions can be mapped to the pairwise ones with some effective (e.g., density-dependent) parameters, the IM could be used to obtain these parameters. The results reliably show that the IM can be effectively used for analysis of pair correlations and interactions in a wide variety of systems and therefore is of broad interest in condensed matter, complex plasma, chemical physics, physical chemistry, materials science, and soft matter.

Emergence and percolation of rigid domains during the colloidal glass transition

Using video microscopy, we measure local spatial constraints in disordered binary colloidal samples, ranging from dilute fluids to jammed glasses, and probe their spatial and temporal correlations to local dynamics during the glass transition. We observe the emergence of significant correlations between constraints and local dynamics within the Lindemann criterion, which coincides with the onset of glassy dynamics in supercooled liquids. Rigid domains in fluids are identified based on local constraints and demonstrate a percolation transition near the glass transition, accompanied by the emergence of dynamical heterogeneities. Our results show that spatial constraint instead of the geometry of amorphous structures is the key that connects the complex spatial-temporal correlations in disordered materials.

Melting of bcc crystal Ta without the Lindemann criterion

Understanding of melting is deeply rooted in the Lindemann criterion which predicts that the transition occurs when the mean vibrational atomic displacement reaches a universal value. The criterion also finds its way in atomic description of kinetics of various structural phase transitions involving liquid and amorphous phases. Here we show using atomistic modeling in bcc crystal tantalum that neither the universal displacement exists nor melting occurs at the anticipated value from the Lindemann criterion. Instead, before and at melting a series of strongly correlated atomic diffusional motions are set in with the atomic displacement far more complicated than that predicted by Lindemann based on independent atomic vibrations. The displacement leads to formation of new extended atomic configurations composed of lattice chains and loops of Ta atoms still residing on the crystal lattice. It is the proliferation of these lattice chains that leads to melting.

Two-dimensional crystals of star polymers: a tale of tails

The formation of non-hexagonal crystalline structures by the organisation of colloidal nanoparticles often involves the use of complex particles with anisotropic shape or interactions or the imposition of non-uniform external fields. Here we explore how unusual symmetries can be created using experimentally realistic particles that interact through isotropic and purely repulsive potentials. In particular, we use simulations to explore the phase behavior of two-dimensional systems of star polymers. We uncover how the tail of the pair potential has a large role in dictating the phase behavior. Star polymers interacting in the far field with a Gaussian potential only form hexagonal phases, while an exponential tail gives rise to stable primitive oblique and honeycomb lattices. We identify the ratio in strength between long and short range interactions and the nature of the transition between these regimes as crucial parameters to predict when non-hexagonal crystals of star polymers can be stable. This leads to experimental design rules for creating star polymers which should exhibit unusual lattice formation.

Transformations of body-centered cubic crystals composed of hard or soft spheres to liquids or face-centered cubic crystals

The monodispersed hard-sphere system is one of the simplest models for the study of phase transitions. Despite intensive studies of crystallization and melting of hard-sphere face-centered cubic (FCC) crystals, the phase transformations of hard-sphere body-centered cubic (BCC) crystals have not been explored because hard spheres cannot form a stable BCC lattice. In fact, unstable BCC hard-sphere crystals and their related phase transformations can be experimentally achieved. Here, we measured the kinetics of the melting and solid-solid transformations of BCC hard-sphere crystals at various volume fractions via molecular dynamics simulations. When the volume fraction ϕ < 0.494, the system melts catastrophically. At ϕ > 0.545, the BCC crystal transforms to a metastable polycrystal consisting of FCC and hexagonal close-packed (HCP) domains, which is different from those crystallized from supercooled liquids, and then slowly equilibrates toward the FCC crystal. At 0.494 < ϕ < 0.545, the BCC crystal transforms to an intermediate-order metastable state consisting of BCC and non-crystal particles without FCC and HCP symmetries and then equilibrates toward the coexistence of the FCC crystal and liquid. We further studied the melting and BCC-FCC transitions of crystals composed of soft spheres with potential u(r) = ϵ(r/σ)^-n . The unstable BCC crystals at n = 12, 9, 8 exhibit similar melting and BCC-FCC transitions as hard-sphere BCC crystals, while the metastable BCC crystals at n = 5, 6, 7 melt quickly at low densities but take very long time for the BCC-FCC transition at high densities. We also estimate the BCC-FCC interfacial energy and critical nucleus size. These results cast light on the melting and solid-solid transformations of atomic BCC crystals, which exist widely in nature.

Structurally Flexible Oxocarbenium/Borohydride Ion Pair: Dynamics of Hydride Transfer on the Background of Conformational Roaming

We apply Born-Oppenheimer molecular dynamics to the practically significant [dioxane-H⁽⁺⁾-acetone][(C₆F₅)₃B-H^(-)] and [Et₂O-H⁽⁺⁾-OCPr₂][(C₆F₅)₃B-H^(-)] ion pair intermediates. Dynamics of hydride transfer in cation/anion ion pair takes place on the background of large-amplitude configurational changes. Geometry of oxocarbenium/borohydride ion pairs is flexible, meaning that we uncover significant actual structural disorder at a finite temperature. Therefore, although the starting structure can be fairly close to the configurational area of the hydride transfer transition state (TS) and despite a low potential energy barrier (ca. 1.5 kcal/mol, according to the literature), already at T ≈ 325 K the system can remain ignorant of the TS region and move round and about ("roam") in the configurational space for a period of time in the range between 10 and 100 ps. This indicates structural flexibility of oxocarbenium/borohydride ion pair on apparently a flat potential energy "landscape" of cation/anion interaction, and this has not been taken into consideration by the free energy estimations in static considerations made thus far. The difference between the dynamics-based representation of the system versus the static representation amounts to the difference between quasi-bimolecular versus unimolecular descriptions of the hydride transfer step.

Doping colloidal bcc crystals - interstitial solids and meta-stable clusters

The addition of a small amount of dopant impurities to crystals is a common method to tune the properties of materials. Usually the doping grade is restricted by the low solubility of the dopants; increasing the doping concentration beyond this solubility limit leads to supersaturated solutions in which dopant clusters dominate the material properties, often leading to deterioration of strength and performance. Descriptions of doped solids often assume that thermal excitations of the on average perfect matrix are small. However, especially for bcc crystals close to their melting point it has recently become clear that the effects of thermal disorder are strong. Here we study the doping of weak bcc crystals of charged colloids via Brownian dynamics simulations. We find a complex phase diagram upon varying the dopant concentration. At low dopant concentrations we find an interstitial solid solution. As we increase the amount of dopants a complex meta-stable liquid-in-solid cluster phase emerges. Ultimately this phase becomes meta-stable with respect to macroscopic crystal-crystal coexistence. These results illustrate the complex behaviour that emerges when thermal excitations of the matrix drive impure crystals to a weak state.

Triple Junction at the Triple Point Resolved on the Individual Particle Level

At the triple point of a repulsive screened Coulomb system, a fcc crystal, a bcc crystal, and a fluid phase coexist. At their intersection, these three phases form a liquid groove, the triple junction. Using confocal microscopy, we resolve the triple junction on a single-particle level in a model system of charged PMMA colloids in a nonpolar solvent. The groove is found to be extremely deep and the incommensurate solid-solid interface to be very broad. Thermal fluctuations hence appear to dominate the solid-solid interface. This indicates a very low interfacial energy. The fcc-bcc interfacial energy is quantitatively determined based on Young's equation and, indeed, it is only about 1.3 times higher than the fcc-fluid interfacial energy close to the triple point.