Structural diversity in condensed matter: A general characterization of crystals, amorphous solids, and the structures between.

A definition of structural diversity, adapted from the biodiversity literature, is introduced to provide a general characterization of structures of condensed matter. Using the favored local structure lattice model as a testbed, the diversity measure is found to effectively filter extrinsic noise and provide a useful differentiation between crystal and amorphous structures. We identify an interesting class of structures intermediate between crystals and glasses that are characterized by a complex combination of short-range ordering and long-range disorder. We demonstrate how the diversity can be used as an order parameter to organize various scenarios by structure change in response to increasing diversity.

Direct measurement of the structural change associated with amorphous solidification using static scattering of coherent radiation.

In this paper, we demonstrate that the weak temperature dependence of the structure factor of supercooled liquids, a defining feature of the glass transition, is a consequence of the averaging of the scattering intensity due to angular averaging. We show that the speckle at individual wavevectors, calculated from a simulated glass former, exhibits a Debye-Waller factor with a sufficiently large temperature dependence to represent a structural order parameter capable of distinguishing liquid from glass. We also extract from the speckle intensities a quantity proportional to the variance of the local restraint, i.e., a direct experimental measure of the amplitude of structural heterogeneity.

Translation-rotation coupling and the kinematics of non-slip boundary conditions: A rough sphere between two sliding walls.

A non-slip constraint between a particle and a wall is applied at the microscopic level of collision dynamics using the rough sphere model. We analyze the consequences of the translation-rotation coupling of a rough sphere confined between two parallel planar walls and establish that shearing the walls past each other (i) preferentially deposits energy into the rotational degree of freedom and (ii) results in a bounded oscillation of the energy of the confined particle.

Amorphous solidification of a supercooled liquid in the limit of rapid cooling.

We monitor the transformation of a liquid into an amorphous solid in simulations of a glass forming liquid by measuring the variation of a structural order parameter with either changing temperature or potential energy to establish the influence of the cooling rate on amorphous solidification. We show that the latter representation, unlike the former, exhibits no significant dependence on the cooling rate. This independence extends to the limit of instantaneous quenches, which we find can accurately reproduce the solidification observed during slow cooling. We conclude that amorphous solidification is an expression of the topography of the energy landscape and present the relevant topographic measures.

Crystal Growth Rates from Molecular Liquids: The Kinetics of Entropy Loss.

It has been established empirically that the rate of addition of molecules to the crystal during crystal growth from the melt is proportional to exp(-|ΔSfus|/R), where ΔSfus is the entropy of fusion. Here we show that this entropic slowdown arises directly from the separation of the entropy loss and energy loss processes associated with the freezing of the liquid. We present a theoretical treatment of the kinetics based on a model flat energy landscape and derive an explicit expression for the coupling magnitude in terms of the crystal-melt interfacial free energy. The implications of our work for nucleation kinetics are also discussed.

A general structural order parameter for the amorphous solidification of a supercooled liquid.

The persistent problem posed by the glass transition is to develop a general atomic level description of amorphous solidification. The answer proposed in this paper is to measure a configuration's capacity to restrain the motion of the constituent atoms. Here, we show that the instantaneous normal modes can be used to define a measure of atomic restraint that accounts for the difference between fragile and strong liquids and the collective length scale of the supercooled liquid. These results represent a significant simplification of the description of amorphous solidification and provide a powerful systematic treatment of the influence of microscopic factors on the formation of an amorphous solid.

Influence on crystal nucleation of an order-disorder transition among the subcritical clusters.

Studies of nucleation generally focus on the properties of the critical cluster, but the presence of defects within the crystal lattice means that the population of nuclei necessarily evolve through a distribution of precritical clusters with varying degrees of structural disorder on their way to forming a growing stable crystal. To investigate the role precritical clusters play in nucleation, we develop a simple thermodynamic model for crystal nucleation in terms of cluster size and the degree of cluster order that allows us to alter the work of forming the precritical clusters without affecting the properties of the critical cluster. The steady state and transient nucleation behavior of the system are then studied numerically, for different microscopic ordering kinetics. We find that the model exhibits a generic order-disorder transition in the precritical clusters. Independent of the types of ordering kinetics, increasing the accessibility of disordered precritical clusters decreases both the steady state nucleation rate and the nucleation lag time. Furthermore, the interplay between the free-energy surface and the microscopic ordering kinetics leads to three distinct nucleation pathways.

Local symmetry predictors of mechanical stability in glasses.

The mechanical properties of crystals are controlled by the translational symmetry of their structures. But for glasses with a disordered structure, the link between the symmetry of local particle arrangements and stability is not well established. In this contribution, we provide experimental verification that the centrosymmetry of nearest-neighbor polyhedra in a glass strongly correlates with the local mechanical stability. We examine the distribution of local stability and local centrosymmetry in a glass during aging and deformation using microbeam x-ray scattering. These measurements reveal the underlying relationship between particle-level structure and larger-scale behavior and demonstrate that spatially connected, coordinated local transformations to lower symmetry structures are fundamental to these phenomena. While glassy structures lack obvious global symmetry breaking, local structural symmetry is a critical factor in predicting stability.

Deposition control of model glasses with surface-mediated orientational order.

We introduce a minimal model of solid-forming anisotropic molecules that displays, in thermal equilibrium, surface orientational order without bulk orientational order. The model reproduces the nonequilibrium behavior of recent experiments in which a bulk nonequilibrium structure grown by deposition contains regions of orientational order characteristic of the surface equilibrium. This order is deposited, in general, in a nonuniform way because of the emergence of a growth-poisoning mechanism that causes equilibrated surfaces to grow slower than non-equilibrated surfaces. We use evolutionary methods to design oscillatory protocols able to grow nonequilibrium structures with uniform order, demonstrating the potential of protocol design for the fabrication of this class of materials.

Translational-rotational coupling during the scattering of a frictional sphere from a flat surface.

At a macroscopic level, concepts such as "top spin," "back spin," and "rolling" are commonly used to describe the collision of balls and surfaces. Each term refers to an aspect of the coupling of rotational motion during the collision of a spherical particle with a planar surface. In this paper, we explore the mechanisms of energy transfer involving the collision of a rotating sphere and a surface using a model of frictional interactions developed for a granular material. We present explicit analytical treatments for the scattering and derive expressions for two important limiting classes: energy conserving collisions and collisions subject to rapid transverse dissipation.

How real are liquid groundstates? Ultra-fast crystal growth and the susceptibility of energy minima in liquids.

We calculate the degree to which the final structure of the local groundstate in a liquid is a function of the strength of a perturbing potential applied during energy minimization. This structural susceptibility is shown to correlate well with the observed tendency of the liquid adjacent to a crystal interface to exhibit a crystalline groundstate, a feature that has been strongly linked to the observation of ultra-fast crystal growth in pure metals and ionic melts. It is shown that the structural susceptibility increases dramatically as the interaction potential between atoms is softened.

How a supercooled liquid borrows structure from the crystal.

Using computer simulations, we establish that the structure of a supercooled binary atomic liquid mixture consists of common neighbor structures similar to those found in the equilibrium crystal phase, a Laves structure. Despite the large accumulation of the crystal-like structure, we establish that the supercooled liquid represents a true metastable liquid and that liquid can "borrow" the crystal structure without being destabilized. We consider whether this feature might be the origin of all instances of liquids with a strongly favored local structure.

Erratum: Structural Origin of Enhanced Dynamics at the Surface of a Glassy Alloy [Phys. Rev. Lett. 119, 245501 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.245501.

Crystal growth rates and liquid dynamics at the crossover between stable crystal phases.

The crystal growth rates from a binary A50B50 Lennard-Jones liquid are calculated as a function of the variation of the interspecies interaction length σAB. At the crossover in stability between the CsCl and NaCl crystal phase, the growth rate slows down and exhibits a maximum in the activation energy for atomic attachment to the growing crystal. Using assignment theory to determine the size of the transformation displacement, we show that these trends can be explained in terms of the changes in the cage size of the liquid.

The displacement field associated with the freezing of a melt and its role in determining crystal growth kinetics.

The atomic displacements associated with the freezing of metals and salts are calculated by treating crystal growth as an assignment problem through the use of an optimal transport algorithm. Converting these displacements into timescales based on the dynamics of the bulk liquid, we show that we can predict the activation energy for crystal growth rates, including activation energies significantly smaller than those for atomic diffusion in the liquid. The exception to this success, pure metals that freeze into face-centered cubic crystals with little to no activation energy, are discussed. The atomic displacements generated by the assignment algorithm allows us to quantify the key roles of crystal structure and liquid caging length in determining the temperature dependence of crystal growth kinetics.

Formation of Ultrastable Glasses via Precipitation: A Modeling Study.

The precipitation of a glass forming solute from solution is modeled using a lattice model previously introduced to study dissolution kinetics of amorphous materials. The model includes the enhancement of kinetics at the surface of a glass in contact with a plasticizing solvent. We demonstrate that precipitation can produce a glass substantially more stable than that produced by very long time annealing of the bulk glass former. The energy of these ultrastable amorphous precipitates is found to be dominated by residual solvent rather than high energy glass configurations.

Assessing the utility of structure in amorphous materials.

This paper presents a set of general strategies for the analysis of structure in amorphous materials and a general approach to assessing the utility of any selected structural description. Two measures of structure are defined, "diversity" and "utility," and applied to two model glass forming binary atomic alloys, Cu50Zr50 and a Lennard-Jones A80B20 mixture. We show that the change in diversity associated with selecting Voronoi structures with high localization or low energy, while real, is too weak to support claims that specific structures are the prime cause of these local physical properties. In addition, a new structure-free measure of incipient crystal-like organization in mixtures is introduced, suitable for cases where the stable crystal is a compound structure.

The mechanism of the ultrafast crystal growth of pure metals from their melts.

Pure metals can have ultrafast growth rates from their melts, such as a crystal of pure nickel that grows at a rate reaching 70 m s-1. These extraordinary growth rates suggest that metallic crystals might provide the next generation of phase-change materials. The huge crystal growth rates of metals are the consequence of kinetics without activated control, in sharp contrast to the prediction of the 'classic' theory of crystal growth. While the existence of barrierless growth kinetics is now well established in atomic melts, the physical explanation for the absence of an activation barrier to ordering remains unclear. It is something of a paradox that diffusion in the liquid metal is governed by thermal activation while the movement of the same atoms organizing into a crystal is not. Here we use computer simulations of crystallization in pure metals to explicitly resolve the origin of the barrierless growth kinetics.

Composition susceptibility and the role of one, two, and three-body interactions in glass forming alloys: Cu50Zr50 vs Ni50Al50.

In this paper, we compare the composition fluctuations and interaction potentials of a good metallic glass former, Cu50Zr50, and a poor glass former, Ni50Al50. The Bhatia-Thornton correlation functions are calculated. Motivated by the observation of chemical ordering at the NiAl surface, we derive a new property, R^cn(q), corresponding to the linear susceptibility of concentration to a perturbation in density. We present a direct comparison of the potentials for the two model alloys using a 2nd order density expansion, and establish that the one-body energy plays a crucial role in stabilizing the crystal relative to the liquid in both alloys but that the three-body contribution to the heat of fusion is significantly larger in NiAl than CuZr.