The microscopic pathway to crystallization in supercooled liquids

Despite its fundamental and technological importance, a microscopic understanding of the crystallization process is still elusive. By computer simulations of the hard-sphere model we reveal the mechanism by which thermal fluctuations drive the transition from the supercooled liquid state to the crystal state. In particular we show that fluctuations in bond orientational order trigger the nucleation process, contrary to the common belief that the transition is initiated by density fluctuations. Moreover, the analysis of bond orientational fluctuations shows that these not only act as seeds of the nucleation process, but also i) determine the particular polymorph which is to be nucleated from them and ii) at high density favour the formation of fivefold structures which can frustrate the formation of crystals. These results can shed new light on our understanding of the relationship between crystallization and vitrification.Comment: to appear in "Scientific Reports

Assessing the role of static lengthscales behind glassy dynamics in polydisperse hard disks

The possible role of growing static order in the dynamical slowing down towards the glass transition has recently attracted considerable attention. On the basis of random first-order transition (RFOT) theory, a new method to measure the static correlation length of amorphous order, called "point-to-set (PTS)" length, has been proposed, and used to show that the dynamic length grows much faster than the static length. Here we study the nature of the PTS length, using a polydisperse hard disk system, which is a model that is known to exhibit a growing hexatic order upon densification. We show that the PTS correlation length is decoupled from the steeper increase of the correlation length of hexatic order, while closely mirroring the decay length of two-body density correlations. Our results thus provide a clear example that other forms of order can play an important role in the slowing down of the dynamics, casting a serious doubt on the order agnostic nature of the PTS length and its relevance to slow dynamics, provided that a polydisperse hard disk system is a typical glass former

Understanding water's anomalies with locally favored structures

Water is a complex structured liquid of hydrogen-bonded molecules that displays a surprising array of unusual properties, also known as water anomalies, the most famous being the density maximum at about $4^\circ$C. The origin of these anomalies is still a matter of debate, and so far a quantitative description of water's phase behavior starting from the molecular arrangements is still missing. Here we provide a simple physical description from microscopic data obtained through computer simulations. We introduce a novel structural order parameter, which quantifies the degree of translational order of the second shell, and show that this parameter alone, which measures the amount of locally favored structures, accurately characterizes the state of water. A two-state modeling of these microscopic structures is used to describe the behavior of liquid water over a wide region of the phase diagram, correctly identifying the density and compressibility anomalies, and being compatible with the existence of a second critical point in the deeply supercooled region. Furthermore, we reveal that locally favored structures in water not only have translational order in the second shell, but also contain five-membered rings of hydrogen-bonded molecules. This suggests their mixed character: the former helps crystallization, whereas the latter causes frustration against crystallization.Comment: 10 pages, 5 figure

Water-like anomalies as a function of tetrahedrality

Tetrahedral interactions describe the behaviour of the most abundant and technologically important materials on Earth, such as water, silicon, carbon, germanium, and countless others. Despite their differences, these materials share unique common physical behaviours, such as liquid anomalies, open crystalline structures, and extremely poor glass-forming ability at ambient pressure. To reveal the physical origin of these anomalies and their link to the shape of the phase diagram, we systematically study the properties of the Stillinger-Weber potential as a function of the strength of the tetrahedral interaction $\lambda$. We uncover a new transition to a re-entrant spinodal line at low values of $\lambda$, accompanied with a change in the dynamical behaviour, from Non-Arrhenius to Arrhenius. We then show that a two-state model can provide a comprehensive understanding on how the thermodynamic and dynamic anomalies of this important class of materials depend on the strength of the tetrahedral interaction. Our work establishes a deep link between the shape of phase diagram and the thermodynamic and dynamic properties through local structural ordering in liquids, and hints at why water is so special among all substances

Common mechanism of thermodynamic and mechanical origin for ageing and crystallisation of glasses

The glassy state is known to undergo slow structural relaxation, where the system progressively explores lower free-energy minima which are either amorphous (ageing) or crystalline (devitrification). Recently, there is growing interest in the unusual intermittent collective displacements of a large number of particles known as "avalanches". However, their structural origin and dynamics are yet to be fully addressed. Here, we study hard-sphere glasses which either crystallise or age depending on the degree of size polydispersity, and show that a small number of particles are thermodynamically driven to rearrange in regions of low density and bond orientational order. This causes a transient loss of mechanical equilibrium which facilitates a large cascade of motion. Combined with previously identified phenomenology, we have a complete kinetic pathway for structural change which is common to both ageing and crystallisation. Furthermore, this suggests that transient force balance is what distinguishes glasses from supercooled liquids.Comment: 13 pages, 13 figure

Importance of many-body correlations in glass transition: an example from polydisperse hard spheres

Most of the liquid-state theories, including glass-transition theories, are constructed on the basis of two-body density correlations. However, we have recently shown that many-body correlations, in particular bond orientational correlations, play a key role in both the glass transition and the crystallization transition. Here we show, with numerical simulations of supercooled polydisperse hard spheres systems, that the lengthscale associated with any two-point spatial correlation function does not increase toward the glass transition. A growing lengthscale is instead revealed by considering many-body correlation functions, such as correlators of orientational order, which follows the lengthscale of the dynamic heterogeneities. Despite the growing of crystal-like bond orientational order, we reveal that the stability against crystallization with increasing polydispersity is due to an increasing population of icosahedral arrangements of particles. Our results suggest that, for this type of systems, many-body correlations are a manifestation of the link between the vitrification and the crystallization phenomena. Whether a system is vitrified or crystallized can be controlled by the degree of frustration against crystallization, polydispersity in this case.Comment: To appear in J. Chem. Phys. for a special issue on the Glass Transitio

RESPONSE OF PUBLIC LAND RANCHERS TO POLICY CHANGES

Policy analysis and planning requires that we know what the likely responses of affected parties to given policy changes. We conducted a random survey of ranchers holding 1998 public land grazing permits in all western states to determine the social and economic characteristics of permit holders, to assess their attitudes about public land policies, and to gauge their responses to three policies related to public land grazing. Respondents were asked how their operations would change due to three different levels of AUM reductions, three different grazing fee increases, and to changes in allowed season of use. The respondents were clustered into eight different types of ranchers using management objective, education, business organization, ranch size, labor, income, and financial aspects. Perceived ranching objectives included preserving family tradition, culture, and values; raising family in a rural setting; living closer to friends and family; earning a good return on investment; avoiding difficulty obtaining a job outside the ranch due to skills; protecting environmental resources; and planning to pass business on to children. Based on the clusters, different policy choices will have differential impacts depending on the type of rancher and individual management goals. Their responses to the various policy choices indicate that analysis using the refined clusters will lead to a different impact assessment compared to using average responses for the population.Agricultural and Food Policy, Land Economics/Use,

The interplay of sedimentation and crystallization in hard-sphere suspensions

We study crystal nucleation under the influence of sedimentation in a model of colloidal hard spheres via Brownian Dynamics simulations. We introduce two external fields acting on the colloidal fluid: a uniform gravitational field (body force), and a surface field imposed by pinning a layer of equilibrium particles (rough wall). We show that crystal nucleation is suppressed in proximity of the wall due to the slowing down of the dynamics, and that the spatial range of this effect is governed by the static length scale of bond orientational order. For distances from the wall larger than this length scale, the nucleation rate is greatly enhanced by the process of sedimentation, since it leads to a higher volume fraction, or a higher degree of supercooling, near the bottom. The nucleation stage is similar to the homogeneous case, with nuclei being on average spherical and having crystalline planes randomly oriented in space. The growth stage is instead greatly affected by the symmetry breaking introduced by the gravitation field, with a slowing down of the attachment rate due to density gradients, which in turn cause nuclei to grow faster laterally. Our findings suggest that the increase of crystal nucleation in higher density regions might be the cause of the large discrepancy in the crystal nucleation rate of hard spheres between experiments and simulations, on noting that the gravitational effects in previous experiments are not negligible.Comment: 16 pages, 15 figures, 2 tables; Soft Matter (2013