Researchers Gain Insights into How Melting Occurs in 2D Systems

A fact known worldwide is that in Winter snow falls, and in Spring, it melts. However, the question remains how is this phase change driven?

Despite the fact that melting is a well-known phenomenon experienced in everyday life and having a role in various commercial and industrial processes, at a fundamental level, there remain many mysteries related to this transformation that are yet to be uncovered.

In the year 2015, a research team headed by Sharon Glotzer from the University of Michigan worked at the Department of Energy’s (DOE) Oak Ridge National Laboratory and employed high-performance computing to analyze melting in two-dimensional (2D) systems.

This problem could provide a clear understanding of surface interactions that occur in materials significant for technologies such as solar panels, and also regarding the mechanism that causes three-dimensional (3D) melting. The researchers investigated the impact of particle shape on the physical changes during 2D solid-to-fluid melting transition.

The researchers employed the Cray XK7 Titan supercomputer at the Oak Ridge Leadership Computing Facility (OLCF), which is a DOE Office of Science User Facility, to show that the symmetry and shape of particles can have a drastic impact on the melting process. This fundamental discovery could help scientists looking for nanoparticles that have properties suitable for energy applications.

In order to overcome the problem, the research team headed by Glotzer was in need of a supercomputer with the potential to simulate systems of up to 1 million hard polygons. The hard polygons in this case are simple particles varying from triangles to 14-sided shapes that are used as a substitute for atoms.

In contrast to conventional molecular dynamics simulations attempting to mimic nature, hard polygon simulations provide a pared-down environment in which the researchers can assess shape-influenced physics.

Within our simulated 2-D environment, we found that the melting transition follows one of three different scenarios depending on the shape of the systems’ polygons. Notably, we found that systems made up of hexagons perfectly follow a well-known theory for 2-D melting, something that hasn’t been described until now.

Joshua Anderson, Research Scientist, University of Michigan

Shifting Shape Scenarios

In 3D systems such as a thinning icicle, melting is in the form of a first-order phase transition, suggesting that the collections of molecules contained in these systems occur in liquid or solid form, with no intermediate phase when latent heat is present. Latent heat is the energy that causes a solid-to-fluid phase change.

In 2D systems, such as thin-film materials used in batteries and other technologies, the process of melting is highly complex and at times manifests an in-between phase, namely, the hexatic phase.

The hexatic phase is a state characterized as a halfway point between an ordered solid and a disordered liquid. In the 1970s, for the first time, John Kosterlitz, David Thouless, Burt Halperin, David Nelson, and Peter Young theorized the hexatic phase of 2D melting, which is a fundamental feature of the KTHNY theory, named after the researchers (with the first letters of their last names).

Along with physicist Duncan Haldane, Kosterlitz and Thouless won the Nobel Prize in Physics in the year 2016 for their contributions to the field of 2D materials research.

The arrangement of atoms defines the solid, liquid, and hexatic systems at the molecular level. Two types of order - translational and orientational - are present in a crystalline solid. The well-defined paths between atoms over distances, such as blocks in a cautiously constructed Jenga tower, are defined by the translational order.

The clustered and relational order shared between atoms and groups of atoms over distances is defined by the orientational order. Imagine the same Jenga tower being turned unevenly following multiple rounds of play. In such cases, although the typical shape of the tower is unaltered, its order is fragmented.

There is no translational order in the hexatic phase, but there is an orientational order. (It is known that there is neither translational order nor orientational order in a liquid, although there is a short-range order, i.e. there are some specific average number of neighbors nearby  but without a predicable order.)

A leadership-class computer with the ability to calculate large hard-particle systems is required to calculate the existence of a hexatic phase. For this, the research team headed by Glotzer acquired permission to use the OLCF’s 27-petaflop Titan using the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. The team ran the graphics processing unit (GPU)-accelerated HOOMD-blue code to increase the time on the machine.

On Titan, 64 GPUs were used by HOOMD-blue for every massively parallel Monte Carlo simulation of up to 1 million particles. A total of 11 different shape systems exerting an external pressure to push the particles together were analyzed by the researchers. In total, 21 different densities were adopted to simulate each of the systems, where the highest densities represented a solid state and the lowest densities represented a fluid state.

The simulations revealed multiple melting scenarios contingent on the shape of the polygons. The melting behavior of systems including polygons with equal to or more than seven sides was closely identical to that of hard disks (or circles) presenting a continuous phase transition from the solid phase to the hexatic phase and a first-order phase transition from the hexatic phase to the liquid phase.

Here, a continuous phase transition denotes a constant modification of area due to a change in external pressure. A first-order phase transition occurs due to a discontinuity in which the volume jumps across the phase transition as a result of change in external pressure. A first-order solid-to-liquid phase transition was found to be exhibited by pentagons and fourfold pentilles, i.e. irregular pentagons possessing two different edge lengths.

However, the hexagon systems were found to perfectly follow the phase transition outlined in the KTHNY theory. Here, the particles were found to shift from the solid to hexatic phase and from the hexatic to fluid phase in a perfect continuous phase transition pattern.

It was actually sort of surprising that no one else has found that until now. because it seems natural that the hexagon, with its six sides, and the honeycomb-like hexagonal arrangement would be a perfect match for this theory.

Joshua Anderson, Research Scientist, University of Michigan

Where the hexatic phase normally includes a six-fold orientational order.

Upon recently receiving a 2017 INCITE allocation, the research team headed by Glotzer is, at present, working toward making good use of its leadership-class computing prowess to address 3D phase transitions.

The researchers are now analyzing the way in which fluid particles are crystallized into complex colloids. Colloids—such as stained glass, paper, milk, and fog—are mixtures where particles are suspended throughout another substance.

“We’re planning on using Titan to study how complexity can arise from these simple interactions, and to do that we’re actually going to look at how the crystals grow and study the kinetics of how that happens,” stated Anderson.