Shape and symmetry determine two-dimensional melting transitions of hard regular polygons

The melting transition of two-dimensional (2D) systems is a fundamental problem in condensed matter and statistical physics that has advanced significantly through the application of computational resources and algorithms. 2D systems present the opportunity for novel phases and phase transition scenarios not observed in 3D systems, but these phases depend sensitively on the system and thus predicting how any given 2D system will behave remains a challenge. Here we report a comprehensive simulation study of the phase behavior near the melting transition of all hard regular polygons with $3\leq n\leq 14$ vertices using massively parallel Monte Carlo simulations of up to one million particles. By investigating this family of shapes, we show that the melting transition depends upon both particle shape and symmetry considerations, which together can predict which of three different melting scenarios will occur for a given $n$. We show that systems of polygons with as few as seven edges behave like hard disks; they melt continuously from a solid to a hexatic fluid and then undergo a first-order transition from the hexatic phase to the fluid phase. We show that this behavior, which holds for all $7\leq n\leq 14$, arises from weak entropic forces among the particles. Strong directional entropic forces align polygons with fewer than seven edges and impose local order in the fluid. These forces can enhance or suppress the discontinuous character of the transition depending on whether the local order in the fluid is compatible with the local order in the solid. As a result, systems of triangles, squares, and hexagons exhibit a KTHNY-type continuous transition between fluid and hexatic, tetratic, and hexatic phases, respectively, and a continuous transition from the appropriate "x"-atic to the solid. [abstract truncated due to arxiv length limitations]

Bulk Metallic Glasses Deform via Slip Avalanches

Inelastic deformation of metallic glasses occurs via slip events with avalanche dynamics similar to those of earthquakes. For the first time in these materials, measurements have been obtained with sufficiently high temporal resolution to extract both the exponents and the scaling functions that describe the nature, statistics and dynamics of the slips according to a simple mean-field model. These slips originate from localized deformation in shear bands. The mean-field model describes the slip process as an avalanche of rearrangements of atoms in shear transformation zones (STZs). Small slips show the predicted power-law scaling and correspond to limited propagation of a shear front, while large slips are associated with uniform shear on unconstrained shear bands. The agreement between the model and data across multiple independent measures of slip statistics and dynamics provides compelling evidence for slip avalanches of STZs as the elementary mechanism of inhomogeneous deformation in metallic glasses.Comment: Article: 11 pages, 4 figures, plus Supplementary Material: 16 pages, 8 figure

Mechanical Properties and Phase Transitions in Hard Polygons and the Origin of Colloidal Crystal Photonic Band Gaps

The synthesis of nanoparticles and colloids with anisotropic interactions and intricate shapes has led to the possibility of an assortment of complex self-assembled soft matter phases. In the first part of this work, I construct a theoretical minimal model to investigate the role of translational and rotational entropy in self-assembled solids of hard particles. Using computer simulations, I calculate the frequency of each normal mode of the solid and find the entropy contained in each translational and rotational wave. I show the entropy of a solid of hard hexagons is distributed nontrivially at many length scales among translational and rotational modes and construct maps in reciprocal space showing which fluctuations have more entropy. In the second part, I show that a solid of hard squares, like hard regular triangles, exhibit a strange high-density chiral symmetry-breaking transition. I show this transition is in the Ising universality class and that it is driven by a competition between rotational and translational entropy. In the third part of this work, I explore the origins of photonic band gaps in a wide variety of crystal structures formed of dielectric spheres. This problem has significant interest in the context of self-assembled soft matter as a route to design color-changing colloidal materials. I examine what characteristics of electromagnetic modes are responsible for opening a band gap in photonic materials. This problem is well-understood for photonics in two dimensions, but my coauthors and I show that the design heuristics developed for that problem do not hold in three dimensions.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/151475/1/jamesaan_1.pd

Laser Shock Peening on Zr-based Bulk Metallic Glass and Its Effect on Plasticity: Experiment and Modeling

The Zr-based bulk metallic glasses (BMGs) are a new family of attractive materials with good glass-forming ability and excellent mechanical properties, such as high strength and good wear resistance, which make them candidates for structural and biomedical materials. Although the mechanical behavior of BMGs has been widely investigated, their deformation mechanisms are still poorly understood. In particular, their poor ductility significantly impedes their industrial application. In the present work, we show that the ductility of Zr-based BMGs with nearly zero plasticity is improved by a laser shock peening technique. Moreover, we map the distribution of laser-induced residual stresses via the micro-slot cutting method, and then predict them using a three-dimensional finite-element method coupled with a confined plasma model. Reasonable agreement is achieved between the experimental and modeling results. The analyses of serrated flows reveal plentiful and useful information of the underlying deformation process. Our work provides an easy and effective way to extend the ductility of intrinsically-brittle BMGs, opening up wider applications of these materials

Experimental Evidence for Both Progressive and Simultaneous Shear During Quasistatic Compression of a Bulk Metallic Glass

Two distinct types of slip events occur during serrated plastic flow of bulk metallic glasses. These events are distinguished not only by their size but also by distinct stress drop rate profiles. Small stress drop serrations have fluctuating stress drop rates (with maximum stress drop rates ranging from 0.3–1 GPa/s), indicating progressive or intermittent propagation of a shear band. The large stress drop serrations are characterized by sharply peaked stress drop rate profiles (with maximum stress drop rates of 1–100 GPa/s). The propagation of a large slip is preceded by a slowly rising stress drop rate that is presumably due to the percolation of slipping weak spots prior to the initiation of shear over the entire shear plane. The onset of the rapid shear event is accompanied by a burst of acoustic emission. These large slips correspond to simultaneous shear with uniform sliding as confirmed by direct high-speed imaging and image correlation. Both small and large slip events occur throughout plastic deformation. The significant differences between these two types require that they be carefully distinguished in both modeling and experimental efforts