Robustness of Dynamical Cluster Analysis in a Glass-Forming Metallic Liquid using an Unsupervised Machine Learning Algor
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Robustness of Dynamical Cluster Analysis in a Glass-Forming Metallic Liquid using an Unsupervised Machine Learning Algorithm Abhishek Jaiswal1 and Yang Zhang1,2,* 1 Department of Nuclear, Plasma, and Radiological Engineering, 2Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A. ABSTRACT We performed dynamical cluster analysis in a Cu-Zr-Al based glass-forming metallic liquid using an unsupervised machine learning algorithm. The size of the dynamical clusters is used to quantify the onset of cooperative dynamics as the underlying mechanism leading to the Arrhenius dynamic crossover in transport coefficients of the metallic liquid. This technique is useful to directly visualize dynamical clusters and quantify their sizes upon cooling. We demonstrate the robustness of this algorithm by performing sensitivity analysis against two key parameters: number of mobility groups and inconsistency coefficient of the hierarchical cluster tree. The results elucidate the optimized range of values for both of these parameters that capture the underlying physical picture of increasing cooperative dynamics appropriately. INTRODUCTION Bulk metallic glasses (BMGs) have been in the widespread use for many technological applications owing to their intriguing physical and chemical properties [1–4]. From a fundamental science perspective, interest in BMGs have been motivated by their relevance to glassy dynamics [5]. The fundamental simplicity of metallic liquids lacking internal degrees of freedom present in many van der Waals liquids, although characterized by complex, many-body, and many-elemental interactions, motivates the study of glass-forming metallic liquids as an interesting class of liquid systems. Nowadays, metallic glass forming liquids can be reliably studied using classical Molecular Dynamics (MD) simulations on large systems accelerated by use of simple many body interaction potentials. Many recent theoretical developments have focused on the dynamic heterogeneity as a “dynamic” correlation length that could potentially quantify the glass transition [6]. Dynamic heterogeneity, or spatially heterogeneous dynamics, is the existence of spatially distinct regions composed of several particles (intermediate length scale), whose relaxation times differ from each other [7]. At high enough temperatures, particle motions are uncorrelated and thus each region is in principle composed of a single particle. When the system is cooled, particle motions start to become increasingly correlated, due to influence from the energy landscape, and such regions start to form and grow in size, therefore, the dynamic correlation length also increases [8]. The crossover temperature marks the onset of such correlated motions or dynamic heterogeneity. At this crossover temperature deviations in high-temperature Arrhenius behavior of transport properties like viscosity, diffusion coefficient, or structural relaxation times have been observed in both experiments and simulations [9–11]. In
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