Abstract. We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multi-scale network based approach for the data mining of such structures. The approach is based on "community detection" wherein interacting particles are partitioned into "an ideal gas" of optimally decoupled groups of particles. Specifically, we construct a set of network representations ("replicas") of the physical system based on interatomic potentials and apply a multiscale clustering ("multiresolution community detection") analysis using information-based correlations among the replicas. Replicas may be (i) different representations of an identical static system or (ii) embody dynamics by when considering replicas to be time separated snapshots of the system (with a tunable time separation) or (iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A80B20, a ternary model system with components "A", "B", and "C" in ratios of A88B7C5 (as in Al88Y7Fe5), and to atomic coordinates in a Zr80Pt20 system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between (i) physical transitions or crossovers and (ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We briefly also consider continuum approaches and discuss the shear penetration depth in elastic media; this length scale increases as the system becomes increasingly rigid.
Undoped and europium doped CaMoO4 and SrMoO4 scheelites are synthesized using a complex polymerization method. The phase purity of the sample is confirmed using powder X-ray diffraction (PXRD). X-ray photoelectron spectroscopy (XPS) was carried out to confirm the oxidation states of various constituents and dopant elements and also the presence of oxygen vacancies. Interestingly both CaMoO4 and SrMoO4 on irradiation with UV light give blue and green emission respectively. On europium doping, it was found that molybdate to Eu(3+) ion energy transfer is more efficient in SrMoO4:Eu compared to CaMoO4:Eu. It is also justified using a luminescence lifetime study which shows biexponential decay in the case of CaMoO4:Eu corresponding to both the host and europium ion; whereas a single lifetime is observed in the case of SrMoO4:Eu. Anomalies in host-dopant energy transfer are suitably explained using density functional theory (DFT) calculations and XPS. The actual site symmetry for the europium ion in CaMoO4 and SrMoO4 was also evaluated based on a Stark splitting pattern which turns out to be D2 and C2v respectively although it is S4 for Ca/Ba(2+) in AMoO4. This is also reflected in higher Ω2 values for SrMoO4:Eu than CaMoO4:Eu.
Recent decades have experienced the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of contending atomic- and largerscale configurations. In order to obtain a more detailed understanding of such systems, we need tools that enable the detection of pertinent structures on all spatial and temporal scales. Towards this end, we suggest a new method that applies to both static and dynamic systems which invokes ideas from network analysis and information theory. Our approach efficiently identifies basic unit cells, topological defects, and candidate natural structures. The method is particularly useful where a clear definition of order is lacking, and the identified features may constitute a natural point of departure for further analysis.
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