2012/05/15 by Cédric Gommes, Cedric J. Gommes, Yang Jiao +5
Earth and Planetary Sciences · Engineering · Materials Science · Physics and Astronomy · #Advanced Semiconductor Detectors and Materials #FOS: Physical sciences #Machine Learning in Materials Science #Phase Equilibria and Thermodynamics #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.1205.3382
Accepted for publication in Physical Review E
arxiv created 2012/05/15 · openalex publication_date 2012/05/15 · arxiv updated 2012/05/16 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28
Two-point correlation functions provide crucial yet incomplete characterization of microstructures because different microstructures may have the same correlation function. In an earlier Letter [Phys. Rev. Lett. 108, 080601 (2012)], we addressed the degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation and additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically an energy profile corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of this profile is a measure of the roughness of the energy landscape, which can be used as a proxy for ground-state degeneracy. The relationship between roughness metric and ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the degeneracy of a variety of microstructures, including hard disks and Poisson point processes as well as those with known degeneracies (single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the information content of any two-point correlation function, which makes our results broadly applicable to any field in which correlation functions are employed.