On the reconstruction of polycrystalline microstructures from two-point correlation statistics

Hansen, Brett; Adams, Brent L.; Lyon, Mark; Henrie, Alisa J.

doi:10.1007/s10820-005-0884-3

Cited by 20 publications

(8 citation statements)

References 11 publications

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“…It has also been shown that the structural ambiguity is considerably larger for a radial function without angular information, which is the only data available from small-angle scattering experiments. However, if angular information is employed successful microstructure reconstructions can often be obtained [18][19][20][21].…”

Section: S T R I B Umentioning

confidence: 99%

Density of States for a Specified Correlation Function and the Energy Landscape

2012

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The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are described in terms of the roughness of the energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered systems.

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Section: S T R I B Umentioning

confidence: 99%

Density of States for a Specified Correlation Function and the Energy Landscape

2012

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“…The DDF, calculated using the morphological parameters, is comprised of N × N number of grain pairs. Each pair contributes a D m i j to DDF according to Equation (17), and each D m is logistically distributed. It is concluded that since DDF for the entire sample shows a good match with the exact DDF, the functional form proposed for D m i j (Equation (16)) is both robust and is statistically representative.…”

Section: Distance-disorientation Functionmentioning

confidence: 99%

“…Considerable research was performed in the field of application of n-point correlation statistics to the problems of three-phase microstructure reconstructions [3,[11][12][13][14][15][16][17][18]. The main idea is to reconstruct the full microstructure media from the n-point correlation statistics using different optimization and homogenization techniques.…”

Section: Introductionmentioning

confidence: 99%

Analytical estimation of distance–disorientation function of the material microstructure

Staraselski¹,

Brahme²,

Inal³

et al. 2013

Philosophical Magazine

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This work presents a new functional approach to estimate the distancedisorientation correlation function of a given microstructure. The proposed approach separates the crystallographic domain into texture defined by its Euler angles (φ 1 , , φ 2 ) and geometrical domain defined by distance distribution function D i j . The crystallographic domain is treated as independent (known) variable and an analytical estimate for the Euclidian distance distribution function (D i j ) is obtained. The proposed analytical solution for the estimation of D i j is based on existing statistical growth models and the logistic probability distribution function. The solution is optimized for the measured experimental data and takes into account morphological features of the microstructure such as grain volume, grain radius and grain size as well as their distribution inside the material. An analytical model is proposed for constructing the distance-disorientation function (DDF) using the estimated Euclidian distance between pixel pairs. The new functional solution is a highly effective way to calculate DDF values, making it suitable for application to the real microstructure optimization problems. The DDF obtained by using the results of probabilistic solution is validated by comparing them with the DDF obtained from experimental electron back-scatter diffraction data.

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“…Despite the widespread use of correlation functions, the nature of the structural information they contain remains an open area of active research [20][21][22][23][24][25][26][27][28]. The central question of the present paper can be put as follows: how accurately is a microstructure known when the only data available is a two-point correlation function?…”

Section: Introductionmentioning

confidence: 99%

“…In the field of computer vision, it has been shown that finite textures are completely characterized by their orientation-dependent correlation functions [33]. Many theoretical examples of microstructures with a low degeneracy can be accurately reconstructed from their correlation function alone [24,25,34,35]. All these examples have in common that they incorporate orientation information [36].…”

Section: Introductionmentioning

confidence: 99%

Microstructural degeneracy associated with a two-point correlation function and its information content

2012

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A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural 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 of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., 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.

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On the reconstruction of polycrystalline microstructures from two-point correlation statistics

Cited by 20 publications

References 11 publications

Density of States for a Specified Correlation Function and the Energy Landscape

Density of States for a Specified Correlation Function and the Energy Landscape

Analytical estimation of distance–disorientation function of the material microstructure

Microstructural degeneracy associated with a two-point correlation function and its information content

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