Access the full text.
Sign up today, get DeepDyve free for 14 days.
Andrea Arguelles, J. Turner (2017)
Ultrasonic attenuation of polycrystalline materials with a distribution of grain sizes.The Journal of the Acoustical Society of America, 141 6
(1984)
The choice of parameters of the grain structure, Zavod
(2011)
Computer synthesis and statistical analysis of distribution of structural characteristic for the granular composite materials
(2009)
The distribution of particle sizes during fragmentation
(1984)
The choice of parameters of the grain structure
D. Levine (1997)
Statistics for Managers Using Microsoft® ExcelTechnometrics, 43
(2012)
The new paradigm of applied statistics, Zavod
(1977)
II. Critical diffusion in binary systems and kinetics of phase separation
(2012)
The new paradigm of applied statistics
K. Binder (1977)
Theory for the dynamics of "clusters." II. Critical diffusion in binary systems and the kinetics of phase separationPhysical Review B, 15
(2018)
Grain growth—unresolved issues, Mater
(1968)
Theoretical problems of quantitative microscopic analysis, Zavod
(1986)
The logarithmically normal law of particle size distribution during fragmentation
(2000)
Monte Carlo simulation of a homogeneous structure of single-phase alloys
D. Zöllner, P. Streitenberger (2006)
Three-dimensional normal grain growth: Monte Carlo Potts model simulation and analytical mean field theoryScripta Materialia, 54
(1986)
The logarithmically normal law of particle size distribution during fragmentation, in Teoriya veroyatnostei i matematicheskaya statistika (Theory of Probability and Mathematical Statistics)
P. Rios, D. Zöllner (2018)
Critical assessment 30: Grain growth – Unresolved issuesMaterials Science and Technology, 34
(1997)
Estimation of gamma distribution parameters
Анастасия Ильиных, Валерий Вильдеман, V. Marina (2011)
Computer Synthesis and Statistical Analysis of the Distribution of Structural Characteristics of Granular Composite Materials
L. Kiss, J. Soderlund, G. Niklasson, C. Granqvist (1999)
The real origin of lognormal size distributions of nanoparticles in vapor growth processesNanostructured Materials, 12
G. Gottstein (2004)
Physical Foundations of Materials Science
(2004)
Physical Foundations of Materials
(1999)
The real origin of lognormal distribution of nanoparticles in vapor growth processes, Nanostruct
A. Tewari, A. Gokhale (2001)
Estimation of three-dimensional grain size distribution from microstructural serial sectionsMaterials Characterization, 46
Grain growth — unresolved issues
D. Zöllner, P. Streitenberger (2010)
Grain Size Distributions in Normal Grain GrowthPractical Metallography, 47
(1984)
The method of presenting the measurement result taking into account its statistical nature, Metrologiya
(1950)
Dispersion analysis of spherical particles in opaque structures
(1968)
Theoretical problems of quantitative microscopic analysis
P. Gubanov, I. Maksimov (2008)
Coalescence kinetics under the action of alternative grain growth mechanismsCrystallography Reports, 53
D. Levine, David Stephan, T. Krehbiel, M. Berenson (2008)
Statistics for Managers
(1987)
Diffusive decomposition of solid solutions, Sov
(1977)
Stereologiya v metallovedenii (Stereology in Metal Science), Moscow: Metallurgiya
(1970)
Stereometricheskaya metallografiya (Stereometric Metallography)
S.V. Shevchenko (2015)
The formation of the microstructure of polycrystalline materials and statistics on the distribution of grains by their average sizes: the possibility of description based on the Smoluchowski coagulation equationNanosyst. Nanomater. Nanotechnol, 13
M. Hillert (1965)
On the theory of normal and abnormal grain growthActa Metallurgica, 13
(2008)
Coalescence kinetics under the action of alternative grain grows mechanisms, Crystallogr
(1997)
Estimation of gamma distribution parameters, Obozr
(1984)
The method of presenting the measurement result taking into account its statistical nature
(1950)
Dispersion analysis of spherical particles in opaque structures, Zavod
V. Slezov, V. Sagalovich (1987)
Diffusive decomposition of solid solutionsPhysics-Uspekhi, 30
A statistical analysis of the grain size distribution is necessary both for the construction and development of the theory of grain growth and microstructure formation and for the description of the size dependences of the characteristics of the physical and mechanical properties of polycrystalline materials. The grain size distribution is one of the most important characteristics of the uniformity of the structure and, consequently, the stability of the properties of products during operation. The results of the study of single-phase and equiaxed polycrystalline microstructure using Monte Carlo modeling of parameters and grain size distribution functions are presented. Statistical parameters (mean values, variances, and coefficients of variation) and distribution functions of characteristics of grain microstructure are given. It is found that the distribution function of effective grain sizes for the studied model of a polycrystal is most adequately described by the γ distribution. It should be used in the analysis of experimental grain size distribution functions for single-phase polycrystalline materials with equiaxed grains. It is shown that the population mean (expected value) of the effective sizes (projection diameters) of grains with the γ-distribution function can be taken as a statistically substantiated and reliable estimate of the mean grain size; the parameters of the γ-distribution function must be preliminarily determined when studying the grain structure of a polycrystalline material. The results of statistical modeling are confirmed by experimental data of metallographic analysis of microstructures of model and industrial materials with varying degrees of grain structure inhomogeneity.
Inorganic Materials – Springer Journals
Published: Dec 1, 2021
Keywords: microstructure; grain size; statistical modeling; Monte Carlo method; grain size distribution
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.