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**Statistical analysis of microstructures in materials science.**
*(English)*
Zbl 0960.62129

Wiley Series in Statistics in Practice. Chichester: Wiley. xii, 381 p. (2000).

The investigation of three-dimensional structures is a fundamental aspect of nearly all scientific disciplines dealing with condensed matter. In material sciences and technology this involves examining and understanding the nature and variety of microstructures. To understand how the underlying microstructures determine some of the very specific properties of today’s high-performance materials, it is essential to be able to quantitatively describe relevant features of the three-dimensional form of microstructures. The data required comes from detailed measurements of flat or thin sections of material and the transformation from the two-dimensional image to the three-dimensional structure exploits the models and methods developed in a particular area of mathematics known as stochastic geometry.

This book treats one key aspect of any microstructure – its geometry. The book sets out to show how stochastic geometry can be successfully applied to real microstructural problems in material sciences and technology. The book starts with an overview of the fundamental geometrical parameters used in a three-dimensional description of microstructures based upon flat or thin sections. This is followed by a presentation of both manual and automatic measurement techniques, including discussion of their relative advantages and special features. The statistical analysis of the data collected is then dealt with in detail, and finally, its stereological interpretation within a material science framework is discussed.

Particular attention is given to the description of the spatial size and shapes of grains and particles. Special consideration is given to recent developments in both stochastic geometry and the relevant computer simulation techniques. New and easily realizable solutions to classic stereological problems are presented and applied to problems in the area of high-performance materials.

The book combines general discussion, description of methods, algorithms, and actual working programs. It is assumed that the reader is familiar with the basic statistical methods used in natural sciences and engineering but has no in-depth knowledge of stochastics or statistics, and is able to read computer programs in C, that being the language of the software codes. The idea is that the codes should be as portable as possible across different platforms, operating systems, and C compilers. The programs should run without modifications on any compiler that implements the ANSI C standard.

From the contents: Methodological tools. Statistical estimation of basic characteristics. Nonspherical particles of constant shape. Size-shape distribution of particles. Arrangement of objects. Single-phase polyhedral microstructures. Characteristics of geometric objects. Software utilities.

This book treats one key aspect of any microstructure – its geometry. The book sets out to show how stochastic geometry can be successfully applied to real microstructural problems in material sciences and technology. The book starts with an overview of the fundamental geometrical parameters used in a three-dimensional description of microstructures based upon flat or thin sections. This is followed by a presentation of both manual and automatic measurement techniques, including discussion of their relative advantages and special features. The statistical analysis of the data collected is then dealt with in detail, and finally, its stereological interpretation within a material science framework is discussed.

Particular attention is given to the description of the spatial size and shapes of grains and particles. Special consideration is given to recent developments in both stochastic geometry and the relevant computer simulation techniques. New and easily realizable solutions to classic stereological problems are presented and applied to problems in the area of high-performance materials.

The book combines general discussion, description of methods, algorithms, and actual working programs. It is assumed that the reader is familiar with the basic statistical methods used in natural sciences and engineering but has no in-depth knowledge of stochastics or statistics, and is able to read computer programs in C, that being the language of the software codes. The idea is that the codes should be as portable as possible across different platforms, operating systems, and C compilers. The programs should run without modifications on any compiler that implements the ANSI C standard.

From the contents: Methodological tools. Statistical estimation of basic characteristics. Nonspherical particles of constant shape. Size-shape distribution of particles. Arrangement of objects. Single-phase polyhedral microstructures. Characteristics of geometric objects. Software utilities.

Reviewer: E.M.Psyadlo (Odessa)

### MSC:

62P30 | Applications of statistics in engineering and industry; control charts |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

60D05 | Geometric probability and stochastic geometry |

62M30 | Inference from spatial processes |