Abstract

The present paper is devoted to the possibilities to classify the spatial arrangement of the elements (features) of a stochastic process with geometrical objects. The fundamental quantities describing point processes were introduced. Experimental possibilities of structural objects determination, possibilities of evaluation of the size distribution of the secondary phases, testing of planar point structures (estimation of the process intensity, square method and characteristics of the second order) were estimated. Interparticle distances, namely mean interparticle distance, mean minimum distance, mean visibility and mean path of spherical contact were defined. Selected processes were described and demonstrated from simulated realizations on Al-Al4C3 dispersion strengthened material, prepared by a powder metallurgy method of reaction milling. Interparticle distances of Al4C3 particles were evaluated. Polygonal methods and quadrant counts method were used for characterization of the particle arrangement.

Highlights

  • Intensive research and development of new materials and their challenging technologies belong among those matters which become determining for the recent worldwide industrial and economical progress

  • Particles in real material can be visualized in the cross section of the microstructure by optical microscopy and scanning electron microscopy (SEM) or in a projection by transmission electron microscopy (TEM)

  • Properties of Voronoi tessellation and their various generalizations were studied in the monograph [23].The dual representation formed in the above way described completely the given point system

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Summary

Introduction

Intensive research and development of new materials and their challenging technologies belong among those matters which become determining for the recent worldwide industrial and economical progress. C) Characteristics of the second order These characteristics describe in detail the spatial distribution of points They can be determined using, for example, the K-function K(r), whose course is given by the dependence between the number of points in the circular surrounding r of the typical process point on the size of r. D) Mean path of spherical contact λυ This is the mean value of the distance from the randomly selected point of the matrix to the nearest particle It determines the distribution of sizes of the maximum spheres inscribed into the matrix in its internal points; it depends on the spatial distribution of particles [20]. It has suitable limit properties, and can be measured manually. Thin foils if the thickness L= (2000 ± 500) Å were prepared by spark cutting followed by electropolishing and did not include coarse particles

Schematic illustration of interparticle distances
Findings
Conclusions
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