Research Catalog

Title

Stochastic models of heterogeneous materials / H. Hermann.

Author

Hermann, H.

Publication

Zürich ; Brookfield, VT : Trans Tech Publications, ©1991.

Items in the Library & Off-site

Details

Description

iv, 177 pages : illustrations; 25 cm

Series Statement

Materials science forum, 0255-5476 ; v. 78

Uniform Title

Materials science forum ; v. 78.

Subject

• Solid state physics > Mathematical models
• Stochastic analysis
• Materials > Analysis
• Science des matériaux
• Modèles mathématiques
• Probabilités
• Heterogenes System
• Stochastisches Modell
• Physique de l'état solide > Modèles mathématiques
• Analyse stochastique
• Matériaux > Analyse

Bibliography (note)

• Includes bibliographical references (p. 164-172) and index.

Contents

• 1. Construction of models and basic properties -- 1.1. Random point fields -- 1.1.1. Poisson point field -- 1.1.2. Hard-core point fields -- 1.1.3. Cluster point fields -- 1.2. Random mosaics -- 1.2.1. Poisson mosaics -- 1.2.2. Dirichlet and Voronoi mosaics -- 1.3. Germ-grain models -- 1.3.1. Models with non-overlapping grains -- 1.3.2. Boolean models -- 1.3.3. Special Boolean models -- 1.3.4. A variable analytical surface fractal -- 2. Relationship between models and experimentally accessible parameters -- 2.1. Density -- 2.2. Small-angle scattering -- 2.2.1. Basic formulae -- 2.2.2. General relations for two-phase systems -- 2.2.3. Isolated particles -- 2.2.4. Interparticle interference -- 2.2.5. Small-angle scattering from stochastic two-phase structures -- 2.3. Wide-angle scattering -- 2.3.1. Models of microheterogeneity -- 2.3.2. Wide-angle scattering of amorphous Fe-B alloys -- 2.3.3. Microheterogeneous Carbon -- 2.3.4. Limit of low spatial resolution -- 2.4. Characterization of planar mosaics -- 2.4.1. General results -- 2.4.2. First order statistics -- 2.4.3. Variability characteristics -- 2.4.4. Variability characteristics of the Poisson-Dirichlet mosaic -- 2.4.5. Cell-area distributions of Dirichlet mosaics -- 2.5. Stereology of germ-grain models and random mosaics -- 2.5.1. The fundamental mean-value formulae of stereology -- 2.5.2. Planar sections of germ-grain models -- 2.5.3. Stereology of spatial mosaics
• 2.5.4. Cell-area distributions of planar sections of spatial Voronoi mosaics -- 3. Applications -- 3.1. Absorption of X-rays in random powder specimens -- 3.1.1. Single-phase powders -- 3.1.2. Multi-phase powders -- 3.1.3. Microabsorption correction in quantitative X-ray phase analysis -- 3.2. Voronoi analysis of atomic short-range order in amorphous structure models -- 3.2.1. Dense random packing of spheres -- 3.2.2. Voronoi analysis of dense random packing models -- 3.2.3. Radical plane polyhedra -- 3.2.4. Dirichlet analysis of a plane model with directional atomic short-range order -- 3.3. Structure -- property relationships of amorphous iron-boron alloys -- 3.3.1. Microphase separation in rapidly quenched amorphous alloys -- 3.3.2. Elastic moduli and internal stresses of iron-boron metallic glasses -- 3.3.3. Relaxation phenomena in metallic glasses -- 3.3.4. Magnetic moment of amorphous Fe-B alloys.

ISBN

• 0878495487
• 9780878495481

OCLC

• ocm25070813
• 25070813
• SCSB-9171071

Owning Institutions

Princeton University Library