Lineal-path function for random heterogeneous materials

Journal Article · Wed Jan 15 04:00:00 EST 1992 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.45.922· OSTI ID:7272663

Lu, B ^[1]; Torquato, S ^[2]

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1. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (United States)
2. Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (United States)

A fundamental morphological measure of two-phase heterogenous materials is what we refer to as the lineal-path function {ital L}({ital z}). This quantity gives the probability that a line segment of length {ital z} is wholly in one of the phases, say phase 1, when randomly thrown into the sample. For three-dimensional systems, we observe that {ital L}({ital z}) is also equivalent to the area fraction of phase 1 measured from the projected image onto a plane: a problem of long-standing interest in stereology. We develop a theoretical means of representing and computing the lineal-path function {ital L}({ital z}) for distributions of {ital D}-dimensional spheres with arbitrary degree of penetrability using statistical-mechanical concepts. In order to test our theoretical results, we determined {ital L}({ital z}) from Monte Carlo simulations for the case of three-dimensional systems of spheres and found very good agreement between theory and the Monte Carlo calculations.

• DOE Contract Number: FG05-86ER13482
• OSTI ID: 7272663
• Journal Information: Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 45:2; ISSN PLRAA; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360602* -- Other Materials-- Structure & Phase Studies
665000 -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
CLUSTER MODEL
COMPOSITE MATERIALS
COMPUTERIZED SIMULATION
CORRELATION FUNCTIONS
CRYSTAL STRUCTURE
DISTRIBUTION FUNCTIONS
FUNCTIONS
HETEROGENEOUS EFFECTS
MANY-DIMENSIONAL CALCULATIONS
MATERIALS
MATHEMATICAL MODELS
MICROSTRUCTURE
MONTE CARLO METHOD
MORPHOLOGY
NUCLEAR MODELS
POROUS MATERIALS
SIMULATION
SPHERES
TRANSPORT THEORY