3D continuum percolation approach and its application to lava-like fuel-containing materials behaviour forecast

Zhydkov Zhydkov

doi:10.5488/cmp.12.2.193

Abstract

The paper is devoted to the theoretical study of elementary permeable objects percolation and its application to real physical objects. Spheres and isotropic oriented capped sticks were chosen as elementary geometrical objects for percolation simulation, physically adequate for radiation defects behaviour description in brittle dielectrics, particularly in the so-called Lava-like Fuel Containing Materials (LFCM), where it effects their mechanical steadiness. LFCMs is high-radioactive glass, which was formed during active stage of well-known heavy nuclear accident, that occurred at Chornobyl nuclear facility in 1986. Physical processes taking place in the materials are of great practical interest. Furthermore, when applying percolation models to LFCM objects, an approximate behaviour forecast can be created. From the results of simulation, it appears that physical properties of the LFCM should drastically change within in the period of 2015 2045 calendar years, depending on variations in nuclear fuel content.

Highlights

The percolation approach is widely used in solid-state physics, for its description as a unified system, containing inclusions of another structure
When the system or material is near a critical point or starts to undergo a structural phase transition, the properties of such a system are best modelled by continuum percolation with objects of a corresponding shape and size and are properly distributed, in contrast to site or bond percolation where sites or bonds are in a discrete lattice and randomly occupied
The 3D percolation problem on random sites with permeable spheres or sticks as percolating objects is an appropriate way of stimulating the behaviour of radiation damages ensemble in like Fuel Containing Materials (LFCM)

Summary

Introduction

The percolation approach is widely used in solid-state physics, for its description as a unified system, containing inclusions of another structure. In most systems inclusions of another structure are physically small and randomly distributed, which makes percolation the best tool for modelling the phase transitions and critical behaviour in unified systems, containing the inclusions. Percolation problems of this kind are known as three-dimensional (3D) continuum percolation of hard-core or soft-core (permeable) geometrical objects and they were the object of persistent research in the 80’s [1,2,3,4,5,6]. From the practical point of view, LFCM mechanical steadiness to external impacts is of especial interest, because LFCM mechanical destruction and transformation into high-dispersive state, regarding its high specific radioactivity, is a potentially dangerous event

Percolation problem on soft spheres

Percolation task on soft sticks

Application to the real material

Findings

Conclusions