Revelation of nuclear tracks and dislocations: A Monte Carlo simulation of mineral etching

Abstract

A simple atomistic Monte Carlo simulation suggests that there are up to four stages in the evolution of an etch pit in the (0 0 1)-surface of an idealised regular lattice. During the first stage, the etch pit is an inverted pyramid; its horizontal and vertical dimensions increase at a constant rate; the apparent horizontal ( v h) and vertical ( v d) growth rates are faster than during all subsequent stages but nevertheless less than the step retreat rate ( v s) on account of surface etching ( v v). The pyramid apex is truncated in the second stage; it is thereafter bounded by an expanding bottom plane and shrinking lateral walls; this is accompanied by a gradual decrease of v h; v d drops to a negative value indicating a slow decrease of the etch-pit depth; the bottom plane acquires a concave-up curvature; the outward curvature of the walls, initiated during the first stage, increases. During the third stage the etch pit consists of a single concave-up bottom plane; v h and v d decrease at declining rates; consecutive etch-pit profiles are scalable in the horizontal direction. The hypothetical fourth stage is inferred but not documented by the simulations; it sets in when v h is reduced to zero; unless this corresponds to an as yet unidentified steady-state condition, the etch pit from here on forth shrinks until it eventually disappears altogether. The sole cause for this succession is the process of stochastic rounding of confined steps and faces. The triangular footprint of recoil-track, fission-track, ion-track and dislocation etch pits in trioctahedral mica and its compliance with the monoclinic symmetries implies that the relevant periodic bond chains are O–Mg/Fe–O chains in the octahedral layer. The size distribution of etched recoil tracks is due to (1) depth variations resulting from the size distribution of the latent tracks, (2) the random truncation of the surface tracks, (3) the variable rate of etch-pit enlargement and (4) the fact that new tracks are exposed at the surface due to surface etching. The greater size of dislocation, fission-track and ion-track etch pits is due to their greater extent below the surface. The increase of the number of etched tracks with etching time due to bulk etching is non-linear because the bulk etch rate v v is not constant. The evolution of etch-pit shape with continued etching can also cause loss of tracks due to observation effects related to loss of contrast.