Morphological instabilities in pattern formation by precipitation and crystallization processes

Abstract

Morphological instabilities in periodic patterns occurring both in precipitation and crystallization processes (Liesegang rings and crystal zoning) are investigated and compared with similar patterns in geological samples (zebra rocks and mud bands in snow sediments). In classical Liesegang systems, undisturbed parallel or concentric precipitation bands are emanated from even or concentric diffusion sources in homogeneous diffusion matrices of gelatine or other gels. In the case of superposing diffusion sources, sources with undulatory curvatures or local diffusion barriers there may occur several types of instabilities within the sequence of regular patterns: (a) gaps within the bands forming radial alleys free of precipitate, (b) transition from broken bands to speckled patterns and (c) apparent branching of bands linked together by so-called anastomoses. Calculations with a competitive particle growth (CPG) model show that lateral instabilities in Liesegang bands (gaps and radial alleys of gaps) are the result of Ostwald ripening effects taking place after precipitation. Apparent branching of bands or formation of anastomoses can be simulated with a prenucleation model according to Ostwald's supersaturation theory. Similar irregularities can be observed in zebra rocks (e.g. banded siderite) whose bandings are commonly explained by sequential sedimentation processes. A very different mechanism is assumed to be responsible for the origin of mud bands in snow sediments. An initially homogeneous distribution of intrinsic mud in snow sediments can be arranged into parallel bands according to a crystal zoning mechanism which is based on repeated thawing and freezing of the snow sediment due to the daily alternation of sun and darkness.

Morphological Characteristics of Liesegang Rings and Their Simulations

“…In silica gel, only chains of single crystals are formed instead of continuous rings of amorphous precipitate. 37 Continuous rings both with branch points and blank alleys are obtained in gelatin gels (Figures 1-4). Gelatin is known to serve both as protective colloid, stabilizing the colloid phase, and poisoning colloid, 64 which hinders freshly formed particles from rapid and radius-dependent growth at the expense of solute phase.…”

“…Also, morphological characteristics of bands, such as the formation of precipitate-free alleys, single filaments, or spots, can be described by employing postnucleation models. [33][34][35][36][37] With respect to morphological defects of bands, Liesegang first pointed out that the sharp localization of precipitation bands were due to strong attraction of precipitate to solute material. 38 Precipitation filaments once formed are thus hindered not only in radial but also in transversal growth.…”

“…42 The influence of diffusion source geometry on ring formation was reconsidered later, 43 also with respect to geoscience. 34,35,37 A further interesting case of ring instability is the formation of tree-like crystal growth within the bands. 44,45 The development of spirals was frequently reported in the literature.…”

Zebra rocks: compaction waves create ore deposits

“…A striking example of waves in rocks is the zebra texture, a pattern that can be found in a variety of rock types ranging from claystones 12 , siderite- 13 , 14 and sphalerite mineralization 15 to hydrothermal dolomite formations 15 – 23 . In this work, we focus on the latter case, in which the texture of the periodic banded dolomites (zebra dolomites) consists of alternating dark and light bands (Fig.…”

“…That impurity rich layers in rocks can be the result of a similar mechanism had already been suggested by Krug et al . 13 . Effective cleansing and impurity redistribution by dissolution-precipitation can be achieved in rocks during grain growth as pointed out by Jessell et al .…”