The variation and visualisation of elastic anisotropy in rock-forming minerals

Abstract

All minerals behave elastically, a rheological property that controls their ability to support stress, strain and pressure, the nature of acoustic wave propagation and influences subsequent plastic (i.e. permanent, non-reversible) deformation. All minerals are intrinsically anisotropic in their elastic properties – that is, they have directional variations that are related to the configuration of the crystal lattice. This means that the commonly used mechanical elastic properties that relate elastic stress to elastic strain, including Young’s modulus (E), Poisson’s ratio (ν), shear modulus (G) and linear compressibility (β), are dependent on crystallographic direction. In this paper, we explore the ranges of anisotropy of E, ν, G and β in 86 rock-forming minerals, using previously published data, and show that the range is much wider than commonly assumed. We also explore how these variations (the directionality and the magnitude) are important for fundamental processes in the solid earth, including deformation (mechanical) twinning, coherent phase transformations and brittle failure. We present a new open source software package (AnisoVis, written in MATLAB), which we use to calculate and visualise directional variations in elastic properties of rock-forming minerals. Following previous work in the fields of chemistry and materials, we demonstrate that by visualising the variations in elasticity, we discover previously unreported properties of rock forming minerals. For example, we show previously unreported directions of negative Poisson’s ratio and negative linear compressibility and we show that the existence of these features is more widespread (i.e. present in many more minerals) than previously thought. We illustrate the consequences of intrinsic elastic anisotropy for the elastic normal and shear strains within α-quartz single crystal under different applied stress fields; the role of elastic anisotropy on Dauphiné twinning and the α-β phase transformations in quartz; and stress distributions around voids of different shapes in talc, lizardite, albite, and sanidine. In addition to our specific examples, elastic anisotropy in rock-forming minerals to the degree that we describe has significant consequences for seismic (acoustic) anisotropy, the focal mechanisms of earthquakes in anisotropic source regions (e.g. subducting slabs), for a range of brittle and ductile deformation mechanisms in minerals, and geobarometry using mineral inclusions.

Exploration of glassy state in Prussian blue analogues

“…More details can be obtained by analysing the spatial dependence of mechanical properties calculated from the elastic component (Fig. 4A, S34 to S41, and Table S4) 77,78 3/4•3.5H2O, results in a dramatic decrease in the average K and E values to 37.3 (−67.5 %) and 84.4 (−25.6 %) GPa, respectively (Fig. 4A, S32 and S42 to 45).…”

Experimental and Theoretical Investigations of Hard Rocks at High Temperature: Applications in Civil Engineering

“…However, their results showed that in charge and discharge cycles, the efficiency of the best configurations was about 68%. Healy et al [27] demonstrated that minerals were intrinsically anisotropic, thus can become elastic and affect the rock structure, consequently the physical and mechanical properties of these rocks. At the same time, Gautam et al [28] revealed using microscopic analysis that feldspar minerals have a low and isotropic thermal expansion which do not affect the molecular structure of red and white Jalore granitic rocks for nuclear waste repository.…”

Modeling and Numerical Analysis in 3D of Anisotropic and Nonlinear Mechanical Behavior of Tournemire Argillite under High Temperatures and Dynamic Loading

“…From the experimental point of view, previous elucidated works and others [19][20][21] have been done in this literature. However, few theoretical studies had been done and numerical results in this field were obtained.…”