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# Calcite Deformation Twins: From Crystal Plasticity to Applications in Geosciences

Olivier Lacombe

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Olivier Lacombe. Calcite Deformation Twins: From Crystal Plasticity to Applications in Geosciences. Geosciences, 12, pp.280, 2022, 10.3390/geosciences12070280. [https://hal.science/hal-03931460](https://hal.science/hal-03931460)

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Editorial

# Calcite Deformation Twins: From Crystal Plasticity to Applications in Geosciences

Olivier Lacombe

Institut des Sciences de la Terre de Paris—ISTEP, Sorbonne Université, CNRS-INSU, Campus Pierre et Marie Curie, 4 place Jussieu, 75005 Paris, France; olivier.lacombe@sorbonne-universite.fr

E-twinning is the dominant mechanism of plastic deformation of calcite at low temperature (<300 °C), and in most limestones, e-twins are, at the crystal scale, the dominant microstructures. Intracrystalline twin lamellae are caused by lattice rotation between rows of atoms along the {01-12} (or {018}) e-plane in response to shear stress. Once a twin is formed, progressive deformation can either create new twins elsewhere or deform the twinned rock portion by other mechanisms. Mechanical twinning accommodates only a very limited amount of the bulk strain accommodated by the rock, so twinning deformation generally co-exists with other deformation mechanisms, such as brittle failure and cataclasis, porosity reduction, pressure solution, or dislocation creep.

Recent experimental work has enabled significant progress in the understanding of the initiation and growth of calcite twins and of their controlling factors, as well as of the contribution of twinning to the deformation of calcite grains at various conditions [1-5]. Coevally, inversion techniques that allow for the determination of principal stress or strain orientations and differential stress magnitudes from naturally deformed calcite-bearing rocks have been developed [6-8]. These techniques were widely applied in paleo-tectonic studies, e.g., as in [9-13].

Despite significant advances, one pending question about twinning in calcite is related to the existence of a critical resolved shear stress and (if it does exist) to its actual significance. Many paleopiezometric approaches have been built around the concept of a constant critical resolved shear stress for twinning, with a value of ~10 MPa being commonly adopted (e.g., [14–16]). In this view, the so-called critical resolved shear stress would correspond to the stress associated with plastic twin propagation across the grain (controlled by external stress and governed by a Schmid-type criterion) rather than to the stress associated with twin nucleation (likely controlled by the local lattice structure and stress concentrations). The idea that the critical resolved shear stress is the empirical stress at which a statistically significant number of twin nucleation sites become suddenly active provides a possible elegant way to reconcile the picture of the twin-forming process with the practical existence of a critical resolved shear stress [4]. The adoption of a single critical resolved shear stress for twinning has been challenged [17] because the differential stress necessary to produce twinning is dependent upon grain size [1] and strain (calcite hardens once twinned) [18]. Further experimental work has thus been devoted to better constraining the stress conditions for twinning, including estimates of the value of the macroscopic (empirical) critical resolved shear stress and its variation with grain size [1] and strain [18]. Recent calcite twin-based paleopiezometric studies take into account the dependence of the critical resolved shear stress on these parameters ([6,12]).

Considering the long-lasting investigations on deformation twinning in calcite, and the remaining questions under debate (i.e., the existence of a real or apparent critical resolved shear stress, twins as strain or stress indicators, and twin morphology as a paleothermometer), it was highly stimulating to try to demonstrate the recent advances on the topic by gathering both review papers and contributions reporting original developments and applications.

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**Citation:** Lacombe, O. Calcite Deformation Twins: From Crystal Plasticity to Applications in Geosciences. Geosciences **2022**, *12*, 280. https://doi.org/10.3390/geosciences12070280

Received: 14 July 2022

Accepted: 15 July 2022

Published: 17 July 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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**Copyright:** © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
The review paper by Lacombe et al. [19] is the cornerstone of the Special Issue. It is a follow-up of the review papers by [20–22] and provides an overview of the recent progress on the understanding of the formation of calcite twins, their measurement, and their use as tectonic markers and as a stress-strain gauge. The paper summarizes our current knowledge on twin nucleation and growth, and critically discusses the concept of critical resolved shear stress. Calcite twin measurement techniques are presented together with their pros and cons. The classical use of calcite twin morphology as a geothermometer is critically discussed. Inversion techniques allowing for the use of calcite twins as indicators of orientations and/or magnitudes of stress and strain are summarized, and the benefits for paleo-tectonic studies are illustrated through several examples. Finally, the paper addresses the successful combination of calcite twinning paleopiezometry with the mechanical analysis of fractures and stylolite roughness paleopiezometry.

Three papers within the volume deal with paleopiezometry or with the reconstruction of regional paleostress orientations from calcite twins. Rutter et al. [23] use electron backscatter diffraction (EBSD) to determine the orientation of mechanically twinned grains in Carrara marble experimentally deformed to a small strain at room temperature and at a moderate confining pressure. Although the thickness of the deformation twins was mostly too small to permit a determination of their orientation by EBSD, the authors have measured their orientations by calculating possible twin orientations from the host grain orientation, and then comparing calculated traces to the observed twin traces. The validity of the Turner and Weiss method for principal stress orientations was confirmed, particularly when based on a calculation of the resolved shear stress. The authors show that methods of paleopiezometry based on twinned volume fraction must be rejected. They further explore a practical paleopiezometric approach based on twin density and find that twin density correlates positively with resolved shear stress. However, the intrinsic variability of the results imposes a limit on the achievable accuracy of this approach.

In their study, Parlangeau et al. [24] have deformed samples of Carrara marble in uniaxial compression and at low temperature. The experiments were monitored in situ using a Scanning Electron Microscope and a deformation analysis was performed at regular intervals via image correlation. The authors show that twinning occurs as a result of an accumulation of strain visible before the appearance of the first twinned plane, followed by a densification and a progressive thickening of the twin lamellae. Fracturing only appears in a late stage as a precursor to the collapse of the sample. The application of the Calcite Stress Inversion Technique [6] to the twinned planes formed during the experiment shows a good consistency with the applied macroscopic stress. The Schmid factors extracted from this analysis are correlated to the loading curves. For crystals of about 200 µm in diameter, the critical resolved shear stress value falls in the range 6.75–8.25 MPa. These new results help improve our knowledge of the variation of the critical resolved shear stress for twinning in calcite as a function of grain size.

The last stress paper reports a regional application of an improved version of the calcite twin inversion technique by Shan et al. [8]. Starting from the established model that during the Mesozoic era NE to NNE-trending folds overprinted E–W-trending folds to form the Longshan dome in the central South China continent, Zheng et al. [25] performed a paleostress analysis using calcite twins to test this model and to provide new constraints on the process of reworking the continent. The paleostress reconstruction from limestone samples collected on the flanks of the dome allowed for the identification of several states of stress, either related to layer-parallel shortening or not. The authors propose a challenging complex deformation sequence where NE to NNE-trending folds predate E–W-trending folds. The ~ N–S regional compression responsible for the former folds may have a more profound effect than previously thought.

The last two papers deal with strain analysis from calcite twins. The paper by Groshong [26] presents a personal account of the origin and development of the pioneering twinned-calcite strain gauge technique [27], its experimental verification, and its relationship to stress analysis. The method enables the calculation of the 3D deviatoric
strain tensor based on five or more twin sets. A minimum of about 25 twin sets should provide a reasonably accurate result for the magnitude and orientation of the strain tensor. The experiments confirmed a magnitude accuracy of 1% strain over the range of 1–12% axial shortening. Samples with more than 40% negative expected values imply multiple or rotational deformation. If two deformations are at a high angle with respect to one another, the strain calculated from the positive and negative expected values separately provides a good estimate of both deformations.

Craddock et al. [28] present an application of Groshong’s twinned-calcite strain gauge technique through a regional study in the foreland of the Alpine orogen. The authors have studied samples from the internal Alpine nappes northwestward across the Alps and Alpine foreland to the older extensional margin along the Atlantic coast in Ireland. Along the coast of Northern Ireland, twinned calcite has recorded a sub-horizontal SW-NE shortening strain with a vertical extension and no strain overprint. This sub-horizontal shortening is parallel to the margin of the opening of the Atlantic Ocean, and this penetrative fabric is only observed ~100 km inboard of the margin to the southeast. The strain regime related to the younger collisional Alpine orogeny is dominated by SE-NW sub-horizontal shortening preserved in limestones and calcite veins in France, Germany, and Britain. This layer-parallel shortening strain, preserved across the foreland in the plane of the Alpine thrust shortening (SE-NW), is compared with twinning strains from the frontal Jura Mountains, the Molasse basin, the Pre-Alp nappes, the Helvetic and Penninic nappes, and the internal Tauern window. The results highlight the record of a consistent Alpine orogenic strain up to ~1200 km northwest from the Alps.

This new collection of high-quality articles will hopefully show that it is worth making an effort to better understand how twins develop in calcite single grains and aggregates and how twinning accommodates internal strain during the progressive deformation of calcite-bearing rocks. One should keep in mind that in fold-and-thrust belts and sedimentary basins where limestones are deformed in the diagenetic domain, calcite twin analysis remains to date the most powerful and widely accepted paleopiezometric technique [29].

**Funding:** This research received no external funding.

**Acknowledgments:** Geosciences’ in-house editors are gratefully acknowledged for their cooperation and support during manuscript processing. I also warmly thank the contributing authors for submitting their research to the Special Issue and the reviewers who helped ensure a high scientific standard to the contributions.

**Conflicts of Interest:** The author declares no conflict of interest.

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