Rheology of Earth Materials :

Closing the gap between timescales in the laboratory and in the mantle

13 February 2021 - New publication in Tectonophysics

When dislocations in quartz confess about climb

In naturally deformed samples, microstructures are often the only record left by past tectonic events and their detailed study is essential to decipher the thermomechanical history experienced by the rocks. In this paper which just appeared in Tectonophysics, we characterize dislocation microstructures in quartz grains from a Bohemian (Czech Republic) granulite.

A dislocation with a Burgers vector b gliding on a plane with normal ng (index “g” stands for glide) produces a shear proportional to tensor bng. Here, ⊗ is the dyadic product (the dyadic product of two vectors a and b is a second order tensor with component Aij= ai bj). To express the associated symmetric strain tensor, one defines the Schmid tensor:

For instance, a dislocation loop with a Burgers vector along y and gliding in the xy plane generates a S23 strain component:

Similarly, for a climbing dislocation:

This technique requires the knowledge of Burgers vectors as well as the indexing of the planes that contain the dislocations.

For the determination of Burgers vectors, we used the Ishida fringe technique (Ishida et al. 1980) which gives access to the g.b product from the number of thickness fringes terminating on the dislocation line:

For the indexing of the geometrical elements of the dislocation lines, we used transmission electron microscopy tomography of dislocations. This powerful technique imposes very constraining experimental conditions. The first is the perfect alignment of the diffraction vector with the tilt axis. The second is the recording of several images at different angles. To apply this technique to a material highly sensitive to electron irradiation, we have developed a methodology to reconstruct good quality volumes from a small number of images. This method consists in tracing the lines of dislocations before reconstruction. With this method, an electron tomography volume has been reconstructed with only 4 redrawn projected images and an angular range of only +/- 24°, i.e. projection angles of -24°,-8°, 8° and 24°.

The example below shows the characterization of a dislocation <a> which presents segments in different planes. These are identified by rotating the 3D model until curved segments appear straight. The electron diffraction pattern then allows to identify the planes which are viewed edge-on.

In quartz which has a trigonal structure, basal glide involves three <a> slip directions. As a function of increasing temperature, a transition from  -basal to <c> prismatic ({m}) glide is reported. Ball and White (1978) pointed the apparent difficulty of satisfying the von Mises criterion for general plasticity by activation of  -basal and  -prismatic glide alone. It has been proposed that the deformation of quartzite in the crust involves activation of dislocation climb to allow general plasticity of the polycrystalline aggregate. This fundamental limitation can also be solved by activation of  glide in pyramidal planes.

After Meng et al. 2019


In this study, all possible Burgers vectors of the quartz structure i.e. <a>, [c] and <c+a> have been characterized in a single grain. All dislocations exhibit rather complex 3D configurations and tomography allows us to exclude cross-slip as the most prevalent process, since dislocation segments in glide configurations are almost never found. Climb is a major process acting in this specimen. We have derived all parameters which are necessary to infer the strain components produced by the dislocations characterized either by glide or by climb:

The combination of glide and climb satisfies the five necessary systems of the von Mises-Taylor criterion. We find that the dislocation microstructure characterized is sufficient to produce a general deformation since all components of the strain tensor are non-zero and independent. In the literature, it has usually been assumed that the von Mises-Taylor criterion is satisfied by climb (implied by <a> or [c] dislocations) or by <c+a> glide. We find here a completely different situation where <c+a> climb is critical to ensure general deformation.

In most recent studies of quartz plasticity based on EBSD measurements, Visco-Plastic Self-Consistent (VPSC) models have been based on glide only and on a succession of slip systems with increasing temperature: <a>-glide is successively activated in the easy basal plane, and then in the rhombohedral planes followed by  <a>-prismatic and finally  <c>-prismatic (see Morales et al. 2011, Keller and Stipp, 2011 and Morales et al. 2014). The role of <c+a> glide has only been marginally considered. Our measurements, which need to be confirmed by further characterizations, suggest that these interpretations should be reconsidered.



  • Y. Ishida, H. Ishida, K. Kohra, H. Ichinose, (1980): Determination of the Burgers vector of a dislocation by weak-beam imaging in a HVEM. Philos. Mag. A 42 (1980), 453–462. doi:10.1080/01418618008239369.
  • L.M. Keller, S. Stipp, The single-slip hypothesis revisited: Crystal-preferred orientations of sheared quartz aggregates with increasing strain in nature and numerical simulation. Journal of Structural Geology, 33 (2011) 1491-1500. https://doi.org/10.1016/j.jsg.2011.07.008
  • L.F.G. Morales, D. Mainprice, G.E. Lloyd, R.D. Law, Crystal fabric development and slip systems in a quartz mylonite: an approach via transmission electron microscopy and viscoplastic self-consistent modelling, Deformation Mechanisms, Rheology and Tectonics: Microstructures, Mechanics and Anisotropy, David J. Prior, Ernest H. Rutter, Daniel J. Tatham, 2011, 151-174. https://doi.org/10.1144/SP360.9
  • L. F.G. Morales, G.E. Lloyd, D. Mainprice, Fabric transitions in quartz via viscoplastic self-consistent modeling part I: Axial compression and simple shear under constant strain. Tectonophysics, 636 (2014) 52-69. https://doi.org/10.1016/j.tecto.2014.08.011


To learn more:

A. Mussi, J. Gallet, O. Castelnau & P. Cordier (2021) Application of electron tomography of dislocations in beam-sensitive quartz to the determination of strain components. Tectonophysics, 803, 228754. https://doi.org/10.1016/j.tecto.2021.228754


This paper has been published in Tectonophysics in a special issue in honor of Adolphe Nicolas entitled:

Upper mantle deformation, seismic anisotropy, and mid-oceanic ridge dynamics

Adolphe Nicolas passed away in March 2020, after more than 50 years of contributions to our understanding of how deformation occurs in the Earth. An editorial team composed of Andréa Tommasi, Alain Vauchez, Shaocheng Ji, Juergen Koepke, Katsuoshi Michibayashi, Jose Alberto Padron-Navarta and Satish Sing decided to publish a Special Issue to honor Adolphe's legacy to Earth Sciences by illustrating the impact of his contributions on today research.

This special issue is intended to cover the large range of domains to which he contributed during his career:

  • his early works on rock deformation processes and his collaboration with JP Poirier, which, by "transferring" knowledge from Materials Sciences to Earth Sciences, provided a new understanding of rock microstructures, crystallographic orientations, and deformation mechanisms, setting the basis for the kinematic interpretation of solid-state flow of rocks; (It is in this section that we place our contribution)
  • his pioneering contribution to understanding the causes of seismic anisotropy, which promoted the use of seismic anisotropy measurements to map the upper mantle deformation;
  • his extensive work on peridotite massifs and ophiolites, which greatly contributed to our understanding of deformation processes in the oceanic and continental mantle;
  • his 20 years of investment in mapping the Oman and UAE ophiolite; these studies have stimulated the development of a physics-based understanding of the processes active at midocean fast-spreading ridge systems, from asthenospheric upwelling patterns to the hydrothermal exchanges at the ridge axis.