Ripplocations provide a new mechanism for the deformation of phyllosilicates in the lithosphere

Deformation in Earth’s lithosphere is localised in narrow, high-strain zones. Phyllosilicates, strongly anisotropic layered minerals, are abundant in these rocks, where they accommodate much of the strain and play a significant role in inhibiting or triggering earthquakes. Until now it was understood that phyllosilicates could deform only by dislocation glide along layers and could not accommodate large strains without cracking and dilation. Here we show that a new class of atomic-scale defects, known as ripplocations, explain the development of layer-normal strain without brittle damage. We use high-resolution transmission electron microscopy (TEM) to resolve nano-scale bending characteristic of ripplocations in the phyllosilicate mineral biotite. We demonstrate that conjugate delamination arrays are the result of elastic strain energy release due to the accumulation of layer-normal strain in ripplocations. This work provides the missing mechanism necessary to understand phyllosilicate deformation, with important rheological implications for phyllosilicate bearing seismogenic faults and subduction zones.


Supplementary Note 1: Kink band morphology and formation
As described in the main text of this article, previous studies of kink bands have attributed their formation to the development of complex arrays of dislocation walls, which result in bending of the (001) plane within a finite region on the order of 1-2 µm 1,2 . However such a mechanism is unable to account for the degree of lattice curvature that we report in this study. In addition basal dislocations alone struggle to explain observed kink band asymmetry. Etheridge et al. 1 lay out a detailed description of kink band morphology and constitution. They define kink band asymmetry as: Where φ is the angle between (001) in the limb outside the kink band and the axial plane of the KBB and φK is the angle between (001) in the limb inside the kink band and the axial plane of the KBB.
The angle between the basal planes of the undeformed limb of the kink band and the deformed limb is known as the angle of bending (ω). According to Etheridge et al. 1 kink asymmetry is dependent on temperature and orientation with greater amounts of asymmetry in specimens deformed along [010] and in those deformed at higher temperatures, however, asymmetric kink bands occur at all conditions. This asymmetry of kink bands is the most difficult aspect of their morphology to explain through basal slip alone as it, by necessity, results in an expansion of the basal plane spacing in the region contained within the kink band. Previous authors 1-3 agree that this asymmetry, and the resultant c-axis parallel strain, requires some other deformation mechanism in addition to basal dislocation glide, and invoke non-basal slip and/or fracturing to account for this, despite little unequivocal evidence. Ripplocations as a recently recognised defect 4 are directly characterised by such an expansion in the basal plane spacing and, consequently, perfectly describe this phenomenon. Descriptions of kink bands on the scale of both optical microscopy 1 and TEM 2 report basal delaminations around and across KBBs. These delaminations possess variable symmetry and curvature and are similar in form to those described in this study and associated with the release of stored c-axis parallel strain. The distribution of these structures along KBBs is also in strong agreement with the computational models of Gruber et al. 5 (supplementary movie 4 of Gruber et al. 5 ) which model kink band formation using ripplocations instead of basal dislocations.

Supplementary Note 2: Sample locations and geological background
The three naturally deformed samples used in this study were collected from viscously deformed granitic orthogneiss rocks of the Cossatto-Mergozzo-Brissago (CMB) line and the associated Pogallo line shear zones in north western Italy. The CMB line is a vertical tectonic discontinuity which separates the lower crustal Ivrea-Verbano zone to the NW from the mid-upper crustal Serie dei Laghi to the SE. It was active at lower amphibolite facies conditions during the Permian and accounts for several tens of km of lateral displacement 6 . The Pogallo line is a slightly younger amphibolite to upper greenschist facies shear zone which cuts the CMB line at a very low angle 7 . The orthogneiss samples used were composed primarily of quartz and both plagioclase feldspar and K-feldspar.
Micas constituted between 15% and 20% of the samples with biotite usually comprising just over half of this with the remainder being muscovite.
The undeformed sample was a block of Westerly granite from Rhode Island, USA, which is a medium grained, relatively biotite-rich (5-10%) intrusive igneous rock. It is a useful standard material used extensively for deformation experiments in rock mechanics as it is homogeneous and has undergone very limited natural deformation.

Supplementary Note 3: Brittle v viscous character of ripplocations and the pressure sensitivity of micas
It is not clear whether deformation by ripplocations falls under the category of a brittle or a viscous mechanism. Unlike a brittle fracture they do not represent the permanent breaking of bonds but nor do they occur through in plane motion of one plane of atoms relative to another as in dislocation glide. In addition, their effects, such as kinking, are prevalent in phyllosilicates across the entire range of conditions within the Earth's crust and occur alongside both classically brittle and viscous processes. A key effect of ripplocations is the expansion of the unit cell parallel to the c-axis. Where this occurs in a recoverable manner, which essentially consist of stretching the interlayer bonding, it may be that this can be considered a viscous mechanism. However, once the unit cell expansion is too great, and the bonding is broken rather than stretched, a true delamination is formed, and the mechanism is better described as brittle. In reality, the boundary between these two states may be somewhat blurred, micro-scale delaminations may exist in a transient form that are small enough to heal and leave behind a regular lattice.
Viscous dislocation glide is possible in micas even at the pressure and temperature conditions of the Earth's surface 8 , where brittle mechanisms dominate in most minerals. Brittle behaviour is characterised by a proportional increase in yield strength with increasing lithostatic pressure, as higher pressures increase the energy required to break bonds. This response is observable in mica rich rocks up to their dehydration temperature 9 but is often coupled with a lack of microstructural evidence for brittle deformation. This unusual pressure sensitivity of phyllosilicates can now be explained by ripplocations. Gruber et al. 5 showed that the nucleation and motion of ripplocations is strongly dependent on their confinement (or the lithostatic pressure). At the same time, they do not result in fractures or other brittle features but rather produce a bending of lattice planes and kinking. Such observations strongly suggest that ripplocations are the mechanism responsible for this, until now, poorly understood mechanical response of phyllosilicates.  (c) Plot of K/Si ratio v time spent exposed to the beam as recorded in biotite from two different samples, POG 3, an ultramylonite and POG 7, a protomylonite. K is lost but the rate of decrease reduces over time and considerable K is retained in the biotite even after 15 minutes or more exposure. This is in contrast to the rapid and near total loss of Na previously reported in paragonite over a shorter timescale 28 .        Supplementary figure 13. EDX Spectra acquired from a biotite in the Westerly granite sample. The exposure value indicates the amount of time the point had been exposed to the beam prior to beginning the acquisition, this increases from 0 s in (a) to 360 s in (b) and 720 s in (c). A small decrease in the height of the K peak at approximately 3.3 keV occurs over time. Acquisition time was 120 live seconds per spectrum, accelerating voltage used was 200 keV.