Liassic limestones on the coast of Somerset in the UK contain dense arrays of calcite microveins with a common, but poorly understood microstructure, characterized by laterally wide crystals that form bridges across the vein. We investigated the mechanisms of formation and evolution of these ‘wide-blocky’ vein microstructures using a combination of high-resolution analytical methods, including virtual petrography, optical cathodoluminescence and scanning electron microscopy techniques (e.g. energy-dispersive X-ray spectrometry, back-scattered electron imaging, cathodoluminescence and electron back-scattered diffraction), laboratory experiments and multiphase field modelling. Our results indicate that the studied veins formed in open, fluid-filled fractures, each in a single opening and sealing episode. As shown by the optical and electron back-scattered diffraction images, the vein crystals grew epitaxially on grains of the wall rock and we hypothesize that their growth rates differed depending on whether the crystals were on a wall rock grain substrate that fractured intergranularly (slow growth rates) or transgranularly (rapid growth rates). Our multiphase field models support this hypothesis, showing that wide, blocky crystals only form where there are significant differences in the growth rate and are dependent on the type of seed grain. These results provide strong evidence for extreme growth competition, a process that we propose controls vein-filling in many micritic carbonate reservoirs, as well as demonstrate that the characteristics of the fracture wall can affect the filling processes in syntaxial veins.

Supplementary material: The description and images of the studied thin sections are available at https://doi.org/10.6084/m9.figshare.c.5172371. High-resolution optical microscopy mosaics (under plane-polarized- and crossed polarized light) of the thin section collection in PetroScan file format are available on request from the authors.

Fluids have major roles in the Earth's crust: they can alter porosity and permeability, transport material, dissolve and precipitate minerals and interact with deformation (Connolly 2010; Laubach et al. 2019). Syn-tectonic calcite- or quartz-filled veins are common in low-grade metamorphic rocks in the upper and middle crust (Beach 1977; Ramsay and Huber 1984; Passchier and Trouw 2005), where they precipitate from aqueous fluids within fractures. The precipitation of vein-filling minerals is controlled by poorly understood coupled and commonly cyclic mechanical, hydraulic and chemical processes (Tsang 1991; Berkowitz 2002; Rutqvist 2015; Berkowitz et al. 2016).

Fracture mechanics and fracture-filling in deep, hydrothermal and reactive environments are relevant to both, basic geoscience and applied studies, related to crustal rheology and transport. Examples include the seismic cycle (Sibson et al. 1988; Micklethwaite and Cox 2006), the evolution of ore deposits (Cox 2005) and the production and injection of fluids from and into the subsurface (Knipe 1993; Stephanson et al. 1997; Tsang 1999; Philip et al. 2005; Lander et al. 2008; Dockrill and Shipton 2010; Olson et al. 2010; Lander and Laubach 2014), with special relevance for the subsurface integrity of reservoirs (Rossi et al. 2002).

Many veins evolve by means of repeated microcracking followed by the precipitation of vein-filling minerals after each opening increment: the crack–seal mechanism (Ramsay 1980). Veins formed by crack–seal processes usually contain a series of solid and/or fluid inclusion bands that are parallel to the vein walls. Such inclusions are interpreted as evidence for repeated opening and filling of the pre-existing veins as a result of cyclic changes in fluid pressure or far-field stresses (Ramsay 1980; Fisher and Brantley 1992). Each crack increment is usually of the order of a few micrometres (Cox and Etheridge 1983; Cox et al. 1987; Williams and Urai 1989; Xu 1997; Renard et al. 2005).

The cracking event locally increases the permeability of the rock, whereas during the sealing event growing crystals fill and seal the crack and (partly) restore the rock's strength (Cox et al. 1987; Toriumi and Hara 1995; Virgo et al. 2014). The strength and secondary permeability of the rock is thus dependent on the progress and extent of mineral filling in veins. In turn, the fracture characteristics affect crystal growth: the fracture aperture and surface roughness (at both the macro- and atomic scales) control advective flow, but also the development of facets on the growing crystals (Urai et al. 1991).

Vein-fill crystals have a rich variety of morphologies (e.g. fibrous, elongate or blocky) depending on their formation mechanism(s) (Bons et al. 2012). The microstructures of veins are an important source of information on the kinematics and the hydraulic and mechanical state of the deforming crust (Urai et al. 1991; Oliver and Bons 2001; Passchier and Trouw 2005; Bons et al. 2012). The morphological characteristics of the vein minerals contain information on the relative opening and filling rates of fractures and the timing of fracturing (Laubach et al. 2004; Becker et al. 2011; Ankit et al. 2015a; Fall et al. 2015; Lander and Laubach 2015).

The evolution of vein microstructure is best understood for antitaxial veins, which are commonly fibrous (Ankit et al. 2013). The mineralogy of such veins is different from that of the wall rock and fracturing always localizes at the vein–wall rock interface as a result of poor adhesion. Veins grow by small- (submicron-) scale increments that limit the development of crystal facets (Bons et al. 2012). Crystal interfaces that are initially rough develop facets during the filling phase, but these facets disappear during the final sealing phase (Nollet et al. 2005). Urai et al. (1991) proposed a kinematic model for the formation of fibrous vein morphologies by a crack–seal mechanism, showing that fibres may or may not track the opening trajectory of the vein depending on the boundary conditions. Building on this, front-tracking numerical models of antitaxial crack–seal veins were used to explore the effects of the crystal growth rate and morphology, the crack aperture and roughness, and the opening frequency and opening trajectory (Bons et al. 2001; Hilgers et al. 2001; Koehn et al. 2001).

Antitaxial veins are, however, relatively rare, and are limited to calcite veins in black slates (e.g. Hilgers and Urai 2002), gypsum veins in mudstones (e.g. Philipp 2008) and halite veins in mudstones (e.g. Leitner et al. 2014). The vast majority of veins in rocks at depths of 1–10 km and at 100–350°C grow epitaxially from both sides of the fracture (syntaxial or ataxial veins; Hilgers et al. 2001; Passchier and Trouw 2005), where the vein mineralogy is the same as that of the wall rock. In some cases, syntaxial veins do not grow by the reactivation of pre-existing veins, but form new veins in each crack–seal cycle. This process is referred to as a crack–jump mechanism (Caputo and Hancock 1999; Virgo et al. 2014). Because of the difficulty in modelling fracture re-opening at different locations and simultaneous crystal growth from two opposing sides of the crack, the growth and fill mechanisms of syntaxial veins remain poorly understood.

We investigated the mechanisms of syntaxial vein growth in a suite of calcite veins in Jurassic micritic limestones that display little-studied ‘wide-blocky’ microstructures. We use the term wide-blocky to refer to vein crystals that bridge the vein and are laterally wider than the aperture of the vein. The morphology of equant-blocky and elongate-blocky syntaxial vein microstructures is generally well described and has been modelled by Ankit et al. (2013). By contrast, wide-blocky veins, although observed in several micritic carbonate reservoirs in Italy (Bons et al. 2012) and Oman (Arndt 2015), have rarely been described in detail or interpreted in terms of their formation mechanisms.

We present here a conceptual model to explain the fundamental processes involved in the development of wide-blocky microstructures on the basis of observations from natural veins, an analysis of fracture surface morphology and numerical simulations. We distinguish three types of veins based on their microstructural differences, where the crystal size distributions and the relationships between vein aperture and calcite crystal sizes can be successfully modelled in terms of extreme growth competition.

Our study area is located on the southern side of the Bristol Channel Basin in Somerset, UK (Fig. 1) and features rhythmic sequences of limestone, marl and shales of Liassic age (Palmer 1972; Whittaker and Green 1983; Cox et al. 1999). The sedimentary sequence was deposited during north–south extension and the formation of east–west-striking sedimentary basins and normal faults. Normal faults in the study area are regularly spaced and mostly dip towards the south (Dart et al, 1995), with displacements of up to 100 m (Peacock and Sanderson 1999).

The veins studied in this project are present in limestone layers (Fig. 2a). They are filled with calcite crystals and orientated sub-perpendicular to the bedding. The veins are sub-parallel to east–west-striking normal faults and are considered to be part of their fault damage zone (Caputo and Hancock 1999; Peacock and Sanderson 1999, 2018). Nixon et al. (2019) reported that faults with large displacements (>15 m) have narrow damage zones (<10 m), whereas faults with small displacements (<15 m) have wide damage zones (>20 m). No correlation was observed between vein intensity and the thickness of the limestone layers. However, especially high vein intensities were noted along the fault tips and intersections, correlating with high local stresses (Nixon et al. 2019). A decrease in vein spacing and an increase in aperture towards the faults was noted by Rawnsley et al. (1998). Peacock and Sanderson (1992) suggested that calcite veins were precursors for the faults, whereas Rawnsley et al. (1998) showed that high-density microveins formed later than the set of calcite veins that predate the faults. Roberts et al. (1999) proposed that the dilation of pre-existing calcite vein sets resulted from fault propagation.

The majority of the veins studied here are dense arrays of parallel microveins <1 mm wide (Fig. 2b–d). To explain the formation and distribution of these microveins, Caputo and Hancock (1999) proposed a crack–jump mechanism as opposed to a crack–seal process (Ramsay 1980), suggesting that the formation of new veins is more common than the reactivation of pre-existing veins.

Sample preparation

Samples containing typical arrays of microveins were collected from Lilstock, Blue Anchor and Kilve beaches (Fig. 1). In total, 18 double-polished ultra-thin sections (<10 µm thick) were prepared for microstructural and petrological analysis (see Supplementary Material). The most important benefit of ultra-thin sections is that they allow the imaging of grains that are smaller than the thickness of conventional thin sections (c. 30 µm) and have the ability to detect crystal boundaries in the narrowest veins (apertures c. 10 µm). In addition, as a result of the high birefringence of calcite, sections thinner than the standard thickness are required for observing the first- and second-order interference colours that reveal intracrystalline microstructures. We cut the samples for thin sections sub-parallel to bedding and perpendicular to the vein orientation to study the crystal growth morphology with respect to the fracture opening direction. For optical microscopy, thin sections were polished mechanically and finished with a 1 µm diamond paste. For the scanning electron microscopy (SEM) electron back-scattered diffraction (EBSD) and cathodoluminescence analyses, the thin sections were further polished with a colloidal silica solution for c. 3 min to chemically remove the surface damage caused by mechanical polishing.

Three-point bending test

Fracturing experiments were performed on pristine natural samples to study the fracture morphology prior to the growth of vein crystals. As suggested by Arndt (2015), the proportion of intergranular v. transgranular fracture pathways might control the formation of wide-blocky crystals. To quantify this parameter for numerical modelling, we produced mode I fractures at room temperature using the three-point bending method. Samples were cut in blocks of c. 4.5 cm × 2 cm × 1 cm from a single-veined, but unfoliated, limestone sample collected at the Lilstock locality. The blocks lacked visible natural fractures. A U-shaped notch (2 mm deep) was cut into the upper surface of the samples to stabilize the steel rod under the press. This arrangement produced mode I fractures sub-parallel to the pre-existing veins (misorientation <5°). The experiments were carried out with a Zwick uniaxial press with loading rates of 0.3 or 0.5 mm min−1. All experiments were stopped once the sample fractured.

Imaging techniques

Thin sections were scanned using a PetroScan Virtual Microscope (Schmatz et al. 2010; Virgo et al. 2016) with a 10× objective under plane-polarized light and at ten different orientations of crossed polarizers. The PetroScan system, developed by RWTH Aachen University and the Fraunhofer Institute for Applied Information Technology, consists of a high-end polarization microscope equipped with a camera and an automated sample stage and image post-processing software. It allows the digitization of entire rock thin sections at high magnifications. With crossed polarizers, the extinction behaviour of each pixel is extracted from scans taken at several rotation angles and fitted to sin2θ curves that represent changes in the pixel intensity in a 360° interval (Heilbronner and Pauli 1993). High-resolution digital mosaics were used for image analysis and as a reference layer for SEM-based energy-dispersive X-ray spectrometry (EDS), back-scattered electron (BSE), EBSD and cathodoluminescence images. Full resolution scans of the studied thin sections are available on request from the authors.

A selected set of uncoated thin sections was imaged with a Cambridge Image Technology CL8200 Mk5-2 cold-cathode optical cathodoluminescence system. The imaging conditions were c. 15 kV accelerating voltage, 335 µA gun current and 0.003 mbar chamber pressure.

Secondary electron, BSE imaging and EDS analyses of experimentally fractured and natural vein samples were performed on tungsten-coated thin sections with a Zeiss SUPRA 55 field-emission scanning electron microscope at the Institute for Structural Geology, Tectonics and Geomechanics, RWTH Aachen University. To estimate the amount of broken grains on fracture surfaces, secondary electron imaging was performed on the experimentally broken samples at a working distance of c. 7 mm, an accelerating voltage of 3 kV and a magnification of 4000× for segmentation and 8000× for documenting the details of the fracture surfaces. BSE imaging and EDS measurements were performed at working distances of c. 10 mm and accelerating voltages of 15–20 kV.

EBSD analyses of natural, calcite-filled veins were carried out at the Central Facility for Electron Microscopy, RWTH Aachen University using a Zeiss Gemini SEM 300 instrument equipped with an Oxford Symmetry EBSD system. Analyses were performed under variable pressure conditions on samples that were tilted 70° at working distances of c. 10 mm using an accelerating voltage of 20 kV and 1 µm step sizes. The data were indexed with Aztec analytical software and post-processed with Oxford Instruments HKL Channel 5 software using the noise reduction method of Bestmann and Prior (2003).

The SEM cathodoluminescence analyses were performed at the Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin with a Zeiss Sigma High Vacuum FE-SEM instrument equipped with an Oxford X-Max 50 mm2 silicon drift detector, a pole piece-mounted BSE detector and a Gatan MonoCL4 system. Carbon-coated samples were imaged at accelerating voltages of 5 kV with a 120 mm aperture, a 130–150 μs dwell time, sample currents of c. 3.5 nA and a resolution of 2048 × 2048 pixels following the guidelines of Ukar and Laubach (2016). Under these conditions, image smearing caused by calcite phosphorescence was rarely a problem.

Image analysis

We measured the fraction of the total fracture surface areas made up by calcite cleavage planes to estimate the proportion of transgranularly broken wall rock calcite grains on the experimental fracture surfaces. The cleavage planes were recognized in secondary electron images as flat and smooth surfaces in the midst of rougher morphologies (Fig. 3b, c). First, four mosaics consisting of 16 images each were taken in different regions of the experimental fracture surfaces at 4000× magnification. The smooth areas that were interpreted to be calcite cleavages planes were then manually segmented from these image mosaics (Fig. 3d). The areas occupied by the segmented cleavage planes were calculated from binarized images using the Fiji/ImageJ (https://imagej.net/Fiji) Particle Analysis tool and plotted as histograms of the diameter of the circle that had an equivalent area to that of the cleavage plane (Fig. 3e).

Size analysis of vein crystals was performed on 59 veins from six thin sections (Fig. 4a). Photomicrograph mosaics were imported into the Fiji/Image J software and the vein apertures and crystal widths were measured with a line measurement tool. The vein apertures were determined as an average from at least ten measurements perpendicular to the vein walls for each data point in Figure 5b. The crystal width was measured along the median line of each vein, in the direction parallel to the fracture walls (Fig. 5b). The average crystal width for each vein was calculated from 20–70 measurements.

ImageJ/Fiji software was also used to determine the wall rock 2D porosity using BSE images. The images were transformed into 8-bit files. The darkest pixels that represent porosity were segmented by thresholding and measured as a proportion of the total number of pixels in the images.

Multiphase field modelling

A thermodynamically consistent multiphase field model was used to model crystal growth in calcite veins. For a detailed discussion of the model equations and numerical implementation, interested readers are referred to Ankit et al. (2013), Wendler et al. (2016) and Prajapati et al. (2017).

We consider a domain Ω consisting of N phase-field order parameters, which are collected in the phase-field vector ϕ(x,t)=[ϕ1(x,t),,ϕN(x,t)]. Each phase-field ϕα(x,t)[0,1] describes the volume fraction of a particular phase at position x and time t. The interface between the different order parameters is characterized by a diffuse region of finite width, in which the magnitude of phase-field ϕαvaries smoothly from 1 inside the bulk phase to 0 outside. The diffuse interface width is related to the length scale parameter ε. At each computational grid point, the summation constraint α=1Nϕα=1 is ensured. The total free energy in the computational domain is given by
F(ϕ,ϕ)=Ω[ϵa(ϕ,ϕ)+1ϵw(ϕ)+fbulk(ϕ)]dΩ=Fintf+Fbulk
with the gradient energy density ϵa(ϕ,ϕ),the potential free energy density 1ϵw(ϕ),and the bulk free energy density fbulk(ϕ). The first two terms represent the interfacial energy density contribution. We use an anisotropy formulation in the gradient energy density to model a faceted grain growth and an obstacle-type potential energy density (e.g. Ankit et al. 2013; Prajapati et al. 2017). The bulk free energy density is linearly interpolated in a diffuse interface region.
Based on the work of Steinbach (2009), the evolution equation for each phase-field ϕαreads as
ϕαt=1NϵαβN[Mαβ(n^)(δFintfδϕαδFintfδϕβ8ϕαϕβπ(δFbulkδϕβδFbulkδϕα))].
The mobility Mαβ(n^)of the α–β interface is given by
Mαβ(n^)=Mαβ0aαβkin(n^)
with the kinetic coefficient Mαβ0and the kinetic anisotropy aαβkin(n^)which is dependent on the interface normal vector n^. In this approach, the mobility is not interpolated, which allows the use of different mobilities for different phases and prevents unphysical retarded movement of solid–solid–liquid triple points. We follow the approach of Wendler et al. (2016) for modelling a faster growth rate of rough non-equilibrium crystal surfaces and a decreased growth velocity after the crystal facets have formed (e.g. Lander et al. 2008) and use
aαβkin(n^)=(1+δ(maxk{n^ηk,αβ}maxk1{n^ηk,αβ}))maxk{n^ηk,αβ}
for the kinetic anisotropy. Heremaxk{}gives the largest and maxk1{}the second largest argument of the scalar products. With the kinetic anisotropy strength parameter (δ) the growth rate difference between rough and faceted crystal surfaces can be adjusted.

Microstructures

Wall rock

The limestone samples that contain the studied veins are mudstones and wackestones (Dunham 1962). They are composed of microfossils (c. 2–15%), micritic calcite (80–90%) and accessory phases (<5%), including quartz, dolomite, albite, clays and pyrite (Fig. 2d, e). Wall rock calcite grains average c. 10 µm in diameter and usually form c. 50 µm wide clusters, whereas the quartz, albite and dolomite occur as single grains. Calcite shows subhedral shapes in the outermost part of the clusters (Fig. 2e). Dolomite is mostly euhedral and displays chemical zoning in the BSE images. Clays line the calcite grain boundaries, whereas pyrite forms sub-micrometre, equidimensional grains that aggregate in spheroidal framboids with diameters ranging from 1 to 50 µm. Pyrite framboids usually aggregate in elongated vein-parallel bands. The bioclast fragments and pyrite bands that are cut by veins typically show minimal or no lateral offset, indicating that these are opening mode (mode I) fractures (Figs 2d and 5f). The vein walls are usually irregular rather than straight as they circumvent, instead of breaking, micritic carbonate grains of the wall rock. This is best seen in the BSE images of natural samples, which demonstrate that vein walls usually follow the boundaries of calcite grains or accessory phases (Fig. 2e).

Image analysis of BSE images indicates 0.1–0.9% porosity for the limestone wall rock, depending on the sample and the location of the measurement area (Fig. 2e). The largest pores are a few micrometres in diameter, but most pores are <1 µm.

Veins

Most of the veins in the studied samples are sub-parallel. Cross-cutting relationships are rare, whereas deflection geometries at the intersections of two veins are common (Fig. 2b, c). Most veins are <1 mm wide and can be classified as microveins (Fig. 2b–d). The widest veins are 1–5 mm in aperture and relatively scarce (Figs 2b and 5e, f). Although hardly visible to the naked eye, microveins are pervasive throughout the samples, forming bundles that can contain >30 individual veinlets, spaced 1–50 µm apart (Fig. 2d).

All the veins in the studied samples are partially to completely filled by calcite crystals. The elemental compositions of vein calcite and wall rock calcite are indistinguishable in EDS images, but in the BSE images the vein calcite can be recognized by its brighter colour than the wall rock calcite, allowing the wall rock–vein interfaces to be traced accurately (Fig. 2e).

The size of the vein-filling calcite crystals varies depending on the aperture of the vein, so that larger veins tend to be filled with wider crystals (Figs 4a, b and 5a–d). We distinguish three types of vein, depending on their aperture and crystal morphologies. Type 1 veins are the narrowest (<50 µm) and are filled by equant calcite crystals. In some areas, a single-crystal bridges the vein, whereas in others the vein is bridged by two or three calcite crystals (Figs 4 and 5a, b). The larger the vein aperture, the wider the crystals it contains and the more prevalent the single-crystal bridges become.

Type 2 veins are 50–100 µm wide and dominated by wide-blocky crystals that bridge the vein. The wide-blocky crystals have large aspect ratios, with their longest dimension parallel to the vein walls. These veins are characterized by a marked increase in the average width of the vein-filling crystals (Figs 4 and 5a–d). Small euhedral crystals rim the vein walls, but these are typically enclosed by larger wide-blocky crystals. Multi-crystal (complex) bridges in are rare type 2 veins.

Veins that are wider than 100 µm (type 3) display elongate-blocky (Fisher and Brantley 1992) crystal morphologies, with their longest dimension orientated perpendicular to the vein walls (Figs 4a, b and 5e, f,). In contrast with the type 2 veins, the average crystal width does not depend on the vein aperture and is similar to that of the widest type 2 veins (Fig. 4a). Type 3 veins >100 µm show a strong increasing crystal size gradation from the walls to the centre of the vein (Fig. 5e), whereas the smaller type 3 veins do not (Fig. 5f).

Most type 1 and type 2 microveins lack wall rock inclusion bands, but these are common in type 3 veins (Fig. 5a–f). The spacing between the inclusion bands varies from c. 10 µm to hundreds of micrometres. In many cases, the inclusion bands are not continuous across crystal boundaries, instead occurring as sub-parallel stacks within crystal interiors (Figs 4a, b(iii) and 5f).

Calcite crystal morphologies in veins

Rare examples of the widest (type 3), incompletely filled veins served to investigate the morphological characteristics of vein crystals. The crystals show euhedral terminations with sharp, well-defined edges and planar interfaces (Fig. 6a). In some areas, they are slightly weathered or broken. Exposed facets display a wide range of morphologies, including rhombohedral (Fig. 6b) and, in some cases, elongated crystals possibly belonging to the scalenohedral type (Fig. 6c).

Vein textures in cathodoluminescence

Optical cathodoluminescence images show marked differences between the luminescence of vein and wall rock calcite (Fig. 7). Calcite in the wall rock is usually dark orange luminescent, with the exception of bioclasts, which are bright orange luminescent (Fig. 7a, b). Calcite in most veins is dark brown luminescent and it is referred to as type A calcite (Fig. 7a–c). The luminescence of type A calcite remains dark brown, even where the veins cut across bright orange luminescent bioclasts along the vein wall (Fig. 7b). Brighter linear features within the type A domains represent crystal boundaries or growth zones and twin planes, as identified in the optical images. In some cases, type A calcite contains pale brown patches within a crystal. In a very few cases, such patches extend beyond the boundaries of individual crystals (Fig. 7c). Type B vein calcite is bright orange luminescent. Type B domains are rare, observed in the central parts of microveins and usually do not exceed 500 µm in size (Fig. 7a). In areas that contain type B calcite, the boundary of the vein is rimmed by a narrow zone of type A calcite (Fig. 7d and e). Type B calcite displays rhombic and/or triangular morphologies that are connected to the wall rock interfaces and extend towards the vein interior, where they form euhedral facets. In some cases, type A calcite forms bridges composed of one or more crystals that connect both sides of the wall rock across the vein (Fig. 7d, e). Type B calcite domains are polycrystalline, consisting of multiple smaller crystals, as identified in cross-polarized images, that show variations in their luminescence intensity. However, in some cases, a single calcite crystal can consist of a type A core and a type B rim. Some fractures are only partially filled, preserving pores in their central parts; the pores are typically adjacent to type B calcite that shows euhedral terminations towards the pores (Fig. 7d, e).

SEM cathodoluminescence images reveal patchy patterns and zonation bands within vein-filling calcite crystals that are not visible using any other imaging technique (e.g. optical microscopy, optical cathodoluminescence or BSE) (Fig. 8). Some crystals show micron-scale banding around a bright luminescent crystal core with irregular boundaries (Fig. 8a–c). The zonation bands are typically a few microns wide and consist of straight segments with sharp corners, resembling crystal facets. They truncate at calcite crystal boundaries or against the vein wall. In some cases, both the irregular, bright cores and zonation bands are truncated within the crystal interior by a darker luminescent band parallel to the wall rock (Fig. 8b). Another common cathodoluminescence texture in the imaged veins is arrays of fine bands that resemble herringbone-like structures (see Ukar and Laubach 2016) (Fig. 8a, b). Multiple parallel herringbone arrays are present within a single crystal. Under cross-polarized light, the same calcite crystals show subtle undulose extinction and twinning, which do not coincide with any of the observed cathodoluminescence patterns (Fig. 8d–f).

Crystallographic orientations

In cases where calcite veins cut micritic wall rock grains, the vein crystals usually have the same extinction angle as the cut wall rock grains, indicating epitaxial growth that maintains crystallographic continuity between the wall rock and the vein crystals (Fig. 9a, b). Similarly, in veins that cross-cut carbonate bioclasts, vein calcite has the same extinction angle and interference colours as the bioclasts (Fig. 5d). These relationships can be best observed using a combination of high-resolution EBSD maps and BSE images (Fig. 9a, b). Wall rock calcite usually shows a sharp boundary with vein calcite in BSE images, but no difference in crystallographic orientation can be observed across the vein boundary in the EBSD maps. No preferred crystallographic orientation was observed in the wall rock (Fig. 9d), nor among the 46 large wide-blocky crystals that were analysed statistically (Fig. 9c).

Experimental fracture surfaces

The morphology of the experimental fractures produced using three-point bending tests in order to understand the characteristics of the possible initial fracture morphology showed good correspondence with the natural vein geometries. The experimental fractures are sub-parallel to the adjacent natural veins, rarely cross-cutting or converging with them (Figs 2d, e, 3a and 5a–d).

Optical and secondary electron images show that the experimental fracture surfaces follow mixed pathways along grain boundaries, including micritic, microfossil and accessory mineral grains, and transgranularly along cleavage planes of broken calcite grains (Fig. 3b, c). In the secondary electron images the grain boundaries can be recognized as rough, irregular surfaces and the fossils are clearly distinguishable by their patterned intraparticle nanoporosity and rounded outer shapes, whereas the cleavage planes of calcite have flat faces with hackles and steps. The grains are usually coated by clay minerals, organic material and/or dust particles, as shown by the EDS and BSE images (Fig. 2e) of the polished sections, whereas the cleavage plane surfaces are smooth and devoid of grain coatings (Fig. 3c).

For modelling purposes, all the identifiable cleavage planes were manually segmented from secondary electron image mosaics. Figure 3d shows an example of one of the segmented areas where the cleavage planes constitute c. 10% of the fracture surface. The cleavage planes are irregularly distributed and constitute between 8 and 12% of the total area of the fracture surface in the four areas analysed. The cleavage plane diameters range between 2 and 18 μm, averaging 4–6 μm (684 data points) and c. 50% of the cleavage planes have diameters that are larger than the average wall rock grain size (Fig. 3e).

Multiphase field model

The multiphase field simulations were set up in a 2D domain with an equidistant computational grid of (2500Δx × 245Δx) cells (Table 1). The initial simulation set-up for a fracture aperture of 7 Dm (Dm = average calcite grain size in wall rock) is shown in Figure 10a, b. The initial wall rock grain structure was generated with a Voronoi algorithm and the grains in the wall rock were set to be orientated randomly, consistent with the EBSD data from natural samples (Fig. 9a, d). Under diagenetic conditions, Lander and Laubach (2015) documented faster growth rates on anhedral (broken) surfaces than the euhedral facets of quartz crystals. Fast growth rates on transgranularly broken dolomite grains in carbonate host rock were also reported and modelled by Gale et al. (2010). In addition, Ajdukiewicz and Larese (2012) and Williams et al. (2015) showed that epitaxial mineral precipitation is slower on grain boundaries with nucleation discontinuities (such as defects or microscale coatings) than on fresh fracture surfaces. Using this as a guideline, wall rock calcite grains that were broken along cleavage planes were considered to be fertile seed grains with faster growth rates. The distribution of these fertile grains was incorporated into the simulations based on the distribution of the segmented calcite cleavage surfaces determined from secondary electron images of experimentally broken samples along profile 1 in Figure 3d. Transgranularly fractured (broken) grains were mirrored on the other side of the fracture, whereas the rest of the wall rock grains were not mirrored to represent intergranular fracture paths. The intergranularly broken grains were assigned a mobility reducing factor (ξ = M0fert.gr,-liq/M0hind.gr,-liq) from 1 (fastest growth) to 20 (slowest growth) to represent the contrast in growth rates compared with the transgranular fracture surfaces (Table 1). Solid–solid interfaces (crystal boundaries) were set to be immobile so that crystal growth only occurred at solid–liquid interfaces. Fracture apertures were scaled using the apertures of natural veins with respect to the average calcite grain size in the wall rock (Dm) using factors from 1 (narrowest) to 12 (widest). The fractures open in a single step in all simulations. Different aperture sizes were obtained by shifting the lower wall rock sideways along the y-axis using the geometric shift algorithm of Prajapati et al. (2018). Crystal growth was considered to be syntaxial in all cases, where crystals grew epitaxially on wall rock calcite grains from both fracture walls towards the fluid-filled vein centre (Figs 5c, d, 7d, e and 9a, b).

In the analysed natural veins, calcite crystals display rhombohedral and scalenohedral morphologies (Fig. 6). As the rhombohedral shape is one of the most common calcite forms in nature and dominantly rhombohedral shapes were also observed in the cathodoluminescence images of natural veins (Fig. 7d, e), the vein crystals in simulations were modelled using right-handed projections of rhombohedral calcite (Fig. 10c). Test runs using scalenohedral crystal shapes showed only small differences in the final vein morphologies, indicating little effect of crystal form on the simulated microstructures. We used the following vertices for the anisotropy formulation of the gradient energy density and the mobility for a right-handed projection of rhombohedral calcite in Figure 10c (Table 1), so that the crystals developed flat facets and sharp corners, according to the crystal symmetry of calcite:
η1,2=[0,±0.75]η3=[1,0.25]=η4
Simulations were performed using a constant driving force for all crystals (Table 1). All the model equations were implemented in the Pace3D (Parallel Algorithms for Crystal Evolution in 3D) software package (version 2.5.1).

Numerical modelling

Figure 11 shows three types of vein microstructures that form by crystal growth in open, fluid-filled fractures with a range of apertures (Dm 1–12). Figure 11a is an example where vein crystals grow epitaxially on all wall rock grains at the same rate, independent of the growth surface being transgranular or intergranular. The narrowest veins (Fig. 11a; Dm 4) display equant-blocky morphologies with crystals growing epitaxially on the wall rock grains and stretched crystal morphologies evolving on transgranularly broken calcite grains that are mirrored on both sides of the vein. The widest veins (Fig. 11a; Dm 12) display elongate-blocky textures with the largest crystal dimension perpendicular to the vein walls and the crystal size increases towards the centre of the vein.

Figure 11b, c show simulations with varied growth rates. Mirrored grains that represent transgranular fracture surfaces have the fastest growth rates. The growth rate of the rest of the grains is reduced by the growth-inhibiting factor ξ. Wide-blocky textures only form when growth inhibition is introduced for some crystals. If the growth rate of the fast-growing crystals is five times faster than that of the rest of the crystals (Fig. 11b), then the lateral extent (parallel to the vein walls) of wide-blocky crystals increases with increasing fracture aperture. If the growth rate of the fast-growing crystals is 20 times faster than that of the rest of the crystals (Fig. 11c), then the width of the wide-blocky crystals does not vary with fracture aperture. In cases where the differences in growth rate are large, only fast-growing crystals bridge the fracture, whereas the rest of the crystals are quickly outcompeted during the early stages of vein-filling. The simulations that best recreate the vein width–crystal shape and size relationships observed in the Somerset veins are those where the ξ value is c. 5. In such scenarios, the narrowest veins (Fig. 11; Dm 1) display equant-blocky and stretched crystal morphologies, whereas wide-blocky morphologies dominate in veins with large apertures (Fig. 11; Dm 7–Dm 12).

The formation of mineral veins involves a complex interplay between mechanical and chemical processes that results in a wide range of macro- and microstructures (Laubach et al. 2019). Although the kinematics of formation of equant-blocky and elongate-blocky vein microstructures is generally well understood (e.g. Bons et al. 2012), wide-blocky veins, similar to those documented in this study, have rarely been described in detail or interpreted in terms of their formation mechanisms. Here we elaborate on our conceptual model and the fundamental processes involved in the development of wide-blocky microstructures. Our model is based on observations from natural veins in Somerset, experiments on fracture formation and the results of numerical simulations using the multiphase field method.

Formation of wide-blocky microstructures

Vein formation starts with extensional fracturing in fine-grained limestone layers. As shown in Figure 3a, the natural vein geometries compare well with the fractures produced in the laboratory and illustrate that fractures follow a mixed-mode pathway composed of transgranular and intergranular crack segments along the wall rock. Our results are similar to the experiments performed by Arndt (2015) on micritic carbonates from the Oman Mountains. The fracture surface is mineralogically heterogeneous as a result of the polymineralic composition of the limestone (Figs 2e and 3b, c) and only c. 10% of it is transgranular along the cleavage planes of calcite grains (Fig. 3d). The rest of the fracture intersects calcite grain boundaries and accessory minerals. It is unclear whether the experimental fractures that were produced in the laboratory under dry conditions, at room temperature and by rapid loading are the same as those formed under natural conditions, presumably at higher temperatures and fluid pressures and under slow loading. However, the similarities between the natural and experimental fractures give a first-order indication of the complexity of natural fracture surfaces and a justification to use the experimental data as the input for the multiphase field simulations.

A fluid supersaturated with Ca ions is required to initiate the growth of vein crystals. The Somerset veins show abundant microstructural evidence for syntaxial vein-filling mechanisms, including crystal terminations towards the vein interior, cathodoluminescence banding patterns that are interpreted as growth zoning from the vein walls towards the centre, as well as epitaxial relationships between the wall rock grains and vein crystals (Figs 5a–c,7d, e, 8 and 9a, b). We interpret the opening of type 1 and type 2 veins as a one-step process, as indicated by the general absence of wall rock inclusion bands (Fig. 5a–d) and the strong quantitative relationship between the vein aperture and calcite crystal width (Fig. 4a, b). By contrast, most of the type 3 veins contain numerous wall rock inclusion bands parallel to the vein walls. Such systematic arrangements of narrow inclusion bands indicate multiple events of fracture localization in pre-existing veins (Ramsay 1980) (Figs 5f and 12). These inclusion bands cannot be created in a single high-energy fracturing event because they do not show any indications of lateral displacement or rotation, which would be expected if they had formed in a turbulent fluid.

Clues about the crystal growth processes during the early stages of vein-filling can be obtained from cathodoluminescence images of the parts of the veins that contain interfaces between type A and type B calcite, representing two stages of filling (Fig. 7d, e). Early type A calcite shows a heterogeneous distribution along the vein, where narrow rims of small crystals line the vein walls and only a few crystals have larger sizes or completely bridge the fracture. This is similar to the observations by Gale et al. (2010) in dolostone host rock and indicates a variance in growth rate along different parts of the fracture surface. We suggest that the large crystals formed where transgranularly broken wall rock grains were exposed along the fracture, serving as fertile seeds and promoting the rapid epitaxial precipitation of material. Supporting microstructures include large broken lithoclasts or fossils adjacent to particularly large wide-blocky vein crystals (Fig. 5d). Intergranular crack segments are partly covered by organic particles or clay minerals that surround the grain boundaries (Fig. 2e). As suggested by Ajdukiewicz and Larese (2012) and Williams et al. (2015), the reduced growth rates on such surfaces result from a higher amount of nucleation discontinuities on growth surfaces (defects or microparticles) that reduce the rates of epitaxial precipitation. In addition, smaller or more fragmented growth surfaces develop euhedral facets faster, leading to a rapid decrease in the growth rate compared with crystallographically irrational surfaces (Heald and Renton 1966; Lander et al. 2008). The final vein crystal morphologies are therefore strongly controlled by the availability, size and distribution of irrational fracture surfaces, where transgranularly broken, clean calcite cleavage planes provide areas for rapid calcite precipitation. We tacitly assume that the cleavage cracks are not growth facets (Aquilano et al. 2016) and therefore grow rapidly.

In fractures with large apertures (Dm > c. 4), calcite crystals that nucleate on fertile transgranularly broken grains quickly outgrow their neighbours in a rapid process that we refer to as extreme growth competition. The characteristic crystal size gradation that is expected to form by normal growth competition is underdeveloped in the studied veins. Instead, the veins are dominated by a few large wide-blocky crystals that grow rapidly on clean, fertile calcite cleavage planes. We infer that the prevalence of normal growth competition v. extreme growth competition can be distinguished by the final vein microstructures. Normal growth competition, which is mainly controlled by crystal structural anisotropy and starts on a randomly orientated substrate, produces systematic gradients with increasing crystal size and a decreasing number of crystals towards the vein interior. Small, outcompeted vein crystals along fracture margins have a boundary with a different crystal on each side. By contrast, such gradients are localized or non-existent in veins that form by extreme growth competition and most of the small crystals along the vein margins tend to be completely enclosed by the larger wide-blocky crystals.

The reason for the predominance of wide-blocky over elongate-blocky microstructures in the Somerset samples is most likely related to the nature of the host rock. Wide-blocky textures require significant (by a factor of c. 5) differences in growth rate between slow- and fast-growing crystals. Such differences can be achieved in polymineralic host rocks with medium cohesion and coated grain boundaries, enabling a variety of fracture pathways and, as a result, a heterogeneous substrate for the growth of vein crystals.

Crystal size variations in wide-blocky veins

A distinctive feature of the type 1 and type 2 microvein morphologies is the positive correlation between increasing vein apertures and the width of the vein crystals (Fig. 4a). We suggest that this relationship can be explained by a geometric control as illustrated in Figure 12. If the growth rates of vein crystals are different, then the slow-growing crystals will only be able to reach the other side of the fracture and form a bridge at small opening apertures, as in type 1 veins (Fig. 12a). When such a bridge is formed, it blocks the lateral expansion of the neighbouring crystals, limiting the ultimate width the bridge-forming crystals can attain. At wider apertures, fast-growing crystals have more time to overtake the slow-growing crystals and expand sideways before the latter can form a bridge (Fig. 12b). This concept explains the observed transition between type 1 (<50 µm) and type 2 (50–100 µm) microveins (Fig. 4a). In type 2 veins the crystal size rapidly increases with increasing vein aperture, whereas in type 1 veins the aperture and crystal size follow a 1:1 relationship. We suggest that the transition from a linear 1:1 relationship in type 1 veins to a steeper positive slope in type 2 veins marks the threshold fracture aperture size at which slow-growing crystals rapidly lose the ability to bridge a fracture. The lack of a relationship between vein aperture and calcite crystal size in type 3 veins wider than 100 µm (Fig. 4a) indicates a change from a single-seal (single crack–seal increment) to a multi-seal mechanism. This inference is supported by an abundance of wall rock inclusion bands in type 3 veins (Fig. 5e, f).

Although all type 2 microveins display wide-blocky microstructures, the aspect ratios of crystals vary along the same vein and, more significantly, between veins of different apertures (Figs 4a and 5a–d). Crystal size variations within a single vein can be explained by the random distribution of fertile transgranular fracture surfaces along the vein wall. If several transgranularly broken wall rock grains are close to each other, then the vein crystals that grow rapidly from these surfaces limit the lateral expansion of each other, preventing the development of wide-blocky crystals. The opposite is true when transgranular fracture surfaces are far apart. Similarly, wider crystals are expected to form on larger seed surfaces.

Transition from crack–jump to crack–seal mechanisms

Bedding-perpendicular type 1 and type 2 microveins in the Lilstock area (Fig. 1) have been used as the type example of the crack–jump model of vein formation (Caputo and Hancock 1999; Caputo 2005). In contrast with vein formation by multiple crack–seal events, where a vein is repeatedly opened and sealed (Ramsay 1980), the crack–jump mechanism operates when the veins have a higher tensile strength than the wall rock. In this scenario, the veins are opened and sealed only once, as fracturing dominantly takes place in the relatively weaker wall rock, away from the sealed veins (Caputo and Hancock 1999; Holland and Urai 2010).

We observed evidence of both processes in the studied samples depending on the vein aperture. As discussed earlier, type 1 and type 2 veins represent crack–jump behaviour, whereas the type 3 veins formed by multiple reactivation episodes of the existing veins. An opening aperture of c. 100 µm marks the transition between the two mechanisms in the studied veins, as indicated by the presence of multiple wall rock inclusion bands, mostly in veins above this threshold. As shown by Hilgers et al. (2001) and Laubach and Ward (2006), wide fractures are less likely to achieve complete sealing. Thus, although completely sealed veins are stronger than the wall rock and cannot localize the next fracture (Holland and Urai 2010; Virgo et al. 2014), veins with initial large apertures are likely to remain partly open and preserve the porosity. Partly porous fractures are more easily reactivated (Fig. 13). In wide veins, wall rock inclusions form parallel arrays of discontinuous bands, often not extending over the boundaries of a single crystal (Fig. 5f). As shown in Figure 13, such arrays may form due to fracture propagation in the wall rock at sites where the crystals form bridges across the vein.

Comparison with numerical modelling

With its diffuse interface approach, the multiphase field method obviates the necessity for extensive interface-tracking algorithms and can efficiently treat the moving boundary problems computationally, becoming a powerful tool to model vein-filling (Ankit et al. 2013, 2015a, 2015b; Wendler et al. 2016; Prajapati et al. 2017, 2018). The multiphase field simulations presented in this study (Fig. 11) demonstrate the ability of the models to closely reproduce the textures in the Somerset microveins (Figs 5a–d and 11b), including vein morphologies as well as the positive correlation between vein apertures and vein crystal width (Fig. 4a, b). A key assumption in successfully reproducing the wide-blocky microstructures is the incorporation of differences in growth rate, where the c. 10% of crystals growing on transgranular fractured surfaces have faster growth rates than the rest of the crystals. Differences in growth rates in nature may show a higher variability than in our simulations. There could be three or more different rates within the same vein, depending on the thickness of the coating on the grain boundaries, the density of the nucleation discontinuities, the chemical variation in the seed grains and other factors. This is impossible to measure or quantify at the moment, but it could be addressed in future models. However, based on the good fit between the modelled vein morphologies and the microstructures of the Somerset veins, we infer that the simplified assumptions made in our models are meaningful. The best fit is obtained when the difference in growth rate between the fast- and slow-growing crystals is a factor of c. 5 (Fig. 11b). Such conditions allow slow-growing crystals to bridge the narrowest fractures, but not those with apertures >Dm 12, corresponding well with observations in natural microveins (Fig. 4a). A further increase in fracture aperture does not significantly impact the width of the average crystal, except in the case of the widest type 3 veins, where fast-growing crystals can enter a crystallographically controlled growth competition and develop typical elongate-blocky microstructures (Fig. 11a).

During normal growth competition, all crystals grow at the same rate and competition is controlled by the crystallographic orientation of the neighbours. The result is an equant- or elongate-blocky vein morphology, depending on the vein aperture. Although these are typical in many single-seal veins worldwide (Bons et al. 2012), they are uncommon in the Somerset microveins and are only observed in the wider type 3 veins (Fig. 5e). In the third modelled scenario, only a few crystals are allowed to grow and the rest of the fracture surface is inert (Fig. 11c). As a result, wide-blocky morphologies are produced, but the size of the vein crystals remains constant, regardless of the vein aperture. This scenario was not observed in the studied veins. Overall, our results show that the multiphase field technique is a powerful and flexible tool for simulating a variety of vein microstructures that occur in nature. The multiphase field method allows the incorporation of natural crystal morphologies, system thermodynamics and the structural characteristics of the initial fracture surfaces. Simulations can be finely calibrated, scaled and compared with natural examples. Our choice to use 2D, not 3D, simulations in this study was made to reduce computational costs, but 3D simulations are possible (Ankit et al. 2015b).

This study provides a detailed description and interpretation of the development of the wide-blocky vein microstructures common in micritic carbonate rocks. We integrated microtextural observations from natural samples with numerical modelling of syntaxial crystal growth in fractures. We show that wide-blocky vein morphologies form in fluid-filled open fractures by a process that we refer to as extreme growth competition. Extreme growth competition takes place by rapid epitaxial growth on a few seed grains along fracture surfaces, such as the freshly broken cleavage planes of calcite, in contrast with the comparatively slow growth on wall rock grain boundaries coated with clays, organic material or dust particles. The morphology and mineralogy of the initial fracture surface therefore has major implications for the rates of vein-filling and the resulting crystal morphologies.

We interpret type 1 (1–50 µm) and type 2 (50–100 µm) microveins to be the result of single-seal, crack–jump mechanisms, whereas the wider type 3 veins (>100 µm) form by multiple crack–seal events. The initial fracture aperture is probably one of the main controls that determines whether the vein undergoes reactivation. The strength of sealed veins is higher than that of the wall rock, thus narrow fractures (<100 µm) become completely sealed faster and withstand subsequent rupture events without reactivation. By contrast, wider veins preserve porosity and can localize subsequent fracturing along the sealed sections.

Assuming syntaxial calcite crystal growth within single-increment fractures and faster epitaxial growth rates on fertile seed grains, multiphase field simulations successfully reproduce the range of microstructures observed in the Somerset veins, including the transition to wide-blocky morphologies between type 1 and type 2 veins and the positive relationship between vein aperture and crystal width.

We thank Sara Elliott for assistance with the scanning electron microscopy–cathodoluminescence imaging and post-processing.

LS: conceptualization (equal), formal analysis (lead), investigation (lead), methodology (equal), visualization (lead), writing – original draft (lead), writing – review and editing (equal); MS: formal analysis (supporting), investigation (supporting), methodology (supporting), software (lead), software (supporting), visualization (supporting), writing – original draft (supporting), writing – review and editing (supporting), writing – review and editing (supporting); JLU: conceptualization (equal), funding acquisition (lead), methodology (equal), resources (lead), writing – review and editing (equal); EU: investigation (supporting), writing – review and editing (supporting); MS: formal analysis (supporting), investigation (supporting), methodology (supporting), software (lead), software (supporting), visualization (supporting), writing – original draft (supporting), writing – review and editing (supporting), writing – review and editing (supporting); BN: software (supporting), writing – review and editing (supporting); AS: formal analysis (supporting), methodology (supporting), visualization (supporting), writing – review and editing (supporting).

We thank the German Science Foundation DFG for funding this project (grants NE 822/34-1 and UR 64/17-1). E. Ukar acknowledges financial support (grant DE-FG02-03ER15430) from the CSGB Division, Office of Basic Energy Science, US Department of Energy.

The datasets generated during and/or analysed during the current study are not publicly available due to the large file sizes, but are available from the corresponding author on reasonable request.

Scientific editing by John MacDonald