Large grain-size-dependent rheology contrasts of halite at low differential stress: evidence from microstructural study of naturally deformed gneissic Zechstein 2 rock salt (Kristallbrockensalz) from the northern Netherlands

. Constitutive laws to predict long-term deformation of solution-mined caverns and radioactive-waste repositories in rock salt play an important role in the energy transition. Much of this deformation is at differential stresses of a few megapascals, while the vast majority of laboratory measurements are at much higher differential stress and require extrapolation. This can be much improved by including microstructural data of samples deformed in natural laboratories. Deformation of rock salt can occur by dislocation creep and grain-size-dependent dissolution– precipitation creep processes (pressure solution); this mechanism is not commonly included in current engineering predictions. Herewe show evidence for large grain-size-dependent differences in rock salt rheology based on microstructural observations from Zechstein rock salt cores of the northern

Abstract.Constitutive laws to predict long-term deformation of solution-mined caverns and radioactive-waste repositories in rock salt play an important role in the energy transition.Much of this deformation is at differential stresses of a few megapascals, while the vast majority of laboratory measurements are at much higher differential stress and require extrapolation.This can be much improved by including microstructural data of samples deformed in natural laboratories.Deformation of rock salt can occur by dislocation creep and grain-size-dependent dissolutionprecipitation creep processes (pressure solution); this mechanism is not commonly included in current engineering predictions.
Here we show evidence for large grain-size-dependent differences in rock salt rheology based on microstructural observations from Zechstein rock salt cores of the northern Netherlands that experienced different degrees of tectonic deformation.We studied the relatively undeformed horizontally layered Zechstein 2 (Z2) salt (Stassfurt Formation) from Barradeel and compared it with a much more strongly deformed equivalent in diapiric salt from Winschoten, Zuidwending, and Pieterburen.We used optical microscopy of thin gamma-irradiated sections for microtectonic analysis, recrystallized grain-size measurements and subgrain-size piezometry, electron microscopy with energydispersive X-ray spectroscopy, and X-ray diffraction analysis for second-phase mineralogy.Subgrain-size piezometry shows that this deformation took place at differential stresses between 0.5 and 2 MPa.
In the undeformed, layered salt from Barradeel we find centimetre-thick layers of single crystalline halite (Kristalllagen or megacrystals) alternating with fine-grained halite and thin anhydrite layers.The domal salt samples are typical of the well-known "Kristallbrockensalz" and consist of centimetre-size tectonically disrupted megacrystals surrounded by fine-grained halite with a grain size of a few millimetres.We infer high strains in the fine-grained halite as shown by folding and boudinage of thin anhydrite layers, as compared to the megacrystals, which are internally much less deformed and develop subgrains during dislocation creep.Subgrain size shows comparable differential stresses in Kristallbrocken as in matrix salt.The fine-grained matrix salt is dynamically recrystallized to some extent and has few subgrains and microstructures, indicating deformation by solution-precipitation processes.We infer that the finer-grained halite deformed dominantly via pressure solution and the megacrystals dominantly by dislocation creep.
The samples show that the fine-grained matrix salt is much weaker than Kristallbrocken because of different dominant deformation mechanisms.This is in agreement with microphysical models of pressure solution creep in which grain size has a significant effect on strain rate at low differential stress.Our results point to the importance of pressure solution creep in rock salt at low differential stresses around en-1 Introduction 1.1 Salt rheology, deformation processes, and associated microstructures -relevance of natural laboratories Salt -unlike most sedimentary rocks -is very weak and deforms like a viscous fluid, even at low temperatures and shallow depths, and its presence in sedimentary basins fundamentally changes their evolution by salt tectonic processes (Jackson et al., 1994;Urai et al., 2008;Jackson and Hudec, 2017).This has long been recognized for salt diapirs (Trusheim, 1957;Schultz-Ela et al., 1993;Kukla et al., 2019), salt glaciers (Wenkert, 1979;Talbot, 1979;Talbot and Aftabi, 2004;Závada et al., 2012), salt decoupling (Peel, 2014;Rowan and Krzywiec, 2014;Tȃma et al., 2021), and at a smaller scale for internal salt flow creating folding or boudinage (van Gent et al., 2011;Fiduk and Rowan, 2012;Strozyk et al., 2014;Dooley et al., 2015;Rowan et al., 2019;Adamuszek et al., 2021).Rock salt is the host of many large engineering constructions like salt caverns and radioactive-waste repositories, and the long-term operation and abandonment of these structures requires predictions of deformation up to thousands of years (Brouard et al., 2004;Chemia et al., 2009;Bräuer et al., 2011;Baumann et al., 2018).This deformation takes place at differential stresses of below a few megapascals; however the measurement of salt rheology in the laboratory is problematic because of the long duration of the required experiments (Brouard et al., 2004;Bérest et al., 2010).Because laboratory experiments are limited in time, they are commonly conducted at relatively high deviatoric stresses and strain rates at which dislocation creep processes are expected and inferred to be the dominant deformation mechanism (Wawersik and Zeuch, 1986;Carter et al., 1993;Hunsche and Hampel, 1999;Hampel et al., 2007;Urai and Spiers, 2007;Urai et al., 2008;Hampel, 2016).Therefore, most of the long-term predictions of salt deformation have been made based on extrapolation of such experimentally derived power law creep rheology to low differential stress (Albrecht et al., 1993;Bräuer et al., 2011), although some predictions include both mechanisms (Buijze et al., 2022).However, it has been documented in the geological and materials science literature that below a certain differential stress in rock salt there can be a dramatic grain-sizedependent change in deformation mechanism from disloca-tion creep to pressure solution creep, and this can change the creep rate by many orders of magnitude (Urai et al., 1986b;Spiers et al., 1990;van Keken et al., 1993;Spiers and Carter, 1998).
In recent years, the validity of dislocation creep-based extrapolations was extensively discussed in the engineering community, and very slow creep tests were carried out that indeed show much faster deformation than power law creep rates would predict (Popp and Hansen, 2018;Bérest et al., 2019).
An important contribution to this discussion comes from materials science, where microphysical processes are related to constitutive laws by state variables such as water content (at grain boundaries), solid solution, and second-phase impurities and grain size (Carter and Hansen, 1983;Heard and Ryerson, 1986;Urai et al., 1986b;Hunsche et al., 2003;Bérest et al., 2019;Spiers et al., 1990).Recent experiments show that the presence of secondary minerals such as phyllosilicates adds further complexity in the dissolution-precipitation process with potential influence on pressure solution creep rates (Macente et al., 2018;Schwichtenberg et al., 2022).
For steady-state and non-dilatant deformation the microphysics-based deformation rate of rock salt is given by Eq. ( 1) for dislocation creep and Eq. ( 2) for solution-precipitation creep, with the sum of both being the total strain rate (Eq.3): (Wawersik and Zeuch, 1986;Spiers et al., 1990;Carter et al., 1993;van Keken et al., 1993;Hunsche and Hampel, 1999;Urai et al., 2008).Thereby A and B are material constants, Q DC and Q PS are apparent activation energies for dislocation creep and pressure solution creep, R is the gas constant, T is absolute temperature, σ 1 − σ 3 is the differential stress, D G is the grain size, and n and m are stress and grain size exponents.For a compilation of parameters for the two mechanisms, we refer to Urai et al. (2008) and references therein (e.g.Spiers et al., 1990;van Keken et al., 1993;Brouard and Bérest, 1998;Hunsche and Hampel, 1999;Hunsche et al., 2003).
Because of the large differences in the stress and grain size exponents of the two mechanisms, pressure solution creep will dominate deformation at low differential stress and small grain size, and dislocation creep will dominate deformation at high differential stress and large grain size.Key parameters in the evolution of grain size are the structure and mobility of brine-filled grain boundaries, which can change as a function of differential stress (Drury and Urai, 1990;van Noort et al., 2008), and the migration of grain boundaries, which can change the grain size (Urai et al., 1986a;Peach et al., 2001;Schenk and Urai, 2004;Schenk et al., 2006;Schmatz et al., 2011).
Because of the extremely long experiments (several years) required to measure pressure solution creep rates in rock salt at low differential stress (Bérest et al., 2019) and the very small strains reached in these experiments, it is useful to compare these results with naturally deformed samples.The differential stresses during natural deformation can be measured using subgrain-size piezometry and are commonly found to be between 0.5 and 5 MPa (Carter et al., 1982;Schléder and Urai, 2005;Leitner et al., 2011;Rowan et al., 2019), but at much higher strains than can be achieved in low-stress laboratory experiments.In addition, relative differences in rheology can be measured in layered salt (Talbot, 1979;Carter et al., 1982;Schmalholz and Podladchikov, 2001;Schléder and Urai, 2005;Hudleston and Treagus, 2010;Leitner et al., 2011;Komoróczi et al., 2013;Zulauf et al., 2014;Závada et al., 2015;Schmalholz and Mancktelow, 2016;Adamuszek et al., 2021;Schléder and Urai, 2007).Microstructural observations of naturally deformed samples show that dislocation creep, dynamic recrystallization, and pressure solution creep can be readily distinguished, indicated by plastic crystal deformation forming slip bands and subgrains (dislocation creep), grain boundary migration recrystallization (dynamic recrystallization), and growth bands and crystal elongation (pressure solution creep) (Desbois et al., 2010(Desbois et al., , 2012;;Závada et al., 2012Závada et al., , 2015)).

Kristallbrockensalz
The Kristallbrockensalz (z2HS3) in the Zechstein 2 (Stassfurt Formation in Germany) is a well-known tectonite in the Permian Basin (e.g.Czapowski, 1987;Popp et al., 1999;Urai et al., 2019).Richter-Bernburg (1953) described Trümmersalze (German Trümmersalze: debris salt) with Kristallbrocken (German Kristallbrocken: crystal fragments) as large, sharp-edged crystal porphyroclasts inside a fine recrystallized matrix (Küster et al., 2008).Vintage mine photographs from northern Germany show layer-parallel boudins of Kristallbrocken, large rotations of fragments, and regular boudinage in multiple 20 cm thick layers (Richter-Bernburg, 1953;Simon, 1972).It is interpreted to have formed by sedimentation of fine-grained matrix salt, layers of single crystalline halite (German Kristalllagen: crystal layer; Seidl, 1914), and thin anhydrite layers.Although the genesis of extraordinarily large Kristalllagen is not clear, different models have been proposed that suggest post-sedimentary diagenetic grain growth or coalescence of fine-grained halite (Küster et al., 2011).Deformation of the formation resulted in an augen gneiss structure, with the Kristallbrocken decreasing in size with tectonic strain (Küster et al., 2008(Küster et al., , 2009;;Urai et al., 2019).Pape et al. (2002) presented samples from the Gorleben salt dome and showed that the de-positional setting of Kristalllagen halite was shallow marine based on the occurrence of abundant fluid inclusion trails in chevron patterns.Another argument for Kristallbrocken being fragments from a primary layering is based on observations of internal laminations of fluid and solid inclusions (Richter-Bernburg, 1953;Simon, 1972;Pape et al., 2002).Following earlier interpretations (Richter-Bernburg, 1953;Simon, 1972), Pape et al. (2002) hypothesized that rupturing of halite crystal layers is attributable to early diagenetic destruction of layers from subaquatic gliding.This is in contrast to other interpretations (Löffler, 1962) where the so-called Augensalz (another name for Kristallbrockensalz) is interpreted to have formed from rupturing of halite crystal layers during tectonic flow, with clear halite crystallizing in the boudin necks.Extensive studies of distribution of bromide content, Kristallbrocken texture and microstructure, abundant sulfate and fluid inclusions in Kristallbrocken, and interpretation of their formation and deformation mechanisms were presented by Küster et al. (2008Küster et al. ( , 2009Küster et al. ( , 2011;;Küster, 2011).The structural characteristics of the Kristallbrockensalz were attributed to brittle deformation, dislocation glide, and a strong competence contrast between porphyroclastic Kristallbrocken and fine-grained mylonitic matrix halite (Küster et al., 2008).Küster et al. (2009) described the matrix halite and inferred a secondary and dynamically recrystallized microstructure of sub-structured and sub-structure-free grains.Lobate grain boundaries were interpreted to have formed by grain boundary migration recrystallization, and it was later stated that due to the lack of crystallographic preferred orientation and high water contents, fluid-assisted solution-precipitation creep or grain boundary migration might have been controlling factors for the dominant deformation mechanisms (p.139 in Küster, 2011).It was hypothesized that second-phase inclusions, large grain size, and the monocrystallinity of Kristallbrocken contribute to the observed rheology contrasts (Küster et al., 2008).In a more recent report from the KEM-17 study (Urai et al., 2019) boudinaged and folded anhydrite layers as well as boudinaged Kristallbrocken surrounded by recrystallized halite and original fine-grained halite were described in Zuidwending and Winschoten samples.

Aim of the study
In this study we build on the observations briefly reviewed above; add our new observations of samples with Kristalllagen and Kristallbrocken from the Zechstein of the Netherlands (Fig. 1); and hypothesize that the large competence contrast and different deformation styles between Kristallbrocken and fine-grained matrix salt are caused by the different microphysical deformation mechanisms, with dislocation creep and ductile rupturing (boudinage) being dominant in the Kristallbrocken and grain-size-dependent pressure solution creep being dominant in the fine-grained matrix.If this hypothesis is supported by our data, it provides further evihttps://doi.org/10.5194/se-14-271-2023 Solid Earth, 14, 271-291, 2023 dence for the operation of grain-size-dependent creep in rock salt at the conditions relevant for the operation of engineered structures in rock salt.

Materials and methods
We studied 21 samples from drill cores from the areas of Barradeel (BAS), Pieterburen (PBN), Zuidwending (ZWD), and Winschoten (WSN, near Heiligerlee) Zechstein salt structures (Fig. 1).We use the term domal salt to refer to the subsurface diapirs in the Zechstein basin.BAS, ZWD and WSN samples were collected and prepared for the KEM-17 study without gamma-irradiating them (Urai et al., 2019).The samples were selected in the TNO (Netherlands Organisation for Applied Scientific Research) central core storage facility in Zeist and core shed of the mining company (BAS).They were cut perpendicular to the bedding in a dry laboratory with a diamond saw cooled by a small amount of slightly undersaturated salt brine to reduce mechanical damage (Schléder and Urai, 2005).
To decorate crystal defect structures in NaCl, samples were irradiated in the research reactor FRM-II at the TU Munich in Garching with varying dose rates between 6 and 11 kGy h −1 to a total dose of 4 MGy at a constant temperature of 100 • C (Urai et al., 1986b;Garcia Celma et al., 1988;Schléder andUrai, 2005, 2007).Thin sections of unirradiated samples were dry-polished to a thickness of ap-proximately 1 mm, and gamma-irradiated thin sections were dry-polished to a thickness of approximately 50 µm to reach optical transparency.To decorate grain boundaries and subgrain boundaries, the samples were chemically etched with slightly undersaturated brine, which was removed with a jet of n-hexane using the technique described in Spiers et al. (1986) and Urai et al. (1987).The thin sections were imaged in reflected and transmitted light using a Zeiss optical microscope (Axioscope) with the stitching panorama function of the ZEN imaging software.Reflected-light panoramas with 25× magnification were used for grain boundary digitization (Fig. 3) after making sure that the grain size distribution is sufficiently well captured.
Halite grain and subgrain boundaries were manually traced with a touch pen and tablet for statistical analysis.Grain and subgrain sizes for piezometry were analysed with Fiji (Schindelin et al., 2012) and calculated as equivalent circular diameter (Schléder and Urai, 2005;Lopez-Sanchez and Llana-Fúnez, 2015), and differential stresses σ were calculated as follows according to Carter et al. (1993)  (4) Electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDS) mapping has been used to identify the chemical composition and distribution of second-phase impurities in halite.We used an Oxford Instruments X-Max 150 EDS system at the Institute of Structural Geology, Tecton-ics and Geomechanics (RWTH Aachen University) at 15 kV acceleration voltage.The samples were sputter-coated with approximately 7 nm of tungsten for conductivity.Crystallographic orientations were measured by means of electron backscatter diffraction (EBSD) on one thin section using a Symmetry EBSD camera by Oxford Instruments attached to a GeminiSEM 300 SEM by Carl Zeiss Microscopy.The measurement was performed at an acceleration voltage of 20 kV and a probe current of approximately 10 nA.To avoid charging of the uncoated specimen, the analysis was performed in variable-pressure mode using nitrogen at a pressure of 30 Pa in the sample chamber.In a first measurement series, approximately half of the entire thin section was scanned by 30 small measurement areas with a step size of 20 µm, which afterwards were manually merged to a large dataset, finally covering an area of approximately 1.8 cm × 3 cm.The central Kristallbrocken region was subsequently measured again with higher spatial resolution by four measurements using a step size of 5 µm, which after merging covered an area of approximately 0.7 cm × 1.4 cm.All EBSD data were collected and indexed in "refined accuracy" mode with AZtec V 5.1 by Oxford Instruments.The final indexed datasets were further evaluated with OIM Analysis V 8.0 by Ametek-EDAX.Prior to the electron microscopical investigations, the samples were freshly polished and etched again using the method described above and coated with tungsten (in the case of the EDS measurements) or left uncoated (in the case of the EBSD measurements).
Qualitative X-ray diffraction analysis (XRD) to identify impurity content was performed on a Bruker D8 equipped with a graphite monochromator and a scintillation counter.Scans were measured with Cu-Kα radiation.

Relatively undeformed Barradeel samples
The Zechstein salt at Barradeel is sub-horizontally layered as seen in seismic data (Strozyk et al., 2014;Barabasch et al., 2019) and has a total thickness of 800 m with a 580 m thick Zechstein 2 (Z2) salt at a depth of up to 3 km based on well data (BAS-01; Kaart boringen | NLOG, 2022).Salt cores have mostly sub-horizontal layering, except for sample KS-15, where layering is vertical, indicating local folding, which is common in these settings (Fig. 2a and b).
The salt is layered with centimetre-scale milky to honeycoloured halite layers interbedded with millimetre-thick anhydrite bands (Fig. 2a).There are large variations in grain size of halite, with 1 to 5 cm thick single megacrystal layers (Kristalllagen) alternating with layers of fine-grained (about 3 mm) and very fine-grained (about 0.2 mm) halite layers (Fig. 2a and c).
Kristalllagen are clear or milky with internal laminae (Fig. 2a and b) due to variable content of fluid and solid inclusions of sulfate minerals (Fig. 2e) as previously described (Simon, 1972;Küster et al., 2011).The Kristalllagen have bedding perpendicular or inclined cleavage cracks without displacement of layering, the cracks presumably caused by drilling (Fig. 2a and c).However, in sample KS-15 the Kristalllage is displaced by a few millimetres along cracks next to small folds in anhydrite bands (Fig. 2b and d), which points to tectonic origin.Gamma decoration in Kristalllagen is mostly homogenous blue (Fig. 2c and d), except for a few dark laminae, which are interpreted as healed cracks in sample KS-07 that show the same orientation as an open crack in the same crystal.A Kristalllage in sample KS-07 has abundant slip bands oriented at 45 • to the cleavage crack, consistent with slip on the [110] system (Fig. 2c).Kristalllagen are subgrain-free as seen in reflected light on etched surfaces (Fig. 2c).In sample KS-16 (Fig. 3) microstructures are very similar, with thicker anhydrite laminae.Cellular structures formed by dark-blue gamma decoration (Fig. 2e) locally coincide with barely visible subgrain boundaries on etched surfaces (supplement 1 in Barabasch et al., 2022) but do not correspond to the abundant inclusions.Some megacrystals have single 1 mm large subgrains with small angle misorientation of slip bands and hopper crystal cores indicated by arrays of cubic fluid inclusions with fluid and gas bubbles (supplement 1 in Barabasch et al., 2022).
The fine-and very fine-grained halite grains are equigranular, in layers of two distinct grain size classes of fine-grained (about 3 mm) and very fine-grained (about 0.2 mm) (Fig. 2c, g, h and supplement 1 in Barabasch et al., 2022).Grain boundaries are slightly curved, forming 120 • angles at triple junctions (Fig. 2f and h).In reflected light, etched surfaces show that the only porosity in the salt is that of isolated fluid inclusions in grain boundaries (supplement 1 in Barabasch et al., 2022).Fine-grained halite grains have white cores and blue growth bands visible through gamma decoration (Fig. 2c  and g).Most grains have bright crystal cores with a characteristic arrangement of cubic and chevron-shaped fluid inclusion trails and abundant impurities (Fig. 2g).
The layers with very fine grain sizes are rich in dispersed anhydrite and polyhalite (0.1 to 1 mm) located usually at grain boundaries (Fig. 2c, f, g, h).
Anhydrite layers of up to 5 mm thickness consist of micrometre-to millimetre-sized anhydrite and polyhalite grains and occasionally include 0.1 to 1 mm sized halite crystals (Fig. 2c, d, g, h).These layers are straight or locally folded and continuous., 2007).The bedding as seen in cores is mostly vertical and strongly deformed, with the older Z2 salt in the centre of the sampled diapirs, except for the Pieterburen structure, where the younger salt is in the centre (Geluk et al., 2007).
The samples come from 260 to 1800 m depth.
The deformed diapiric salt consists of Kristallbrocken, surrounded by fine-grained and very fine-grained matrix halite and folded or boudinaged anhydrite bands (Fig. 3) together with dispersed anhydrite and polyhalite inclusions, also confirmed by XRD measurements (supplement 5 in Barabasch et al., 2022).These inclusions locally have a lighter-bluecoloured halite rim, but in the majority of cases the inclusions are not associated with colour changes in the surrounding halite crystal.The rock salt has a typical gneissic appearance consistent with earlier descriptions of Kristallbrockensalz (Küster et al., 2008, 2011, andreferences therein).
The Kristallbrocken megacrystals are between 5 mm and 3 cm thick (comparable to the thickness of Kristalllagen in Barradeel) with a strongly elongated shape up to decimetres long (possibly longer, but this could not be confirmed due to limitations of core dimensions; Fig. 4a-d).Kristallbrocken grains can be correlated to adjacent ones by thickness and inclusion content (Figs. 3,4).In a number of cases, Kristallbrocken can be seen to contain a fracture along which the two megacrystals are displaced, and in other cases the two megacrystals are boudinaged with the boudin necks filled with inclusion-free overgrowth on the megacrystals or with fine-grained matrix halite in the boudin neck (Figs. 3,4).
A good example is presented in Fig. 4d (BS-A), where two 1 cm thick Kristallbrocken parts can be correlated by thickness, enrichment of inclusions in the upper part, and adjacent anhydrite bands.The 2 cm boudin neck contains epitaxially grown (see EBSD below), inclusion-free halite from both crystals and fine-grained matrix halite (Fig. 4d).Both inclusion-free overgrowths also have a lighter-blue gamma irradiation colour.Two thin adjacent anhydrite layers are also discontinuous, in coherence with the boudinaged Kristallbrocken.A 3 cm thick Kristallbrocken below is also displaced and has a small inclusion-free overgrowth.Both inclusion-free parts of the crystal also have lighter-blue gamma irradiation colour.
Gamma-decorated slip bands and subgrains are present in all Kristallbrocken, visible as white or dark-blue subgrain boundaries and in reflected light on etched surfaces (Fig. 5a, supplement 2 in Barabasch et al., 2022).Subgrain sizes are on average 100 to 200 µm (Table 1), and subgrains can be either rounded or elongated with preferred orientation of subgrain boundaries forming a subgrain boundary network.Figure 5d shows one of the interpreted subgrain networks, and Table 1 shows the subgrain-size statistics of all samples.Images of all other samples are included in supplement 2 in Barabasch et al. (2022), together with their interpretation and subgrain size distribution.Planar arrays of fluid inclusions are present in some Kristallbrocken (Fig. 5a).These are interpreted to be healed microcracks (supplement 1 in Barabasch  https://doi.org/10.5194/se-14-271-2023Solid Earth, 14, 271-291, 2023  -f, 6), very similar to those observed and discussed by Küster et al. (2011).
The fine-grained matrix halite has a grain size of approximately 1 mm (Fig. 7).Halite grains are mostly elongated (KS-06, Kbx1, BS-B; Fig. 3).The fine-grained matrix halite grains commonly have white cores and blue rims (BS-A, KS-13A, KS-05, kbx2; Figs. 3, 4b, and d and 5g).An interesting observation is that in some of these grains (Fig. 5g), which are elongated, the white core has the blue overgrowth only in the direction of elongation (e.g.p. 36 in supplement 1 in Barabasch et al., 2022).Very fine-grained matrix halite grains are equiaxed with a similar white core and blue mantle to the fine-grained matrix halite and are associated with a high fraction of impurities, which have grain sizes of approximately 0.2 mm (KS-13A and B; Fig. 4b).
While in the Barradeel samples the boundary between the Kristalllagen and the fine-grained halite is sharp, in the domal salt this boundary is less sharp, and the fine grains (without subgrains) are locally also present in the Kristallbrocken around their edges (KS-02, KS-11, KS-08; Fig. 3).These are interpreted to have formed by fluid-assisted grain boundary migration recrystallization, following the interpretation of Küster et al. (2008Küster et al. ( , 2011)).The recrystallizing halite grains are free of fluid inclusions, with occasional second-phase in- clusions at grain boundaries (BS-A, KS-13A, KS-13B, KS-05, and KS-02; Figs.4b and d and 5b, e, f).Such recrystallized parts and the presumed primary fine-grained matrix halite cannot clearly be distinguished, and grain-size measurements regarding fine-grained matrix halite in Fig. 7 comprise both classes, referring to the halite-labelled grains in Fig. 3.The grain boundaries in halite in all samples are rich in fluid inclusions and occasional second-phase inclusions.In contrast to the observations of Küster et al. (2008), subgrains are infrequent in fine-grained salt in the samples studied, making up less than 1 % of the total matrix halite volume.When possible, subgrains were digitized (Fig. 3, supplement 1 in Barabasch et al., 2022), and piezometry results are presented in Table 1.
Thin anhydrite layers, when enclosed in fine-grained or very fine-grained matrix halite, are strongly deformed by folding and boudinage.The concentric folding in sample KS-13A (Fig. 4b) indicates that the viscosity of the anhydrite is much higher than that of the surrounding halite (Adamuszek et al., 2011(Adamuszek et al., , 2021)).These structures indicate that the matrix halite was clearly more strongly deformed than the Kristallbrocken.Anhydrite layers directly adjacent to Kristallbrocken are much less deformed but are ruptured together with the Kristallbrocken to form coherent boudins.

EBSD results
EBSD data from sample BS-A are presented in Fig. 8. Figure 8a shows inverse pole figure maps for the points indexed as halite with respect to the horizontal direction and the direction perpendicular to the image plane, respectively.The large Kristallbrocken grains are labelled 1-5.The two parts of the halite boudin show different crystallographic orientation with a deviation of approximately 60 • in the horizontal plane (supplement 3 in Barabasch et al., 2022).Further each Kristallbrocken (1-5) has different crystallographic orientation (Fig. 8a). Figure 8b shows pole figures of the matrix halite after excluding these five Kristallbrocken grains from the calculation.The small orientation distribution densities (< 1.8 times random) show that the fine-grained matrix halite has no significant crystallographic preferred orientation (CPO), especially considering the fact that with approximately 1400 grains covered, the statistical base for calculation is comparatively small.The kernel average misorientation (KAM) map in Fig. 8c shows that the matrix halite is more or less subgrain-free, with very few exceptions in large matrix halite grains, whereas subgrains are present in Kristallbrocken 1 and 5 and in boudin necks of Kristallbrocken 3 and 4.An interesting aspect of the subgrain boundary network is their locally fibrous morphology in the overgrowths in boudin necks; these are interpreted as grown-in subgrains (Fig. 8) (Means and Ree, 1988).Figure 8d shows the cumulative reference orientation deviation over the areas of Kristallbrocken 3 and 4, based on the more highly resolved EBSD measurements of the central Kristallbrocken region.The corresponding reference points are marked with white crosses for each of the two grains.Colour jumps at the boundary of the individual measurement areas appear due to the movement of the specimen and subsequent recalibration between the individual measurements and should be neglected.

Comparison to previous studies
Our observations of the Kristallbrockensalz samples correspond closely with those of earlier studies, the most extensive of which is the work of Küster (2011) on samples from the same stratigraphic unit, but several hundred kilometres further towards the basin interior.The key shared observations of both studies are internally deformed megacrystals with solid (polyhalite and anhydrite) and fluid inclusions, subgrains between 0.05 and 0.5 mm, and ruptured in extension to form boudins with dissolution-precipitation in the boudin necks.These megacrystals are surrounded by finergrained halite, with a grain size around 1 mm and some grains containing subgrains and others being subgrain-free.Grain boundaries contain fluid inclusion arrays, and the matrix contains boudinaged and strongly folded thin anhydrite layers indicating high strain in the matrix.Following the interpretation of Löffler (1962) we interpret rupturing of boudins to be tectonic and in contrast to other hypotheses (Pape et al., 2002;Richter-Bernburg, 1953) that rupturing of halite crystal layers is not formed diagenetically from subaquatic gliding; although we cannot completely exclude fractures during diagenesis, the presence of abundant subgrains in Kristallbrocken requires differential stresses that cannot be generated close to the surface, and this deformation is consistent with formation of boudins.
The interpretation of these observations by Küster et al. (2008Küster et al. ( , 2011) ) was that Kristallbrockensalz resembles porphyroclasts in gneissic or mylonitic rocks with a strong rheology contrast between Kristallbrocken and matrix.Kristallbrocken formed from Kristalllagen (of diagenetic origin) by plastic deformation with active [110] slip accompanied by subgrain formation and by rupturing in extension, while the matrix salt was weaker and more strongly deformed than the Kristallbrocken and deformed by dislocation creep and dynamic recrystallization.We measured subgrain size in the studied micrographs and found comparable average subgrain sizes in Kristallbrocken (Fig. 2.10 in Küster, 2011) and in matrix halite (Fig. 7f in Küster et al., 2008), both from Teutschenthal, that indicate similar stress values of a few megapascals when compared to our samples (Table 1, Fig. 9).The same studies also suggest that matrix halite was secondary, replacing Kristallbrocken by recrystallization.The inferred strong rheology contrast was suggested to be related to "monocrystallinity" (large grain size) and the abundant inclusions in Kristallbrocken by restricting dislocation mobility (Küster et al., 2008).
sured grain sizes were comparable, but slightly smaller than grain sizes measured on similar samples from the KEM-17 report (Urai et al., 2019), and stresses from piezometry between 0.8 and 1.5 MPa (Urai et al., 2019) also fit our observations.Our data suggest that subgrains in fine-grained halite are slightly smaller than subgrains in the associated Kristallbrocken (Fig. 9).
Based on results of both studies we also conclude that Kristallbrocken deformed by dislocation creep and that there is a large rheology contrast between Kristallbrocken and matrix, a widely occurring phenomenon in the Zechstein basin.However, our results of the Barradeel samples (which we interpret as an undeformed equivalent of the diapiric salt samples) clearly show that much of the fine-and very finegrained halite was already present before the onset of salt tectonic deformation and not only formed by recrystallization of the Kristallbrocken.Because Küster et al. (2008Küster et al. ( , 2011) ) did not investigate undeformed equivalents, they did not have access to this information.
The original hypothesis by Küster et al. (2008Küster et al. ( , 2011) ) implies that the matrix salt is a dynamically recrystallized equivalent of the Kristallbrocken and deforms by equal contributions of dislocation creep and pressure solution creep (De Bresser et al., 1998, 2001;Ter Heege et al., 2005a, b).If this is the case, the predicted weakening would be relatively small (a factor of 2 in strain rate at the same differential stress) and could not explain the large differences in strain between Kristallbrocken and matrix.Additionally, if one would take the mean grain sizes from the matrix (Fig. 7), assume that these are recrystallized grain sizes, and then apply the recrystallized grain-size piezometer from Ter Heege et al. (2005a), one would get unrealistically high stresses between 5 and 10 MPa for the deformation.Large differences in strain could also be enhanced by the presence of solid inclusions in the Kristallbrocken as proposed by Küster et al. (2008Küster et al. ( , 2011)); however this would lead to larger density of dislocation around the inclusions with corresponding darker colour after gamma irradiation (Garcia Celma et al., 1988), which was not observed.Finally, solid solution impurities could make the Kristallbrocken more competent (Heard and Ryerson, 1986).The most common solid solution impurity in halite is bromide, but the Kristallbrocken in a previous study have a comparable structure in samples where bromide concentration in Kristallbrocken is the same as in the matrix, and in samples where the bromide concentrations are different (Küster, 2011), again not supporting this hypothesis.However, we note that a more extensive analysis of solid solution impurity in these samples would help to further test this hypothesis.Another effect that may make the Kristallbrocken stronger is the presence of thin adjacent anhydrite layers which can form a stronger sandwich; however microstructures with or without sandwiched anhydrite layers are very similar, so this effect cannot be major either (samples BS-A and KS-13A in Fig. 3).

Dominant grain-size-dependent deformation mechanism and rheology contrast
Here we present an alternative hypothesis to explain the rheology contrast: we propose that the matrix deformed by dominant pressure solution creep, while the Kristallbrocken deformed by dislocation creep.Because pressure solution creep is strongly grain-size-dependent (see Eq. 2), this difference is caused by the large difference in grain size between Kristallbrocken and matrix, which we interpret to be sedimentary or early diagenetic, somewhat modified by dynamic recrystallization.Evidence for dominant pressure solution creep in the fine-grained and very fine-grained matrix is provided by the oriented overgrowth bands (Poirier, 1985) (Fig. 5g), the epitaxial overgrowths in boudin necks (Fig. 4d), and the absence of crystallographic preferred orientation as shown by EBSD (Fig. 8).Examples of rock salt microstructures indicating pressure solution creep were presented by Desbois et al. (2010) and Závada et al. (2012), and our microstruc- tures are very similar to these.The presence of abundant fluid inclusions at grain boundaries and the evidence for fluid-assisted grain boundary migration recrystallization in both studies show that the required fluid is widely available in this stratigraphic unit.The studied diapiric samples have comparable mean grain sizes in the fine-grained salt around 1 or 2 mm (Fig. 7), while folding of anhydrite layers was best observed in Zuidwending samples, and overgrowth in boudin necks is especially pronounced in Pieterburen samples (Figs. 3, 4).
To quantify the stress-strain rate conditions corresponding to this hypothesis, in Fig. 10 we plot the data from this study in a differential stress vs. strain rate diagram for a ref-erence temperature of 60 • C. For dislocation creep, we used the BGR (German Federal Institute for Geosciences and Natural Resources)-recommended values (Liu et al., 2017;Eickemeier et al., 2021;Popp, 2022) for Kristallbrockensalz, together with a small selection of characteristic values for rock salts from the Kriechklassen (German Kriechklasse: creep classes) and plotted our samples for the values of differential stress obtained from subgrain-size piezometry, using the grain sizes of Kristallbrocken and matrix to estimate the expected strain rates.It can be seen that the corresponding strain rates differ by 4 orders of magnitude, in agreement with the inferred large differences in strain between Kristallbrocken and matrix (Fig. 10).

Dynamic recrystallization and grain boundary mobility
The dynamic recrystallization of Kristallbrocken is also recognized in grains directly next to Kristallbrocken (Figs. 4b and d and 5b, e, and f), with a very interesting change in the solid inclusions present in the Kristallbrocken; these are completely reworked by grain boundary migration (Fig. 5e) and not present in the same configuration in the new grains.
In our interpretation the fraction of newly recrystallized grains in the matrix is relatively minor, and grain size is similar to the ones already present in the undeformed samples, providing the small grains for dominant pressure solution creep.The small grain size in the matrix is interpreted to be pre-deformational as in relatively undeformed Barradeel samples; hardly influenced by dynamic recrystallization as seen by only minor subgrains and a small grain size, which would indicate unrealistically high differential stresses when plotted in the Ter Heege et al. ( 2005a) recrystallized grain-size piezometer (Sect.4.1).Recrystallization reduces the size of large single Kristallbrocken crystals and increases the relative content of finer-grained salt.Overgrowth of large Kristallbrocken crystals (increasing their size) has been observed in boudin necks.Hopper crystals indicating primary grains (Pape et al., 2002) were preserved in some BAS samples but not found in highly deformed domal salt.The relatively minor newly recrystallized grain fraction in the strongly deformed diapiric salt samples is interesting and suggests that grain boundary mobility in nature is lower than in the models of Peach et al. (2001) and Schléder and Urai (2005) and that recrystallization and grain growth in salt is more sluggish than previously thought.

Kristallbrockensalz bulk rheology
It is interesting to speculate on the deformation of initial layered salt with the very long Kristalllagen.During shearing, this rock must have had an extremely anisotropic rheology due to the weak fine-grained and very fine-grained salt depending on the orientation of the original layering with respect to the shortening direction.In coaxial deformation the Kristalllagen could have carried most of the stress in the salt rock and deformed accordingly by dislocation creep (Bons and Urai, 1994).Once the Kristalllagen were sufficiently fragmented, the rheology of the Kristallbrockensalz becomes a mixture rheology (Bons and Urai, 1994), such that when the Kristallbrocken can form a load-bearing framework, the rock salt deforms by power law creep dominated by dislocation creep in the Kristallbrocken, but when there is a sufficient matrix present, the rock salt deforms by Newtonian viscous creep dominated by pressure solution (Jessell et al., 2009).Based on subgrain-size analysis we inferred similar differential palaeostresses in Kristallbrocken and matrix halite (Fig. 9; even though we had a limited number of measurements in matrix halite), which suggest that in our sam-ples the second model was dominant.The different crystallographic orientation of individual Kristallbrocken with respect to the bedding (Fig. 8a) has not been studied previously and might contribute to the understanding of Kristalllagen formation (Küster, 2011).The absence of a crystallographic preferred orientation of individual Kristallbrocken neither promotes nor prevents the activation of different slip systems and hence would not significantly influence the bulk rheology (Linckens et al., 2016).However, to substantiate this observation and hypothesis, more studies of Kristallbrocken crystallographic orientation with respect to bedding on different samples are required.

Implication of our results on engineering predictions
In current constitutive models used in salt engineering (Albrecht et al., 1993;Hunsche et al., 2003;Bräuer et al., 2011;Kukla et al., 2011;Liu et al., 2017;Popp, 2022) it was long recognized that the creep strain rate of rock salt (as measured at relatively high differential stress) can show differences of several orders of magnitude at the same differential stress and temperature.Based on an extensive dataset, such observations provided the basis for the definition of Kriechklassen, which were used to model the evolution of engineered structures (Liu et al., 2017) and are still used to describe a non-Newtonian rheology in salt tectonics numerical modelling (Granado et al., 2021).However, as is reviewed above, extrapolation of these data to low differential stress predicts creep rates that are orders of magnitude lower than measured in experiments (Brouard and Bérest, 1998;Bérest et al., 2019) and predicted by microphysical models of pressure solution creep (Spiers et al., 1986;Urai et al., 1986b;Spiers et al., 1990).Integration of these mechanisms into engineering constitutive equations is sometimes conducted (e.g.Zill et al., 2022;Buijze et al., 2022).However, because data on the grain size of the rock salt to be modelled are usually not available, these could still be improved considerably.
Together with microstructural characterization, we recommend including grain sizes in engineering predictions based on grain-size-dependent pressure solution creep classes.

Conclusion
In this study, we present examples of flat-lying and diapiric Zechstein salt from the same formation (Z2), which was naturally deformed under low differential stresses between 1 and 2 MPa, providing a natural laboratory to study salt rheology under conditions which are difficult to study in the laboratory but relevant for predicting the evolution of engineered structures over long timescales.The gneissic Kristallbrockensalz deforms by dislocation creep and pressure solution processes depending on the grain size.The fine-grained matrix halite is weaker and deforms with a higher strain rate by pressure solution and dynamic recrystallization, while the Kristallbrocken mega grains tectonically boudinage and deform by dislocation creep.We infer that this large rheology contrast in halite deformation at low differential stresses is caused by grain-size-dependent dissolution-precipitation creep.
Further studies to better define solid solution impurity contents, the role of mineral impurities, and the contribution of dynamic recrystallization with grain boundary migration to solution precipitation processes will help to test the operating deformation mechanisms in more detail.
At present, grain-size measurements are not available for most of the Zechstein salts used in salt engineering, and we recommend the creation of a salt microstructure knowledge base which will help predict creep rates at low differential stress.AS did EBSD measurements and Fig. 8. JB and JLU prepared the manuscript with contributions from all co-authors, who were all involved in scientific discussions.
Competing interests.The contact author has declared that none of the authors has any competing interests.
Disclaimer.Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figure 2 .
Figure 2. (a) Reflected-light photograph of slabs (KS-07 from Barradeel) used for microstructural analysis showing layered white-and honey-coloured salt with variable grain sizes and milky Kristalllagen with internal lamination.(b) Slab specimen KS-15 of Barradeel used for microstructural analysis showing layered transparent and white salt with Kristalllagen up to 5 cm thickness with cracks.Small fold in 5 mm thick anhydrite band is bend following the displaced crystal layer.(c) Overview of thin gamma-decorated section of sample KS-07 in transmitted light (location indicated in a) showing Kristalllagen with abundant inclusions and decorated slip bands, dark-blue decorated bands parallel to crack, and layers of fine-and very fine-grained halite with white cores and blue rims.(d) overview of gamma-decorated thin section of sample KS-15 in transmitted light (location indicated in b) showing inclusion-poor crystal layers that are slightly displaced and layers of fine-grained halite, with some grains showing a white overgrowth.Anhydrite-halite band is slightly bent and contains abundant halite mineral inclusions of up to 2 mm.(e) Micrograph (location indicated in c) showing gamma-decorated slip bands and blue cellular structures at two different scales, abundant solid inclusions up to 200 µm, and fluid inclusions with gas bubbles.(f) Reflected-light image of Kristallbrocken and fine-grained halite with fluid inclusions and anhydrite at grain boundaries.(g) Transmitted-light micrograph showing white cores in halite with growth bands and slip bands.Finely dispersed anhydrite bands are next to very fine-grained halite.(h) Photomontage of transmittedlight image (with λ plate) and reflected-light image showing fluid inclusions at grain boundaries of fine-grained halite, polyhalite, anhydrite, and anhydrite band enriched with small anhydrite minerals.

Figure 4 .
Figure 4. (a) Transmitted-light salt core slab (Zuidwending) showing Kristallbrocken (KB), folded 3 mm thick anhydrite band in a fine-grained halite matrix, and unfolded but boudinaged 3 mm thick anhydrite band next to Kristallbrocken.(b) Gamma-irradiated transmitted-light scan (samples KS-13A and B) location indicated in (b) showing white cores and blue growth rims in fine-grained halite.(c) Salt core slab photograph of Pieterburen slab and photomontaged transmitted-light image of thick section showing Kristallbrocken (KB) with clear halite on the grain edges of Kristallbrocken grains (modified after Sadler, 2012).(d) Transmitted-light scan of gamma-irradiated sample BS-A showing lighter-blue cores and dark-blue growth rims in a fine-grained halite matrix.

Figure 5 .
Figure 5. (a) Transmitted-light micrograph of gamma-irradiated KS-08 (Winschoten) sample showing abundant dark inclusions in Kristallbrocken, slip bands, and white gamma-decorated subgrain boundaries.(b) Transmitted-light micrograph of gamma-irradiated KS-05 (Winschoten) sample showing abundant dark inclusions, slip bands, and white gamma-decorated subgrain boundaries in Kristallbrocken next to anhydrite band and inclusion-poor light halite in between.(c) Reflected-light image of sample KS-08 (Winschoten) Kristallbrocken with abundant subgrains and mineral inclusions used for piezometry.Exact location indicated in Fig. 3 (KS-08, s2).(d) Digitized subgrain boundaries are an example of the data used for piezometry.(e) Transmitted-light micrograph of gamma-irradiated sample KS-13B (Zuidwending) showing Kristallbrocken (KB) grain with gamma-decorated subgrains and abundant primary dark solid inclusions (white arrow).Clear halite grain shows array of reworked elongated clear anhydrite minerals parallel to grain boundary (white arrow) as well as abundant fluid inclusions at grain boundaries.(f) Transmitted-light micrograph of gamma-irradiated Zuidwending sample KS-02 showing subgrain structures, abundant dark inclusions, and clear elongated halite grains next to it.(g) Transmitted-light micrograph of gamma-decorated halite grains showing light cores and directional overgrowth of elongated fine-grained halite in sample BS-B (Pieterburen).(h) Transmitted-light micrograph of thick section showing abundant fluid inclusions at fine-grained halite grain boundary of Pieterburen sample (Sadler, 2012).

Figure 6 .
Figure 6.(a) EDS map of KS-05 (Winschoten) showing anhydrite-polyhalite band, as well as Kristallbrocken with smaller anhydrite and polyhalite inclusions.(b) SEM micrograph of polyhalite and anhydrite inclusions in fine-grained halite.(c) SEM micrograph of Kristallbrocken broken along grain boundary showing fluid inclusion imprints and abundant magnesium and potassium sulfate inclusions.

Figure 7 .
Figure 7. (a) Grain-size histograms of fine-grained matrix halite for each sample presented in Fig. 3 including statistical parameters.Grains smaller than 0.117 mm were not mapped due to image resolution.(b) Fractions of matrix halite, Kristallbrocken, and anhydrite/polyhalite and gypsum for each sample.

Figure 8 .
Figure 8.(a) Inverse pole figure maps for halite grains with large Kristallbrocken grains labelled 1-5.(b) Pole figures of fine-grained matrix halite excluding five Kristallbrocken grains show no significant crystallographic preferred orientation (CPO).(c) Kernel average misorientation (KAM) map overlaid with white low-and high-angle grain boundaries (misorientation > 5 • ).KAM map was calculated over a distance of 40 µm (second neighbour) with a threshold of 3 • in order to enhance the small-angle subgrain boundaries.KAM shows subgrain-free matrix halite with few exceptions in large matrix halite grains, Kristallbrocken 1 and 5 with subgrains, and subgrains in boudin necks of Kristallbrocken 3 and 4. (d) Cumulative reference orientation deviation map over the areas of Kristallbrocken 3 and 4, based on more highly resolved EBSD measurements.Reference points for each of the two grains are indicated.Panels (a) and (b) consist of 30 individual measurements, which due to image distortion under 70 • tilt cannot be stitched perfectly.Therefore, in some cases an artificial separation of areas belonging to the same grain is visible.

Figure 10 .
Figure 10.Comparison of differential stresses measured in Kristallbrocken and matrix halite for samples where both were available (σ = 107 • (D −0.87 ), D = subgrain size;Carter et al., 1993;Schléder and Urai, 2005) with 95 % confidence intervals based on all measured subgrains per sample.Measurements indicate comparable differential stresses for both halite types, but slightly lower values for differential stress in Kristallbrocken of this study.Differential stresses from Teutschenthal were measured based on micrographs presented inKüster et al. (2008) for matrix halite andKüster (2011) for Kristallbrocken and show comparable, slightly lower differential stresses.
Author contributions.JB carried out the study and designed figures.JLU and JS designed the study.JK and JLU selected samples.