Shatter Cones in Hypervelocity Impact Experiments: Structure, Formation and Comparison to Natural Impact Craters

Home , Chladni (crater), Delaunay (crater), Kamil Crater, Lechatelierite, Pilot crater, Pseudotachylyte

Shatter cones in hypervelocity impact experiments: Structure, formation and comparison to natural impact craters

DISSERTATION Zur Erlangung des akademischen Grades “doctor rerum naturalium“ (Dr. rer. nat.) Der Fakultät für Umwelt und natürliche Ressourcen Der Albert-Ludwigs-Universität Freiburg i. Brsg.

vorgelegt von

Jakob Wilk Geb. in Berlin, Pankow

Freiburg im Breisgau 2017

Dekan: Prof. Dr. Tim Freytag Erstbetreuer/Referent: Prof. Dr. Thomas Kenkmann Korreferent: Prof. Dr. Alex Deutsch Zweitbetreuer: Prof. Dr. Stefan Hergarten Tag der Disputation:

ABSTRACT

Impact processes have dominated the formation and development of planetary bodies in our solar system. The study of impact crater formation provides deeper knowledge of early Earth’s history and enables us to understand a surface process profoundly shaping the surface of most rocky planetary bodies. The highly dynamic process of impact cratering causes a series of characteristic effects in the targeted rocks, which are referred to as shock metamorphic effects. These shock effects provide a valuable tool to analyze impact craters and their formation. Shatter cones are diagnostic for shock metamorphism. They are the only macroscopic effect caused by shock, thus, being unambiguously identifiable in the field, provide a valuable tool to find and verify impact structures.

Over the last decades, hypervelocity impact experiments and shock recovery experiments fundamentally enhanced our understanding of impact cratering, by controlled laboratory conditions. With this technique, e.g., microscopic effects were calibrated to corresponding shock pressures, or the effect of target properties on the cratering process was extensively studied. However, in only few experiments shatter cones were found and analyzed. Thus, the conditions of shatter cone formation remained unclear. Physical boundary conditions, e.g., pressure-temperature conditions or formation accompanying strain rates are unknown, as well as the timing of shatter cone formation is part of an ongoing scientific debate.

By chance several shatter cone fragments where found in the MEMIN (Multidisciplinary Experimental and Modeling Impact Research Network) experiments, enabling us to systematically study the shatter cone formation. The scope of this thesis is to narrow down the physical boundary conditions of shatter cone formation, and to develop a model for their formation based on the macro- and microstructural investigations. Therefore, the MEMIN experiments were systematically analyzed to delimit the conditions under which shatter cones do or do not form.

We recovered in total 24 shatter cone fragments from the ejecta of 37 MEMIN experiments. In addition, several craters showed shatter cone-like striae in the craters sub-surface. Shatter cones where recovered from nearly all target lithologies and experiments with different projectile types. We found initial impact velocity to be the driving factor when it comes to whether or not shatter cones will develop. On the basis of the microstructural analysis and iSale simulations, we determined pressure-temperature conditions to be 2- 5 GPa and in the excess of 2000°C during shatter cone formation. In addition, shear movement along the shatter cone surface has been quantified and prominent extensional features were documented. Surface parameters (e.g., apices, bifurcation, curvature, and fracture roughness) were analyzed with 3D data sets and showed good correlation of the experimentally produced shatter cones with natural samples. Also, the morphological data was used to derive a phenomenological model of shatter cone formation. As a synthesis of the experimental work we can state, that shatter cones must be formed early in the cratering process under shock compression, and that shatter cone surfaces develop as mixed-mode fracture under extremely high strain rates.

ZUSAMMENFASSUNG

Impaktprozesse sind grundlegend die Entstehung und Entwicklung planetarer Körper in unserem Sonnensystem. Die Bildung von Meteoritenkratern zu erforschen, heißt einen Einblick in die frühe Erdgeschichte zu bekommen und einen Prozess zu verstehen, der aktiv die meisten festen planetaren Oberflächen bestimmt. Meteoriteneinschläge erzeugen eine Reihe von charakteristischen Eigenschaften im Gestein, die sogenannte Stoßwellenmetamorphose, im Zuge des hoch dynamischen Prozesses. Diese Effekte, helfen Meteoritenkrater zu erkennen und ein besseres Prozessverständnis zu entwickeln. Von diesen charakteristischen Merkmalen sind Strahlenkegel (shatter cones) der einzig makroskopische Effekt der Stoßwellenmetamorphose. Strahlenkegel sind als diagnostisches Mittel Meteoritenkrateridentifizierung anerkannt und können durch ihre sehr markanten Strukturen gut bereits im Gelände erkannt werden.

Unter kontrollierten Laborbedingungen haben Hochgeschwindigkeitseinschlagsexperimente und Stoß- wellenrückgewinnungsexperimente in den letzten Jahrzenten das Verständnis von Krater- bildungsmechanismen grundlegend Verbessert. Entstehungsregime von Mikroskopischen Stoßwellen- Effekten wurden kalibriert, oder zum Bespiel der Einfluss von Porosität oder Lagenbau auf die Kraterbildung untersucht. Strahlenkegel hingegen, sind in Experimenten – auch auf Grund ihrer Häufigkeit - kaum untersucht worden. So kommt es, dass viele Aspekte der Entstehung von Strahlenkegeln immer noch unklar sind. Physikalische Rahmenbedingungen, wie Verformungsraten, Bildungsdrücke oder - temperaturen sind unklar, ebenso ist der Zeitpunkt zur Ausbildung der Strahlenkegel strittig.

Die MEMIN (Multidisciplinary Experimental and Modeling Impact Research Network) Experimente gaben die Möglichkeit die Entstehung von Strahlenkegeln systematisch zu erforschen. Ziel dieser experimentellen Arbeit ist es, physikalische Rahmenparameter einzugrenzen und ein Modell zur Stahlenkegelbildung auf dieser Grundlage zu entwickeln. Hierfür sind eine Reihe Makro- und Mikrostrukturelle Analysen an den MEMIN Experimenten durchgeführt und mit natürlich gebildeten Strahlenkegeln verglichen worden.

Aus dem Untersuchten Ejecta-Material von 37 MEMIN Experimenten wurden 24 Strahlenkegel-Fragmente geborgen. Darüber hinaus wurden Krateruntergründe mehrerer MEMIN Kampagnen untersucht und am Kraterboden Strahlenkegel-typische Striationen (striae) gefunden. Die Strahlenkegel wurden in fast allen Lithologien dokumentiert und es zeigte sich, dass Impakt-Geschwindigkeit der wichtigste Faktor ist um die Strahlenkegelnildung zu begünstigen. Auf Grundlage der Mikrostrukturellen Untersuchungen und iSale Modellierungen konnten die Bildungsbedingungen der gefundenen Fragmente auf 2-5 GPa und hohe Prozesstemperaturen von >2000° C abgegrenzt werden. Zudem wurden Scher- und Extensionsprozesse an den Bruchflächen dokumentiert. Oberflächeneigenschaften (Apizes, Bifurkation, Kurvatur, Rauigkeit der Bruchoberfläche) wurden mit Hilfe gewonnener 3D Daten analysiert und zeigen zum einen die Übereinstimmung der experimentellen und natürlichen Strahlenkegel, und halfen des Weiteren ein phänomenologisches Modell zu entwickeln. Aus der vorliegenden Arbeit geht hervor, dass Strahlenkegel bereit früh im Kraterbildungsprozess angelegt werden und die Bruchbildung durch Risswachstum unter Mixed-mode-Beanspruchung und extrem hohe Verformungsraten bestimmt wird.

STATEMENT OF THE CONTRIBUTIONS

This thesis is structured as cumulative work and is comprised of the published peer-reviewed papers, and one submitted manuscripts. The PhD candidate is first author of two papers, and second author of one accepted paper. Minor contributions to publication in the form of data acquisition and single paragraphs had been made within MEMIN and in the context of crater research. This publication has been added in the appendix. The Introductory chapter has been written for this Thesis, with the intension to make an unfamiliar reader able to follow the individual publications, without any further background information being necessary. The papers are used as the chapter 2.-4. And citations are listed at the end of each chapter. The papers of this thesis are listed below:

Wilk, J., and Kenkmann, T. (2016). Formation of shatter cones in MEMIN impact experiments. Meteoritics and Planetary Science 51 (8): 1477-1496. doi: 10.1111/maps.12682. Wilk., J., Hamann, C., Fazio, A., Luther, R., Hecht, L., Langenhorst, F., and Kenkmann T. (submitted). Melt formation shatter cone recovered from the MEMIN impact experiments in sandstone. Meteoritics and Planetary Science. Kenkmann T., Hergarten, S., Kuhn, T., and Wilk, J. (2016). Formation of shatter cones by symmetric fracture bifurcation: Phenomenological modeling and validation. Meteoritics and Planetary Science 51 (8): 1519-1533. doi: 10.1111/maps.12677.

Note that the second paper (chapter 3) was written chronologically as the last manuscript. It was rearranged, because the developed model in chapter 4 in this thesis represents a conceptual idea grounded on observation made to a certain extend as shown in the previous chapters. The experimental work was conducted at the Fraunhofer Ernst-Mach-Institute (EMI), Freiburg, Germany by Tobias Hoerth, Christoph Michalski and Max Gulde together with EMI technicians and the MEMIN team. Herbert Ickler (Albert-Ludwigs-Universität Freiburg, ALU) prepared recovered rock samples and blocks. Surface analysis of the shatter cone samples was made with the WLI and SEM equipment available at the ALU. The MfN (Museum für Naturkunde, Berlin) offered a valuable collaboration by using their SEM for chemical mappings and their PhD Student Christopher Hamann, who made the EMPA measurements shown in chapter 3. Agnese Fazio from the Friedrich-Schiller-Universität Jena made the presented TEM measurements. The work of this thesis was performed under the supervision of Thomas Kenkmann, Stefan Hergarten and the research group coordinators Michael H. Poelchau and Matthias Ebert.

ACKNOWLEDGEMENTS

The work of this thesis was funded by the German Research foundation (DFG) project KE 732/22-1 as part of the DFG research unit FOR-887: “Experimental Impact Cratering: The MEMIN program”. First and foremost I want to thank Prof. Dr. Thomas Kenkmann for the opportunity to participate in this interdisciplinary and challenging research project, and for his supervision of my almost entire academic endeavor till now – which was most likely challenging as well. I also want to thank Prof. Dr. Stefan Hergarten, who kindly agreed to co-supervise this thesis.

My sincere thanks go to the entire MEMIN group of technicians, project coordinators (Michael and Matthias), and PhD students at the EMI, MfN, FSU and of course ALU for three years of interesting research and cooperation.

In particular I want to thank Christopher Hamann for intensive discussions and a fruitful collaboration, the Freiburgers Tim Krüger, Alexa Pietrek, Rebecca Winkler, Gerwin Wulf, and (again) Matthias Ebert and Michael Poelchau for a good time during this project. Furthermore I want to thank Manuela Tombrink and Herbert Ickler, who – as the ingenious preparatory he is – helped to prepare the samples necessary for this thesis.

I would like to thank my family and friends who had been a huge support throughout the duration of my studies. Especially my parents, my sister, and Katrin, who have always been encouraging to me. Last but not least, I want to thank my grandfather Prof. Tannert in particular, who would have had his 86th birthday at the date this thesis was printed, and at least for two of this three years pushed me over some of the obstacles with his motivating spirit.

TABLE OF CONTENTS

ABSTRACT ...... 1

ZUSAMMENFASSUNG ...... 2

STATEMENT OF THE CONTRIBUTIONS ...... 3

ACKNOWLEDGEMENTS ...... 4

TABLE OF CONTENTS ...... 5

1. INTRODUCTION ...... 9

1.1 Studying impact craters? ...... 9

1.2 Impact craters on Earth ...... 10

1.3 Thesis Motivation ...... 13

1.4 Impact Crater Formation ...... 14

1.5 Shock phenomena and impact related deformation ...... 20

1.6 References ...... 26

2. FORMATION OF SHATTER CONES IN MEMIN IMPACT EXPERIMENTS ...... 31

2.1 Abstract ...... 31

2.2 Introduction ...... 31

2.3 Methods ...... 34

2.3.1 Experimental Setup ...... 34

2.3.2 Target material ...... 35

2.3.3 Experiment and sample preparation ...... 36

2.3.4 Surface characterization by white light interferometry ...... 37

2.3.5 SEM analysis of shatter cone sections and surfaces ...... 39

2.4 Results ...... 39

2.5 Discussion ...... 43

2.5.1 Occurrence of shatter cones ...... 43

2.5.2 Quantitative description of shatter cones...... 49

2.5.3 Melt formation ...... 49

2.6 Conclusion ...... 52

2.7 Acknowledgement ...... 53

2.8 References ...... 53

3. MELT FORMATION ON SHATTER CONES RECOVERED FROM THE MEMIN IMPACT EXPERIMENTS IN SANDSTONE ...... 59

3.1 Abstract ...... 59

3.2 Introduction ...... 60

3.3 Methods ...... 62

3.3.1 Experimental Setup and Material ...... 62

3.3.2 Sample Preparation and Characterization ...... 65

3.4 Results ...... 69

3.4.1 Occurrence and Morphology ...... 69

3.4.2 Melt Texture Characteristics ...... 69

3.4.3 Melt Surface Composition ...... 71

3.4.4 Melt Surface Composition ...... 76

3.4.5 TEM Analysis and Shock Indicators along the Shatter Cone Surface ...... 77

3.5 Discussion ...... 80

3.5.1 Characteristics of Shatter Cone Formation in the MEMIN Experiments ...... 80

3.5.2 Succession of Events at Shatter Cone Surfaces as Revealed by Microstructural Analysis: A Synthesis ...... 80

3.5.3 A comparison of Natural and Experimentally Produced Shatter Cone Surfaces ...... 83

3.5.4 Melt Composition and P-T-Constraints ...... 84

3.6 Conclusion ...... 86

3.7 Acknowledgement ...... 87

3.8 References ...... 89

4. FORMATION OF SHATTER CONES BY SYMMETRIC CRACK BIFURCATION: PHENOMENOLOGICAL MODELING AND VALIDATION ...... 94

4.1 Abstract ...... 94

4.2 Introduction ...... 95

4.3 Shatter cone formation models ...... 98

4.4 A side step: crack bifurcation during dynamic fragmentation ...... 99

4.5 The approach ...... 101

4.6 Morphometry ...... 102

4.6.1 Methods ...... 102

4.6.2 Results ...... 103

4.7 Phenomenological geometric modeling ...... 105

4.7.1 Model set-up ...... 106

4.7.2 The overall geometry ...... 107

4.7.3 Apex angles and bifurcation angles ...... 108

4.8 Results ...... 111

4.9 Discussion ...... 112

4.10 Conclusions ...... 115

4.11 Acknowledgement ...... 115

4.12 References ...... 115

5. Robust Optical Tracking of Individual Ejecta Particles in Hypervelocity Impact Experiments . 123

5.1 Abstract ...... 123

5.2 Introduction ...... 123

5.3 Methodology ...... 125

5.3.1 Experimental setup ...... 125

5.3.2 Particle tracking ...... 126

5.4 Results and discussion ...... 129

5.4.1 Launch time and position ...... 129

5.4.2 Particle velocity ...... 130

5.4.3 Particle size ...... 132

5.5 Conclusion ...... 134

5.6 Acknowledgement ...... 134

5.7 Associated content ...... 135

Supporting Information ...... 135

5.8 References ...... 135

Appendix D / List of thesis related-publications ...... 137

Peer-reviewed Articles: ...... 137

Conference Abstracts (as first author): ...... 137

Appendix E / Statement of Authorship ...... 139

1. INTRODUCTION 1.1 Studying impact craters? The field of impact cratering emerged in the mid-20th century mainly out from astronomical studies of lunar craters, meteorite research and the field of explosion craters (Melosh 1989). Even though Astronomers, like Tycho Brahe and Johannes Kepler already in the 16th century, systematically studied extraterrestrial bodies, and physicist Ernst Chladni connected well-established meteorite-finds with an extraterrestrial origin in the 16th century, it took almost two more centuries for the scientific community to fully discard the outdated idea of an empty interplanetary space and embrace the concept of impact cratering (a full discussion is given in Sagan 1980, Marvin 1996, and McSween 2000). In the beginning 20th century, it became acknowledged, that Chladnis basic concept of meteorites passing through Earth’s atmosphere under high speeds could produce an impact crater if the bolide was big enough. The first unequivocal proof was made by Daniel Moreau Barringer in 1906, who proved a 1.18 km wide bowl shaped cavity in Arizona to be the result of a meteorite impact, when he recovered up to 18t of nickel-iron meteorite fragments in the craters surrounding (Melosh 1989, McSween 2000). After Barringers discovery, an increasing number of mainly small impact structures, such as the 110 m-sized Kaalijarv Crater in Estonia (Reinwaldt 1928), where connected to meteorite material. Dietz (1946) and Baldwin (1949) introduced the basic conceptual ideas for an impact cratering process, by systematically analyzing lunar craters and establishing empirical size-energy relations for impact craters on the moon. Unique features, like shatter cones (e.g. Dietz 1960), were associated with meteorite impact and helped the recognition of craters in addition to the cosmochemical fingerprint. That way, in a publication of 1987, Grieve listed already 116 impact structures (Melosh 1989), which increased to 190 confirmed impact structures to date (Earth Impact Database July 2017, Fig.1.1). With a paper titled Why study impact craters? Eugene Shoemaker intended to break ground for unstudied, and not-understood aspects of impact cratering which is, to his words “the most fundamental process that has taken place on the terrestrial planets” (Shoemaker 1977, p. 1). Since Shoemaker’s quotation big leaps for a better process-understanding have been made: it is acknowledged that impact processes governed the formation of all terrestrial planets and their satellites as well as controlled the growth of massive planetesimals and planetary cores in the accretion disk of the early solar system 4.6 billion years ago; the origin of the Moon can be linked to a collision, likely of Mars-sized bolide with proto Earth (Hartmann and Davis 1975, Melosh and Sonett 1986, Taylor 1998, Canup and Asphaug 2001); impact processes influenced Earth’s internal differentiation and heat budget, up to its crustal and atmospheric evolution (Shuvalov 2009), as well as overall water budget (Kramers 2003, Yokochi and Marty 2004). Impact cratering is linked to the question of interplanetary life transfer/lithopanspermia (Cockell et al. 2002, Sephton 2004), as well as it has proven to be destructive on a global scale, with the Chicxulub Impact having triggered the Paleogene-Neogene mass extinction (e.g. Alvarez et al. 1980, Bohor et al. 1984, Morro 2006, Pälike 2013, Reimold and Koeberl 2008, Schulte et al. 2006, and Schulte et al. 2010). Beyond Earth, impact 9

cratering is a dominant ongoing surface process on Mars, Mercury or the Moon (with the majority of sampled lunar rocks being impact breccias [e.g. Hertogen et al. 1977]), and more infrequent on Titan or Venus, as well as it determines significantly the shape of smaller bodies in the solar system. In addition to the scientific value of studying impact craters, some of the mapped craters (Fig.1.1) can also be connected to regional structures of significant economic relevance, e.g., the Sudbury Igneous Complex or the Ek oilfield in the Gulf of Mexico (Therriault et al. 2002, Reimold et al. 2005a). 1.2 Impact craters on Earth The overall impact probability can be concluded from the planetary record. With the help of radiometric datable samples from the Moon, the probability can be attached to an actual timeframe. This way, Hartmann (1965) as well as Neukum and König (1976) developed a cumulative method counting Moon-craters and later on deduced hereof the size-frequency distribution assessing the frequency of meteoritical bombardment (Neukum and Ivanov 1994). The formula is several times refined according to flux, velocity, gravity, strength, or orbital parameters of the desired setup (Ivanov 2001, Stöffler et al. 2006) and applied on other planetary surfaces (cumulative size-frequency distribution for lunar craters shown in Fig.1.4, from Neukum et al. 1974). Even the revised production function has limitations and is depending on the interpretation of the evolution of the solar system, e.g., like the assumption of the LHB (lunar cataclysm), the counted surface is assumed to have a single homogenous age (no surface resetting like melt- pools or erosion) and the minimum and maximum concerned crater size is 10 m to 100 km respectively. To assess the actual hazards of an impact event, not only the overall probability but as well the energy absorbed by the rocks and the volume of the ejected material, e.g., crater effectivity, is very important. The probability of size, speed and impact angle is fairly covered by observations of orbital parameters and the size-frequency distribution, but which devastation will actually follow is strongly depending on target properties and not yet fully understood. Thus, the complexity of target inhomogeneity, scaling and impact velocities is making the terrestrial record, with varying scales from hundreds of meters to hundreds of kilometers, the major source of ground truth data (Grieve and Therriault 2004). Massive meteorite impacts such as for Vredefort (d = 160 km)1, Chicxulub (d = 150 km)1, or Sudbury (d = 130 km)1 are ‘ancient history’ – or at least very improbable (Fig. 1.4), however, impact cratering is an ongoing process which is still very active in our solar system (e.g., the 4 km sized comet Shoemaker-Levy 9 impacting on Jupiter in 1994 [Zahnle and MacLow 1994]). The recognition that Earth- approaching objects pose a finite hazard to life has led to a flood of new discoveries and funding of the Planet Crossing Asteroid Survey in 1973, which systematically surveys for potential hazardous objects (PHAs). The survey discovered to date (July 2017) 16383 so called near earth orbiting asteroids (NEAs).

1 Rim-to-rim diameter for the corresponding structure (from Spray, www.passc.net/EarthImpactDatabase/); maximum structural damage diameter of the crater can be considerably larger, e.g., Sudbury 260 km. 10

Figure 1.1: Overlay of the currently listed impact craters in the earth impact database in ArcGIS; a listing of 190 (July 2017) known terrestrial impact structures can be found at http://www.unb.ca/passc/ImpactDatabase/index.html.

Figure 1.3: Fate of a large iron meteoroid entering Earth’s Figure 1.2: Orbits of 1400 Potentially Hazardous Asteroids atmosphere (meteoroid’s tensile strength = 500 MPa, entrance (PHAs) in the Inner Solar System from Mercury through Jupiter angle = 15°). Depending on mass, velocity and diameter it will as of early 2013; shown objects are at least 140 meters in size and hit the earth intact (no breakup), will burn up or break apart; come at least as close as 7.5 million kilometers to the Earth’s orbit When the meteorite remains intact, it will cause a crater, broken (https://www.jpl.nasa.gov/spaceimages/details.php?id=PIA17041). up it will produce a crater strewn field which will have increasing overlap with increasing size and diameter (redrawn from Melosh 1989; p.210, fig.11.4).

Whereas in 1995 only 70 NEAs have been spotted, we believe today the positions of almost all NEAs larger than 1 km in diameter are known (Fig. 1.2). However, Tunguska or Meteor Crater sized bodies remain hard to predict, even though, smaller objects yield a considerable damage potential (e.g., Chelyabinsk; Brown et al. 2013, Popowa et al. 2013). The group of near earth asteroids is subdivided into Aten, Apollo and Amor type bodies, according to orbital parameters respectively to earth. If the Minimum Orbital Intersection Distance (MOID) is 0.05 AU or less and their absolute magnitude is brighter than 22.0 they are considered as potentially hazardous (PHAs). Luckily, most of the incoming iron meteoroids below 50 m and stony meteoroids below 100 m will not be able to overcome earth atmosphere (Fig. 1.3). Nevertheless, under certain impact angles also smaller objects with a comparable low strength will be able to pass and survive the aerodynamic stresses (Kenkmann et al. 2010). Meteorites which successfully pass the atmosphere without being decelerated to rate of fall and maintaining their high impact velocities (average projectile velocities of 18 to 25 kms-1 for asteroids and 30 to 75 kms-1 for comets), will form a crater with two possible morphologically end members. The average crater size of the current crater record is about 2 to 4 km, but there are huge discrepancies in overall sizes (Reimold and Koeberl 2008). Looking at the overall map of impact craters (Fig. 1.1), one can see a strong heterogeneity in regional distribution. If impact cratering is the only remaining active surface process, crater population will be saturated after time, depending on crater size and surface of the planetary body. However, earth is effectively obscuring and diminishing the crater record.

Two thirds of Earth’s crust are covered by Figure 1.4: Cumulative size-frequency calibration distribution for impact craters with data from Shoemaker et al. 1970, Hartmann and oceanic crust, which is on average renewed after Wood 1971, and Baldwin 1971 (Neukum et al. 1974, p. 227, fig. 10). 60 Ma and leaving no oceanic crust older (with 12

the exception of a few Thethys remnants) than 200 Ma (van Thienen 2003). In a study of Hergarten and Kenkmann (2015) it is shown, with Earth diminishing the crater record through an active atmosphere, sedimentation, and plate tectonics, it is likely that all impact craters exposed at the Earth’s surface larger than 6 km-diameter are discovered - even though Kenkmann et al. (2015) added with the verification of the partially buried Saqqar impact structure in Saudi Arabia, a 34 km complex crater to the Earth Impact Database. As for buried, and likely metamorphosed structures, as well as for as for craters smaller than 6 km in diameter, Hergarten and Kenkmann (2015) stated the crater record would be incomplete. According to their estimations 260 exposed craters with diameters between 0.25 km and 1 km, and at least 90 craters with diameters between 1 km and 6 km should be discovered on Earth’s surface (Hergarten and Kenkmann

2015). 1.3 Thesis Motivation Cratering experiments onto solid rock have enabled the cratering community to study shock metamorphic effect over a broad range of target, projectile and velocity setups under well-defined laboratory conditions (e.g. Shoemaker et al. 1963; Gault and Greeley, 1978; Polanskey and Ahrens 1990; Love et al., 1993; Housen and Holsapple, 2003; Burchell and Whitehorn 2003; Ai and Ahrens 2004). However, only a few have investigated sub-surface processes (Maurer and Rinehart, 1960; Kenkmann et al., 2011; Onose et al., 2011) and even fewer could reproduce the necessary boundary conditions to produce and find shatter cones (Moore et al., 1962; Schneider and Wagner, 1976; Roddy and Davis, 1977). With a significant part of the worldwide crater record hidden in the subsurface, metamorphosed or eroded to deeper level, where dominantly low shock features remain – studying these effects, like shatter cones, will help to better asses and constrain new discovered as well as known structures, in terms of size, energy or erosional level. So far, shatter cones have been widely used to identify impact structures. They are the only macroscopic shock indicator and their distinct cone-shaped fracture surface, with diverging striae, and hierarchical bifurcation (horse-tailing) makes them easy identifiable in the field. Nonetheless, their occurrence is heterogeneous throughout the crater record and their formation and the physical boundary conditions are still subject of debate (Baratoux and Reimold 2016). The occurrence of shatter cones for the verification of shock has to be important, especially for small craters and lacustrine target rocks, which often lack other identifiable shock features. Thus, shatter cones play also today an important role for the discovery and verification of impact craters: identification of the Agoudal structure (Chennaoui Aoudjehane et al. 2016), the Tunnunik impact structure (Dewing et al. 2013), or the Jebel Waqf as Suwwan impact structure (Salameh et al. 2006) have been achieved by shatter cones. Only for the latter structure, later studies have shown sparsely documented PDFs from isolated chert nodules (Schmieder et al. 2011). In addition shatter coning is present in meteorites (Killgore et al. 2011, McHone et al. 2012) and nuclear explosion craters (Moore et al. 1962, Bunch and Quade 1968).

With the MEMIN (Multidisciplinary Experimental and Modeling Impact Research Network) experiment group, we were able to produce shatter cones in different hypervelocity impact settings under controlled conditions (Kenkmann et al. 2012, Wilk and Kenkmann 2016). As part of the MEMIN project, we want to understand, under which laboratory conditions do shatter cones form and delimit conditions at which no shatter cones can form. The scope of the presented thesis is to enhance the qualitative and quantitative understanding of the shatter cones geometry and the physical boundary conditions necessary for the formation of shatter cones by experimental analysis. As well as enable us to make a unified model for the generation of shatter cones in consistency with the microscopic and macroscopic observations, as well as with the derived boundary conditions. 1.4 Impact Crater Formation The variety of crater forms can be generalized into a gravity dominated, complex crater form, which is a strong modification of the original transient cavity during the impact (Fig.1.6 - right), and simple craters which can be gravity or strength dominated (Fig.1.6 - left). The complex craters are characterized by an uplifted central area (in form of a central uplift or a central peak ring structure) as well as a flat floor and a slightly raised and terraced rim. The modification of the structure can be increasingly complex with size leading to a multitude of variations with single or multiple peaks, pits, or peak ring and inner ring structures (Melosh and Ivanov 1999) up to the poorly understood multi ring basins. On the other side is the so called simple crater. Its shape is much more influenced by the strength of the target rocks. Nevertheless, the frontier of the strength/gravity regime, which occurs on much smaller craters in the magnitude of tens of meters on earth, is not to be confused with the transition zone between simple and complex craters, which occurs e.g., on Moon between 23 km (Holsapple 1993) and 20 km (Melosh 1989). The simple crater shows a bowl shaped cavity and a stronger elevated rim in comparison with the complex crater, thus its overall looks are much more close to the transient cavity (uppermost stages in Fig.1.6). In general the depth-to-diameter ratio is much higher for simple craters than for complex craters (Melosh, 1989). As a rule of thumb for large craters, the diameter can be related to the kinetic energy of the projectile (Short 1966):

-3 0.294 d = 9.47*10 (1/2*mv²) (1)

If the cratering process is more or less subject to gravity, or if it is dominated by the strength of the target is decided in relatively small craters. As a rough perception for the controlling regime Holsapple (1993) made the estimation: ρgL > Y gravity regime (2)

ρgL < Y strength regime (3)

Whereas L being the projectile diameter, g as gravitational acceleration, ρ is the projectile density and Y as an experimental material parameter corresponding to the target’s strength. Otherwise in conclusion the

transition zone is determined by Y= ρgL (Housen and Holsapple 2011). Therefore we comfortably assume that the transition zone already occurs in relatively small craters. For example if we take the ratio of the lithostatic to inertial forces ( 2 = g*L / vi², with vi being the impact velocity), which is representing the gravitational effects as the inverse of the Froude number (Housen and Holsapple 2011), and compare it to

3µ/2 the pure influence of rock strength on the crater size ( 4 = (ρ *vi² / Y) , with µ being an experimental determined material parameter), then they should equal out at the transition zone (Holsapple 1993).

Figure 1.5: Schematic diagram of initial contact and compression phase shock, up to subsequent excavation Kenkmann et al. 2014 (p.161, fig. 4). With increasing distance material is deformed to different stages of shock metamorphism due to the attenuation of the expanding shock wave (SIV – S0).

Figure 1.6: propagation of the shock front and associated change of state parameters (from: Stoßwellen in Geomaterialien, lecture & exercise, WS2011/12, Geosciences/Geology; F.Schäfer, Fraunhofer EMI, slide 42)

The process of “hypervelocity impact crater” (French, 1998) formation has been divided by Gaul et al. (1968) into three stages. These are the compression, excavation and modification stage. During these three stages, most of the projectiles kinetic energy will be transferred into deformation work and heat within the target by nucleation of a supersonic shock wave expanding outwards from the target-projectile boundary. The resulting supersonic shock wave propagates through the target within the matter of a few micro seconds but also through the meteorite itself (Melosh 1989, Langenhorst 2002). Compression Stage During the contact and compression phase, when the meteorite hits the surface, it comes to a sudden pressure buildup. On the frontier from compressed to uncompressed material the kinetic energy of the suddenly stopped projectile is transferred into the shock wave. The emerging “shock front” represents a discontinuity in all state parameters, hence, pressure, temperature, volume, and internal energy (Grieve et al. 1996, Stöffler and Langenhorst 1994). The projectile emits two wave fronts of opposite nature into the target, the compressional wave and the load removal (Fig.1.6). The compression ends, as the reflected wave has propagated through the meteorite, the projectile may evaporate or melt due to the sudden release and the corresponding sudden increase in temperatures. Therefore, the duration of the contact and compression phase (τ) is depending on the projectile’s size (Melosh 1989):

τ = L / vi (4)

or for oblique impacts with the impact angle θ

τ = L / (vi sin θ) (5)

Then, the molten part of the projectile can mix with the melt generated in the target rocks, which are subject to the same abrupt change in physical properties (state parameters as discussed above), as well as with its solid components. Like the shock wave, the tensile wave is propagating downwards, trapping all particles in between, creating a vector of acceleration (Fig.1.6). Successively the crater cavity starts to develop and irreversible deformation is created in the impacted material. Many shock metamorphic effects, such as Planar Deformation Features, Planar Fractures, phase transitions or the formation of frictional melting along pseudotachylite-like shear planes manifest at this stage. The fractures induced in the early stage are irregular, developed transgranular in the microscale and short, mainly due to the high strain rates with a fracture length

Lmax = εfailure* Vshear wave/ dε/dt (Melosh 1989). Excavation Stage At this stage an almost coherent ejection cone is formed and leads to irreversible deformation, like partial melting and fragmentation as well as spallation of distal surfaces. The transient cavity reaches its full

extent and molten material is smashed and thrown straight up and out of the crater as well as into the crater flanks. As excavation goes on, the particle ejection of the steep taper gradually moves on ballistic paths to the outside while the crater rim is forming a stratigraphic inverted ejection lip. The time (Td) for the transient cavity reaching its maximum cratering depth (Hat) and the time (Tf) to reach the maximum diameter of the transient crater (Dat) can be estimated by free fall, neglecting the target properties (Melosh 1989):

1/2 Td ~ ( 2 * Hat / g ) (6)

1/2 Tf ~ ( Dat / g ) (7)

For a Ries-sized crater, this would suggest a time of roughly 28.6 seconds to reach the maximum depth of 4 km for the expanding transient cavity. However, the actual excavated material will probably not include basement rocks from this 4 km depth. Experimental work and computer simulations suggest, that the lowermost excavated horizon is situated only one-third to one-half as deep as the maximum depth of the transient cavity (Melosh 1989, Artemieva et al. 2013). The ejecta dynamics can be very complex. Mass dislocation occurs at different particle trajectories (streamlines) which are dependent to the growth of the transient cavity (Maxwell 1977). The streamlines originate in an initially radial manner from the impact center but are quickly diverted progressing outward the crater (material flow lines in Fig.1.5 and 1.6). Whereas mass going into the crater as fractured or molten material can be injected into the crater, streamlines directed outward will curve upward, forming a lip and excavating material as a coherent ejecta curtain at ballistic pathways. Depending on the ejection velocity Ve and angle φ, material is deposited radial symmetrically in a certain proximity (Rb) to the crater (Melosh 1989):

Rb = (Ve² / g ) * sin(2φ) (8)

Nevertheless, the radial symmetrical streamline-models are only an approximation for the ejection process. Local substrate can be incorporated into the ballistic deposited ejecta (Grieve and Therriault 2004) as well as morphological variations can occur for oblique impacts, e.g., for impact angles below ~75° we see a preferred downrange deposition of the ejecta (Elbeshausen and Wünnemann 2008). While material is excavated in the ejecta curtain or injected into the crater walls, some material, especially the molten and vaporized portion, will form an ejecta plume (Artemieva et al. 2002). According to Artemieva et al. (2002) ejected particle will follow the equation of motion (as long as no atmospheric disturbances occur, e.g. wake effect, caused by very fast projectiles):

푑푢 1 m = 푚푔 + 3 휋 푑µ (푢 − 푢) + 퐶 휋 푑2휌 (푢 − 푢)² (9) 푑푡 푔 4 푑 푔 푔

This motion is controlled by gravity (right side) and Stokes’ drag forces (left side), whereas m is particle mass, d particle diameter, u and ug are particle and gas velocity, ρg and µ are gas density and viscosity and

Cd is the drag coefficient (Artemieva et al. 2002). In addition, the whole mass of material removed from inside the crater during this process is strongly related to target properties, e.g., water saturation, porosity (Poelchau et al. 2011), impact angle and projectile mass. Modification and Collapse Stage The last phase of crater formation is the modification phase. The post-cratering modification (Gault et al. 1968) begins when the transient cavity reached its maximum size and all material is excavated (Melosh 1989). The transient crater is gravitationally forced to collapse and mass is displaced from the inflated and extremely elevated crater rim to the crater center, hence downward and inward sliding of distal parts occur. This and the experienced sudden uplift or rebound, which the center of the structure is going through due to the pressure relief following from the destruction of the projectile (unloading), can then lead to the formation of a central uplift, similar to the reaction of a water surface to a drop of rain (Melosh 1989; Piezarro and Melosh 1999). However some complex impact structures, like the Ries, Haughton or Zhamanshin impact structure do not possess an apparent morphological central uplift (Grieve and Therriault 2004). T he amount of structural uplift (SU) experienced by the basement rocks underneath the crater can be massive and is numeralized by different authors on the study of terrestrial impact craters in relation to the final structural diameter D (Grieve and Pilkington 1996):

SU = 0.086 * D1.03 (10)

Depending on rock strength and seismic activity, the upward movement of the crater center is followed by downward and outward movements, by which the central uplift collapses. As the crater wall collapses, listric normal faults can rotate and move blocks towards the crater, significantly widening the whole resulting crater basin. The radial inward sliding of material might provoke thrusting and could result in the formation of radial transpression ridges (Kenkmann and von Dalwigk 2000). During the whole process, flow field deviations might occur due target inhomogeneities (shistosity, prominent joints or lithologic transitions), but the general particle flow should be radial-symmetrical, producing an almost perfectly circular crater down to impact angles of 10-15° (Gault and Wedekind 1978), below which oblique crater forms will develop with a stronger modification of the central uplift and a very strong modification of the ejecta pattern as discussed before (figure 1.7). The fluidized material behavior during the process in contrast to the final uplift of the crater structure is not fully understood. For now, it is assumed that at a certain frequency, excited by the impact, the strength within a specific grain and block size is virtually annihilated. Once the stimulus is terminated, the rock regains its strength. This process is called acoustic fluidization. It is a plausible idea and a working model for shifting from one crater formation stage to another, but conclusive field observations consolidating this model are still sparse (Melosh 1989, Kenkmann

Figure 1.7: Sketch of compression, excavation and modification of a simple (left side) and complex (right side) impact structure in a layered target. Progression of morphology with size and time of the developing crater structure for simple, complex and peak-ring craters (like the Ries or Siljan Crater) is exemplary shown; note final simple crater for a complex structure is much bigger with respect to the transient crater in comparison to the simple crater (redrawn after Melosh 1989, p. 128, fig.8.2 and page 142 fig.8.14; particle flow paths after French 1998, p.22, fig. 3.4). 19

and von Dalwigk 2000). O’Keefe & Ahrens (1993) showed for small craters that shock heating and quick heat transfer of and within the target material can result in some decrease of target strength. Nevertheless, especially the complex crater formation suggest an extremely reduced rock strength to produce the morphologies caused by the collapse, hence a rock weakening must occur temporarily also in bigger structures.

1.5 Shock phenomena and impact related deformation As the compressive shock wave expands outwards from the point of impact and the structural formation progresses, a series of deformation features from the micro- to the macroscale are imprinted to the target rocks. Generally the stresses induced by the passage of the shock wave can vary from the scale of some hundred MPa up to several hundred GPa and the resulting shock deformation is typically characterized by very high strain rates, in the order of 10³ to 1060s-1 (Melosh 1989, French 1998). These typical high compressive stresses and strain rates are hardly realized under crustal conditions (Kenkmann et al. 2014), and the resulting shock metamorphic effects are an important fingerprint and often the first hint or the last evidence of an impact. Even if the morphological crater is already erased, the shocked minerals can be preserved in ejecta blankets or the structures basement (Langenhorst 2002). For some of these features (e.g. shatter cones), the temporal sequence is unclear. Experiments and numerical simulation can deliver key data to narrow the corresponding ambient conditions. Since this thesis is focused on the formation shatter cones and its boundary conditions, shatter cones themselves and some of its accompanying shock metamorphic effects will be highlighted in this introduction. Shatter Cones A macro- to even megascopic feature is the formation of shatter cones. Shatter cones are acknowledged to be diagnostic for impact structures (Baratoux and Reimold 2016), and can be reproduced in very high energy impacts or explosion tests related to shock waves (Shoemaker et al. 1961, Moore et al. 1962, Bunch and Quaide 1968, Schneider and Wagner 1967, Roddy and Davis 1977, Kenkmann et al. 2012, and Wilk and Kenkmann 2016). The shatter cones surfaces always converges into an apex and displays diverging sets of striae. The distinctive fine striations are typically very well pronounced in dense, fine grained to micritic material (e.g. Malmian limestone of the Steinheim Crater, Fig. 1.10). Unlike slickensides, those fine striations are nonparallel and diverging in “horsetailing” formations (French 1998). These fine lineations are thought to represent intersections of adjacent curved fracture surfaces (Kenkmann et al. 2016). The fracture surfaces themselves can be conical and show multiple interpenetrating sets. Only slightly curved surfaces with diverging striae can be found as well (French and Koeberl 2010). Complete coning on the other hand is rare, as well two opposing cones, developed in one hand specimen can occur (Milton 1977, Osinksi and Spray 2006).

Figure 1.8: oblique crater formation in iSALE with an impact angle of 30° (Elbeshausen and Wünnemann 2008, p.2, fig.2).

Figure 1.9: left - shatter cone in limestone of the Steinheim Basin (Okrusch and Matthes 2014, p.325, fig.24.7); middle - photomicrograph of PDFs in quartz (http://www.unb.ca/passc/ImpactDatabase/); right - coesite in diaplectic quartz grain (Okrusch and Matthes 2014, p.325, fig.24.8)

Figure 1.10: left - shatter cone developed in fine-grained limestone from the Steinheim crater, showing internesting, diverging striations from multiple apexes (French and Koeberl 2010, p.130, fig.5); right – P-T diagram comparing metamorphic regimes realized in earth’s crust compared to the metamorphic regime controlling impact processes (modified from French 1998).

On average, shatter cones have long been believed to point inward and upward, towards the source of the shock wave (French 1998, Ferrière and Osinski 2013), and have been used to reconstruct the impact or shock center in some cases, e.g. Kentland (Dietz 1960), Siljan (Svensson 1973), Slate Island (Stesky and Halls 1979), or Beaverhead impact structure (Hargraves et al. 1990) with mixed success. However, shatter cones can be found with all types of orientations with respect to the impact center – even pointing away, apparently due to target heterogeneities (Baratoux and Reimold 2016). It was also suggested to use the distribution of shatter cones to assess the obliquity of impact craters (Osinski and Ferrière 2016). Even though shatter cones were commonly associated with the central uplift of complex impact craters (French 1998), they can be abundant in all major stratigraphic settings and impactites (Osinski and Ferrière 2016). They are frequently reported from allochthonous breccias and crater fill deposits (Osinksi and Spray 2006, Osinski and Ferrière 2016), e.g. in the fallback breccia of the Sudbury impact structure (Gibson and Spray 1998), as clasts in lithic and impact melt-bearing breccias of Gosses Bluff (Milton et al. 1996), as individual cones or nests in polymict breccias of the Vista Alegre impact structure (Pittarello et al. 2015), or as clasts in proximal ejecta and as breccia dikes intruded into the crater floor for the Haughton and Tunnunik impact structure (Dewing et al. 2013, Osinski and Ferrière 2016). They also have even been identified in suevite recovered from the El’gygytgyn ICDP drill cores (Raschke et al. 2013) and even in distal ejecta parts of the Ries crater (Sach 2014). These finds emphasize the nature of an early shatter cone formation. Shatter cones are considered to form under low pressures starting at 2 GPa (French 1998, Ferrière and Osinski 2010). This is strongly supported by impact experiments, e.g., Schneider and Wagner (1967) as well as by Roddy and Davis (1977), how suggested that shatter cones start to develop under low shock pressures of 2 to 6 GPa. However, some authors advocate for shatter cone formation also in higher pressure regimes, e.g. Osinski and Spray (2006), who suggested shatter cones could have formed within a regime of 25 GPa in the Haughton impact structure. Nevertheless, the authors generally agreed, that shatter cones would start to form under low pressures of 2 GPa. Ferrière et al. 2010 also noted, that shatter cone formation could be present under higher shock pressures, based on the observation of PDFs in shatter cones from the Keurusselkä impact structure. Pseudotachylites Another macroscopic feature cause by impact deformation are pseudotachylites. They are well known from active tectonic environments, long-lasting shearing and folding zones, e.g., the Pyrenees, the Exterior Hybrids or the Alps. They have been first described by Shand in 1916 in the Parys region of the Vredefort impact structure (Magloughlin and Spray 1991). The descriptive definition of those veins has been continuously developed from a simply glassy basaltic, aphanitic vein with sharp boundaries to the host rock - up to the process encompassing term of an ultracataclasite/ultramylonite mixture within a glassy matrix as the result of friction melting along 22

slip surfaces (Philpotts 1964, Bischoff and Oskierski 1984, Reimold 1995, White 1996, Hornemann et al. 2000, Melosh 2005). Today pseudotachylites are understood as the fine-grained to quenched textured fault rocks related to rapid fault movements related to earthquakes. Nevertheless, they are also known from multiple impact structure like Vredefort, Sudbury, Siljan or Rochechouart (Fig.1.10). In structural geology as well as in impact cratering, they are understood to combine three different and also contrasting processes: 1. formation of frictional melting vs. 2. cataclastic fracturing of the host rock and 3. mylonite formation. To make those processes work with one another, pseudotachylites strongly depend on the velocity shear stress displacement relations (Spray 1995). In contrast to shatter cones, the formation of pseudotachylites is linked to the crater modification and collapse stage.

Figure 1.11: left - Pseudotachylite from Western Greenland (Ramsay and Huber 1983, p.587, fig.25.35); right - sketch of a pseudotachylitic thin section from the Rochechouart impact structure (Pohl J. 1987, p.21, fig.12).

Figure 1.12: left - pressure intervals with corresponding occurrence of shock effect based on experiments with non-porous samples used for shock barometry (Langenhorst 2002; fig.6, p.269); right – PT-conditions in impact cratering compared to endogenic metamorphism of crustal rocks (Kenkmann et al. 2014; fig.1, p.157).

Microscopic Shock Effects From shock experiments, several mechanisms, which occur on the microscale, have been identified and calibrated to corresponding pressure conditions (Fig.1.12): cataclasis (including pseudotachylites, microfractures and the formation of gauge zones), intracrystalline plasticity (including deformation twins, undulatory extinction, kink bands) and solid state phase transformation and melting (Stöffler and Langenhorst 1994). Due to the high temperatures after an impact event, also post-shock effects like the formation of Ballen quartz and cherckerboard feldspars occur (Langenhorst 2002), of which Ballen quartz is documented so far only in impact structures, but their exact formation mechanism remains unclear (Ferrière et al. 2008). The most notable shock effects, are so called planar fractures (PFs), planar deformation features (PDFs), which are bona-fide shock metamorphic effects, and accounted as proof of a hypervelocity impact. PFs are a parallel concatenation of planar brittle failures within the grain (Stöffler and Langenhorst 1993). They are open fissures parallel to rational crystallographic planes with low Miller indices and start to develop close to the Hugoniot Elastic limit, showing a typical width of 5 to 10 µm and typical spacing of minimum 15 and more than 20 µm (French 1998, Stöffler and Langenhorst 1994, Langenhorst 2002). Based on the PFs, thinly spaced lamellae can branch off from one side of the fracture plane. Those structures are called feather features (FFs) and can be shear indicative along the fracture plane (Poelchau and Kenkmann 2011). PDFs are strictly parallel planar lamella of opaque appearance, representing dislocations in the mineral lattice. They form multiple sets of closely spaced parallel planar regions with-in the quartz grain. In comparison to PFs the PDF spacing is more closely with typical 2 to 10 µm (French 1998). PDFs show high resistance against post-shock annealing and react to alteration with dissolution into inclusion trails (Fig.1.13), thus remaining clearly identifiable (Langenhorst 2002). PDFs are sharp and well defined throughout the hosting quartz grains and can be therefore relatively accurate indexed, compared to FFs and PFs (Poelchau and Kenkmann 2011). In general, the crystallographic orientations of PDFs in quartz is corresponding to causative shock pressures. Another interesting small scale feature is the development of mechanical Brazil twins exclusively parallel to the c-axis in quartz. The occurrence of those twins was reproduced experimentally with high shear stresses of 3 to 4 GPa (Langenhorst 2002) and they appear as narrow lamellae developed to the basal plane of the quartz grain.

In addition to the formation PFs and PDFs, SiO2 phase transformation of quartz to coesite or stishovite is a strong argument for impact cratering, when the regional geological context is understood. In general, the effects on SiO2 with increasing shock pressures go along with a continuous change towards lower birefringence in-between the pressure range of 25 GPa and 35 GPa for quartz, as well as in the following amorphous state - diaplectic glass (Stöffler and Langenhorst 1994). At higher pressures (>45 GPa), most phases will lose crystal bound water (Stöffler and Grieve 2007) and gradually melting of other

phases than SiO2 phases (then lechatelierite) occur, e.g., melting of plagioclase (maskelynite) at 42 to 45

GPa and melting of pyroxene at 60 GPa (Stöffler and Grieve 2007). The modification of SiO2 into coesite and stishovite occurs at higher pressures as well as the modification of graphite into diamond with pressures from 40 GPa and temperatures of 900°C on, whereas on higher shock pressures, shock vaporization of rocks will deploy, e.g., for granite at 100 to 150 GPa (Stöffler and Grieve 2007).

Figure 1.13: left – planar fractures (PF) with extending feather feature lamellae (FF) in quartz indicating a dextral sense of shear (Poelchau and Kenkmann 2001, p.2, fig.1); right - two sets of planar deformation features in a quartz grain in a thin section from the Ries crater (image taken with crossed nicols, note that one set is outlined by fluid inclusion plains).

Figure 1.14: Shock metamorphism for quartz and feldspar respectively to shock pressures and temperatures based on experimental results from quartzite and granite by Huffman and Reimold (1996) and Grieve et al. (1996) for the included SiO2 phase diagrams (Blenkinsop 2000, p.86, table 8.9).

1.6 References

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2. FORMATION OF SHATTER CONES IN MEMIN IMPACT EXPERIMENTS

This chapter has been published as peer-reviewed article as follow:

Wilk J., and Kenkmann T. (2016) Formation of shatter cones in MEMIN impact experiments. Meteoritics & Planetary Science 51:1477-1496.

2.1 Abstract Shatter cones are the only macroscopic feature considered as evidence for shock metamorphism. Their presence is diagnostic for the discovery and verification of impact structures. The occurrence of shatter cones is heterogeneous throughout the crater record and their geometry can diverge from the typical cone shape. The precise formation mechanism of shatter cones is still not resolved. In this study we aim at better constraining the boundary conditions of shatter cone formation in impact experiments and test a novel approach to qualitatively and quantitatively describe shatter cone geometries by white light interferometry. We recovered several ejected fragments from MEMIN cratering experiments that show slightly curved, striated surfaces and conical geometries with apices of 36° to 52°. These fragments fulfilling the morphological criteria of shatter cones were found in experiments with 20 to 80 cm sized target cubes of sandstone, quartzite and limestone, but not in highly porous tuff. Targets were impacted by aluminum, steel and iron meteorite projectiles at velocities of 4.6 to 7.8 km/s. The projectile sizes ranged from 2.5 to 12 mm in diameter and produced experimental peak pressures of up to 86 GPa. In experiments with lower impact velocities shatter cones could not be found. A thorough morphometric analysis of the experimentally generated shatter cones was made with 3D white light interferometry scans at micrometer accuracy. SEM analysis of the surfaces of recovered fragments showed vesicular melt films alternating with smoothly polished surfaces. We hypothesize that the vesicular melt films predominantly form at strain releasing steps and suggest that shatter cones are probably mixed mode fractures. 2.2 Introduction Of all terrestrial planets, Earth “has retained the poorest sample of the record of hypervelocity impact throughout geologic time” (Grieve and Therriault 2004, p. 199; Hergarten and Kenkmann 2015). Being subject to resurfacing and recycling processes, to weathering and hydrothermal alteration, impact craters can be strongly modified over time. Thus shock phenomena preserved within the crater or in the ejecta blanket play an important role for the discovery and verification of impact craters (e.g. French 1998; Langenhorst 2002; French and Koeberl 2010). Shatter cones are the only known macroscopic feature considered as evidence for shock metamorphism. Conveniently identifiable in the field, shatter cones are the “index fossil of astroblemes”, as stated by Dietz 1960 (p. 1784). Shatter cones are conical fracture

surfaces with distinct and hierarchical striation patterns. The shatter cone surface typically converges conically into an apex. The slightly curved surfaces are marked by multiple inter-penetrating sets of fine striae. Unlike slickensides, the fine striae are nonparallel and diverge into “horsetailing” formations (French 1998). Shatter cones develop their fine striae very well in dense, fine grained to micritic material (French and Koeberl 2010). They form in a great variety of rocks, even in coarse-grained granitoids, or in fine- grained claystone or micritic limestone. The occurrence of shatter cones, for the verification of shock, is especially important in fine-grained marine or lacustrine target rocks or in smaller impact structures (e.g., Kaalijärv; Dietz 1968), which often lack other identifiable shock features. A number of recent discoveries have been based on the findings of shatter cones, e.g. at the Tunnunik (Dewing et al. 2013) or the Jebel Waqf as Suwwan (Salameh et al. 2006) impact structures. However, the occurrence of shatter cones is not uniform throughout the crater record. A consensus exists that the formation of shatter cones is related to the passage of the shock front or the release from shock loading (Gash 1971; Baratoux and Melosh 2003; Sagy et al. 2004; Dawson 2009; Baratoux and Reimold 2016). The available models can explain the cone geometry but do not provide a satisfying concept that explains also the presence of diverging striations and grooves, and their hierarchical bifurcation that leads to the horsetailing effect (Kenkmann et al. 2016, 2016). Shatter cones are not only found in the crater floor or the central uplifts of complex impact structures (Ferrière and Osinski 2013), but they are also found in allochthonous breccias of meteorite impact craters (Osinski and Spray 2006) and even in their distal ejecta (e.g., at the Ries crater, Germany; Sach 2014). They are furthermore known from meteorites (Killgore et al. 2011; McHone et al. 2012; Ferrière et al. 2013) and have been recovered from experimental hypervelocity impacts and nuclear explosion craters (Shoemaker et al. 1961; Moore et al. 1962; Bunch and Quaide 1968; Schneider and Wagner 1976; Roddy and Davis 1977; Kenkmann et al. 2012). Terrestrial impact craters are formed by events with high kinetic energies, for instance 5x1021 J for a Ries sized bolide (Hörz 1982), and differ widely in magnitude from shock and impact experiments with several kJ on the laboratory scale, and for explosion craters up to 1012 J (Roddy and Davis 1977). However, impact experiments can give insights into detailed aspects of the cratering process by confining the boundary conditions for up-scaling and by varying different parameters of the cratering process under controlled conditions (Cintala et al. 1999). They are also useful to establish parameters essential for numerical simulations (such as strength-models and material specific failure criteria) by benchmarking and validating the numerical models with analog experiments (Pierazzo et al. 2010; Wünnemann et al. 2011; Güldemeister et al. 2013). Cratering experiments in solid rocks have been conducted for a broad range of target, projectile and velocity conditions by Shoemaker et al. (1963), Gault and Greeley (1978), Polanskey and Ahrens (1990), Love et al. (1993), Housen and Holsapple (2003), Burchell and Whitehorn (2003), and Ai and Ahrens (2004). Recently, a large number of impact experiments into solid rocks have been conducted in the framework of the MEMIN (Multidisciplinary Experimental and Modeling Impact Research Network) program (Kenkmann et al. 2011, 2013; Poelchau et al. 2013). Such 32

experiments are suited to investigate the deformation inventory of the crater subsurface (Maurer and Rinehart 1960; Kenkmann et al. 2011; Onose et al. 2011; Buhl et al. 2013a, 2013b), and also to search for shatter cones and to constrain the formation conditions (Shoemaker et al. 1961; Moore et al. 1962; Schneider and Wagner 1976; Roddy and Davis 1977; Kenkmann et al. 2012). The occurrence of shatter cones in artificially produced explosion craters was first documented by Dietz (1960), who reported shatter cones from explosion craters in tuff from the Rainer nuclear explosion chamber, Nevada. Bunch and Quaide (1968) found shatter cones in the ejecta from the 0.42 kt Danny Boy nuclear crater, Nevada. They recovered the cones from moderately-shocked subandesite blocks and described a coating of rock flour on of the shatter cone surfaces. In 1969 Roddy and Davis also published shatter cone findings from 0.5 to 100 t TNT (roughly 2.1 to 418 gigajoules), large-scale explosion experiments that formed craters in tonalite. Roddy and Davis (1977) found the conical fracture surfaces in the exposed crater subsurface as well as in allochthonous breccias. They were able to estimate the formation pressure at 2 to 6 GPa. Shoemaker et al. (1961) were the first to produce shatter cones in impact experiments. They recovered shatter cones from the crater floor of cratering experiments into sandy dolomite and estimated a lower limit for shatter cone formation in the order of 470 MPa. Moore et al. (1962) were able to experimentally produce shatter cones in a series of hypervelocity impacts into basalt, sandstone, dolomite, and nephrite. Moore et al. (1962) described their findings as cone- shaped shear fractures and related the features to shatter cones by weakly developed grooves and striae that converged into an apex. The features were found in the crater subsurface with the apex pointing roughly towards the impact direction. Moore et al. (1962) pointed out intense pulverization at the presumed shatter cone surface. In 1976, in a series of experiments with light gas guns, Schneider and Wagner were able to produce millimeter-sized shatter cones in the crater floor of limestone targets. The shatter cones were developed in experiments with peak pressures below 3 to 4 GPa (Schneider and Wagner 1976). In accordance with previous findings of shatter cones in experiments and explosion craters, Schneider and Wagner also described a coating of the shatter cone surfaces by rock flour. Even though the impact experiments by Schneider and Wagner (1976) showed difficulties to estimate the shock pressures locally for the small-scale experiments, they suggested that shatter cone development started below shock pressures of a few gigapascals, which was backed up with the experimental observations of Shoemaker et al. (1961) and Roddy and Davis (1969). However, there is only vague agreement so far on the shock pressure range for formation of shatter cones. The occurrence of shatter cones also in higher pressure regimes appears to be very plausible, e.g. for the Haughton impact structure where shatter cones formed in zones proximal to the impact center, that likely had experienced shock pressures of 25 GPa (Osinski and Spray 2006). The formation of shatter cones in higher pressure regimes is also indicated by the occurrence of shatter cones together with PDFs, for example in the Keurusselkä impact structure (Ferrière et al. 2010; Hasch et al. 2016). Nevertheless, the experimental observations are in accordance with the lower limit of the general shock 33

pressure magnitude given in the literature for shatter cones in impact craters - ranging from 2 to 30 GPa (French 1998; Osinski and Spray 2006; Ferrière and Osinski 2010) or up to 30 to 45 GPa (Nicolaysen and Reimold 1999). Here, we present the first findings of shatter cones in ejecta generated in hyper-velocity cratering experiments. Our study was aimed at constraining the physical boundary conditions necessary for the formation of shatter cones by examining shatter cone like features found in MEMIN cratering experiments. Furthermore, we apply new techniques to qualitatively and quantitatively measure the geometrical parameters of shatter cones. 2.3 Methods 2.3.1 Experimental Setup The impact cratering experiments were conducted at the Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institut (EMI), in Freiburg and Efringen-Kirchen, Germany. The acceleration facilities used for the high-speed experiments at EMI are the SLGG (“space” light gas gun) and the XLLGG (“extra-large” light gas gun). The SLGG is a mid-sized, two-stage light gas gun with 8.5 mm caliber launch tube for 2-5 mm projectiles, of 5 m length, and achieving maximum velocities of 9 km/s, depending on the sabot weight. The XLLGG has a 39 mm caliber launch tube and is used for larger projectile sizes of 10 to 12 mm (for a comprehensive description the reader might refer to Schäfer et al. 2006; Lexow et al. 2013, and references therein). The two light gas accelerators allow to greatly vary projectile and target sizes. The projectiles were mounted in 39 mm and 8.5 mm nylon sabots, respectively, which guided the projectiles down the launch tube and were separated from the projectile by aerodynamic drag shortly after leaving the tube. The sabot is then impacted into a steel plate and should not enter the target chamber (Fig. 2.1). In the experiments presented, the facilities where employed to accelerate spheres of 2.5 mm, 5 mm (for the SLGG), 10 mm and 12 mm (for the XLLGG) to impact speeds of 2.5 km/s to 7.8 km/s (the corresponding experiments are listed in Table 1). Projectiles made of steel, aluminum, and iron-meteorite spheres had masses between 0.0667 g and 7.336 g, and the kinetic impact energies varied from 673 J to 82.7 kJ. The projectiles impacted into dry sandstone, water-saturated sandstone, quartzite, tuff, and limestone cubes. Temperature and moisture of the dry samples were controlled by storage under room conditions (for a detailed description we refer to Poelchau et al. 2013 and Buhl et al. 2013a). The Ernst-Mach-Institute already had experience with steel and aluminum projectiles (Schneider and Wagner 1976; Schäfer et al. 2006). In addition we chose in the MEMIN experiments to use projectile spheres turned from Campo del Cielo meteorite. The Campo del Cielo and the steel (alloy) projectiles (D290-1 high-speed steel) had proven good traceability in projectile/target mixing processes, and have been shown to reproduce genuine melt textures (Hamann et al. 2015; Ebert et al. 2014). The aluminum (55X G28J1) projectiles were chosen to achieve the very high impact velocities in the MEMIN experiment series.

2.3.2 Target material The sandstones used in the MEMIN experiments are Seeberger Sandstone (Sb) and Adamswiller Sandstone (Aw). The Seeberger Sandstone is a well sorted fluvial quartz sandstone of uppermost Triassic age (Stück et al. 2011) that is quarried in central Germany. The rock has a mean grain size of 100 ± 25 µm (Sommer et al. 2013) and was chosen as a target material for its quartz-dominated mineralogical composition (Poelchau et al. 2013). A modal analysis of the rock is given by Ebert et al. (2013), showing about 89 vol% quartz (equivalent to ~ 94.8 wt% SiO2). The quartz grains are sub-rounded and cemented by quartz, phyllosilicates and accessory phases (Buhl et al. 2013). Uniaxial compression tests showed strength values of ~70 MPa for dry samples and ~57 MPa for wet samples (Poelchau et al. 2013). The sandstone has a bulk density of 2.05 ± 0.04 g/cm³ (Poelchau et al. 2013) and undamaged, a p-wave velocity of 2915 m s-1 (Moser et al. 2013). The Adamswiller Sandstone used in the MEMIN pilot experiments is also known as the “grès rose des Vosges” (red sandstone from the Vosges) and is mined in the Alsace region. It is a lower Triassic (Alberti 1834), coarse grained and very hematite-rich sandstone with mudstone pebbles. The quartzite was quarried in the Taunus Mountains, Western Germany. It has an age of 405 Ma and has experienced a low-grade Variscan metamorphism (Poelchau et al. 2014), but the sedimentary layering is still apparent. Fractures are present on a decimeter scale and the quartzite has an average grain size of ~185 µm (Poelchau et al. 2014). The so-called Treuchtlinger Marmor is a fossil rich, Upper Jurassic, biosparitic limestone quarried in southern Germany. It is a very common building stone in the region and was taken because of its ready availability as a dimension stone. It has plenty fossilized algae, sponge, ammonites and belemnites and is by far the most heterogeneous target material in our series. The Weiberner Tuff from the volcanic Eifel region in Southwest Germany, has a Pleistocene age (Lothar 1984). It consists of a fine- grained, highly porous microcrystalline matrix of mostly feldspathic components, phyllosilicates, olivine, augite, as well as other accessory components like titanite, with numerous lithic sandstone, shale, pumice and basalt clasts ranging in size up to 10 mm. It has a bulk density of 1.42 ± 0.01 g/cm³ (Poelchau et al. 2014).

Fig. 2.1. Schematic setup of a two-stage light gas gun with target cubes and ejecta catchers built into the target chamber (modified from Poelchau et al. 2013).

Table 2.1. Experimental impact conditions for the MEMIN experiments.

Impact Projectile mass Experiment Facility Target material Block size (cm) Projectile type L (mm) direction (g)

D2 XLLGG Sandstone ⊥ 50x50x50 Steel 10 4.10 D3 XLLGG Sandstone ⊥ 50x50x50 Iron meteorite 10 4.12 D4 XLLGG Sandstone ⊥ 50x50x50 Iron meteorite 10 4.14 D5 XLLGG Sandstone ⊥ 50x50x50 Iron meteorite 10 4.120 E1 XLLGG Sandstone ⊥ 80x80x50 Steel 12 7.313 E2 XLLGG Sandstone wet ⊥ 80x80x49 Steel 12 7.323 E3 XLLGG Sandstone wet ⊥ 80x80x50 Iron meteorite 12 7.087

E4 XLLGG Sandstone ⊥ 80x80x50 Steel 12 7.336 E5 XLLGG Tuff n.d. 80x80x50 Steel 12 7.312 E6 XLLGG Quartzite ⊥ 80x80x40 Steel 12 7.311 A3 SLGG Sandstone ⊥ 20x20x20 Steel 2.5 0.067 A5 SLGG Sandstone ⊥ 20x20x20 Steel 2.5 0.0672 A6 SLGG Sandstone ⊥ 20x20x20 Steel 2.5 0.0671 A7 SLGG Sandstone || 20x20x20 Steel 2.5 0.067 A8 SLGG Sandstone || 20x20x20 Steel 2.5 0.0672 A11 SLGG Sandstone wet ⊥ 20x20x20 Steel 2.5 0.067 A12 SLGG Sandstone wet ⊥ 20x20x20 Steel 2.5 0.0667 A13 SLGG Sandstone. wet ⊥ 20x20x20 Steel 2.5 0.0676 A15 SLGG Sandstone ⊥ 20x20x20 Aluminum 5 0.1792 A16 SLGG Sandstone ⊥ 20x20x20 Aluminum 2.5 0.0224

K1/A14 SLGG Limestone n.d. 20x20x20 Steel 2.5 0.0673

Pilot 3231 XLLGG Sandstone (Aw) ⊥ 100x50x50 Steel 10 ~4.08 Pilot 3242 XLLGG Sandstone (Aw) || 100x50x50 Steel 10 ~4.08 Pilot 3243 XLLGG Sandstone (Aw) ⊥ 100x50x50 Steel 10 ~4.08 C 3297 XLLGG Sandstone ⊥ 40x40x40 Iron meteorite 10 ~4.10

L = projectile diameter. Impact direction represents shot direction with respect to the stratigraphic layering of the target blocks (⊥= impact perpendicular to the layering, ||= parallel to the layering, n.d. = no apparent stratification of the target block). XLLGG stands for “extra- large” light gas gun and SLGG for “space” light gas gun. The steel projectiles refer to the high alloyed steel (D290-1), the iron meteorite is a sphere made of Campo del Cielo and the aluminum projectiles are made of 55X G28J1 aluminum. Aw = Adamswiller Sandstone.

2.3.3 Experiment and sample preparation Directly after conduction of the experiments, we documented the experiments in the target chamber by means of detailed photographs with a SLR Canon Eos 550D camera (Fig. 2.2). Then, the cratered target blocks and the ejecta catchers were removed from the target chamber and weighed to determine the excavated mass and cratering efficiency. The excavated crater volume was documented by scanning the crater morphology by laser scanning techniques (eScan3DTM by Digital Corp). The resulting 3D morphology of the crater cavity and crater efficiency estimations were carried out by Dufresne et al. (2013). A detailed description of the overall ejecta material is given in Sommer et al. (2013). By chance, a shatter cone-like

fragment was recovered in the ejecta material, which triggered a systematic search for shatter cones in the materials of the existing experiments. During hand–picking, the ejecta was then thoroughly re-examined with an Olympus BH-2 coaxial reflected light microscope, purposely in the search for shatter cones. So far we have recovered 23 shatter cone fragments in 7 experiments from the ejecta generated in all 25 experiments listed in Table 1. We also found one cone-shaped spall fragment in the crater floor of an impact experiment into Seeberger Sandstone A15 (Fig. 2.3). In addition, we carried out a thorough subsurface analysis of pilot experiments 3231, 3242 and 3243 by carefully opening already existing tensile cracks with small chisels by hand - but have not found any shatter cones so far. The recovered fragments from the ejecta were photographically documented and mounted onto an aluminum prism with sticky wax for further analysis with white light interferometry. 2.3.4 Surface characterization by white light interferometry A morphometric analysis of each specimen was carried out with a Bruker AXS Contour GT-K0 white light interferometer (WLI). The WLI is a non-contact, non-intrusive optical surface analytical tool generating 3D point clouds of the sample surface based on the optical interference of light. The WLI allows to conduct high-resolution analysis of small-scale surfaces where µm spatial resolution is needed. We used this technique for characterizing the surface topography of our recovered fragments, in particular to measure the geometrical parameters such as apical angles, amplitude of striated cone surfaces, or the curvature of cones. The WLI has three main components. The vertical movable upper casing, a 5x objective lens (which can be replaced with an objective turret), and a horizontally movable and tiltable sample table. A CCD sensor and the light source are integrated into the upper casing. Into the 5x objective a beam splitter and a reference mirror are integrated. Bigger samples are secured on the horizontally movable sample table with play dough, and small fragments are embedded in sticky wax against an aluminum prism that can be screwed onto the table. The light emitted in the upper section can either be polychromatic or monochromatic and is produced by a diode. In our case green light and white light are accessible. The topographic heights of our samples easily exceed the given wavelength for the green light source (with an intensity peak at 565 nm to 580 nm), leaving multiple interference maxima of higher order. Therefore, we used white light in our analysis. As the light is directed from the upper casing through the beam splitter (a prism with a half transparent mirror), it is separated into a reference beam and the measuring beam. The measuring beam is directed onto the sample and the reference beam heads towards the reference mirror. The scanning beam and the reference beam are then reflected from their allocated targets and brought to interference. If both beams have the same travel path length, positive interference occurs, otherwise destructive interference will occur, which is used to determine the vertical distance to the sample. In the WLI the reference mirror has a fixed distance, whereas the distance to the sample surface is varied in each measuring step with the vertical 37

movable upper casing. This procedure is called the vertical scanning mode. In this mode and with white light we achieved a vertical resolution of 2 to 9 µm. The quality of our measurements is influenced by sample characteristics, such as reflectance and environmental measuring conditions such as vibrations. The spatial resolution is dependent on the pixel size of the sensor and the used 5x objective lens, leading to a resolution in x- and y-direction of 1,966 µm. The entire setup is operated with a PC and the Bruker Vision64 software, which controls the measurement and allows post processing of the measured data. We are also able with the software to extract additional surface characteristics from the WLI data, such as surface roughness or spikiness of a scale limited surface (kurtosis). In material science the surface roughness of 3D textures is typically described by the kurtosis of a scale limited surface (DeCarlo 1997; Hansson and Hansson 2011). The kurtosis of a scale limited surface (the Sku value) is based on a histogram of the heights of all measured points from the scaled surface and the symmetry and deviation from an ideal normal distribution:

1 1 4 푆푘푢 = 4 [ ∬ 푧 (푥, 푦)푑푥푑푦] 푆푞 퐴 퐴

In this equation 푥and 푦 define the sample area (퐴 ) and 푧 gives the height values for the area (푥, 푦). Sq is the root mean square of the surface, a weighted mean of the height values (Leach 2008). Examples for various materials and results of different surface processes from literature are listed in Table 2. Spiky, but otherwise planar surfaces like a glass plate or an unpolished cutting surface appear to have high Sku values between 30 and > 140, whereas surfaces that have undergone normal abrasion or fracture processes tend to have smaller kurtosis values.

Fig. 2.2. Sandstone and quartzite cubes with 20 cm side length after impact experiments. Both sandstone cubes were impacted roughly perpendicular to stratigraphic layering. The sandstone blocks were impacted with the SLGG (space light gas gun) facility for the NEOShield Program at the Fraunhofer Ernst-Mach-Institute in Freiburg (Hoerth et al. 2015). Hoerth et al. used aluminum spheres of 5 mm diameter and impacted the target rocks with velocities between 3 and 7 km/s. The quartzite block was impacted with a basalt projectile with a diameter of 6.2 mm and an impact velocity of 5.46 km/s. The sandstone block b as well as the quartzite block c display extensive spallation features at the block sides and pervasive fracturing throughout the block. Note the whitish halo in the central parts of all three examples. The whitened zone represents most likely the original extent of the transient crater cavity.

Fig. 2.3. Sandstone block A15 and the crater cavity filled with synthetic resin in top view and in a cross section. Note the small but pronounced conical peak in the crater center, in both viewing directions

2.3.5 SEM analysis of shatter cone sections and surfaces In addition to the morphometric analysis, scanning electron microscopy was carried out with a Zeiss Leo 1525 field-emission scanning electron microscope equipped with a tungsten mono-crystal cathode and operated with the Oxford Instruments software tool INCA. Secondary electron (SE) images were taken of the shatter cone surfaces as well as of thin sections cut perpendicular to the shatter cone symmetry axis. Experimental conditions were 15 to 20 kV, and working distances varied from 11 to 13 mm. 2.4 Results So far we have recovered 23 fragments with fracture surfaces of distinctly conical geometry or with a slightly curved surface, marked by fine striations (Fig. 2.4a-h). The millimeter to half centimeter sized cones have been recovered from the ejecta of sandstone, quartzite and limestone blocks impacted by aluminum, meteorite and steel projectiles. Table 2.3 lists those experiments where shatter cone fragments could be found. Except for tuff, they are present in all other target lithologies. They occur both in small- scale experiments with 2.5 mm and 5 mm projectiles (SLGG-experiments) and in experiments with 10 and 39

12 mm projectiles (XLLGG). Shatter cones are present in craters formed at impact velocities ranging from 4.56 km/s to 7.75 km/s under dry and water saturated conditions. They do not occur at lower velocities. The fragments were recovered from crushed material with reduced porosity. The shatter cone fragments in the dry sandstone and the quartzite targets have a somewhat brighter appearance in comparison to the undamaged or only slightly damaged material. The crushed material in which the shatter cones were formed corresponds to the “zone of pervasive grain crushing and compaction” mapped by Buhl et al. (2013a) in Seeberger sandstone targets. We observe this brightening typically also for other crushed or shocked ejecta in comparison to the less damaged host rock and ejecta (Ebert et al. 2013). Some of the fragments were also coated with crushed, powdered host-rock material. The wet sandstone samples showed, in particular, distinct surface features in the form of a macroscopically visible dense and yellowish coating of the whole striated surface (Fig. 2.4g). The cone sizes vary only slightly from 2 to 3.5 mm. A trend for bigger cone shaped fragments corresponding to large projectiles or experiments was not found. However, some of the slightly curved and striated surfaces found in XLLGG experiment E3 have sizes of up to 6 mm (Fig. 2.4g, h). The best developed shatter cone surfaces have been found in the sandstone experiment A15 with a 5 mm aluminum projectile and in limestone experiment K1 with a 2.5 mm steel projectile.

Table 2.2. Typical kurtosis (Sku) values of different materials and surface processes from literature and measurements in the lab.

Typical Sku Material values Fracture surface in Seeberger Sst 2.8 to 3.2 Fracture surface in Carrara Marble 2.7 to 3 Fracture surface in granite 3.6 to 3.9 Calcareous slickenside 2.0 to 2.5 Turned metal surface 2 to 4 [a] Grinded metal surface 2 to 6 [a] Milled metal surface 2 to 10 [a] Sandblasted metal surface 2.5 to 3 [a] Metal surface after unlubricated sliding 3.4 to 3.9 [b] Extensional rough crack in metal 2.7 [c] Unpolished thin section 30 to 40 Microscope slide 140 Aeolian transported sand 1.1 [d] Fluvial transported sand 1.4 [d] Acid-etched fractures in carbonates 6.1 to 30.8 [e] SSt – sandstone; [a]: data for metal surfaces from Stout (1980); [b]: data from friction experiments from Azvedo and Marques (2010); [c]: data for fatigue induced rough crack in metal from Billy et al. (1981); [d]: data for aeolian and fluvial transported sand from Lindé and Mycielska-Dowgiallo (1980); [e]: data for etched carbonate fracture surface from Rodrigues et al. (2012)

In addition to the conical fractured and striated fragments, undulating and radial features have been found on a 40 cm sized cube of sandstone in a pilot experiment. The block was impacted by a 10 mm Campo del Cielo meteorite projectile with an impact velocity of 4.76 km/s. The rock was pervasively fractured. An extensive spallation feature at the impacted block face, parallel to the impact direction was uncovered (Fig. 2.5). The exposed surface displays ridges and grooves diverging in a radial manner, complementary to the striations of shatter cones. Taking strength scaling of the ejected material into account, we see a broad scattering for the occurrence of shatter cone fragments. The experiments with the highest cratering efficiency (A12) seemingly favor the formation of shatter cones. In contrast, tuff is devoid of shatter cones. However, shatter cone fragments are found in water saturated as well as in dry experiments, with the most findings of shatter cone fragments made in A15 so far. A clear dependency on crater efficiency or target material groups with respect to porosity or water saturation is not obvious (Fig. 2.6). So far we scanned several promising fragments from experiments A15 and E1 (Fig. 2.7). For A15 we found typical conical or curved surfaces with diverging patterns clearly pointing towards an apex. The apical angles range from 36° to 52°. For the curved fragments of E1 we see very fine developed diverging striae, which may also represent sub-cones diverging on the fracture surface. We extracted cross sections perpendicular to the symmetry axis of the striated and conical fracture surfaces (Fig. 2.8). In addition, we also took WLI scans from shatter cone samples of the Rochechouart (Fig. 2.8e), Haughton (Fig. 2.8f) and Steinheim impact craters. Qualitatively we observe the same topology of alternating-groove-and-striae wave patterns typical for shatter cones both in the hand specimens and the fragments from the experiments. From the WLI data we extracted values for the surface roughness (kurtosis). The Sku values obtained from the MEMIN experiments range from 1.5 to 2.91 for the surfaces of the shatter cones formed in the dry sandstone of experiment A15. This overall roughness is in agreement with the Sku values for surfaces that experienced considerable abrasion or mechanical stresses, but they are rather spiky in comparison to etched or polished surfaces. For a more quantitative comparison we also measured the kurtosis of shatter cones in the micritic limestone of the Steinheim Crater. For these we observed a range of Sku values of 2 to 4.5, which is overlapping with our measurements for the cones experimentally formed in the sandstone. The SEM analysis of the recovered fragments shows abundant transgranular fractures and intense crushing and grain comminution, as well as reduction of pore space (Fig. 2.10a). On the surface of the scanned shatter cone sections of experiment A15 shown in Figure 2.10b, we observed a 1 to 2 µm thick coating of glassy material. This texture on the shatter cone edge becomes even more apparent when we observe the shatter cone surface in plane view. The foamy texture becomes a continuous sheet of melt films showing a step-wise alternation with smoothly polished surfaces (Fig. 2.11a).

Fig. 2.4. Shatter cone fragments from the MEMIN experiment. (a-d) Fragments from the A15 experiment (impact of 5 mm aluminum onto sandstone with an impact velocity of 6.97 km/s). (e) Limestone fragment from experiment K1/A14 (steel projectile onto a limestone block); the surface is slightly striated and resembles the increasing distal widening of the cone resulting in a hyperbolic shape of the surface parallel to the symmetry axis, as it is also observed partially in natural shatter cones. (f) Four curved fragments marked with diverging striae from the impact experiment E1 with a 12 mm steel projectile onto sandstone; note the friable appearance of the crushed and fractured material. (g, h) Conical (g) and undulating (h) fracture surfaces with fine striae; - note these fragments of the cratering experiments (Campo del Cielo meteorite into water saturated sandstone with an impact speed of 4.59 km/s) resemble the smooth surfaces coated by rock flour shown by Schneider and Wagner (1976) from their impact experiments into limestone. 42

Table 2.3. Impact conditions for experiments that produced shatter cone fragments.

Impact speed Shatter Experiment Target material Block size (cm) Projectile type L (mm) Kinetic energy [J] V [cm³] P [GPa] [km/s] cone count E1 Sandstone 80x80x50 Steel 12 4.560 76032 1393 46 2 E3 Sandstone wet 80x80x50 Iron meteorite 12 4.590 74655 1829 - 3 4.709 81060 1684 66 1 E6 Quartzite 80x80x40 Steel 12 5.250 919 34.2 - 2 A12 Sandstone wet 20x20x20 Steel 2.5 A15 Sandstone 20x20x20 Aluminum 5 6.970 4353 42.9 66 12 A16 Sandstone 20x20x20 Aluminum 2.5 7.750 673 2.6 79 2 5.320 952 - 86 1 K1/A14 Limestone 20x20x20 Steel 2.5 V: crater volume; P: experimental peak pressures in the runs from which we recovered shatter cone fragments in the ejecta. For the pressure calculations we were using the planar impact approximation as described by Melosh, 1989 (chapter 4.5.1, pp.54-58) with C and S values for equivalent target lithologies from Ahrens and Johnson, 1995 (chapter 3-4, pp.37-41).

2.5 Discussion 2.5.1 Occurrence of shatter cones Shatter cones in cratering experiments have so far been found in andesite, tonalite, dolomite, sandstone, nephrite and limestone (Shoemaker et al. 1961; Moore et al. 1962; Bunch and Quaide 1968; Schneider and Wagner 1976; Roddy and Davis 1977). In the MEMIN experiments, we were able to produce shatter cones in limestone and sandstone. In addition, we can report on shatter cones from experiments in quartzite and highly water saturated sandstone. However, comparing the impacted lithologies with respect to porosity or water saturation, as well as taking crater efficiency into account, we were not able to establish a clear trend in our observations, which could indicate the formation of shatter cones to be more likely in one specific target material than in others (Fig. 2.6). As in the explosion cratering experiments of Bunch and Quaide (1968), we found shatter cones in the ejecta material, which had not been documented from high velocity impact cratering experiments before. For terrestrial craters, recovering shatter cones in allochthonous units is no exceptional case. Well established examples are shatter cones recovered from the Black Member of the Onaping Formation in Sudbury (French 1967); shatter cones in crater-fill melt rocks and megablocks of Haughton Crater as reported by Osinski and Spray (2006); shatter cones found in suevite recovered from the El’gygytgyn ICDP drill cores obtained in 2008/2009 by Raschke et al. (2013), and shatter cones from the polymict impact breccia of the Vista Alegre (Pittarello et al. 2015) and from the Araguainha (Tohver et al. 2012) impact structure. In the case of the Ries and Steinheim craters, the type locality Steinheim is known for well- developed shatter cones. They typically formed in the Upper Jurassic limestones of the structural crater floor and in the Middle Jurassic Opalinus Clays of the central uplift. For the Ries Crater itself, shatter cones had first been confirmed from crystalline rocks of ‘Mayers Keller’ and from the ‘Nördlingen 1973’ drill core (Schmidt-Kaler et al. 1974). More recent findings also show Ries shatter cones in the distal ejecta located in the Molasse of the North Alpine Foreland Basin (Sach 2014). With the broad range of terrestrial impact

craters with shatter cones found in turbulent mixed or ejected material, finding shatter cones also in the ejecta of hypervelocity impact experiments should be expected, as confirmed by our experiments.

Fig. 2.5. Sandstone block exhibiting a radial Fig. 2.6. Pi-group plot for transient crater volumes for the MEMIN striated spallation surface on the XY-plane. On top experiments with 2.5-12mm projectiles (modified from Poelchau et al. is the original block still in the target chamber. It 2014). On the ordinate 휋v (as the equivalent of mass displaced from the shows extensive fracturing. The spallation surface, crater relative to projectile mass) times 휋4 (the density ratio) was plotted which we also see in the bottom picture, is partially together with 휋3 (the ratio of the material strength to inertial forces) on the uncovered. The smaller section shown at the abscissa. The dashed trend line shows data for craters formed in basalt after bottom was cut out from the upper bisected part of Moore and Gault (1962). the original block. The impact direction was parallel to the Z-direction.

The shatter cones found in the MEMIN impact experiments typically have a distinctive macroscopic appearance, which makes them identifiable in the bulk ejecta mases recovered. The fragments have a brightened appearance, display coating of the shatter cone surface by rock powder – comparable to the intense pulverization described by Moore et al. (1962, p. 4), and the cone material tends to be extremely friable and fragile. Those three aspects were also observed for the shatter cone fragments found in the cratering experiments by Schneider and Wagner (1976). Interestingly, these authors found their fragments exclusively within the spallation zone and the crater floor. We did, however, recover all fragments presented here exclusively - as mentioned - in the ejecta. Fortunately, we can circumscribe the origin of the recovered fragments based on their appearance. The macroscopic observations of rock powder coating and textural whitening in the MEMIN experiments are common for material with crushed porosity and intense grain comminution on the microscale, as already shown in a study by Ebert et al. (2013). This has been confirmed here with thin sections from the sandstone fragments of experiment A15 (Fig. 2.10). Buhl et al. (2013a,

2013b) subdivided the MEMIN crater subsurface into zones with respect to the inherited deformation features. Their observations for the subsurface of the transient cavity, and the ‘inner zone of pervasive grain crushing and compaction’ (Buhl et al. 2013a) are coherent with our observations on shatter cone fragments. This zone can be observed in situ as a whitish halo on the crater floor. Measuring the width of this area for the given MEMIN experiments results in 15% to 38% of the apparent crater diameter. The crater examples (Fig. 2.2) well illustrate that obviously a lot of spallation is happening in the cratering experiments, resulting in much wider apparent crater diameters compared to the original widths of the transient craters. Nevertheless, taking the zone of crushing into account and comparing our results to the previous cratering experiments by Schneider and Wagner (1976), we are confident to say our fragments belong to the ejected material from within the transient cavity or the ejecta curtain. This puts our material roughly in between the pressure regime above the Hugoniot elastic limit of quartz and below the experimental peak pressures given in Table 2.3. We will investigate whether these boundary conditions determined for this suite of fragments are applicable to shatter cones recovered from ejecta in nature. The described intense level of comminution has also been observed in natural impact craters, for example at the Araguinha impact structure in Brazil. The 40 km wide Araguinha impact structure in Brazil has an inner 10 to 12 km wide ring (Lana et al. 2008). In the central part of the structure shatter cones are well documented (Dietz and French 1973). They can be found within megabreccias surrounding the central granite core (Hippertt et al. 2014) as well as in clasts of polymict breccia (Tohver et al. 2012). Interestingly, Hippertt et al. (2014) observed a high degree of microbrecciation on the level of whole-grain and/or grain- boundary fragmentation in shatter cone bearing sandstones of the central uplift, comparable to the material we recovered from the inner zone of pervasive grain crushing and compaction.

Fig. 2.7. (a) WLI scan of the shatter cone fragment shown in Fig. 2.4a. Note the multiple sets of striae diverging on the curved fracture surface. (b, d) Shatter cone surface of the fragment shown in Fig. 2.4g. The surface is clearly striated. The spikes surrounding the fragment is noise from reflections off the embedding material. In (b) the cone shape is clearly visible. (c, g, h) WLI scans of the shatter cone fragments recovered from the experiment E1. (e, f) Examples of poorly developed shatter cone fragments with weakly developed striae.

Fig. 2.8. (a, b) Topographic profiles of the WLI measurements from the fragment shown in Fig. 2.7 (E1), resembling the undulating and sinusoidal characteristics of natural shatter cone examples (e, f). (c, d) Profiles derived from the WLI measurements of experimental shatter cones from E1 and A15; - note that the profiles are exaggerated in the Y-direction. (e, f) Topographic profiles of shatter cone surfaces taken perpendicular to the cone symmetry axes, derived from WLI measurements of hand specimens from the Rochechouart (e) and the Haughton (f) impact structure.

Fig. 2.9. WLI profiles perpendicular to the symmetry axis of the conical fragments of the A15 experiment shown in Fig. 2.7. The ordinate of both profiles is strongly exaggerated to emphasize the small sub-cone structures. Examples of the locations for measuring height h and the secant length s are shown as well.

Fig. 2.10. Secondary electron microphotographs of thin sections cutting the shatter cone surface of fragments from experiment A15 (SE mode with 15 kV). The cross sections are taken roughly perpendicular to the fracture surface. Note the intense grain comminution and pore space reduction in Fig. 2.10a. The transition from shatter cone subsurface to actual shatter cone surface is shown in Fig. 10b marked by the fine, µm wide bright layer.

Fig. 2.11. Secondary electron microphotographs showing the surface of fragments from experiment A15 with distinctive striae and steps (SE mode with 20 kV). Note the tiny microspherules in Fig. 2.11b.

2.5.2 Quantitative description of shatter cones The distinctive arrangement of longitudinal ridges and grooves on conical or curved surfaces presented in the WLI data is well known from shatter cones. The topological features in the WLI cross sections and the surface roughness parameters are in accordance with the observations by Kenkmann et al. (2016). Applying geometric evaluation as shown in Kenkmann et al. (2016), we can extract a segment height h and a secant length s from the cross section of the presumed cone ridges (Fig. 2.9). From this the sub-cone convexity ß of the segment can be derived according to Kenkmann et al. (2016): 2ℎ ß = 푡푎푛 푠 4

We were able to extract the parameters for the fragments from cratering experiment A15 shown in Figure 7. The curvature for the experimentally produced shatter cones of experiment A15 is determined in the profile of Figure 9a as 73° and in the profile of Figure 9b as 78°. The fragments of A15 also show relatively large apical angles of 36° to 52°. This is in accordance with observations made by Kenkmann et al. (2016) for natural shatter cones, in which the higher curvatures are also representative for the samples with higher apical angles of sub-cones; namely, Steinheim cones have a curvature ß of 60° and a mean sub-cone angle of 39°, and the sample from the Siljan impact structure has a curvature ß of 65° and a mean sub-cone angle of 46°. The WLI method has clear limitations. Larger samples, with significant topography exceeding several centimeters, are not manageable with the technique. This leads often to the problem that only subsets or regions of interest from natural shatter cones can be analyzed. In these cases, the WLI has shown to be at least a good complementary method to the laser scanning techniques which have severe problems with the resolution of very fine and small features on the µm to mm scale, and rely on interpolation methods for generating a continuous 3D mesh. Due to the very high spatial resolution, this is not necessarily needed for interferometer scans, which makes this technique very well suited for the analysis of small-scale features.

2.5.3 Melt formation The occurrence of melt films observed in SEM analysis is coherent with the observations of other authors regarding natural shatter cones. In Gay (1976) shatter cone striae decorated with microspherules were reported from the Vredefort impact structure. Wieland et al. (2006), Gibson and Spray (1998), Nicolaysen and Reimold (1999), and most recently Hasch et al. (2016) and Pittarello et al. (2015) showed melt features on shatter cone samples. The surface features on the shatter cones produced in the water saturated sandstone in the MEMIN experiments strongly resemble the smoothened and polished surfaces shown by Schneider and Wagner (1976). The melt textures observed in the MEMIN samples do overlap very well with the description given by Gibson and Spray (1998) for melt features observed on the surface 49

of shatter cones from the Sudbury impact structure and with the melt observed on shatter cone surfaces from the Vredefort impact structure shown by Nicolaysen and Reimold (1999). In the SEM image we show smooth, almost polished surfaces marked by very fine melt striations. This is very similar to the fine, and sometimes intricate melt fibers shown by Gibson and Spray (1998) as well as to the “rod-like” glassy particles described by Nicolaysen and Reimold (1999, p. 4926). The authors in both cases attributed these features to rapid shearing and a very localized concentration of deformation along the shatter cone surface. We also believe that the elongated features are arguably produced by frictional sliding parallel to the propagation direction of the shatter cone itself. As a result shatter cones would be shear or mode II fractures. In addition, we observed “frothy”, reticulate melt films, but believe them to be the product of extension. It is not unlikely that the foamy melt textures might have formed during rapid extension of the fracture surface. The melt coating and the frothy textures are a continuous feature over the entire shatter cone surfaces, thus, it evidently involves melting of accessory phases in the sandstone as well (e.g., rutile as described in Buhl et al. 2013). Melting of refractory accessory phases would be reasonable if we consider melt formation due to rapid pressure release and subsequently extension. We think melt formation in both manners plays a role in shatter cone formation; therefore, shatter cone surfaces should be characterized as mixed mode I/II fractures. The apparent fine striae of the melt surfaces are in some cases decorated by small spherules (Fig. 2.11b). Similar features have also been found on natural samples from the Sudbury (Gibson and Spray 1998) and from the Vredefort impact structure (Gay 1976; Gay et al. 1978, Nicolaysen and Reimold 1999).

Fig. 2.12. (a) Impact velocities plotted against the estimated kinetic energy and (b) maximum Hugoniot pressure of the experiments for our shatter cone producing experiments and non shatter cone yielding experiments from the MEMIN program and the work by Schneider and Wagner (1976). The calculated energy and pressure estimations are listed in Table 2.4.

Table 2.4. Comparison of experimental results from MEMIN with the impact experiments by Schneider and Wagner (1976, p. 41).

Calculated Calculated Experimen Projectile Impact speed Hugoniot Target material Projectile type L (mm) kinetic energy t mass [mg] [km/s] pressure [J] [GPa] MEMIN experiments with shatter cones: 7313 4.56 46 76031.8 E1 Sandstone Steel 12 E3 Sandstone wet Iron meteorite 12 7087 4.59 - 74654.8 7311 4.71 66 81059.5 E6 Quartzite Steel 12 66.7 5.25 - 919.2 A12 Sandstone wet Steel 2.5 A15 Sandstone Aluminum 5 179.2 6.97 66 4352.8 A16 Sandstone Aluminum 2.5 22.4 7.75 79 672.7 67.3 5.32 86 952.4 K1/A14 Limestone Steel 2.5 MEMIN experiments without shatter cones: D2 Sandstone 4100 4.40 43 39688.0 Steel 10 D3 Sandstone Steel 10 4120 4.56 45 42834.8 D4 Sandstone 4140 3.50 29 25357.5 Steel 10 D5 Sandstone 4120 2.50 16 12875.0 Steel 10 E2 Sandstone wet Steel 12 7323 4.58 - 76805.1 E4 Sandstone Steel 12 7336 4.68 48 80338.0 E5 Tuff 7312 4.76 39 82731.8 Steel 12 A3 Sandstone Steel 2.5 67.0 5.00 54 837.5 A5 Sandstone 67.2 5.10 55 873.9 Steel 2.5 A6 Sandstone 67.1 4.80 50 773.0 Steel 2.5 A7 Sandstone Steel 2.5 67.0 4.90 52 804.3 A8 Sandstone Steel 2.5 67.2 5.10 55 873.9 A11 Sandstone wet Steel 2.5 67.0 5.30 - 941.0 A13 Sandstone wet Steel 2.5 67.6 5.25 - 931.6

Schneider and Wagner 1976 experiments with shatter cones: 1 Limestone Steel 1.5 13.8 3.30 42 75.1 3 Limestone Steel 2.0 32.9 3.70 50 225.2 4 Limestone Copper 2.0 37.4 3.50 - 229.1 5 Limestone Bronze 2.0 36.9 3.40 - 213.3 6 Limestone Steel 1.5 13.8 3.60 48 89.4 7 Limestone Steel 1.5 13.8 3.50 46 84.5 10 Limestone Aluminum 2.5 22.1 4.30 43 204.3 11 Limestone Aluminum 2.5 22.1 3.60 33 143.2

Schneider and Wagner 1976 experiments without shatter cones: 2 Limestone 32.9 1.30 12 27.8 Steel 2.5 8 Limestone Aluminum 2.5 22.1 2.80 24 86.6 9 Limestone 22.1 2.40 19 63.6 Aluminum 2.5 12 Limestone 22.1 5.10 55 287.4 Aluminum 2.5 13 Limestone Steel 1.5 13.8 2.60 30 46.6 14 Limestone Steel 1.5 13.8 2.50 29 43.1

2.5.2 Apparent boundary conditions In the MEMIN experiments we can reach localized high peak pressures of up to 86 GPa for the given experiments (Table 2.3). For this reason we also see a variety of shock features from crushing, over PF and PDF formation, up to melting and vaporization, as well documented in Ebert et al. (2013). Nevertheless, with the given fast shock wave attenuation rates, the volume of higher shocked particles is very limited. Flyer plate tests, which are performed in addition to the impact experiments (Kowitz et al. 2013a and b), can probably contribute much better to compare shock effects in detail with modeled shock attenuation. Nevertheless, in addition to the described macroscopic features, the shatter cone fragments microscopically show also a distinctive fracture behavior due to the passage of the shock wave. The deformation is marked by intense crushing as well as grain comminution and pore space reduction. We were not yet able to identify specific shock features, like PDFs, alongside the shatter cone fracture surfaces but might be able to do so in the future with investigations at the TEM scale. The occurrence of shatter cones in the MEMIN experiments as well as by Schneider and Wagner (1976) is listed in Table 2.4. We do observe a slight trend that indicates that the impact velocity could be more decisive for the formation of shatter cones than the mass of the projectile (Fig. 2.12a). Also both experimental campaigns show a lower limit for shatter cone formation as pointed out in Figure 2.12b. MEMIN experiments below 46 GPa and impact velocities below 4.6 km/s were not able to produce shatter cones. In Schneider and Wagner’s experiments below a calculated peak pressure of 33 GPa and impact velocities below 3.3 km/s no shatter cones were found. Shatter cones formed in the MEMIN experiments might belong to shatter cones of type 1b as classified by Ferrière and Osinski (2013). This group comprises well-developed shatter cones formed in material with no recognizable porosity and sparse occurrence of PFs. So far, we did not find clear indication of other definite shock metamorphic effects in the documented fragments other than shatter cone formation and melting. 2.6 Conclusion We document shatter cones produced in MEMIN impact cratering experiments. The only millimeter sized conical fragments with curved as well as striated fracture surfaces are mainly found in sandstone experiments but were also recovered in the ejecta of quartzite and limestone experiments (Table 2.3). The majority of the found shatter cones are 2 to 3.5 mm in size. Bigger fragments of up to 5 mm in size have only been found in the XLLGG experiment E3. We could, however, not yet establish a clear dependence of shatter cone formation on crater efficiency, target lithology, porosity, or water saturation in our experiments. Our morphometric analysis of the shatter cone topology reveals similarities between experimentally and naturally formed shatter cones. The apical angles of the recovered experimental shatter cones range from 36° to 52° and have curvatures of 73° to 78°. Shatter cones appear preferentially in the impact cratering 52

experiments with higher impact velocities (above 4.6 km/s). In our experiments, the minimum pressure for shatter cone formation appears to exceed the Hugoniot elastic limit of quartz. The occurrence of shatter cone fragments in the ejecta of the MEMIN experiments advocates a formation of shatter cones in the rather early stages of crater formation but after grain crushing and porosity reduction. The occurrence of glassy textures at the shatter cone surface is consistent with the observations made by other authors on natural shatter cones. The observed vesicular melt films probably formed at strain releasing steps, advocating an extensional component in the process of shatter cone formation. In combination with the fine shear-attributed striae at the shatter cone surfaces, we suggest shatter cones developed in the manner of mixed mode I/II fractures. 2.7 Acknowledgement This work was possible due to funding by the German Research Foundation (DFG), grant KE 732/22-1. This project is part of the DFG research unit FOR-887: “Experimental Impact Cratering: The MEMIN program”. Sincere thanks go to the EMI representatives and the laboratory team that made the experiments possible, in particular Tobias Hörth, Michael Poelchau, and Frank Schäfer. We are grateful to Matthias Ebert of the MEMIN team for the first discovery of shatter cones and to Fiona Reiser for her SEM analysis. We also thank Lidia Pittarello and Christiano Lana for their constructive and helpful reviews, as well as Wolf Uwe Reimold for editorial handling.

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3. MELT FORMATION ON SHATTER CONES RECOVERED FROM THE MEMIN IMPACT EXPERIMENTS IN SANDSTONE

This chapter has been submitted as peer-reviewed article as follow:

Wilk J., Hamann C., Fazio A., Luther R., Hecht L., Langenhorst F., and Kenkmann T. (submitted) Formation of shatter cones in MEMIN impact experiments. Meteoritics & Planetary Science.

3.1 Abstract Shatter cones are diagnostic for the recognition of meteorite impact craters. They are unambiguously identifiable in the field and the only macroscopic shock-deformation feature. However, the physical boundary conditions and exact formation mechanism(s) are still subject of debate. Melt films found on shatter cone surfaces may allow to constrain pressure-temperature conditions during or immediately after their formation. Within the framework of the MEMIN research group, we recovered 24 shatter cone fragments from the ejecta of hypervelocity impact experiments. Here, we focus on silicate melt films (now quenched to glass) found on shatter cone surfaces formed in experiments with 20–80 cm sized sandstone targets, impacted by aluminum and iron meteorite projectiles of 5 and 12 mm diameter at velocities of 7.0 and 4.6 kms-1, respectively. The recovered shatter cone fragments vary in size from 1.2 to 9.3 mm. They show slightly curved, striated surfaces, and conical geometries with apical angles of 36°–52°. The fragments were recovered from experiments with peak pressures ranging between 46–86 GPa, and emanated from a zone of 0.38 crater radii. The shatter coned material experienced low bulk shock pressures of 0.5–5 GPa, whereas deformation shows a steep increase towards the shatter cone surface leading to localized melting of the rock, resulting in both vesicular as well as polished melt textures visible under the SEM. Subjacent to the melt films are zones of fragmentation and brittle shear, indicating movement away from the shatter cone apex of the rock that surrounds the cone. Smearing and extension of the melt film indicates subsequent movement in opposite direction to the comminuted and brecciated shear zone. We believe the documented shear textures and the adjacent smooth melt films can be related to frictional melting, whereas the overlaying highly vesiculated melt layer could indicate rapid pressure release. From the observation of melting and mixing of quartz, phyllosilicates, and rutile in this overlaying textures we infer high, but very localized post- shock temperatures exceeding 2000°C. The molten upper part of the shatter cone surface cross-cuts the fragmented lower section, and is accompanied by PDFs developed in quartz parallel to the {1122} plane.

Based on the overprinting textures and documented shock effects we hypothesize shatter cones start to form during shock loading and remain an active fracture surface until pressure release during unloading and infer that shatter cone surfaces are mixed mode I/II fracture surfaces. 3.2 Introduction Impact structures are exposed to resurfacing and recycling processes on all planetary bodies, diminishing the impact record, especially on Earth (Grieve and Therriault 2004; Hergarten and Kenkmann 2015). Some impact-related shock-metamorphic effects are different to any other geological feature and potentially remain preserved in the ejecta blanket or the crater floor long after the obliteration of the crater itself (French 1998; Langenhorst 2002). The only macroscopic shock-metamorphic effects are shatter cones, which play an important role for the discovery and validation of impact structures in the field (for a comprehensive review we refer to Baratoux and Reimold 2016). By definition, the occurrence of shatter cones must be pervasive in the rock and cones or cone segments can occur either individually or as hierarchically related sets. The shatter cone surface is conically curved and typically converges into an apex (Gibson and Spray 1998). The distinct conical and curved fracture surfaces of shatter cones are marked by diverging striae. Unlike slickensides, the fine striae are nonparallel and typically diverge into “horsetailing” formations (French 1998; Gibson and Spray 1998), which are thought to represent intersection lineations of adjacent curved fracture surfaces (Kenkmann et al. 2016). Shatter cones are considered to form at shock pressures as low as 2 GPa (French 1998; Osinski and Spray 2006; Ferrière and Osinski 2010). Over and above that, planar fractures (PFs) and planar deformation features (PDFs) in quartz grains, both associated with shatter cones, also indicate higher possible formation pressures of 25–30 GPa (Hargraves and White 1996; Osinski and Spray 2006; Ferrière and Osinski 2010) or up to 30–45GPa (Nicolaysen and Reimold 1999). Shatter cones were frequently found in artificially produced explosion craters from both conventional TNT explosions as well as from nuclear explosions (Dietz 1960; Bunch and Quaide 1968; Roddy and Davis 1977). For example, Roddy and Davis (1977) estimated formation pressures for shatter cones in their experiments ranging between 2 and 6 GPa. In impact experiments, shatter cones were first reported by Shoemaker et al. (1961) from experiments using sandy dolomite as target. Subsequently, shatter cones were produced in impact experiments performed by Moore et al. (1962) into basalt, sandstone, dolomite, and nephrite targets as well as in impact experiments performed by Schneider and Wagner (1976), who shot amongst others steel and aluminum projectiles onto limestone targets. Unfortunately, neither Moore et al. (1962) nor Schneider and Wagner (1976) estimated shock pressures for shatter cone formation in their experiments. However, Schneider and Wagner (1976) delimited, that shatter cones must have formed below the estimated experimental peak pressures of 30 to 40 GPa. Interestingly, they also pointed out that the cone-shaped fragments had a striking surface coating, and that the fragments where recovered, similar to Moore et al. (1962), from intensely pulverized material. 60

To date, several models of shatter cone formation exist. Most of the authors, in essence, link their formation to the presence of material heterogeneities and formation upon decompression in the trailing end of the shock wave (Baratoux and Melosh 2003; Sagy et al. 2004; Wieland et al. 2006; Dawson 2009; Baratoux and Reimold 2016; Osinski and Ferrière 2016). The model of Baratoux and Melosh (2003) focuses on tensional hoop stresses caused by material heterogeneities. The model describes the cone-shaped fracture surface, but indispensably links the shatter cone shape to the width of the compressive pulse and the heterogeneities’ size. Models focusing primarily on the branching fracture mechanism were put forward by Sagy et al. (2004) and Kenkmann et al. (2016). Sagy et al. (2004) explained the formation of curved or spoon-like fracture surfaces by tensile fractures propagating close to the Rayleigh wave speed. In this model, the characteristic striations are caused by material heterogeneities. Dawson (2009) argued that shatter-cone formation is the result of adiabatic shear banding, however, Dawson’s model discards intense fracturing at the shatter cone surface. A phenomenological approach was taken by Kenkmann et al. (2016), who explained the horse-tailing effect by cascading bifurcations of curved fracture planes whose intersection lines are the diverging striations. This model is capable of constructing the hierarchical structure of shatter cones to any order and readily explains their formation without the previous precondition of existing material heterogeneities. An increasing number of reports has described vesiculated melt films and cataclasis associated with the fracture surface of shatter cones (e.g., Gay et al. 1978, Gibson and Spray 1998, Nicolaysen and Reimold 1999, Crósta et al. 2012, Fazio et al. 2014, Pittarello et al. 2015, Hasch et al. 2016, Wilk and Kenkmann 2016, Hamann et al. 2016, Wilk et al. 2016). Reports of such shatter cone melt films might constrain the pressure-temperature (P-T) conditions during or immediately after shatter cone formation and will be discussed in this study. Melt formation on shatter cone surfaces was first studied by Gay (1976) and Gay et al. (1978), who analyzed glassy micro-spherules adhering to shatter cone surfaces from the Vredefort impact structure. Gay et al. (1978) ascribed their formation to shear movement along the shatter cone surface. However, this explanation was later repealed by Gibson and Spray (1998), who interpreted the micro- spherules as condensates. Nonetheless, Gibson and Spray (1998) endorsed the idea of a shear component during shatter cone formation and showed several melt textures associated with shatter cone surfaces from the Sudbury impact structure (e.g., in the form of intricate melt fibers and smears), and compared them with pseudotachylites. Nicolaysen and Reimold (1999) came to a similar conclusion by investigating shatter cones from the Vredefort impact structure. They analyzed melt films on shatter cone surfaces and on “multiply striated joint sets” (MSJS). Both were showing crushed lithic as well as glassy material at their surfaces. They quantified the unequivocal shear displacement and conclusively explained “rod-like” glassy particles (Fig. 10; p. 4926) as a product of frictional sliding along the fracture surface. Fazio et al. (2014) reported on vesiculated melt films on shatter cone surfaces from Kamil crater, Egypt, and explained their

formation by frictional heating and localized shock deformation. In addition, Fazio et al. (2014) showed stretched vesiculated melt, indicating surface separation under still hot conditions. Pittarello et al. (2015) and Hasch et al. (2016) documented coatings on shatter cone surfaces from the Vista Alegre and the Keurusselkä impact structures, respectively. Both authors conclusively identified the coatings as melt layers connected to the shatter cone formation. Unfortunately the coatings did not preserve the original melt textures, since the fracture surfaces shown by Hasch et al. (2016) undergone partially strong alteration, whereas the coatings reported by Pittarello et al. (2015) were mostly recrystallized in dendritic patterns with residues of an amorphous phase within the groundmass adhering to a so far unidentified phase. Hasch et al. (2016) also showed that such melt layers frequently branch and estimated a displacement along the fractures of minimum 100 µm based on cut and dragged grains. Shatter cones from both craters show cataclasite situated subjacent to the melt layers, showing locally concentrated shock deformation (Pittarello et al. 2015; Hasch et al. 2016). Wilk and Kenkmann (2016) recovered shatter cones from a variety of experimentally produced hypervelocity impacts into sandstone, quartzite, and limestone. The experimentally produced shatter cones were found in ejecta material exhibiting reduced porosity and crushed grains, which was interpreted as an indicator for their early formation (Wilk and Kenkmann 2016). Moreover, these shatter cone surfaces showed polished or striated surfaces alternating with foamy and vesicle rich structures. We are convinced that the distinct observations made on shatter cone surfaces is key to improve our understanding of shatter cone formation. In this study, we present a detailed description of unaltered melt textures on shatter cone surfaces along with cataclasis and indications for shock metamorphism found in MEMIN experiments. We will compare our findings to microstructures found in the literature of natural shatter cone samples and assess the role of possible shear and tensile failure for their formation. In addition, the experiments allow to constrain the physical boundary conditions for shatter cone formation. 3.3 Methods 3.3.1 Experimental Setup and Material A series of hypervelocity impact cratering experiments were performed with two different two-stage light gas guns situated at the Fraunhofer Institute for High-Speed Dynamics, Ernst- Mach-Institute (EMI): the “space” light gas gun (SLGG) and the “extra-large” light gas gun (XLLGG). The SLGG is a mid-sized two-stage light gas gun with an 8.5 mm caliber launch tube for 2–5 mm projectiles, achieving maximum velocities of 9 km s-1, depending on the sabot weight. The 39 mm caliber XLLGG is used for larger projectile sizes of 10–12 mm (for a full description of the experimental assembly and parameters we refer to Schäfer et al. 2006; Lexow et al. 2013; Kenkmann et al. this issue, and references therein). In the framework of MEMIN different parameter studies were carried out (Poelchau et al. 2013, and Kenkmann et al. this issue). Here, we 62

report on experiments A15-5185 (A15) and E3-3384 (E3). We found the similar melts films also on fragments recovered from the experiments E1, A12 and A16. In comparison to the experiments A15 and E3, the recovered shatter cones where not as abundant (Table 3.1) and – especially the melt films – not as well preserved. In addition, shatter cones from experiments E3 are the largest (still mm-sized) recovered fragments, promising better handling for subsequent thin section and TEM preparation. Experiment A15 was carried out with a 5-mm-diameter aluminum projectile shot onto dry sandstone at an impact velocity of 6.97 km s-1, yielding an impact energy of 4.35 kJ. Experiment E3 was conducted with a 12-mm-diameter Campo del Cielo iron meteorite projectile shot onto a sandstone block with 50% water saturation at an impact velocity of 4.59 km s-1, yielding an impact energy of 74.66 kJ. Projectiles were embedded in 39 mm and 8.5 mm cylindrical nylon sabots. The sabot guided the projectile down the launch tube and was separated from the projectile by aerodynamic drag shortly after leaving the tube, i.e., the sabot was generally not entering the target chamber. In the target chamber, witness plates of Vaseline and phenolic foam were positioned vis-à-vis the target block to capture ejecta particles. In the target chamber, the target surfaces of the sandstone blocks were positioned perpendicular to the impact direction. In both experiments, bedding planes within the sandstone were oriented parallel to the target surface and approximately perpendicular to the impact direction. In experiment A15 the dry sandstone cube had an edge length of 20 cm. The wet sandstone block in experiment E3 was 80 x 80 x 50 cm in size. The wet sandstone was soaked in water under ambient conditions prior to the experiment (for a detailed description sample preparation we refer to Poelchau et al. 2013 and Buhl et al. 2013). We used Seeberger Sandstone in both MEMIN experiments A15 and E3. The Seeberger Sandstone is a well-sorted, porous (porosity 23 ± 1 vol.%), fluvial quartz sandstone of uppermost Triassic age (Stück et al. 2011; Ebert et al. this issue). The rock has a mean grain size of 100 ± 25 µm (Sommer et al. 2013) and was chosen as a target material due to its quartz-dominated mineralogical composition (Poelchau et al. 2013). A modal analysis of the rock is given by Ebert et al. (2014), showing about 89 vol.% quartz (equivalent to ~ 94.8 wt% SiO2). Quartz grains are sub-rounded and cemented by quartz, ~10 vol.% phyllosilicates (kaolinite - Kln, two types of illite - Ill, and muscovite - Ms) and accessory phases like rutile, zircon, pyrite, and iron oxides/hydroxides (Buhl et al. 2013; Ebert et al. 2014). Uniaxial compression tests showed strength values of ~70 MPa for dry samples and ~57 MPa for wet samples (Poelchau et al. 2013). The sandstone has a bulk density of 2.05 ± 0.04 g cm-3 (Poelchau et al. 2013) and a p-wave velocity of 2915 m s-1 (Moser et al. 2013).

Fig. 3.1 Shatter cone fragments recovered from experiment in dry (experiment A15-5185 ) and water saturated (experiment E3-3384) sandstones. Fragments A15-I to A15-III shown in figure a to c showing curved surfaces with fine diverging striae. Fragments E3-I to E3-III shown in figure d to f are marked with a distinct and already macroscopically visible film.

Fig. 3.2 WLI scans of the shatter cone fragments shown in Fig. 3.1 and to from (a) experiment A15-5185 and (b) experiment E3-3384. The surface is clearly curved and striated. The spikes surrounding the fragment result from measuring the sticky wax in which the fragments are embedded.

Fig. 3.3 (a) WLI scans of a shatter cone surface from the Rochechouart impact structure. (b) Topography profiles derived from the WLI point cloud perpendicular to the shatter cone symmetry axis. 64

3.3.2 Sample Preparation and Characterization Directly after conducting the experiments, we documented the target chamber by means of detailed photography and thoroughly examined the crater and ejecta particles in-situ. After removing the target and the witness plates from the target chamber, both were weighted to determine the excavated mass. The 3D crater morphology was documented by laser scanning techniques (eScan3DTM by Digital Corp). By hand picking the ejecta was thoroughly examined with an Olympus BH-2 coaxial reflected light microscope and potential shatter cone fragments were selected among recovered ejecta particles (Fig. 3.1). All conical fragments with curved and striated surfaces were investigated morphologically using a Bruker AXS Contour GT-K0 white light interferometer (WLI), followed by a detailed 3D morphometric analysis of each specimen (Figs. 3.2 and3. 3). The WLI is a non-contact, non-intrusive optical surface analytical method that generates 3D point clouds of the sample surface based on the optical interference of light. We used this tool to characterize the surface topography of our recovered fragments (cf. Wilk and Kenkmann 2016), and compared cross sections through the point cloud perpendicular to the shatter cones symmetry axis (Figs. 3.2 and 3.3). Those fragments showing the characteristic features of shatter cones were further investigated by scanning electron microscopy (SEM) in order to investigate large areas of the topography and the interior regions of the shatter cones. Scanning electron microscopy in secondary (SE) and backscattered (BSE) electron mode was carried out with a Zeiss Leo 1525 field-emission SEM, equipped with a tungsten cathode at the

Albert-Ludwigs-University Freiburg (ALU) and a JEOL JSM-6610LV SEM equipped with a LaB6 cathode at the Museum für Naturkunde Berlin (MfN). Depending on sample requirements and analytical intent, we used either 10 or 15 kV acceleration voltage and variable beam currents and working distances (10 to 13 mm). Shatter cone surfaces and melt films were microstructurally characterized using both SE and BSE imaging on topographic samples surfaces that, in some cases, were carbon-coated to avoid electric charging during imaging. Semi-quantitative major-element compositions (in point analyses and element distribution maps, normalized to 100 wt%) of the melt coatings were obtained in-situ from the shatter cone surfaces by energy-dispersive X-ray spectroscopy (EDX), using a Bruker XFlash 5010 silicon drift detector attached to MfN’s JEOL JSM-6610LV SEM. Typical EDX detection limits were 0.1 wt% for all analyzed elements. We prepared a representative thin section with orientation perpendicular to the shatter cone surface and parallel to the shatter cone symmetry axis from a carefully selected shatter cone from

experiment E3 (the fragment is shown in Fig. 3.2b; the location of the thin section is marked in Fig. 3.4a). Subsequent to carbon-coating, we measured the major-element composition of the sectioned melt coatings using a JEOL JXA-8500F field-emission electron microprobe (EMPA) at MfN. Wavelength-dispersive X-ray spectroscopy (WDX) was carried out with an acceleration voltage of 15 kV, a beam current of 15 nA, and a working distance of ~11 mm. Due to the small dimensions of individual melt areas and mineral fragments, we used a fully focused electron beam with spot sizes <1 µm for WDX point analyses. Counting times in WDX mode varied between 10 and 60 s on peak and 5 and 30 s on lower and upper background, respectively. TAP, PET, and LIF crystals were used for analysis. Standardization was based on the main Smithsonian international standards suite (Jarosewich et al. 1980) of MfN’s micro-analytical facility. Raw data were processed for matrix effects using a conventional ZAF routine incorporated into the JEOL operating system, and the resulting data were normalized to 100 wt% to (A) ensure comparability of volatile-bearing phyllosilicates and volatile-free, phyllosilicate-derived silicate melts, and (B) to ensure inter-comparability between normalized SEM-EDX data and EMPA-WDX data. Typical

EMPA detection limits were as follows: 0.01 wt% for SiO2, Al2O3, Cr2O3, CaO, MgO, Na2O, and

K2O; 0.02 wt% for TiO2 and FeO; and 0.03 wt% for ZrO2. Accuracy of the WDX data is better than 3% for major elements >5 wt% and in the range of 10–15% for minor elements <0.5 wt%; precision is better than 5% for major elements >5 wt% and in the range of several ten percent for minor elements <0.5 wt%. From experiment E3 one well-developed shatter cones specimen was carefully selected, based on the pre-characterization by SEM and WLI, to be prepared for transmission electron microscopy (TEM) by aid of the focused-ion beam (FIB) technique. A TEM-foil (thickness ~200 nm) was cut via FIB preparation using the FEI Quanta3D FEG dual beam workstation installed at the Institute of Geoscience of the Friedrich-Schiller-University of Jena (FSU). The ion gun was operated at an acceleration voltage of 30 kV and at decreasing beam currents from 30 nA for the trench milling to 0.1 nA for the final thinning and cleaning. The area selected for the foil preparation was first covered by a thick protective platinum strap (up to 6 µm). The length of the FIB lamella was limited due to the intensely fractured shatter cone subsurface. The TEM investigation was carried out at the Institute of Geoscience of the FSU using a FEI Tecnai G2 FEG microscope. The TEM was operated at an acceleration voltage of 200 kV. Bright-field (BF) images and selected area electron diffraction (SAED) patterns were collected with a Gatan UltraScan 2k CCD camera and analyzed with Fiji (Schindelin et al. 2012).

In addition to the petrographic analysis, the experiments A15 and E3 were modeled in i-SALE-2D at the MfN. The iSALE model was combined with in-situ measurements of the visible inner zone of pervasive grain crushing, which is pronounced in some of the MEMIN experiments as a shock-whitened zone within 15 – 38 % of the apparent crater diameter (Buhl et al. 2013, Ebert et al. 2013, Wilk and Kenkmann 2016). The shatter cone fragments in the MEMIN experiments are often coated by rock powder and show a shock- whitening themselves. Thus, in-situ measurements of the target material should provide a rough estimation for the maximum extend of the possible shatter coned material. For the iSALE model, we used tracer particles that follow the material flow to derive peak pressures during the cratering event. Re-setting the tracers to their original position, we can give an estimate on the possible pressure range of the recovered ejecta material by overlaying the in-situ measurements with the peak pressure isobars.The experimental setup was simulated using the iSALE-2D Eulerian shock physics code in the “Chicxulub” version (Wünnemann et al. 2006), which is based on the SALE hydrocode solution algorithm (Amsden et al. 1980). To simulate impact processes in solid materials SALE was modified to include an elasto-plastic constitutive model, fragmentation models, various equations of state (EoS), and multiple materials (Melosh et al. 1992; Ivanov et al. 1997). More recent improvements include a modified strength model (Collins et al. 2004) and the ε-α porosity compaction model (Wünnemann et al. 2006; Collins et al. 2011). We model the MEMIN scenarios A15 and E3 using a tillotson equation of state for the aluminium projectile, and an analytical equations of state (ANEOS) for the spherical meteoritic projectile (Thompson und Lauson 1972) and for the sandstone and water-saturated sandstone targets (Melosh 2007, Güldemeister et al. 2013) . We use a Johnson-Cook parametrisation for the strength of the Campo del Cielo projectile and a Von Mises strength for the aluminium projectile. For the targets, we use strength and porosity parameters according to previous studies by Güldemeister et al. (2015) for the constitutive model proposed by Collins et al. (2004), including an intact and a damaged yield surface. We use a resolution of 50 cells for the projectile radius (CPPR) for both models. The high resolution zone is set to 1200 x 2500 cells and 1500 x 2000 cells in horizontal and vertical direction for the A15 and E3 models, respectively. Detailed parameters are given in the Appendix.

Table 3.1. Experimental impact conditions of MEMIN experiments from which shatter cone fragments were recovered. Block size Impact speed Shatter Experiment Facility Target material Projectile type L [mm] Projectile mass [g] V [cm³] P [GPa] [cm] [km s-1] cone count E1 XLLGG Sandstone 80x80x50 D290-1 steel 12 4.560 7.313 1393 46 2 E3 XLLGG Sandstone wet 80x80x50 Campo del Cielo 12 4.590 7.087 1829 - 4 E6 XLLGG Quartzite 80x80x40 D290-1 steel 12 4.709 7.311 1684 66 1 A12 SLGG Sandstone wet 20x20x20 D290-1 steel 2.5 5.250 0.0667 34.2 - 2 A15 SLGG Sandstone 20x20x20 55X G28J1 aluminum 5 6.970 0.1792 42.9 66 12 A16 SLGG Sandstone 20x20x20 55X G28J1 aluminum 2.5 7.750 0.0224 2.6 79 2 K1/A14 SLGG Limestone 20x20x20 D290-1 steel 2.5 5.320 0.0673 - 86 1 XLLGG=“extra-large” light gas gun; SLGG=“space” light gas gun; L = projectile diameter; V: crater volume; P: experimental peak pressure calculated by using the planar impact approximation as described by Melosh, 1989 (chapter 4.5.1, pp.54-58) with C and S values for equivalent target lithologies from Ahrens and Johnson, 1995 (chapter 3-4, pp.37-41). The impact direction was perpendicular to the apparent stratification of the target blocks. 67

Fig. 3.4 SE images of a shatter cone surface from experiment E3-3384 fragment E3-I. (a) Overview image of the melt-coated surface. Note the centerline from the lower left to the upper right, which is marking plane of the thin section. The surface shows the striated and melt-coated surface, which is markedly different to the fractured sandstone underneath. (b) Fractured sandstone (left) underneath the melt coating (right), which shows polished ridge sections and mainly vesicular grooves. See (a) for location of this image. (c) Further enhanced subset of (b), revealing the intricate fibers and melt splats overlying fractured lithic components (e.g., rutile grain in the left part) in detail.

3.4 Results 3.4.1 Occurrence and Morphology Altogether, 24 shatter cone fragments were recovered from almost every targeted lithology in experiments exceeding impact velocities of 4.59 km s-1 (Table 3.1) (for further information see also Wilk and Kenkmann 2016). The fragments we considered to represent shatter cones have curved and conical geometries marked by diverging striation patterns (Figs. 3.1 and 3.2) and occur in intensely crushed and friable ejecta that has a somewhat brighter textural appearance than unshocked material, which we refer to as shock-whitening (Fig. 3.1). The shatter cone fragments are 1.2–9.3 mm in size and show apical angles of 36°–52°. For characterizing the surface topography, we extracted characteristic peak amplitudes or cone segment heights h (after Kenkmann et al. 2016) and cone segment widths or secant lengths s, respectively (Gibson and Spray 1998). Both h and s values as well as the ratio of segment height to width (h/s) for shatter cones produced in experiments A15 and E3 are given in Table 3.2. The cross sections derived from the experimental fragments have h values for the groove-and-ridge pattern of 10–570 µm. Small fragments from experiment A15 tend to have low h values of 10–125 µm, whereas large fragments from experiment E3 vary in h from 129–570 µm (Table 3.2). The segment widths s are 1.9–3.0 mm for E3 fragments and 80–820 µm for A15 fragments. For comparison, natural shatter cones from the Rochechouart (Fig. 3.3), Haughton, and Steinheim impact structures were scanned with the WLI method; h, s, and h/s values obtained from these samples are reported in Table 3.2 as well. Older data of h/s ratios obtained with a laser scanning device (Kuhn 2011) of shatter cones from the Charlevoix, Siljan, Wells Creek, Steinheim, and Marquez impact structures are additionally reported in Table 3.2. Table 3.2 reveals that, irrespective of their size, h/s ratios of experimentally produced shatter cones (0.07–0.25) are similar to natural samples (0.05–0.12). 3.4.2 Melt Texture Characteristics Some of the shatter cone fragments formed in sandstone have a distinct and macroscopically visible yellowish coating, which stretches over the entire cone and includes the fine striae. SEM imaging revealed that the surficial coating is a vesicular melt film (now quenched to glass) that alternates with smooth surfaces that are markedly different from the fractured and crushed sandstone underneath (Figs. 3.4b, 3.4c, and 3.5b). The terms “melt film” and “glass” are used synonymously throughout the following chapters. We found the 69

melt films partially developed or stretching over most of the fracture surface for 17 of 22 analyzed shatter cones in sandstone from experiment E1, E3, A12, A15 and A16. The fragments A15-I, E3-I, E3-II and E3- III shown in the SEM analysis in figure 3.4 to 3.10 had continuous melt films preserved and showed little rock powder residue on top. In the thin section of fragment E3-I, the smooth coating of glassy material is 10–20 µm thin on average, but may reach up to 100 µm where it is highly vesiculated. The sandstone underneath displays abundant transgranular fractures and intense grain comminution. We also observed scattered micro-spherules attached to the surface or trapped in vesicles. In plane view the shatter cone surface is covered by a continuous sheet of melt with different textures: (A) smooth, almost polished surfaces, marked by very fine melt striations (Figs. 3.6a and 3.7a), alternating with (B) a “frothy”, reticulate film with melt smears and intricate fibers (Figs. 3.5 and 3.6); both of these textures can be superimposed by (C) vesicle-rich melt splats and splashes (Figs. 3.5a and 3.6a). The entire melt film is intersected by the formation of sharp polygonal cracks along the surface, typical for rapid cooling and thermal contraction (Fig. 3.6a). The smooth melt films (A) are preferentially visible at the ridges of the superordinate striation pattern and always appear elongated to the groove-and-ridge system (Fig. 3.4). The very fine (≤ 1µm) melt striations are strongly elongated and stretched parallel to the shatter cone surface as well as to the ridge-and- groove system (Figs. 3.5–3.7). Hence, the striations imply a shear movement along the shatter cone surface parallel to the ridges and grooves. The frothy and reticulate melt (B) is marked by fine, intricate fibers, smeared towards the cone apex and also elongated parallel to the grooves and ridges (Figs. 3.4–3.7). The frothy textures show a patchier distribution than the smooth films and resemble the initial distribution of phyllosilicates in the sandstone. Smeared and elongated melt vesicles (Figs. 3.5–3.9) also show movement of the shatter cone surrounding towards the shatter cone apex. This is accompanied by extensional features and “zip-like” melt separation from the fracture surface (Fig. 3.8b). The vesicle-rich melt splats and splashes (C) appear less smeared than the frothy reticulate textures and have irregular and curved fibers, overlaying the subjacent melt films. In contrast to the textures (A) and (B), these splats and the vesicles therein do not show any shear movement. Together with the frothy reticulate melt (B), the vesicle-rich melt splats show mixing and mingling of melts of initially monomineralic composition, as illustrated in elemental distribution maps (Figs. 3.10 and 3.11). In the thin section (Figs. 3.7b–3.9), we observed clasts entrained within the melt, especially in the melt splats and vesiculated parts (Fig. 3.9b). Clasts also indicate transport parallel to the shatter cone surface, where the melt film is in contact with the cataclastic zone and fractures occasionally cut through grains (Fig. 3.7b). Often, rutile and zircon grains, indicating incipient melting of the clasts by rounded and truncated grain boundaries, are disseminated in these melts (Fig. 3.9b). Below the melt film, an up to 30 µm thick zone of fragmentation and shearing usually exists (Figs. 3.8a and 3.8b). This cataclastic zone is characterized by brittle deformation rather than melting (Figs. 3.8c and 3.9b). Sporadically, melt veins of the melt film are injected into the brecciated subsurface which is otherwise free from melt. The deformation is characterized by strong fragmentation of quartz, rutile, and zircon and includes kinked and 70

smeared phyllosilicates. Close to the fracture surface, extensional cracks parallel to the surface are abundant (Figs. 3.8 and 3.9), whereas 100–150 µm further below, pores are closed but fractures become rare. Close to the shatter cone surface transgranular fractures are abundant (Fig. 3.7b) and clasts are rotated and/or in sharp contact to the overlying melt film that cuts through bordering fragments (Fig. 3.7b). In the upper 10– 20 µm, fragments are sheared away from the cone’s apex, displaying a minimal offset of 60–80 µm along the fracture surface (Figs. 3.7 and 3.9). The different shear directions and the maintained offset will be discussed in the next chapter. 3.4.3 Melt Surface Composition The three different melt textures described above also show distinct compositional trends. Qualitative EDX analysis of the shatter cone surfaces from E3-I and E3-III suggest that the smooth and evened surfaces with fine melt striae (A) are high in SiO2 (96 wt%). However the presence of Al2O3 and

TiO2 (~2–6 wt%) indicates that (A) is not a pure silica melt (lechatelierite). The composition of these melt films is close to the bulk chemistry of the sandstone but enriched in TiO2, which is likely caused by additional melting of, and mixing with, accessory rutile (Fig. 3.12). On the shatter cone surface, the frothy reticulate melt with the intricate and smeared fibers (B) closely mimics the composition of phyllosilicate minerals present in the target. Compared to the phyllosilicates prior to impact, this melt is also slightly enriched in Ti, closely following a mixing trend with rutile (Fig. 3.12). The frothy, reticulate, and primarily phyllosilicate-derived melt (B) often merges with the highly vesiculated TiO2–Al2O3-rich melt (C) and elemental distribution maps indicate complex and delicate mixing of these two melts (Figs. 3.10 and 3.11).

The same trend exists also for the smooth and primarily SiO2-rich melt (A) that has mixed to some extent with the other two melts. As shown in Fig. 3.12, the vesicle-rich melt splats and splashes (C) are characterized by high TiO2 (~43–65 wt.%) and Al2O3 (~2–8 wt.%) contents, being primarily a mixture of phyllosilicates and accessory phases (i.e., rutile and zircon). This melt occurs randomly intercalated with or was superimposed on the other melt films, thus, also limited amounts of the presumably SiO2-rich melt and/or a pure silica melt (lechatelierite) were incorporated (Fig. 3.10). Throughout the thin section, we generally observed preferential melting of phyllosilicates (Figs. 3.9b, 3.10, and 3.11; cf. Ebert et al. this issue). As illustrated in Fig. 3.11, we often detected phyllosilicate-dominated melts that incorporated clastic debris of quartz and accessory phases. In some cases, incipient melting of rutile (Fig.3.11a) and zircon (Fig. 3.11b) was followed by subsequent, but limited, mixing with the phyllosilicate melt (Fig. 3.12).

Fig. 3.5 SE images of a shatter cone surface from experiment E3-3384 fragment E3-I and fragment E3-III. (a) The shatter cone melt coating shows polished, smoothened surfaces alternating with frothy, reticulate melt textures, both smeared towards the cone’s apex. (b) Occasionally, the melt coating is fractured, revealing underlying lithic components.

Fig. 3.6 SE images of a shatter cone surface from experiment E3-3384 fragment E3-III. (a) Overview image of fractured and cracked shatter cone melt surface, locally exhibiting vesiculated melt splats (central part of the image). (b) Intricate melt fibers and sheared vesicles of the melt coating. Note the small vertical extent of the melt coating (lower left corner). See (b) for location of this image.

Fig. 3.7 (a) SE image of a shatter cone melt surface from experiment A15-5185 fragment A15-I, showing the same smooth surfaces with fibers alternating with reticulate melt textures as for experiment E3-3384. (b) BSE image of a section obtained from a shatter cone melt surface from experiment E3-3384 fragment E3-I. The section was taken perpendicular to the shatter cone melt film. Note the presence of sub-round to angular mineral clasts (dominantly rutile and quartz) in the frothy material, as well as the sharply cut zircon grain (white; in the middle of the image). 72

Fig. 3.8 BSE image of the shatter cone melt film present in the section taken perpendicular to the shatter cones symmetry axis (see Fig. 3.4a). Note that the shatter cone apex is towards the right side in each image. Brittle shear movement is well illustrated in (a), as well as “zip-like” parting of the melt film in roughly 45° towards the surface (b). (c) Below the melt film, a zone of grain comminution is visible, with clasts oriented elongated parallel to the fracture surface. Abbreviation: Rt = rutile.

Fig. 3.9 Continuation along the shatter cone melt film towards the apex with (a) sharply cut accessory phases (mainly rutile) and (b) highly vesiculated melt splats. Abbreviations: Rt = rutile; Zrn = zircon.

Fig. 3.10 Elemental distribution maps for Ti, Al, Si, and K superimposed onto the corresponding BSE images obtained from the shatter cone surface of experiment E3-3884 fragment E3-II (a) and fragment E3-III (b), illustrating differences in composition of the three melts and delicate mixing between monomineralic melts derived from quartz (blue), phyllosilicates (green), and rutile (red).

Fig. 3.11 Elemental distribution maps for Al, Si, Zr, and Ti superimposed onto the corresponding BSE images obtained from the sectioned shatter cone melt surface of experiment E3-3884 fragment E3-I (see Fig. 3.9b). (a) Phyllosilicates (blue) in the subsurface are strongly deformed, showing extensive kinking and comminution. Eventually, melting of the phyllosilicates produced a reticulate melt froth that incorporated clasts of quartz (green), rutile (red), and zircon (yellow) that show incipient grain-boundary melting (e.g., zircon-derived melts in the central-right part of the image, illustrated in yellow). (b) The zircon grain in the central part of the image is shaved off on top, with processed material being molten and sheared to the left along the melt zone/comminution zone interface. Note again the abundantly disseminated mineral clasts in the melt froth. Incipient melting of this clastic debris is illustrated by varying colors of the melt froth (ranging between blue and green).

Table 3.3. Representative EDX data of shatter cone melt coatings, obtained from topographic sample surfaces (cf. Figs. 3.4–3.6).

wt% SiO2 TiO2 Al2O3 Cr2O MgO FeOt CaO Na2O K2O ZrO2 SiO2/Al2O3 SiO2/K2O Al2O3/K2O Surface texture (A): smooth, vesicle-free melt with fine striae #1 98 0.7 1.0 bdl bdl bdl bdl bdl 0.3 bdl 98 327 3.4 #2 96 1.4 1.7 bdl bdl bdl bdl bdl 0.5 bdl 56 192 3.4 #3 94 4 1.2 bdl bdl bdl bdl bdl 0.3 bdl 78 313 4.0 #4 92 2.1 4 bdl bdl bdl bdl bdl 1.8 bdl 21 51 2.4 Average 96 1.8 1.9 bdl bdl bdl bdl bdl 0.6 bdl 63 214 3.3 Surface texture (B): frothy reticulate melt surfaces #1 62 0.8 27 bdl 0.9 1.5 bdl bdl 8 bdl 2 8 4 #2 62 1.0 26 bdl 0.6 1.6 bdl bdl 9 bdl 2 7 3 #3 59 4 25 bdl 0.7 1.7 bdl bdl 10 bdl 2 6 3 #4 55 3 28 bdl 0.9 1.6 bdl bdl 11 bdl 2 5 2 Average 60 2 27 bdl 0.8 1.6 bdl bdl 10 bdl 2 6 3 Surface texture (C): highly vesiculated melt splats and splashes #1 59 25 12 bdl 0.5 0.8 bdl bdl 2.4 bdl 5 24 6 #2 57 30 9 bdl 0.4 0.9 bdl bdl 3 bdl 6 20 5 #3 46 43 7 bdl 0.3 0.9 bdl bdl 2.3 bdl 7 20 5 #4 42 56 2.4 bdl bdl bdl bdl bdl bdl bdl 21 — — #5 41 48 8 bdl 0.3 0.8 bdl bdl 2.1 bdl 7 20 5 Data obtained by SEM-EDX from rough, topographic shatter cone surfaces. Note that all data have been normalized to 100 wt% and only significant digits are reported. #1–#5 = selection of representative measurements; FeOt = total Fe (FeO + Fe2O3) reported as FeO; bdl = below detection limit.

Table 3.4. Representative WDX and EDX data of sectioned shatter cone melt coatings (cf. Figs. 3.8 and 3.9) in comparison to the compositions of the phyllosilicates and the bulk sandstone.

wt% SiO2 TiO2 Al2O3 Cr2O MgO FeOt CaO Na2O K2O ZrO2 Total SiO2/Al2O3 SiO2/K2O Al2O3/K2O Shatter cone melt coatings WDX #1 52.4 10.9 17.0 1.23 0.55 0.99 0.08 0.06 6.39 1.32 90.9 3.1 8.2 2.7 #2 51.4 10.7 21.5 1.51 0.71 1.53 0.03 0.02 6.98 0.26 94.6 2.4 7.4 3.1 #3 43.4 11.6 25.4 1.96 0.83 1.72 0.04 0.06 7.83 1.46 94.3 1.7 5.5 3.2 #4 41.8 16.1 25.3 1.83 0.82 1.70 0.05 0.03 8.36 0.20 96.2 1.7 5.0 3.0 #5 36.1 28.3 23.5 2.10 0.73 1.51 0.04 0.04 3.30 0.57 96.2 1.5 10.9 7.1 Average 43.8 13.9 23.5 2.03 0.78 1.58 0.05 0.04 7.11 1.01 93.8 1.9 6.2 3.3 Shatter cone melt coatings EDX #1 95.9 0.7 2.8 bdl bdl bdl bdl bdl 0.6 bdl 100.0 34.3 159.8 4.7 #2 60.1 9.9 19.7 1.4 0.7 1.4 bdl bdl 6.9 bdl 100.1 3.1 8.7 2.9 #3 51.4 17.7 19.5 2.1 0.8 1.9 bdl 5.8 0.9 bdl 100.1 2.6 8.9 3.4 #4 44.8 16.7 23.2 2.5 1.1 2.5 bdl bdl 9.0 0.1 99.9 1.9 5.0 2.6 #5 37.0 27.0 20.4 2.3 0.8 2.1 bdl bdl 7.4 3.0 100.0 1.8 5.0 2.8 Average 52.0 14.2 20.6 2.0 0.8 1.8 bdl bdl 7.3 1.4 100.0 4.6 17.3 3.0 Phyllosilicates and bulk sandstone Kaolinite 87.9 bdl 37.0 bdl 0.15 0.36 0.13 0.03 0.37 bdl 85.9 1.3 129.4 99.8

Illite (low K2O) 54.3 0.18 21.6 bdl 2.55 7.92 0.41 0.07 5.44 bdl 92.5 2.5 10.0 4.0

Illite (high K2O) 46.8 0.81 31.2 bdl 1.56 3.38 0.07 0.56 8.63 bdl 93.0 1.5 4.8 3.6 Muscovite 47.2 0.98 30.4 bdl 2.37 4.01 bdl 0.56 9.74 bdl 95.3 1.6 4.9 3.1 Bulk sandstone 94.77 0.31 3.11 bdl 0.12 0.45 0.05 0.15 0.23 bdl 99.19 30.5 412.0 13.5 Data obtained by EMPA-WDX and -EDX from a polished section and reported with measurement error in parentheses. Note that EDX data have been normalized to 100 wt% and only significant digits are reported. #1–#5 = selection of representative measurements; FeOt = total Fe (FeO + Fe2O3) reported as FeO; bdl = below detection limit. Phyllosilicate data from Ebert et al. (this issue); bulk sandstone data from Ebert et al. (2014).

Fig. 3.12 Major-element compositions of the sandstone components prior to impact (data from Ebert et al. submitted) compared to the major-element compositions of the shatter cone melt coatings (data obtained via SEM-EDX and EMPA-WDX from Exp. E3- 3384). Individual compositions are plotted in the pseudo-ternary system SiO2–TiO2–(Al2O3–K2O) (a) and in the binary mixing diagrams TiO2 vs. Al2O3 (b), TiO2 vs. SiO2 (c), and K2O vs. SiO2 (d). See text for discussion.

3.4.4 Melt Surface Composition The three different melt textures described above also show distinct compositional trends. Qualitative EDX analysis of the shatter cone surfaces from E3-I and E3-III suggest that the smooth and evened surfaces with fine melt striae (A) are high in SiO2 (96 wt%). However the presence of Al2O3 and

enriched in Ti, closely following a mixing trend with rutile (Fig. 3.12). The frothy, reticulate, and primarily phyllosilicate-derived melt (B) often merges with the highly vesiculated TiO2–Al2O3-rich melt (C) and elemental distribution maps indicate complex and delicate mixing of these two melts (Figs. 3.10 and 3.11).

The same trend exists also for the smooth and primarily SiO2-rich melt (A) that has mixed to some extent with the other two melts. As shown in Fig. 3.12, the vesicle-rich melt splats and splashes (C) are characterized by high TiO2 (~43–65 wt.%) and Al2O3 (~2–8 wt.%) contents, being primarily a mixture of phyllosilicates and accessory phases (i.e., rutile and zircon). This melt occurs randomly intercalated with or was superimposed on the other melt films, thus, also limited amounts of the presumably SiO2-rich melt and/or a pure silica melt (lechatelierite) were incorporated (Fig. 3.10). Throughout the thin section, we generally observed preferential melting of phyllosilicates (Figs. 3.9b, 3.10, and 3.11; cf. Ebert et al. submitted). As illustrated in Fig. 3.11, we often detected phyllosilicate-dominated melts that incorporated clastic debris of quartz and accessory phases. In some cases, incipient melting of rutile (Fig. 3.11a) and zircon (Fig. 3.11b) was followed by subsequent, but limited, mixing with the phyllosilicate melt (Fig. 3.12).

3.4.5 TEM Analysis and Shock Indicators along the Shatter Cone Surface The shatter cone fragment E3-II recovered from experiment E3 was selected for TEM investigations in order to prove the amorphous nature of the foamy and the continuous coating and to identify possible shock effects within the adjacent quartz grains. Figure 3.13 shows the area selected for the preparation of a shatter cone cross-section via FIB milling. The selection criteria for the preparation of the TEM-foil were (A) a sufficiently flat area in the topmost part of the fragment to avoid difficulties during thinning and lifting out of the foil, (B) the occurrence of a thin glass coating on the shatter cone surface, both foamy and continuous, to observe the contact with the sandstone, and (C) an orientation at right angle to the striae (Fig. 3.13). The resulting TEM-foil (Fig. 3.14) has an area of ~75 µm2 (excluding the platinum strap). The foamy and continuous glass coating occupies about one third of the TEM-foil and has a maximum thickness of 3.8 µm (dominating the left side of Fig. 3.14). We note that the ion-milling procedure tended to enlarge the size of vesicles in the sample. The sandstone substrate is characterized by numerous fractures; most of them developed parallel to the glass coating. The fractures impeded the preparation of the TEM-foil and a portion of ~5.5 µm2 was lost (see central part of Fig. 3.14). SAED patterns were obtained from the foamy coating and did not show discrete diffraction spots but a broad and diffuse diffraction ring typical for amorphous material (Figs. 3.15a and 3.15b). At the contact with the underlying sandstone, the glass locally forms networks of veins surrounding sandstone clasts and/or single quartz grains (e.g., Fig. 3.15c). As shown in the SEM images (e.g., Figs. 3.7b and 3.11), relict quartz grains occur within the glass coating (Figs. 3.15a and 3.15c). These grains are generally round to sub-round due to melting of the grain edges (thermal abrasion). In contrast to the SEM thin section that occupied a larger area, the only mineral phase detected in the TEM-foil was quartz.

Most of the quartz grains are defect-free and display no diagnostic shock features. However, a few quartz grains that are situated close to the vein network contain amorphous lamellae. They are arranged in one or maximum two sets (Figs. 3.15c and 3.15d). Some of them are bent and do not crosscut the entire grain. They have a maximum thickness of 9 nm and are spaced less than 80 nm. The crystallographic orientation of one set of those lamellae (Fig. 3.15d) was inferred from the corresponding SAED pattern of the grain. These lamellae are parallel to the crystallographic plane {1122}, which is a documented orientation for PDFs in quartz (Albat and Mayer 1989) and is found in moderately shocked material (Stöffler and Langenhorst 1994).

Fig. 3.13 SE image of the area selected for the TEM-foil preparation; experiment E3-3384 fragment E3-II. The white box indicates the area where the platinum strap was applied.

Fig. 3.14 Low-magnification TEM-bright-field (BF) image of the TEM-foil cut from the surface of a shatter cone fragment recovered from experiment E3-3384. The dashed lines highlight the frothy glass coating. Due to the FIB milling, the size of the vesicles of the foamy coating became wider. An area of ~5.5 µm2 was lost during the preparation due to the presence of numerous fractures. The white square boxes (a) and (b) refer to the TEM-BF images in Figs. 3.16a and 3.16c, respectively.

Fig. 3.15 TEM images obtained from the TEM-foil shown in Fig. 3.14. (a) BF image of area (a) of Fig. 3.14, showing the contact between the foamy glass coating and the underlying sandstone (in this case, quartz). The dashed circle indicates position and size of the selected area aperture used to collect the diffraction pattern shown in (b). (b) Diffraction pattern obtained from the position marked in (a), proving the amorphous nature of the frothy coating decorating the shatter cone surfaces. (c) BF image of area (b) of Fig. 3.14, showing the contact between the continuous glass coating and the underlying sandstone. In this area, a network of glassy veins has developed within the sandstone, surrounding some quartz grains. (d) BF image of a quartz grain showing amorphous lamellae (PDFs) parallel to {112̅2}. See (c) for location of this image. 79

3.5 Discussion

3.5.1 Characteristics of Shatter Cone Formation in the MEMIN Experiments Within the range of MEMIN experiments, it appears that higher impact velocities (≥4.6 km s-1) promote the formation of shatter cones. Their formation is however relatively independent of projectile size or target lithology (Wilk and Kenkmann 2016). Shatter cone formation is limited to crushed and powdered material, which has a brighter textural appearance than the unshocked target material. Due to this shock whitening (Ebert et al. 2013), we were able to relate the shatter cone fragments to the “inner zone of pervasive grain crushing and compaction” (Buhl et al. 2013), which is easily identifiable in most of the MEMIN craters. The width of this area showed a range of 15–38% of the apparent crater diameter. From field studies of the Haughton and Tunnunik impact structures, Osinski and Ferrière (2016) derived a similar relation for shatter cone occurrence in par-allochthonous material with respect to radial distance, being up to 40% of the apparent crater diameter. For the impact experiments A15 and E3, we can estimate a minimum formation pressure of 0.5-2 GPa from iSALE-2D models for this material. The experimentally produced shatter cone fragments with sizes ranging between 1.2 and 9.3 mm are smaller than what is typically reported for natural shatter cones, which more commonly occur on the centimeter to decimeter-scale. However, owing to the hierarchical order of subcone ridges, millimeter-sized shatter cone fragments are also abundant in nature. Thus, reported data topographic features (e.g. Gibson and Spray 1998), such as segment height (typically on the mm-scale for natural samples and on the µm- scale for experimental samples) and segment width, differ significantly. Nevertheless, the tendency of experimental shatter cone fragments of segment height typically being smaller than the segment width is similar to observations made for natural shatter cones by Gibson and Spray (1998) and Kuhn (2011). In addition, WLI data from Wilk and Kenkmann (2016) showed a similar relation of fracture surface roughness and apical angles (with a range of 36° to 52°) for the experimental shatter cones in comparison to natural samples from the Siljan and Rochechouart impact structure.

3.5.2 Succession of Events at Shatter Cone Surfaces as Revealed by Microstructural Analysis: A Synthesis This section provides an outline of the temporal sequence of deformation that we propose to take place at the surface of the experimentally produced shatter cones. This sequence is causally linked to the passage of the shock wave (Fig. 3.16). Phase I: Initiated by the elastic precursor wave, tensile fractures propagate through the rock at a velocity that approaches the limit of Rayleigh waves. The curved fracture planes regularly branch at their fracture tip and cause hierarchical subcone pattern and diverging lineations (Kenkmann et al. 2016). Owing to symmetrical

branching, subsequent fracture orientation is forced into directions that contain a shear component. Thus, the fractures become mixed mode I and II fractures with a shearing and opening component. This phase I causes brittle shear and grain comminution along the shatter cone surface. Fragmentation and shearing of clasts (e.g., quartz, rutile, and zircon), as well as smearing and elongation of phyllosilicates, indicates displacements of 60 µm and the shear sense is that the rocks surrounding the cone are sheared away from the cone apex. Phase II: While the shock wave is approaching and reaches its full magnitude, shearing under enhanced confinement continues and leads to frictional melting (Melosh 2005). Frictional melting occurs within a narrow zone along the shatter cone surface. Remnants of this precursor melt might be the observed melt veins injected into the cataclasite, as well as the smooth polished melt films with fine striae (A). Also within this phase PDFs might form in quartz along the shatter cone surface. Phase III: The onset of pressure release leads to progressive melt production (especially of the phyllosilicate portion of the sandstone) and, where temperatures are high enough, incipient melting of incorporated clasts. Adiabatic pressure release is indicated by vesiculated melt smears due to rapid fracture opening. Reverse shearing results from a release of stored elastic energy of the rock. This reverse shearing is documented by the elongation of vesicles and beginning fracture separation. Some of the still-hot phyllosilicate melt is smeared in reverse direction towards the cones apex, producing the frothy reticulate melt textures (B). Further degassing of the melt is producing the highly vesiculated melt splats (C) and separation of the fracture surface recoil at the end of the reticulate melt fibers.

Phase IV: The transition between Phase III and IV is smooth and gradational. Unloading further amplifies degassing of melts (e.g., volatile-bearing, phyllosilicate-derived melts; cf. Ebert et al. submitted). Tensile fracture separation continues, but reverse shear movements decay. Microstructures that are associated with this stage include highly vesiculated textures without a preferred orientation/alignment of vesicles and, if temperatures were initially high enough, possibly condensation of vaporized material in the form of micro- spherules on the shatter cone surface (cf. Gibson and Spray 1998).

Fig. 3.16 Phases I-IV of gradual deformation along the shatter cone surface. I: brittle shear and grain comminution along the shatter cone surface; Ia: illustrated are fragmentation and shearing of clasts (e.g., quartz, rutile, and zircon) as well as smearing and elongation of phyllosilicates upon arrival of the elastic precursor front. II: ongoing shearing with subsequent frictional melting. III: onset of reverse shear and fracture separation resulting in elongation of vesicles (IIIc). Incipient melting of incorporated clasts starts in the transition to IV, which is characterized by complete fracture separation and the end of shear. IVd: highly vesiculated textures on the shatter cone surface.

3.5.3 A comparison of Natural and Experimentally Produced Shatter Cone Surfaces Macroscopically, the visible surface coatings on the experimentally produced shatter cones strongly resemble the smoothened surfaces shown by Schneider and Wagner (1976), as well as the “brown coatings” reported by Fazio et al. (2014; Fig. 15, p. 2192). Reports on the melt thickness range from an average of 50 µm for shatter cones from the Vista Alegre impact structure (Pittarello et al. 2015) to a maximum of 500 µm of the glass layer on shatter cones from the Vredefort impact structure (Nicolaysen and Reimold 1999). In comparison, the thickness of the observed melt films in the MEMIN experiments significantly varies and ranges from 10 to 100 µm, depending on location (Figs. 3.8 and 3.9). We observed a mean thickness of glassy material of 10–20 µm, whereas melt films at topographic indentations often appear thicker. Moreover, the primary rock texture seems to influence the development of melts, resulting in thin and/or highly vesicular melt films. Those highly vesicular melt films were also found by Fazio et al. (2014), who similarly reported on quartz relics within the melt. Our reticulate melt film with smears and fibers (B) strongly resembles the melt textures documented by Gibson and Spray (1998) for shatter cones from the Sudbury impact structure. They described fibers and smears as well as a reticulate basaltic foam or “froth”, which appeared to be “plastically deformed” and “stretched out like chewing gum” up to 50 µm (Gibson and Spray 1998, p. 311). As in our case, the fine, and sometimes intricate, melt fibers exhibit recoil at their ends, which lead the authors to conclude that the fracture surface must have been considerably hot when it parted. Melt films observed by Fazio et al. (2014) showed vesicles with a coherently stretched and sheared fabric within a silica-rich glass coating on shatter cones, identical to our observations. We believe that in our case the observed surface textures, e.g., elongated vesicles and parting melt layers, indicate a shear movement of the shatter cone surrounding in direction of the cone axis (Figs. 3.5–3.9). Shatter cone melt films were previously compared with pseudotachylitic melt (Gibson and Spray 1998; Nicolaysen and Reimold 1999; Wieland et al. 2006; Fazio et al. 2014; Pittarello et al. 2015). However, some of the authors evaluated this scenario for shatter cone melt films being produced only by frictional heating to be unlikely due to limited or non-observable slip (Wieland et al. 2006; Pittarello et al. 2015). Along shatter cone surfaces limited shear displacement of 50–100 µm was estimated by Nicolaysen and Reimold (1999), whereas Gibson and Spray (1998) argued that symmetric slip on the shatter cone surface limited any offset along the fracture surface. Hasch et al. (2016) documented a minimum offset of 100 µm for shatter cones from the Keurusselkä impact structure. So far, no further estimations of shear displacement along shatter cone surfaces were made. We find clear indication of limited movement by dragged and sheared-off clasts (Figs. 3.7b, 3.8a, 3.9b), showing a minimal displacement of 60 µm, coinciding with the observations of Hasch et al. (2016) and Nicolaysen and Reimold (1999). Shear displacement for the now lost opposite fracture surface should be expected and will have a similar magnitude. In addition, some of the original brittle shear movement is obscured within the melt. Oscillating movement, as thought to occur during frictional heating in seismic fault, does not seem to apply to the formation of shatter cones, hence, 83

slip only occurs over short distances. Taking the cone length of 6.1 mm exemplarily into account as the minimum fault length, the relative displacement is approximately 1–2% of the minimum fault length. Compared to the rough estimations given by Melosh (2005) for frictional melting during pseudotachylite formation, melting due to shear and frictional heating alone is probably be limited. Therefore, we argue that further shock loading and unloading increases melt formation in the subsequent steps and resulting in superposition of melt textures (phases III and IV). This model of progressing formation can also be an explanation for the sheared melt textures (B) and un-sheared, superimposing melt textures (C). A thin and likely glass coating on shatter cone surfaces was also reported by Schmieder et al. (2015) from the Agoudal impact structure. The authors documented Fe-Ni phosphide aggregates, identified as schreibersite adhering to the glass-like shatter cone coatings. Schmieder et al. (2015) connected the schreibersite aggregates to the Agoudal IIAB iron meteorite and suggested an early and rapid injection of meteoritic material into transient, developing shatter cone fracture surfaces, matching their results with the formation of shatter cone surfaces as tensile fracture planes (Johnson and Talbot 1964, Baratoux and Melosh 2003, Sagy et al. 2004, and Kenkmann et al. 2016). Interestingly, Schmieder et al. (2015) showed schreibersite aggregates sheared across the shatter cone surface, parallel to the direction of the shatter cones striae. Similar textures are found in our study (e.g. Fig. 3.5b) for dispersed crushed and sheared zircon or rutile grains. With our proposed succession of events we advocate for an early formation these brittle shear textures during phase I, which are later overlapped by the melt textures. In this regard, shear directions of micro-tectonized aggregates on natural samples could validate or invalidate our observations on experimentally produced shatter cones. 3.5.4 Melt Composition and P-T-Constraints

The SEM analysis of the smoothened surfaces (A) on the shatter cone surface show a SiO2-rich melt and/or a pure quartz melt (lechatelierite). These SiO2-rich melt textures (A) are not unambiguously identifiable in the corresponding thin section. We envisage that the small vertical extent (“thinness”) of the melt coating (some 1–5 µm maximum; e.g., Figs. 3.6b and 3.10) combined with the analytical conditions during SEM surface analysis (e.g., relatively large excitation volume of the electron beam) resulted in analyses that produced mixed compositions from domains within the melt coating and the sandstone (i.e., mainly quartz) underneath (see Fig. 3.10a). In comparison, Nicolaysen and Reimold (1999) described a pure SiO2 and SiO2–Al2O3 melt accompanied by “SiO2 rods” oriented parallel to the striae on the shatter cone surface for samples from the Government Reef Formation in Vredefort. Gibson and Spray (1998) documented for shatter cones in quartz-rich, metasedimentary rocks from Sudbury that some of the melt textures can resemble a biotite-like composition, whereas others are almost pure SiO2. Even though the frothy reticulate melt (B) and the highly vesiculated melt (C) show a different degree of degassing and amount of clastic debris, preferential melting of phyllosilicates is dominating the observed textures (cf. Ebert et al. this issue). The phyllosilicates that originally decorated the pores of the 84

sandstone were smeared across the fracture surface. Subsequently, comminuted material was incorporated into these melts and partially molten. Hence, phyllosilicates play an important role during fracture propagation in sandstone and possibly even acted as a lubricant. As documented by the sharp increase of deformation from the subsurface towards the fracture surface, it is possible that the propagating fracture tip and the softer, smeared phyllosilicates lead to local pressure peaks. Güldemeister et al. (2013) found strong amplification of shock pressures by pore space collapse modelled in iSALE for material with porosities of 20-50%. There, shock pressures of initially 6 GPa were amplified to 17.5 GPa, and pressures of 14 GPa amplified to 61 GPa, at the location of the original pore. In the elemental distribution maps (Fig. 3.11) we documented Zr-enriched, frothy silicate melt surrounding individual zircon grains. The interfaces between such zircon grains and the surrounding silicate melt appear to be sharp and abrupt which we interpret as incipient melting of zircon, qualitatively similar to the observations by Timms et al. (2017) of a ‘halo’ of Zr-enriched silicate melt around zircon grains from Mistastin Lake impact glasses or from impact experiments with zircon-bearing quartz sand (Hamann et al. 2016). For rutile grains we detect only marginally melt with high TiO2 contents along the grain boundaries. Even though we did not detect melt schlieren of pure rutile composition, we believe a likewise explanation of incipient decomposition of rutile and in-situ incorporation of the decomposition products into the surrounding silicate melt as for the zircon is valid. Incipient melting of rutile and zircon, together with mixing of different monomineralic precursor melts, supports high temperatures localized within a narrow, µm-thick zone along the shatter cone surface. Incipient melting of rutile and zircon suggests peak temperatures along the shatter cone surface in excess of ~1850 °C (the melting point of rutile under crustal conditions) to maybe some 2000 °C (upper temperature limit of crystalline zircon; e.g., Kusaba et al. 1985; Cavoise et al. 2016, Timms et al. 2017). Stages of increased shock metamorphism localized along the shatter cone surface could explain melting of rutile and zircon and where previously proposed as an explanation of melt formation along shatter cone surfaces (e.g., Dawson 2009; Gibson and Spray 1998). Gibson and Spray (1998) noted that extreme stages of shock (>60 GPa) would occur very localized only at the shatter cone fractures interface itself. Shock features have been abundantly found in shatter coned material (Carter et al. 1968, Hargraves and White 1996, Ferrière and Osinksi 2010, Hasch et al. 20016 and Zaag et al. 2016), as well as PDFs were observed within the cataclastic zone in this study. However, due to the lack of abundant shock metamorphic features other than melt, we do not think that high shock pressures are realized along the shatter cone surface. In the study of Kowitz et al. 2016, with water saturated (low-porosity) Seeberger Sandstone, samples shocked to samples shocked to 10 GPa showed optically well-developed PDFs and samples shocked to 17.5 GPa would already show a formation of 20–50% diaplectic quartz glass, which we do not observe in our case proximal to the shear zone. Also Ebert et al. (this issue) showed that phyllosilicates have been completely molten in the Seeberger Sandstone in shock recovery experiments above 17.5 GPa, which is not the case for the comminuted phyllosilicates widely distributed in the 85

cataclastic shear zone directly beneath the melt film. This advocates for a combination of intense heating by friction and shock. This could also explain the progressive formation of the frothy textures and the vesiculated melt splats and splashes. However, the formation of condensates is unlikely in this scenario, since much higher shock pressures would be required to facilitate initial vaporization. Due to their small size, the geochemical analysis of micro-spherules found on the shatter cone surfaces turned out to be challenging. However, the formation of such droplets is likely connected to the experimental conditions in the target chamber (e.g., melt spherules derived from the blast tank, the sabot impact plate, etc,), rather than to the physical target rock properties. Investigation of the TEM-foil proved the amorphous nature of the shatter cone surface and we were able to show incipient melting of individual mineral grains and sandstone clasts within the melt and at the contact to the comminuted material below. Within the melt film we found isolated quartz grains, suspended in the melt and close to the cataclastic zone, with narrow-spaced (≤80 nm) amorphous lamellae. Those shock lamellae have a crystallographic orientation parallel to the plane of {1122}, which is an orientation not un- typical for PDFs in quartz (Albat and Mayer 1989, Stöffler and Langenhorst 1994). Due to their amorphous nature and crystallographic orientation, we think the observed lamellae are PDFs. Despite that, it has to be cautiously considered that the lamellae do not cross the entire grain and some of them are extremely bent close to the apparent grain boundary. 3.6 Conclusion Shatter cones were experimentally produced in the MEMIN hypervelocity impact experiments at varying impact conditions. The shatter cones investigated here were found in experiments with dry and water-saturated sandstone impacted by 2.5 mm aluminum and 12 mm iron meteorite projectiles at impact velocities of 6.97 km s-1 and 4.59 km s-1, respectively. Shatter cones were recovered from ejecta material, which is consistent with natural shatter cone findings in allochthonous impact breccias, indicating a formation prior to the onset of excavation (e.g. French 1969, Gostin et al. 1986, Osinksi and Spray 2006, Thover et al. 2012, Raschke et al. 2013, Sach 2014, Pittarello et al. 2015, Osinksi and Ferriére 2016). The recovered shatter cone fragments are covered by µm-thick, amorphous coatings on cataclastically formed fracture surface. The total thickness of comminuted and partially melted rock is 140 µm, locally reaching up to 300 µm. The comminuted and brecciated shear zone at the surface of the shatter cone shows a minimum offset of 60–80 µm parallel to the fracture surface with a shear sense that the (missing) rock surrounding the shatter cone moves away from the cone apex. Phyllosilicates are comminuted and smeared along the fracture surface in the shear zone underneath. The intricate melt textures at the surface show smearing and extension of melt sub-parallel to the fracture surface in opposite direction to the comminuted and brecciated shear zone. As suggested by Gibson and Spray (1998) and Nicolaysen and Reimold (1999), these observations suggest rapid shearing and localized microstructural deformation

along the shatter cone surface. In addition to the early initiation of melt formation by frictional heating, we argue the following progression of reaching peak pressure and subsequent unloading is able to attain the high temperatures needed for melting of the accessory phases and the strong vesiculation of the textures in the sandstone. Based on the melt textures, we can estimate high post-shock temperatures (possibly up to 2000 °C) along the shatter cone surfaces. In addition, we can further constrain pressure conditions of shatter cone formation in the MEMIN experiments to a range of 0.5 GPa to a maximum of 10 GPa. By comparing our results to the observations made by Kowitz et al. 2016 and Ebert et al. (this issue), we deem pressures much higher than 2 GPa unlikely for the bulk rock and based on the observed beginning of PDF formation favor ~ 2 GPa as the formation regime of our recovered fragments. Together with the documented melt films and the shear-attributed grain comminution, we believe that shatter cone formation models may account for the mixed mode I/II fracture (sliding and opening) character of shatter cones as well as the intense deformation along the fracture surface. In the presented MEMIN experiments, phyllosilicates play a distinct role to facilitate fracture propagation and movement along the fracture surfaces, which might be an interesting aspect to be further studied for shatter cones in nature and experiment.

3.7 Acknowledgement This work is part of the DFG research unit FOR-887: “Experimental Impact Cratering: The MEMIN program” grants KE 732/22-1, LA 830/18-1 and He-2893/8-2. FL is also grateful to DFG for support provided via the Gottfried Wilhelm Leibniz program (LA 830/14-1). AF thanks the Alexander von Humboldt Foundation for providing a research fellowship. Sincere thanks go to the EMI representatives and the laboratory team that made the experiments possible, in particular Tobias Hörth, Michael Poelchau, and Frank Schäfer. We thank Nicole Güldemeister for fruitful discussions and Hans-Rudolf Knöfler for sample preparation. We gratefully acknowledge the developers of iSALE-2D, including Gareth Collins, Kai Wünnemann, Dirk Elbeshausen, Boris Ivanov, and Jay Melosh. We also acknowledge the developer of the pySALEPlot tool Tom Davison, and the developer of the VIMoD software Dirk Elbeshausen. iSALE – Website: www.isale-code.de

Appendix A15–5185 E3-3384 Projectile Target Projectile Target

Aluminium Sandstone CdC/ iron Wet Sandstone General parameters Poisson ratio 0.33 0.3 0.25 0.3

Specific heat capacity [J/(kg K)] 896 800 200 800

Strength parameters Von Mises yield strength [MPa] 800 - - -

Johnson-Cook parametrisation:

Strain coefficient a [MPa] - - 175 -

Strain coefficient b [MPa] - - 280 -

Strain exponent - - 0.32 -

Strain rate coefficient c - - 0.001 -

Thermal softening - - 0.55 -

Reference temperature [K] - - 293 -

Lundborg parametrisation intact yield surface:

0 푌푖 [kPa] - 200 - 200

휇푖 - 1.8 - 1.8 푚 푌푖 [MPa] - 170 - 170 damaged yield surface:

0 푌푑 [Pa] - 0 - 0

휇푑 - 0.67 - 0.67 푚 푌푑 [MPa] - 170 - 170 Thermal Softening (Ohnaka) Softening constant 1.2 1.2 - 1.2

Melt temperate [K] 933 1873 1500 1873

Simon approximation:

Simon constant 6 ∙109 6 ∙109 6 ∙109 6 ∙109

Simon exponent 3 3 3 3

Porosity parameters

Initial distension α0 - 1.3333 - 1.1429*

Elastic volumetric threshold εe - -0.001 - -0.001

Transition distension αx - 1.1 - 1.1

Compaction efficiency κ - 0.98 - 0.98

Speed of sound ratio χ - 0.6 - 0.6 * Pores are 50% water saturated and the porosity here is 12.5%. 88

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Roddy D. J. and Davis L. K. 1977. Shatter cones formed in large-scale experimental explosion craters. In impact and explosion cratering, edited by Roddy D.J., Pepin R.O., and Merill R.B. New York: Pergamon Press. pp. 715-750.

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4. FORMATION OF SHATTER CONES BY SYMMETRIC CRACK BIFURCATION: PHENOMENOLOGICAL MODELING AND VALIDATION

This chapter has been published as peer-reviewed article as follow:

Kenkmann T., Hergarten S., Kuhn T., amd Wilk J. (2016) Formation of shatter cones by symmetric crack bifurcation: phenomenological modeling and validation. Meteoritics & Planetary Science 51:1519-1533.

4.1 Abstract Several models of shatter cone formation require a heterogeneity at the cone apex of high impedance mismatch to the surrounding bulk rock. This heterogeneity is the source of spherically expanding waves that interact with the planar shock front or the following release wave. While these models are capable to explain the overall conical shape of shatter cones they hamper to explain the sub-cone structure and the diverging and branching striations that characterize the surface of shatter cones and lead to the so-called horse-tailing effect. Here we use the hierarchical arrangement of sub-cone ridges of shatter cone surfaces as key for understanding their formation. Tracing a single sub-cone ridge from its apex downward along the master-cone one can observe that each ridge branches after some distance into two symmetrically equivalent sub-cone ridges. These bifurcate again and the new branches do the same. We propose that sub-cone ridges represent convex-curved fracture planes and their intersection corresponds to the bifurcation axis. The characteristic diverging striations are interpreted as the intersection lineations delimiting each sub-cone. Multiple symmetric crack branching is the result of rapid fracture propagation that may approach the Raleigh wave speed. We present a phenomenological model that fully constructs the shatter cone geometry to any order. The overall cone geometry including apex angle of the master cone and the degree of concavity (horse-tailing) is largely governed by the convexity of the sub-cone ridges. Straight cones of various apical angles, constant slope, and constant bifurcation angles form if the sub-cone convexity is low (30°). Increasing sub-cone convexity leads to a stronger horse-tailing effect and the bifurcation angles increase with increasing distance from the master-cone apex. The model predicts possible triples of enveloping cone angle, bifurcation angle, and subcone angle. Measurements of these quantities on four shatter cones from different impact structures and lithologies agree well with model predictions.

4.2 Introduction Shatter cones are the only macroscopically visible shock indicator. Since it became clear that their formation is related to impact cratering (Dietz 1947), they have been intensely used to identify impact structures. Dietz (1960, 1968) interpreted structures like Steinheim, Germany (Figs. 4.1a, 4.2a), Kentland, USA, or Flynn Creek, USA as eroded impact structures. Many other impact structures on Earth were discovered on the basis of shatter cone findings since then, e.g., Sierra Madera, USA (Howard and Offield 1968), Haughton Dome, Canada (Robertson 1975) (Fig. 4.1b), Vredefort, South Africa (Simpson, 1981), Jebel Waqf as Suwwan in Jordan (Salameh et al. 2006), or recently the Tunnunik impact structure, Canada (Dewing et al., 2013). Proposed impact structures like Santa Fe, USA (Fackelman et al. 2008) or recently Agoudal, Morocco (Lorenz et al. 2015) exclusively rely on shatter cone findings. Shatter cones have been described from about 70 of the 188 documented impact structures on Earth so far (Ferrière and Osinski, 2010) and were also discovered in meteorites (Dietz 1966; McHone et al. 2012; Ferrière et al. 2016). They do not occur in every impact crater; for instance, they have not been discovered in the well-studied Barringer crater, USA, so far. Shatter cones are striated conical fracture surfaces. Their sizes range from a few millimeters to more than 10 m. The striations are sharp narrow grooves between broader convexities (Milton 1977). Subsidiary segments lie with their apices on the flanks of the master cone and build a hierarchical system of sub-cones. Diverging and branching striations built a “horsetail” pattern. Shatter cones are formed in a great variety of target rocks, including granite, basalt, chert, limestone, dolostone, sandstone, but coarser grained rocks tend to yield less well-developed shatter cones. Shatter cones formed in fine-grained micritic limestones - in particular those from Steinheim (Figs. 4.1a, 4.2a), Wells Creek, Haughton, and Jebel Waqf as Suwwan structures (Fig. 2b) - have the most delicate and finest structured surfaces. Apices of Fig.4.1. A) Large shatter cone (50 9 40 9 40 cm) formed in upper shatter cones sometimes emanate from planar Jurassic micritic limestone from the central uplift of Steinheim discontinuities within the rocks such as lithological impact structure, Germany. Note the delicate striae with hierarchical arrangement and horse-tailing effect. B) Complete boundaries or bedding planes, but the preservation shatter cone in dolomite from the Haughton structure, NW territories, Canada. The apex is preserved. of first-order shatter cone apices is generally low. In 95

rare circumstances master- or first-order cone apices are preserved (Fig. 4.1b) and do not show lithological irregularities. Most of published theories of shatter cone formation call for an inclusion with positive or negative shock impedance (e.g. pores) at the tip of the cone. The apical angles of shatter cones range between 60-120° with 90° as a mean value (Milton 1977). However, Nicolaysen and Reimold (1999) describe much wider angles for shatter cones of the Vredefort impact structure, South Africa. Multiply-striated joint sets fall into this category of relatively “flat” shatter cones, which may tie shatter cones with striated planar faults of tectonic origin. Gay (1976), Gibson and Spray (1998), and Pittarello et al (2015) observed localized melt films and spheres on shatter cone surfaces that were interpreted as the result of localized frictional melting. Shatter cones occur in situ in the rocks below the crater floor, usually in the central uplift and the surrounding ring syncline of complex impact structures, but they are also observed in allochthonous breccias as clastic fragments indicating their early formation time during the cratering process (French, 1998). Due to excavation these shatter cones can be found outside the crater. When shatter cones are in place and the rocks of the crater floor are restored to their pre-impact orientation, their apices and symmetry axes often point inward and upward (Dietz 1968; Milton 1977) suggesting that shatter cone axes are statistically predominantly oriented perpendicular to the shock front with apices facing the shock front. However, numerous deviations from this like antipodal shatter cones of opposite orientation are reported in the literature. So far, there is only a rough consensus about the range of shock pressure magnitudes at which shatter cones may form: The spectrum comprises: “...2-10 GPa, possibly up to 30 GPa…” (French 1998), “…an interval between a few Gigapascal and ~20 GPa…” (Ferrière and Osinski 2010), “…4 and 30-45 GPa shock pressure…”(Nicolaysen and Reimold 1999), and 2-6 GPa (Sagy et al. 2004). Based on meso-scale numerical modeling Baratoux and Melosh (2003) derived shock pressures between 3 and 6 GPa. Sagy et al. 2002 used shock pressure isobars derived from numerical modeling of the Vredefort impact structure to narrow down the occurrence of shatter cones to a shock pressure range of 5-30 GPa (Sagy et al. 2002). The first shatter cone produced in the laboratory was reported by Shoemaker et al. (1961) using a dolomite target. Shatter cones were also reported from nuclear explosion test sites (Bunch and Quaide 1968) and from large-scale 0.5 and 100 t TNT explosion craters (Roddy and Davis 1977). The latter formed in tonalite at shock pressures of 2-6 GPa. Schneider and Wagner (1976) produced millimeter-sized shatter cones in limestone targets within the crater´s spallation zones at impact velocities of about 3 km/s and higher by using spherical metal projectiles. However, it was difficult to determine the local shock pressure in these small-scale experiments. Shatter cones were also successfully formed in MEMIN impact experiments in different target lithologies (Kenkmann et al. 2012; Wilk and Kenkmann 2016).

Fig. 4.2 A) Enveloping cones of a shatter cone assembly from Steinheim impact structure, Germany, intersect and penetrate each other. The surface of each cone comprises smaller-scale subcones that bifurcate downslope. Bifurcation points are marked by stars and the subcone ridges are delineated by white lines. B) Shatter cone in limestone from the central uplift of Waqf as Suwwan impact structure, Jordan, shows acute-angled subcones. C) Subcones with acute apical angles of ~35° in limestone, Steinheim impact structure. D) Subcone apices of shatter cones from Marquez Dome impact structure, Texas, USA. The angles range from 20° to 40°.

4.3 Shatter cone formation models Two models of shatter cone formation assume point inhomogeneities at the cone apex of high impedance contrast towards the surrounding rock (Johnson and Talbot 1964; Baratoux and Melosh 2003). This heterogeneity is the source of spherically expanding waves that interact with either the planar shock front or the following release wave. These models provide an explanation of the conical shape of shatter cones (Johnson and Talbot 1964; Baratoux and Melosh 2003). A different approach focusing on the striated shatter cone surface based on dynamic fracture theory was proposed by Sagy et al. (2002, 2004). Dawson (2009) explained shatter cone formation by adiabatic shear banding. The existing formation models are briefly outlined below (also see Baratoux et al. 2016). Johnson and Talbot (1964) proposed that shatter cones form when the elastic precursor of the shock front is scattered by heterogeneity in the rock. The scattered elastic wave interferes with the direct wave in such a form, that under certain conditions the Hugoniot elastic limit is exceeded in a conical region behind the heterogeneity while the region outside of the cone behaved elastically and became mechanically separated from the cone when the plastic wave arrives. Gash (1971) suggested that the cone shape develops by superposition of a primary spherical stress wave that expands from the point of impact with a secondary release wave reflected from the free surfaces (target surface). In this model shatter cones are only formed in a limited angular range beneath the shock center, but this range is inconsistent with the occurrence of shatter cones in natural impact craters. Based on physical arguments this model is nowadays largely discarded by most researchers (Baratoux and Melosh 2003). Baratoux and Melosh (2003) proposed that shatter cones are conical tensile fractures that develop by constructive interference of the tensional hoop stresses at the tail of the compressive shock wave with tensional scattered waves radiated from voids or low impedance materials in the rocks. The shock wave must travel faster in the rock than in the heterogeneity by a minimum factor of about two and the dimensions of the heterogeneity must be comparable to the width of the shock wave to allow for cone-like fracturing (Baratoux and Melosh 2003). According to their numerical model using the Grady-Kipp-Melosh fragmentation model (Melosh et al. 1992) the apical angle depends on both the properties of the heterogeneity and the decay time of the shock wave. Shatter cones occur only when the ratio between the pulse width and the size of the heterogeneity is close to one. All types of rock certainly contain abundant small-scale heterogeneities such as microscopic flaws, grain boundaries, microfossils, pore space or impedance contrasts between adjacent minerals. However, such heterogeneities are dispersed and distributed all over the rock. It is therefore questionable why only a few of them should be the locus of shatter cones while the gross of them plays no role in shatter cone formation. The model of Baratoux and Melosh (2003) might be specifically applicable to rocks that contain secondary porosity, formed by localized dissolution (e.g. of shells) during diagenesis. This type of porosity 98

is commonly uneven distributed in the rock and voids are larger than primary pore space. However, pore space is not expected to occur in magmatic or metamorphic rocks. Shatter cones of the type locality Steinheim are perfect examples of shatter cone formation in macroscopically very homogeneous rocks (Figs. 4.1a, .2a). Moreover, both models do not explain the hierarchical sub-cone pattern of shatter cone surfaces. Like Baratoux and Melosh (2003), Sagy et al. (2002, 2004) suggested that shatter cones are Mode I tensile fracture planes. Arguments for this are (1) the characteristic striations display diverging pairs of grooves being geometrically inconsistent with fracture-parallel shear, (2) no evidence of detectable slip and shear, and (3) thin melt coatings can occur on shatter cone surfaces. Radially propagating shock waves produce tensile stresses normal to the compressive (radial) direction in the trailing part of the shock wave. These tensile stresses generate tensile fractures that propagate outwards from the axis of impact. Based on this, the model of Sagy et al. (2002, 2004) propose two processes: First, the extreme loading causes fractures to propagate at velocities close to the Rayleigh wave speed VR and start to form branched fracture networks. Investigating shatter cones from the Vredefort impact structure Sagy et al. (2004) observed that the branched fractures are asymmetric and curved and have spoon-like geometries. Second, V-shaped striations on the shatter cone surface are explained by the concept of ‘‘front waves’’. Sharon et al. (2001, 2002) have experimentally revealed this localized wave type, which is excited when a rapidly moving fracture front encounters an inhomogeneity in the material. The inhomogeneity induces a pair of propagating front waves that creates diverging tracks on the fracture surface emanating from inhomogeneity. The propagation velocity V of the main tensile fracture can be determined from the angle α/2 between the front wave and the tensile fracture: cos(α/2) = V/VFW (Sharon et al. 2004). At Vredefort, Sagy et al. (2002) measured that the mean striation angles systematically increase from 17° to 46° with distance from the impact center. However this trend was disputed by Wieland et al. (2006), who did not find a statistically significant trend in bifurcation angles. We see a shortcoming in the model of Sagy et al. (2004) in the circumstance that V-shaped striations are explained as the traces of fracture front waves (Sharon and Fineberg 1996; Sharon et al. 2001). To our knowledge it has not been experimentally proven that fractures that asymmetrically branch from a main fracture can branch again and develop front waves while they are branching again. Dawson et al. (2009) explored shatter cone formation through 3D numerical simulations using a crack band model – a technique for simulating fracture or shear banding with a continuum, strain softening, elasto- plastic model. Simulations of planar, plastic shocks show that a small flaw or inhomogeneity can trigger the formation of a conical shear band with apex pointing toward the shock source. These results suggest that adiabatic shear banding might be an alternative formation mechanism for shatter cones. 4.4 A side step: crack bifurcation during dynamic fragmentation Impact loading is a special case of dynamic loading. Numerous experimental studies on dynamic loading exist in the literature of material science. They include studies on metals, glasses, polymers, but also 99

rocky materials and concrete (e.g., Ravi-Chandar 2004; Hiermaier 2008). The response of structures to dynamic loading depends on the loading rate through the rate dependency of the growing micro-cracks and through the influence of structural inertia forces, which can significantly change the state of stresses and strains of the material (Ozbolt et al. 2011). Moreover, the failure mode and cracking pattern depend on the loading rate (Zhang and Zhao 2013). In general, there is a tendency that with the increase of loading rate the failure mode changes from Mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches a critical speed Vc of propagation, bifurcation of the crack takes place. The terms “fracture branching” and fracture bifurcation” are used synonymously throughout the text. For a statically fractured specimen there is hardly any crack branching observable (Zhang et al. 1999). During dynamic loading the crack propagation velocity is not constant. When the critical crack speed

Vc is reached and exceeded, the crack velocity develops strong oscillations (Fineberg et al. 1992; Adda- Bedia 2005; Bouchbinder and Procaccia 2007). This culminates in crack branching and the crack speed rapidly decreases. But it soon started to re-accelerate again until, after some distance, the crack branches again (Bordas et al. 2008). Different types of crack branching exist: Incipient branching forms micro-branches that propagate only micrometer away from the main fracture and then become arrested. Such micro-branches are the nuclei for front waves (Sagy et al. 2002, 2004). A growth criterion for a branched crack must be based on the equality between the energy flux into the two propagating tips and the surface energy that is added as a result of this propagation (Griffith 1920). For arrested micro-branches, the energy for crack branching to occur is consumed and no further energy is available for further growth. The critical velocity at the onset of micro-branching in amorphous material starts at 0.3-0.4 VR (Sagy et al. 2006; Bouchbinder and Procaccia

2007) and larger micro-branches, at scales of a few mm, are observed for average velocities above 0.5VR. At asymmetric macro-branches the majority of the fracture energy is concentrated in the fracture that shows the lowest reorientation with respect to the original crack. Symmetrically bifurcating macro-cracks deposit equal portions of energy into both branches and may develop at 0.8-0.85 VR (Bouchbinder and Procaccia 2007) or, in case of shock loading, at even higher velocities. Of great importance for the understanding of shatter cones in rock is the work by Bieniawski (1968) (Fig. 4.3) who recorded dynamic fracture propagation in a thin slice of norite obtained by ultra-high speed camera. At least four generations of symmetric crack branching are visible. The bifurcation angle  and the distance between two bifurcation points remain constant from one cycle to the next. The fracture propagation velocity in the experiment was 1875 m/s or

0.679 VR (Bieniawski (1968). Based on the preceding discussion, this paper explores symmetric crack branching as a process to explain the hierarchical subcone patterns of shatter cones.

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Fig. 4.3. Photographic record of fracture propagation in a thin slice of norite obtained by a ultra-high-speed camera at 1.5 million frames per second (modified after Bieniawski 1968). At least four bifurcation generations are visible. The bifurcation angle φ of ~21° and the propagation distance between two bifurcation points remain constant from one cycle to the next. The fracture propagation velocity is 1875 m s-1 or 0.679 VR.

4.5 The approach Sagy et al. (2002, 2004) were the first who introduced the concept of branched tensile fractures for understanding grooves and ridges of shatter cone surfaces. Here we take the idea of crack branching and build a geometric phenomenological model to explain the shatter cone morphologies. Our hypothetical model of crack branching however works fundamentally different from that of Sagy et al. (2002, 2004) and does not require front waves to explain the diverging striations. We propose that sub-cone ridges represent convex-curved fracture planes and their intersection corresponds to the bifurcation axis. The characteristic diverging striations are interpreted as the intersection lineations delimiting each sub-cone. We assume that the fracture front is highly segmented because of the heterogeneous nature of rocks and the presence of grains, anisotropies, pore-space, micro-cracks, etc. (Sharon and Fineberg, 1996). Detailed studies of crack patterns within impact craters in rock targets, e.g., Polanskey and Ahrens (1990), Ahrens and Rubin (1993) and Buhl et al.(2013) indicate that three families of cracks are produced upon impact onto rock targets namely (i) radial, (ii) concentric, and (iii) spall fractures. Radial fractures initiate first directly at the trailing end of the shock wave and reach their peak tensile value behind the compressive wave, immediately prior to the arrival of the shear wave (Ahrens and Rubin, 1993; Baratoux and Melosh, 2003). If their propagation direction deviates from a radial orientation with respect to the impact center they develop to mixed mode fractures. We assume that such tensile and mixed mode fractures propagate in a segmented, finger-like fashion and reach velocities close to VR at the tip of such advancing fingers (Fig. 4.4a). The geometries of the propagating fracture planes correspond to the convexly curved sub-cones of shatter cones. The splitting of the cone into two new sub-cones marks a symmetric bifurcation event when a critical fracture propagation velocity is reached (Fig. 4.4b). We hypothesize that the bifurcation axis corresponds to the initial intersection of the newly formed sub-cones. This is fundamentally different from the model of Sagy et al. (2002, 2004) who suggests that an oblate branch bifurcates from its parent fracture

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(e.g., a larger shatter cone) and expands to form a spoon-like surface. After bifurcation the just formed fracture branch propagates anew. While the velocity initially dropped after bifurcation it soon re-accelerates (see previous section) thereby enlarging its fracture plane to a new sub-cone. At the critical velocity a new cycle of bifurcation develops. The diverging striations between the sub-cone ridges are simply the grooves that formed by the intersection of the sub-cones (Fig. 4.4c). In the following we will first present observation obtained from various shatter cone localities and lithologies and present morphometrical measurements of apical angles of the master-cones, bifurcation angles, and convexity measurements of the sub-cone ridges. We then describe the fundamentals of our phenomenological model in plane view and three-dimensionally. Results of the model include a parameter study. The discussion sheds light on the applicability of the model to natural shatter cones and the usage of the model to infer parameters of shatter cone formation. 4.6 Morphometry

4.6.1 Methods Since apical angles of the master cones are rarely preserved they are determined indirectly by dip azimuth and dip angle measurements of sub-cones. Our model will demonstrate that this method contains a systematic error due to a decrease of the slope with increasing distance from the apex. The deviation could be minimized if measurements from cone subsets are taken that are close to the master apex. The method also works if sector. For both the measurements of apical angles as well as for bifurcation angles the shatter cone samples were locked into a fixed position and were measured with a geologic compass attached with a needle extension that was fixed to the cover flap. Equal area stereographic projections were used to analyze space data. Standard deviations for plunge azimuth and angle are ~5°. Bifurcation angles were determined at the plane of the shatter cone surface utilizing a binocular. A laser scanning device (Escan-3D) is used to create digital elevation models (DEM) of the shatter cone samples and to construct cross sections perpendicular to the master-cone apices. The spatial resolution at a distance of 30 cm between scanner and object is 76 µm. To fully record the shatter cone morphology it is required to scan the object from different vantage points and to allow for large overlaps. Calibration tools and marker points allow to merge the scans. We used the Kriging method and Delaunay triangulation to generate surfaces. Profiles were extracted using Surfer© by Golden Software. The characteristics of shatter cones were also investigated with high-resolution surface scans obtained by white-light-interferometry (WLI). The WLI is a non-contact, non-intrusive optical surface analysis, which allows to obtain digital elevation models (DEM) of small scale surfaces using either a continuous spectrum or a monochromatic light source in a vertical scanning mode or a phase shift scanning mode. It allows measuring apical angles of master cones and their sub-cone apices, amplitude of striated cone surfaces, or the curvature of cones. We used a Bruker AXS Contour GT-K0 white light interferometer 102

operated with Bruker Vision64 software. The vertical resolution in the used setup ranges between 2 and 9 μm; spatial resolution is 1.96 μm. Post processing and interpolation of the original point cloud were carried out with ArcGIS.

4.6.2 Results We systematically analyzed shatter cone samples formed in various lithologies from Steinheim crater (Germany), Siljan (Sweden), Charlevoix (Canada), and Marquez (USA) (Table 4.1) and determined the apical angle , the bifurcation angle , and the sub-cone convexity . Figure 5 displays a digital elevation model of a 12 x 3 mm section of Steinheim shatter cone obtained with a white-light-interferometer. The DEM documents the delicate topography of the shatter cones that is structures by sub-cone ridges and grooves. The multiple branching of sub-cone ridges is clearly visible. Bifurcation points are roughly equi distant. The results of lineation measurements are presented in Fig. 4.6. The lineation measurements define small circles in an equal area Schmidt projection whose diameter correspond to the master-cone angle alpha. The scattering of data indicates an error of +/- 5°. The measured master-cone angles range between 85° and 110° (Table 4.1). These measurements are within the range reported by Milton (1977).

Table 4.1 Characteristics of the investigated shatter cone samples. For the determination of the convexity of sub-cone ridge angle ß we refer to Fig.5 and Eq. 21.

crater lithology size of shatter master-apex Bifurcation sub-cone ß cone (l x w x h) angle  [°] angle  [°] convexity [cm] [°] Steinheim, limestone, 12 x 14 x 8 100 +/- 5 38.5 +/- 13.6 60 Germany micritic Siljan, granite, 26 x 14 x 6 110 +/- 5 46.1 +/- 12.0 65 Sweden coarse-grained Charlevoix, gneiss, 8 x 11 x 5 85 +/- 5 47.7 +/-8.3 56 Canada foliated Marquez, limestone, 5 x 8 x 3 --- 26.7 +/-7.3 42 TX, USA marly

Measurements of bifurcation angles show a large scattering as indicated in the histograms of Fig. 4.7. This scattering is partly due to measurement errors but partly reflects a systematic variation of bifurcation angles with the order of bifurcation cycles as will be shown later. Taking the mean angle it is conspicuous that the bifurcation angle in limestone targets is more acute (26.7°-38.5°) (Table 1) and in crystalline material more obtuse (46.1°-47.7°). 103

The wavy topography with alternating sub-cone ridges and grooves is demonstrated in surface topography profiles of Figure 8. We determined ratios between secant/chord length s and height h. The circular segment ß, here named as the sub-cone convexity is given by:

2ℎ ß = tan 푠 4

(1)

The sub-cone convexity ß ranges between 42-65° for the investigated samples. The secant length in limestones is larger than in crystalline material.

Fig. 4.4. Sketch illustrating the hypothetical bifurcation of propagating fractures in our model. A) The propagation velocity is close to VR. Once the energy flux at the fracture tip exceeds a critical value symmetric fracture branching starts at the advancing tip. B) While the new fractures are growing, they start to intersect with the parent and the adjacent fractures, and form intersections. C) The V-shaped striations at the shatter cone surface are the grooves between adjacent subcone ridges.

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4.7 Phenomenological geometric modeling

Table 4.2 Characterization of the investigated shatter cone samples. For the determination of the sub-cone ridge angle ß we refer to Fig.5 and Eq. 21.

Crater Lithology Size of shatter cone Enveloping Bifurcation Subcone (l x w x h) [cm] cone-apex angle a (°) angle φ (°) convexity b (°) Steinheim, limestone, 12 x 14 x 8 100 +/- 10 35 60 Germany micritic Siljan, granite, 26 x 14 x 6 110 +/- 10 45 65 Sweden coarse-grained Charlevoix, gneiss, 8 x 11 x 5 85 +/- 10 50 56 Canada foliated Marquez, limestone, 5 x 8 x 3 --- 28 42 TX, USA marly

Fig. 4.5. Digital elevation model of a 12 9 3 mm section of a Steinheim shatter cone. Data were obtained with a white-light interferometer. The DEM clearly shows subcone ridges that branch down slope with roughly constant bifurcation angle.

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4.7.1 Model set-up We trace the crest line of sub-cone ridges from the master-cone apex downward (see for comparison Fig. 4.2a. Let us assume that the sub-cone and its crest line has a certain length and then splits symmetrically into two sub-cones both of them having the same geometry. The angle at which both crest lines divide is the bifurcation angle . Doing so the number of sub-cones N doubles with distance from the apex. We define that each bifurcation cycle denotes one order n. Starting with a limited number of sub-cones N0 , e.g. N0 = 1, the number of them of each order increases by:

푛−1 푁 = 푁0 × 2 (2)

In plane view along the shatter cone axis the sub-cone ridges can be described as circular segments with radius r1 and central angle ß, a chord length s, and an arc length b1 (Fig. 4.9). The total arc length bn at any order is:

−1 푠1 푏푛 = 2 N 푟1 푠𝑖푛 ( ) 2 푟1 (3)

Each ridge bifurcates when it reaches a given arc length b1. The two new branches grow on the ridge they are emanating from, while the old ridge continues growing at the same rate as the radius of the cone becomes larger.

In the following we use non-dimensional coordinates based on the height z1 and the radius r1 of the root cone at the stage of the first bifurcation (Fig. 9):

푥 푦 푧 푋 = , 푌 = , 푎푛푑 푍 = 푟1 푟1 푟1 (4)

Considering the length of the ½ b1 line yields: 훽 훽 (1 + 푞) 푠𝑖푛 = sin 4 2 (5)

훽 훽 As the term at the right-hand side can be written in the form: 2 sin cos , we obtain the relationship 4 4 훽 푞 = 2 cos − 1 4 (6)

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Then the relative increase in perimeter f resulting from the bifurcation is:

훽 2 1 푓 = 2 = = 훽 훽 (1 + 푞) 1 + 푞 cos 4 4 (7)

These basic relations also hold for subsequent bifurcations. As a consequence of Eq. (6), the height of each cone until it bifurcates decreases by the factor q from order to order and thus constrains the degree of cone concavity (horse-tailing). Then the total height at the nth order is readily obtained from a geometric series:

푛−1 1 − 푞푛 푍 = ∑ 푞푖 = 푛 1 − 푞 푖=0 (8)

Fig. 4.6. Equal area stereographic plots of shatter cone lineations (black dots) after Kuhn (2011). Shatter cone apex angles are determined by the measurement of surface striae. Shading indicates the density distribution of measurements. Small circles were fitted manually to the density distribution. The opening angle of the enveloping cones is given in the middle of the projection. A) Steinheim, Germany. The enveloping cone apex angle is well defined because striae measurements cover various and opposite faces of the cone. B) Siljan, Sweden. One half of the cone is preserved. C) Charlevoix, Canada. Only a small fraction of the cone is available for measurements. Unfortunately, no data are available for the shatter cone sample from Marquez Dome.

4.7.2 The overall geometry

Assigning an overall radius to the resulting object consisting of several cones is, however, more difficult. Figure 4.10 illustrates the evolution of the first three generations in plane view perpendicular to the master-cone axis. As shown in Fig. 4.10 b, the centers of the second generation at height Z2 (i.e., when they bifurcate) are located vertically above the rim of the root cone at Z1. This property is also easily verified theoretically using the geometry shown in Fig. 4.9. As a consequence, the axes of the cones of the second generation are inclined (as all further, too), but this inclination practically only has a tangential component with regard to their parent, so that this inclination does not contribute to the overall radius. As a result, the

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radius of the second generation is R2 = 2 (Fig. 4.9). This property is, however, lost in the next generation (Fig. 4.10 c) due to the inclination of the first generation, but the second generation located in the middle have a very small inclination as the effects of the first and second order almost compensate each other here.

Therefore, these two cone segments lead to a total radius R3 ~ 3, suggesting a relation

푅푛 ≈ 푛 (9) for the radius at the cones close to the Y axis (i.e., roughly in direction of the root cone segment). This finding is numerically verified in Fig. 11 for different angles β. It turns out that this approximation provides a useful approximation for the mean effective radius of all cones of the respective generation. Combining Eqs. 8 and 9 leads to the following approximation of the effective radius of the entire object:

log (1 − (1 − 푞)푍) 푅(푍) ≈ log 푞 (10) or in absolute coordinates: 푧 log (1 − (1 − 푞) ) 푧 푟(푧) ≈ 푟 1 1 log 푞 (11)

4.7.3 Apex angles and bifurcation angles

Radius r1 and height z1 of the root cone define the horizontal and vertical length scales of the model. While rescaling both uniformly does not change the geometric properties, their ratio affects, e.g., the apex angles and the angles of bifurcation. The apex angle 1 of the root cone is related to r1 and z1 by

훼 푟 tan 1 = 1 2 푧1 (12)

The individual radii of its descendants are the same, but the height is reduced from one generation to the next by the factor q (Eq. 5), so that 훼 훼 tan 1 tan 푛 = 2 2 푞푛−1

(13)

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The angle of bifurcation of the second generation, 2, is the angle between the ridge lines given by ß ±2 sin 푟1 4 푢⃑⃑⃑⃑±⃑ = ß (2 cos − 1) 푟 4 1 ( 푞 푧1 ) (14)

The vectors correspond to lines from the green markers to the cyan colored markers in Fig. 4.10 with a vertical component qz1. The angle of bifurcation 2 is then given by the relation → . → 푢+ 푢− 푐표푠 휑2 = |→ | . |→ | 푢+ 푢− (15)

It is more convenient to compute half of this angle using the trigonometric identity

휑 1 − cos 휑 푡푎푛 2 = √ 2 2 1 + cos 휑2 (16)

|→ | . |→ | − → . → 푢 푢 푢 푢 = √ + − + − |→ | . |→ | + → . → 푢+ 푢− 푢+ 푢− (17) ß 8 푠𝑖푛2 푟2 4 1 = √ ß 2 2 (2 cos − 1) 푟2 + 2푞2푧2 4 1 1 (18) ß 2 푠𝑖푛 푟2 = 4 √ 1 ß 2 2 2 cos − 1 푟1 + 푧1 4 (19) ß 2 푠𝑖푛 훼 = 4 푠𝑖푛 1 ß 2 cos − 1 2 4 (20)

In the geometrical concept described above, the inclination of the axes of the higher-order cones has been reproduced by applying a simple shear in the x-y-plane. This shear makes computing the angles of

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bifurcation at higher orders complicated. However, this shear was introduced for simplicity, while the relationship between each cone and its subsequent second generation should be self-similar in it spirit, except for a shortening by the factor q in vertical direction from generation to generation. With regard to the original concept, the generalization of Eq. 20 towards higher orders simply reads: It is more convenient to compute half of this angle using the trigonometric identity

ß 휑 2 푠𝑖푛 훼 푡푎푛 푛+1 = 4 푠𝑖푛 푛 ß 2 2 cos − 1 2 4 (21) The resulting angles of bifurcation are plotted in Fig. 4.12.

Fig. 4.7. Sections perpendicular to the shatter cone axis document the alternation of ridges and grooves at the shatter cone surface (Kuhn 2011). We derive characteristic amplitudes A and wavelength ½ k. A) 5.9 mm/44 mm; B) 2.9 mm/20 mm; C) 2.6 mm/21 mm; D) 3.4 mm/37 mm.

Fig. 4.8. Histograms of bifurcation angles φ after Kuhn (2011). A) Steinheim shatter cones in limestone display acute subcones (mode: 26°, median: 35°). B) Siljan shatter cones in granite show an unskewed distribution of subcone angles b (mode: 45°, median: 44.5°). C) Shatter cones from Charlevoix have subcone angles b with a mode of 53° and a median of 50°. D) The subcones of shatter cones from the Marquez Dome formed in marly limestone are acute- angled with a mode of 31° and a median of 28°.

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4.8 Results The model is visualized in Figure 4.11 where three cycles of bifurcation (n = 4) are shown. The resulting geometry is entirely governed by the convexity of the ridges ß. The initial cone is reproduced in each bifurcation cycle at double quantity. The striations always follow the crest line of the ridges. Each sub- cone adapts to the parent cone and is therefore asymmetric. This has the consequence that the cone axis is tilted with respect to its base (simple shear). Figure 4.11 only displays one segment of angle ß of a full cone. The geometric construction of the model shows that ridges that bifurcate may start to interpenetrate with neighboring ridges from a certain generation onward. However this strongly depends on the sub-cone angle ß. If ß, for instance, is 120° (Figs. 4.10, 4.11d) this starts to occur after the first bifurcation when the cones are growing (n=2). The mutual interpenetration of curved fractures is also observed in natural shatter cones (Figs. 4.1a, 4.2a), where they can reach deep into the cone's interior. Figure 4.12 shows the resulting overall geometries for shatter cones with 9 cycles of bifurcation (n=10), where the final number of sub-cone ridges has accumulated to N = 512 in one cone segment of angle ß. Note that the master cone apex is in the origin of coordinates. The overall cone concavity increases with increasing convexity (ß) of the sub‐ cones due to the stronger vertical shortening (Eq. 6). For sub-cones with a gentle convexity of 30° the resulting shatter cones are almost perfect linear cones. If the sub-cone angle ß is large, the resulting shatter cone gets a concave or trumpet shape. At increasing order, increasingly large horizontal bars give the range of radius of the shatter cone. The bars refer to the outer radius of the innermost ridge, the mean outer radius, and the outer radius of the outermost ridge of the respective generation. The solid lines describe the approximation by Eq. 10. The master-cone angle can be chosen arbitrarily, but this influences the angle of bifurcation  (Fig. 4.13). Straight cones generally show acute‐ angled bifurcations and sub‐ cone ridges of low curvature. Bifurcation angles remain constant, even at higher orders. In contrast, pronounced convex sub‐ cone curvatures (ß > 90°) lead to successive opening of bifurcation angles with increasing distance from the shatter cone apex, in particular if the first-order apex angle ranges between 15-75°. Fig.4.9. Basic geometric outline of the model perpendicular to the

axis of the enveloping cone showing how the traces of the subcones develop from the first order to the second order.

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4.9 Discussion Our phenomenological model is based on a simple principle, namely the permanent bifurcation of fractures that have curved geometries. This model deduces the main morphological characteristics of shatter cones which are: (i) apex, (ii) sub-cone ridges of hierarchical order, and (iii) cone geometry with horse- tailing effect. The standard shatter cone shows a downward decrease in slope (trumpet-shape) that is known as horse-tailing. The sub-cone convexity ß and the master-cone angle  determine how rapidly this effect emerges. Our geometric model has a limitation that occurs when Z is not growing from one bifurcation cycle to the next. In other words when the cone slope asymptotical approaches zero. Such shatter cone morphologies are unknown from nature. This is due to the fact that crack branching and propagation in such an orientation are not any more supported by the tensile stress field in the hinterland of the shock wave. A propagation in this direction would mean that shear fractures instead of Mode I or mixed mode fractures, would occur. However, it appears reasonable that shatter cones will be modified when a reorganization of the transient stress field in the expanding crater floor takes place. This seems to correlate with the preferred formation of concentric fractures (Ahrens and Rubin, 1993). Probably this is a mechanism that is responsible for the formation of multiply- striated joint sets observed at the Vredefort Dome in South Africa (Nicholaysen and Reimold, 1999). Our model can be tested against natural shatter cones. Figure 4.13 displays the angles  and  of the shatter cones from Steinheim, Siljan and Charlevoix. The data for the Steinheim shatter cone () do not perfectly fit to the model; however they are in the range of error. Given that  and ß are measured correctly,  should be rather 45° than 35°. Multiple sources of error could be responsible for this slight discrepancy including a systematic error to determine the master-cone apex angle by measuring cone lineations. In particular at higher orders and large sub-cone angles ß the lineations do not necessarily point towards the apex. Data of measured , and  for the Siljan and Charlevoix shatter cones perfectly match the Fig.4.10. The first three generations of cones in plane view.

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with model results. For the Marquez shatter cone the apical angle  was not determined. Using our model and the ß and  measurements we obtain a relatively tight cone of about 70°. However, further measurements are required to validate the phenomenological model. It remains obscure why the branched fracture network forms curved instead of plane cracks. Probably, the convex curvature allows to better retain a fracture orientation that is suitable to accommodate tensile fracturing. Nevertheless deviations from the ideal tensile direction are unpreventable. Hence fractures develop from Mode I fractures to mixed mode fractures and shearing is expected to occur on the fracture surfaces. Bifurcation pushes the simultaneously formed fractures off each other and bring them in an orientation that is even more unfavorable with respect to “ideal” propagation direction as tensile fractures. The hypothetical symmetric branching scenario proposed in our model (Fig. 4.4) fundamentally differs from that of Sagy et al. (2002, 2004). Theoretical studies of dynamic crack branching need to prove if such a bifurcation style is feasible. It has a lot to commend it that symmetric instead of asymmetric branching takes place during shatter cone formation. The experimental study by Bieneawski (1968) (Fig.4.3) quite plainly showed that symmetric fracture branching in rock is possible and can lead to numerous bifurcation cycles. In contrast, the energy distribution in asymmetric crack branching (Sagy et al. 2002, 2004) is uneven with a minor component allocated to the spoon-like branch that will consequently cannot branch any further. The presented model is capable to model cones from almost straight to strongly concave slopes (trumpet shape). These shapes are a consequence of the horse-tailing effect observed at most shatter cones. Based on digital shape models Baratoux et al. (2016) describe shatter cones partly by single-sheet hyperboloids. This is in contrast to our measurements and the prediction from the phenomenological model. In any case, to cover these morphologies we will expand the model and may include hyperbolic functions to describe the morphologies of the sub-cone ridges. Natural shatter cone sometimes show several, very different, orientations at the centimeter to decimeter scale. Even antipodal shatter cones whose apices point in opposite directions occur and they are not rare. The orientation of the shatter cone reflects the propagation direction of the branched fracture network and thereby indicates the spatial variation of the propagating shock front. Causes for such strong deviations from a uniform shock front are inhomogeneities of the target. Reflection and refractions of shock waves occur within the target at different scales whenever impedance mismatches exist. The target may contain numerous lithological boundaries, inclined bedding planes, regional joint systems and tectonic shear zones, to mention just a few larger scale heterogeneities. The proposed model considers the dynamic fracture propagation from one direction only and describes the subsequent branched fracture network in a homogeneous rock. The model is not designed for the implementation of anisotropies, large-scale heterogeneities, or the superposition of various shatter cones. Previous studies have documented a wide range of shock pressures (2-30 GPa) at which shatter cones form. This study suggests that it is not the stress 113

magnitude alone that determines whether or not shatter cones form. It is also the rate of loading and unloading that may govern shatter cone formation through the rate dependency of the growing micro-cracks. If, on the one hand, the loading rate is too low, micro-cracks can coalesce to form larger fractures but the crack propagation velocity is too low to allow crack branching. If, on the other hand, the loading rate is too high, fractures cannot coalesce to form shatter cone fracture surfaces. These rocks are subjected to pulverization, which characterizes highly shocked rocks. Consequently, the rise and decay time to the pressure plateau may control the formation of shatter cones. Different rise and decay times may occur during attenuation of the shock wave as it laterally spreads. The abrupt and discontinuous ascent to a certain shock pressure level may smear in particular if the rock contains abundant impedance mismatches.

Fig. 4.11. Perspective view of the modeled cone segments. Three bifurcation cycles lead to the order n = 4. The curvature b of the subcone has a strong influence on the overall shape of the shatter cone.

Fig. 4.12. Vertical profiles through the model cones. Note that Fig. 4.13. Relationship between the enveloping cone apex angle the apex corresponds to the point of origin. The cones are a, the angle of bifurcation φ, and the curvature of the subcones visualized over 10 bifurcation cycles (10 orders) for different b for different orders n. Straight cones (red lines) generally subangles b. The error bars refer to the outer radius of the show acute-angled bifurcations and subcone ridges of low innermost ridge, the mean outer radius, and the outer radius of curvature. Bifurcation angles remain constant, even for higher the outermost ridge of the respective generation. The solid lines orders. In contrast, pronounced convex subcone curvatures (b > describe the approximation by Equation 7. The overall cone 90°) lead to a successive opening of bifurcation angles with concavity (horse-tailing) increases with increasing convexity of increasing distance from the shatter cone apex—in particular, if the subcones. For subcones with a gentle curvature of 30° the the first-order apex angle falls into the range between 15 and resulting enveloping cones have an almost constant slope without 75°. Data measurements on shatter cones from Charlevoix, concavity. Steinheim, and Siljan impact structures are given with error bars. 114

4.10 Conclusions We present a geometric model of shatter cone formation that reproduces various apical angles and linear or horse-tailing slopes. The model further includes a hierarchical sub-cone pattern that produces the well- known diverging grooves as intersection lineations between the adjacent sub-cones. The convexity of sub- cone ridges largely governs the overall cone geometry. It is believed that these sub-cone ridges represent rapidly propagating fractures. As these mixed mode fractures propagate at the trailing end of the shock wave at a velocity close to that of the Raleigh wave speed, symmetric bifurcation at the crack tip takes place at constant distances. A shatter cone is built up by numerous cycles of fracture bifurcation and ultimately leads to an exponential enlargement of the fracture surface. A heterogeneity at the tip of the apex that scales with the shock pulse is not required in our model.

4.11 Acknowledgement This work was conducted in the framework of the research unit MEMIN (FOR-887), grant KE-732/22-1 and we are grateful for ongoing support by the Deutsche Forschungs-Gemeinschaft DFG. Constructive reviews by L. Feriérre and D. Baratoux helped to improve the quality of the manuscript. We also thank U. Reimold for editing.

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Appendix A / List of Figures Figure 1.1: Overlay of the currently listed impact craters in the earth impact database in ArcGIS

Figure 1.2: Orbits of 1400 Potentially Hazardous Asteroids (PHAs) Figure 1.3: Fate of a large iron meteoroid Figure 1.4: Cumulative size-frequency calibration distribution for lunar impact craters

Figure 1.5: Schematic diagram of initial contact and compression phase shock Figure 1.6: Propagation of the shock front and associated change of state parameters Figure 1.7: Sketch of compression, excavation and modification of a simple and complex impact structure Figure 1.8: Oblique crater formation in iSALE Figure 1.9: Different shock metamorphic effects Figure 1.10: Shatter cone in nature and P-T diagram for shock metamorphism Figure 1.11: Pseudotachylites Figure 1.12: Pressure intervals with corresponding occurrence of shock effect Figure 1.13: PDFs and PFs Figure 1.14: Shock metamorphism for quartz and feldspar Figure 2.1. Schematic setup of a two-stage light gas gun Figure 2.2. Sandstone and quartzite cubes Figure 2.3. Sandstone block A15 Figure 2.4. Shatter cone fragments from the MEMIN experiment Figure 2.5. Sandstone block Figure 2.6. Pi-group plot for transient crater volumes for the MEMIN Figure 2.7. WLI scan of the shatter cone fragment Figure 2.8. Topographic profiles of the WLI measurements Figure 2.9. WLI profiles perpendicular to the symmetry Figure 2.10. Secondary electron microphotographs of shatter cone thin sections Figure 2.11. Secondary electron images of shatter cone surfaces Figure 2.12. Impact velocities plotted against the estimated kinetic energy Figure 3.1 Shatter cone fragments recovered from experiment A15

Figure 3.2 WLI scans of the shatter cone fragments

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Figure 3.2 WLI scans of a shatter cone surface from the Rochechouart impact structure Figure 3.4 SE images of a shatter cone surface from experiment E3 Figure 3.5 SE images of a shatter cone surface from experiment E3 Figure 3.6 SE images of a shatter cone surface from experiment E3-3384 Figure 3.7 SE image of a shatter cone melt surfaces Figure 3.8 BSE image of the shatter cone melt film Figure 3.9 Continuation along the shatter cone melt film Figure 3.10 Elemental distribution maps Figure 3.11 Elemental distribution maps Figure 3.12 Major-element compositions diagram Figure 3.13 SE image of the area selected for the TEM-foil preparation Figure 3.14 Low-magnification TEM-bright-field Figure 3.15 TEM images obtained from the TEM-foil Figure 3.16 Phases I-IV of gradual deformation along the shatter cone surface Figure 4.1 Large shatter cone formed in upper Jurassic micritic limestone Figure 4.2 Master-cones of the shatter cone assembly from Steinheim impact structure Figure 4.3. Photographic record of fracture propagation in a thin slice of norite Figure 4 Sketch illustrating the hypothetical bifurcation of propagating fractures in our model Figure 5 Digital elevation model of a 12 x 3 mm section of a Steinheim shatter cone Figure 6 Equal area stereographic plots of shatter cone lineations Figure 7 Histograms of bifurcation angles Figure 8 Sections perpendicular to the shatter cone master axis Figure 9 Basic geometry of the model of the first and second order in plane view. Figure 10 The first three generations of cones in plane view.

Figure 11. Perspective view of the modelled cone segments. Figure 12. Vertical profiles through the model cones. Figure 13 Relationship between the first-order apex angle, the angle of bifurcation, and the curvature

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Appendix B / List of Tables

Table 2.1. Experimental impact conditions for the MEMIN experiments.

Table 2.2. Typical kurtosis (Sku) values Table 2.3. Impact conditions for experiments that produced shatter cone fragments. Table 2.4. Comparison of experimental results from MEMIN with other impact experiments Table 3.1. Experimental impact conditions of MEMIN experiments with shatter cones. Table 3.2. Topography of shatter cones in experiment and nature.

Table 3.3. Representative EDX data of shatter cone melt coatings

Table 3.4. Representative WDX and EDX data of sectioned shatter cone melt coatings Table 4.1 Characteristics of the investigated shatter cone samples Table 4.2 Characterization of the investigated shatter cone samples.

Appendix C / Publication as third author (submitted)

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5. ROBUST OPTICAL TRACKING OF INDIVIDUAL EJECTA PARTICLES IN HYPERVELOCITY IMPACT EXPERIMENTS

This chapter has been submitted as peer-reviewed article as follow:

Gulde M., Kortmann L., Ebert M., Watson E., Wilk J., Schäfer F. (submitted) Robust optical tracking of individual ejecta particles in hypervelocity impact experiments. Meteoritics & Planetary Science.

5.1 Abstract New insights into the kinematics of ejecta clouds and the dynamics of crater formation are gained from the introduction of an approach to track individual particles ejected from a horizontal hypervelocity impact of a 2 mm aluminum sphere at 6.3 km/s into vertically aligned Carrara marble. Particle trajectories are determined with 500 ns temporal resolution inside a 1 - 2 mm thick laser light sheet illuminating a single plane within the ejecta plume. In contrast to optical flow analysis, the methodology presented here enables us to track individual particles instead of relying on field averaged information. This is realized by correlating particles not via their geometric shape but through their trajectory directly. It robustly identifies even partially obscured or strongly tumbling particles, allowing for a comprehensive physical description of the highly dynamical excavation process based on the precise determination of position, time, and ejection velocity of each individual particle. Specifically, we find ejecta particles launched in a short window of about 0 - 25 µs after impact and up to a radial distance of 10 mm from the impact location. During this time interval, the transient crater radius grows from 2±1 mm to 6±2 mm. Velocities between 70 m/s and 1 km/s are observed and reveal a substantial steepening of the ejecta curtain within 15 µs after the impact. We additionally determine the particle size and find a µ-parameter of 0.6 for Carrara marble which is consistent with theoretical predictions for nonporous materials.

5.2 Introduction The formation and evolution of solid bodies in our solar system have been dominated by hypervelocity impacts (Housen et al. 1983). Apart from the evolved hemispherical cavity, the ejecta blanket is the second most conspicuous feature of an impact process. Mass, size, and velocity distribution of the ejecta debris are key characteristics for describing the physical processes within the ejecta plume during the highly dynamic excavation stage of the crater formation (Housen and Holsapple 2011; Melosh 1989). Since

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meteorite impacts are inherently challenging to investigate directly in nature (with few exceptions, e.g., the collision of Shoemaker-Levy 9 with Jupiter), several mechanical and optical methods have been developed to study transient impact events in the laboratory. In the pioneering study of Piekutowski et al. (1977) a light sheet perpendicular to the target surface has been used to obtain the particle motion information within a single plane of the ejecta plume. In subsequent years, this Laser Light Sheet (LLS) technique has been improved on, e.g., by the use of fast digital image sensors (Barnouin-Jha et al. 2007; Cintala et al. 1999) and optical flow-field techniques (Anderson et al. 2003; Heineck et al. 2002; Hermalyn et al. 2008). All of these experimental studies deal with the ejection process in a gravity-dominated regime; hence, they used unconsolidated target material, e.g., quartz sand (Cintala et al. 1999; Anderson et al. 2003) or glass beads (Barnouin-Jha et al. 2007). The response of small bodies to impacts is governed by either gravity or material strength, depending on their relative magnitudes (Holsapple and Housen 2007). Generally, cratering at large sizes is gravity dominated, but at small scales is strength dominated. Three experimental impact studies focused on ejecta velocity distributions by using strength dominated targets: Gault et al. (1963) impacted basalt with Al spheres at 6.25 km/s; Housen (1992) used weakly cemented basalt as targets and impacted Al projectiles at 1.9 km/s; Michikami et al. (2007) sintered glass beads to produce solid targets with different porosities, which were then impacted with Al projectiles at speeds ranging from 1.2 to 4.5 km/s. In these studies, the authors employed high-speed framing cameras (without LLS- or optical flow field techniques) in order to record the excavation process and extract the corresponding ejecta velocities. Especially, Michikami et al. (2007) emphasized significant problems in measuring these velocities using the different frames of the high-speed camera. In this case, the velocity of most of the individual fragments could not be measured, because most ejecta were too small and the ejecta trajectories overlap each other in the field of view due to one directional observation (Michikami et al. 2007). However, identifying and tracking individual particles over several recorded pictures still poses a challenge, especially when particles are partially obstructed or tumbling. In this study, we present a novel approach for the robust identification and characterization of individual ejecta particles. Specifically, we do not rely on cross-correlation to determine field averaged velocity information as in optical flow methods, but can individually track even very small particles with high accuracy. In the following, we describe in detail the applied methodology and present the results from a horizontally moving 2 mm Al sphere impacting perpendicularly on solid non-porous Carrara marble at 6.3 km/s.

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5.3 Methodology

5.3.1 Experimental setup In the present experiment, we employ a 18 W continuous wave (CW) laser with a center wavelength of 532 nm to illuminate a single plane within the ejecta plume (Fig. 5.1). Specifically, the laser beam is guided through an LLS optical assembly to generate a 1 - 2 mm thick light sheet. This sheet passes through the center of the future impact region and is aligned perpendicularly to the target surface and coplanar to the camera’s field of view (FOV). The target surface is aligned vertically, i.e., parallel to the gravity vector.

Fig. 5.1 Experimental setup, gravity vector indicated by g. CW laser beam passes through LLS optics (LLSO) to illuminate thin plane within ejecta plume. FOV recorded by high-speed camera, ejecta collected in catchers. LoF: Line of fire. PS1/2: Photoelectric sensors. M: Mirror.

We employ a high-speed complementary metal-oxide-semiconductor camera with micro- to nanosecond exposure times to capture the ejecta trajectories of particles propagating through the light sheet during the impact event. In the case of an impact perpendicular to the target surface, the ejecta distribution is cylindrically symmetric. Hence, the spatial resolution can be maximized by observing only one-half of the emerging ejecta plume after the impact. In particular, we set the FOV such that its borders align with the line of fire on one and the target’s surface on the other side. In the current setup, the size of the FOV can be varied between 4 x 2.5 cm² and 8 x 5 cm². In the experiment, an aluminum sphere with 2 mm diameter is accelerated to a velocity of 6.3 km/s and impacted perpendicularly on a cubic Carrara marble block in vacuum. The impact is conducted using a horizontal two stage light-gas gun at Fraunhofer EMI . The gun’s functional principle is detailed in Lexow et al. (2013) and references within. The experimental parameters as used in the following analysis are detailed in Tab. 5.1.

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To assure a correct triggering of the camera, two photoelectric sensors measure the projectile’s speed in free flight and calculate the respective time of impact on the target surface. Complementary to the measurements of the high-speed camera, vertical ejecta catchers made from phenolic foam and vaseline are situated 30 cm away from the target surface to collect ejected particles for manual analysis.

Table 5.1: Experimental parameters employed in the analysis.

Projectile Al, spherical, 2 mm diameter (a = 1 mm)

Carrara marble block (25 cm edge length) Density: 2.7 g/cm³ Porosity: < 1 % Target properties Uniaxial compressive strength: 60 ± 8 MPa Tensile strength: 7.3 ± 2.6 MPa Young’s Modulus: 17.0 ± 3.4 GPa*

Impact velocity U = 6.3 km/s

Recording 120 images in 240 µs, 500 ns exposure time, FOV: 4.2 x 2.6 cm2

Illumination 18 Watt continuous -wave at 532 nm

Environment 20 °C, 104 Pa ambient pressure *Poelchau et al. (2015)

5.3.2 Particle tracking In the following, we record the dynamics of the ejecta during and after the impact. Specifically, we identify individual particle occurrences in every recorded frame. Subsequently, occurrences from different frames are correlated using basic physical assumptions about the ejecta trajectory. In a first step, to extract the trajectory and velocity of each individual particle, the particle occurrences are determined for every recorded frame by finding local brightness maxima (Fig. 5.2A, detailed description in the Supporting Information). In addition to the particle’s position within the light sheet, its timestamp is saved so that each found maxima has a unique coordinate triple in position-time (XYT) space. Notably, in the current experiment, we focused on the fast ejecta and excluded frame volumes displaying spallation (see Supporting Information). Up to this point, there is no connection between detected particle occurrences from different frames. Before correlating individual particles, we make certain assumptions about the trajectories.

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Fig. 5.2 A: XYT point cloud plot, axes orientation with respect to target surface. Gravity vector indicated by g. Detected particle occurrences (blue dots) and exemplary, calculated particle trajectory (large red dots). Orange dot: impact position. B: Exemplary frames from particle path as displayed in A. Target surface indicated by blue line. Particle position and velocity illustrated by red arrow on particle trajectory (black dashed line). Insets display instantaneous particle velocity and magnified region around particle, line of fire from left to right. Dynamic range optimized for each frame individually.

(i) Within the experimentally observed time frame and FOV, Particles experience very little deceleration, which would manifest itself as slight upward bends in XYT space (Fig. 5.2A). However, this effect is too small to be made out without in-depth analysis. Physically, particle deceleration is mostly caused by atmospheric braking. In the present experiment, the change in velocity for the longest 10 % of trajectories amounts to as little as 4 - 6 % between beginning and end of observation. This result agrees well with a rough estimate of the maximum atmospheric braking from theoretical considerations (Schultz and Gault 1982): vv = -38 airmarble cwsrejecta 2.4 % with air= 1.2 10-4 g/cm3and marble= 2.7 g/cm3 being the densities of air (at 20 °C and 104 Pa) and Carrara marble, respectively, cW5.7 the drag coefficient (for a small sphere travelling at v = 70 m/s (Haider and Levenspiel 1989)), s=2.5 cm the average length of the longest 10 % of trajectories found, and rejecta= 100 µm the ejecta radius. (ii) Particle propagation in the recording plane is not subjected to substantial directional change, e.g., from collisions with other ejecta or gravitational acceleration, and therefore manifests itself as lines. To check this assumption, particle trajectories can be qualitatively assessed via multiframe integration, similar to the technique employed by, e.g., Cintala et al. (1999). This allows a precise determination of the 127

trajectory shape, which in the current experiments displays no visible deviations from straight lines (Fig. 5.2A, B). Clearly, this has two main reasons: The experimental setup is such that gravity acts perpendicularly to the plane of observation. Substantial out-of-plane movement, if occurring, would ultimately result in particles moving out of the light field and hence not being observable any longer. However, at such high ejecta velocities as in the current experiment, the time span for crossing the camera’s FOV is too short for considerable particle movement in the vertical direction due to gravitational acceleration (cf. Tab. 5.1). Particularly, even at the lower end of the velocity distribution, particles could only fall at most few micrometers and are thus unable to move out of the LLS volume. Additionally, adjacent particles move in similar directions, therefore minimizing the probability and impact of inter-particle collisions. With particles moving in lines in the xy-plane as well as the absence of strong deceleration effects, particle trajectories can be well approximated as lines in XYT space, too. Hence, the correlation between particle occurrences found in different frames is performed by finding these lines within the XYT point cloud (Fig. 5.2A). Specifically, an iterative RANdom SAmple Consensus (RANSAC) algorithm is applied (Fischler and Bolles 1981): Pairs of points in XYT space are used to generate lines within the point cloud. All points within a certain threshold distance perpendicular to such a line are labeled inliers, whereas all other points are outliers. If an initial point pair and the respective connecting line results in a sufficiently large number of inliers in a sequence of frames, the line is considered a particle trajectory (Fig. 5.2B, dashed black lines). As an additional constraint, particle trajectories are only considered valid if subsequent observations of the same particle are not further apart than 20 µs (i.e., 10 frames, not observed during the analysis). This ensures that no false correlations are made between different particles. A detailed description of the correlation method is found in the Supporting Information. To minimize the overall computation time for large point clouds with some ten thousand detected particle occurrences, the algorithm is performed in parallel on a graphics processing unit. After a line is positively identified as a particle trajectory, the exact line position is optimized by linear regression of all inliers. In order to establish a one-to-one correspondence between particles and lines, coordinates from identified particle trajectories are removed from the point cloud in future searches. The algorithm starts out searching for long trajectories first and subsequently reduces the number of minimally required inliers, until no more lines can be identified. Since it is possible to accidentally find false trajectories, given the large number of points in the XYT cloud, their validity is tested against some basic physical assumptions, including the particle’s maximum velocity, its propagation direction, as well as the XYT line slope in comparison to the other slopes in the immediate vicinity. In the current experiment, this results in the rejection of around 2 % of all trajectories. Some exemplary frames with particle positions determined via their trajectory intersection are displayed in Fig. 5.2B. 128

5.4 Results and discussion

5.4.1 Launch time and position Once a set of trajectories and velocities is established for a given XYT point cloud, the particles are backpropagated to find their original launch position and time, defined as its XYT coordinates upon leaving the pre-impact target surface. Even though the deceleration does not lead to a visible deviation of the trajectory from a line shape, it does influence the launch coordinates of the ejected particle. To account for this effect, we assume a uniform deceleration of the particles (e.g. Schultz and Gault 1982) with mean velocity vejecta and radius rejecta of:

abrake= -3/8 airmarble cw vejecta2/ rejecta -810-5 vejecta2/ rejecta.

Trajectories of particles with negative starting positions or times with respect to the impact are removed, which leads to the exclusion of around 5 % of the total trajectories. Figures 3A and B display the resulting distributions of observed starting times and positions, respectively.

Fig. 5.3 Distribution of backpropagated launch times (A) and launch positions (B) of recorded particles. N = 734. Upper abscissa dimensionless.

Even though ejecta are tracked for a total timespan of more than 250 µs, launch times are within a narrow window of about 10 µs full width at half maximum, with earlier times clearly dominating the distribution (Fig. 5.3A). This result fits well with the formation time of the transient crater, which is estimated to take place on a time scale of few tens of microseconds. The launch position ranges from the impact point (x = 0) to around 10 mm with a maximum between 2 mm and 4 mm (Fig. 5.3B). Notably, nearly no particles are ejected below 1 mm. The results are consistent taking into account the projectile radius (1 mm) as the lower and the maximum transient crater radius (12 mm) as the upper limit for particle ejection. The maximum transient crater radius is determined by fitting a paraboloid of revolution into the

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final crater (Kenkmann et al. 2011; Dufresne et al. 2013). Details on the final crater are found in the Supporting Information. Assuming that ejecta mainly stems from the outer region of the forming crater, knowledge of the launch coordinates can be employed to get an estimate of the transient crater radius (Hermalyn and Schultz 2011). Figure 5.4 displays the median of launch position as a function of launch time. Few microseconds after the impact, the median ejection position is on the order of 2 mm and triples to about 6 mm after 25 µs. As visible in Fig. 5.3A, the number of particles ejected beyond 25 µs is very small and does not allow a reliable statement on the transient crater size after that time. Interestingly, we observe a substantial difference between the transient crater size when compared to the maximum transient crater size as determined after the experiment (Fig. 5.4, red dashed line). This indicates that the cratering process is not complete after 25 µs.

Fig. 5.4 Transient crater radius estimated from median ejecta launch position. Maximum transient crater radius indicated by dashed red line (12 mm). Upper abscissa and right ordinate dimensionless.

5.4.2 Particle velocity Trajectories in XYT space additionally carry the information about the instantaneous particle velocities. Figure 5.5A displays the speed distribution of particles, color-coded with the time of ejection. Within the manuscript, we use the term “velocity” whenever we refer to the vector properties of the particle’s movement, while “speed” designates the respective scalar quantity. Particle speeds range between 70 m/s and 1 km/s, whereas the majority of particles moves with speeds between 150 m/s and 400 m/s. While early ejecta (blue) displays evenly distributed speeds, later ejecta becomes significantly slower (red).

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Notably, the ejection angle also changes considerably with time, as can be examined in Fig. 5B. Here, the radial and perpendicular velocity components are shown independently, again color-coded with the time of ejection. During the cratering process, we observe a strong steepening of the ejecta curtain, visible by the increase in the ratio of perpendicular to radial velocity components. While the fast particles early after the impact move in a direction between 45° and 60°, later particles with lower velocities leave the target close to the surface normal. At this point, the underlying mechanics of this steepening remain an open question and will need to be investigated in more detail (Sommer et al. 2013; Hoerth et al. 2013).

Fig. 5.5 Velocity distribution color-coded as a function of time. A: Particle velocity distribution at time of ejection. B: Radial and perpendicular velocity components. Dashed lines indicate ejection angles of 45°, 60°, and 75° with respect to target surface. Upper abscissae and right ordinate dimensionless.

Figure 5.6 illustrates the observed behavior of median ejection speed as a function of launch position. Very close to the impact point, particle speeds are as high as 800 m/s and decrease quickly to below 200 m/s when ejected further away from the crater center. From dimensional analysis, we expect the relation to follow a power-law of the form

v x(-1/µ) with an exponent of µ 0.55 - 0.60 for nonporous materials as indicated by the dashed lines (Housen et al. 1983; Housen and Holsapple 2011).

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Fig. 5.6 Ejecta speed as a function of launch position. Power laws are illustrated by respective dashed lines. Upper abscissa and right ordinate dimensionless.

In an intermediate region between 2.0 mm and 4.5 mm away from the impact point, a µ-parameter of 0.6 describes the experimental data. However, we do not observe clean cutoffs as theoretically predicted. At early times and close to the impact point, when velocities are highest and particles smallest, particles are challenging to detect. We therefore likely underestimate the mean velocity of particles close to the impact point. In contrast, larger particles are well visible and hence overrepresented, causing a bias that may obstruct a possible clear cutoff at larger launch positions.

5.4.3 Particle size The trajectories in XYT space allow us to identify the respective particles in each frame. From here, we derive the particle size in two steps: First, we determine the visible particle area averaged over all frames which display occurrences of the particle. Second, assuming a spherical geometry and homogeneous density, we calculate the characteristic particle diameter and mass. Details on the algorithm are available in the Supporting Information. The inset in Fig. 5.7 displays the size distribution as derived from the image analysis (green line). The largest fraction of detected particles lies between 600 µm and 1.2 mm. Below 600 µm, the number of particles strongly decreases until the resolution threshold of the employed camera in the current setup at around 200 µm. As detailed above, this decrease stands in contrast to theoretical predictions and results from our limited capability to detect increasingly small particles below 500 µm (cf. Fig. 5.6). A manual size

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analysis of particles found within the ejecta catchers supports our assumption (inset Fig. 5.7, brown line). While the trend to find less particles with increasing size is qualitatively similar in both cases, the manual approach allows the detection of a large number of very small particles not accessible by the image analysis. Details on the manual particle size determination are found in the Supporting Information.

Fig. 5.7 Cumulative mass ratio of particles in LLS with speed larger than s. The functional relation between 200 m/s < v < 600 m/s is well described by a power-law (fit: dashed red line). Inset: Size distribution from image analysis (green line) compared to manual analysis from ejecta catchers (brown line). Upper abscissa dimensionless.

In dimensional analysis, the high-pressure properties of a material, as well as many dynamic characteristics of the excavation process, can be described by the µ-parameter, which scales the respective governing power-laws (cf. Fig. 5.6) (Holsapple and Schmidt 1987). Its determination poses an important test of the validity of our approach. Specifically, µ should lie between the theoretical limits of = 1/3 (so- called momentum scaling) and = 2/3 (so-called energy scaling). As mentioned above, nonporous materials such as marble are expected to have an exponent of close to = 0.6 (Housen and Holsapple 2011). The exponent can be derived in different ways, amongst others by determining the integrated mass of particles ejected with speeds larger than a given value as a function of speed (Fig. 5.7). In contrast to the particle size distribution, the cumulative mass plot agrees very well with theoretical predictions: for low speeds, the normalized curve plateaus at one and increasingly steepens for faster particles. Between 200 m/s and 600 m/s, the data is well described by a power law with a scaling factor of close to µ = 0.6. As predicted,

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the plot increasingly deviates from the power-law behavior for higher speeds. This is caused by the underestimation of small particles as discussed in Housen and Holsapple (2011).

5.5 Conclusion We have introduced a novel methodology to determine the trajectories and velocities of individual particles after hypervelocity impacts. Specifically, we can robustly correlate particles between frames, even when they display very heterogeneous surfaces, are strongly tumbling, or are partially obstructed. The approach is based on a small set of physically motivated assumptions and does not employ region-averaged flow fields for velocity determination. In contrast to correlation relying on changing two-dimensional particle projections, we identify particles via their unique trajectory in XYT space. This allow us to describe individual particles, making the approach a powerful tool for the observation of fast moving complex shapes such as the ejecta from hypervelocity impacts. The knowledge of the trajectory, velocity, and size of each individual particle allows a comprehensive description of the ejection dynamics with very high precision. We compared the results with available data as well as theoretical predictions and found them to be in very good agreement. In particular, we found a µ-parameter of 0.6 for Carrara marble, which is well in the range of values expected for such a low-porosity material and consistent with previous values from other methods. In the near future, we plan to extend this methodology to study different materials under various conditions. Especially, we would like to increase the spatial-temporal resolution to be able to more accurately track very fast, micrometer-sized particles such as those expected directly after the first contact between projectile and target (Yang and Ahrens 1995). More generally, we believe that the ability to reliably identify the dynamical key characteristics of fast moving particles will serve as an important enhancement in the experimental analysis of cratering processes as well as substantially support the validation of numerical impact models.

5.6 Acknowledgement This work has been supported by Deutsche Forschungsgemeinschaft (DFG) grants FOR 887, TH 805/4-2, SCHA 1612/1-2. We would like to thank Martin Hunzinger from Fraunhofer EMI for support in designing the experimental setup. We gratefully acknowledge support from Hans-Peter Osterer in conducting the experiments at the Fraunhofer EMI. Furthermore, we would like to thank Heiko Neumann from Ulm University and Pierre Bayerl from Airbus DS Electronics and Border Security GmbH for instrumental discussions on the point cloud approach. The clarity of this work’s presentation has greatly benefitted from the insightful recommendations of Jennifer Anderson from Winona State University.

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5.7 Associated content

Supporting Information Particle detection; Particle correlation via RANSAC; Trajectory length distribution; Particle size determination; Manual particle size determination; Crater volume; Videos of impact and point cloud generation; The Supporting Information is available online.

5.8 References

Anderson J. L., Schultz P. H., and Heineck, J. T. (2003). Asymmetry of ejecta flow during oblique impacts using three‐ dimensional particle image velocimetry. Journal of Geophysical Research: Planets, 108(E9):1-10

Barnouin-Jha O. S., Yamamoto S., Toriumi T., Sugita S., and Matsui, T. (2007). Non-intrusive measurements of crater growth. Icarus, 188(2), 506–521.

Cintala M. J., Berthoud L., and Hörz F. (1999). Ejection-velocity distributions from impacts into coarse-grained sand. Meteoritics & Planetary Science 34: 605–623.

Fischler M. A., and Bolles R. C. (1981). Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381-395.

Gault D. E., Quaide W. L., Oberbeck V. R. (1963). Spray ejected from the lunar surface by meteoroid impact. NASA Tech. Note D-1767.

Haider A. and Levenspiel O. (1989). Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technology 58.1: 63-70.

Heineck J. T., Schultz P. H., and Anderson J. L. B. (2002). Application of three-component PIV to the measurement of hypervelocity impact ejecta. J. Visualization 5(3):233–241.

Hermalyn, B., Schultz, P. H., Anderson, J. L. B., Heineck, J. T. (2008). Time-resolved Assessment of Ejecta-Mass Distribution Using 3D-PIV. 39th Lunar and Planetary Science Conference, pp. 2292.

Hermalyn B. and Schultz P. H. (2011). Time-resolved studies of hypervelocity vertical impacts into porous particulate targets: Effects of projectile density on early-time coupling and crater growth. Icarus 216:269–279.

Hoerth T., Schäfer F., Thoma K., Kenkmann T., Poelchau M. H., Lexow B., and Deutsch A. (2013). Hypervelocity impacts on dry and wet sandstone: Observations of ejecta dynamics and crater growth. Meteoritics and Planetary Science 48:23–32.

Holsapple K. A. and Housen K. R. (2007). A crater and its ejecta: An interpretation of Deep Impact. Icarus 191:586– 597.

Holsapple K. A. and Schmidt R. M. (1987). Point Source Solutions and Coupling Parameters in Cratering Mechanics. Journal of Geophysical Research 92:6350.

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Housen K. R. (1992). Crater ejecta velocities for impacts on rocky bodies. 23rd Lunar and Planetary Science Conference, pp. 555–556

Housen K. R. and Holsapple K. A. (2011). Ejecta from impact craters. Icarus 211(1):856-875.

Housen K. R., Schmidt R. M., and Holsapple K. A. (1983). Crater ejecta scaling laws: Fundamental forms based on dimensional analysis. Journal of Geophysical Research: Solid Earth 88(B3):2485-2499.

Kenkmann T., Wünnemann K., Deutsch A., Poelchau M. H., Schäfer F., and Thoma K. (2011). Impact cratering in sandstone: The MEMIN pilot study on the effect of pore water. Meteoritics & Planetary Science 46:890–902.

Lexow B., Wickert M., Thoma K., Schäfer F., Poelchau M. H., and Kenkmann T. (2013). The extra-large light-gas gun of the Fraunhofer EMI: Applications for impact cratering research. Meteoritics & Planetary Science 48: 3–7.

Melosh H. J. (1989). Impact cratering: A geologic process, New York: Oxford University Press. 253 p.

Michikami T., Moriguchi K., Hasegawa S., and Fujiwara A. (2007). Ejecta velocity distribution for impact cratering experiments on porous and low strength targets. Planetary and Space Science 55:70–88.

Piekutowski A. J., Andrews R. J., and Swift H. F. (1977). Studying small-scale explosive cratering phenomena photographically. 12th International Congress on High Speed Photography International Society for Optics and Photonics. pp. 177-183

Poelchau, M. H., Michalski, C., Deutsch, A., Thoma, K., Schäfer, F., & Kenkmann, T. (2015, March). Experimental Cratering in Carrara Marble: Latest Results from the MEMIN Research Unit. 46th Lunar and Planetary Science Conference, abstract #2447

Schultz, P. H., & Gault, D. E. (1982). Impact ejecta dynamics in an atmosphere: Experimental results and extrapolations. Geological Society of America Special Papers, 190, 153-174.

Sommer F., Reiser F., Dufresne A., Poelchau M. H., Hoerth T., Deutsch A., Kenkmann T., and Thoma K. (2013). Ejection behavior characteristics in experimental cratering in sandstone targets. Meteoritics and Planetary Science 48:33–49

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APPENDIX D / LIST OF THESIS RELATED-PUBLICATIONS

Peer-reviewed Articles: Wilk, J., and Kenkmann, T. (2016). Formation of shatter cones in MEMIN impact experiments. Meteoritics and Planetary Science 51 (8): 1477-1496. doi: 10.1111/maps.12682. Kenkmann T., Hergarten, S., Kuhn, T., and Wilk, J. (2016). Formation of shatter cones by symmetric fracture bifurcation: Phenomenological modeling and validation. Meteoritics and Planetary Science 51 (8): 1519-1533. doi: 10.1111/maps.12677. Wilk., J., Hamann, C., Fazio, A., Luther, R., Hecht, L., Langenhorst, F., and Kenkmann T. (submitted). Melt formation shatter cone recovered from the MEMIN impact experiments in sandstone. Meteoritics and Planetary Science. Max, G., Kortmann, L., Ebert, M., Wilk, J., and Schäfer, F. (submitted). Robust Optical Tracking of Individual Ejecta Particles in Hypervelocity Impact Experiments. Meteoritics and Planetary Science.

Conference Abstracts (as first author):

The Surface Structure of Shatter Cones in Natural and Experimental Impact Craters J.Wilk and T. Kenkmann GeoFrankfurt 2014, Session A04

The Surface Structure of Shatter Cones in Experimental Impact Craters J.Wilk and T. Kenkmann 46th Lunar and Planetary Science Conference 2015, Abstract #2637 http://www.hou.usra.edu/meetings/lpsc2015/pdf/2637.pdf

Formation of Shatter cones in the MEMIN Impact Experiments J.Wilk and T. Kenkmann 78th Annual Meeting of the Meteoritical Society 2015, Abstract #5102 MetSoc Abstract #5102 http://www.hou.usra.edu/meetings/metsoc2015/pdf/5102.pdf

Shatter Cones from the MEMIN Impact Experiments J.Wilk and T. Kenkmann Bridging the Gap III 2015, Abstract #1066 http://www.hou.usra.edu/meetings/gap2015/pdf/1066.pdf

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The Surface Structure of Shatter Cones in Experimental Impact Craters J.Wilk and T. Kenkmann GeoBerlin 2015, Session A3-02 http://gfzpublic.gfz- potsdam.de/pubman/item/escidoc:1314059:6/component/escidoc:1314081/Geoberlin_2015.pdf

Melt Formation on Shatter Cone Surfaces in Sandstone, Part I: Surface Morphology Wilk, J., Hamann, C., Kenkmann, T., Hecht, L. 47th Lunar and Planetary Science Conference 2016 Abstract No. #2636. http://www.hou.usra.edu/meetings/lpsc2016/pdf/2636.pdf

Melt Formation on Shatter Cone Surfaces Recovered from the MEMIN Hypervelocity Impact Experiments in Sandstone Wilk, J., Hamann, C., Hecht, L., Kenkmann, T. 79th Annual Meeting of the Meteoritical Society 2016 Abstract No. #6523.

Shatter Cone Formation in Experiments and Models and Implications to Nature T. Kenkmann, and J.Wilk Shock Workshop 2017: Shock metamorphism in terrestrial and extra-terrestrial rocks

New Insights into Shatter Cones Formation from MEMIN Experiments J.Wilk, T. Kenkmann, and C. Hamann European Planetary Science Congress 2017

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APPENDIX E / STATEMENT OF AUTHORSHIP

I hereby certify that this thesis has been composed by myself and describes my own work unless otherwise acknowledged in the text. All references and verbatim extracts have been quoted and all sources of information have been specifically acknowledged. This thesis has not been accepted in any previous application for a degree.

Ich erkläre hiermit, dass ich die vorliegende Arbeit ohne unzulässige Hilfe Dritter und ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe. Die aus anderen Quellen direkt oder indirekt übernommenen Daten und Konzepte sind unter Angabe der Quelle gekennzeichnet. Insbesondere habe ich hierfür nicht die entgeltliche Hilfe von Vermittlungs- bzw. Beratungsdiensten (Promotionsberaterin / -berater oder anderer Helferinnen / Helfer) in Anspruch genommen. Die Arbeit wurde bisher weder im In- noch im Ausland in gleicher oder ähnlicher Form einer anderen Prüfungsbehörde vorgelegt.

Freiburg, den ______Unterschrift: ______

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