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Abstract In this paper, we are interested in the following question: given an arbitrary Steiner triple systemonvertices and any 3‐uniform hypertreeonvertices, is it necessary thatcontainsas a subgraph provided? We show the answer is positive for a class of hypertrees and conjecture that the answer is always positive.
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High‐resolution microstructural and compositional analyses of shock deformed apatite from the peak ring of the Chicxulub impact crater
Abstract The mineral apatite, Ca5(PO4)3(F,Cl,OH), is a ubiquitous accessory mineral, with its volatile content and isotopic compositions used to interpret the evolution of H2O on planetary bodies. During hypervelocity impact, extreme pressures shock target rocks resulting in deformation of minerals; however, relatively few microstructural studies of apatite have been undertaken. Given its widespread distribution in the solar system, it is important to understand how apatite responds to progressive shock metamorphism. Here, we present detailed microstructural analyses of shock deformation in ~560 apatite grains throughout ~550 m of shocked granitoid rock from the peak ring of the Chicxulub impact structure, Mexico. A combination of high‐resolution backscattered electron (BSE) imaging, electron backscatter diffraction mapping, transmission Kikuchi diffraction mapping, and transmission electron microscopy is used to characterize deformation within apatite grains. Systematic, crystallographically controlled deformation bands are present within apatite, consistent with tilt boundaries that contain the <c> (axis) and result from slip in <> (direction) on(plane) during shock deformation. Deformation bands contain complex subgrain domains, isolated dislocations, and low‐angle boundaries of ~1° to 2°. Planar fractures within apatite form conjugate sets that are oriented within either {, {, {, or. Complementary electron microprobe analyses (EPMA) of a subset of recrystallized and partially recrystallized apatite grains show that there is an apparent change in MgO content in shock‐recrystallized apatite compositions. This study shows that the response of apatite to shock deformation can be highly variable, and that application of a combined microstructural and chemical analysis workflow can reveal complex deformation histories in apatite grains, some of which result in changes to crystal structure and composition, which are important for understanding the genesis of apatite in both terrestrial and extraterrestrial environments.
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- PAR ID:
- 10456817
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Meteoritics & Planetary Science
- Volume:
- 55
- Issue:
- 8
- ISSN:
- 1086-9379
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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