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Balcite (Ba x Ca 1− x CO 3 ) is a synthetic analog of rhombohedral carbonate minerals like calcite and dolomite that is disordered on both the cation and anion sublattices. Here, we show that multiple exotic superlattice structures, including a dolomite analog that we call balcomite, can form from balcite at elevated temperatures. The second-order balcite-to-balcomite conversion at temperatures between 150–600 °C is driven by the preference of barium and calcium for different oxygen coordination numbers and facilitated by local carbonate reorientation. At elevated pressure, further superlattice order arises from cation segregation in all three dimensions, producing a supercell with the same R 3̄ m symmetry as balcite but 6× larger. This highly ordered structure relaxes back to the balcomite structure upon returning to ambient conditions. None of the three naturally occurring polymorphs of Ba 0.5 Ca 0.5 CO 3 (alstonite, paralstonite, barytocalcite) formed from balcite despite being putatively energetically favored. Instead, alstonite transformed to a balcomite-like structure via a first-order process after transiently converting to a paralstonite-like structure via a second-order process. Together, these results show that high temperature transformation pathways between structures in the barium calcium carbonate system can be driven by coarsening and are facilitated by similarity in short-range order, conceptually analogous to previously described low-temperature transformations. Many of the exotic high temperature carbonate structures are unstable, but may participate in transformation pathways between naturally observed metastable mineral phases, suggesting important roles for ephemeral phases in shaping past and current mineral distributions. 

Strongly consistent distributed systems are easy to reason about but face fundamental limitations in availability and performance. Weakly consistent systems can be implemented with very high performance but place a burden on the application developer to reason about complex interleavings of execution. Invariant confluence provides a formal framework for understanding when we can get the best of both worlds. An invariant confluent object can be efficiently replicated with no coordination needed to preserve its invariants. However, actually determining whether or not an object is invariant confluent is challenging. In this paper, we establish conditions under which a commonly used sufficient condition for invariant confluence is both necessary and sufficient, and we use this condition to design a general-purpose interactive invariant confluence decision procedure. We then take a step beyond invariant confluence and introduce a generalization of invariant confluence, called segmented invariant confluence, that allows us to replicate non-invariant confluent objects with a small amount of coordination. We implement these formalisms in a prototype called Lucy and find that our decision procedures efficiently handle common real-world workloads including foreign keys, escrow transactions, and more. 

Systematically reasoning about the fine-grained causes of events in a real-world distributed system is challenging. Causality, from the distributed systems literature, can be used to compute the causal history of an arbitrary event in a distributed system, but the event's causal history is an over-approximation of the true causes. Data provenance, from the database literature, precisely describes why a particular tuple appears in the output of a relational query, but data provenance is limited to the domain of static relational databases. In this paper, we present wat-provenance: a novel form of provenance that provides the benefits of causality and data provenance. Given an arbitrary state machine, wat-provenance describes why the state machine produces a particular output when given a particular input. This enables system developers to reason about the causes of events in real-world distributed systems. We observe that automatically extracting the wat-provenance of a state machine is often infeasible. Fortunately, many distributed systems components have simple interfaces from which a developer can directly specify wat-provenance using a technique we call wat-provenance specifications. Leveraging the theoretical foundations of wat-provenance, we implement a prototype distributed debugging framework called Watermelon. 

Abstract The direct observation of amorphous barium carbonate (ABC), which transforms into a previously unknown barium carbonate hydrate (herewith named gortatowskite) within a few hundred milliseconds of formation, is described. In situ X‐ray scattering, cryo‐, and low‐dose electron microscopy were used to capture the transformation of nanoparticulate ABC into gortatowskite crystals, highly anisotropic sheets that are up to 1 μm in width, yet only about 10 nm in thickness. Recrystallization of gortatowskite to witherite starts within 30 seconds. We describe a bulk synthesis and report a first assessment of the composition, vibrational spectra, and structure of gortatowskite. Our findings indicate that transient amorphous and crystalline precursors can play a role in aqueous precipitation pathways that may often be overlooked owing to their extremely short lifetimes and small dimensions. However, such transient precursors may be integral to the formation of more stable phases.