Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host

Raman elastic thermobarometry has recently been applied in many petrological studies to recover the pressure and temperature (P–T) conditions of mineral inclusion entrapment. Existing modelling methods in petrology either adopt an assumption of a spherical, isotropic inclusion embedded in an isotropic, infinite host or use numerical techniques such as the finite-element method to simulate the residual stress and strain state preserved in the non-spherical anisotropic inclusions. Here, we use the Eshelby solution to develop an analytical framework for calculating the residual stress and strain state of an elastically anisotropic, ellipsoidal inclusion in an infinite, isotropic host. The analytical solution is applicable to any class of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit expressions are derived for some symmetry classes, including tetragonal, hexagonal, and trigonal. The effect of changing the aspect ratio on residual stress is investigated, including quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Quartz is demonstrated to be the least affected, while rutile is the most affected. For prolate quartz inclusion (c axis longer than a axis), the effect of varying the aspect ratio on Raman shift is demonstrated to be insignificant. When c/a=5, only ca. 0.3 cm−1 wavenumber variation is induced as compared to the spherical inclusion shape. For oblate quartz inclusions, the effect is more significant, when c/a=0.5, ca. 0.8 cm−1 wavenumber variation for the 464 cm−1 band is induced compared to the reference spherical inclusion case. We also show that it is possible to fit an effective ellipsoid to obtain a proxy for the averaged residual stress or strain within a faceted inclusion. The difference between the volumetrically averaged stress of a faceted inclusion and the analytically calculated stress from the best-fitted effective ellipsoid is calculated to obtain the root-mean-square deviation (RMSD) for quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random crystallographic orientation) faceted inclusions, we show that the volumetrically averaged stress serves as an excellent stress measure and the associated RMSD is less than 2 %, except for diamond, which has a systematically higher RMSD (ca. 8 %). This expands the applicability of the analytical solution for any arbitrary inclusion shape in practical Raman measurements

Organizational structure and communication networks in a university environment

The ``six degrees of separation" between any two individuals on Earth has become emblematic of the 'small world' theme, even though the information conveyed via a chain of human encounters decays very rapidly with increasing chain length, and diffusion of information via this process may be very inefficient in large human organizations. The information flow on a communication network in a large organization, the University of Oslo, has been studied by analyzing e-mail records. The records allow for quantification of communication intensity across organizational levels and between organizational units (referred to as ``modules"). We find that the number of e-mails messages within modules scales with module size to the power of $1.29\pm .06$, and the frequency of communication between individuals decays exponentially with the number of links required upwards in the organizational hierarchy before they are connected. Our data also indicates that the number of messages sent by administrative units is proportional to the number of individuals at lower levels in the administrative hierarchy, and the ``divergence of information" within modules is associated with this linear relationship. The observed scaling is consistent with a hierarchical system in which individuals far apart in the organization interact little with each other and receive a disproportionate number of messages from higher levels in the administrative hierarchy.Comment: 9 pages, 3 figure

The mechanism of porosity formation during solvent-mediated phase transformations

Solvent-mediated solid-solid phase transformations often result in the formation of a porous medium, which may be stable on long time scales or undergo ripening and consolidation. We have studied replace- ment processes in the KBr-KCl-H2O system using both in situ and ex situ experiments. The replacement of a KBr crystal by a K(Br,Cl) solid solution in the presence of an aqueous solution is facilitated by the gen- eration of a surprisingly stable, highly anisotropic and connected pore structure that pervades the product phase. This pore structure ensures efficient solute transport from the bulk solution to the reacting KBr and K(Br,Cl) surfaces. The compositional profile of the K(Br,Cl) solid solu- tion exhibits striking discontinuities across disc-like cavities in the product phase. Similar transformation mechanisms are probably important in con- trolling phase transformation processes and rates in a variety of natural and man-made systems.Comment: 22 pages, 7 figure

Volume changes in solids induced by chemical alteration

It is a fundamental issue in material science to understand the mechanical effects of chemical alterations. Often the replacement of one chemical component by another in a solid induces local volume changes. Experiments on chemical alteration in “model” materials reveal an intricate dynamics of elastic stress build-up, fracturing and creation of porosity. In that way permeability is increased and provides a positive feedback on the process rate. Important examples from geology are presented

Reservoir properties and reactivity of the Faroe Islands Basalt Group : Investigating the potential for CO2 storage in the North Atlantic Igneous Province

Funding Information: We acknowledge funding from the University of Oslo through the Department of Geosciences, the European Research Council (ERC) through the ERC Advanced Grant Disequilibrium metamorphism of stressed lithosphere (DIME) (ERC-2015-AdG_669972), the Cambridge Arctic Shelf Program (CASP) through the Andrew Whitham CASP Fieldwork Awards 2020, and the Faculty of Mathematics and Natural Sciences at the University of Oslo through the project CO2Basalt. S. Planke acknowledges support from the Norwegian Research Council through center of Excellence funding to CEED (project no. 223272). H. J. Kjøll acknowledges AkerBP for funding through the project 8040 Paleocene. In addition, we thank the University of Iceland for covering the costs of the kinetic experiments. We would like to thank the Faroese Geological Survey (Jarðfeingi), Øyvind Hammer at the Museum of Natural History (Norway), Benjamin Bellwald at Volcanic Basin Energy Research (VBER), John Aiken from the Njord center, and Benoit Cordonnier from the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, for their contributions to the project. Finally, we thank Sigurður Gíslason and the Carbfix team for providing laboratory facilities and assistance during part of this research. Funding Information: We acknowledge funding from the University of Oslo through the Department of Geosciences, the European Research Council (ERC) through the ERC Advanced Grant Disequilibrium metamorphism of stressed lithosphere (DIME) ( ERC-2015-AdG_669972 ), the Cambridge Arctic Shelf Program (CASP) through the Andrew Whitham CASP Fieldwork Awards 2020, and the Faculty of Mathematics and Natural Sciences at the University of Oslo through the project CO2Basalt. S. Planke acknowledges support from the Norwegian Research Council through center of Excellence funding to CEED (project no. 223272 ). H. J. Kjøll acknowledges AkerBP for funding through the project 8040 Paleocene. In addition, we thank the University of Iceland for covering the costs of the kinetic experiments. We would like to thank the Faroese Geological Survey (Jarðfeingi), Øyvind Hammer at the Museum of Natural History (Norway), Benjamin Bellwald at Volcanic Basin Energy Research (VBER), John Aiken from the Njord center, and Benoit Cordonnier from the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, for their contributions to the project. Finally, we thank Sigurður Gíslason and the Carbfix team for providing laboratory facilities and assistance during part of this research.Peer reviewedPublisher PD

Continental crust beneath southeast Iceland

The magmatic activity (0–16 Ma) in Iceland is linked to a deep mantle plume that has been active for the past 62 My. Icelandic and northeast Atlantic basalts contain variable proportions of two enriched components, interpreted as recycled oceanic crust supplied by the plume, and subcontinental lithospheric mantle derived from the nearby continental margins. A restricted area in southeast Iceland—and especially the Öræfajökull volcano—is characterized by a unique enriched-mantle component (EM2-like) with elevated 87Sr/86Sr and 207Pb/204Pb. Here, we demonstrate through modeling of Sr–Nd–Pb abundances and isotope ratios that the primitive Öræfajökull melts could have assimilated 2–6% of underlying continental crust before differentiating to more evolved melts. From inversion of gravity anomaly data (crustal thickness), analysis of regional magnetic data, and plate reconstructions, we propose that continental crust beneath southeast Iceland is part of ∼350-km-long and 70-km-wide extension of the Jan Mayen Microcontinent (JMM). The extended JMM was marginal to East Greenland but detached in the Early Eocene (between 52 and 47 Mya); by the Oligocene (27 Mya), all parts of the JMM permanently became part of the Eurasian plate following a westward ridge jump in the direction of the Iceland plume

Structures Related to the Emplacement of Shallow-Level Intrusions

A systematic view of the vast nomenclature used to describe the structures of shallow-level intrusions is presented here. Structures are organised in four main groups, according to logical breaks in the timing of magma emplacement, independent of the scales of features: (1) Intrusion-related structures, formed as the magma is making space and then develops into its intrusion shape; (2) Magmatic flow-related structures, developed as magma moves with suspended crystals that are free to rotate; (3) Solid-state, flow-related structures that formed in portions of the intrusions affected by continuing flow of nearby magma, therefore considered to have a syn-magmatic, non-tectonic origin; (4) Thermal and fragmental structures, related to creation of space and impact on host materials. This scheme appears as a rational organisation, helpful in describing and interpreting the large variety of structures observed in shallow-level intrusions