Contributions of multiple climate hazards and overgrazing to the 2009/2010 winter disaster in Mongolia

Mongolian pastoral husbandry is subject to various climate hazards such as dzud (Mongolian for “severe winter conditions”). Dzud in the 2009/2010 winter affected 80.9% of the country and killed more than 10 million livestock (23.4% of the total). To understand the natural and man-made mechanisms of this dzud, we examined the contributions of dzud-causing factors such as climate hazards (cold temperatures and heavy snow) and winter–spring livestock grazing (measured as overgrazing rate), which created a distinct regional pattern of high livestock mortality using a regression tree method. The regression tree model accounted for 58% of the total spatial variation of the mortality and identified various types of dzud in each region. Results showed that during the 2009/2010 winter, almost all of Mongolia experienced extreme cold temperatures, with abnormally large amounts of snow. In addition, more than half of the territory was overgrazed because of the lower pasture biomass resulting from summer drought and livestock overpopulation. At the regional scale, high livestock mortalities occurred in moderately to heavily overgrazed regions in south-central and western Mongolia, resulting from the combination of these factors. Conversely, areas with lower livestock mortalities (or non-dzud) coincided with sufficient pasture capacity in the north and east, even under extreme cold and snow. This indicates the importance of controlling the number of livestock to below the pasture carrying capacity regardless of an inter-annually varying climate. Moreover, we identified critical thresholds of each factor across which serious disasters occurred. These thresholds are practically useful for future livestock management of pasture land.     

Livestock productivity as indicator of vulnerability to climate hazards: a Mongolian case study

Mongolia is subject to regular peaks of livestock winter mortality called dzuds. Several kinds of dzud exist and the ‘white dzud’, characterized by heavy stochastic snowfalls preventing livestock to access forage, is considered the most common. Droughts and high livestock densities are thought to be part of the dzud process by affecting body condition, which increases vulnerability to snowfalls. Guided by the equilibrium/nonequilibrium framework, we studied how rainfall, animal numbers and pasture health (defined as the integrity of ecological processes sustaining grass growth) impact livestock body condition in a case study of West Mongolia. We studied this parameter through livestock productivity (LP) as a proxy, defined as the annual number of newborns per breeding-age female. We found no significant impact of rainfall or livestock numbers, alone or combined. We found through the study of pasture use, defined as the ratio forage consumed/forage available, an impact of the combined effect of rainfall, animal numbers and pasture health. We observed in addition sharp LP decreases prior to dzuds, which suggests that the above-mentioned drivers interact to weaken livestock which increases its vulnerability to winter hazards. This tends to show that in our case study, dzuds are not the simple consequence of stochastic hazards striking randomly, but instead, the final stage of a chain of events that involves dry years, high livestock densities and pasture degradation. This also indicates that dzud early warning indicators could be designed based on LP monitoring.     

Mongolian herders’ vulnerability to <Emphasis Type="Italic">dzud</Emphasis>: a study of record livestock mortality levels during the severe 2009/2010 winter

The livelihoods of people inhabiting inland Eurasia have long been jeopardized by repeated natural hazards associated with a harsh environment and a cold, arid climate. Dzud is a Mongolian word indicating harsh winter conditions. In the present study, we considered dzud damage (e.g., livestock loss) to result from a combination of climate hazard (e.g., cold surges) and herders’ socioeconomic vulnerability. For this study, we integrated crucial socioeconomic factors accounting for major spatiotemporal variations in Mongolia by applying principal component analysis (PCA) to a comprehensive province-level, multiyear dataset. We subsequently characterized the regionality of herders’ vulnerability to the dzud event that occurred during the 2009/2010 winter by conducting a cluster analysis of the provincial principal component (PC) scores for the pre-dzud year (2009). Our results revealed a distinct geographical pattern of vulnerability. Herding households in the northern and northeastern (relatively wet and plain) areas were found to be well prepared for harsh winters, with shelters against wind and availability of forage, including hay, as well as easy access to major urban markets. By contrast, herding households in the southern and southwestern (arid and mountainous) areas were poorly prepared, with inadequate circumstances that facilitate pursuing of otor (movement of nomadic herders in search of better pastures) and lack of access to markets and dzud relief support because of their remote locations. The time coefficients of PC 2, related to winter preparedness, indicated that vulnerability increased between 2003 and 2009 (the pre-dzud year). This was partly responsible for the record-level mortality observed in 2010 across the southern and southwestern rural region, in conjunction with harsh winter weathers.     

Towards a better understanding of the evolution of the flood risk in Mediterranean urban areas: the case of Barcelona

Dam failure constitutes a grave threat to human life. However, there is still a lack of systematic and comprehensive research on the loss of life (L) caused by dam break in China. From the perspective of protecting human life, a new calculation method for L occurred in dam break floods is put forward. Fourteen dam failure cases in China are selected as the basic data by three-dimensional stratified sampling, balancing spatial, vertical elevation and temporal representations, as well as considering various conditions of the dam collapse. The method includes three progressive steps: Firstly, some impact factors of loss of life (IFL) are selected by literature survey, i.e., severity of dam break flood (S _F), population at risk (P _R), understanding of dam break (U _B), warning time (T _W) and evacuation condition (E _C). And the other IFL of weather during dam break (W _B), dam break mode (M _B), water storage (S _W), building vulnerability (V _B), dam break time (T _B) and average distance from affected area to dam (D _D) are also taken into account to get a more comprehensive consideration. According to disaster system and disaster risk, these eleven IFL are divided into four categories. Through the improved entropy method, eight key IFL are further selected out of the eleven. Secondly, four L modules are built based on four categories, which are L-causing factor module (M ₁), L-prone environment module (M ₂), affected body module (M ₃) and rescue condition module (M ₄). Eventually, by using two methods of multivariate nonlinear regression and leave-one-out cross-validation in combination with coupled four modules, the calculation method for L is established. Compared with the results of Graham method and D&M method, the result of the proposed one is much closer to the actual value and performs better in fitting effect and regional applicability. In the application, L calculation and consequence assessment are carried out in the example of Hengjiang reservoir that has already broken down. At the same time, L calculation and risk prediction are used in the analysis of Yunshan reservoir, which is under planning. The proposed method can not only be applied to estimate L and its rate (f _L ) under various types of dam break conditions in China, but also provide a reliable consequence assessment and prediction approach to reduce the risk of L.     

Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P _f ?<?0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (P _f ) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P _f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P _f and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.     

Navigating the future of tsunami risk communication: using dimensionality,interactivity and situatedness to interface with society

Two-dimensional paper maps are well-established tsunami risk communication tools in coastal communities. Advances in GIS, geovisualization and spatial interface technologies suggest new opportunities to deliver tsunami risk communication using 3D, interactive and situated risk visualization. This paper introduces a set of geovisual interface constructs—dimensionality–interactivity–situatedness (DIS)—and evaluates their presence, absence and distribution in 129 examples of existing academic and public visual tsunami risk communication. The resulting analyses reveal structural differences in the distributions of DIS found in each of academic and public risk communication literatures, and opportunities for interactive location-aware risk communication. The second half of this paper reports on three new tsunami risk visualization interfaces informed by and developed to demonstrate how we might explore new undeveloped risk communication territory revealed by the DIS cube analysis. We discuss the design, rationale and implications of: EvacMap; ARRO3D; and Tsunamulator. These risk visualization interfaces deliver location-aware, user-centred risk maps, as well as virtual risk maps and tsunami simulations that can be viewed while standing in situ in coastal environments. This work is a first step intended to help the risk communication community systematically engage an emerging territory of interactive and location-aware 3D visualizations. This work aims to facilitate and encourage progress towards developing a new strand of interactive, situated geovisual risk communication research, by establishing these guiding constructs, their relationship to existing works and how they may inform the design of future systems and usability research.     

Lower Bathonian Belemnites and Biostratigraphy of the Central and Southern Parts of the East European Platform: Part 1. Megateuthididae

Belemnites from the lower Bathonian of the Russian Plate are revised on the basis of the study of two reference sections—Pletnyovka and Sokur quarries. The first part of the study deals with the members of the family Megateuthididae. They include eight species of the genus Barskovisella gen. nov., neoendemic to the territory of the Russian Plate and originating from high Boreal taxa—species of the genus Paramegateuthis Gustomesov, 1960, which immigrated to the Middle Russian Sea in the early Bathonian via a short-lived meridional strait. The new genus includes six new species described in the present paper—Barskovisella pseudoishmensis sp. nov., B. issae sp. nov., B. variabilis sp. nov., B. barskovi sp. nov., B. gracilis sp. nov., and B. renegata sp. nov. The beds with Barskovisella, a new belemnite-based unit, corresponding to the Oraniceras besnosovi ammonite zone and including four successive phylogenetic biohorizons well comparable in resolution with ammonite-based infrazonal subdivisions, are introduced.     

Optimal choice of the softening length and time step in <Emphasis Type="Italic">N</Emphasis>-body simulations

A criterion for the choice of optimal softening length ε for the potential and the choice of time step dt for N-body simulations of a collisionless stellar system is analyzed. Plummer and Hernquist spheres are used as models to analyze how changes in various parameters of an initially equilibrium stable model depend on ε and dt. These dependences are used to derive a criterion for choosing ε and dt. The resulting criterion is compared to Merritt’s criterion for choosing the softening length, which is based on minimizing the mean irregular force acting on a particle with unit mass. Our criterion for choosing ε and dt indicate that ε must be a factor of 1.5–2 smaller than the mean distance between particles in the densest regions to be resolved. The time step must always be adjusted to the chosen ε (the particle must, on average, travel a distance smaller than 0.5 ε during one time step). An algorithm for solving N-body problems with adaptive variations of the softening length is discussed in connection with the task of choosing ε, but is found not to be promising.     

Paleogene biostratigraphy of the North Circum-Caspian region (implication of the dinocysts and nannoplankton from the Novouzensk reference borehole), Part 1: Age substantiation and correlation of deposits

Eight zonal dinocyst assemblages and three bio stratigraphic units ranked as “beds with flora” are first distinguished in the Danian—lower Lutetian interval of the Paleogene succession, penetrated by the reference borehole Novousensk no. 1, where eight standard and one local nannoplankton zones are simultaneously recognized. The direct correlation of nannoplankton and dinocyst zones is used to refine the paleon-tological substantiation and stratigraphic position of regional lithostratigraphic units, ranges of hiatuses, and the correlation with the general stratigraphie scale. The nannoplankton of the Danian NP2 Cruciplacolithus tenuis and NP3 Chiasmolithus danicus zones is characteristic of the Algai Formation (Fm). The nannoplankton of the NP4 Coccolithus robustus Zone and dinocysts of the D3a Alterbidinium circulum Zone from the Tsyganovo Fm characterizes the Danian top. The Lower Syzran Subformation (Subfm) corresponds to the upper part of the NP4 Coccolithus robustus Zone (Neochiastizygus junctus local zone) and to the D3b (part) Cerodinium depressum Zone of the Selandian dinocysts. The latter spans part of the Upper Syzran Subformation, whose characteristic nannofossils are the nannoplankton of the NP5 Fasciculithus tympaniformis Zone and the dinocysts of the D3b (part) Isabelidinium? viborgense Zone of the Selandian. The Novouzensk Fm is represented by a succession of the dinocyst Cerodinium markovae Beds and the standard D4c Apectodinium hyperacanthum Zone of the upper Thanetian. The coccolitophorids of the lower Thanetian NP6 Heliolithus kleinpelli Zone occur at the formation base. The Bostandyk Fm includes successive bio stratigraphie units of the Ypresian. In the dinocyst scale, these are the D5a Apectodinium augustum Zone, the Pterospermella Beds (DEla Zone of the North Sea scale), and zones DBlb-c Deflandrea oebisfeldensis, D7c Dracodinium varielon-gitudum, and D8 Dracodinium politum—Charlesdowniea coleothrypta, while units of the nannoplankton scale correspond to the NP12 Martasterites tribrachiatus and NP13 Discoaster lodoensis zones. The Kopterek Fm yields Lutetian nannofossils: the nannoplankton of the NP14 Discoaster sublodoensis Zone and the dinocysts of the Wetzeliella coronata—Areosphaeridium diktyoplokum Beds. Three meaningful hiatuses are established at the Danian base, Selandian top, and in the lower Ypresian.     

Interaction between risk perception and sense of place in disaster-prone mountain areas: a case study in China’s Three Gorges Reservoir Area

Residents of rural mountain settlements are constantly threatened by disasters such as landslides. Their risk perception directly or indirectly affects their behavioral choices. Introducing the concept of sense of place, this paper details its interactions with the risk perception of mountain hazards. Rural residents (n = 348) in landslide-threatened areas of the Three Gorges Reservoir Area were questioned about their sense of place and risk perception. Partial least squares structural equation modeling was used to explore the interactions between various dimensions, and hypothetical tests were conducted. We found that dimensions of risk perception, such as Possibility and Unknown, had direct, negative impacts on the dimensions of sense of place, such as Society bond and Place dependence. Possibility had an indirect, yet more significant effect on Place attachment and Place identity, acting through Society bond. Rural residents often overestimate disaster risks due to fatalism, and a fear of the unknown stemming from low scientific literacy, which reduces their Place dependence. A complex interaction between sense of place and risk perception was observed. The findings provide a scientific basis for the government to formulate integrated policies regarding settlement relocation, disaster prevention and mitigation, and sustainable development.     

High-pressure phase transitions of CaRhO<Subscript>3</Subscript> perovskite

High-pressure phase transitions of CaRhO₃ perovskite were examined at pressures of 6–27 GPa and temperatures of 1,000–1,930°C, using a multi-anvil apparatus. The results indicate that CaRhO₃ perovskite successively transforms to two new high-pressure phases with increasing pressure. Rietveld analysis of powder X-ray diffraction data indicated that, in the two new phases, the phase stable at higher pressure possesses the CaIrO₃-type post-perovskite structure (space group Cmcm) with lattice parameters: a = 3.1013(1) Å, b = 9.8555(2) Å, c = 7.2643(1) Å, V _m  = 33.43(1) cm³/mol. The Rietveld analysis also indicated that CaRhO₃ perovskite has the GdFeO₃-type structure (space group Pnma) with lattice parameters: a = 5.5631(1) Å, b = 7.6308(1) Å, c = 5.3267(1) Å, V _m  = 34.04(1) cm³/mol. The third phase stable in the intermediate P, T conditions between perovskite and post-perovskite has monoclinic symmetry with the cell parameters: a = 12.490(3) Å, b = 3.1233(3) Å, c = 8.8630(7) Å, β = 103.96(1)°, V _m  = 33.66(1) cm³/mol (Z = 6). Molar volume changes from perovskite to the intermediate phase and from the intermediate phase to post-perovskite are –1.1 and –0.7%, respectively. The equilibrium phase relations determined indicate that the boundary slopes are large positive values: 29 ± 2 MPa/K for the perovskite—intermediate phase transition and 62 ± 6 MPa/K for the intermediate phase—post-perovskite transition. The structural features of the CaRhO₃ intermediate phase suggest that the phase has edge-sharing RhO₆ octahedra and may have an intermediate structure between perovskite and post-perovskite.     

Antimicrobial resistance and prevalence of extended-spectrum beta-lactamase genes in <Emphasis Type="Italic">Escherichia coli</Emphasis> from major rivers in Podhale,southern Poland

The aim of this study was to assess the antimicrobial resistance and the prevalence of genes determining the presence of extended-spectrum beta-lactamase (ESBL) enzymes in Escherichia coli isolated from two major rivers of the Podhale region in southern Poland. In total, 196 E. coli isolates were analyzed—98 from each river—Bia?ka and Zakopianka, collected in 8 campaigns, over the period of two years. Antimicrobial resistance was assessed using disk diffusion method and PCR tests were conducted to detect the ESBL genes. In E. coli isolated from Bia?ka, the resistance to amoxicillin/clavulanic acid was detected most frequently (54.08%) and ESBL was detected in 14.29% of strains. In strains isolated from Zakopianka, most frequent resistance was observed toward ticarcillin (51.02%), while ESBL was observed in 16.33% of isolates. In the total pool of isolates, the resistance to amoxicillin/clavulanic acid was most frequent (48.98% of isolates) and ESBL producers comprised 15.30% of E. coli isolates derived from both rivers. Multidrug resistance was observed less frequently in strains derived from Bia?ka (4 isolates resistant to 10 and more antimicrobials) than from Zakopianka, where 10 isolates were resistant to 10 and more antibiotics. Out of the tested ESBL genes blaTEM was detected most frequently (45.4% of isolates), whereas blaCTX-M1 and blaCTX-M3 were recorded in one isolate.     

Representatives of genera <Emphasis Type="Italic">Malbosiceras</Emphasis> and <Emphasis Type="Italic">Pomeliceras</Emphasis> (Neocomitidae,Ammonoidea) from the Berriasian of the Crimean Mountains

The revised representatives of ammonite genera Malbosiceras and Pomeliceras from the Berriasian of the Crimean Mountains are classed with seven species, four of the first genus [M. malbosi (Pictet), M. chaperi (Pictet), M. broussei (Mazenot), M. pictetiforme Tavera] and three of the second one [P. aff. boisseti Nikolov, P. breveti (Pomel), P. (?) funduklense Lysenko et Arkadiev sp. nov.]. The identified species are described. The genus Mazenoticeras is considered as synonym of Malbosiceras. The above species prove that all the Berriasian zones (jacobi, occitanica and boissieri) are characteristic of corresponding deposits in the Crimean Mountains.     

Systematic paleontology,biostratigraphy, paleobiogeography of <Emphasis Type="Italic">Loftusia</Emphasis> (foraminifera) and <Emphasis Type="Italic">Rudist</Emphasis> assemblages in a regressive sequence in the Hekimhan-Malatya area (Eastern Anatolia) Turkey

The Maastrichtian regressive sequence of the Hekimhan-Malatya area in Eastern Turkey consists of dolomitic limestones, limestones and calcareous mudstones which are dominated by rudists and Loftusia (foraminifera) assemblages. Several Loftusia species indicating middle to late Maastrichtian age such as Loftusia anatolica Meriç, L. baykali Meriç, L. coxi Henson, L. harrisoni Cox, L. minor Cox and L. morgani Douvillé have been recorded. Other benthic foraminifers present include Orbitoides medius d’ Archiac, Omphalocyclus macroporus (Lamarck), Laffitteina conica Drooger, Laffitteina mengaudi (Astre) and Laffitteina oeztuerki Inan. The rudists are abundant in the dolomitic limestones in the study area. The genus Miseia Patrulius is dominant and represented by Miseia bilacunosa Özer and Miseia hekimhanensis Karacabey-Öztemür. The Loftusia species and the Rudists assemblage indicates middle to late Maastrichtian age for the formation. The paleobiogeographic distribution of the assemblage has been discussed taking this find into account.     

Diffusive fractionation of volatiles and their isotopes during bubble growth in magmas

Bubbles grow in decompressing magmas by simple expansion and by diffusive supply of volatiles to the bubble/melt interface. The latter phenomenon is of significant geochemical interest because diffusion can fractionate elements and isotopes (or isotopologues) of dissolved components. This raises the possibility that the character of volatile components in bubbles may not reflect that of volatiles dissolved in the host melt over the lifetime of a bubble—even in the absence of equilibrium vapor/melt isotopic fractionation. Recent experiments have confirmed the existence of an isotope mass effect on diffusion of the volatile element Cl in silicate melt [Fortin et al. (Isotopic fractionation of chlorine during chemical diffusion in a dacitic melt and its implications for isotope behavior during bubble growth (abstract), 2016 Fall AGU Meeting, 2016)], so there is a clear need to understand the efficacy of diffusive fractionation during bubble growth. In this study, numerical models of diffusion and mass redistribution during bubble growth were implemented for both “passive” volatiles—those whose concentrations are generally well below saturation levels—and “active” volatiles such as CO₂ and H₂O, whose elevated concentrations and limited solubilities are the cause of bubble nucleation and growth. Both diffusive and convective bubble-growth scenarios were explored. The magnitude of the isotope mass effect on passive volatiles partitioned into bubbles growing at a constant rate R in a static system depends upon R/D _L, K _d and D _H/D _L (K _d = bubble/melt partition coefficient; D _H/D _L = diffusivity ratio of the heavy and light isotopes). During convective bubble growth, the presence of a discrete (physical) melt boundary layer against the growing bubble (of width x _BL) simplifies outcomes because it leads to the quick onset of steady-state fractionation during growth, the magnitude of which depends mainly upon R?x _BL/D _L and D _H/D _L (bubble/melt fractionation is maximized at R?x _BL/D _L ≈0.1). Constant R is unrealistic for most real systems, so other scenarios were explored by including the solubility and EOS of an “active” volatile (e.g., CO₂) in the numerical simulations. For plausible decompression paths, R increases exponentially with time—leading, potentially, to larger isotopic fractionation of species partitioned into the growing bubble. For volatile species whose isotope mass effects on diffusion have been measured (Cl, Li), predicted isotope fractionation in the exsolved vapor can be as large as ?4‰ for Cl and ?25‰ for Li.     

<Emphasis Type="Italic">Salpingoporella</Emphasis> (dasycladalean algae) species from the Lower Cretaceous carbonate facies of Kopet Dagh basin (NE Iran)

Salpingoporella species from algal bearing of Barremian-Aptian limestones in the Kopet Dagh basin (NE of Iran) are described. Different species (S. cemi, S. hasi, S. heraldica, S. hispanica, S. milovanovici, S. muehlmbergi, S. parapiriniae, S. piriniae, S. cf. biokovensis, S. steinhauseri, S. polygonalis) are investigated from different biometrical aspects such as depositional environments and biogeographical distribution as well as their systematic palaeontology from two formations (the Tirgan and Sarcheshmeh formations) in nine stratigraphic sections.     

Soil bacterial strains with heavy metal resistance and high potential in degrading diesel oil and <Emphasis Type="Italic">n</Emphasis>-alkanes

Four bacterial strains, capable of degrading diesel oil, n-alkanes or hexadecane, were isolated from soils contaminated with petroleum oil and identified. Strains of Pseudomonas sp., Pseudomonas putida TPHK-1 and Pseudomonas aeruginosa TPHK-4, were more efficient in degrading high concentrations of the hydrocarbons than the other two strains, Stenotrophomonas maltophilia TPHK-2 and Acenitobacter sp. TPHK-3. P. putida TPHK-1 exhibited tolerance to very high concentrations of heavy metals such as cadmium, lead, zinc and copper. The innate ability of P. putida TPHK-1, as evidenced by the amplified genes alkB1 and alkB2 that encode alkane hydroxylases, and cat12o and cat23o coding for catechol dioxygenase, in degrading diesel oil in the presence of heavy metals is far greater than that of the strains reported in the literature. Heavy metal tolerance coupled with rapid degradation of hydrocarbons, even at high concentrations, suggests that P. putida TPHK-1 has a great potential in remediating soils contaminated with mixtures of hydrocarbons and heavy metals.     

Elastic behavior of vanadinite,Pb<Subscript>10</Subscript>(VO<Subscript>4</Subscript>)<Subscript>6</Subscript>Cl<Subscript>2</Subscript>, a microporous non-zeolitic mineral

The high-pressure behavior of a vanadinite (Pb₁₀(VO₄)₆Cl₂, a = b = 10.3254(5), c = 7.3450(4) Å, space group P6₃/m), a natural microporous mineral, has been investigated using in-situ HP-synchrotron X-ray powder diffraction up to 7.67 GPa with a diamond anvil cell under hydrostatic conditions. No phase transition has been observed within the pressure range investigated. Axial and volume isothermal Equations of State (EoS) of vanadinite were determined. Fitting the P–V data with a third-order Birch-Murnaghan (BM) EoS, using the data weighted by the uncertainties in P and V, we obtained: V ₀ = 681(1) Å³, K ₀ = 41(5) GPa, and K′ = 12.5(2.5). The evolution of the lattice constants with P shows a strong anisotropic compression pattern. The axial bulk moduli were calculated with a third-order “linearized” BM-EoS. The EoS parameters are: a ₀ = 10.3302(2) Å, K ₀(a) = 35(2) GPa and K′(a) = 10(1) for the a-axis; c ₀ = 7.3520(3) Å, K ₀(c) = 98(4) GPa, and K′(c) = 9(2) for the c-axis (K ₀(a):K ₀(c) = 1:2.80). Axial and volume Eulerian-finite strain (fe) at different normalized stress (Fe) were calculated. The weighted linear regression through the data points yields the following intercept values: Fe _a (0) = 35(2) GPa for the a-axis, Fe _c (0) = 98(4) GPa for the c-axis and Fe _V (0) = 45(2) GPa for the unit-cell volume. The slope of the regression lines gives rise to K′ values of 10(1) for the a-axis, 9(2) for the c-axis and 11(1) for the unit cell-volume. A comparison between the HP-elastic response of vanadinite and the iso-structural apatite is carried out. The possible reasons of the elastic anisotropy are discussed.     

Activity–composition relations for phases in petrological calculations: an asymmetric multicomponent formulation

For petrological calculations, including geothermobarometry and the calculation of phase diagrams (for example, P–T petrogenetic grids and pseudosections), it is necessary to be able to express the activity–composition (a–x) relations of minerals, melt and fluid in multicomponent systems. Although the symmetric formalism—a macroscopic regular model approach to a–x relations—is an easy-to-formulate, general way of doing this, the energetic relationships are a symmetric function of composition. We allow asymmetric energetics to be accommodated via a simple extension to the symmetric formalism which turns it into a macroscopic van Laar formulation. We term this the asymmetric formalism (ASF). In the symmetric formalism, the a–x relations are specified by an interaction energy for each of the constituent binaries amongst the independent set of end members used to represent the phase. In the asymmetric formalism, there is additionally a "size parameter" for each of the end members in the independent set, with size parameter differences between end members accounting for asymmetry. In the case of fluid mixtures, for example, H₂O–CO₂, the volumes of the end members as a function of pressure and temperature serve as the size parameters, providing an excellent fit to the a–x relations. In the case of minerals and silicate liquid, the size parameters are empirical parameters to be determined along with the interaction energies as part of the calibration of the a–x relations. In this way, we determine the a–x relations for feldspars in the systems KAlSi₃O₈–NaAlSi₃O₈ and KAlSi₃O₈–NaAlSi₃O₈–CaAl₂Si₂O₈, for carbonates in the system CaCO₃–MgCO₃, for melt in the melting relationships involving forsterite, protoenstatite and cristobalite in the system Mg₂SiO₄–SiO₂, as well as for fluids in the system H₂O–CO₂. In each case the a–x relations allow the corresponding, experimentally determined phase diagrams to be reproduced faithfully. The asymmetric formalism provides a powerful and flexible way of handling a–x relations of complex phases in multicomponent systems for petrological calculations.