ALBERT

Description: The crystal structure of the organic mineral refikite has been determined. The mineral was found in joints in bark and wood from pine trees in the ‘V Borkách’ peat deposit near the town of Krásno, Slavkovsky les Mountains, western Bohemia, Czech Republic. It forms white to light-yellow polycrystalline crusts or randomly intergrown, transparent, colourless, very thin, acicular crystals up to 0.2–0.5 mm long. Sometimes, colourless-to-white elongated prismatic crystals up to 1–1.5 mm in size were encountered. The mineral is soft (Mohs hardness ~1) and very brittle, with an uneven fracture. No visible cleavage was discerned. Crystals have a greasy-to-glassy lustre; fine crystal aggregates have a pearly lustre. Refikite, empirical formula C 20 H 34 O 2 or C 19 H 33 COOH, is a derivative of abietic acid. It is orthorhombic, space group P 2 1 2 1 2, with a = 22.6520(7), b = 10.3328(3), c = 7.6711(2) Å, V = 1795.49(9) Å 3 , Z = 4. Refikite comprises two closely related compounds based on perhydrophenanthrene. The major component has two axial methyl groups, one terminal carboxylic group and one terminal propan-2-yl (isopropyl) group joined to the three fused rings in the same fashion as in abietic acid. However, the fused ring system is fully reduced (contains single bonds only). In the minor component, the terminal propan-2-yl group is replaced by a propen-2-yl (methylvinyl) group. The crystal structure is stabilized by strong O···H–O hydrogen bonds. High-resolution mass spectroscopy (HRMS) confirmed a molecular mass of 306 and the formula C 20 H 34 O 2 . Hydrogen-1 and carbon-13 nuclear magnetic resonance (NMR) spectroscopy showed the presence of four methyl groups in the major component; infrared (IR), Raman and NMR spectra are consistent with the structure. The HRMS, IR and Raman spectroscopy methods confirmed the presence of a minor component containing the propen-2-yl group replacing the propan-2-yl group. This is also reflected in a shortened C15–C17 single bond metric of 1.468(6) Å shown by single-crystal X-ray analysis. The trivial name of the major component of refikite is tetrahydroabietic acid or abietan-18-oic acid. This work represents the first proof of the existence of abietic acid derivatives as naturally occurring species.

Description: Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses of symmetric matrices satisfying linear constraints. This class includes Gaussian graphical models. We develop a general theory of exponential varieties. These are derived from hyperbolic polynomials and their integral representations. We compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials.

Description: The crystal structure of rabejacite from Jáchymov, ideally Ca 2 [(UO 2 ) 4 O 4 (SO 4 ) 2 ](H 2 O) 8 , was solved by charge flipping from single-crystal data and refined to R 1 = 11.94% for 1422 unique observed reflections [ I 〉 3( I )]. According to single-crystal X-ray data, rabejacite is triclinic, space group P 1I, with a = 8.7434(11), b = 8.309(3), c = 8.8693(10) Å, α = 77.86(2), β = 104.635(11), = 82.935(18)°, V = 598.8(3) Å 3 and Z = 1, with D calc = 4.325 g cm –3 . The structure refinement proved that rabejacite is related to the zippeite group of minerals, as it is based upon the structural sheets of the zippeite topology of composition [(UO 2 ) 4 O 4 (SO 4 ) 2 ] 4– . Located in the interlayer between the sheets, which are stacked perpendicular to [010], are Ca 2+ cations and H 2 O groups. Ca 2+ ions are [7]-coordinated, by three uranyl O atoms from adjacent sheets and four H 2 O groups. An additional H 2 O group, which is not bonded directly to any cation, is located in the interlayer. Along with rabejacite, its Cu-rich variety was found in the specimens examined and characterized structurally. Its crystal structure ( R 1 = 10.15% for 1049 reflections with I 〉 3( I )) is practically the same as that of rabejacite, but there is an additional Cu 2+ site located in between pairs of Ca polyhedra. The structural formula is (Ca 1.56 Cu 0.40 ) 1.90 [(UO 2 ) 4 O 4 (SO 4 ) 2 ](H 2 O) 8 , Z = 1. Its existence suggests a greater diversity in zippeite crystal chemistry than was thought previously and also the possibility of a new Cu 2+ -dominant zippeite mineral besides pseudojohannite.

Description: The crystal structure of sopcheite, Ag 4 Pd 3 Te 4 , has been solved using single-crystal diffraction data for a crystal from the Lukkulaisvaara intrusion, Karelia. The crystal structure is orthorhombic, space group Cmca , a = 12.212(2) Å, b = 6.138(2) Å, c = 12.234(3) Å, V = 917.1(4) Å 3 and Z = 4. The refinement of the fully anisotropic model led to an R index of 6.47% for 413 unique reflections. Sopcheite crystallizes in a layered structure. The Pd(1) and Pd(2) atoms assume a nearly planar coordination by four Te atoms. Each of the [PdTe 4 ] rectangles shares two opposite Te–Te edges with adjacent rectangles forming six-membered rings with the shape of elongated hexagons. These hexagons are oriented parallel to (100) and form layers of a herringbone pattern. Silver atoms form four-membered rings [Ag 4 ] of almost square shape. The [Ag 4 ] rings are located approximately in the centre of elongated hexagons composed of [PdTe 4 ] rectangles. The crystal structure is stabilised by a number of metal–metal interactions. The crystal structure of the synthetic phase Ag 4 Pd 3 Te 4 was also determined by single-crystal X-ray diffraction (XRD). It corresponds to the structure of sopcheite from the Lukkulaisvaara intrusion. Electron backscatter diffraction data obtained on material from other reported sopcheite occurrences are entirely consistent with this structure model, which is however incompatible with the sole powder XRD pattern reported so far for sopcheite. Combined with the absence of phase transition in Ag 4 Pd 3 Te 4 up to its breakdown temperature, these results imply revision of the previously published crystallographic data of sopcheite.

Description: The crystal structure of the synthetic analogue of the mineral temagamite, Pd 3 HgTe 3 , was solved and refined to an R -factor of 0.0522 from single-crystal X-ray diffraction data. The structure is trigonal, space group P 3 m 1, with a = 7.8211(6) Å, c = 17.281(1) Å, V = 917.8(1) Å 3 (hexagonal setting) and Z = 6. Layer modules (A–F) stacked along the c -axis form the crystal structure of Pd 3 HgTe 3 . Module A is composed of isolated octahedra [PdTe 6 ], which share faces with adjacent octahedra from neighbouring modules. The edge-sharing [PdTe 6 ] octahedra and [PdTe 4 ] squares form the modules B and F, whereas the corner-sharing [PdTe 4 ] squares constitute modules C, D and E. The Hg atoms occupy the anti-cubooctahedral voids formed by Te atoms. The Pd–Pd and Pd–Hg bonds are also present in the structure. The symmetry of temagamite was revised based on the structural results of this study.

Description: The Protocol for the Analysis of Land Surface Models (PALS) Land Surface Model Benchmarking Evaluation Project (PLUMBER) was designed to be a land surface model (LSM) benchmarking intercomparison. Unlike the traditional methods of LSM evaluation or comparison, benchmarking uses a fundamentally different approach in that it sets expectations of performance in a range of metrics a priori—before model simulations are performed. This can lead to very different conclusions about LSM performance. For this study, both simple physically based models and empirical relationships were used as the benchmarks. Simulations were performed with 13 LSMs using atmospheric forcing for 20 sites, and then model performance relative to these benchmarks was examined. Results show that even for commonly used statistical metrics, the LSMs’ performance varies considerably when compared to the different benchmarks. All models outperform the simple physically based benchmarks, but for sensible heat flux the LSMs are themselves outperformed by an out-of-sample linear regression against downward shortwave radiation. While moisture information is clearly central to latent heat flux prediction, the LSMs are still outperformed by a three-variable nonlinear regression that uses instantaneous atmospheric humidity and temperature in addition to downward shortwave radiation. These results highlight the limitations of the prevailing paradigm of LSM evaluation that simply compares an LSM to observations and to other LSMs without a mechanism to objectively quantify the expectations of performance. The authors conclude that their results challenge the conceptual view of energy partitioning at the land surface.