ALBERT

Description: We prove the $L_p$ Poincaré inequalities with constant $C\sqrt {p}$ for $1$ -cocycles on countable discrete groups under Bakry–Émery's $\Gamma _2$ -criterion. These inequalities determine an analog of subgaussian behavior for 1-cocycles. Our theorem improves some of our previous results in this direction, and in particular implies Efraim and Lust-Piquard's Poincaré-type inequalities for the Walsh system. The key new ingredient in our proof is a decoupling argument. As complementary results, we also show that the spectral gap inequality implies the $L_p$ Poincaré inequalities with constant $C{p}$ under some conditions in the noncommutative setting. New examples which satisfy the $\Gamma _2$ -criterion are provided as well.

Description: The UG-2 chromitite of the Bushveld Complex in South Africa contains the world’s largest resources of platinum group elements (PGEs). However, only limited work has been conducted on the fine-scale chemical variation of chromite, and the distribution of PGEs and platinum group minerals (PGMs) within the UG-2. In the present study, one drill core (155 cm long) covering the sequence of the UG-2 chromitite at the Karee mine in the western Bushveld Complex was studied in detail. Geochemically, Pt correlates well with Pd, but not with Ni, Cu, and S, and Pt and Pd show high concentrations at the bottom and in the center of the main UG-2 layer. The mineral chemistry of chromite is characterized by distinct cryptic variation, leading to the division of the UG-2 sequence into 10 distinct sublayers. From bottom to top (with exception of the basal sublayer), each sublayer is defined by an upward decrease of Mg# combined with increases of Cr# and TiO 2 . It is proposed that these trends reflect magmatic differentiation of individual chromitite entities, which coalesced to form a massive chromitite seam. Sulfides (pentlandite, chalcopyrite) interstitial to chromite grains are rare, and associated PGM grains are mainly Pt-Fe alloy, laurite, and cooperite-braggite. The PGEs are bimodally distributed in the UG-2. Platinum and the IPGE (Os, Ir, Ru) are dominantly present as discrete PGMs, whereas large proportions of Pd and Rh are hosted in the crystal lattice of pentlandite. Palladium and rhodium contents of pentlandite reach a maxima of 2.2 wt % Pd and 3.0 wt % Rh. The present data suggest that a succession of chromitite sublayers formed due to magmatic differentiation and segregated sequentially on top of each other, finally forming a massive chromitite seam. Contemporaneously with chromite segregation, PGE-rich magmatic sulfides segregated with chromite grains, but large proportions of these sulfides were subsequently removed mainly by reaction of sulfide with chromite, thereby upgrading the PGE contents of the remaining sulfides. Upon cooling, the PGE-bearing sulfide droplets recrystallized, leading to a bimodal distribution of the PGEs in the UG-2. The bulk of the Pd and Rh is hosted in pentlandite, whereas Pt and the IPGEs, apparently incompatible in the remaining sulfides, formed a distinct suite of discrete PGMs.

Description: 〈span〉Sphalerite and arsenopyrite can host trace elements (〈span〉e.g.〈/span〉, Ge, Cd and Au) that are important for high technology applications. These trace elements are incorporated into the structure of the host mineral (〈span〉e.g.,〈/span〉 by substitution) if inclusions are apparently absent. Focused ion beam technique and transmission electron microscopy combined with electron microprobe analysis allow for the correlation from micrometre to the nanometre scale in order to investigate the locations of trace elements 〈span〉in situ〈/span〉 within the host minerals. Therefore, Ge-rich sphalerite from the Tres Marias Zn–Pb–Ge deposit in Mexico and auriferous arsenopyrite from the Ashanti Au mine in Ghana are investigated. Sphalerite from Tres Marias contains Ge concentrations of up to 1430 μg/g and is characterised by elevated Fe contents. Germanium is homogeneously distributed within the sphalerite lattice without the presence of distinct Ge-bearing phases in the form of inclusions or exsolutions. In arsenopyrite from the Ashanti mine, Au occurs as oriented sub-microscopic discrete phases showing at least two distinct orientations, which cause the observed trace-element concentrations visible at larger scale. The formation of nanometre-sized gold particles in arsenopyrite is interpreted as enrichment of Au at the interface of crystallising arsenopyrite with the hydrothermal fluid and subsequent crystallisation of nanometre-sized gold grains at the surface of arsenopyrite after the critical concentration for nucleation was overstepped.〈/span〉

Description: Synthetic fluid inclusions formed in high P-T experiments, which are subsequently analyzed with LA-ICP-MS, enable us to collect thermodynamic data to constrain metal transport in aqueous fluids as well as partitioning of metals between coexisting phases. The most essential prerequisite for such studies is to ensure that equilibrium conditions between liquid and solid phases are reached prior to the formation of synthetic fluid inclusions in the host mineral. Various methods have been proposed by different authors to achieve this goal, but to this point our knowledge on the best approach to synthesize equilibrated fluid inclusions under constrained pressure, temperature, and compositional ( P , T , and X ) conditions remains poor. In addition, information on the time needed to reach equilibrium metal concentrations in the fluid as well as on the timing of the onset of fluid inclusion formation in the host mineral are scarce. The latter has been tested in a series of time-dependent experiments at 800 °C and 200 MPa using scheelite (CaWO 4 ), molybdenite (MoS 2 ) and metallic gold as dissolving phases and using different approaches to optimize the formation of equilibrated fluid inclusions. Both $${f}_{{\mathrm{O}}_{2}}$$ and $${f}_{{\mathrm{s}}_{2}}$$ were fixed during all experiments using the pyrite-pyrrhotite-magnetite buffer (PPM). As an intermediate in situ quenching of the sample charge plays an important role in the synthesis of fluid inclusions, we further tested the efficiency of such an intermediate quench for re-opening fluid inclusions formed at 600 °C and 200 MPa. Our results reveal that fluid inclusions start forming almost instantaneously and that equilibrium between fluid and solid phases occurs in the timescale of less than two hours for molybdenite and gold up to ca. 10 h for scheelite. The best approach to synthesize equilibrated fluid inclusions at 800 °C was obtained by using an intermediate quench on a previously unfractured quartz host. Experiments at 600 °C showed similar results and illustrate that this should be the method of choice down to this temperature. Below 600 °C pre-treatment of the quartz host (HF etching and/or thermal fracturing) becomes important to produce large enough fluid inclusions for the analyses via LA-ICP-MS and special care must be taken to prevent premature entrapment of the fluid. Fluids with 8 wt% NaCl in equilibrium with scheelite, molybdenite and gold at 800 °C and 200 MPa have concentrations of ca. 7300 ppm W, 1300 ppm Mo, and 300 ppm Au, respectively, which is in good agreement with results from other studies or extrapolation from lower temperatures. It can be concluded that the formation of synthetic fluid inclusions from an equilibrated fluid is possible, but different experimental designs are required, depending on the investigated temperature. In general, dissolution of solid phases seems to be much faster than previously assumed, so that experimental run durations can be designed considerably shorter, which is of great advantage when using fast-consuming mineral buffers.

Description: 〈span〉Sphalerite and arsenopyrite can host trace elements (〈span〉e.g.〈/span〉, Ge, Cd and Au) that are important for high technology applications. These trace elements are incorporated into the structure of the host mineral (〈span〉e.g.,〈/span〉 by substitution) if inclusions are apparently absent. Focused ion beam technique and transmission electron microscopy combined with electron microprobe analysis allow for the correlation from micrometre to the nanometre scale in order to investigate the locations of trace elements 〈span〉in situ〈/span〉 within the host minerals. Therefore, Ge-rich sphalerite from the Tres Marias Zn–Pb–Ge deposit in Mexico and auriferous arsenopyrite from the Ashanti Au mine in Ghana are investigated. Sphalerite from Tres Marias contains Ge concentrations of up to 1430 μg/g and is characterised by elevated Fe contents. Germanium is homogeneously distributed within the sphalerite lattice without the presence of distinct Ge-bearing phases in the form of inclusions or exsolutions. In arsenopyrite from the Ashanti mine, Au occurs as oriented sub-microscopic discrete phases showing at least two distinct orientations, which cause the observed trace-element concentrations visible at larger scale. The formation of nanometre-sized gold particles in arsenopyrite is interpreted as enrichment of Au at the interface of crystallising arsenopyrite with the hydrothermal fluid and subsequent crystallisation of nanometre-sized gold grains at the surface of arsenopyrite after the critical concentration for nucleation was overstepped.〈/span〉