High-pressure behavior of intermediate scapolite : compressibility, structure deformation and phase transition

Scapolites are common volatile-bearing minerals in metamorphic rocks. In this study, the high-pressure behavior of an intermediate member of the scapolite solid solution series (Me47), chemical formula (Na1.86Ca1.86K0.23Fe0.01)(Al4.36Si7.64)O24[Cl0.48(CO3)0.48(SO4)0.01], has been investigated up to 17.79 GPa, by means of in situ single-crystal synchrotron X-ray diffraction. The isothermal elastic behavior of the studied scapolite has been described by a III-order Birch\u2013Murnaghan equation of state, which provided the following refined parameters: V0 = 1110.6(7) \uc53, KV0 = 70(2) GPa (\u3b2V0 = 0.0143(4) GPa 121) and KV\u2032 = 4.8(7). The refined bulk modulus is intermediate between those previously reported for Me17 and Me68 scapolite samples, confirming that the bulk compressibility among the solid solution increases with the Na content. A discussion on the P-induced structure deformation mechanisms of tetragonal scapolite at the atomic scale is provided, along with the implications of the reported results for the modeling of scapolite stability. In addition, a single-crystal to single-crystal phase transition, which is displacive in character, has been observed toward a triclinic polymorph at 9.87 GPa. The high-pressure triclinic polymorph was found to be stable up to the highest pressure investigated

A strip-like tiling algorithm

AbstractWe extend our previous results on the connection between strip tiling problems and regular grammars by showing that an analogous algorithm is applicable to other tiling problems, not necessarily related to rectangular strips. We find generating functions for monomer and dimer tilings of T- and L-shaped figures, holed and slotted strips, diagonal strips and combinations of them, and show how analogous results can be obtained by using different pieces

Short-Term Repeated-Sprint Training (Straight Sprint vs. Changes of Direction) in Soccer Players

Repeated-sprint training (RST) is considered a critical training method in team sports. It is well known that RST effects may depend on several variables such as the duration of the protocol and repeated-sprint methodology. Few studies have evaluated very short-term protocols and compared different RST modalities. The aim of this study was to compare the effectiveness of 2 week RST including straight sprints or changes of direction (CODs) on physical performance in a sample of soccer players. This study used a randomised pre-post parallel group trial design. The participants were assigned to either an RST group using straight sprints (RST-SS = 18 players) or an RST group using CODs (RST-COD = 18 players). The protocols were: 3 sets of 7 x 30 m sprints for the RST-SS and 7 x 20 + 20 m (one COD of 180 degrees) for the RST-COD, with 20 s and 4 min recovery between sprints and sets, respectively. The following evaluations were performed: 10 and 20 m sprint, agility test, repeated sprint test (RSTbest and RSTmean), and Yo-Yo Recovery Level 1. After the training period, the RST-SS did not report any performance variation, while the RST-COD showed improvements in the 10 m sprint and RSTbest (effect size = 0.70 and 0.65, respectively). The between-group analysis did not report any statistical difference between the RST-SS and the RST-COD. In conclusion, this study did not support the utilisation of a very short-term RST protocol with soccer players, however, the RST-COD presented some additional benefits in sprint performance compared to the RST-SS

The stability and melting of aragonite: An experimental and thermodynamic model for carbonated eclogites in the mantle

Subduction of calcium carbonate, sequestered in the oceanic crust by hydrothermal metamorphism and biogenic action, accounts for a significant flux of carbon into the mantle, where it contributes to the genesis of carbonatitic and silica-undersaturated melts. However, the reported phase relations in the system CaCO3, notably the transition boundary from disordered calcite (calcite V, here ccv) to aragonite (ara), vary considerably among different studies. Moreover, the thermodynamic properties of ccv and of liquid CaCO3 (CaCO3L) remain to be determined. In order to address the dearth of experimental data on phase relations, and to determine a set of internally consistent thermodynamic properties for ara, ccv and CaCO3L, multi-anvil experiments were performed at 3\u20136 GPa and 1300\u20131750 \ub0C. By re-evaluating all experimental data, the transformation of ccv-ara fits the equation Tccv-ara = 397.6 + 320.17 7 P and the melting curve Tm = 1578.9 + 139.65 7 P 12 11.646 7 P2, where pressure is in GPa and temperature in K. Thermodynamic properties retrieved for calcite V and liquid CaCO3 are used to compute phase diagrams of relevance for chemical compositions representative of eclogite heterogeneities of the astenospheric mantle, and compared with experimentally derived phase relationships. Aragonite represents a carbonate of major abundance in carbonated eclogites at high temperature, close to the solidus; its ability to fractionate REE and Ba-Sr contributes to the peculiar geochemical signatures of silica undersaturated magmas. The relatively refractory nature of aragonite impacts on our understanding of the deep carbon cycle

High-pressure behavior of synthetic mordenite-Na: an in situ single-crystal synchrotron X-ray diffraction study

The high-pressure behavior of a synthetic mordenite- Na (space group: Cmcm or Cmc21) was studied by in situ single-crystal synchrotron X-ray diffraction with a diamond anvil cell up to 9.22(7) GPa. A phase transition, likely displacive in character, occurred between 1.68(7) and 2.70(8) GPa, from a C-centered to a primitive space group: possibly Pbnm, Pbnn or Pbn21. Fitting of the experimental data with III-BM equations of state allowed to describe the elastic behavior of the high-pressure polymorph with a primitive lattice. A very high volume compressibility [KV0 = 25(2) GPa, \u3b2V0 = 1/KV0 = 0.040(3) GPa\u20131; KV\u2032 = ( 02KV/ 02P)T = 2.0(3)], coupled with a remarkable elastic anisotropy (\u3b2b > > \u3b2c > \u3b2a), was found. Interestingly, the low-P and high-P polymorphs show the same anisotropic compressional scheme. A structure collapse was not observed up to 9.22(7) GPa, even though a strong decrease of the number of observed reflections at the highest pressures suggests an impending amorphization. The structure refinements performed at room-P, 0.98(2) and 1.68(7) GPa allowed to describe, at a first approximation, the mechanisms that govern the framework deformation in the low-P regime: the bulk compression is strongly accommodated by the increase of the ellipticity of the large 12-membered ring channels running along [001]

Ettringite at high pressure: structure evolution and elastic behaviour

In order to predict the elastic properties of the complex multi-component Portland cement, database of the thermodynamic parameters of the main constituents is needed. Ettringite (ideally Ca6Al2(SO4)3(OH)12\ub727H2O, with a=b \uf07e 11.21 and c \uf07e 21.43 \uc5, Sp. Gr. P31c) is a common crystalline phases in Portland cements. It contains more than 45 wt% of H2O. In the early hydration stages, the crystallization of ettringite governs the set rate of the highly reactive Ca3Al2O6 phase (also known as \u201cC3A\u201d), whereas in aged cements its formation is associated to degradation processes1. The crystal structure of ettringite is rather complex and it consists of [Ca3[Al(OH)6]\ub712H2O]-columns (in which Al(OH)6-octahedra are alternated with triplets of Ca(OH)4(OH2)4-polyhedra) and sulphate groups connected by a complex H-bonding net2. Previous studies on the behavior of ettringite at high pressure reported only the isotropic compressional behavior of ettringite 3,4. Because of that, the linear bulk moduli (Ka and Kc) and a full description of the deformation mechanisms at the atomic scale are still missing. We compressed a single crystal of ettringite up to 4.2 GPa by means of in-situ synchrotron X-ray diffraction, using a diamond-anvil cell and the mix methanol:ethanol (4:1) as P-transmitting fluid. Ettringite shows a marked anisotropic compressional pattern (Ka 21(1) GPa, Kc 47(1) GPa), which dramatically changes at P>3 GPa (Fig. 1). At P>3 GPa, the bulk modulus KV of ettringite drops from 26.6(5) to 10.4(8) GPa. Such a softening is governed by the structural changes which affect mainly the elastic behavior on the ab plane (Ka drops from 21(1) to 7.3(8) GPa whereas Kc decreases only moderately). The structure refinements reveal that the elastic softening reflects the collapse of the H-bonding net, due an average decrease of the Odonor\ub7\ub7\ub7Oacceptor distances (up to 0.20 \uc5 in some cases), which mainly affect the interaction between the sulphate groups and the Ca(OH)4(OH2)4-polyhedra lying in the ab plane

Synchrotron radiation μ X-ray diffraction in transmission geometry for investigating the penetration depth of conservation treatments on cultural heritage stone materials

The assessment of the penetration depth of conservation treatments applied to cultural heritage stone materials is a burning issue in conservation science. Several analytical approaches have been proposed but, at present, many of them are not fully exhaustive to define in a direct way the composition and location of the conservation products formed after inorganic mineral treatments. Here, we explored, for the first time, the analytical capability of synchrotron radiation m X-ray diffraction in transmission geometry (SR-mTXRD) for the study of the crystal chemistry and penetration depth of the consolidating phases formed after the application of diammonium hydrogen phosphate (DAP) treatments on a porous carbonatic stone (Noto limestone). The SR-mTXRD approach provided unambiguous information on the nature of the newly formed calcium phosphates (hydroxyapatite, HAP, and octacalcium phosphate, OCP) with depth, supplying important indications of the diffusion mechanism and the reactivity of the substrate. Qualitative and semi-quantitative data were obtained at the microscale with a non-destructive protocol and an outstanding signal-to-noise ratio. The SR-mTXRD approach opens a new analytical scenario for the investigation of a wide range of cultural heritage materials, including natural and artificial stone materials, painted stratigraphies, metals, glasses and their decay products. Furthermore, it can potentially be used to characterize the penetration depth of a phase \u201cA\u201d (or more crystalline phases) in a matrix \u201cB\u201d also beyond the cultural heritage field, demonstrating the potential wide impact of the study

On the P-induced behavior of the zeolite phillipsite : an in situ single-crystal synchrotron X-ray diffraction study

The elastic behavior and the structural evolution at high pressure of a natural phillipsite have been investigated by in situ single-crystal X-ray diffraction up to 9.44 GPa, using a diamond anvil cell and the nominally penetrating P-transmitting fluid methanol:ethanol:water (16:3:1) mix. Although no phase transition was observed within the P-range investigated, two different compressional regimes occur. Between 0.0001 and 2.0 GPa, the refined elastic parameters, calculated by a second-order Birch\u2013Murnaghan equation of state (BM-EoS) fit, are V0 = 1005(1) \uc53, K0 = 89(8) GPa for the unit-cell volume; a0 = 9.914(7) \uc5, Ka = 81(12) GPa for the a-axis; b0 = 14.201(9) \uc5, Kb = 50(5) GPa for the b-axis; and c0 = 8.707(2) \uc5, Kc = 107(8) GPa for the c-axis (Ka:Kb:Kc ~1.62:1:2.14). Between 2.0 and 9.4 GPa, a P-induced change in the configuration of H2O molecules, coupled with a change in the tilting mechanisms of the framework tetrahedra, gives rise to a second compressional regime, in which the phillipsite structure is softer if compared to the first compressional range. In the second compressional regime, the refined elastic parameters, calculated by a second-order BM-EoS fit, are V0 = 1098 (7) \uc53, K0 = 18.8(7) GPa for the unit-cell volume; a0 = 10.07(3) \uc5, Ka = 30(2) GPa for the a-axis; b0 = 14.8(1) \uc5, Kb = 11(1) GPa for the b-axis; and c0 = 8.94(2) \uc5, Kc = 21(1) GPa for the c-axis (Ka:Kb:Kc ~2.72:1:1.90). The evolution of the monoclinic \u3b2 angle with pressure shows two distinct trends in the two compressional regimes: with a negative slope between 0.0001 and 2.0 GPa, and a positive slope between 2.0 and 9.4 GPa. The mechanisms, at the atomic scale, that govern the two compressional regimes of the phillipsite structure are described

Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory

We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.Comment: 14 pages, 9 figures; introduction expanded, references added; published versio