Elasticity of plagioclase feldspars

AbstractElastic properties are reported for eight plagioclase feldspars that span compositions from albite (NaSi3AlO8) to anorthite (CaSi2Al2O8). Surface acoustic wave velocities measured using Impulsive Stimulated Light Scattering and compliance sums from high‐pressure X‐ray compression studies accurately determine all 21 components of the elasticity tensor for these triclinic minerals. The overall pattern of elasticity and the changes in individual elastic components with composition can be rationalized on the basis of the evolution of crystal structures and chemistry across this solid‐solution join. All plagioclase feldspars have high elastic anisotropy; a* (the direction perpendicular to the b and c axes) is the softest direction by a factor of 3 in albite. From albite to anorthite the stiffness of this direction undergoes the greatest change, increasing twofold. Small discontinuities in the elastic components, inferred to occur between the three plagioclase phases with distinct symmetry ( , , and ), appear consistent with the nature of the underlying conformation of the framework‐linked tetrahedra and the associated structural changes. Measured body wave velocities of plagioclase‐rich rocks, reported over the last five decades, are consistent with calculated Hill‐averaged velocities using the current moduli. This confirms long‐standing speculation that previously reported elastic moduli for plagioclase feldspars are systematically in error. The current results provide greater assurance that the seismic structure of the middle and lower crusts can be accurately estimated on the basis of specified mineral modes, chemistry, and fabric

Micropetrology: Are Inclusions Grains of Truth?

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High-pressure behaviour of zoisite

A high-pressure single-crystal X-ray diffraction (XRD) study has been carried out on two natural zoisite samples Ca 2Al 3-xFexSi 3O 12OH, one Fe-free (x = 0) and one Fe-rich (x = 0.12). The unit-cell parameters were determined for the Fe-free sample at 18 different pressures up to 7.76 GPa and for the Fe-rich sample at 13 different pressures up to 7.63 GPa. The P(V) data for both of the samples were fitted by a third-order Birch-Murnaghan equation of state (BM3 EoS). The equation of state coefficients are: V 0 = 903.39(5) \uc5 3, K T0 = 122.1(7) GPa, and K\u2032 0 = 6.8(2) for the Fe-free sample and V 0 = 906.95(5) \uc5 3, K T0 = 119.1(7) GPa, and K\u2032 0 = 7.3(2) for the Fe-rich sample. This shows that the addition of Fe in to the crystal structure of zoisite leads to a slight softening of the structure. Both compositions exhibit axial compressibilities \u3b2c > \u3b2 a 6b \u3b2 b, with the compressibilities of the a and b axes of the two samples being indistinguishable. The softening of the bulk modulus of zoisite with Fe content follows from softening of the c-axis of the structure. A high-pressure structural study of the Fe-free sample showed that the main compression mechanisms in the structure are the compression of soft inter-octahedral distance along [001] and soft intra-octahedral distances along [010] directions, while along [100] the main compression occurs because of the compression of stiff intra-octahedral distances. The substitution of Fe on to the M3 octahedral site of the structure leads to an increase of the intra-octahedral distance of the M3 that triggers the rotation of M12 and therefore leads to the softening of the M12 inter-octahedral distances that accounts for the softening of the c-axis of the structure

Low-temperature behavior of natural kalsilite with P31c symmetry: An in situ single-crystal X-ray diffraction study

The low-temperature behavior of a natural kalsilite (ideal formula KAlSiO4) with P31c symmetry has been investigated by in situ single-crystal diffraction. A series of intensity data collections and structural refinements have been performed at 298, 250, 200, 150, and 100 K on decreasing temperature, and 175, 225, and 275 K on increasing T. The variations of the unit-cell parameters of kalsilite as a function of T are continuous, and show no evidence of any phase transitions or thermo-elastic anomalies in this temperature range. An expansion is observed along [0001] with decreasing temperature. The axial and volume thermal expansion coefficients ({alpha}j = lj-1{middle dot}{partial}lj/{partial}T, {alpha}V = V-1{middle dot}{partial}V/{partial}T) between 298 and 100 K, calculated by weighted linear regression through the data points, are {alpha}a = {alpha}b = 1.30(6){middle dot}10-5, {alpha}c = -1.5(1){middle dot}10-5, {alpha}V = 1.1(2){middle dot}10-5 K-1. The main structural change on decreasing temperature is a cooperative anti-rotation of tetrahedra forming the six-membered rings lying parallel to (0001). This tetrahedral rotation is coupled with a change in the distances between the extra-framework cations and the framework O atoms. A small decrease in the tetrahedral tilts perpendicular to [0001] is responsible for the negative thermal expansion along [0001]; the implications of these mechanisms for thermal expansion in nephelines and kalsilites are discussed

"EosFit-Pinc: A simple GUI for host-inclusion elastic thermobarometry"—Reply to Zhong et al.

We provide a further algebraic proof that the lines of entrapment conditions for inclusions calculated with the formula of Guiraud and Powell (2006) are not thermodynamic isomekes and therefore do not represent exactly lines of possible entrapment conditions

Percepción de la seguridad ciudadana de los vecinos del distrito de Surco, Sector Surco Viejo, posterior a la inversión municipal en seguridad, Lima – 2016

La presente investigación titulada “Percepción de la seguridad ciudadana de los vecinos del distrito de Surco, Sector Surco Viejo, posterior a la inversión municipal en seguridad, Lima – 2016” tiene como objetivo principal determinar el nivel de percepción de Seguridad Ciudadana de los vecinos, en el distrito de Surco, sector Surco Viejo, luego de la inversión municipal. La población está conformada por los vecinos concurrentes al Mercado Jorge Chávez 02 de Surco Viejo, y la muestra está constituida por 61 vecinos concurrentes a dicho centro de abastos en días de semana, éstos fueron seleccionados de manera aleatoria en días de semana, el diseño es descriptivo; asimismo, para recoger los datos se utilizó la técnica de la encuesta, a través de un cuestionario sobre seguridad ciudadana, subdividido en 2 dimensiones. Luego de aplicar los instrumentos y realizar el análisis estadístico se encontró que la seguridad ciudadana es percibida en un nivel poco favorable 38% y desfavorable 38%, la dimensión ordenamiento ciudadano es percibido en nivel poco favorable 41% y desfavorable 33% y la dimensión prevención del delito es percibida en 36% nivel poco favorable y 49% desfavorable. Se concluyó que la seguridad ciudadana es de nivel poco favorable y desfavorabl

Numerical investigation of a two-bladed propeller inflow at yaw

The development of faster computing power and nonintrusive experimental techniques has allowed for the advancement in computational fluid dynamics (CFD) validation and the greater understanding of aerodynamic conditions previously deemed too extreme to accurately measure. To this end, a numerical study is conducted that focuses on a propeller at yaw. Current low-order methods are reliant upon an accurate inflow profile to determine overall blade loading patterns. To improve such methods, CFD can be used to determine an initial inflow profile from which to conduct additional lower-order calculations. Therefore, to ensure that CFD is able to accurately capture yawed inflow profiles, a validation study is conducted that compares numerical simulations against experiments. Good agreement is found between the two methods, and subsequently the azimuthal variation in skin friction and induced angle of attack, as a result of the yawed conditions, is analyzed

The nonlinear anomalous lattice elasticity associated with the high-pressure phase transition in spodumene: A high precission static compression study

The high-pressure behavior of the lattice elasticity of spodumene, LiAlSi2O6, was studied by static compression in a diamond-anvil cell up to 9.3 GPa. Investigations by means of single-crystal XRD and Raman spectroscopy within the hydrostatic limits of the pressure medium focus on the pressure ranges around similar to 3.2 and similar to 7.7 GPa, which have been reported previously to comprise two independent structural phase transitions. While our measurements confirm the well-established first-order C2/c-P2(1)/c transformation at 3.19 GPa (with 1.2% volume discontinuity and a hysteresis between 0.02 and 0.06 GPa), both unit-cell dimensions and the spectral changes observed in high-pressure Raman spectra give no evidence for structural changes related to a second phase transition. Monoclinic lattice parameters and unit-cell volumes at in total 59 different pressure points have been used to re-calculate the lattice-related properties of spontaneous strain, volume strain, and the bulk moduli as a function of pressure across the transition. A modified Landau free energy expansion in terms of a one component order parameter has been developed and tested against these experimentally determined data. The Landau solution provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P (tr), thus giving Landau parameters of K (0) = 138.3(2) GPa, K' = 7.46(5), lambda (V) = 33.6(2) GPa, a = 0.486(3), b = -29.4(6) GPa and c = 551(11) GPa

Phase stability, elastic behavior, and pressure-induced structural evolution of kalsilite: A ceramic material and high-T/high-P mineral

The phase stability, elastic behavior, and pressure-induced structural evolution of a natural metamorphic kalsilite (ideal formula KAlSiO4) from Punalur (Kerala district in southern India), with P31c symmetry and a K/Na molar ratio of ~350, has been investigated by in situ X-ray single-crystal diffraction up to ~7 GPa with a diamond-anvil cell under hydrostatic conditions. At high-pressure, a previously unreported iso-symmetric first-order phase transition occurs at ~3.5 GPa. The volume compression of the two phases is described by third-order Birch-Murnaghan equations-of-state: V0 = 201.02(1) A3, KT0 = 59.7(5) GPa, K' = 3.5(3) for the low-P polymorph, and V0 = 200.1(13) A3, KT0 = 44(8) GPa, K' = 6.4(20) for the high-P polymorph. The pressure-induced structural evolution in kalsilite up to 7 GPa appears to be completely reversible. The compression of both phases involves tetrahedral rotations around [0001], which close up the channels within the framework. In addition, compression of the low-pressure phase involves tilting of the tetrahedra. The major structural change at the phase transition is an increase in the tilting of the tetrahedra, but with a reversion of the tetrahedral rotations to the value found at ambient conditions. This behavior is in distinct contrast to that of nepheline, which has a tetrahedral framework of the same topology