1,721,169 research outputs found
About the relations between finite strain in non-cubic crystals and the related phenomenological P-V Equation of State
No full textThe notion of scalar strain in minerals is crucial for the formulation of P-V Equations of State (EoS). A scalar strain, , holding for any crystal symmetry has been derived by a rigorous and general approach, and then used to develop the related phenomenological P-V EoS. , which depends on V and the trace of the G*G0 matrix, can be split into two components, M and , where the former takes values close to those of the scalar strain according to Birch. M, providing the main contribution (often larger than 80%) to , is appropriate for the formulation of an EoS as M/V behaves regularly in the limit of an unstrained configuration. The phenomenological EoS based on M shows the same dependence on the elastic parameters (bulk modulus and derivatives versus pressure) of the usual Birch-Murnaghan EoS, and yields comparable results. Slight deviations occur for low symmetry minerals. This work is meant to contribute (i) to shed light on the relationships between scalar strain and related P-V EoS’s, and (ii) to provide a most general EoS which includes, as a particular case, the Birch-Murnaghan model and explains why this latter is reliable for crystal symmetry other than the cubic one, for which it was originally derived
Thermoelastic and structural properties of forsterite as a function of p and T: a computer simulation study, by semi-classical potentials and quasi-harmonic approximation
No full textA theoretical study of some thermoelastic and structural properties of forsterite, at non-ambient conditions, is presented in this work. A site-dependent potential (NP) has been developed, and successfully used to carry out theoretical investigations on the lattice parameters, specific heat and tensorial elastic properties of forsterite, at P and T conditions representative of the actual thermobaric environment of the upper mantle of the Earth. Calculations have been performed in the framework of lattice dynamics and of quasi-harmonic approximation. The results, from high temperature or high pressure simulations, have been compared with experimental data. Calculations at high pressure and high temperature have provided unprecedented data, which are not easy to achieve experimentally
Neutron powder diffraction and Rietveld analysis; applications to crystal chemical studies of minerals at non ambient conditions
No full textThe coherent diffraction of neutrons from powder samples combined with the Rietveld refinement method has proven to be a versatile tool, providing insights into a variety of mineralogical crystal-chemical studies that require measurements at non-ambient conditions. The relatively low absorption which neutrons suffer, the ease in taking sample-environment devices onto experimental stations at neutron facilities, the coherent-neutron-scattering length contrasts between quasi-isoelectronic species and the independence of coherent-neutron-scattering power of the scattering vector, underlie the success in using this radiation in mineralogy. The literature reporting neutron powder-diffraction studies of minerals at non-ambient conditions has been reviewed and the results obtained over the last 20 years or so are briefly reported in order to provide an indication of the diversity of applications of the technique. A few applications have been selected for a more in-depth analysis of the results (i.e., micas); further applications are discussed in detail in the accompanying paper by Redfern (2002). The results reported are gathered into four sections, according to the experimental conditions used: high temperature (cation partitioning, phase transitions), low temperature (location of light atoms, hydrogen bonding, occupancy factors of quasi-empty sites), high pressure (hydrogen bonding, phase transitions, cation partitioning) and high pressure and temperature (cation partitioning)
Quasi-harmonic computer simulations of the structural behaviour of pyrope at high pressure and high temperature
No full textNumerical simulations, using empirical interatomic potentials within the framework of lattice dynamics and quasi-harmonic approximation, have been carried out to model the behaviour of the structure and of some thermoelastic properties of pyrope at high pressure and high temperature conditions (0-50 GPa, 300-1500 K). Comparison with observed data, available as a function either of P or of T, suggests that the pressure effects are satisfactorily modelled, whilst the effect of T on the simulations is underestimated. The cell edge, bond lengths and polyhedral volumes have been studied as a function of P along five isotherms, spaced by 300 K steps. These isotherms tend to converge at high pressure, which demonstrates that the pressure effects become dominant compared to those of thermal origin in affecting the structural properties far from ambient conditions. The cell parameter, bond distances, and other structural and thermoelastic quantities determined through simulations have been parametrised as a function of P and T by polynomial expansions. Bulk modulus and thermal expansion have been discussed in the light of the high-temperature-Birch-Murnaghan and of the Vinet P - V - T equations of state. The predictions of the bulk modulus versus P and T from the present calculations and from the Vinet-EOS agree up to 10 GPa, but they differ at higher pressure
Pressure volume temperature equations of state: a comparative study based on numerical simulations
No full textThe P-V-T equation of state (EoS) models of Birch-Murnaghan, Vinet and Poirier-Tarantola have been compared with one another and discussed in the light of their ability to reproduce thermoelastic functions and parameters by means of fitting to pressure-volume-temperature data artificially generated for spinel, corundum and forsterite. Numerical simulations relying upon semi-empirical potentials, lattice dynamics and the quasiharmonic approximation have been used to generate P-V-T data. The results obtained indicate that all the P-V-T- EoSs tested predict bulk modulus at ambient conditions with errors confined, at worst, within a few percent, and reproduce correctly its dependence on temperature. The derivatives of the bulk modulus versus P and PT are less satisfactorily modelled. The bulk thermal expansion is determined by EoSs within a few percent error, but the deviations increase significantly if the approximation of linear dependence of EoS on temperature is used (linearised thermal pressure model)
Tungusite: new data, relationship and structural model
No full textNew chemical analyses, electron and X-ray powder diffraction data, and comparison with gyrolite and reyerite shows the ideal formula for tungusite. A structural model for tungusite is derived by splitting the double tetrahedral layer of reyerite and inserting a trioctahedral X sheet which is ideally occupied by Fe2+. Polytypism phenomena due to different relative positions between tetrahedral and X sheets are discussed. A substitutional solid solution includes tungusite (x = y = z = 0, M = Fe2+) and gyrolite (x = 1, y = 1, z = 6, M = Ca). -from Author
Profile fitting intergration of single crystal diffraction data
No full textProfile-fìtting methods have received great attention in
the area of structure analysis from powder diffraction
data. Although the use of profile fitting for the
reliable extraction of integrated intensities from singlecrystal
diffraction data, has long been proposed in the
literature, a' limited number of applications and tests
of the method have been perfonned on single-crystal
X-ray or neutron diffraction profiles. The profìle-fìtting
technique is bere employed lo extraet integrated intensities
from tW0 troublesome data sets of single-crystal,
diffraction profìles, one affected by multiple scattering
effects (X-ray) and the other showing scano truncation
(neutrons). It is sbown that the proposed implementation
of the profile-fìtting procedure bas great advantages in
producing reliable integrated intensities compared with
conventional integration methods. Furthermore, during
the data precessìng, any anomalous diffraction profile
is easily detected and proper analysis of instrumental
background and scan-trnncation effects is performed.
The method thus allows effective evaluation of the
quality of the treated data set. It is proposed that the
profìle-fitting tecbnique for the extraction of singlecrystal
integrated intensities be used routinely when
diffraction data of superior quality are neéded for crystal
structure analysis
Theoretical structure factors and electron density of magnesite (MgCO3)
No full textTheoretical structure factors Fq of rhombohedral magnesite (MgCO3) have been computed by quantum-mechanical periodic Hartree-Fock methods and compared with observed |Fo| (literature data) and conventional Fc (independent-spherical-atom model) values. The corresponding Roq, Roc and Rqc agreement factors (overall values 2.03, 2.11 and 1.80%, respectively) are analysed versus sin(θ)/λ, showing the effects of chemical bonding and of experimental errors. Difference electron density maps Δρoq, ΔρOC and Δρqc have been calculated for the CO3 and the C - O - Mg planes. Features of the C - O covalent bonding and oxygen lone pair are compared and discussed
How stacking disorder can conceal the actual structure of micas : the case of phengites
No full textThe present study deals with how stochastic stackings of tetrahedral/octahedral phengitic sheets bearing diverse cation distributions affect diffraction signals and the structural inferences therefrom derived. The interest for such minerals is dictated by that the stability of phengite polytypes, their cation distributions and P/T conditions of crystallization are related to each other. We focus our attention on layers' probabilistic sequences that preserve the topology of the polytypes 2M1(SG: C2/c) and 3T(SG: P3112). Neutron diffraction intensities are modelled by a Monte Carlo approach and then used as artificial experimental data for conventional structure refinements that yield the occupancy factors in the fourfold (Si, Al) and sixfold (Al, Mg) coordination sites of 2M1 and 3T. The cation ordering from structure refinement tallies with the one of the "average structure" of a stochastic stacking, but it can significantly differ from those of the individual tetrahedral/octahedral sheets. For instance, sheets having ordered cation arrangements can lead to a stochastic structure which is supposed to bear a fully disordered cation partitioning according to structure refinement. This affects the configuration entropy contributions: the values obtained by conventional refinements can deviate from the correct ones up to 30 %. The analysis of the equivalent reflection intensities brings to light the anomalies hinting at the occurrence of such stacking disorder (using modelled reflections, the mean ratio between standard deviation and average intensity of symmetry equivalent reflections is ideally 0 for perfect crystal structures, but it can amount up to 6 in stochastically disordered phengites). However, taking into account the instrumental uncertainties and the deviations from ideality of actual crystals, such phenomena are very difficult to be detected experimentally
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