Series Of Structure Refinements Research Articles

Wardite (NaAl3(PO4)2(OH)4·2H2O) at High Pressure: Compressional Behavior and Structure Evolution

The high-pressure behavior of wardite, NaAl3(PO4)2(OH)4·2H2O (a = 7.0673(2) Å, c = 19.193(9) Å, Sp. Gr. P41212), has been investigated by in-situ single-crystal synchrotron diffraction experiments up to 9 GPa, using a diamond anvil cell under quasi-hydrostatic conditions. This phosphate does not experience any pressure-induced phase transition, or anomalous compressional behavior, within the pressure-range investigated: its compressional behavior is fully elastic and all the deformation mechanisms, at the atomic scale, are reversible upon decompression. A second-order Birch–Murnaghan Equation of State was fitted to the experimental data, weighted by their uncertainty in pressure (P) and volume (V), with the following refined parameters: V0 = 957.8(2) Å3 and KV0 = −V0(∂P/∂V)P0,T0 = 85.8(4) GPa (βV0 = 1/KV0 = 0.01166(5) GPa−1). Axial bulk moduli were also calculated, with: K0(a) = 98(3) GPa (β0(a) = 0.0034(1) GPa−1) and K0(c) = 64(1) GPa (β0(c) = 0.0052(1) GPa−1). The anisotropic compressional scheme is: K0(a):K0(c) = 1.53:1. A series of structure refinements were performed on the basis of the intensity data collected in compression and decompression. The mechanisms at the atomic scale, responsible for the structure anisotropy of wardite, are discussed.

Allanite at high pressure: effect of REE on the elastic behaviour of epidote-group minerals

The compressional behaviour of a natural allanite from Lago della Vecchia (upper Cervo valley, Italy) metagranitoids [A1( $$ {\text{Ca}}_{0.69}{\text{Fe}}_{0. 3 1}^{ 2+ } $$ )Σ1.00A2(Ca0.46Ce0.24La0.12Sm0.02Pr0.05Nd0.09Th0.02)Σ1.00M1( $$ {\text{Al}}_{0.65}{\text{Fe}}_{0. 3 4}^{ 3+ } $$ Ti0.02)Σ1.01M2(Al0.99)M3( $$ {\text{Fe}}_{0. 5 4}^{3 + } {\text{Fe}}_{0. 3 6}^{ 2+ } $$ Mg0.06 $$ {\text{Ti}}_{0.0 2}^{ 4+ } $$ Al0.01)Σ0.99Si1,Si2,Si3(Si2.80Al0.20)Σ3.00O11(OH,O)] has been investigated up to 16 GPa (at 298 K) by means of in situ synchrotron single-crystal X-ray diffraction. Experiments have been conducted under hydrostatic conditions, using a diamond anvil cell and the mix methanol:ethanol:water = 16:3:1 (up to 10 GPa) and neon (up to 16 GPa) as pressure-transmitting media. No phase transition has been observed within the pressure-range investigated. Data collected in decompression prove that, at least up to 16 GPa (at 298 K), the deformation mechanisms are fully reversible. A third-order Birch–Murnaghan Equation of State (BM-EoS) was fitted to the P–V data (up to 10 GPa), giving: V0 = 470.2(2) A3, KP0,T0 = 131(4) GPa and K′= 1.9(8). The evolution of the lattice parameters with pressure shows a slight anisotropic compression pattern, with KP0,T0(a):KP0,T0(b):KP0,T0(c) = 1.24:1.52:1. The monoclinic β-angle decreases monotonically with pressure, with: βP(°) = βP0 – 0.0902(4)P (R2 = 0.997, with P in GPa). The main deformation mechanisms at the atomic scale are described based on a series of structure refinements at different pressures. A comparison between the compressional behavior of allanite, epidote and clinozoisite is carried out.

Anisotropic compressional behavior of ettringite

The high-pressure behavior of a natural ettringite [Ca6Al2(SO4)3(OH)12·27H2O, a = 11.2104(2) Å, c = 21.4350(3) Å, sp. gr. P31c] has been studied by single-crystal X-ray diffraction with a diamond-anvil cell up to 4.22 GPa, using the methanol:ethanol = 4:1 mixture as a hydrostatic pressure-transmitting fluid. The isothermal bulk modulus (K0 = −V(∂P / ∂V)) was found to be 26.6(5) GPa. Ettringite shows a significant anisotropic compressional pattern, being more compressible on (001) than along [001] (i.e. the fibers growing axis), with K(c)0 ~ 2K(a,b)0. The mechanisms at the atomic scale, which govern the structure deformation, have been described by a series of structure refinements up to 2.3 GPa. The structure evolution in response to the applied pressure indicates a plausible densification of the hydrogen-bond network between the Ca(OH)4(H2O)4 polyhedra and the SO4 tetrahedra, which results in a softening and ultimately in a collapse of the whole structure at pressures > 3 GPa.

Armstrongite at non-ambient conditions: An in-situ high-pressure single-crystal X-ray diffraction study

Abstract The high-pressure behavior of a natural armstrongite [(Ca0.96Ce0.01Yb0.01)Zr0.99Si6O14.97·2.02H2O, a∼14.03 A, b∼14.14 A, c∼7.85 A, β∼109.4°, Sp. Gr. C2/m], a microporous heterosilicate, has been studied by single-crystal X-ray diffraction with a diamond-anvil cell up to 8 GPa, using the methanol:ethanol:H2O = 16:3:1 mixture as a pressure-transmitting fluid. A first-order phase transition, characterized by a triplication of the unit-cell volume, was detected between 4.01 (5) and 5.07 (5) GPa. The isothermal bulk modulus (KV0 = -V (∂P/∂V)) of the high-pressure polymorph was found to be ∼50% higher than that obtained for the low-pressure one (i.e., KV0 = 45 (1) GPa for the high-pressure polymorph, KV0 = 31.2 (6) GPa for the low-pressure polymorph), indicating a remarkable change in the structure compressibility. The mechanisms at the atomic scale, which govern the structure deformation of the low-P polymorphs, are described based on a series of structure refinements up to 4 GPa, and a comparison with those experienced by the structure at high temperature is provided. As observed for other microporous silicates, the polyhedral tilting is the main deformation mechanism able to accommodate the effects of the applied pressure. No evidence of crystal-fluid interaction, with a selective sorption of molecules of the pressure-transmitting fluid through the cavities, was observed at high pressure.

High‐pressure behavior of (Cs,K)Al4Be5B11O28 (londonite): A single‐crystal synchrotron diffraction study up to 26 GPa

AbstractThe compressional behavior and the P‐induced deformation mechanisms at the atomic scale of (Cs,K)Al4Be5B11O28 (londonite, a ~7.31 Å and space group P3m) were investigated by in situ single‐crystal synchrotron X‐ray diffraction with a diamond anvil cell up to 26 GPa. No phase transition was observed within the P‐range investigated: this material exhibits isotropic compression (i.e., with cubic symmetry) in response to the applied pressure. Fitting the P–V data with a Birch‐Murnaghan isothermal equation of state, we obtained: V0=390.8(3) Å3, KP0=212(7) GPa (β0=1/KP0=0.0047(1) GPa−1) and K′=4.6(6). A series of structural refinements, based on the high‐pressure intensity data, were performed. The stiffness of londonite (similar to that of carbides) is governed by its close‐packing structure, and in particular by the very low compressibility of B‐ and Be‐tetrahedra and the modest compressibility of the Al‐octahedra. The Cs‐polyhedra are the most compressible units of the structure. The effects of pressure can be accommodated by intrapolyhedral compression or deformation, leading to a modest bulk compression. The high amount of boron in londonite (B2O3 ~50 wt%) makes its synthetic counterpart a potential neutron absorber. In addition, the high content of Cs makes londonite‐type materials as potential hosts for nuclear waste.

Applications of Bayesian corrections for systematic errors in Rietveld refinements

Recently, a Bayesian statistics approach for correction of systematic errors in Rietveld refinements has been developed and implemented as a patch toGSAS-II. This paper demonstrates the benefits of the proposed method in a series of structural refinements from diffraction data collected for one sample using four different powder diffractometers,i.e.synchrotron and laboratory X-ray and two time-of-flight neutron instruments. Differences between the parameters estimated while fitting these four data sets provided magnitudes of the systematic errors while also highlighting the efficacy of the Bayesian procedure for their correction. Structural parameters estimated from the standard Rietveld refinements using the four data sets differed significantly. In all cases, the agreement improved markedly after applying the Bayesian error-correction procedure. The Bayesian refinements were paired with a Markov chain Monte Carlo algorithm, which was implemented as part of the same patch toGSAS-II, to confirm that uncertainties in the refined parameters obtained using the much faster least-squares minimization were realistic.

Elastic behavior and pressure-induced structure evolution of topaz up to 45 GPa

The behavior of a natural topaz, Al2.00Si1.05O4.00(OH0.26F1.75), has been investigated by means of in situ single-crystal synchrotron X-ray diffraction up to 45 GPa. No phase transition or change in the compressional regime has been observed within the pressure-range investigated. The compressional behavior was described with a third-order Birch–Murnaghan equation of state (III-BM-EoS). The III-BM-EoS parameters, simultaneously refined using the data weighted by the uncertainties in P and V, are as follows: KV = 158(4) GPa and KV′ = 3.3(3). The confidence ellipse at 68.3 % (Δχ2 = 2.30, 1σ) was calculated starting from the variance–covariance matrix of KV and K′ obtained from the III-BM-EoS least-square procedure. The ellipse is elongated with a negative slope, indicating a negative correlation of the parameters KV and KV′, with KV = 158 ± 6 GPa and KV′ = 3.3 ± 4. A linearized III-BM-EoS was used to obtain the axial-EoS parameters (at room-P), yielding: K(a) = 146(5) GPa [βa = 1/(3K(a)) = 0.00228(6) GPa−1] and K′(a) = 4.6(3) for the a-axis; K(b) = 220(4) GPa [βb = 0.00152(4) GPa−1] and K′(b) = 2.6(3) for the b-axis; K(c) = 132(4) GPa [βc = 0.00252(7) GPa−1] and K′(c) = 3.3(3) for the c-axis. The elastic anisotropy of topaz at room-P can be expressed as: K(a):K(b):K(c) = 1.10:1.67:1.00 (βa:βb:βc = 1.50:1.00:1.66). A series of structure refinements have been performed based on the intensity data collected at high pressure, showing that the P-induced structure evolution at the atomic scale is mainly represented by polyhedral compression along with inter-polyhedral tilting. A comparative analysis of the elastic behavior and P/T-stability of topaz polymorphs and “phase egg” (i.e., AlSiO3OH) is carried out.

A low temperature X-ray single-crystal diffraction and polarised infra-red study of epidote

The effects of low-temperature on the crystal structure of a natural epidote [Ca1.925Fe0.745Al2.265Ti0.004Si3.037O12(OH), a = 8.8924(7), b = 5.6214(3), c = 10.1547(6)A and β = 115.396(8)° at room conditions, Sp. Gr. P21 /m] have been investigated with a series of structure refinements down to 100 K on the basis of X-ray single-crystal diffraction data. The reflection conditions confirm that the space group is maintained within the T-range investigated. Structural refinements at all temperatures show the presence of Fe3+ at the octahedral M(3) site only [%Fe(M3) = 70.6(4)% at 295 K]. Only one independent proton site was located and two possible H-bonds occur, with O(10) as donor and O(4) and O(2) as acceptors. The H-bonding scheme is maintained down to 100 K and is supported by single crystal room-T polarised FTIR data. FTIR Spectra over the region 4,000–2,500 cm−1 are dominated by the presence of a strongly pleochroic absorption feature which can be assigned to protonation of O(10)–O(4). Previously unobserved splitting of this absorption features is consistent with a NNN influence due to the presence of Al and Fe3+ on the nearby M(3) site. An additional relatively minor absorption feature in FTIR spectra can be tentatively assigned to protonation of O(10)–O(2). Low-T does not affect significantly the tetrahedral and octahedral bond distances and angles, even when distances are corrected for “rigid body motions”. A more significant effect is observed for the bond distances of the distorted Ca(1)- and Ca(2)-polyhedra, especially when corrected for “non-correlated motion”. The main low-T effect is observed on the vibrational regime of the atomic sites, and in particular for the two Ca-sites. A significant reduction of the magnitude of the thermal displacement ellipsoids, with a variation of U eq (defined as one-third of the trace of the orthogonalised U ij tensor) by ~40% is observed for the Ca-sites between 295 and 100 K. Within the same T-range, the U eq of the octahedral and oxygen sites decrease similarly by ~35%, whereas those of the tetrahedral cations by ~22%.

Dehydration dynamics of Ba-phillipsite: an in situ synchrotron powder diffraction study

The stepwise dehydration process of the Ba-exchanged form of the zeolite phillipsite was studied by in situ synchrotron X-ray powder diffraction. A series of structure refinements were performed using the Rietveld method on powder diffraction data measured in the interval between 332 and 712 K. At 482 K, more than half of the water molecules were lost. The continuous water loss causes the Ba cations to migrate inside the zeolite channels in order to achieve a stable coordination with the framework oxygens.

A single-crystal neutron diffraction study of the temperature dependence of hydrogen-atom disorder in benzoic acid dimers

Hydrogen-atom transfer across the hydrogen bonds of benzoic acid dimers has been studied previously by spectroscopic and X-ray methods, but no high-resolution neutron single crystal structures have ever been reported. The system is of interest because the hydrogen-atom dynamics change from classical Arrhenius behaviour to phonon-assisted quantum tunnelling as a function of decreasing temperature. Here we present a series of neutron single-crystal structure refinements at five temperatures ranging from 175 K, where Arrhenius behaviour holds, down to 20 K, where translational tunnelling is dominant. The refinements yield accurate atomic coordinates, thermal parameters and site occupancy factors for all atoms, and show that conversion of the B dimer configuration to the lower energy A dimer configuration in the range 175 to 50 K is primarily enthalpy driven, in good agreement with spectroscopic data. Site occupancies for the hydrogen-bonded hydrogen atom at 20 K do not fit the trend in occupancies observed at the four higher temperatures, and a further series of structure refinements at temperatures below 50 K is planned to investigate this.