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The incomplete miscibility of Al into the ferrihydrite structure has been a recurring issue in understanding the environmental geochemistry of this important oxyhydroxide. During co-precipitation from acidic aqueous solution, ferrihydrite has been observed to accept only up to ∼25 at.% Al without the formation of multi-phasic Al and Fe oxyhydroxides. Using basic chemistry and crystal-chemical relationships we propose here that the saturation limit of Al substitution in the structure of Fe oxyhydroxides is controlled by Al – Al avoidance in a manner that conforms to Pauling's distortion rule. Employing this hypothesis, we show that the predicted miscibility limit for Al incorporation is 25 at.% in ferrihydrite and 33 at.% in goethite, in agreement with previous observations. These results indicate that the classical f-phase model for ferrihydrite best represents observations. Incorrect assignment of Fe site occupancy and other shortcomings of the akdalaite/tohdite model for ferrihydrite are also discussed.
The risk of overfitting pair distribution function (PDF) data for highly defective material (Farrow et al., 2007) is illuminated with the example of the nanocrystalline hydrous ferric oxyhydroxide, ferrihydrite. Two structural models have been published by Michel et al. (2007, 2010) using this method, both of which contradict the standard ‘ferrihydrits’ model established by X-ray diffraction (Drits et al., 1993), and confirmed by single-crystal electron nanodiffraction (Janney et al., 2001) and neutron diffraction (Jansen et al., 2002). Although PDF data are reproduced equally well with the two regression models, neither model is realistic: the first (fhyd6) violates Pauling's 2nd rule, and the second (ferrifh), Pauling's 3rd rule.
Some of the proofs in the above paper are incomplete.
The pressure term in the incompressible elasticity equation needs to be considered and estimated in order to pass to the limit in the homogenization process. This will require Sections 2.2 and 3.2 to be rewritten.
A corrected version will be submitted in due course.
We study incompressible two-dimensional elasticity problems with high-contrast coefficients. The Keller–Dykhne duality relations are extended to the case of Hooke's laws which are equicoercive and uniformly bounded in L1 but not in L∞. A compactness result is obtained for Hooke's laws which are uniformly bounded from above and such that their inverses are bounded in L1 but not in L∞, with a refinement in the periodic case. Moreover, we establish a compactness result in for a sequence of two-dimensional vector-valued functions in which are only bounded in L2.
A new structural model for ferrihydrite that challenges the standard ferrihydrite model established by X-ray diffraction and confirmed by neutron diffraction and single-crystal electron nanodiffraction was recently proposed by Michel et al. (2007a) from the simulation of the pair distribution function obtained by Fourier transformation of diffraction data measured at λ = 0.137 Å. The new ferrihydrite model is isostructural to akdalaite (Al10O14(OH)2), a mineral having the Baker-Figgis δ-isomer of the Al13-Keggin structure as its structural motif. The new model is unrealistic because: (1) it is completely periodic (i.e. defect-free); (2), it has 20% tetravalent octahedral iron (VIFe4+), 20% divalent tetrahedral iron (IVFe2+), and some IVFe–O distances equal to or larger than the VIFe3+–O distances, thus violating Pauling's 2nd rule; (3) it does not describe X-ray diffraction and EXAFS spectroscopic data; and, (4) it is inconsistent with electron microscopy results and contradicts previous X-ray scattering studies.
Vernadite is a nanocrystalline turbostratic phyllomanganate containing Ni, and is widespread in surface environments and oceanic sediments. To improve our understanding of Ni uptake in this mineral, two series of analogues of vernadite (δ-MnO2) were prepared with Ni/Mn atomic ratios of 0.002—0.105 at pH4 and 0.002—0.177 at pH 7. Their structures were characterized using X-ray powder diffraction (XRD). The δ-MnO2 nano-crystals are essentially monolayers with coherent scattering domains sizes of ∼10 Å perpendicular to the layering and ∼55 Å within the layer plane. For Ni/Mn < 0.01, the layer charge deficit is apparently balanced entirely by interlayer Mn, Na and protons. At higher Ni/Mn, Ni occupies the same site as interlayer Mn above and below vacant sites within the MnO2 layer and at sites along the edges of the layer. However, the layer charge is balanced differently at the two pH values. At pH 4, Ni uptake is accompanied by a reduction in structural Na and protons, whereas interlayer Mn remains strongly bound to the layers. At pH 7, interlayer Mn is less strongly bound and is partially replaced by Ni. The results of this study also suggest that the number of vacant octahedral sites and multi-valent charge-copmpensating interlayer species are underestimated by the currently used structure models of δ-MnO2.
In this paper, we compare a biomechanics empirical model of the heart fibrous structure to two models obtained by a non-periodic homogenization process. To this end, the two homogenized models are simplified using the small amplitude homogenization procedure of Tartar, both in conduction and in elasticity. A new small amplitude homogenization expansion formula for a mixture of anisotropic elastic materials is also derived and allows us to obtain a third simplified model.
Most clinical studies on carbon dioxide (CO2) (λ = 10.6.mm) laser stapedotomy have been carried out with the laser guided by a conventional lens-based micromanipulator, with the attendant risks of correct aiming (HeNe) and surgical (CO2) beam misalignment. Hence, engineering advances have attempted to improve laser targeting as well as the spot size focus. The development of the mirror-based micromanipulator was a response to this need but no data concerning its use in stapes surgery is available. We performed a retrospective case-series review of patients treated for otosclerosis between 1992 and 2000. Primary laser stapedotomy was performed in 218 consecutive patients. In the first 78 procedures, the aiming beam (HeNe, λ = 632 nm) and surgical beam (CO2) were guided with a conventional lens-based micromanipulator whereas in the subsequent 140 procedures, they were guided by using a mirror-based micromanipulator. Hearing was tested at six and 12 months. The mean (SD) air-bone gap was 5 dB (4.5) and 4.5 dB (3.9). The mean closure was 15 dB (9.9) and 14.4 dB (9.4). The mean change in the high-tone bone-conduction level was 5.5 dB (7.3) and 7.8 dB (7.5). Overheating of the facial canal produced transient facial paralysis in one case and was due to misalignment of the beams with the lens-based micromanipulator. Use of the mirror-based micromanipulator obviated the need to verify alignment. The light-weight and superior optical yield of this system made it possible to reduce the number of impacts on the footplate by the integral restitution of the energy source. This study demonstrated that the CO2 laser is an effective method for performing stapedotomy. In addition, microtrauma to the labyrinth is reduced by its ability to perform calibrated footplate fenestration without mechanical or vibrational injury to the inner ear. The optical reflection micromanipulator simplified beam alignment and enhanced surgical comfort.
The temporal dynamics of large-scale structures in a plane turbulent mixing layer
are studied through the development of a low-order dynamical system of ordinary
differential equations (ODEs). This model is derived by projecting Navier–Stokes
equations onto an empirical basis set from the proper orthogonal decomposition
(POD) using a Galerkin method. To obtain this low-dimensional set of equations, a
truncation is performed that only includes the first POD mode for selected streamwise/spanwise
(k1/k3) modes. The initial truncations
are for k3 = 0; however, once
these truncations are evaluated, non-zero spanwise wavenumbers are added. These
truncated systems of equations are then examined in the pseudo-Fourier space in
which they are solved and by reconstructing the velocity field. Two different methods
for closing the mean streamwise velocity are evaluated that show the importance
of introducing, into the low-order dynamical system, a term allowing feedback between
the turbulent and mean flows. The results of the numerical simulations show a
strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the
correct energy distributions in the cross-stream direction. These models also indicated
that the events associated with the centre of the mixing layer lead the temporal
dynamics. For truncations involving both spanwise and streamwise wavenumbers,
the reconstructed velocity field exhibits the main spanwise and streamwise vortical
structures known to exist in this flow. The streamwise aligned vorticity is shown to
connect spanwise vortex tubes.
A channel flow DNS database at Reτ = 590 is used to assess the validity of modelling
the redistribution term in the Reynolds stress transport equations by elliptic relaxation.
The model assumptions are found to be globally consistent with the data. However, the
correlation function between the fluctuating velocity and the Laplacian of the pressure
gradient, which enters the integral equation of the redistribution term, is shown to
be anisotropic. It is elongated in the streamwise direction and strongly asymmetric
in the direction normal to the wall, in contrast to the isotropic, exponential model
representation used in the original elliptic relaxation model. This discrepancy is the
main cause of the slight amplification of the energy redistribution in the log layer
as predicted by the elliptic relaxation equation. New formulations of the model are
proposed in order to correct this spurious behaviour, by accounting for the rapid
variations of the length scale and the asymmetrical shape of the correlation function.
These formulations do not rely on the use of so-called ‘wall echo’ correction terms to
damp the redistribution. The belief that the damping is due to the wall echo effect is
called into question through the present DNS analysis.
electrostrictive ceramics like 0.9 PMN-0.1 PT show large reduction of the apparent Young's
modulus (more than 50%) as a function of the electric field. In the literature, this result
is always obtained in the direction of the applied electric field. We performed some
measurements of the elastic modulus in the direction perpendicular to the electric field and
we found an unexpected small variation (less than 6%). This result shows that the apparent
mechanical properties are much more dependent of the direction of the electrical field than
Haslea ostrearia, the peculiar diatom that develops in oyster-ponds and synthesizes a water-soluble blue pigment (marennine), was grown
in a semi-continuous mode over a wide range of irradiances (20–750 μmol; m−2 s−1). Growth, photosynthesis and pigment content were
determined for algae maintained in exponential growth phase by regular dilution with fresh medium. Increasing the growth irradiance
resulted in a decrease in the chloroplast length, but had no clear influence on the size of the cellular compartments pigmented by
marennine accumulation. Growth rates increased with irradiance from 20 to 100 μmol; m−2 s−1 and were constant from 100 to 750 μmol;
m−2 s−1. Increasing growth irradiance caused a decrease in the cellular content of chlorophylls a and c and fucoxanthin, in contrast to
diadinoxanthin. Algae acclimated to high irradiance had lower maximum photosynthetic rate (Pnm) and maximum light utilization
coefficient (α) when expressed on a per cell basis. On a chlorophyll a basis, the higher the growth irradiance, the lower the maximum
light utilization coefficient and the higher the maximum photosynthetic rate. No photoinhibition was observed at irradiances up to
1500 μmol; m−2 s−1 whatever the growth irradiance. In vivo chlorophyll a fluorescence showed that cells grown at high irradiance had
effective photosystem II quantum efficiency (measured at the growth irradiance) considerably lower than that of cells grown at low
irradiance. Thus H. ostrearia withstands high light exposure, consistent with the observation that this alga can outcompete other diatoms
encountered in oyster-ponds characterized by low turbidity and shallow depth.
The Pyrenean population of Spanish wild goat (Capra pyrenaica pyrenaica) is nearly extinct. To find the most appropriate source of individuals for supplementing the Pyrenean population, we identified Evolutionary Significant Units (ESUs) among populations of the Capra pyrenaica species. We have examined sequence variability of portions of the mitochondrial DNA (mtDNA) control region and cytochrome b (cyt b) gene. Samples were from seven populations of Spanish wild goat distributed over the species' geographic range. The level of divergence between the Pyrenean and other Spanish haplotypes is almost as high as the divergence between the Alpine (C. ibex ibex) and the Spanish wild goats. In addition, the Pyrenean goat is morphologically distinct from other Spanish wild goats. Therefore the Pyrenean population should be considered as an ESU. For the reinforcement, we suggest either using individuals from the most polymorphic Spanish population, or mixing individuals from diverse Spanish origins, since all the other Spanish populations are equally genetically distant from the Pyrenean population.
Celadonite, glauconite and Fe-illite samples were studied by XRD, EXAFS, IR and Mössbauer spectroscopy. The samples were monomineralic and corresponded to 1M polytype. In the OH-stretching region of the IR spectra the content of each definite pair of cations bonded to OH groups was determined. The number of heavy (Fe) and light (Al, Mg) octahedral cations nearest to Fe was found by the EXAFS technique. The predicted quadrupole splitting values for each definite arrangement of cations nearest to Fe3+ were used to interpret the Mössbauer spectra. After the fitting procedure, the intensity of each doublet corresponded to a definite set of local cation arrangements around Fe3+ and to a definite occurrence probability of these arrangements. Computer simulation and the experimental data obtained were used to reconstruct the distribution of isomorphous octahedral cations in the 2:1 layers. For all samples, R2+ cations prefer to occupy one of the two symmetrically independent cis-sites and R2+-R2+ and/or Al-Fe3+ were prohibited in the directions forming ± 120° with the b axis. Therefore, octahedral sheets of the samples revealed domain structure, in which domains differ in size, in the nature of predominant cation and/or by cation ordering.
The first stages of the hydrolysis of Fe(III) in presence of PO4 were studied at the local (P k-edge and Fe k-edge EXAFS spectroscopy) and semi-local scale (SAXS). The presence of PO4 hinders the polymerization of iron at the edge sharing dimer step. Phosphate probably governs the local structure leading to the formation of small and dense clusters. The fitting of both k-edge EXAFS spectroscopies requiered the use of a new 3D model of each nucleation step.
The structure of 6-line and 2-line ferrihydrite (Fh) has been reconsidered. X-ray diffraction (XRD) curves were first simulated for the different structural models so far proposed, and it is shown that neither of these corresponds to the actual structure of ferrihydrite. On the basis of agreement between experimental and simulated XRD curves it is shown that Fh is a mixture of three components: (i) Defect-free Fh consisting of anionic ABACA . . . close packing in which Fe atoms occupy only octahedral sites with 50% probability; the hexagonal unit-cell parameters are a = 2-96 Å and c = 9-40 Å, and the space group is P1c. (ii) Defective Fh in which Ac1Bc2A and Ab1Cb2A structural fragments occur with equal probability and alternate completely at random; Fe atoms within each of these fragments have identical ordered distribution with in the hexagonal super-cell with a = 5.26 Å. (iii) Ultradispersed hematite with mean dimension of coherent scattering domains (CSD) of 10-20 Å. The main structural difference between 6-line and 2-line Fh is the size of their CSD which is extremely small for the latter structure. Nearest Fe-Fe distances calculated for this new structural model are very close to those determined by EXAFS spectroscopy on the same samples.
Synthetic 2-line and 6-line ferrihydrite and feroxyhite samples prepared from ferric salt solutions have been investigated by EXAFS spectroscopy. All these materials have been found to be short-range ordered, consisting of Fe octahedra linked by comers, edges, and faces. Their local structures are related to those of well-crystallized (oxyhydr)oxides, and the absence of hkl reflections in some samples is attributed to the small size of coherent scattering domains. The presence of face sharings indicates that these materials have structural similarities with hematite. Based on Fe-Fe distances and the analysis of the static disorder, it has been concluded that the local structure of feroxyhite is close to that of hematite, whereas ferrihydrite has common structural features with both hematite (αFe203) and cdβFeOOFI. The local structure of ferrihydrite thus differs from that of aqueous Fe polymers obtained by the partial hydrolysis of ferric nitrate and chloride solutions. Differences of local structures among hydrous Fe oxides and aqueous polymers have been interpreted on the basis of a room temperature stability phase diagram established for well-crystallized (oxyhydr)oxides.
Powder X-ray diffraction (XRD) curves were calculated for the different structural models so far proposed for feroxyhite (δFeOOH). The influence on XRD features of different structural parameters, including site occupancy of Fe atoms, atomic coordinates, content and distribution of stacking faults, and dimension of coherent scattering domains, were considered. On the basis of agreement between experimental and simulated curves it is shown that δFeOOH is a mixture of feroxyhite proper and ultradispersed hematite in the 9 : 1 volume ratio. Feroxyhite proper consists of hexagonal close packing of anions containing 5% stacking faults. Iron atoms occupy only octahedral sites and are distributed in such a way that face-sharing filled octahedral pairs regularly alternate with vacant octahedral pairs along the c axis. This distribution of Fe atoms is quite similar to that established by Patrat et al. (1983), but in each pair, Fe atoms are displaced by the same value of 0.3 Å in opposite directions away from the centre of their octahedron. Nearest Fe-Fe distances calculated for the model proposed (2.88, 3.01, 3-39 and 3-73 Å) practically coincide with those found by EXAFS spectroscopy for the same sample (2-91, 3.04, 3.41 and 3.7-3.8 Å).