IR spectroscopic characterization of NH4-analcime

 The IR spectrum of ammonium-exchanged natural analcime (basalt, Nidym River, Siberian platform) exhibits several features that suggest a lowered symmetry for the NH₄ ⁺ ion and that this is influenced by hydrogen bonding within the framework. These features are: the pronounced splitting into three components and high-frequency shift of the ν₄-bending mode; appearance of the ν₁-stretching mode which is predicted to become IR-active when the ideal T _d symmetry of NH₄ ⁺ ion is violated, and the low-frequency shift of the ν₁- and ν₃-stretching modes. The absence of absorption lines in the 1800–2400-cm⁻¹ region indicates that hydrogen bonding between the framework and the NH⁺ ₄ ion is very weak. The three-component splitting of the ν₄-bending mode indicates that the symmetry of NH⁺ ₄ ion is lower than C_3v. This implies that at least two N–H bonds of the NH⁺ ₄ ion are disturbed by hydrogen bonding. Computer analysis of the normal vibrations of the NH⁺ ₄ molecule for different symmetry types (using harmonic approximation) indicates that the best fit to the observed ν₄ triplet frequencies for C₁ symmetry implies a deviation of the valent angle ∠H–N–H from ideal T _d symmetry of around ±2.5°. The factors governing the behaviour of the NH⁺ ₄ ion in the analcime structure are discussed. The geometry of the nearest environment of the NH⁺ ₄ ion in the analcime structure is analyzed with respect to the present IR data. Received: 2 January 2002 / Accepted: 26 June 2002 Acknowledgements We thank Dr. D. Harlov and an anonymous reviewer for their helpful comments, as well as Dr. I.A. Belitsky and Dr. S.V. Goryainov for discussion of the material. This work is supported by RFBR grants 01-05-65414, 00-05-65305 and 02-05-65313.     

The Kappa model of probability and higher-order rock sequences

In any depositional environment, the sequence of sediments follows specific high- and low-frequency patterns of rock occurrences or events. The occurrence of a rock in a spatial location is conditional to a prior rock event at a distant location. Subsequently, a third rock occurs between the two locations. This third event is conditional to both prior events and is driven by a third-order conditional probability P(C ∣ (A ∩ B)). Such probability has to be characterized beyond the classic conditional independence model, and this research has found that exact computation requires a third-order co-cumulant term. The co-cumulants provide the higher-order redundancy among multiple indicator variables. A Bayesian analysis has been performed with “known” numerical co-cumulants yielding a novel model of conditional probability that is called the “Kappa model.” This model was applied to three-point variables, and the concept has been extended for multiple events P(G ∣ A ∩ B ∩ C ∩ D... ∩ N), allowing the reproduction of complex transitions of rocks in sequence stratigraphy. The Kappa model and co-cumulants have been illustrated with simple numerical examples for clastic rock sequences. In addition, the co-cumulant has been used to discover an extension of the variogram called the indicator cumulogram. In this way, multiple prior events are no longer ignored for evaluating the probability of a posterior event with higher-order co-cumulant considerations.     

Location and quantitative analysis of OH in coesite

 The incorporation of hydrogen (deuterium) into the coesite structure was investigated at pressures from 3.1 to 7.5 GPa and temperatures of 700, 800, and 1100 °C. Hydrogen could only be incorporated into the coesite structure at pressures greater 5.0 GPa and 1100 °C . No correlation between the concentration of trace elements such as Al and B and the hydrogen content was observed based on ion probe analysis (1335 ± 16 H ppm and 17 ± 1 Al ppm at 7.5 GPa, 1100 °C). The FTIR spectra show three relatively intense bands at 3575, 3516, and 3459 cm⁻¹ (ν₁ to ν₃, respectively) and two very weak bands at 3296 and 3210 cm⁻¹ (ν₄ and ν₅, respectively). The band at 3516 cm⁻¹ is strongly asymmetric and can be resolved into two bands, 3528 (ν_2a) and 3508 (ν_2b) cm⁻¹, with nearly identical areas. Polarized infrared absorption spectra of coesite single-crystal slabs, cut parallel to (0 1 0) and (1 0 0), were collected to locate the OH dipoles in the structure and to calibrate the IR spectroscopy for quantitative analysis of OH in coesite (ɛ _{i ,tot}=190 000 ± 30 000 l mol⁻¹ _H2O cm⁻²). The polarized spectra revealed a strong pleochroism of the OH bands. High-pressure FTIR spectra at pressures up to 8 GPa were performed in a diamond-anvil cell to gain further insight into incorporation mechanism of OH in coesite. The peak positions of the ν₁, ν₂, and ν₃ bands decrease linearly with pressure. The mode Grüneisen parameters for ν₁, ν₂, and ν₃ are −0.074, −0.144 and −0.398, respectively. There is a linear increase of the pressure derivatives with band position which follows the trend proposed by Hofmeister et al. (1999). The full widths at half maximum (FWHM) of the ν₁, ν₂, and ν₃ bands increase from 35, 21, and 28 cm⁻¹ in the spectra at ambient conditions to 71, 68, and 105 in the 8 GPa spectra, respectively. On the basis of these results, a model for the incorporation of hydrogen in coesite was developed: the OH defects are introduced into the structure by the substitution Si^4+(Si2)+4O²⁻= ^[4]□^(Si2) + 4OH⁻, which gives rise to four vibrations, ν₁, ν_2a, ν_2b, and ν₃. Because the OH(D)-bearing samples do contain traces of Al and B, the bands ν₄ and ν₅ may be coupled to Al and/or B substitution. Received: 19 December 2000 / Accepted: 23 April 2001     

The orientation and vibrational states of H2O in synthetic alkali-free beryl

 The polarized single-crystal Raman spectra of synthetic H₂O-containing alkali-free beryl were recorded at room and low temperatures, and the polarized single-crystal IR spectra at room temperature. The H₂O molecule in the channel cavities is characterized by a Raman-active symmetric stretching vibration (ν₁) at 3607 cm⁻¹ and an IR-active asymmetric stretch (ν₃) at 3700 cm⁻¹ at room temperature. At low temperatures this ν₃ mode is observed in the Raman. Weak ν₁ and ν₃ modes of a second type of H₂O are also observed in the Raman spectra but only at 5 K. The H⋯·H vector of the most abundant type of H₂O is parallel to the channel axis of beryl along [0 0 0 1]. The components of the polarizability tensor of the ν₁ mode of H₂O are similar to, but not exactly the same as, those of a free H₂O molecule. The Raman measurements indicate that the H₂O molecule is rotationally disordered around [0 0 0 1]. External translation and librational modes of H₂O could be observed as overtones with the internal H₂O-stretching modes. In the case of the librational motions, normal modes could also be observed directly in the Raman spectra at ∼200 cm⁻¹. The energies of the translational modes can be determined from an analysis of the overtones and are about 9 cm⁻¹ in energy (i.e., T_z). The energies of the librational modes are about 210 cm⁻¹ for R_x and 190 cm⁻¹ for R_y. Received: 8 April 1999 / Accepted: 5 April 2000     

Evidence for kinks in structural and thermodynamic properties across the forsterite–fayalite binary from thin-film IR absorption spectra

Infrared absorbance spectra over ∼100 to 1,800 cm⁻¹ were collected from optically thin films of 21 samples with compositions spanning the forsterite–fayalite binary. Polarization information from previous specular reflectance data on end-members was used in tracing the peaks across the entire binary. Peak positions (ν_i) were constrained by Lorentzian decompositions. Fitting also constrained widths for singlet peaks but for doublets and triplets, variation in ν_i with composition among the constituent polarizations alters widths from intrinsic. Because film thicknesses of 0.6–1.4 μm were estimated, our band strengths are approximate; however, relative intensities should be correct. Only for a few peaks does ν_i vary smoothly across the entire binary; instead, distinct linear trends exist for Fe- and Mg-rich olivines. Discontinuities and kinks in ν_i(X) occur at X = Mg/(Fe + Mg) = 0.7 and are accompanied by a change in intensity patterns. This interesting behavior was not revealed in previous spectra of powder dispersions. The contrasting character of IR vibrations for Fe- and Mg-rich olivines is inferred to arise from structural variations because (1) frequency is related to bond length, (2) other factors affecting frequency (cation mass and probably bonding type) vary linearly across the binary, and (3) available data on unit cell parameters are consistent with distinct trends for forsterites and fayalites. Vibrational components of heat capacity (C _V) and enthalpy (H) calculated from ν_i, were found to be slightly more negative than linear interpolations between values for forsterite and fayalite. Our computations give smaller negative excesses from ideality in H than do previous calorimetric measurements, but are equal within experimental uncertainties.     

The single-crystal,polarized-light,FTIR spectrum of stoppaniite,the Fe analogue of beryl

We report here a single-crystal polarized-light study of stoppaniite, ideally (Fe,Al,Mg)₄(Be₆Si₁₂O₃₆)(H₂O)₂(Na,□), from Capranica (Viterbo). Polarized-light FTIR spectra were collected on an oriented (hk0) section, doubly polished to 15 μm. The spectrum shows two main bands at 3,660 and 3,595 cm⁻¹; the former is strongly polarized for E ⊥c, while the latter is polarized for E //c. A sharp and very intense band at 1,620 cm⁻¹, plus minor features at 4,000 and 3,228 cm⁻¹ are also polarized for E //c. On the basis of literature data and considering the pleochroic behavior of the absorptions, the 3,660 cm⁻¹ band is assigned to the ν₃ stretching mode and the 1,620 cm⁻¹ (associated with an overtone 2*ν₂ at 3,230 cm⁻¹) band to the ν₂ bending mode of “type II” water molecules within the structural channels of the studied beryl. The sharp band at 3,595 cm⁻¹ is not associated with a corresponding ν₂ bending mode; thus it is assigned to the stretching vibration of O–H groups in the sample. The minor 4,000 cm⁻¹ feature can be assigned to the combination of the O–H bond parallel to c with a low-frequency metal-oxygen mode such as the Na–O stretching mode. The present results suggest that the interpretation of the FTIR spectrum of Na-rich beryl needs to be carefully reconsidered.     

A New Approach to the Modeling of the Pressure Dependency of the Strength of Rocks

Based on the hypothesis that shearing stresses and normal tensile stresses both play a decisive role in fracturing and brittle failure of rock material, a novel strength criterion was developed in one of the earlier works of the author. In the criterion, a certain parameter ν′ occurs which depends on the structure of the material. Originally, the parameter was treated as a constant, which resulted in a linear form of the strength function ^F σ ₁ = f(σ ₃), where σ ₃ = σ ₂. Although the linear strength criterion is sometimes found to be applicable to various particular rock materials, it is not, in general, of a universal character. Analysis of the triaxial test results for 75 different sandstones revealed that parameter ν′ usually increases in an exponential or linear manner as confining pressure increases, and only in isolated cases does it seem to be independent of the confining pressure. For these three types of function ν′ = f(p) appropriate strength criteria ^F σ ₁ = f(σ ₃) are given in the present paper. These criteria were used to fit all of the collected empirical data sets. In general, a very good fit to the data was obtained.     

Multiple-Point Simulations Constrained by Continuous Auxiliary Data

An important issue of using the multiple-point (MP) statistical approach for reservoir modeling concerns the integration of auxiliary constraints derived, for instance, from seismic information. There exist two methods in the literature for these non-stationary MP simulations. One is based on an analytical approximation (the “τ-model”) of the conditional probabilities that involve auxiliary data. The degree of approximation with this method depends on the parameter τ, whose inference is difficult in practice. The other method is based on the inference of these conditional probabilities directly from training images. This method classifies the auxiliary data into a few classes. This classification is in general arbitrary and therefore inconvenient in practice, especially in the case of continuous auxiliary constraints. In this paper, we propose an alternative method for performing non-stationary MP simulations. This method accounts for the data support in the modeling procedure and allows, in particular, continuous auxiliary data to be integrated into MP simulations. This method avoids the major limitations of the previous methods, namely the use of an approximate analytical model and the reduction of the auxiliary data into a limited number of classes. This method can be easily implemented in the existing MP simulation codes. Numerical tests show good performance of this method both in reproducing the geometrical features of the training image and in honouring the auxiliary data.     

The cosmic vacuum and the rotation of galaxies

The rotational effect of the cosmic vacuum is investigated. The induced rotation of elliptical galaxies due to the anti-gravity of the vacuum is found to be 10⁻²¹ s⁻¹ for real elliptical galaxies. The effect of the vacuum rotation of the entire Universe is discussed, and can be described by the invariant ω _ν = ω ₀ ∼ $ \sqrt {G\rho v} $ \sqrt {G\rho v} . The corresponding numerical angular velocity of the Universe is 10⁻¹⁹ s⁻¹, in good agreement with modern data on the temperature fluctuations of the cosmic background radiation.     

Structural and vibrational behaviour of fluorapatite with pressure. Part II: in situ micro-Raman spectroscopic investigation

 High-pressure Raman investigations were carried out on a synthetic fluorapatite up to about 7 GPa to analyse the behaviour of the phosphate group's internal modes and of its lattice modes. The Raman frequencies of all modes increased with pressure and a trend toward reduced splitting was observed for the PO₄-stretching modes [(ν_3a(A_g) and ν_3b(A_g); ν_3a(E_2g) and ν_3b(E_2g)] and the PO₄ out-of-plane bending modes [ν_4a(A_g) and ν_4b(A_g)]. The pressure coefficients of phosphate modes ranged from 0.0047 to 0.0052 GPa⁻¹ for ν₃, from 0.0025 to 0.0044 GPa⁻¹ for ν₄, from 0.0056 to 0.0086 GPa⁻¹ for ν₂ and 0.0046 for ν₁ GPa⁻¹, while the pressure coefficients of lattice modes ranged from 0.0106 to 0.0278 GPa⁻¹. The corresponding Grüneisen parameters varied from 0.437 to 0.474, 0.428, 0.232 to 0.409 and 0.521 to 0.800 for phosphate modes ν₃, ν₁, ν₄, ν₂, respectively, and from 0.99 to 2.59 for lattice modes. The vibrational behaviour was interpreted in view of the high-pressure structural refinement performed on the same crystal under the same experimental conditions. The reduced splitting may thus be linked to the reduced distortion of the environment around the phosphate tetrahedron rather than to the decrease of the tetrahedral distortion itself. Moreover, the amount of calcium polyhedral compression, which is about three times the compression of phosphate tetrahedra, may explain the different Grüneisen parameters. Received: 25 April 2000 / Accepted: 20 December 2000     

Monitoring of the radio emission of the Crab Nebula pulsar at low frequencies

Results of long-term (2002–2010) monitoring of giant radio pulses of the pulsar PSR B0531+21 in the Crab Nebula at ν = 44, 63, and 111 MHz are reported. The observations were conducted on the LPA and DKR-1000 radio telescopes of the Lebedev Physical Institute. The giant pulses were analyzed using specialized software for calculating the magnitude of the scattering τ _sc , signal-to-noise ratio, and other required parameters by modeling the propagation of a pulse in the scattering interstellar medium. Three pronounced sharp increases in the scattering were recorded in 2002–2010. Analysis of the dependence between the variations of the scattering and dispersion measure (data of Jodrell Bank Observatory) shows a strong correlation at all frequencies, ≈0.9. During periods of anomalous increase in scattering and the dispersion measure, the index γ in the frequency dependence of the scattering in the Crab Nebula, τ _sc (ν) ∝ ν ^−γ , was smaller than the generally accepted values γ = 4.0 for a Gaussian and γ = 4.4 for a Kolmogorov distribution. This difference in combination with the piece-wise power-law spectrum may be due to the presence of a dense plasma structure with developed Langmuir turbulence in the nebula, along the pulsar’s line of sight. The magnetic field in the Crab Nebula estimated from measurements of the rotation measure toward the pulsar is 100 μG.     

Raman spectra of methane hydrate up to 86 GPa

High-pressure Raman studies of methane hydrate were performed using a diamond anvil cell in the pressure range of 0.1–86 GPa at room temperature. Raman spectra of the methane molecules revealed that new softened intramolecular vibration mode of ν ₁ appeared at 17 GPa and that the splitting of vibration mode of ν ₃ occurred at 15 GPa. The appearance of these two modes indicates that an intermolecular attractive interaction increases between the methane molecules and the host water molecules and between the neighboring methane molecules. These interactions might result in the exceptional stability of a high-pressure structure, a filled ice Ih structure (FIIhS) for methane hydrate, up to 40 GPa. At 40 GPa, a clear change in the slope of the Raman shift versus pressure occurred, and above 40 GPa the Raman shift of the vibration modes increased monotonously up to 86 GPa. A previous XRD study showed that the FIIhS transformed into another new high-pressure structure at 40 GPa. The change in the Raman spectra at 40 GPa may be induced by the transition of the structure.     

Estimation of Probabilities of Three Kinds of Petrologic Hypotheses with Bayes Theorem

Physical-chemical explanations of the causes of variations in rock suites are evaluated by comparing predicted to measured compositions. Consistent data turn an explanation into a viable hypothesis. Predicted and measured values seldom are equal, creating problems of defining consistency and quantifying confidence in the hypthesis. Bayes theorem leads to methods for testing alternative hypotheses. Information available prior to data collection provides estimates of prior probabilities for competing hypotheses. After consideration of new data, Bayes theorem updates the probabilities for the hypotheses being correct, returning posterior probabilities. Bayes factors, B, are a means of expressing Bayes theorem if there are two hypotheses, H ₀ and H ₁. For fixed values of the prior probabilities, B > 1 implies an increased posterior probability for H ₀ over its prior probability, whereas B < 1 implies an increased posterior probability for H ₁ over its prior probability. Three common problems are: (1) comparing variances in sets of data with known analytical uncertainties, (2) comparing mean values of two datasets with known analytical uncertainties, and (3) determining whether a data point falls on a predicted trend. The probability is better than 0.9934 that lava flows of the 1968 eruption of Kilauea Volcano, Hawaii, are from a single magma batch. The probability is 0.99 that lava flows from two outcrops near Mount Edziza, British Columbia, are from different magma batches, suggesting that the two outcrops can be the same age only by an unlikely coincidence. Bayes factors for hypotheses relating lava flows from Volcano Mountain, Yukon Territory, by crystal fractionation support the hypothesis for one flow but the factor for another flow is so small it practically guarantees the fractionation hypothesis is wrong. Probabilities for petrologic hypotheses cannot become large with a single line of evidence; several data points or datasets are required for high probabilities.     

A statistical-mechanics model of ordering in aluminosilicate solid solutions

A statistical-thermodynamic approximation for order-disorder phase transitions in aluminosilicate solid solutions is presented. The approximation involves estimating the number of configurations with long range order parameter Q and short range order parameter σ, using an approximation to the probability that a configuration with the correct amount of long range order will also have the correct amount of short range order. This estimate is then used to give a free energy F(Q, σ, x, T), where x is the concentration of Al in the structure, and hence quantities such as T _c (x) are estimated. The predictions of the model for T _c (x) and the critical concentration x _c at which T _c falls to zero are shown to be in good agreement with the results of Monte Carlo simulations. Received: 14 May 1997 / Revised, accepted: 2 June 1997     

Single crystal raman studies of pyrite-type RuS2, RuSe2, OsS2, OsSe2, PtP2, and PtAs2

Single crystal Raman spectra of pyrite-type RuS₂, RuSe₂, OsS₂, OsSe₂, PtP₂, and PtAs₂ are presented and discussed with reference to the energies of the X-X stretching modes _x-x (A _g, F _g) and the X₂ librations (E, 2F_g). The main results obtained are (i) strong Raman resonance effects, (ii) different sequences for _x-x (A _g) and (E _g), i.e., R_{x_2 } $$ " align="middle" border="0"> for PtP₂ and PtAs₂ and R_{x_2 } $$ " align="middle" border="0"> for OsS₂, owing to the interplay of intraionic and interionic lattice forces, (iii) greater strengths for the intraionic P-P and As-As bonds compared to the S-S and Se-Se bonds, respectively, and (iv) a strong influe_gnce of the metal ions on the strength of the X-X bonds.This is contribution LXI of a series of papers on lattice vibration spectra     

Electronic absorption by Ti3+ ions and electron delocalization in synthetic blue rutile

Polarized absorption spectra, σ and π, in the spectral range 30000–400 cm⁻¹ (3.71–0.05 eV) were obtained on crystal slabs // [001] of deep blue rutile at various temperatures from 88 to 773 K. The rutile crystals were grown in Pt-capsules from carefully dried 99.999% TiO₂ rutile powder at 50 kbar/1500 °C using graphite heating cells in a belt-type apparatus. Impurities were below the detection limits of the electron microprobe (about 0.005 wt% for elements with Z≥13). The spectra are characterized by an unpolarized absorption edge at 24300 cm⁻¹, two weak and relatively narrow (Δν_1/2≈3500–4000 cm⁻¹), slightly σ-polarized bands ν₁ at 23500 cm⁻¹ and ν₂ at 18500 cm⁻¹, and a complex, strong band system in the NIR (near infra red) with sharp weak peaks in the region of the OH stretching fundamentals superimposed on the NIR system in the σ-spectra. The NIR band system and the UV edge produce an absorption minimum in both spectra, σ and π, at 21000 cm⁻¹, i.e. in the blue, which explains the colour of the crystals. Bands ν₁ and ν₂ are assigned to dd transitions to the Jahn-Teller split upper E_g state of octahedral Ti³⁺. The NIR band system can be fitted as a sum of three components. Two of them are partly π-polarized, nearly Gaussian bands, both with large half widths 6000–7000 cm⁻¹, ν₃ at 12000 cm^–1 and the most intense ν₄ at 6500 cm⁻¹. The third NIR band ν₅ of a mixed Lorentz-Gaussian shape with a maximum at 3000 cm⁻¹ forms a shoulder on the low-energy wing of ν₄. Energy positions, half band widths and temperature behaviour of these bands are consistent with a small polaron type of Ti³⁺Ti⁴⁺ charge transfer (CT). Polarization dependence of CT bands can be explained on the basis of the structural model of defect rutile by Bursill and Blanchin (1983) involving interstitial titanium. Two OH bands at 3322 and 3279 cm⁻¹ in σ-spectra show different stability during annealing, indicating two different positions of proton in the rutile structure, one of them probably connected with Ti³⁺ impurity. Total water concentration in blue rutile determined by IR spectroscopy is 0.10 wt-% OH. The EPR spectra measured in the temperature interval 20–295 K show the presence of an electron centre at temperatures above 100 K and Ti³⁺ ions in more than one structural position, but predominantly in compressed interstitial octahedral sites, at lower temperatures. These results are in good agreement with the conclusions based on the electronic absorption data. Received: 24 March 1997 / Revised, accepted: 14 October 1997     

Refined relationship between the position of the fundamental OH stretching and the first overtones for clays

The aim of this paper is to determine a relationship between the wavenumbers of the first OH-stretching overtones (W_2OH) and the wavenumbers of the OH-stretching fundamentals (W_OH) to help to interpret the near-infrared (NIR) spectra. The first overtone (2OH) bands appear at wavenumbers less than twice those of the fundamental bands (OH), due to the anharmonic character of vibrations, X = W_2OH/2 - W_OH, with X being the anharmonicity constant. Talc samples with various crystal chemistries are used to solve the equation and the experimental data are well fitted with X = –85.6 cm^–1. As far as the authors are aware, it is the first time that the anharmonicity constant for the OH-stretching vibrations is determined for phyllosilicates. The anharmonicity constant remains almost unchanged for several types of clay samples. Therefore the relation, established from talc samples because their absorption bands are narrow and their wavenumber range of OH vibrations is wide, can be used for any other clay minerals.     

Effect of density and compressibility on <Emphasis Type="Italic">K</Emphasis><Subscript>0</Subscript> of cohesionless soils

This paper revisits the earth pressure coefficient at rest K ₀ of granular materials, with the focus being placed on the variation of K ₀ with the internal friction angle, density and compressibility of soils. Following laboratory tests that are carried out to determine K ₀ of two granular materials, the experimental data are interpreted using the original hypoplasticity model for sand proposed by von Wolffersdorff [49]. K ₀ is generally a function of void ratio, stress level and the critical state friction angle; it can be alternatively related to the compressibility of soil. The results show that Jáky’s equation may still be considered as a reasonable representation of K ₀ for granular soils statistically, even though it may not be able to reproduce the experimental data of a specific soil.     

On the velocity covariance for steady flows in heterogeneous porous formations and its application to contaminants transport

We consider groundwater steady flow in a heterogeneous porous formation of random and stationary log-conductivity Y = ln K, characterized by the mean 〈Y〉, and the two point correlation function C _Y which in turn has finite, and different horizontal and vertical integral scales I and I _v , respectively. The fluid velocity V, driven by a given head drop applied at the boundary, has constant mean value U ≡ (U, 0, 0). Approximate explicit analytical expressions for transverse velocity covariances are derived. The adopted methodology follows the approach developed by Dagan and Cvetkovic (Spatial moments of kinetically sorbing plume in a heterogeneous aquifers, Water Resour. Res. 29 (1993) 4053) to obtain a similar result for the longitudinal velocity covariance. Indeed, the approximate covariances of transverse velocities are determined by requiring that they have the exact first order variances as well as zero integral scale (G. Dagan, Flow and Transport in Porous Formations (Springer, 1989)) , and provide the exact asymptotic limits of the displacement covariance of the fluid particles obtained by Russo (On the velocity covariance and transport modeling in heterogeneous anisotropic porous formations 1. Saturated flow, Water Resour. Res., 31 (1995) 129). Comparisons with numerical results show that the proposed expressions compare quite well in the early time regime, and for Ut/I >100. Since most of the applications, like assessing the effective mobility of contaminants or quantifying the potential hazards of nuclear repositories, require predictions over higher times the proposed approximate expressions provide acceptable results. The main advantage related to such expressions is that they allow obtaining closed analytical forms of spatial moments pertaining to kinetically sorbing contaminant plumes avoiding the very heavy computational effort which is generally demanded. For illustration purposes, we consider the movement of one contaminant species, and show how our approximate spatial moments compare with the numerical simulations.     

Calculation of infrared and Raman vibration modes of magnesite at high pressure by density-functional perturbation theory and comparison with experiments

We predict the IR-TO, IR-LO and Raman modes (wave numbers and intensities) of magnesite (MgCO₃) up to 50 GPa, at T = 0 K, using the density-functional perturbation theory up to a third order perturbation, under the harmonic assumption. The predicted IR-TO and Raman mode wave numbers, the mode Grüneisen parameters and the Davydov splittings are systematically compared with experimental data for all modes up to the pressures of 10–30 GPa and for some modes up to 50 GPa. Existing experiments allow extending this comparison only to IR-LO wave numbers of the E _u (ν₃) asymmetric-stretch mode, confirming the odd experimental behavior of this mode at very high pressures. Predicted IR-TO, IR-LO and Raman intensities up to 50 GPa are just tabulated, but data are missing for their comparison with precise experiments. However, the generally good agreement observed between numerical results and experimental data, when their comparison is possible, suggests that first-principles methods are a major help to predict the entire spectrum up to very high pressures.