Segregation, precipitation, and \alpha-\alpha' phase separation in Fe-Cr alloys: a multi-scale modelling approach

Segregation, precipitation, and phase separation in Fe-Cr systems is investigated. Monte Carlo simulations using semiempirical interatomic potential, first-principles total energy calculations, and experimental spectroscopy are used. In order to obtain a general picture of the relation of the atomic interactions and properties of Fe-Cr alloys in bulk, surface, and interface regions several complementary methods has to be used. Using Exact Muffin-Tin Orbitals method the effective chemical potential as a function of Cr content (0-15 at.% Cr) is calculated for a surface, second atomic layer and bulk. At ~10 at.% Cr in the alloy the reversal of the driving force of a Cr atom to occupy either bulk or surface sites is obtained. The Cr containing surfaces are expected when the Cr content exceeds ~10 at.%. The second atomic layer forms about 0.3 eV barrier for the migration of Cr atoms between bulk and surface atomic layer. To get information on Fe-Cr in larger scales we use semiempirical methods. Using combined Monte Carlo molecular dynamics simulations, based on semiempirical potential, the precipitation of Cr into isolated pockets in bulk Fe-Cr and the upper limit of the solubility of Cr into Fe layers in Fe/Cr layer system is studied. The theoretical predictions are tested using spectroscopic measurements. Hard X-ray photoelectron spectroscopy and Auger electron spectroscopy investigations were carried out to explore Cr segregation and precipitation in Fe/Cr double layer and Fe_0.95Cr_0.05 and Fe_0.85Cr_0.15 alloys. Initial oxidation of Fe-Cr was investigated experimentally at 10^-8 Torr pressure of the spectrometers showing intense Cr_2O_3 signal. Cr segregation and the formation of Cr rich precipitates were traced by analysing the experimental spectral intensities with respect to annealing time, Cr content, and kinetic energy of the exited electron.Comment: 16 pages, 14 figures, 52 reference

Studies on the Accumulation of Chromium in Fenugreek

Studying Cr uptake by Fenugreek, we note that the maximum concentration of Cr takes place in the shells of the pods followed by leaves, stems and seeds in that order. Interestingly, applied higher doses of Cr does not increase accumulation of Cr in the stems, rather Cr content in the stems levels off. However, the maximum dispersal/distribution of Cr taken up is in the leaves

Determination of the s-wave Scattering Length of Chromium

We have measured the deca-triplet s-wave scattering length of the bosonic chromium isotopes $^{52}$Cr and $^{50}$Cr. From the time constants for cross-dimensional thermalization in atomic samples we have determined the magnitudes $|a(^{52}Cr)|=(170 \pm 39)a_0$ and $|a(^{50}Cr)|=(40 \pm 15)a_0$, where $a_0=0.053nm$. By measuring the rethermalization rate of $^{52}$Cr over a wide temperature range and comparing the temperature dependence with the effective-range theory and single-channel calculations, we have obtained strong evidence that the sign of $a(^{52}Cr)$ is positive. Rescaling our $^{52}$Cr model potential to $^{50}$Cr strongly suggests that $a(^{50}Cr)$ is positive, too.Comment: v3: corrected typo in y-axis scaling of Figs. 3 and

On the Lichnerowicz conjecture for CR manifolds with mixed signature

We construct examples of nondegenerate CR manifolds with Levi form of signature $(p,q)$, $2\leq p\leq q$, which are compact, not locally CR flat, and admit essential CR vector fields. We also construct an example of a noncompact nondegenerate CR manifold with signature $(1,n-1)$ which is not locally CR flat and admits an essential CR vector fields. These provide counterexamples to the analogue of the Lichnerowicz conjecture for CR manifolds with mixed signature.Comment: 7 page

Observation of ferromagnetism above 900 K in Cr-GaN and Cr-AlN

We report the observation of ferromagnetism at over 900K in Cr-GaN and Cr-AlN thin films. The saturation magnetization moments in our best films of Cr-GaN and Cr-AlN at low temperatures are 0.42 and 0.6 u_B/Cr atom, respectively, indicating that 14% and 20%, of the Cr atoms, respectively, are magnetically active. While Cr-AlN is highly resistive, Cr-GaN exhibits thermally activated conduction that follows the exponential law expected for variable range hopping between localized states. Hall measurements on a Cr-GaN sample indicate a mobility of 0.06 cm^2/V.s, which falls in the range characteristic of hopping conduction, and a free carrier density (1.4E20/cm^3), which is similar in magnitude to the measured magnetically-active Cr concentration (4.9E19/cm^3). A large negative magnetoresistance is attributed to scattering from loose spins associated with non-ferromagnetic impurities. The results indicate that ferromagnetism in Cr-GaN and Cr-AlN can be attributed to the double exchange mechanism as a result of hopping between near-midgap substitutional Cr impurity bands.Comment: 14 pages, 4 figures, submitted to AP

Embeddability for Three-Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants

Let M^3 be a closed CR 3-manifold. In this paper we derive a Bochner formula for the Kohn Laplacian in which the pseudo-hermitian torsion plays no role. By means of this formula we show that the non-zero eigenvalues of the Kohn Laplacian are bounded below by a positive constant provided the CR Paneitz operator is non-negative and the Webster curvature is positive. Our lower bound for the non-zero eigenvalues is sharp and is attained on S^3. A consequence of our lower bound is that all compact CR 3-manifolds with non-negative CR Paneitz operator and positive CR Yamabe constant are embeddable. Non-negativity of the CR Paneitz operator and positivity of the CR Yamabe constant are both CR invariant conditions and do not depend on conformal changes of the contact form. In addition we show that under the sufficient conditions above for embeddability, the embedding is stable in the sense of Burns and Epstein. We also show that for the Rossi example for non-embedability, the CR Paneitz operator is negative. For CR structures close to the standard structure on $S^3$ we show the CR Paneitz operator is positive on the space of pluriharmonic functions with respect to the standard CR structure on $S^3$.Comment: The new version also proves a partial converse. That is for CR structures close to the standard CR structure on the 3-sphere, embedabillity is shown to imply the non-negativity of the CR Paneitz operator on pluriharmonic functions for the standard CR structure. Typos are corrected, and statement of prop. 1.11 revise