Moment Perturbation Research Articles

An examination of vortex convection effects during blade-vortex interaction

AbstractThe experimental results of a parallel Blade-Vortex Interaction (BVI) study are presented. The quality of all pressure data reflects improvements in the Glasgow University BVI facility and in the method of reducing and presenting data. Pressure histories clearly track the passage of a vortex-associated disturbance across the aerofoil. Tracking this disturbance permits an examination of vortex convection velocities, and also allows for a correlation between vortex trailing edge passage and force and moment perturbations.

Atomic short-range order and magnetic-moment distribution in dilute F eMn and F eTi alloys

Neutron measurements on FeMn and FeTi alloys with impurity concentration lower than 3 at. % were done at liquid-nitrogen temperature by using polycrystalline samples quenched from the melt. The most concentrated FeMn alloy exhibited an atomic short-range order characterized by a tendency for clustering of the Mn atoms. Nuclear cross-section data of FeTi alloys could be analyzed by taking in account only the lattice distortions. The measured radial displacements were found to be in reasonable agreement with those calculated within the Krivoglaz model. Positive (+0.62 μB) and negative (−0.50μB) values have been obtained for the magnetic moments on Mn and Ti atoms, respectively. A negative value for the moment perturbation on the two first shells was measured in both cases. These results partly agree with some other determinations and recent calculations.

Excluded volume effects in rotational-isomeric-state chains

An algorithm improving the accuracy of Monte-Carlo calculations of the configurations of off-lattice polymer chains is described. It is used to investigate excluded-volume effects in rotational-isomeric-state polymethylene chains perturbed by Sutherland potentials and a particular Lennard-Jones potential. The importance of accounting properly for chain structure when determining expansion factors is clearly shown. The effective value of the segmental cluster integral is discussed in detail showing that it cannot be calculated directly from the potential function used but is strongly dependent on chain structure. Due to uneven chain expansion, i.e. the different perturbation of the various moments of the end-to-end distance distribution, θ-ranges rather than single θ-points are predicted at infinite chain length. The shortcomings of lattice models for chains are discussed, again emphasizing that chain structure must be included in calculations of chain expansion if meaningful interpretations of experimental expansion coefficients at different temperatures are to be achieved.

Model of ferromagnetic behavior for dilute P tFe alloys

A model is presented to describe the magnetization clouds of ferromagnetic dilute PtFe alloys. An expression is derived for the distribution of magnetic moments in the magnetization clouds indicating an exponential decay of the perturbation of the platinum moments due to the presence of an iron atom at the origin of the cloud. The model indicates that part of the magnetization resides in the platinum atoms, which carry moments proportional to the moments of its neighbors. The magnetization clouds are produced by first-neighbor interactions between localized moments. These interactions repeat themselves throughout the cloud producing the giant moments that have been detected by neutron and magnetization measurements.

Calculation of the Knight shift in palladium

The direct and the exchange core polarization (ECP) contributions of the conduction electrons to the Knight shift of palladium are evaluated. To obtain the wave functions for the conduction electrons and the partial densities of states at the Fermi surface a KKR energy band calculation was performed. The contributions of the core electrons to the Knight shift were determined by using the moment perturbation method (MP). Electron-electron interactions are taken into account by individual enhancement factors for thed ands electrons. The agreement between the theoretical results and the available experimental data is quite satisfactory.

Conduction-electron polarization and moment perturbations in diluteFe3Si-based alloys

The spatial variation of the s-conduction-electron polarization in the ${\mathrm{Fe}}_{3}$Si system is determined from the measured hyperfine fields of the near-stoichiometric ${\mathrm{Fe}}_{3}$Si alloys. This polarization is then combined with the hyperfine-field data from Mn, V, Co, and Ni solutes and used to derive the solute moments and moment perturbations in ${\mathrm{Fe}}_{3}$Si to obtain the solute-moment and host-moment perturbations caused by these impurities. The behavior of these solute moments and moment perturbations is seen to be very similar to that of the same solutes in binary Fe alloys. Since ${\mathrm{Fe}}_{3}$Si is closely related to Heusler alloys, it is suggested that their magnetic behavior is also governed by the same mechanism that determines the magnetic behavior of binary Fe alloys; that is, the conduction $d$-like electrons, not $s$-like electrons, are responsible for the magnetic alignment.

Conduction electron polarization and moment perturbations in dilute Fe3Si based alloys

The spatial variation of the s-conduction electron polarization in the Fe3Si system is determined from neutron scattering, magnetization saturation and hyperfine field measurements. This polarization is then combined with magnetization saturation and hff data for solute atoms Mn, V, Co, and Ni in Fe3Si to obtain the solute moments and host moment perturbations due to these impurities. The behavior of these solute moments and moment perturbations is seen to be very similar to those in binary Fe alloys. Since Fe3Si is closely related to Heusler alloys, it is suggested that their magnetic behavior is also governed by the same mechanism that determines the magnetic behavior of Fe; that is, the conduction d-like electron, not the s-like electrons cause the magnetic alignment.

Coulomb and exchange scattering amplitudes from spin dependent residual resistivities in Fe and Ni hosts

The spin dependent residual resistivities for a large number of solute atoms in Fe and Ni based ternary alloys are analyzed as arising from three main sources. 1. Coulomb scattering from the impurity charge (or volume) perturbation. This amplitude is found to be similar to that for Cu based alloys. 2. Scattering from a localized moment perturbation at the solute atom. Both a potential and exchange amplitude are found to be spin-dependent and about the same per μB for Fe and Ni hosts. 3. A more widespread moment perturbation in the host surrounding the solute atom. The shape of this perturbation depends upon whether direct Coulomb exchange or hybridization effects dominate. In Ni, usually hybridization effects dominate and give predominately negative host perturbations. In Fe, Coulomb exchange dominates and the shape of the host perturbation depends upon the number of itinerant d-like electrons connected with the solute atom.

Electronic structure of ferromagnetic hcp cobalt. III. Magnetic hyperfine field

Using the energy bands and wave functions of ferromagnetic cobalt from a self-consistent hybridized tight-binding---orthogonalized-plane-wave ferromagnetic band calculation, we have obtained the core and the band contributions to the hyperfine field at the cobalt nucleus to be, respectively, -380.1 and -42.7 kOe. The core contribution of -380.1 kOe, in the moment-perturbation (MP) approach, is composed of contributions from $1s$, $2s$, and $3s$ cores, respectively, of -0.07, -272.4, and -107.7 kOe. These values have been transformed to derive the results that would be expected from a unrestricted-Hartree-Fock (UHF) theory, for the core states and give the individual contributions, in order, from $1s$, $2s$, and $3s$ states as -19.0, -528.1, and +154.6 kOe which add up to about the same total core contribution. The most important effect, causing the individual core contributions to differ substantially in the two methods, is shown to result from exclusion-principle-violating (EPV) diagrams. The small difference of the total core contributions from the MP and the UHF approaches arises from EPV diagrams in which the band electrons are involved. The negative band contribution to the hyperfine field is found to arise from the paired $3d$-like and free-like band states, which overwhelm the positive contribution from the unpaired-spin electrons in the majority-spin band. Arguments are proposed to show that the difference between the theoretical value -422.9 kOe for the hyperfine field and the experimental value of -223.0 could arise from the influence of correlation effect on the $3d$-like band electron wave functions, particularly those at the Fermi surface.

Evidence for itinerant 3d-electron spin density oscillations surrounding solute atoms in Fe alloys

Hyperfine field and saturation magnetization data are analyzed to obtain solute transition element moments and Fe moment perturbations in dilute Fe alloys. A direct comparison of these results is made with the neutron scattering data. The host moment perturbations show simple oscillatory behavior which is interpreted as arising from the polarization of itinerant d electrons by localized d moments through mainly Coulomb exchange interactions. The behavior of Ni-based alloys can also be understood within this model.

Determination of moment distributions and hyperfine fields at and surrounding transition-element solute atoms in Fe

A new method is developed which uses the hyperfine spectra of the Fe atoms in dilute Fe alloys to obtain (i) the moment on a transition-metal-solute atom in Fe, (ii) the moment perturbations in the Fe matrix, and (iii) the hyperfine-field shifts at the Fe atoms in the four-nearest-neighbor shells to the solute atom. We find that this method has much more sensitivitiy than the comparable technique using elastic diffuse neutron scattering. A moment perturbation varying as $\frac{1}{{r}^{3}}$ is found to best fit the spectra. For Co and Ni solute atoms we obtain moments of (1.9 \ifmmode\pm\else\textpm\fi{} 0.1)${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ and (1.4 \ifmmode\pm\else\textpm\fi{} 0.1)${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$, respectively. These agree with the neutron-scattering results but are much more accurately determined. The moments at Rh and Pd in Fe are found to be (1.1 \ifmmode\pm\else\textpm\fi{} 0.2)${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ and (0.7 \ifmmode\pm\else\textpm\fi{} 0.2)${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$, in agreement with neutron-scattering results on more concentrated alloys. The hyperfine-field shifts are obtained in a much more fundamental way than the previous analyses of FeCo spectra. This results in very different hyperfine-field shifts than the previous determination. The average-moment and moment-perturbation behavior is discussed from the point of view that the magnetic behavior of the $3d$ transition series is determined by the coupling via exchange and interband mixing of mainly localized moments through a small fraction of itinerant $d$ electrons. This is in contrast to a charge-perturbation-type model where the moment behavior is attributed to arise from the different screening of the spin-up and spin-down $d$ electrons. The latter is not believed to be significant in determining the moment behavior. Using the results of this analysis we derive from only hyperfine-field data the value of the core-polarization hyperfine field in Fe. We find indications that this term may be larger than the values previously obtained by band calculations. From the derived moments of Rh and Pd we can obtain a value for the hyperfine field per ${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ due to core polarization for the $4d$ transition series. We find reasonable agreement with the calculated value. Earlier derivations of the moments of $4d$ and $5d$ solute atoms in Fe, as obtained from their measured hyperfine fields, omitted the large self-polarization conduction-electron term. This is considered here and corrected moment values are obtained.

Detailed57Fe continuous wave NMR spectra in Fe based dilute Fe-Co alloys

The hyperfine field distribution around cobalt impurities in iron has been measured by the continuous wave nuclear magnetic resonance method. Four distinct satellites are observable on the high frequency side shifted by 2.5%, 1.5%, 1.3% and 0.18% from the central resonance and an unresolved structure on the low frequency side. The hyperfine field shifts are positive at the four nearest neighbours and probably negative at the fifth and sixth neighbours. The concentration dependence of the average hyperfine field suggests a considerable conduction electron polarization contribution while the radial dependence reflects that of the moment perturbation. The temperature dependences of the satellites and main line frequencies follow the temperature dependence of the hyperfine field measured in pure iron.

Origin of the Hyperfine Fields in Pure Fe and at Solute Atoms in Fe

The measured spin-density oscillations in Fe (preceding paper) are interpreted as due to $4s$-like conduction-electron polarization and compared with improved Ruderman-Kittel-Kasuya-Yosida-type calculations. The hyperfine field shifts due to a solute atom are shown to be due to moment perturbations rather than charge perturbations, and agreement with the improved RKKY-type calculations is considered to be quite good. We find ${J}_{\mathrm{int}}(q=0)\ensuremath{\sim}+0.5$ eV. There is some indication that the exchange interaction and interband mixing cause comparable polarizations in the region of the nearest-neighbor shell. We find the net integrated $4s$-like polarization in pure Fe to be about +(5-8)%. Using the latest Fe band calculations, we are able to obtain identifications and magnitudes for the terms contributing to the hyperfine field of Fe. With this model we are able to explain the well-known variations of hyperfine fields at solute atoms in Fe. There is shown to be a positive hyperfine field contribution from the polarization induced in the $\mathrm{ns}$-like electron density near the solute atom. This positive polarization is proportional to the volume overlap of the solute atom with the Fe matrix.

Electrical Resistivities of Co(C) and Ni(C) Solid Solutions

From resistivity measurements, both during carburization and after quenching, resistivities of interstitial carbon in Co and Ni were determined. The data are corrected for effects on the host resistivity from the change in Curie temperature with alloying. Representative values for the solute resistivity in μΩ cm/at. % C are: 4.4 at 4.2 K, 5.2 at 300 K, and 0.9 at 1400 K for Co(C); and 3.3 at 4.2 K and 200 K, 1.7 at 650 K, and 2.6 at 1270 K for Ni(C). The large decrease in solute resistivities between 300 K and the Curie temperature is attributed to spin-disorder scattering from the reduced moments of the solvent atom neighbors of interstitial carbon. Quantitative analysis, using simple expressions of Schwerer and Cuddy for solute induced spin-disorder scattering, indicate greater moment perturbations in cobalt than in either of the other two solvents. Subsidiary experiments determine that carbon solutes in cobalt reduce the Curie temperature by (31±2)°C/at. % C.

Core polarization contributions to hyperfine effects of paramagnetic centers in ionic crystals

The theory for exchange core polarization in hyperfine interactions is formulated using the moment perturbation method for the case when the original basis functions are not orthogonal. Such a situation is typical of a wide variety of paramagnetic systems in the solid state, such as color centers and iron group ions in ionic crystals. The procedure consists of collecting terms proportional to μ N in the total energy, including both one- and two-electron operators in the total Hamiltonian. After some manipulation, the core polarization contribution is shown to have the same form as for the orthogonal case with the valence orbital orthogonalized to the unperturbed core wavefunctions. We have applied our analysis to an example, namely the F-center in LiF. A positive contribution from the core polarization was found for both the isotropic and anisotropic hyperfine constants of the nearest neighbor Li + ions adding to the direct effects from overlap in both cases.

Core-Polarization Contribution to the Knight Shift in Beryllium Metal

Direct and core-polarization contributions to the Knight shift in beryllium metal were calculated at a number of symmetry points near the Fermi surface. The direct contribution was evaluated using wave functions for the conduction electrons by the orthogonalized-plane-wave method. The contribution of the core electrons was determined using the moment-perturbation (MP) method developed in an earlier paper. The accuracy of the MP method was rechecked by calculating the core contribution to the hyperfine coupling constant in the $^{3}P_{2}$ state of the beryllium atom. Good agreement was obtained with the result of an earlier self-consistent-field calculation by Goodings. For the ${{\ensuremath{\Gamma}}_{4}}^{\ensuremath{-}}$ level, the direct and core contributions to the Knight shift are 0.01536 and 0.00258%, respectively. For the two degenerate levels of ${H}_{1}$, the direct contributions both vanish while the core-polarization contributions are -0.00061 and -0.00001%. These results lead to the conclusion that core-polarization effects alone can not explain the near-vanishing Knight shift observed experimentally in beryllium metal. Some other contributions such as those from various orbital mechanisms would therefore have to be considered.