Seitz Cell Research Articles

A 57Fe Mössbauer study of nanostructured Sm 2Fe 17− xCo xC 3

Sm 2Fe 17− x Co x C 3 ( x ≤ 2) were synthesized by means of reaction with solid hydrocarbon at 693 K on Sm 2Fe 17− x Co x powders obtained by high energy milling and subsequent annealing at 1125 °C. X-ray diffraction analysis by Rietveld method has shown that both series crystallize in the rhombohedral Th 2Zn 17-type structure. The Curie temperature T C increase of Sm 2Fe 17− x Co x C 3 versus Co content is only ruled by electronic effect less pronounced than for the non-carbonated series. The analysis of their Mössbauer spectra, have been analyzed on the basis of the binomial law. The hyperfine parameter sets were assigned according to the relationship between the Wigner–Seitz cell volume of each iron site and their isomer shift δ so that δ{6c} > δ{18h} > δ{18f} > δ{9d}. It results that Co preferentially occupies the 18h site with the recurrent sequence H HF{6c} > H HF{9d} > H HF{18f} > H HF{18h}. This sequence is in agreement with the number of iron near-neighbors. The increase with Co content of hyperfine field, is correlated to the increase of the core electron polarization field ruled by the asymmetrical filling of the 3d band by the additional 3d Co electron.

Detailed characterization of defect production in molecular dynamics simulations of cascades in Si

Numerous molecular dynamics simulation studies of radiation cascades in Si have elucidated many of the general features of the initial defect production. However, the resulting defect structures have been analyzed with techniques that are not sensitive to changes in the local bonding topology. Here the results of analyzing the ring content in Si cascades, in addition to more traditional defect characterization such as Wigner–Seitz cell analysis, will be presented for recoil energies ranging from 25 eV up to 25 keV. The ring content of local amorphous regions in the cascades will be compared to the ring content in simulations of bulk amorphous Si. The number of atoms in the amorphous regions and the number of point defects as a function of recoil energy are determined.

Relationship between structure and intrinsic magnetic parameters of nanocrystalline Sm 2(Fe,Ga) 17C 2

The nanocrystalline carbides Sm 2Fe 17− x Ga x C 2 ( x ≤ 2) were prepared with a two-step method: high-energy milling with annealing at 1050 °C and carbonation at 420 °C by a solid–solid reaction with heavy hydrocarbon. The Rietveld analysis reveals an anisotropic volume expansion of the R 3 ¯ m unit cell with modifications of the atomic positions compared to those of the non-carbonated alloys. The average iron magnetic moment, for carbonated alloys, deduced from high magnetic field investigations at 4 K, decreases slightly with x. The Curie temperature T C enhancement after carbonation is reduced by the presence of Ga. T C follows the reduction of the Wigner–Seitz cell (WSC) volume of the carbon site affected also by the presence of Ga. A detailed analysis of the Mössbauer spectra has been carried out with a model based on the WSC volume correlation with isomer shift and the statistical distribution of Ga simulated by the multinomial law. The isomer shift sequence of each Fe non-equivalent site, δ{6c} > δ{18h} > δ{18f} > δ{9d} for x < 1 and δ{18h} > δ{6c} > δ{18f} > δ{9d} for x ≥ 1, reflects the perturbation brought about by C and Ga, in perfect agreement with the structural analysis. Upon carbonation the isomer shift increases for 18f and 18h results not only from the volume effect but also from the 4s(Fe)–2p(C) inter-atomic charge transfer, modulated by the 4s(Fe)–4p(Ga) transfer. The hyperfine field sequence H{6c} > H{9d} > H{18f} > H{18h}, deduced from the isomer shift assignment, is in agreement with the number of Fe neighbors.

Combined effect of gallium and carbon on the structure and magnetic properties of nanocrystallineSmFe9

SmFe9−yGaxC carbides(0≤x≤1) were prepared by a two-step method of powder high-energy milling with annealing between873 and 1200 K and a subsequent carbonation with heavy hydrocarbon at 693 K. The x-raydiffraction analysis with the Rietveld technique indicates an anisotropic volume expansionunder carbonation slackened by the gallium substitution. The average saturation magneticmoment per Fe atom, measured with an applied field up to 200 kOe, increases slightly to2.00 µB with Ga content. The Curie temperature, always 15 K above that of the homologous2/17 carbides, is reduced by a dilution effect with Ga substitution and a concomitant increase of thenegative Fe–Fe interactions. The Mössbauer spectra have been analysed on the basis of thebinomial law related to the different Fe environments. The hyperfine parameter assignmentto each individual crystallographic site was performed according to the correlation betweenisomer shift and Wigner–Seitz cell volumes calculated with a specific code in theP 1 space group allowing the splitting of the partially occupied atomic positions. The role ofthe C insertion is shown, on the one hand, by the increase of isomer shift dueto the volume expansion with an enhancement of the charge transfer from therare-earth atoms and, on the other hand, by the hyperfine field increase, pointing outthe predominance of the negative core electron polarization term. The coercivefield of 27 kOe, combined with a Curie temperature of 680 K, makes the alloySmFe8.75Ga0.25C promising for further applications in the field of high-performance permanent magnets.

Effective Charges of Polyelectrolytes in a Salt-Free Solution Based on Counterion Chemical Potential

The phenomenon of counterion condensation around a flexible polyelectrolyte chain with N monomers is investigated by Monte Carlo simulations in terms of the degree of ionization alpha, which is proportional to the effective charge. It is operationally defined as the ratio of observed to intrinsic counterion concentration, alpha = co/ci. The observed counterion concentration in the dilute polyelectrolyte solution is equivalent to an electrolyte solution of concentration co with the same counterion chemical potential. It can be determined directly by thermodynamic experiments such as ion-selective electrode. With the polyelectrolyte fixed at the center of the spherical Wigner-Seitz cell, the polymer conformation, counterion distribution, and chemical potential can be obtained. Our simulation shows that the degree of ionization rises as the polymer concentration decreases. This behavior is opposite to that calculated from the infinitely long charged rod model, which is often used to study counterion condensation. Moreover, we find that, for a specified line charge density, alpha decreases with an increment in chain length and chain flexibility. In fact, the degree of ionization is found to decline with increasing polymer fractal dimension, which can be tuned by varying bending modulus and solvent quality. Those results can be qualitatively explained by a simple model of two-phase approximation.

Characteristics of local photonic state density in an infinite two-dimensional photonic crystal

The local density of photonic states (LDPS) of an infinite two-dimensional (2D) photonic crystal (PC) composed of rotated square-pillars in a 2D square lattice is calculated in terms of the plane-wave expansion method in a combination with the point group theory. The calculation results show that the LDPS strongly depends on the spatial positions. The variations of the LDPS as functions of the radial coordinate and frequency exhibit ``mountain chain'' structures with sharp peaks. The LDPS with large value spans a finite area and falls abruptly down to small value at the position corresponding to the interfaces between two different refractive index materials. The larger/lower LDPS occurs inward the lower/larger dielectric-constant medium. This feature can be well interpreted by the continuity of electric-displacement vector at the interface. In the frequency range of the pseudo-PBG (photonic band gap), the LDPS keeps very low value over the whole Wiger–Seitz cell. It indicates that the spontaneous emission in 2D PCs cannot be prohibited completely, but it can be inhibited intensively when the resonate frequency falls into the pseudo-PBG.

Mössbauer spectral study of RFe 11.3W 0.7 compounds (R=Dy, Ho, Er, and Lu)

The series of compounds RFe 11.3W 0.7, where R=Dy, Ho, Er, and Lu, has been measured by Mössbauer spectroscopy between 15 and 295 K. A model which takes into account the Wigner–Seitz cell local environment of each iron site, the distribution of tungsten atoms on the 8i site, and the temperature-dependent magnetic structures of the compounds has been used to analyse the spectra. The assignment and the temperature dependencies of the hyperfine fields and the isomer shifts are in complete agreement with the Wigner–Seitz cell analysis of the three iron sites in RFe 11.3W 0.7 compounds. The plausible orientations of the iron magnetic moments in the canted magnetic phase of ErFe 11.3W 0.7 compound have been established by a thorough Mössbauer spectral analysis. The Mössbauer spectra of DyFe 11.3W 0.7 clearly show the influence of the two spin re-orientations occurring in this compound and indicate the directions of the iron magnetic moments in both canted and planar magnetic arrangements.

An iron-57 and tin-119 Mössbauer spectral study ofNdMn6−xFexSn6

The iron-57 Mössbauer spectra of theNdMn6−xFexSn6 compoundswith x = 0.5, 1.0, 1.5 and 2.0 have been obtained at 4.2, 78 and 295 K, and the tin-119 Mössbauer spectra of theNdMn6−xFexSn6 compoundswith x = 0.0, 0.5, 1.0, 1.5 and 2.0 have been obtained between 85 and 370 K. A successful andrational analysis of the spectra is based upon a Wigner–Seitz cell analysis of theHoFe6Sn6-structure withthe Immm space groupfor NdMn6Sn6 and of theTbFe6Sn6-structure withthe Cmcm spacegroup for the NdMn6−xFexSn6 compounds with x = 0.5, 1.0, 1.5 and 2.0. Both the iron-57 and the tin-119 spectra reveal that the spinreorientation exhibited by these compounds at low temperature is extremely sensitive tothe cooling rate of the samples. Specifically, samples that are slowly cooled from 295 to 78 Kretain their 295 K magnetic structure and do not exhibit a spin reorientation. Incontrast, samples that are quenched from 295 to 78 K and then further cooled to4.2 K exhibit a spin reorientation. The ca 15 T iron-57 hyperfine fields observedat 4.2 K are unusually small, whereas the ca 25 T tin-119 transferred hyperfinefields observed at 85 K are unusually large. These latter large fields, as well as theimprovement in Curie temperature and magnetization with increasing iron content in theNdMn6−xFexSn6 compounds, are discussed in terms of earlier electronic structure calculations.

Out‐of‐equilibrium nanocrystalline R1–s(Fe, M)5+2s alloys (R = Sm, Pr; M = Co, Si, Ga)

AbstractThe out‐of‐equilibrium hexagonal P6/mmm R1–s(Fe, M)5+2s (R = Sm, Pr and M = Co, Si or Ga) intermetallics are obtained by controlled nanocrystallization. A model is presented to explain the structure of the hexagonal phases, which stoichiometry is consistent with Sm(Fe, M)9 and R(Fe, Ti, Co)10. The Curie temperatures increase versus Ga, Si, Co content. The analysis of the Mössbauer spectra leads to monotonous variation of the hyperfine parameters. The refinement of the Mössbauer spectra was performed on the basis of the correlation between Wigner–Seitz cell volumes obtained from X‐ray diffraction results and isomer shifts. The abundance of each magnetic site was calculated by the multinomial distribution law. For a given substituting Co, Si, Ga content, the sequence for the isomer shift in the hexagonal cell is 2e &gt; 3g &gt; 6l. With increasing M content, the isomer shift of the 3g site remains quasi‐constant. Those approaches lead to the location of Si, Ga, Co in 3g site, Ti in 6l site. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The role of superfluidity in the structure of the neutron star inner crust

A self-consistent quantum approach to describe the inner crust structure of neutron stars is developed, within the Wigner–Seitz approximation. It is based on the generalized energy functional method involving explicitly neutron and proton pairing correlations. The energy functional is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the Wigner–Seitz cell with the one calculated microscopically for neutron matter. It is shown that the neutron and proton superfluidity influences significantly the ground state structure of the inner crust.

Formation and thermal stability of an E9 3-structured NiHf 2 phase in Ni 33Hf 67

The melt-spun Ni 33Hf 67 glassy phase completely crystallizes into an fcc NiHf 2 phase ( a ≈ 12 Å) upon continuous heating or isothermal annealing. Kinetics analysis shows that the NiHf 2 grains are crystallized by nucleation and diffusion-controlled growth of nuclei at an average activation energy of ∼400 kJ/mol. The resulting NiHf 2 grains are extremely fine, ∼10 nm in diameter, and exhibit excellent grain size stability upon subsequent heating over a wide temperature range. The Wigner–Seitz cell calculation results suggest that the fcc phase could be oxygen-stabilized. In the fcc lattice, the octahedral interstitial site with six nearest Hf neighbors is the most likely site for an oxygen atom to occupy. Upon further heating, part of the fcc NiHf 2 crystals transform into two bct phases: the equilibrium bct NiHf 2 and a metastable bct phase with a larger unit cell. Similar to the fcc phase, the metastable bct phase is most likely oxygen-stabilized. We show that the most likely oxygen site in the metastable bct lattice is the center of a tetrahedron with four nearest Hf neighbors. Upon further isothermal annealing at higher temperatures, close to the melting point of the alloy, the transformation from the metastable bct to the stable bct phase takes place.

Correlation between Sm2(Fe,Ga)17 and its precursor Sm(Fe,Ga)9

We have shown that the out-of-equilibrium hexagonal P6∕mmm phase adopts the stoichiometry Sm(Fe,Ga)9 in the Sm–Fe–Ga system. X-ray diffraction analysis has been combined with Mössbauer spectrometry. A specific program for the Wigner–Seitz cell (WSC) volume calculation of the equilibrium and of the metastable structure, deduced from the results given by the Rietveld analysis, was used. The Mössbauer spectra have been simulated with a model based on: (i) the multinomial law related to the statistical distribution of Ga and Sm vacancies obtained by the crystallographic approach, and (ii) the correlation between the WSC volume and the isomer shift of each inequivalent crystallographic site. The specific behavior of the 3g site isomer shift evolution corroborates the structure model. The Curie temperatures of the Sm(Fe,Ga)9 series are higher than those of the Sm2(Fe,Ga)17 alloys. Sm(Fe,Ga)9 represents an interesting host lattice for interstitial C or N atoms, with possible permanent magnet applications.

A comparative Mössbauer spectral study of the electronic and magnetic properties of Nd 6Fe 13Ag and Nd 6Fe 13AgH 13

The Mössbauer spectra of Nd 6Fe 13Ag and Nd 6Fe 13AgH 13 have been measured between 85 and 295 K and analyzed with a model that takes into account the basal magnetic anisotropy, the iron and hydrogen near-neighbor environments of the five crystallographically and magnetically inequivalent 4 d, 16 k, 16 k′, 16 l 1, and 16 l 2 iron sites in the former and the six crystallographically and magnetically inequivalent 4 d, 16 k, 16 k′, 16 l 1, 16 l 2−1 and 16 l 2−2 iron sites in the latter, where the additional site results from a predominance of hydrogen as near-neighbors on the iron 16 l 2 site. The increases in hyperfine field and isomer shift observed upon hydrogenation are in agreement with the increase in Wigner–Seitz cell volumes of each site and the changes in the near-neighbor environments.

A magnetic and Mössbauer spectral study of SmFe 11Ti, LuFe 11Ti, and their respective hydrides

ac Magnetic susceptibility measurements have been carried out on LuFe 11Ti and LuFe 11TiH and reveal the absence of any spin-reorientation between 4.5 and 293 K. Iron-57 Mössbauer spectral measurements between 4.2 and 295 K have been carried out on SmFe 11Ti and LuFe 11Ti and their respective hydrides, SmFe 11TiH and LuFe 11TiH. The Mössbauer spectra have been analyzed with a model that considers both the orientation of the iron magnetic moments and the distribution of titanium atoms in the near neighbor environment of the three crystallographically distinct iron sites. The assignment and the temperature dependence of the hyperfine fields are in complete agreement with the unit cell volume and its expansion upon hydrogenation and with those observed in the related RFe 11Ti and RFe 11TiH compounds. The site assignments and their temperature dependencies of the isomer shifts are in complete agreement both with the Wigner–Seitz cell volumes of the inequivalent iron sites and the crystallographic changes upon hydrogen insertion.

Linear aspects of the Korringa–Kohn–Rostoker formalism

We present the one-dimensional Korringa–Kohn–Rostoker (KKR) method with the aim ofelucidating its linear features, particularly important in optimizing the numericalalgorithms in energy band computations. The conventional KKR equations based onmultiple scattering theory as well as novel forms of the secular matrix with nearly linearenergy dependency of the eigenvalues are presented. The quasi-linear behaviour of theseeigenvalue functions appears after (i) re-normalizing the wavefunctions in such a way that‘irregular’ solutions vanish on the boundary of the ‘muffin-tin’ segments, and (ii)integrating the full Green function over the whole Wigner–Seitz cell. In addition, using theaforementioned approach we derive a one-dimensional analogue of the generalized Lloydformula.The novel KKR approach illustrated in one dimension can be almost directly applied tohigher dimensional cases. This should open prospects for the accurate KKR band structurecomputations of very complex materials.

Molecular dynamics simulation of displacement cascades in Fe–Cr alloys

An embedded atom method (EAM) empirical potential recently fitted and validated for Fe–Cr systems is used to simulate displacement cascades up to 15 keV in Fe and Fe–10%Cr. The evolution of these cascades up to thermalisation of the primary damage state is followed and quantitatively analysed. Particular attention is devoted to assessing the effect of Cr atoms on the defect distribution versus pure Fe. Using the Wigner–Seitz cell criterion to identify point defects, first results show that the main effect of the presence of Cr in the system is the preferential formation of mixed Fe–Cr dumbbells and mixed interstitial clusters, with expected lower mobility than in pure Fe.

Structure and magnetic properties of La(Fe0.88Al0.12)13Cx interstitial compounds

Structure and magnetic properties of La(Fe0.88Al0.12)13Cx interstitial compounds with x=0–0.8, were studied by x-ray diffraction and magnetic measurements. The interstitial compounds retain the NaZn13-type structure and the lattice constant increases with carbon content. The Wigner–Seitz cell volume and void calculations show there are seven different voids in the NaZn13 structure with the void at the 24d site (0, 0.25, 0.25) having the largest volume and the largest number of La neighbors. It is highly likely that the carbon atoms enter the 24d site. The small carbon doping collapses the antiferromagnetic state in La(Fe0.88Al0.12)13 and forms a ferromagnetic state. The magnetic transition temperature increases from 198 K to 280 K and the spontaneous magnetization (5 K) decreases from 22.9 μB to 21.3 μB per formula unit with increasing carbon content from x=0 to 0.8. The change in magnetic properties on carbon addition is attributed to cell volume expansion and Fe–Fe distance variations.

Structural and magnetic properties of the ZrMn6Sn6−xGax (0.25 ⩽ x ⩽ 3.75) compounds

New ZrMn6Sn6−xGax (0.25 ⩽ x ⩽ 3.75) compounds of HfFe6Ge6-type structure have been studied using x-ray diffraction and magnetization measurements. Ga substitution leads to a contraction of the unit-cell volume, and it is found that, among the three metalloid sites available, the Ga atoms mainly occupy the two prismatic sites, with a marked preference for the 2d site of the lower Wigner–Seitz cell volume. The magnetic behaviour of the Mn sublattice evolves from antiferromagnetic (x ⩽ 0.6) to ferromagnetic (x ⩾ 0.9), with a Curie temperature as high as 475 K. The compounds with intermediate Ga contents order ferromagnetically and present a decrease in their magnetization at low temperatures. An overall diminution of the ordering temperature is observed upon the Ga substitution, whereas the values of the maximal magnetization recorded at 5 K in a field of 15 kOe indicate that the Mn magnetic moment remains almost constant (≈ 2.2µB) in this series. The results are discussed and related to previously published data concerning other (X′ = Ga or In) representatives involving a non-magnetic R metal.

Structure and intrinsic magnetic properties of Sm(Fe,Si)9 alloys

Abstract The effect of Si on nanocrystalline metastable P6/mmm SmFe9 alloys was studied. The diffraction domain sizes derived from Rietveld analysis are confirmed by high-resolution transmission electron microscopy. The Curie temperature and the mean magnetic moment per Fe atom increase with Si content. TC is raised around 30 K compared to the equilibrium Sm2(Fe,Si)17 alloys. The hyperfine parameter sets were assigned according to the relationship between the Wigner–Seitz cell volume of each iron site and their isomer shift. Si occupies the 3g site. The hyperfine field decreases with silicon content.

A magnetic and Mössbauer spectral study ofTbFe11Ti andTbFe11TiH

Magnetic and iron-57 Mössbauer spectral measurements between 4.2 and 640 K have been carried out onTbFe11Ti andTbFe11TiH. The insertion ofhydrogen into TbFe11Ti to form TbFe11TiH increases its ordering temperature, magnetization, magnetic hyperfine fields, and isomershifts as a result of lattice expansion. Further, the insertion of hydrogen reinforces the basalmagnetic anisotropy of the terbium sublattice and, as is shown by ac susceptibilitymeasurements and thermomagnetic analysis, the spin reorientation observed inTbFe11Ti at 338 Kdisappears in TbFe11TiH.The Mössbauer spectra have been analysed with a model that considers both the easymagnetization direction and the distribution of titanium atoms in the near-neighbourenvironment of the three crystallographically distinct iron sites. The assignment andthe temperature dependencies of the hyperfine fields and isomer shifts are incomplete agreement with a Wigner–Seitz cell analysis of the three iron sites inRFe11Ti andRFe11TiH,where R is a rare-earth element. A complete analysis of the quadrupoleinteractions in both magnetic phases and in the paramagnetic phase ofTbFe11Ti supports the Mössbauer spectral analysis, and indicates that in the basal magnetic phase theiron magnetic moments are oriented along the equivalent [100] and [010] directions of theunit cell.