scholarly journals Magnetic and structural properties of Sc(Fe1−xSix)2 Laves phases studied by Mössbauer spectroscopy and neutron diffraction

Nukleonika ◽  
2015 ◽  
Vol 60 (1) ◽  
pp. 155-160 ◽  
Author(s):  
Marek Wiertel ◽  
Zbigniew Surowiec ◽  
Mieczysław Budzyński ◽  
Jan Sarzyński ◽  
Anatoly I. Beskrovnyi
Keyword(s):  
Neutron Diffraction ◽  
Long Range ◽  
Hyperfine Magnetic Field ◽  
Hyperfine Coupling Constant ◽  
Neutron Diffraction Pattern ◽  
Range Order ◽  
Long Range Order ◽  
Laves Phases ◽  
Mean Values ◽  
Hyperfine Field Distributions

Abstract The aim of the presented paper is to study an influence of replacement of Fe atoms by Si atoms in quasibinary Sc(Fe1−xSix)2 Laves phases on their structural and magnetic properties. Powder X-ray diffraction (XRD) and neutron diffraction (ND) measurements carried out at different temperatures from 4.3 K up to about 700 K revealed that samples were single phase with cubic C15 structure for Si concentration x from 0.05 to 0.20 and hexagonal C14 structure for higher concentration. The results of 57Fe Mössbauer measurements showed that the Sc(Fe1−xSix)2 compounds with x ≤ 0.30 are ferrimagnetic at 4.3 K. At temperature 80 K in the samples with x = 0.20 and 0.30, a magnetic cluster spin-glass state has been observed, as ferrimagnetic long-range order disappears. Such picture was supported by the results of ND measurements carried out at 8 K, which confirmed the lack of long-range order for x above 0.10 and an occurrence of hyperfine field distributions in the corresponding Mössbauer spectra. At room temperature, samples with x ≥ 0.20 became paramagnetic. A substitution of Si atoms for Fe ones leads to a decreasing of mean values of hyperfine magnetic fields in samples under investigation. From the neutron diffraction pattern analysis of Sc(Fe0.90Si0.10)2Fe magnetic moment was determined as to be equal to 1.5 μB at 8 K. Combining this result with a value of hyperfine magnetic field on 57Fe probes, the hyperfine coupling constant A in Sc(Fe0.90Cu0.10)2 phases is estimated at about 11.6 T/μB at 8 K.

Long-range order inβ-brass studied by neutron diffraction

1974 ◽  
Vol 9 (9) ◽  
pp. 3921-3926 ◽  
Author(s):  
O. Rathmann ◽  
J. Als-Nielsen
Keyword(s):  
Neutron Diffraction ◽  
Long Range ◽  
Range Order ◽  
Long Range Order

Probing the Relationship of Long-Range Order in Nanodomain FeCo Alloys with Ternary Additions Using Neutron Diffraction

2009 ◽  
Vol 41 (5) ◽  
pp. 1144-1150 ◽  
Author(s):  
Ralph Gilles ◽  
Michael Hofmann ◽  
Yan Gao ◽  
Frank Johnson ◽  
Luana Iorio ◽  
...  
Keyword(s):  
Neutron Diffraction ◽  
Long Range ◽  
Range Order ◽  
Long Range Order ◽  
Feco Alloys ◽  
Ternary Additions ◽  
Relationship Of ◽  
The Relationship

Superfluidity and Superconductivity

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Wave Packet ◽  
Long Range ◽  
Cooper Pair ◽  
Bose Condensation ◽  
Range Order ◽  
Condensed State ◽  
Long Range Order ◽  
Coherent Wave

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

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