Invar Region Research Articles

Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions

By means of density functional theory, we perform a focused study of both body-centered-cubic (bcc) and face-centered-cubic (fcc) Fe-Ni random solid solutions, represented by special quasirandom structures. The whole concentration range and various magnetic configurations are considered. Excellent agreement on the concentration dependence of magnetization is found between our results and experimental data, except in the Invar region. Some locally antiferromagnetic fcc structures are proposed to approach experimental values of magnetization. Vibrational entropies of ordered and disordered systems are calculated for various concentrations, showing an overall good agreement with available experimental data. The vibrational entropy systematically contributes to stabilize disordered rather than ordered structures and is not negligible compared to the configurational entropy. Free energy of mixing is estimated by including the vibrational and ideal configurational entropies. From them, low- and intermediate-temperature Fe-Ni phase diagrams are constructed, showing a better agreement with experimental data than the one from a recent thermodynamic assessment for some phase boundaries below 700 K. The determined order-disorder transition temperatures for the $\mathrm{L}{1}_{0}$ and $\mathrm{L}{1}_{2}$ phases are in good agreement with the experimental values, suggesting an important contribution of vibrational entropy.

Solid-state synthesis and phase transformations in Ni/Fe films: Structural and magnetic studies

We have used X-ray diffraction, volume magnetocrystalline anisotropy constant and resistance measurements to study solid-state synthesis in Ni(0 0 1)/Fe(0 0 1), Ni/Fe(0 0 1) and Ni/Fe thin films with the atomic ratio between Fe and Ni of 1:1 (1Fe:1Ni), and 3:1 (3Fe:1Ni). We have found that the formation of Ni 3Fe and NiFe phases in the 1Fe:1Ni films takes place at temperatures ∼620 and ∼720 K, correspondingly. In the case of the 3Fe:1Ni films the solid-state synthesis starts with Ni 3Fe and NiFe phase formation at the same temperatures as for the 1Fe:1Ni films. The increasing of annealing temperature above 820 K leads to the nucleation of a paramagnetic γ par phase at the FeNi/Fe interface. The final products of solid-state synthesis in the Ni(0 0 1)/Fe(0 0 1) thin films are crystallites which consist of the epitaxially intergrown NiFe and γ par phases according to the [1 0 0](0 0 1)NiFe||[1 0 0](0 0 1) γ par orientation relationship. The crystalline perfection and epitaxial growth of the (NiFe+ γ par) crystallites on the MgO(0 0 1) surface allow to distinguish (0 0 2) γ par and (0 0 2)NiFe X-ray peaks (the cell parameters are: a( γ par)=0.3600±0.0005 nm and a(NiFe)=0.3578±0.0005 nm, correspondingly). At low temperatures the paramagnetic γ par phase undergoes the martensite γ par → α ′ phase transition which can be hindered by thermal and epitaxial strains and epitaxial clamping with a MgO substrate. On the basis of the studies of the thin-film solid-state synthesis we predict the existence of two novel structural phase transformations at the temperatures of about 720 and 820 K for alloys of the invar region of the Fe–Ni system.

Solid-state synthesis in Ni/Fe/MgO(001) epitaxial thin films

Solid-state synthesis in Ni/Fe/MgO(001) bilayer epitaxial thin films has been studied experimentally. The phase sequence Fe/Ni→(∼350°C)Ni3Fe→(∼400°C)NiFe→(∼ 550°C)γpar is formed as the annealing temperature increases. The crystal structure in the invar region consists of epitaxially intergrown single-crystal blocks consisting of the paramagnetic γpar and ferromagnetic NiFe phases, which satisfy the orientation relationship [100](001)NiFe ∥ [100](001) γpar. It has been shown that the nucleation temperatures of the Ni3Fe, NiFe, and γpar phases coincide with the temperatures of solid-state transformations in the Ni-Fe system.

Magnetization distribution in the orderedFe72Pt28 Invar alloy

The distribution of magnetization in the ordered Invar alloyFe72Pt28 has been studied as a function of temperature in the range 100–520 K using polarizedneutron diffraction. The temperature range covers both the Invar region and theparamagnetic regime in which the thermal expansion has normal Grüneisen behaviour. Thepolarized neutron data have been analysed in terms of localized iron 3d and Pt 5d momentsallowing local anisotropy of the magnetization distribution on the Fe atoms. The resultssuggest that the Pt atoms carry a small negative moment () in the magnetically ordered state. The fraction of unpaired electrons witheg symmetry is approximately 48% and does not change with temperature. This is in contradiction tomodels of the Invar effect which invoke the thermal population of two states with a different numberof eg and t2g carriers.

Magnetic contribution to the interdiffusion coefficients in bcc (α) and fcc (γ) Fe-Ni alloys

The interdiffusion coefficients in bcc (α) and fcc (γ) Fe-Ni alloys below their Curie temperatures have been calculated based on the magnetic contribution to the free energy for interdiffusion. The free energy for interdiffusion due to magnetic ordering in bcc Fe-Ni alloys is positive. The calculated interdiffusion coefficients in bcc Fe-Ni alloys fit the experimental data quite well. In fcc Fe-Ni alloys, the magnetic contribution to interdiffusion depends on both temperature and composition and is abnormal for Ni compositions in the Invar region. The free energy of vacancy formation is positive and the free energy of vacancy migration is negative, due to the effect of magnetic ordering. The interdiffusion coefficient in the ferromagnetic phase is lower than that extrapolated from the paramagnetic phase for Ni compositions of 50 at. pct and greater and is higher than that extrapolated from the paramagnetic phase for Ni compositions of 40 at. pct and lower.

Coexisting antiferromagnetism and ferromagnetism in mechanically alloyed Fe-rich Fe–Ni alloys: implications regarding the Fe–Ni phase diagram below 400°C

Fe–Ni alloys below the Invar region with compositions Fe100−xNix (x=21, 24, and 27at%) were prepared by high-energy ball milling technique (mechanical alloying). The as-milled samples, characterized by X-ray diffraction and Mössbauer spectroscopy, contain a mixture of α (BCC) and γ (FCC) phases, whereas the samples annealed at 650°C for 0.5h show a single γ (FCC) phase displaying a single line Mössbauer spectrum at room temperature (RT). At low temperature, the Mössbauer spectra of annealed Fe76Ni24 and Fe73Ni27 alloys show the existence of a magnetically split pattern together with a broad singlet, which are ascribed to a high-moment ferromagnetic Ni-rich phase and a low-moment Fe-rich phase, respectively. The Fe-rich phase in annealed Fe76Ni24 alloy, which is paramagnetic at RT, undergoes antiferromagnetic ordering at ∼40K, estimated from the dramatic line broadening of its spectrum, giving rise to a small hyperfine field (e.g. ∼2T at 6K). The coexistence of these phases is attributed to phase segregation occurring in these alloys as a result of enhanced atomic diffusion. The stability of these alloys towards martensitic (FCC→BCC) transformation at low temperatures is discussed in connection with the Fe–Ni phase diagram below 400°C.

Invar behavior of disorderedfcc−FexPt1−xalloys

Using the tight-binding linearized muffin-tin orbital method combined with the coherent-potential approximation (TB-LMTO-CPA) we have calculated the electronic and magnetic structure of disordered fcc ${\mathrm{Fe}}_{x}{\mathrm{Pt}}_{1\ensuremath{-}x}$ alloys in a broad concentration range. The total energy was determined as a function of the lattice constant and of the magnetic moment (fixed-spin moment method). For iron concentrations between $x=0.10$ and $x=0.85$ the equilibrium lattice constant, the bulk modulus, and the magnetic moment were determined in good agreement with available experimental data. No deviations of the magnetization from the Slater-Pauling curve in the Invar region were found. In that region two minima of the total energy exist, one with a high moment and a large lattice constant and the other with a zero moment and a small lattice constant, which explains qualitatively the Invar effect. Both minima become degenerate at the critical concentration, ${x}_{c}=0.76.$ A nonmagnetic ground state was found for $xg{x}_{c}.$ The energy barrier separating these two minima is two times higher in FePt Invar alloys than in the FeNi system. The relativistic effects were included within the scalar relativistic approximation.

Mössbauer study on phase separation in FeNi multilayers under ion bombardment

We investigated the effect of noble gas irradiation (He, Ne, Ar and Xe) on FeNi multilayers with a very thin modulation and nominal composition in the invar region Fe 0.63Ni 0.37. The evaluation of the formation/stability of the FeNi phases formed under irradiation with different ions and doses was followed by conversion electron Mössbauer spectroscopy.

Noncollinear magnetic structure in Ni0.35Fe0.65

Magnetic structure of NicFe1−c alloys in the INVAR region has long been a matter of great scientific interest and controversy. Using the locally self-consistent multiple scattering method, which has recently been extended to treat noncollinear magnetic systems, we studied the magnetic structure of Ni0.35Fe0.65 alloys. To simulate the alloys, we constructed a large fcc based sample which contains 256 sites occupied randomly by Ni and Fe atoms. The ground state magnetic structure is found to consist of noncollinear configurations associated with Fe-rich regions. In particular, Fe sites surrounded completely by other Fe atoms have antiferromagnetic alignments, while Fe sites having less than three Ni nearest-neighbors have a variety of noncollinear arrangements.

Very thin Fe/Ni modulation multilayer films under ion bombardment

We investigated the effect of noble gas irradiation (He, Ne, and Xe) on Fe–Ni multilayers with a very thin modulation and nominal composition in the Invar region Fe0.63Ni0.37. The evaluation of the formation/stability of the Fe–Ni phases formed under irradiation with different ions and doses was followed by conversion electron Mössbauer spectroscopy. The magnetic hysteresis curves were also obtained in order to correlate the hyperfine pattern with magnetic properties. The as-deposited sample reveals mainly the characteristic α-Fe while He- and Ne-irradiated samples clearly show a phase transformation with segregation of γ-FeNi phases with different Ni concentrations, a magnetic atomically ordered phase (∼50% Ni), and a nonmagnetic phase (⩽30% Ni). However, mixing with Ne is more effective than with He for similar doses. The results obtained with Xe showed a large distribution of hyperfine fields similarly to previous results reported for Kr [C. Tosello, F. Ferrari, R. Brand, W. Keune, G. Marest, M. A. El Khakani, J. Parellada, G. Principi, S. Lo Russo, V. Rigato, and S. Enzo, Nucl. Instrum. Methods B 80/81, 417 (1993)].

Numerical studies of the magnetism of FeNiMn alloys in the Invar region

By means of self-consistent semi-empirical LCAO calculations we study the itinerant magnetism of (Fe 0.65Ni 0.35) 1- y Mn y alloys for y = 0−0.22 at T = 0 K, neglecting only the transverse spin components. We find that the magnetic behaviour is quite complicated on a local scale. In addition to ferromagnetic behaviour, metastable spin-glass-like configurations are also found. In the same approach, using a direct numerical calculation by the Kubo formalism without any fitting parameters, we also calculate the electrical conductance in the magnetic state and find that the y-dependence observed in the experiments is well reproduced by our calculations, except that overall our resistivities are too large by a factor of ∼5.

Mössbauer spectroscopy, X-ray diffraction and magnetic measurements of iron-nickel ultrafine particles

Iron-nickel ultrafine particles with a composition in the Invar region (38–50% Ni) were prepared by the gas-evaporation-coalescence technique. The chemical composition was checked by electronprobe microanalysis, while X-ray diffraction Rietveld refinement was used to characterize the structure as well as to estimate the particle size. The temperature and field dependence of the magnetizationM(B, T) was measured for 0≤B≤25 kOe in the temperature range 4.2 K≤T≤400 K. Transmission Mossbauer spectra were taken at room temperature and at liquid helium temperature. The results obtained show that the predominant phase is a disordered Ni-rich alloy.

Local moment disorder in ferromagnetic alloys.

Local moment disorder, defined as a random arrangement of two distinct magnetic states of the same atomic species in a metallic system, is discussed in the framework of the Korringa-Kohn-Rostoker coherent-potential approximation combined with the local-density-functional method and applied to Fe-Cr, Ni-Fe, and Ni-Mn alloys. For Fe-Cr alloys it is found that the disordered-moment state has a higher energy than the ferromagnetic state in the entire region of Fe concentrations. Thus the theory fails to explain the spin-glass state observed around ${\mathrm{Fe}}_{0.14}$${\mathrm{Cr}}_{0.86}$. The theory, on the other hand, can explain the transition of Ni-Fe alloys from ferromagnetism to paramagnetism around the Invar region; the transition, however, is of first order, in contrast to experimental indications. The volume contraction due to the reversal of the magnetic-moment alignment from parallel to antiparallel with respect to the bulk magnetization is also discussed in connection with the Invar anomalies. For Ni-Mn alloys the calculation shows that, when the Mn concentration is larger than 15 at. %, magnetic states with local moments parallel and antiparallel to the average magnetization coexist even in the ferromagnetic region. The results are quite consistent with NMR experiments, which clearly show the existence of the antiparallel Mn local moments in addition to the parallel ones.

Field dependence of the magnetisation of FeNi Invars

We have carried out precise measurements of the magnetisation on fcc FeNi single crystals in the Invar region under magnetic fields up to 18 T at temperatures below 300 K. Iterative least-squares analysis of these observations leads us to the result that the magnetisation change consists of a renormalized spin-wave term and a Stoner-type contribution, the coefficient of which decreases linearly with increasing field up to 18 T.

Field Dependence of the Stoner-Type Contribution to the Magnetization of FCC Fe-Ni Alloys

We have performed magnetization measurements on FCC Fe-Ni alloys in the Invar region in magnetic fields up to 5.27 T at temperatures between 4.2 K and 320 K. An explicit expression of the magnetization is presented as a function of magnetic field B and temperature T , consisting of the renormalized spin wave contribution and the Stoner-type contribution varying with S T 2 . The coefficient S decreases with B , which can be written as S = S 0 (1- S 1 B ). Above about 25 K the observed magnetization is well represented by the expression, while it shows an unusual behavior below 25 K.

Magneto-elastic properties and invar anomaly of Fe-Pd alloys

The magnetic properties and thermal expansion of disordered Fe-Pd alloys have been measured. Elastic constants for the invar region have been also measured. The results suggest that the Fe-Pd system is a conventional ferromagnet. The magnitude of the volume magnetostriction and the coupling constant κC were smallest in the Fe-based invar alloys. A large lattice softening takes place around fcc-fct phase boundary. The different magnetic, volume and structural instabilities among Fe-based invar alloys are discussed.

Evidence for a high-spin Fe state in fcc Fe 1- xNi x thin films in the invar region

Fe 1- x Ni x alloy films with compositions in the Invar region (0.32 < x < 0.39) were prepared by simultaneous co-deposition of Ni and Fe under uhv conditions onto quatrz crystal substrates. The structure of the films was obtained by X-ray diffraction, the composition by electronprobe microanalysis (EPMA). The temperature and field dependence of the magnetization M( B, T) was measured for 0 T < B < 1 T between 4.2 and 300 K. After investigating the structural and magnetic properties of the as-prepared Fe 1- x Ni x electron Mössbauer spectra (CEMS) were taken at room temperature for each Fe 1- x Ni x film as-prepared and after annealing It is possible to achieve Fe 1- x Ni x films as-prepared with pure fcc-structure and also mixtures of bcc and fcc phases. As-prepared films show, in contrast to the behavior of bulk Fe - x Ni x samples, high magnetic saturation moments M s and and large mean hyperfine-fields B̄ hf which follow the Slater-Pauling curve. After annealing the films exhibit bulk behavior. We conclude that Fe 1- x Ni x films as prepared are in a magnetic state of the fcc-phase which is probably related to the occurence of γ 2-Fe. By annealing the films these states convert into the metastable γ-state of the fcc phase with corresponding changes of the magnetic moment and the mean hyperfine field BB̄ hf.

A UV photoemission study of Ni(111), FexNi100-x(111) (x=11, 31, 41, 61 and 66) and polycrystalline Fe

The electronic structure of the system FexNi100-x (x=0, 11, 31, 41, 61, 66 and 100) has been investigated using angle-resolved photoemission from FCC single crystals in the (111) orientation, except in the case of pure Fe, where polycrystalline material was used. The authors observe that in the results k-localised direct transitions gradually change into density-of-states transitions with increasing Fe concentration. A comparison is made with calculated densities of states and other experimental (electronic and magnetic) data. The anomalies in the Invar region (x approximately=65) do not show up in the observed electronic structure.

Role of T2 Term in Temperature Dependence of the Magnetization for Fe-Ni Invar Alloys

Precise measurements of magnetizations for single crystals of FCC Fe–Ni alloys in the Invar region have been made at temperatures from 4.2 K to 300 K in external applied fields up to 16.9 kOe to a relative accuracy of 5×10 -5 . In an analysis of these observed results with iterative least-squares method, it is found that there exists a large Stoner-type contribution varying as T 2.00±0.05 besides the spin-wave one to the temperature change in magnetization and that the coefficient of the Stoner-type contribution increases rapidly with decreasing Ni concentration, showing a maximum at about 35 at%Ni, and decreases for the alloys containing less than 35 at%Ni. It becomes evident that ferromagnetism in FCC Fe–Ni alloys disappears at a critical concentration of about 31 at%Ni. An anomalous behavior of the magnetization at low temperatures is also shown.

Invar anomalies of Fe-Pd alloys

The Mössbauer spectra and the magnetostriction have been observed for Fe 1− x Pd x alloys. The internal field of Fe atoms is 330±10 kOe and is almost constant in the Invar region 0.45⩾ x⩾0.3. The magnetostriction constants as well as forced magnetostriction (∂ω/∂ H) increase with decreasing temperature and with decreasing x. Observed large values of magnetostriction constants are related to a lattice instability of the fcc structure, which is confirmed by the measurement of elastic constants. The magnitude of ∂ω/∂ H is about one-fifth of Fe-Ni Invar. The thermal expansion of Fe 1− x Pd x alloys has also been measured in the whole concentration range. The Invar-like behavior observed in the region 0.28⩾ x#620 originates from an annealing effect of the martensite bcc phase. The spontaneous volume magnetostriction in the fcc region increases with decreasing x. The thermal expansion coefficients (α exp) of fcc alloys are analyzed from the Grüneisen equation. The high-temperature anomaly of α exp is discussed.