N. V. Ershov

Role of magnetism in the formation of a short-range order in iron-silicon alloys

The formation of a short-range order in soft magnetic Fe-Si alloys depending on the annealing temperature has been investigated theoretically and experimentally. The B2-type short-range order has been observed in samples quenched from temperatures T > TC (where TC is the Curie temperature) with the content cSi close to the boundary of the two-phase region. Annealing at temperatures T < TC for the content cSi ≥ 0.08 leads to an increase in the fraction of regions with the D03-type short-range order. The mechanism of the formation of the short-range order in Fe-Si solid solutions has been analyzed by the Monte Carlo simulation with the ab initio calculated interatomic interaction parameters. It has been shown that the energy of the effective Si-Si interaction in bcc iron strongly depends on the magnetic state of the matrix. As a result, the B2-type short-range order is formed at T > TC and is fixed at quenching, whereas the D03-type shortrange order is equilibrium in the ferromagnetic state. The results reveal the decisive role of magnetism in the formation of the short-range order in Fe-Si alloys and allow the explanation of the observed structural features of the alloys depending on the composition and temperature.

X-ray diffraction studies of the structure of nanocrystals in Fe73.5Si13.5B9Nb3Cu1 soft magnetic alloys before and after thermomechanical treatment

The structure of the Fe73.5Si13.5B9Nb3Cu1 soft magnetic alloy has been investigated using X-ray diffraction in transmission geometry. The initial alloy prepared by rapid quenching from the melt has a short-range order (∼2 nm) in the atomic arrangement, which is characteristic of the Fe-Si structure with a body-centered cubic lattice. The alloy subjected to annealing contains Fe-Si nanocrystals with sizes as large as 10–12 nm. The annealing under a tensile load leads to an extension of the nanocrystal lattice so that, after cooling, a significant residual deformation is retained. This can be judged from the relative shifts of the (hkl) peaks in the X-ray diffraction patterns measured for two orientations of the scattering vector, namely, parallel and perpendicular to the direction of the load applied. The deformation is anisotropic: within the accuracy of the experiment, no distortions in the [111] direction are observed and the distortions in the [100] direction are maximum. It is known that crystals with a composition close to Fe3Si exhibit a negative magnetostriction; i.e., their magnetization induced under a load (Villari effect) applied along the [100] direction is perpendicular to this direction along one of the easy magnetization ([010] or [001]) axes. In the alloy, the orientation of the nanocrystal axes is isotropic and the majority of the nanocrystals have a composition close to Fe3Si. The direction of magnetization of these nanocrystals is determined by the residual deformation of their lattice and lies near the plane perpendicular to the direction of the tensile load applied during heat treatment. This is responsible for the appearance of transverse magnetic anisotropy of the easy-plane type in the Fe73.5Si13.5B9Nb3Cu1 alloy.

X-ray diffraction studies of specific features in the atomic structure of Fe-Si alloys in the α area of the phase diagram

The atomic structure of Fe-Si alloys with a silicon concentration of 5–8 at % (α-area of the phase diagram) was studied using X-ray diffraction. The effect of quenching after annealing at a disordering temperature of 850°C on the structural state of the alloys was elucidated. It is shown that the quenched samples are characterized by a short-range ordering; namely, there is a local B2-type order at a concentration of 5–6 at % Si and, in addition, DO3-phase clusters are formed at 8 at % Si. The atomic structure of B2 clusters and their nearest surroundings is established.

Atomic displacements and short-range order in the FeSi soft magnetic alloy: Experiment and ab initio calculations

In order to determine the mechanism responsible for the formation of short-range order in dilute FeSi solid solutions, the chemical bonding, atomic displacements near the metalloid, and the enthalpy of silicon dissolution in iron have been studied within density functional theory. It is found that the directed character of the Si-Fe chemical bond formed upon the p-d hybridization brings about an anisotropy in atomic displacements near silicon atoms. Calculations of the Si-Si effective pairwise interaction energy offer an explanation for the observed features in short-range order in FeSi and suggest that ferromagnetic bcc Fe does not have a tendency toward Si atom clusterization. The mechanism of formation of the anisotropy induced by application of an external load or a magnetic field is discussed.

Relaxation of the state with induced transverse magnetic anisotropy in the soft magnetic nanocrystalline alloy Fe73.5Si13.5Nb3B9Cu1

The residual lattice strains of nanocrystals, which are responsible for the formation of states with transverse magnetic anisotropy in samples of the Fe-Si-Nb-B-Cu alloys (Finemets) subjected to annealing under tensile loading with the subsequent relaxation annealing at temperatures in the range from 500 to 600°C, have been measured using X-ray diffraction. The relative extension and compression of interplanar spacings have been compared with the induced magnetic anisotropy constants determined from the magnetic hysteresis loops. It has been shown that, during the relaxation annealing at the nanocrystallization temperature (500–540°C), the observed decrease in the residual strains is accompanied by a decrease in the transverse magnetic anisotropy constant. A linear correlation between the relative extension and compression of the interplanar spacings for different crystallographic planes and magnetic anisotropy constant has been revealed. The deviation from linearity is observed after annealing at a temperature of 600°C, which is explained by a possible increase in sizes of nanocrystals, changes in their structure, and partial crystallization of the amorphous matrix.

Effect of thermomagnetic and thermomechanical treatments on the magnetic properties and structure of the nanocrystalline soft magnetic alloy Fe81Si6Nb3B9Cu1

The structural and magnetic states of ribbon samples of the soft magnetic alloy Fe-Si-Nb-B-Cu (6 at % Si) have been investigated after the nanocrystallization at a temperature of 550°C in a constant magnetic field (thermomagnetic treatment), in a field of mechanical tensile stresses (thermomechanical treatment), and without external effects. It has been shown that exposure to a constant magnetic field or a field of mechanical tensile stresses gives rise to a longitudinal anisotropy of magnetic properties. The mag- netic hysteresis loop transforms and becomes close to rectangular. This is accompanied by a significant increase in the residual magnetic induction, which approaches the saturation magnetic induction. While the time required to complete the processes of nanocrystallization is as short as 20 min and, under thermome- chanical treatment, the magnetic anisotropy is induced for 20 min, the time it takes to decrease significantly the coercive force of the alloys under thermomagnetic treatment is substantially longer (up to 60 min). After the thermomagnetic treatment, no lattice strains of α-FeSi nanocrystals have been found. Either they do not exist at all, or their values are within the error of the X-ray diffraction experiment. In the samples subjected to annealing under tensile loading, anisotropic lattice strains of nanocrystals with the values increasing pro- portionally to the applied stress have been revealed. The highest strains reaching 1% have been observed after the annealing under a stress of 860 MPa.

Short-range order in Fe1−xSix(x=0.05−0.08) alloys with induced magnetic anisotropy

Previously, iron—silicon alloys were investigated using X-ray diffraction and Mössbauer spectroscopy. It was demonstrated that, at low silicon concentrations, the alloys undergo a local separation into regions of the α iron phase depleted in silicon and silicon-rich clusters with a B2 ordering. The structure of locally ordered regions of the B2 phase is characterized by a pair ordering of silicon atoms: the Si—Si pairs are formed by next-nearest neighbors, and the axes of pairs are oriented along the 〈100〉 directions, which are the easy-magnetization axes. The thermomagnetic treatment in a constant magnetic field applied along the 〈100〉 axis induces an axial magnetic anisotropy, results in the formation of an anisotropic distribution of the B2 phase, and leads to a slight decrease in the volume fraction of the coordination 6: 2 with two silicon atoms in the first coordination shell of the iron atom. Therefore, the formation of an anisotropic local order of pairs of silicon atoms occurs as a result of their reorientation.

Specific features of the local atomic structure of a Fe-Si alloy in the α area of the phase diagram

The atomic structure of Fe-Si alloys with silicon concentrations of 3–8 at % (α area of the phase diagram) was studied by Mössbauer spectroscopy. It is established that plastic deformation under pressure and quenching after annealing at a disordering temperature of 850°C have an effect on the structural state of the alloys. Plastic deformation is shown to lead to a disordered state only at a minimum silicon content (3 at %); in other cases, a solid solution is locally separated into regions enriched in iron or silicon. In quenched samples, the separation is accompanied by a short-range ordering of the B2 type, which is characterized by an increase in the volume fraction of the coordination with two Si atoms in the first configuration shell of Fe; this result is in agreement with previous X-ray diffraction data.

Structure of α-FeSi alloys with 8 and 10 at % silicon

The atomic structure of single-crystal samples of Fe1 − xSix (x = 0.08, 0.10) alloys has been investigated using X-ray diffraction. It has been shown that the body-centered cubic (BCC) lattice of these alloys contain clusters with local ordering of the B2 type, which are characteristic of alloys with depleted composition (x = 0.05−0.06). The Fe3Si phase with the D03 structure has been revealed at silicon concentrations x = 0.08 and 0.10. The volume fraction of Fe3Si-phase regions increases both with an increase in the silicon concentration in the Fe1 − xSix alloy and during annealing of the samples with this silicon concentration at a temperature of 450°C. Based on the results obtained, it has been concluded that the anisotropic distribution of the B2 clusters, which arises as a result of thermomagnetic or thermomechanical treatment, is responsible for the induction and stability of the uniaxial magnetic anisotropy in the Fe1 − xSix (x = 0.05−0.10) alloys.

Lattice distortions near impurity atoms in α-Fe1−x Six alloys

Lattice distortions near impurity atoms in α-Fe1−xSix alloys (x≈0.05–0.06) are studied both experimentally using x-ray diffraction and theoretically by means of ab initio calculations. It is found that the distortions are more complex than experimental data suggest. The displacements of atoms near impurities are not determined by the concentration dependence of the average lattice constant nor by a difference in the ion radii.