Temperature dependence of structural and magnetic transformations in Finemet-type amorphous alloys with Fe substituted for La

Structural and magnetic properties of amorphous and partly crystallized Fe73.5-xLax=0,1,3,5,7Si13.5B9Nb3Cu1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {Fe}_{73.5-{\text{x}}}\text {La}_{\text{x}=0,1,3,5,7}\text {Si}_{13.5}\text {B}_{9}\text {Nb}_{3}\text {Cu}_{1}$$\end{document} alloys were analysed in the temperature ranging from room temperature (RT) to 800 ∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ $$\end{document}C with differential scanning calorimetry (DSC) and thermomagnetic gravimetry (TMG). The Fe(Si) and Fe(B) structures were identified and characterized with set of crystallization temperatures and activation energies. Also, Curie temperatures for amorphous and for crystalline structures were determined and analysed as functions of La content.


Introduction
Alloys, like Fe 73.5 Si 13.5 B 9 Nb 3 Cu 1 (at.%) classical Finemet, appear primarily in amorphous-magnetic phase, which after appropriate thermal or mechanical treatment, are transformed into the phase, when iron-silicides and iron-borides magnetic nano-crystals are embedded in an amorphous residual matrix [1][2][3]. For practical purpose, in order to obtain soft magnetic properties of the material, it is important to get size of nano-crystals, during primary crystallization, smaller than the exchange-correlation length.
So far, many different modifications of the basic FeSiB composition were analysed while searching for better technical properties [3,4]. The analysis was focused rather on products of primary crystallization at lower annealing temperatures with less interest on the secondary crystallization.
In this work, mainly secondary crystallization at higher temperatures and its correlation to magnetization phenomena of Fe 73.5−x La x=0,1,3,5,7 Si 13.5 B 9 Nb 3 Cu 1 , (Finemet with Fe substituted for La) was analysed by means of differential scanning calorimetry (DSC) and performed at the same time, thermomagnetic gravimetry (TMG). Identification of structures and magnetic properties of the present alloys were based on our previous DSC, X-ray diffraction (XRD) and Mössbauer spectroscopy study [3,4] of the alloys with dopants other than La.

Experimental
Samples were prepared by casting melt on a rapidly rotating copper wheel, thus cooling it at 10 7 K s −1 and solidifying in the form of 20-m-thick and 1-mm-width bands of amorphous alloy. Composition of the samples was established through initial weighting and finally checked by analysing spectra presented in Fig. 1

measured and analysed with
Amptek XRF spectrometer.
The DSC heat flow as scans functions of temperature was performed on Setaram DSC 111 at heating rates ranging from 1 to 20 K min −1 with samples of various ( ∼ 20 mg) masses in the ambient N 2 environment.
The thermomagnetic (TM) measurement of material magnetization was simultaneously performed with Setaram-111 in TG-DSC mode. A small neodymium magnet was used to produce a magnetic field B ≈ 0.75 mT around the sample and a magnetic field gradient −∇B ≈ 0.14 mT cm −1 parallel to the sample surface. The temperature ranged from RT up to 1073 K (and backwards).

Calorimetry DSC
All DSC scans, which examples are shown in Figs. 2 and 3, display in fact two main structures, identified in the previous studies of the same basic alloy also with the use of XRD and Mössbauer spectroscopy [3,4]. The first DSC peak corresponds to primary crystallization of silicides, mainly Fe 3 Si with onset points at 450-480 • C in Finemet [1,3]. The secondary structure is related to crystallization of borides, mainly Fe 3 B and Fe 23 B 6 . In Finemet Fe 3 B crystallizes at 540 − 600 • C [1,3], whereas Fe 23 B 6 precipitates at 400 • C and at 670-740 • C [5,6]. Phase transfer parameters substantially depend on composition of the alloy and on details of thermal treatment.
For the present alloys, both primary and secondary crystallization onset points depend on the La content and generally addition of La shifts both peaks to higher temperatures. Increase in onset temperature for the peaks with the La content x = 0 − 7 and heating rate v = 2 and 10 K min −1 is presented in Fig. 4. The peaks are well resolved and allow us to calculate crystallization enthalpies and activation energies.
The effective activation energy for crystallization E a can be determined from the Kissinger equation: where v is the temperature increase rate, R = 8.31 J mol −1 K −1 is the gas constant, T p is the peak temperature and A is a constant. The activation energies E a were calculated by fitting data points with Eq. (1). The calculated activation energy for primary crystallization of pure Finemet ( x = 0 ) E a = 381 kJ mol −1 corresponds to the value of 384 kJ mol −1 from Ref. [1]. The E a values for x = 0 − 7 are presented in Fig. 5. As it is seen in the figure, E a changes irregularly with La content x from 381 to 622 kJ mol −1 for primary  crystallization and from 401 to 609 kJ mol −1 for secondary crystallization. This would suggest either more structures with empty nano-regions requiring energy-consuming rearrangement or an initial thermal treatment (or aging) of the amorphous alloy followed by precipitation of some Fe(Si) nanocrystals and enrichment of the residual amorphous phase with Nb and B, which makes further crystallization more difficult.  Fig. 6. Physically, each alloy is initially amorphous and ferromagnetic and it remains amorphous up to the primary crystallization onset point reported in Fig. 4. The primarily amorphous phase losses ferromagnetic properties at the  Curie temperature of 300-200 • C, as is presented in Fig. 6. At this temperature, total magnetization of the sample drops by approximately M ≈ 10-25 A m 2 kg −1 , as it is shown in Figs. 2 and 3 with thick red line (TM 1up). Pursuing further along TM curve, there is no magnetic response from the amorphous nonmagnetic matrix until crystalline structures are formed in correlation with exo-energetic peaks of crystallization on DSC scans in the figures. This means that some crystallization onset point temperature can be higher than the Curie temperature for the phase. Magnetization of amorphous phase increases nearly linearly from approximately 5 to 10 A m 2 kg −1 , as the La content x changes from 0 to 7, as it is shown in Fig. 6 with the numbers at the experimental points given in g mass units. Magnetization change of samples related next three crystalline structures and characterized by the Brillouin functions remain below 1 A m 2 kg −1 in dependence on La content x. The remaining magnetization of the sample at RT is up to 20% higher than the initial magnetization.

Magnetometry TM
Since amorphous ferromagnets, similarly to crystalline ones, reveal spin wave excitations, the low-temperature magnetization M(T) can be fitted with the Bloch equation: where M = M(0) − M(T) and the B and C parameters of the order 10 −5 K −3∕2 and 10 −8 K −5∕2 , respectively, were found by fitting the experimental data of magnetic scans with Eq. (2). Calculation of B and C allows us to determine the spin wave stiffness constants D ≈ 10 2 meVÅ 2 and find the mean square ranges of exchange interaction ⟨ r 2 ⟩ ≈ 10 Å 2 , considerably less than for crystalline ferromagnets. It implies a range of exchange interaction extending up to fourth or fifth nearest neighbours.
Also, it can be shown that close to the Curie temperature for amorphous phase the experimental data are better approximated by the Heisenberg model with the critical exponent = 0.325 , than by the Weiss mean field model with = 0.5 . This can be understood in terms of taking statistical average in the Heisenberg Hamiltonian H: in the Heisenberg model the spin correlations are taken into account and H contains terms < s i s j > , whereas in the mean field model the correlations are disregarded and H contains forms < s i >< s j > , where s i ,s j are spins of the lattice sites i, j.

Conclusions
Properties of thin Fe 73.5−x La x=0−7 Si 13.5 B 9 Nb 3 Cu 1 alloy foils were measured and analysed with complementary methods DSC and TM. Although the alloys crystallize in principle in two steps, the secondary crystallization reveals rather two tiny phases. The Curie temperature T C for amorphous matrix reaches 320 • C for La-free alloy and drops to 220 • C for Lareach one, with x = 7 . The Curie T C for crystalline phases and also magnetization change at T C do not substantially depend on La content.
Author Contributions Pavol Sovak prepared analysed materials. Michał Wasiak performed DSC and TM measurements. Marek Moneta performed TM measurements and prepared manuscript.
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