Magnetic properties and heat expansion of a binary Fe-Ni amorphous alloys

A comprehensive study of the magnetic properties (magnetostriction, magnetic susceptibility, Curie temperature) andthermal expansion of amorphous alloys of the (Fe1-xNix)78Si9B13 system of five compositions was carried out.The samples were cut from a strip 30 μm thick and had a rectangular shape. Two variants of orientation of the long side ofthe sample were used: along and across the tape (longitudinal and transverse samples). Measurements of magnetization and thermalexpansion were carried out in the temperature range 90 – 300 K in fields up to 6.5 kOe. To determine the change in the length ofthe sample under the influence of a magnetic field or in connection with a change in temperature, we used the method of wireconstantan strain gauges connected according to the DC bridge circuit. The sensitivity of the setup to the relative change in thelength of the sample was 8·10-7. The basis for determining the Curie temperature was the temperature dependence of the initialmagnetic susceptibility obtained by the induction method.It is shown that the linear magnetostriction constant and the Curie temperature decrease with increasing nickelconcentration. The nonlinear character of the Tc(x) dependence indicates an active participation of Ni atoms in the exchangeinteraction in alloys containing boron, in contrast to alloys with phosphorus. The volume (forced) magnetostriction was detectedand estimated from the linear portions of the curves  l l (H) in fields above the saturation field. Bulk magnetostriction, like linear,is positive and also decreases with increasing nickel content in the alloy.Measurements of the dependence  l l (H) at different temperatures showed that the character of the curves does notqualitatively change, the saturation magnetostriction increases with decreasing temperature in the range 300 – 100 K. Theindependence of the character of the curves ( ) ( ) s  l l T on x indicates that the predominance of the single-ion mechanism of theformation of magnetostriction in Ni-substituted iron-based alloys of the studied compositions is preserved.Thermal expansion curves recorded in the range 90 – 300 K do not show anomalies, the linear expansion coefficientmonotonically increases with increasing nickel concentration, which correlates with a decrease in volume magnetostriction

 on x indicates that the predominance of the single-ion mechanism of the formation of magnetostriction in Ni-substituted iron-based alloys of the studied compositions is preserved. Thermal expansion curves recorded in the range 90 -300 K do not show anomalies, the linear expansion coefficient monotonically increases with increasing nickel concentration, which correlates with a decrease in volume magnetostriction.
When measuring the magnetic susceptibility, a piece of tape was wound on the end of a ceramic straw in which there were wires of a thermocouple.

Experimental technique 2.1. Magnetostriction and thermal expansion
To measure magnetostriction and thermal expansion, we used the method of wire strain gauges connected by a bridge circuit. The working sensor R was glued to the sample under investigation, the compensating Rkto a quartz plate. Constantan sensors with equivalent parameters -R = Rk = 100 ± 0.3 Ω were used. The relative change in the length of the sample, equal to the relative change in the length of the wire strain gauge, is calculated by the formula: where C is the strain gauge (strain gauge sensitivity to deformation), R is the resistance of the working sensor, ∆R is the change in the resistance of the working sensor, which is determined by the deviation of the zero pointer from the relation: where stand  is the deviation when the resistance of the magazine connected in series with the working sensor changes by 0.01 Ω, a is the deviation when the resistance of the working sensor changes by ∆R. The sensitivity of the mount to relative deformation was 8·10 -7 .
The temperature dependence of the linear deformation was studied in the temperature range from 90 K to 300 K. The sample temperature was measured with a copperconstantan thermocouple.
The magnetic field was created by an electromagnet. The maximum field in a gap of 108 mm was 6.5 kOe. The sample was located in a plane parallel to the magnetic field.

Magnetic susceptibility. Curie temperature
Measurement of the susceptibility of the sample was carried out in an alternating magnetic field created by a solenoid. The solenoid serves as the primary winding of the air transformer. The secondary winding consists of two coils: a measuring coil, into which the sample under study is placed, and a compensation coil.
Without the sample, the signal from the measuring coil is compensated by the compensation coil, for which the following relationship must be satisfied: Here W1, W2 are the number of turns of the measuring and compensation coils, respectively, S1, S2 are their cross sections.
The final balancing is carried out by selecting the number of turns of the compensation coil and choosing its position in the non-uniform magnetic field of the solenoid.
When a sample is placed in a measuring coil, a signal appears that is proportional to the magnetic permeability (susceptibility) of the sample. The signal is amplified, detected and fed into the "y" input of the two-coordinate self-recording potentiometer.
Thermo-e.m.f. of thermocouple, which is in thermal contact with the sample, is fed to the "x" input. The sample temperature is changed by the furnace. The furnace is wound bifilar, its mode of operation is chosen experimentally. In this work, measurements of magnetostriction were performed for four variants of the geometry of the experiment, which are shown in Table. 1. The x axis is directed along length of ribbon, and the y axis is across. At room temperature, the longitudinal and transverse isotherms of magnetostriction relative to the applied field were measured. At other temperatures, only longitudinal magnetostriction was measured. In both type of samples, cut along the ribbon and across the ribbon, the longitudinal magnetostriction was found to be positive, and the transverse was found to be negative. In fig. 1 ( )  For samples cut along the ribbon, at T = 290 K, saturation is observed in the fields of strength 770 ÷ 330 Oe, depending on the composition. The saturation field decreases with increasing nickel content (Fig. 2). For samples cut across the ribbon, saturation occurs in fields of strength 400 ÷ 340 Oe.
From (6) and (7)  The review in Ref. [3] presents the dependence of magnetostriction on the composition for the system ( )

14 78
Fe, Co, Ni Si B at room temperature. The value of λs in this system (with a higher boron content) is somewhat higher than in the system under study. This difference is associated with a change in the ratio of the number of Si and B atoms. Although for alloys with a high content of cobalt, the type of metalloid atoms does not have a Si B the silicon-boron ratio is 0.69, which is 1.2 times less than in 78 10 12 Fe Si Bthis causes a lower value of λs. The percentage decrease in λs (43%) in the same nickel concentration range practically coincides with that observed in this work.
Study of the temperature dependence of magnetostriction allows one to obtain information about the microscopic nature of anisotropy, since magnetostriction is determined by the derivative of the magnetic anisotropy energy with respect to strain and, therefore, is a reflection of the same microscopic mechanisms that lead to magnetic anisotropy.
To study of the temperature dependence of magnetostriction ( ) l H l  curves were taken at various temperatures. With a change in temperature, the shape of the curves does not change qualitatively, as can be seen from Fig. 4 for a transverse sample of composition 78 9 13 Fe Si B .  In amorphous alloys, two mechanisms of magnetostriction (and microscopic anisotropy) are possible: single-ion and two-ion [4]. It has been established that, for iron-based alloys, the single-ion mechanism predominates, which is caused by magneto-ion being acted upon non-uniform electric field in their local environment [5]. The fact that the character of the temperature dependence of magnetostriction observed in our samples does not change noticeably with an increase in the nickel content (Fig. 5) indicates the preservation of the single-ion nature of microscopic magnetic anisotropy.
The observed dependencies ( ) l H l  have a characteristic paraprocess region: after reaching saturation, the magnetostriction will increase linearly with increasing field. The growth of magnetostriction is caused by the socalled forced magnetostriction, which is due to the fact that a sufficiently strong external magnetic field orients the spins in one direction, overcoming their thermal misorientation [6]. Forced magnetostriction is volumetric in nature - by definition, and is isotropic, as can be seen in Fig.1   Fe Si B . The behavior of the initial magnetic susceptibility as a function of temperature was investigated. With an increase in temperature in the range of 180-610 0 C, the susceptibility practically remains constant. With a further increase it grows rapidly, and then drops sharply as the sample reaches the Curie temperature. Upon subsequent cooling, the course of the heating curve is reproduced until the maximum is reached, below that point the curve χ (T) is significantly higher than during heating: susceptibility increases about 2.5 times for all samples (Fig. 6). The observed increase in susceptibility is due to a decrease in internal stresses in the sample with nickel content in the alloy. The nonlinear character of the dependence Tc (x) is associated with the participation of nickel atoms in the exchange interaction in alloys containing boron. The initial magnetic susceptibility increases after heating to temperatures T> 350 °C due to a decrease in internal stresses in the sample and the associated magnetoelastic anisotropy.
where σ is the stress, K1 is the anisotropy constant.
To determine the temperature above which internal stresses are effectively removed, the sample with the maximum nickel content (x = 0.416) was subjected to heatcooling thermal treatment with a constantly increasing maximum cycle temperature. Тmax equaled 150, 200, 250, 300, 350, 370, 400 о С. The non-reversibility of the curve χ (t) was observed starting from Tmax 350 ° C becoming more pronounced with further growth of Tmax.
It should be noted that heating to Tc, carried out 34  times, led to an embrittlement of samples, which is an indicator of possible partial crystallization processes. The observed susceptibility behavior is consistent with the results given in Ref. [10].
From the dependencies of χ (T) Tc was determined for all compositions. The obtained values are presented in and in Fig. 7. As reported in literature [3], the dependence of the Curie temperature of amorphous alloys on the concentration of (3d + 4s) electrons is similar to the dependence of the magnetic moment, but it is more sensitive to the composition of the transition metals contained in them. Thus, the magnetic moment of the alloy ( ) Fe Ni M . Fe-Ni based alloys are one of the most intensively studied systems. However, the exchange interactions in this system are complex, as indicated by the character of the dependence of Tc on the composition [11].
In this work, the introduction of nickel atoms instead of iron atoms leads to a decrease in Tc from 706 K for x = 0.0 to 683 K for x = 0, 416. The dependence of Tc (x) is nonlinear, which indicates that nickel atoms are actively involved in the exchange interaction. Moreover, the magnetic activity of nickel atoms depends on the metalloid composition: in alloys containing boron, nickel atoms are more magnetically active than in alloys containing phosphorus. Cluster calculations show [5,3]  Fe,Ni P , and indirect Fe-Ni-Fe exchange .
Another feature observed in this work should be noted: with an increase in the nickel content, the susceptibility decreases (Fig. 8).

Thermal expansion
It is known [12] that for crystalline Fe -Ni alloys, a complex dependence of the temperature coefficient of linear expansion (TCLE) on the nickel content is observed. TCLE varies non-monotonously and for most of the compositions of this system has the value of ( ) 61 9 13 10 K In this work, the dependences of the relative elongation on temperature were measured for samples cut along the ribbon.
For all samples a monotonic change in the relative elongation with temperature was observed in the range of 90 300 K  . In fig. 9 ( ) x TCLE depends on volumetric magnetostriction as [12]: