Correlation Between Isothermal Expansion and Functional Properties Change of the Fe81B13Si4C2 Amorphous Alloy

The structural changes effect on functional properties of ribbon shaped samples of the Fe81B13Si4C2 amorphous alloy during annealing process was investigated in this paper. Differential scanning calorimetry method has shown that this alloy crystallizes in one stage, in temperature range from room temperature up to 700 C. Structural relaxation process was investigated by sensitive dilatation method in nonisothermal and isothermal conditions. It has been shown that structural relaxation process occurs in two stages by measuring thermal expansion at constant temperatures of t1 = 420C, t2 = 440C and t3 = 460C. The first stage is characterized by linear logarithmic dependence of thermal expansion upon time at constant temperature. The second stage of structural relaxation process is characterized by linear dependence of isothermal expansion upon the square root of process time. These results imply that the first stage of structural relaxation process is a rapid kinetic process, while the second stage of structural relaxation process is a slow diffusion process. The rate constants k11 = 2,27⋅10 3 s, k12 = 2,79⋅10 s, k13 = 3,6⋅10 s, k21 = 0,67⋅10 s, k22 = 3,72⋅10 s, k23 = 21,53⋅10 s and activation energies E1 = 48,64 kJ/mol and E2 = 366, 23 kJ/mol were determined for both stages of structural relaxation process. The distinct correlation between structural relaxation process and magnetic susceptibility relative change was determined by thermomagnetic measurements. It has been shown that magnetic susceptibility can be increased by up to 80%, by convenient annealings after structural relaxation process, at magnetic field intensity of 8 kA/m.


Introduction
The metallic glasses represent a novel class of metallic materials characterized by amorphous structure and metallic bond providing them with unique physical and mechanical properties that cannot be found either in pure metals or other amorphous materials [1]. These properties are attributed to their microstructure, characterised by the absence of the longrange order atoms [2]. The amorphous state of matter is, however, structurally and thermodynamically unstable and very susceptible to partial or complete crystallization during thermal treatment, which requires good understanding of alloy stability at various temperatures. Generally, the stability is a thermally activated process of transition from disordered amorphous structure to an ordered crystal structure. The requirements for the soft magnetic alloys with nonequilibrium structure produced by melt quenching technique involve the design of the proper chemical composition that provides improved levels of the properties, such as a high glass-forming ability, good casting properties of the alloy which in turn determine the surface quality and uniformity of the melt-spun ribbons, as well as an enhanced thermal stability of both magnetic properties and amorphous structure [3,4,5].
Annealed glassy alloy is far from the equlibrium state. When heated, glassy alloys cristalize upon a certain period. Structural relaxation occurrs before the onset of cristallization. It is only then that slight changes in the atomic structure occur, which provides metastable state. These changes are mainly related either to the disappearance (for T < T g ) or occurrence (for T > T g ) of free volume (T -annealing temperature, T g -glass transition temperature) [6,7,8]. Thermal expansion and viscosity of the glassy alloys are structural relaxation-sensitive [9]. When annealed isothermally, the entire glassy alloy shows practically a linear increase in viscosity with the rise of annealing temperature [9]. Viscosity is expected to attain the constant value when the metal glass reaches the metastable state at the isothermal expansion temperature. Measurements of isothermal thermal expansion are suitable for the obtainment of quantitative data related to the following key parameters of the glassy state: activation energy of relaxation, activation energy of diffusion flow, frequency factor, and the initial defect concentration.
A lot of papers have been dedicated to amorphous alloys ferromagnetism [10][11][12][13][14][15], comprising the results of investigation of magnetic properties for alloys of different content. Generally an amorphous structure is assumed to introduce fluctuations in exchange interactions, which influence magnetic behaviour. It has been shown that exchange interactions of 3d electrons of neighbour atoms are accountable for ferromagnetism of ferrous group metal based amorphous alloys, as well as of crystal alloys, while magnetic properties distinctiveness of amorphous metal alloys is generally determined by locally changeable surroundings of each transition metal (TM) atom [15]. Atomic disorder and defects of different levels play the main role in magnetic properties determination. The results of various elements impact on magnetic moment M r and Curie temperature T C of amorphous metal alloys are very inconsistent [7,16,17,18]. Magnetization J r and Curie temperature T C decrease during the transition from crystal to amorphous state with all ferrous group metal based amorphous alloys. Magnetic moment in TM amorphous alloys is determined by the number of electrons introduced into TM 3d zone [7].
The aim of this paper is investigation of the structural changes effect on thermal and magnetic properties of the Fe 81 B 13 Si 4 C 2 amorphous alloy during annealing process.

Experimental
The subject of the research is ribbon shaped amorphous metal alloy Fe 81 B 13 Si 4 C 2 . The investigated ribbon samples were 30 μm wide. The structural changes effect on functional properties of this alloy during annealing was investigated. Nonisothermal and isothermal ribbon expansion was measured at temperatures t 1 = 420 0 C, t 2 = 440 0 C and t 3 = 460 0 C by 10 -5 m sensitivity dilatometer. X-ray diffraction analysis of the as-cast and annealed samples was performed by the Cu-K α radiation lines. The crystallization process was investigated in a nitrogen atmosphere by the differential scanning calorimetry (DSC) method using SHIMADZU DSC-50 analyzer with nitrogen flow of 20 ml/min. The analyses were conducted in temperature range from room temperature to 700 0 C at heating rate of 20 0 C/min. Temperature dependence of the relative magnetic susceptibility was investigated by the modified Faraday method in the temperature range from room temperature up to 460 0 C, in argon atmosphere, whereby magnetic field gradient was 8 kA/m. Fig. 1 shows DSC thermogram of the alloy sample Fe 81 B 13 Si 4 C 2 , obtained at heating rate of 20 0 C/min. The obtained thermogram shows one exothermic peak at around 500 0 C, which implies that the crystallization process occurs in one stage.   X-ray diffraction pattern of the as-quenched ribbon-shaped alloy sample shows only a broad halo at 2θ range of 40-55 0 suggesting an amorphous structure. Diffraction patterns of the ribbon-shaped alloy samples annealed at temperatures of t ≤ 460 0 C contain the same halo as well as the original sample but also contain one sharp peak at 2θ = 83.2 0 indicating presence of structural deformed crystal phase as consequence of ordering Fe-clusters already present in as-cast alloy. The increase in annealed temperature results in a lower intensity of this peak and the appearance of the new sharp peak at 2θ = 45.6 0 whose height increases with an increase in annealing temperature. The greater intensity of that peak as well as a decrease in its half width indicates the increase in crystallinity of the alloy. This shows that at a higher temperature (above 500 0 C) the process of crystallization occurs.

Results and discussion
The structural relaxation process has been identified by dilatometric method in temperature range of around 100 0 C lower than T CR . Fig. 3 shows temperature dependence of thermal expansion (Δl) of the alloy sample Fe 81 B 13 Si 4 C 2 . Fig. 3 shows temperature dependence of the thermal expansion (Δl) of the same Fe 81 B 13 Si 4 C 2 alloy sample, during first heating of up to 420 0 C, during second heating of up to 440 0 C and during third heating of up to 460 0 C. The analysis of the obtained results shown in Fig.3 points out that the temperature range of linear dependence of thermal expansion increases upon each heating of the sample. During the first heating there is almost linear dependence of thermal expansion up to 150 0 C. During the second heating the range of linear dependence expands up to 200 0 C, and during the third heating up to 450 0 C. It is obvious that such significant expansion of the temperature range of linear dependence is caused by structural relaxation process. Sudden thermal expansion is marked during first heating for the temperature higher than 350 0 C, during second heating for the temperatures over 400 0 C and during third heating for the temperatures over 440 0 C. This sudden expansion is caused by more intensive structural relaxation process leading to gradual change of amorphous structure into crystal at higher temperatures.   Isothermal annealing of amorphous ribbons in the range of structural relaxation temperature causes their timely isothermal expansion. Isothermal expansion of the samples entails the transformation of the unstable amorphous structure into metastable equilibrium, i.e. structural relaxation which leads to a decrease in free volume.
In order to identify these processes, the Fig. 5 shows logarithmic dependence of isothermal expansion ln (Δl) = f (τ) upon time for the samples annealed at 420 0 C, 440 0 C and 460 0 C. Linear dependence ln(Δl) upon time (τ) was obtained for the given time interval. This shows that the first stage of structural relaxation process is a fast kinetic process, characterized by transitions of atoms from higher towards lower energy state. The duration of the first stage of the structural relaxation process decreases with the rise in annealing temperature, i.e. τ 1 = 250 s at t 1 = 420 0 C, τ 2 = 200 s at t 2 = 440 0 C and τ 3 = 180 s at t 3 = 460 0 C.  6). Such dependence of isothermal expansion upon time suggests that the second stage of the structural relaxation process for all three annealing temperatures is a slow diffusion process, whereby the inter-cavity mass moves and the free volume decreases. The rate constants for both stages of the structural relaxation process (k 1 and k 2 ) were determined from the slope Δln(Δl) / Δτ (Fig. 5) and Δl / Δ(τ 1/2 ) (Fig. 6).  Thermomagnetic measurements were used to investigate temperature dependence of the relative change in magnetic susceptibility within three heating cycles in temperature range from room temperature up to 460 0 C. Fig. 8 shows dependence of the relative change in magnetic susceptibility upon temperature of amorphous alloy Fe 81 B 13 Si 4 C 2 . The analysis of the measurement results shown in Fig. 8 shows that upon first heating in the temperature range of amorphous state and upon cooling to room temperature, magnetic susceptibility increases by 20%. After the second heating of up to 440 0 C in the temperature range of amorphous state and upon cooling to room temperature, magnetic susceptibility increases by 80%. The increase in magnetic susceptibility upon each heating is caused by structural relaxation process. This process leads to decrease in the number of defects, mechanical strains and free volume in alloy sample, which enables greater mobility of magnetic domain walls. With simultaneous thermal influence and the influence of external magnetic field, atoms of reversed direction in-between domain walls move towards energetically more favourable domain. All this leads to the increase in magnetic susceptibility upon cooling. Upon each annealing Curie temperature T C slightly increases. This is caused by greater thermal stability of the structure due to structural relaxation process.

Conclusion
Thermal expansion process occurs in analogue way in case of all 3 samples. Temperature range of linear dependence of thermal expansion depends on annealing temperature. It increases with every subsequent sample annealing. Structural relaxation process of amorphous alloy Fe 81 B 13 Si 4 C 2 occurs in 2 stages at all annealing temperatures. The first stage of structural relaxation process is a fast kinetic process, which has a reduced duration with the increase in annealing temperature. The second stage of structural relaxation process is a slow diffusion process. We monitored the temperature dependence of relative change in magnetic susceptibility in 3 heating cycles in temperature range from room temperature up to 460 0 C. The increase in magnetic susceptibility upon each heating is caused by structural relaxation process. With every subsequent annealing T C moves towards higher values as a result of greater thermal stability of the structure due to structural relaxation process. Thus, dilatometric and thermomagnetic measurements have proved that there is a strong correlation between the structural relaxation process and certain thermal and magnetic properties of the investigated alloy.