The Effect of Nickel on the Viscosity of Iron-Based Multicomponent Melts

: In this work, we investigated the temperature dependence of the kinematic viscosity of multicomponent Fe 72.5 − x Ni x Cu 1 Nb 2 Mo 1.5 Si 14 B 9 melts with a Ni content of up to 12.7 at. %. The peculiarities of the temperature dependence of Ni-containing melts were explained by the tendency of Ni atoms to surface segregation. Ni atoms are concentrated near the interfaces of the liquid and solid phases in the mushy zone at the stage of melting and restrain the melting of the solid phase. With increasing Ni content, the Arrhenius type of viscous ﬂow begins at a higher temperature. Ni atoms are concentrated at the periphery of clusters, increasing their size and decreasing their mobility. The movement of Ni-containing clusters increases the activation energy and decreases the kinematic viscosity. The change in the activation energy at a temperature of about 1700 K was associated with a liquid-liquid structure transition (LLST). This structural transition is reversible since it is observed both at the heating and cooling stages. The increase in kinematic viscosity at temperatures above 1900 K was associated with the decomposition of high-temperature clusters based on cementite and silicon oxides.


Introduction
The viscosity is associated with the movement of liquid particles (atoms, molecules, clusters) relative to each other, and it depends on the diffusion mobility of these particles. According to the Stokes-Einstein relation, the diffusion coefficient is inversely proportional to viscosity. Since the temperature dependence of the diffusion coefficient is expressed by the Arrhenius equation [1], the viscosity can be represented in the form [2]: where ν is the kinematic viscosity (m 2 ·s −1 ), ν 0 is the pre-exponential factor with the dimension of the kinematic viscosity, E a is the activation energy of the viscous flow (J·mol −1 ), R is the gas constant (J·K −1 ·mol −1 ), T is the absolute temperature (K). From relation (1) it follows that the viscosity decreases with increasing temperature at the constant activation energy E a . The activation energy depends on the size and interaction of the particles participating in the viscous flow, and the transition of individual particles to a new state occurs after the particle reaches the activated state. Therefore, we can assume that the melt structure remains sufficiently stable if the activation energy does not change. The change in the activation energy on the temperature dependence of the viscosity is associated with a change in melt structure, and this phenomena is interpreted as a liquid-liquid structure transition (LLST) [3][4][5][6][7][8][9][10][11].
LLST is often observed in multicomponent melts since different groups of atoms within them can form clusters that are stable over a wide temperature range. One of the materials of great practical importance is the Fe-Cu-Nb-Si-B alloy, which is used for the production of nanocrystalline soft magnetic materials [12]. At the initial stage of production, a precursor is obtained from the melt in the form of a thin metal ribbon with an amorphous structure. Then, as a result of heat treatment, a nanocrystalline structure with an average grain size of about 10 nm is formed in the ribbon. Together with Nb, the alloy can also contain Mo, V or other inhibitors of nanograin growth, which affect the crystallization process [13]. The alloy may also contain Ni or Co, which affects the constant of magnetic anisotropy and makes it possible to obtain nanocrystalline material with a linear magnetization curve and different levels of magnetic permeability [14][15][16]. Ni atoms have negative energy of surface segregation in iron [17,18]. Therefore, Ni atoms tend to be located near the free surface, slowing down the motion of grain boundaries and smoothing the peak of heat release in the process of nanocrystallization [19]. These features should affect the temperature dependence of the viscosity of Ni-containing iron-based melts.
In this work, we investigated the temperature dependences of the kinematic viscosity of the multicomponent Fe 72.5−x Ni x Cu 1 Nb 2 Mo 1.5 Si 14 B 9 melt with a Ni content of up to 12.7 at. %.

Materials and Methods
Fe 72.5−x Ni x Cu 1 Nb 2 Mo 1.5 Si 14 B 9 alloys with Ni = 0; 2.5; 6.3; 12.7 at. % were smelted in an induction vacuum furnace at a temperature of 1820 K and cooled in a flat mold. The finished ingots were melted again at 1775 K, the melt was held at this temperature for 5 min, and then an amorphous ribbon with a thickness of 20 µm thick and 10 mm wide was obtained using the planar flow casting process. The temperature dependence of the kinematic viscosity was measured on toroidal samples wound from an amorphous ribbon, which was placed in a beryllium oxide cup. The determination of the kinematic viscosity was carried out by the method of torsional vibrations in an atmosphere of pure helium under a pressure of 10 5 Pa [20]. Using this method, the logarithmic decrement was measured, and the kinematic viscosity was calculated from the formulas connecting the logarithmic decrement with the kinematic viscosity. Before the measurement, the melt was kept at a predetermined temperature for 8 min to stabilize the structural state. During heating and cooling, the melt temperature was changed with a step of 30 K at a speed of 30 K/min. The error in the determination of the kinematic viscosity was 3%.
In addition to the main chemical elements, the content of Al, C, N and O was also determined in the alloy. These elements have a high electronegativity and form strong bonds with metals. The nature of these impurities is associated with the charge materials. There is no interaction of the melt with the beryllium oxide cup, as evidenced by the appearance of the cup after high-temperature studies. The content of the main chemical elements, as well as aluminum and carbon, was determined using a DFS-500 Optical Emission Spectrometer, OKB Spectr, Saint-Petersburg, Russia. An ARL 4460 Metals Analyzer Thermo Fisher Scientific, Walthan, MA, USA, was used to determine the N and O content. The error in determining the chemical composition was 1%.

Results
temperature Tmax = 1985 K and cooling of the Fe72.5−xNixCu1Nb2Mo1.5Si14B with Ni = 2.5 (1); 6.3 (2); and 12.7 at. % (3) as Arrhenius plot:  The viscosity should decrease with increasing temperature. However low-temperature regions, which are marked with gray and black symb temperature Tmax = 1985 K and cooling of the Fe72.5−xNixCu1Nb2Mo1.5Si14B with Ni = 2.5 (1); 6.3 (2); and 12.7 at. % (3) as Arrhenius plot:  The viscosity should decrease with increasing temperature. However low-temperature regions, which are marked with gray and black symb RT E a + ν = ν 0 ln ln , Figure 2. Kinematic viscosity on a natural logarithmic scale lnν as a function of the inverse absolute temperature T −1 upon heating to maximum temperature T max = 1985 K and cooling the Fe 72.5−x Ni x Cu 1 Nb 2 Mo 1.5 Si 14 B 9 alloys with Ni content 6.3 at. %. content of 2.5 and 6.3 at. % begin to behave like the Arrhenius type at te tures above 1560 K both at the heating and cooling stages. The melt wi content of 12.7 at. % flows according to the Arrhenius equation when above 1685 K, and at the cooling stage, this type of viscous flow takes plac to a temperature of 1560 K.  Table 1 shows culated activation energies for the low-temperature and high-temperat gions and additionally includes data for the Ni-free melt at the cooling s can be seen that in the low-temperature region the activation energy is low has approximately the same value during heating and cooling. high-temperature region, the activation energy is noticeably higher, a highest value of Ea is in the melt with a high Ni content. The viscosity should decrease with increasing temperature. However, in the lowtemperature regions, which are marked with gray and black symbols, the viscosity increases. This temperature region corresponds to the mushy zone, in which the liquid and solid phases coexist [8]. An increase in the logarithmic decrement and calculated viscosity with increasing temperature is caused by an increase in the volume of the liquid phase in the measuring cup. Melts with a Ni content of 2.5 and 6.3 at. % begin to behave like the Arrhenius type at temperatures above 1560 K both at the heating and cooling stages. The melt with a Ni content of 12.7 at. % flows according to the Arrhenius equation when heated above 1685 K, and at the cooling stage, this type of viscous flow takes place down to a temperature of 1560 K.
The linear sections of the Arrhenius plots in Figures 1-3 are obtained as a result of linear regression of experimental points and they correspond to a melt flow with constant activation energy E a . Upon heating, the activation energy changes at a temperature of 1685 K for all Ni-containing melts. On cooling, the transition temperature drops with increasing Ni content. Table 1 shows the calculated activation energies for the low-temperature and high-temperature regions and additionally includes data for the Ni-free melt at the cooling stage. It can be seen that in the low-temperature region the activation energy is lower and has approximately the same value during heating and cooling. In the high-temperature region, the activation energy is noticeably higher, and the highest value of E a is in the melt with a high Ni content.
At temperatures above 1900 K at the heating stage, the drop in kinematic viscosity is replaced by an increase, see Figures 1-3. An increase in viscosity is observed at temperatures above 1915 K in an alloy with a Ni content of 2.5 at. % and at temperatures above 1955 K in alloys with a Ni content of 6.3 and 12.7 at. %.  5 show the kinematic viscosity on a natural logarithmic scale lnν as a function of the inverse absolute temperature T −1 separately for heating (4) and cooling (5) in Fe 72.5−x Ni x Cu 1 Nb 2 Mo 1.5 Si 14 B 9 alloys. It follows from these figures that, at the heating stage in the temperature range of 1700-1900 K, Arrhenius plots differ insignificantly, while the viscosity is higher in the melt with a low Ni content. After heating to the maximum temperature T max = 1985 K, the melt with a low Ni content of 2.5 at. % has the highest viscosity. The maximum temperature is the starting point for the cooling stage. Therefore, at the cooling stage in the temperature range of 1700-1900 K, melts with a low Ni content have a flatter Arrhenius plot and lower activation energy, see Table 1. In general, at the cooling stage, the kinematic viscosity is lower in alloys with a higher Ni content. At temperatures above 1900 K at the heating stage, the drop in kin viscosity is replaced by an increase, see Figures 1-3. An increase in visc observed at temperatures above 1915 K in an alloy with a Ni content of 2 and at temperatures above 1955 K in alloys with a Ni content of 6.3 and %. Figures 4 and 5 show the kinematic viscosity on a natural logarithm lnν as a function of the inverse absolute temperature T −1 separately for hea and cooling (5) in Fe72.5−xNixCu1Nb2Mo1.5Si14B9 alloys. It follows from these that, at the heating stage in the temperature range of 1700-1900 K, Ar plots differ insignificantly, while the viscosity is higher in the melt with a content. After heating to the maximum temperature Tmax = 1985 K, the mel low Ni content of 2.5 at. % has the highest viscosity. The maximum temp is the starting point for the cooling stage. Therefore, at the cooling stage temperature range of 1700-1900 K, melts with a low Ni content have a Arrhenius plot and lower activation energy, see Table 1. In general, at the stage, the kinematic viscosity is lower in alloys with a higher Ni content.

Discussion
When discussing the experimental results, we will estimate the act energy of a viscous flow. The activation energy is equal to the energy t particle must receive in order to overcome the potential barrier and mov empty place (hole) in the melt. From general considerations, it follows t activation energy is higher for large particles, which have a large size and Based on the theory of the transition state [21], the following relationsh obtained between the reduced activation energy Ea/RT and the size of pa participating in a viscous flow [22]: w h ere C1 is a constant, which in general depends on temperature. Thus, the tion energy of viscous flow increases with increasing particle size.
When discussing the results, we will also use the relationship betwe ticle size and viscosity. Analysis of simple pure metals at the melting te ture, at which oscillations of atoms about equilibrium positions prevail, s [23,24] that the viscosity decreases with an increase in the ratio of the atom to the square of their size m/a 2 . The viscosity should decrease with an incr the number of atoms in the cluster [23]. In the theory of the transition sta the motion of one layer of liquid relative to another occurs due to the trans a particle from one equilibrium state to another in the same layer. In th with an increase in the particle size, their velocity increases and the v decreases. A decrease in viscosity with an increase in the particle nanofluid was observed experimentally [25].

Discussion
When discussing the experimental results, we will estimate the activation energy of a viscous flow. The activation energy is equal to the energy that the particle must receive in order to overcome the potential barrier and move to an empty place (hole) in the melt. From general considerations, it follows that the activation energy is higher for large particles, which have a large size and mass. Based on the theory of the transition state [21], the following relationship was obtained between the reduced activation energy E a /RT and the size of particle a participating in a viscous flow [22]: where C 1 is a constant, which in general depends on temperature. Thus, the activation energy of viscous flow increases with increasing particle size. When discussing the results, we will also use the relationship between particle size and viscosity. Analysis of simple pure metals at the melting temperature, at which oscillations of atoms about equilibrium positions prevail, showed [23,24] that the viscosity decreases with an increase in the ratio of the atom mass to the square of their size m/a 2 . The viscosity should decrease with an increase in the number of atoms in the cluster [23]. In the theory of the transition state [21], the motion of one layer of liquid relative to another occurs due to the transition of a particle from one equilibrium state to another in the same layer. In this case, with an increase in the particle size, their velocity increases and the viscosity decreases. A decrease in viscosity with an increase in the particle size in nanofluid was observed experimentally [25]. Figure 4 shows that with an increase in the Ni content, the Arrhenius type of viscous flow begins at a higher temperature. Boron is introduced into the Fe 72.5−x Ni x Cu 1 Nb 2 Mo 1.5 Si 14 B 9 alloy to lower the melting point. Thus, the melting point of the Fe 83 B 17 eutectic alloy is 1450 K. Therefore, the liquid phase in the mushy zone is formed on the basis of iron-boron, in which Cu, Si and Ni are also present. Ni atoms have a high negative energy of surface segregation and their concentration is highest near the interfaces. It can be assumed that the high concentration of Ni near the interface between the solid and liquid phases restrains the melting of the residual solid phase in the mushy zone. This process also contributes to the active transition of Ni to the liquid phase and the depletion of the solid phase. Similar experimental results were obtained when studying the composition of the solid, partially melted and liquid phases in Ni-containing alloys [26,27].
Electronegativity on the Luo-Benson scale for the main chemical elements Fe, Ni, Cu, Nb, Mo, Si and B are 1.72; 1.90; 2.30; 1.43; 1.46; 3.41 and 3.66, respectively [28]. Boron atoms are most strongly associated with iron atoms since this pair of elements has the most distinct electronegativities. Therefore, in the low-temperature region, the most stable clusters in the melt are formed on the basis of iron boride Fe 2 B with a melting point of 1663 K [29]. Clusters based on FeSi with a melting point of 1683 K are less stable and have a lesser effect on structural transformations [30]. Therefore, the change in the activation energy upon heating above 1685 K, see Figure 4 and Table 1, can be associated with the decay of Fe 2 B-based clusters and the formation of new clusters based on iron triboride FeB 3 . A similar model of structural transformations was proposed in [6]. The narrow temperature range of LLST indicates that only one type of structural transition predominates.
From Figure 4 and Table 1, it follows that upon heating after the transition to the high-temperature region, the activation energy increases. As we assumed earlier, with an increase in the activation energy, the size and mass of the clusters participating in the viscous flow increase. As a result of the transformation of Fe 2 B-based clusters into FeB 3 -based clusters, the number of new B-containing clusters is reduced by three times, while five iron atoms are released for each new cluster. As the temperature rises, the structure of the melt should become more disordered, and various atoms and clusters tend to have a more chaotic distribution. A more uniform arrangement of atoms and clusters corresponds to a larger-scale structure of the multicomponent melt [31]. Clusters can be joined by Ni, Nb, Mo atoms, as well as free Fe and Si atoms, which form a cloud around B-containing clusters. The Ni and Nb atoms have a large negative surface segregation energy of −0.65 eV per atom [17]; therefore, they are located at the cluster periphery. Due to coalescence, clusters can form even larger associates-fractal clusters [32,33].
The Fe 72.5−x Ni x Cu 1 Nb 2 Mo 1.5 Si 14 B 9 melt contains impurities: C = 0.1; Al = 0.05; O = 0.05; and N = 0.005 at. %. These impurities can form clusters based on compounds whose melting temperatures are between 1900 and 2000 K, that is, in the region of kinematic viscosity growth at the heating stage, see Figure 4. Cementite Fe 3 C has a melting point of 1923 K [34]. The melting point of silicon oxide in the β-cristobalite form is 1996 K, and in the β-tridymite form, it is 1943 K [30]. Aluminum oxide Al 2 O 3 and aluminum nitride AlN have a melting point above 2300 K. An increase in kinematic viscosity at temperatures above 1900 K can be associated with the decomposition of high-temperature clusters based on cementite and silicon oxides. A similar increase in viscosity in the high-temperature region was observed in liquid pipe steel [31]. The growth of the viscosity in the hightemperature region in Figure 4 corresponds to the beginning of LLST. With an increase in temperature and after the end of the structural transition, the Arrhenius plot should again become linear with a certain activation energy. This was previously demonstrated in [23] for Fe 84.5 Cu 0.6 Nb 0.5 Si 1.5 B 8.6 P 4 C 0.3 melt.
The wide temperature transition region indicates that this process involves several types of clusters based on phases with different melting points. The maximum heating temperature T max = 1985 K forms the melt structure at the stage of decomposition. At this temperature, the melt with a low Ni content has the highest viscosity, i.e., clusters break up into smaller particles. According to the small-scale structure obtained by the melt at the maximum heating temperature, the melt with a low Ni content has the lowest activation energy, see Table 1.
At the cooling stage, there is also a transition temperature at which the activation energy of the viscous flow changes. The transition temperature is about 1700 K and it is slightly higher than the temperature of 1685 K for LLST at the heating stage. This allows us to assume that the structural transition of Fe 2 B-based clusters into FeB 3 -based clusters is reversible.
It follows from Figures 4 and 5 that melts with Ni have lower viscosity and higher activation energy. This effect of Ni can also be associated with the tendency of Ni atoms to surface segregation. It can be assumed that Ni atoms are concentrated at the periphery of B-containing clusters, increasing their size and decreasing their mobility.

Conclusions
The temperature dependence of the kinematic viscosity of multicomponent Fe 72.5−x Ni x Cu 1 Nb 2 Mo 1.5 Si 14 B 9 melts with a Ni content of up to 12.7 at. % was studied. An increase in the Ni content decreases the melt viscosity and increases the activation energy of the viscous flow. The change in the activation energy at a temperature of about 1700 K was associated with LLST, as a result of which Fe 2 B-based clusters disintegrate and new clusters based on iron triboride FeB 3 are formed. This structural transition is reversible since it is observed both at the heating and cooling stages. The increase in kinematic viscosity at temperatures above 1900 K was associated with the decomposition of high-temperature clusters based on cementite and silicon oxides. At the maximum heating temperature T max = 1985 K, a structure is formed, which is the initial one for the activation energy at the cooling stage. The specific features of the temperature dependence of the kinematic viscosity in Ni-containing melts can be explained by the tendency of Ni atoms to surface segregation. Ni atoms are concentrated near the interface between the liquid and solid phases in the mushy zone at the stage of melting and restrain the melting of the solid phase. Due to the increased Ni content in melts, the Arrhenius type of viscous flow begins at a higher temperature. Ni atoms are concentrated at the periphery of B-containing clusters, increasing their size and decreasing their mobility. The movement of such clusters leads to a decrease in the kinematic viscosity and an increase in the activation energy.

Data Availability Statement:
The data presented in this article is available upon request from the corresponding author.