Thermal-Temporal Treatment Preparation of the Melt Before Amorphization to Obtain Nanocrystalline Magnetic Cores with Unique Magnetic Characteristics

1. Introduction

Soft magnetic nanocrystalline alloys based on the Fe–Si–B–Cu–Nb system (Finemet type) and their analogs remain critically important materials for high-frequency power electronics, next-generation transformers, and electromagnetic shielding applications [1,2,3,4,5,6]. A number of studies have presented a critical analysis of existing theoretical models (in particular, the random anisotropy model), identifying their fundamental shortcomings in fully describing the magnetic behavior of nanocrystalline alloys [7]. Strategic paths for creating next-generation materials that overcome the traditional tradeoff between ultra-low power loss and high saturation induction for use in high-frequency power electronics have been outlined.

Data on the formation mechanisms and methods for producing iron-based nanocrystalline alloys exist, demonstrating how precise adjustment of the chemical composition optimizes their nanoscale microstructure. The ability to achieve high saturation induction (Bs) with low reversal losses positions these alloys as key functional materials for future miniature electronics [8].

Replacing traditional pure electrical iron with amorphous and nanocrystalline soft magnetic materials is being explored to overcome performance limitations in high-frequency magnetic circuits and electromagnetic relays. Dynamic tests and wavelet analysis indicate that the use of nanocrystalline alloys (in particular, 1K107B) significantly improves dynamic response, reduces losses, and increases device accuracy [9]. Laminated nanocrystalline magnetic cores are also used to effectively suppress eddy current losses in high-frequency power electronics. The laminated structure has been shown to not only improve magnetic performance at high frequencies but also significantly enhance the thermal stability of the magnetic cores under harsh operating conditions [10]. Most technological protocols for nanostructure control focus exclusively on annealing after amorphization, while melt preparation before crystallization remains a poorly understood area. Current data confirm that the liquid-metal state is not a passive intermediate phase: its microheterogeneity, cluster dynamics, and relaxation kinetics are directly inherited by the amorphous matrix and determine the uniformity of nanograin nucleation [11,12,13,14].

This review systematizes the results of long-term research in condensed matter physics, the methodology of thermal-temporal treatment (TTT) of melts, and its influence on the properties of nanocrystalline magnetic cores. Particular attention is given to critical temperatures, viscosity hysteresis, liquid-liquid structural transitions (LLTs), and their role in the formation of an equilibrium melt before quenching. The goal of this review is to fill a gap in the literature by linking the fundamental aspects of metallic liquid structure with applied problems in the design of nanomaterials with unique magnetic characteristics.

The behavior of real multicomponent melts based on 3d transition metals cannot be described by the "simple liquid" theory due to directional d-bonds, impurity interactions, and thermal history [15,16,17]. We consider three complementary structural models—cybotactic, quasicrystalline, and quasichemical—and discuss how modern experimental methods (small-angle neutron scattering, in situ X-ray diffraction) confirm the coexistence of several types of clusters in Al-Si, Fe-B, and Fe-Si-B melts near liquidus temperatures [18,19,20]. The dynamics of their dissolution and recombination underlie strategies for controlling the homogeneity of the amorphous precursor [21,22,23].

This paper presents a critical analysis of modern theoretical models (in particular, the random anisotropy model) and identifies their fundamental shortcomings in fully describing the magnetic behavior of nanocrystalline alloys. Strategic pathways are outlined for the development of next-generation materials that overcome the traditional trade-off between ultra-low power loss and high saturation induction for applications in high-frequency power electronics.

2. Structural Models of Multicomponent Metallic Melts

The fundamental question is the structure of the melts. Metallic melts, like any thermodynamic systems, should be divided into two groups: nonequilibrium melts, which temporarily retain structural elements of the original phases, and equilibrium melts, whose structure and properties are determined not by their prehistory but by their composition and state parameters. Both are genetically linked to the original crystalline state. The former by nonequilibrium elements of their structure, the latter by the nature of the interatomic bonds and the short-range order formed [11].

The free energy of such a nonequilibrium system, F = U - TS, exceeds its equilibrium value, F_min, because the entropy of the ordered regions inherited from the original materials is lower than the equilibrium value, S_max. The motivating factor for studying these, from a thermodynamic point of view, obvious states are well-known experimental facts, such as the dependence [6,11] of the property values of molten samples of practically identical chemical composition on their history (initial materials, heating rates and temperatures), the instability over time of the property values of these melts (Figure 1), the discrepancy between the property values obtained during heating and subsequent cooling of the sample.

The relaxation process of nonequilibrium states, if it occurs at all, often continues for hours. More often, metastable states are established, from which the system cannot spontaneously emerge without thermal or mechanical stimulation. In this case, the simplest means of bringing the melt to equilibrium is additional heating to a fixed temperature.

This threshold nature of the system's transition to equilibrium indicates a kinetic rather than diffusional regime for this process; i.e., it is most often not the migration of particles that limits the process, but their detachment from the nonequilibrium formation, which requires a relatively high activation energy.

The behavior of real multicomponent melts based on 3d transition metals cannot be described by the "simple liquid" theory due to the presence of directional d-bonds, impurity interactions, and thermal history [6,11,17].

Three complementary models are used to describe them:

• The sybotactic model: the melt consists of clusters with short-range order, the boundaries of which are blurred by thermal fluctuations. The cluster lifetime depends on the composition and temperature [11,24].

• The quasi-crystalline model emphasizes the ordering tendency, similar to bcc/fcc packings, without the presence of real microcrystals. It allows for the classification of short-range order types by parameters r₁ and z₁ [24,25].

• The quasi-chemical model takes into account the unequal nature of interatomic bonds. The most stable clusters are formed by components with the highest interaction energy (e.g., Fe–O, Fe–B, Fe–Si) [17,26]. This model is a development of the views of Stewart, Frenkel, and Eyring [11,24]. This is particularly true for transition metals, since the purest melt of such an element, due to its dual nature, can be considered a special case of this model. Its essence is as follows.

1. The melt consists of microregions—clusters—in which the arrangement of atoms is characterized by a certain order—short-range order.

2. Due to the intense thermal motion of the particles, the clusters do not have clear boundaries. For the same reason, the lifetime of an equilibrium cluster is limited and depends on the composition (the types of chemical bonds) and temperature. The simultaneous existence of clusters with two or more types of ordering is possible.

3. The energetic disparity between interatomic interactions of different types causes the formation of clusters of different structures and compositions, with have different stability over time. The most stable and long-lived clusters are formed by the most strongly interacting components (for example, iron and oxygen).

It is precisely this emphasis on the disparity of interatomic bonds as the cause of microheterogeneity that fundamentally distinguishes this model of microheterogeneous melt structure from other variants, and therefore it is called quasi-chemical.

Modern experiments (small-angle neutron scattering, in-situ X-ray diffraction) confirm the coexistence of several types of clusters in Al-Si, Fe-B, and Fe-Si-B melts at temperatures close to the liquidus [6,11,20]. The dynamics of their destruction and recombination underlies the control of the homogeneity amorphous precursor [12,18,23,27].

3. Liquid–Liquid Transitions and Relaxation Kinetics

Understanding the nature of liquid structures and properties has always been a hot field in condensed matter physics and metallic materials science. The liquid is not homogeneous and the local structures inside change discontinuously with temperature, pressure, etc. The liquid will experience liquid−liquid structure transition under a certain condition. Liquid−liquid structure transition widely exists in many metals and alloys and plays an important role in the final microstructure and the properties of the solid alloys. This work provides a comprehensive review on this unique structure transition in the metallic liquid together with the recent progress of its impact on the following microstructure and properties after solidification. These effects are discussed by integrating them into different experimental results and theoretical considerations. The application of liquid−liquid structure transition as a strategy to tailor the properties of metals and alloys is proven to be practical and efficient [28].

Significance Contrary to our intuition, even a single-component substance may have more than 2 liquid states. The transition between them is called “liquid–liquid transition (LLT).” Recently, we have accumulated evidence for the presence of LLT. This transition may have a strong influence on crystallization, if it exists below the melting point of the crystal. Here we show that crystal nucleation rate can indeed be enhanced by many orders of magnitude near the spinodal point of LLT. This may be used not only for the control of crystalline morphology but also for searching LLT in a metastable state, which is hidden behind crystallization. Our finding also sheds light on how crystallization and other liquid-state transitions can be coupled [29].

The liquid–liquid transition (LLT) in multicomponent melts is an irreversible destruction of microheterogeneous structures inherited from the solid charge [11,12,17]. Its indicators are:

• Viscosity, density, and electrical resistivity hysteresis during heating–cooling;

• Critical temperature (t_c), at which the energy of thermal motion becomes equal to the rupture energy of the strongest interatomic associations;

• Oscillatory relaxation of properties during isothermal holding, indicating the cooperative destruction of dissipative structures [30,31,32,33].

The microheterogeneous state of a chemically heterogeneous melt is understood as the presence of dispersed particles enriched in one of the components, suspended in an environment of a different composition and separated from it by an interphase surface [17]. The microheterogeneous state is destroyed as a result of an energetic impact on the melt, for example, heating to a temperature specific to each composition. After the irreversible destruction of the microheterogeneous state, the melt passes into the state of a true solution, the conditions of its crystallization change, which is reflected in the microstructure, crystalline structure and mechanical properties of the crystallized metal. The concept of the microheterogeneous state of liquid multicomponent alloys was experimentally substantiated by P. S. Popel, U. Dahlborg, M. Calvo-Dahlborg. Using the method of small-angle neutron scattering in melts of Pb-Sn, Al-Si eutectics, regions enriched in one of the elements, separated from the rest of the liquid alloy by a transition layer, were discovered. Two families of particles have been identified: small particles of 10–40 Å in size and large particles of up to 90 Å in size; as the temperature increases, the particles dissolve and recombine into smaller ones [34].

The relaxation kinetics proceed in a kinetic, rather than a diffusion, regime: the activation energy (34–40 kJ/mol) is comparable to the breaking of metal–oxygen or metal–boron bonds [6,32]. Macroscopic stirring does not accelerate the process, whereas holding at t_c for 5–10 min ensures the transition of the melt to an equilibrium state [13,19,21]. Modern studies confirm that LLT can be used as a strategic tool to control the nucleation rate and crystallite morphology, which determine the mechanical and thermal properties of the material [5,6,32,33].

4. Thermal-Temporal Treatment (TTT) Pre-Conditioning as a Protocol

There are various methods for bringing a melt to equilibrium. The most readily available method for producing an equilibrium melt is high-temperature treatment. Since the process of bringing a system to equilibrium as a result of heating is non-monotonic and greatly accelerates upon reaching critical temperatures, heating the metal to these temperatures is a key feature of new, advanced technologies. When cooling the liquid metal prepared in this way, its original (non-equilibrium) structure is not restored; i.e., before crystallization, the melt structure is at or near equilibrium and differs significantly from the original.

The results of numerous experiments and the resulting concepts formed the basis for a promising technological method for managing the quality of metal products through targeted thermal treatment of the structure of liquid metal. As already noted, this method is called thermal-temporal treatment (TTT) of the melt [11]. In general, the TTT cycle is represented graphically in temperature-time coordinates (Figure 2).

Thermal-temporal treatment (TTT) of the melt is a strictly regulated cycle that ensures the transition of the liquid phase to an equilibrium state before crystallization or amorphization [11,13]. The basic protocol includes:

1. Heating to t_c (or t_an if a temperature anomaly is detected);

2. Holding for τ_obr (determined by the damping of viscosity/magnetic susceptibility oscillations);

3. Accelerated cooling to the tapping/quenching temperature (t_tap);

4. Holding for τ_tap (stabilization before casting).

5. Effective metal stirring allows for a shorter holding time at critical temperatures.

The effectiveness of TTT has been confirmed for over 100 grades of steels and alloys: it reduces chemical inhomogeneity, refines the dendritic structure, and increases plasticity and heat resistance [11,36,37]. In the context of nanomaterials, TTT should be performed immediately before amorphization, since intermediate crystallization and subsequent phase transformations restore the nonequilibrium state of the melt [35,38,39]. Comparison with conventional superheating shows that TTT reduces flow turbulence, improves castability, and increases the thickness stability of the amorphous ribbon [13,19,21].

5. TTT as a Precursor for Amorphization and Nanocrystallization

Studies of the physical properties of liquid iron-, nickel-, and cobalt-based alloys intended for the production of amorphous materials deserve special attention. This is due, on the one hand, to high crystallization rates and the preservation of the structural features of the liquid metal in the solid state, and, on the other hand, to the significant influence of kinematic viscosity and surface properties on the technology for producing amorphous ribbons [35].

Alloys with a high content of amorphizers (Fe-Si-B-Cu-Nb-Mo) are characterized by high absolute viscosity values in the pre-solidus region ((14–20)·10⁻⁷ m²/s), which creates technological difficulties during planar flow casting [35].

A typical temperature dependence of melts with a large number of amorphizing elements is shown in Figure 3.

The critical temperatures t_c, heating to which leads to branching of the polytherms of physical properties, the onset temperatures of hysteresis t_g, and the magnitude of supercooling Δt are determined.

The presence of hysteresis indicates a nonequilibrium initial state of the melt and the need to achieve t_c during the melting process.

It turns out that in some cases, it is advisable to heat the melt only to the anomaly temperature t_an. The required melt holding time at t_c or t_an is determined using the same polytherms and, additionally, by removing the dependence of property values on the isothermal holding time.

The polytherms of viscosity, electrical resistivity, and surface tension demonstrate clear branching at t_c, which correlates with the subsequent homogeneity of nanocrystallization (Figure 3).

The kinematic viscosity (Figure 4) of a Finemet-type nanocrystalline magnetic alloy was studied. The first heating regime was to a temperature below t_с, followed by quenching. The second heating regime was to a temperature above t_с, followed by quenching, as in the first regime. The third heating regime was to a temperature above t_с, followed by supercooling and further quenching.

The best performance properties of the belts were obtained in the third mode.

The optimal mode includes heating above t_c, holding for 5–10 min, cooling to the liquidus (or below, taking into account Δt), holding for 5 min, and instant quenching [35,39].

The application of TTT allows:

• Destruction of inherited carbide, silicide, and oxide clusters;

• Ensuring a uniform distribution of Cu nuclei in the amorphous matrix;

• Reducing the scatter of properties from ribbon to ribbon.

An analysis of the physical property polytherms of liquid iron-, nickel-, and cobalt-based alloys prone to amorphization reveals the following key patterns. Critical temperatures were established for virtually all the alloys studied. Heating to these temperatures leads to branching of the polytherms of kinematic viscosity, surface tension, electrical resistivity, magnetic susceptibility, and other physical properties. This indicates a nonequilibrium state of the initial melts and the need to achieve a critical temperature during their smelting. Moreover, thermal-temporare treatment of the melt should be performed immediately before producing the amorphous ribbon, rather than at the stage of smelting the blank. Intermediate crystallization of the melt and subsequent solid-phase transformations will again lead to a nonequilibrium state of the melt before its amorphization.

Intermediate crystallization nullifies the effect of TTT, which is confirmed by the restoration of viscosity hysteresis (Figure 5) [35,40,41].

6. Structcure–Property Relationships in Nanocrystalline Magnetic Cores

In its initial state, the alloy is X-ray amorphous (Figure 6). The X-ray diffraction pattern shows a diffuse halo without additional reflections from crystalline phases. Crystallization of the alloy upon heating occurs in a single main stage. A single asymmetric exothermic peak is observed on the HTDT curve in the temperature range of 525-600 °C.

After heat treatment at 522 °C, peaks from the crystalline component appear against the background of the amorphous halo. The main crystalline phase is an ordered Fe₃Si solid solution with a lattice parameter of a = 0.56721 nm. With increasing temperature, the intensity of the halo from the amorphous phase decreases, the intensity of the Fe₃Si reflections increases, and superstructural reflections become more pronounced. After heat treatment at 542 °C, the alloy is almost completely crystalline—no heat-generating reactions are observed on the HTDT curves.

In the X-ray diffraction patterns of the alloy heat-treated at higher temperatures (552- 602 °C), the halo from the amorphous phase is absent, the lattice parameter of Fe₃Si does not change within the limits of determination error.

X-ray diffraction patterns (Cu-Kα radiation) of Fe₇₂.₅Cu₁Nb₂Mo₁.₅Si₁₄B₉ ribbons after annealing at selected temperatures. As-quenched state shows broad amorphous halo. Crystallization onset at 522 °C: emergence of ordered Fe₃Si (DO₃) phase (a = 0.5672 ± 0.0003 nm). Complete nanocrystallization at 542 °C; no amorphous residue detected above 552 °C. Peak indexing: ● Fe₃Si (111), ■ Fe₃Si (200), ▲ Fe₂B (minor phase at Ta ≥ 572 °C). Adapted from [6].

Control of the pre-crystallization melt treatment directly determines the annealing parameters and the final magnetic characteristics. Data for the Fe₇₂.Cu₁Nb₂Mo₁.₅Si₁₄B₉ alloy show:

• Optimal annealing: 542–572 °C;
• μ_max: up to 713,000 at 542 °C;
• H_c: minimum 0.41 A/m;
• Grain size: 7–9 nm, with the distribution shifting towards 11–20 nm at T_a > 552 °C.

Magnetic properties of Fe₇₂.₅Cu₁Nb₂Mo₁.₅Si₁₄B₉ nanocrystalline ribbons as a function of annealing temperature (T_an). Samples prepared by planar flow casting (PFC) with TTT-pretreated melt: t_c = 1580 °C, τ_obr = 8 min, cooling rate ≈ 1.2×10⁵ K/s, ribbon thickness 22 ± 2 µm. Measurements at f = 1 kHz, H = 0.4 A/m.

Table 1 shows magnetic properties as annealing temperature.

Grain size distribution in Fe₇₂.₅Cu₁Nb₂Mo₁.₅Si₁₄B₉ nanocrystalline alloys after annealing at selected temperatures. Data from TEM analysis (n = 215 ± 15 grains/sample). Quenching conditions: melt TTT at t_c = 1580 °C, τ = 8 min; planar flow casting, wheel speed 35 m/s, ribbon thickness 22 ± 2 µm.

The low initial permeability at 522 °C is due to a significant fraction of the amorphous matrix and incomplete nanocrystallization. The increase in H_c at T_a > 572 °C is associated with the precipitation of the magnetically hard Fe₂B phase [1,38,42].

Figure 7 shows histograms of grain sizes at different heating temperatures of 522, 552 and 602 °C.

Grain boundaries identified via FFT filtering of HRTEM images. Grain size distributions in Fe₇₂.₅Cu₁Nb₂Mo₁.₅Si₁₄B₉ nanocrystalline alloys after annealing at (a) 522 °C, (b) 552 °C, and (c) 602 °C, determined by TEM image analysis (n > 200 grains per sample). Mean grain size: 7 ± 2 nm (522 °C), 9 ± 3 nm (552 °C), 8 ± 3 nm (602 °C). Note the increased fraction of grains >10 nm at higher T_a (Table 2). Scale bars: 20 nm. Adapted from [6].

The average grain size remained virtually unchanged at these temperatures, equaling 7, 9, and 8 nm, respectively. However, the grain size distribution changed with increasing temperature. At a low temperature of 522 °C, a significant maximum of 2-nm grains was observed. These grains, which lack distinct boundaries, are likely nuclei (clusters) of the crystalline phase in the amorphous matrix. At temperatures of 552 °C and 602 °C, the grain size distribution was virtually identical. Moreover, at the higher temperature compared to 522 °C, the proportion of grains larger than 10 nm increased from 20.5 % to 33.5 % (Table 2).

In the nanocrystalline magnetic alloys Fe72.5Cu1Nb2Mo1.5Si14B9, the low initial permeability corresponds to a structure whose proportion in the residual uncrystallized amorphous matrix is significant. The coercivity of the alloy at an annealing temperature of 522 °C is very low. In this region, the low coercivity does not lead to high initial permeability. The highest initial permeability occurs when the structure is characterized by the largest volume of the ordered Fe₃Si phase. The increase in the coercivity and the decrease in the initial permeability at high temperatures are explained by the formation of the magnetically hard Fe₂B phase [38].

Modern analysis confirms that the homogeneity of the amorphous precursor, ensured by TTT, minimizes local stresses, reduces the density of domain wall defects, and ensures the reproducibility of μ and H_c from batch to batch [14,43,44,45].

7. Challenges, Scalability, and Future Perspectives

Despite its proven effectiveness, the implementation of TTT in the industrial production of nanocrystalline ribbons faces several barriers:

• The lack of in-situ viscosity and density monitoring systems in real-time on melting installations;

• The energy consumption of long isothermal holds;

• The difficulty of scaling protocols for high-entropy and Co/Ni-based alloys.

Future perspectives include:

• Integration of TTT with magnetic pulse and ultrasonic melt processing [3,46];

• Application of CALPHAD and molecular dynamics modeling to predict t_c and τ_obr [4,29];

• Use of machine learning to optimize temperature-time windows for specific chemical compositions [47,48];

• Development of in-situ diagnostics (synchrotron X-ray, neutron scattering) for direct visualization of LLT and cluster dynamics [12,15,28].

This review represents the result of the authors' many years of research in the field of condensed matter physics. It analyzes current trends in the study of metallic liquids at high temperatures, the structure of multicomponent metallic melts, and specific methods for their analysis. The principles of thermal-temperature treatment of melts are presented. Particular attention is paid to the relationship between the liquid and solid states of metals. The essence of advanced technologies for producing amorphous and nanocrystalline materials is revealed [49,50].

8. Conclusions

1. Thermal-Temporal Treatment (TTT) of metallic melts represents a physically grounded methodology for controlling the nonequilibrium state of the liquid phase, thereby ensuring homogeneity of the amorphous precursor and reproducibility of nanocrystallization. The protocol involves heating to critical temperatures (t_c), isothermal holding (τ_obr = 5–10 min), controlled cooling to tapping temperature, and stabilization prior to casting.

2. Critical temperatures, viscosity hysteresis, and relaxation kinetics serve as key indicators of achieving melt equilibration prior to amorphization. The irreversible nature of structural transformations during heating—evidenced by branching polytherms of viscosity, electrical resistivity, and magnetic susceptibility—confirms the elimination of inherited nonequilibrium clusters.

3. An optimized TTT protocol combined with annealing at 542–572 °C enables the formation of Fe₃Si nanograins with a mean size of 7–9 nm, achieving maximum relative permeability μ_max > 600,000 and coercive force H_c < 0.5 A/m. The narrow grain size distribution (σ_d = 3–4 nm) and minimal fraction of magnetically hard Fe₂B phase are critical for superior magnetic softness.

4. Integration of TTT with modern computational materials science methods (CALPHAD, molecular dynamics), in-situ diagnostics (synchrotron X-ray, neutron scattering), and AI-driven optimization opens pathways for designing next-generation nanocrystalline magnetic cores with tailored frequency response and core loss characteristics for high-frequency power electronics operating in the 1.5–380 GHz range.