Influence of multiaxial isothermal forging on magnetocaloric effect and magnetostructural transition in Ni-Mn-Ga-Si alloy

The influence of as-cast and multiaxial isothermal forged structures on the sensitivity of martensite to the magnetic field and on the magnetocaloric effect in Ni-Mn-Ga-Si alloy has been studied. In the multiaxial isothermal forged state, a “ necklace ” structure is observed where large grains of 100 – 200 µ m are encompassed by a layer of fine-grained structure. In this state, the martensitic transformation occurs with a shift towards the low-temperature region of about 10 K. Characteristic points of the martensitic transformation are evaluated in a magnetic field up to 12 T, revealing a sensitivity value of 0.6 K/T for both as-cast and multiaxial isothermal forged samples. Furthermore, an inverse magnetocaloric effect is identified within the martensitic transformation region for both as-cast and multiaxial isothermal forged samples under weak magnetic fields, up to 0.2 T. This inverse effect disappears at a magnetic field of 1.8 T, leaving only the direct magnetocaloric effect observable. These findings shed light on the intriguing interplay between microstructure, magnetic sensitivity, and mag-netocaloric behavior in this Ni-Mn-Ga-Si alloy, offering valuable insights for potential applications in magnetic cooling technologies.


Introduction
The pursuit of future-oriented functional materials has captivated the scientific community, offering the promise of ushering in a new era of advanced instruments, devices, and actuators.Among these materials, Heusler alloys have garnered substantial attention.These alloys exhibit remarkable characteristics, notably the magnetic shape memory effect (MSME) and the magnetocaloric effect (MCE) within the martensitic transformation region.In monocrystalline samples, the MSME is strikingly impressive, reaching up to 12 % [1][2][3][4], driven by the reorganization of the martensitic structure, while exhibiting a reversible deformation of approximately 6 % [5].In contrast, polycrystalline samples typically demonstrate a significantly lower MSME, often around 1 % [6][7][8][9].An intermediate position between a monocrystal and a polycrystal is occupied by samples obtained by directional crystallization of the melt.The formation of a preferred orientation of crystals in the polycrystalline ingot creates a strong texture and anisotropy of physical properties.As a result, the value of magnetic shape memory of about 2 % can be observed in the Ni 50 Mn 28.5 Ga 21.5 alloy [10].The mechanism behind the alteration of sample dimensions under external magnetic fields is the subject of intensive research.It is implemented either by reorientation of the martensitic structure under the influence of a magnetic field [11][12][13], or by magneto-induced martensitic phase transformation [14][15][16][17].The maximum MSME occurs near the martensitic phase transition, characterized by high twin boundary mobility and maximum volume change from austenite to martensite.However, a complete structural transition may be complicated by the high level of defect density arising from thermomechanical treatment [18][19][20][21][22][23].On the other hand, it can have a positive effect in narrowing the range of martensitic transformation (in which case structural defects can act as nucleation centers) and correspondingly reducing the value of the magnetic field required to induce the phase transformation.The range is narrowed because the internal stress fields in the deformed sample are distributed throughout the crystal and, if martensite is locally nucleated, the additional stresses it generates stimulate the appearance of new nuclei in the sample volume [22].It is known that in the region of the Curie point in Heusler alloys a direct magnetocaloric effect (MCE) can be observed (under the condition of a considerable distance of the temperature of the magnetostructural transition from the T C ).During the 1st order magnetostructural transition, the value of the MCE depends on the competition of three subsystems: structural, electronic and magnetic.The ratio of the contribution of the subsystems to the overall MCE is usually defined by the chemical composition of the alloys.Achieving maximum MCE and MSME driven by magneto-induced transitions hinges on the critical magnetic field's sufficiency for complete phase transformation.Reducing the critical field necessitates enhancing the martensitic transformation's sensitivity to magnetic fields and minimizing the magnetostructural transition's hysteresis.
There are a number of Heusler alloys that have been shown to have high values of functional effects for practical applications [2][3][4]7,[24][25][26][27].However, the technical application of Heusler alloys is difficult due to their high brittleness.During multiple cycles of martensitic transformation, defects accumulate at the boundaries of coarse grains, which can be explained by internal stresses caused by phase transformation.Microcracks then form and develop, eventually leading to the destruction of the sample [28][29][30].
Thermomechanical treatment (TMT) by various methods is commonly used as a means of improving the mechanical properties of most metallic materials.Heusler alloys are subjected to treatments such as rolling [31], high pressure torsion [32][33][34][35], forging [20], extrusion [36][37][38][39][40][41].An important point about the use of different treatment methods is the fact that in most cases, as a result of improved mechanical properties, the values of functional effects decrease.We have previously shown that after multiaxial isothermal forging (MIF) at 953-973 K in the Ni-Mn-Ga Heusler alloy, a two-component microstructure of the necklace type is formed, in which initial coarse grains of about 100 µm in size are surrounded by an interlayer of a fine-grained structure [20,22,[39][40][41].This type of structure provides higher fatigue strength because microstresses flow into the area of the fine-grained structure as a result of martensitic transformation.It has been shown that after MIF at 973 K and with a deformation ratio of e = 3.9, the fatigue strength of the alloy increased twofold and its cyclic strength increased fivefold [22].Thus, the improvement of mechanical properties by forging makes it possible to consider these materials suitable for practical applications.
Current study focuses on improving the mechanical properties of magnetocaloric materials while maintaining their smart physical propertiesa challenging issue in magnetocaloric applications.We have studied the effect of thermomechanical treatment, specifically multiaxial isothermal forging, on samples with the same chemical composition as the as-cast sample.In-situ optical studies of martensitic transformation under magnetic fields up to 12 T and magnetocaloric effect under alternating magnetic fields up to 1.8 T are conducted for both states using the example of the Heusler alloy Ni 54.1 Mn 19.6- Ga 24.6 Si 1.7 .The impact of multiaxial isothermal forging on the resulting material's functional properties is comprehensively analyzed.Our findings shed light on the potential of multiaxial isothermal forgedtreated Heusler alloys for practical applications, offering enhanced mechanical properties without compromising functional effects.

Sample
The selected research material is a Ni-Mn-Ga alloy.The alloy was produced through the melting of highly pure Ni, Mn, and Ga elements, utilizing the arc melting method.It is known that the alloy undergoes intense crystallization during this production technique, as it is placed on a copper crucible cooled with water.Consequently, large, elongated crystals are formed.This alloy structure is unsuitable for further thermomechanical treatment (TMT) since a less perfect intergrain boundary tends to accumulate defects and get destroyed, as indicated by sources [28,30,42].To perform the treatment, it is necessary to obtain a singlephase alloy with equiaxed grains.To achieve a more uniform microstructure, the alloy underwent vacuum remelting in a quartz crucible resulting in a homogeneous microstructure with equiaxed grains.The alloy's elemental composition was examined using a Vega 3-SBH (Tescan) scanning electron microscope, which was equipped with an X-Act energy-dispersive attachment (Oxford Instruments).Composition analysis was carried out on the longitudinal and cross sections (in the volume) of the resulting ingot to evaluate the uniformity of the composition distribution (see Attachment 1).The results indicate that the composition contains silicon, which diffused during vacuum remelting from a quartz crucible.The silicon atoms were distributed evenly across the ingot, with no evidence of composition segregation or additional phase formation.The elemental analysis identified the Ni 54.1 Mn 19.6 Ga 24.6 Si 1.7 alloy.The analysis of the alloy composition after TMT revealed that it remained identical to its original state.In future research, two experiments will be conducted on smelting alloys.The first experiment involves remelting the alloy in a ceramic crucible to obtain an alloy without silicon and with an equiaxed grain structure.The second experiment involves the controlled introduction of silicon at the arc smelting stage.To obtain an equiaxed grain structure, the alloy will be slightly extruded to introduce defects, followed by recrystallization annealing.This process will crush the original coarse cast grains.
To conduct the thermo-mechanical treatment, a cylindrical billet measuring 16.3 mm in diameter and 13.3 mm in height was extracted from the ingot in its original form.The schematic directions in the ingot were selected according to Fig. 1(a).The forging process was carried out using a Schenck Trebel RMC 100 complex loading machine.The billet was then deformed up to 35-40 % at a deformation rate of 0.2 mm/min and at a temperature of 953 K.The material underwent a deformation process comprising of seven stages of upsetting, executed according to the following sequence of directions: OY → OX → OZ → OX → OZ → OX → OZ.During the final four stages of deformation, only one OY axis was involved in the upsetting and turning process.The purpose of the process was to induce a texture, both crystallographic and metallographic, in the material.The actual degree of deformation was approximately e≈1.9.The material took the shape of an elongated parallelepiped with dimensions of 11.0 mm × 10.7 mm × 23.8 mm after undergoing the treatment.As previously stated, the OY axis functions as the drawing axis.The OZ axis indicates the direction of the last upsetting, as illustrated in Fig. 1(b).Notably, the TMT process was carried out without using an insulating sheath, i.e., in air, and a layer of oxidation appeared on the surface of the billet upon cooling.The analysis of the microstructure suggests that the area of the material where oxidation processes occur is limited to the near-surface layer at the micron-submicron scale.There is no substantial permeation into the bulk of the billet.

Experimental methods
The microstructural analysis was conducted using a Mira 3 LMH (Tescan) scanning electron microscope in the electron backscatter diffraction mode, with an accelerating voltage of 20 kV.The specimen for investigation was prepared through mechanical polishing on sandpaper with varying grain sizes, and finished with electropolishing in a 10 % HCl − 90 %C 4 H 10 O electrolyte solution.
Electrical resistivity measurements of the sample were recorded using the four-terminal measuring method at temperatures ranging from 190 K to 235 K.A current of 100 mA was passed through the 1x1x7 mm 3 sample.
A study of magneto-induced structural transition was carried out insitu at the Laboratoire des Champs Magnétiques Intenses (LNCMI) in Grenoble, France using an optical microscope [43][44][45] in the bore of a 12 MW water-cooled resistive magnet.This microscope allows the study of the magneto-induced microstructure of the surface of the metallographic section in the temperature range of 77 K to 350 K, and in the magnetic field of up to 14 T. The samples were prepared in the same way as the sample for the structural studies by SEM, which involves mechanical polishing followed by electropolishing.
Direct measurements of the adiabatic temperature change (ΔT ad ) upon magnetic field change were carried out by the modulation method, which enabled the temperature change to be registered with an accuracy of 10 -3 K [46].The technique involves applying an alternating magnetic field to a sample causing it to undergo changes in temperature due to the magnetocaloric effect.The temperature changes are detected using a differential thermocouple by a synchronous detector.One junction of the thermocouple is connected to the studied sample and the other to the heat flow.The measurements were conducted with alternating magnetic fields of 0.05 T (0.3 Hz), 0.2 T (0.3 Hz) and 1.8 T (0.2 Hz).A 1.8 T alternating magnetic field was generated by a regulated permanent magnetic field source [47,48].To measure MCE in small amplitude alternating fields, an electromagnet was employed.

Microstructure
Microstructure of the alloy was investigated by EBSD analysis at room temperature.This method allows for the estimation of grain microstructure parameters and the indirect assessment of internal stress levels in the material.As will be demonstrated later in work, the samples (in the MIF and as-cast states) are in austenite at room temperature.
In the initial as-cast state the section for the study was cut across the axis of the cylindrical billet of the alloy (the XOY plane).Results of the EBSD analysis of the section surface area are presented in Fig. 2. The polished surface of the sample is demonstrated in Fig. 2(a) using an orientation map.The survey encompassed an area of 1 mm x 1 mm with a scanning step of 5 μm.According to the analysis, the microstructure is composed of equiaxed grains that are sized several hundred microns across.The significant variation in color contrast implies a lack of grains with a preferred orientation in the material, meaning there is no crystallographic texture present.The grain boundary map contains both low-angle boundaries (from 2 • to 15 • , red lines) and high-angle boundaries (more than 15 • , black lines), as illustrated in Fig. 2(b).The microstructure is mainly composed of high-angle grains.The low-angle boundaries present in the grains suggest a fully relaxed structure and the absence of internal stresses in the initial as-cast state of the alloy.
The study of the microstructure of the alloy in the MIF state is carried out in the XOY plate.The OY axis is horizontally oriented and the OX axis is vertically oriented relative to the figure.Let us remind that the OY axis is the drawing axis and the OZ axis is the direction of the last upsetting (normal to the figure).Thus, the deformation axis (drawing) lies in the study plane, which, in its turn, is perpendicular to the direction of the last upsetting of the alloy.Data on the EBSD analysis of the section surface area are presented in Fig. 3.
The survey was conducted over an area of 2 x 2 mm 2 with a scanning step of 3 μm.upsetting during forging [20].Based on experimental studies of temperature expansion anisotropy, the formation of a sharp texture at a temperature of approximately 973 K, either at a higher degree of deformation during drawing or by the method of extrusion, does not significantly intensify this effect [22,41].From Fig. 4 it can be seen that the electrical resistivity value of both samples increases in a monotonic manner with the increase in temperature.There is an anomaly in the region of phase transformation that is related to the process of martensitic transformation.Overall, there is a difference in resistivity between the phases.The phase at low temperature exhibits higher resistivity than the one at high temperature.This indicates a reduction of the symmetry in the crystal structure of the martensitic phase during direct martensitic transformation.Additionally, there is a distinct temperature hysteresis effect on electrical resistivity in the phase transformation region.The comparison of electrical resistance in the initial and multiaxial isothermal forged states confirms the EBSD analysis data.As shown in section 3.1, forging results in the formation of an evolved substructure, indicating high levels of internal stresses and defect density.The electrical resistivity also increases due to

Field-induced evolution of martensitic transition
In-situ studies of martensitic transition in the initial as-cast sample and the MIF one were carried out with the use of the previously developed optical microscope in magnetic fields up to 12 T (see Chapt.2.2).Magnetostructural transition from the ferromagnetic martensitic phase to the weakly magnetic austenitic phase occurs in Ni-Mn-Ga alloys.Therefore, applying a magnetic field to the sample at a temperature near the onset of direct martensitic transformation induces strong magnetic (martensitic) phase nucleation and growth.Prior to magnetisation, the  sample was heated above the A f temperature and then cooled to the experimental temperature to eliminate residual martensite from previous magnetic field activations.Residual martensite, as demonstrated in a previous study [44], can function as the center for magneto-induced nucleation at lower magnetic field strengths, thereby influencing the determination of critical fields of the martensitic transition induced by a magnetic field.Fig. 5 shows micrographs of the metallographic section of the samples of both the initial as-cast state and MIF samples (more details in Attachment 2).Fig. 5(a) reveals that magneto-induced martensitic transition of both samples was detected at magnetic fields up to 12 T, at the temperature of the onset of martensitic transition M s .To facilitate comparison, microstructure of the samples at temperatures above and below the austenite finish (A f ) and martensite finish (M f ) temperatures respectively, are shown in Fig. 5(b).By comparing these images, we can differentiate martensite and austenite formed under the influence of a magnetic field from those formed by temperature change.
Fig. 5(a) demonstrates that at 0 T magnetic field, the sample has several areas with very few visible martensitic twins.These twins were formed when the sample was cooled down to the M s temperature.As the magnetic field is activated, the volume of the magneto-induced martensite increases.This is evident from the growth of martensitic twins on the metallographic surface.The magnetic field activation also induces new areas with characteristic martensitic twins on the metallographic surface.However, even when the magnetic field reaches 12 T, there are still areas where there is no formation of martensitic twins.This indicates that a magnetic field of 12 T is not enough to complete magneto-induced martensitic transition at the M s temperature.The microstructure images of the partially formed magneto-induced martensite reveal different textures in terms of martensitic twins across separate grains of the sample.Reducing the magnetic field causes a decrease in the surface area covered by martensitic twins in the metallographic section.When the magnetic field reaches 0 T, residual martensite is visible on the metallographic surface indicating the irreversible nature of the magnetostructural transition in this case.In previous work [43][44][45], we demonstrated that the sample completely transforms into austenite state during observation when the magnetic field is reduced to 0 T (with no residual martensite visible) at temperatures above the A f one.In our case (not presented), we also observed the disappearance of the partially formed martensite at a temperature of 227 K (above the A f temperature).It is important to note that the totality of the results obtained from studying the evolution of the magnetoinduced martensitic transition using the optical method on a series of Heusler alloys [43,44] allows us to judge that the differences between "surface" and "bulk" transitions have a small difference, which does not affect the main points of the author's discussion.
Results of the study of the alloy in the MIF state are illustrated on the right in Fig. 5.The formation of smaller martensitic twins in the forged samples is a unique feature of martensitic phase formation in a magnetic field.At the M s temperature, a magnetic field of 12 T alone is not sufficient to complete the transition.By in-situ observing the martensitic transformation under the influence of a magnetic field, we have determined the sensitivity of the martensitic transition to a magnetic field k, which remains the same for both samples and is approximately 0.6 К/T.Using formula (1), taking into account the sensitivity of the martensitic transition k and the characteristic temperature values of the transition, it is possible to ascertain the critical field, H cr1 , required to complete the martensitic transition in a field at the M s temperature.
Values μ 0 H cr1 for the initial as-cast sample and the MIF one have been determined using equation ( 1), which are equal to 30 T and 17 T, respectively.Narrowing of the hysteresis generated by MIF leads to a decrease in the critical field of magnetostructural transition completion.
Obviously, the decrease in the critical field of martensitic transition resulting from MIF causes a decrease in the value of the magnetic field required to reach the maximum value of MSME.Therefore, MIF might be a promising tool for producing materials with high sensitivity to a magnetic field and possessing MSME.

Magnetocaloric effect
The magnetocaloric effect (MCE) has been studied using a unique facility (see Chap. 2.2.).This involves subjecting a sample to an alternating magnetic field of varying strength and frequency.Initially, a sample consisting of 2x2 mm 2 plates was cut along the plane perpendicular to the axis of the cylindrical billet.The plates were cut in mutually perpendicular directions while the sample was deformed in order to investigate the potential anisotropy of the MCE.Two pairs of plates were cut -one parallel to the axis of the drawing and the other perpendicular to the drawing axis.The measurements were carried out according to the following protocol: the sample was cooled to below the temperature of the direct martensitic transformation (M f ), an alternating magnetic field was switched on and the sample was heated at a rate of 1.5 K/min.A thermocouple was utilised to record cyclic temperature variations of the MCE sample.The dependence curves ΔT ad (T) H are illustrated in Fig. 6, whereas Table 1 presents the direct and inverse MCE values at the corresponding maximum temperatures (T max ).
Fig. 6(a) shows the initial state data for the alloy measured at a 0.05 T and 0.2 T alternating magnetic field at a 0.3 Hz frequency.The figure indicates the presence of direct MCE in the Curie point region and inverse MCE in the martensitic transformation one.The maximum value of the inverse MCE is − 0.077 K for the field of 0.02 T. The presented results show that the Ni-Mn-Ga-Si alloy has a positive sensitivity coefficient of the magnetostructural transition to the magnetic field in both the initial and the forged states, the value of which is 0.6 K/T.It is known that Fig. 6.Magnetocaloric effect under alternating magnetic fields of 0.05 and 0.2 T and at a frequency of 0.3 Hz in the initial as-cast state and after being exposed to MIF one cutting along (b) and across (c) the drawing axis.Magnetocaloric effect under an alternating magnetic field of 1.8 T and at a frequency of 0.2 Hz in various structural states (d).

Table 1
Maximum values of direct and inverse MCE in the region of martensitic transformation and magnetic transition (near T c ) for the initial as-cast state, as well as for both MIFs state along and across the drawing.alloys with a positive sensitivity coefficient of the magnetostructural transition have a direct MCE in the region of the magnetostructural transition.The observed maximum of the inverse MCE is located in the A s temperature region.Under these conditions, the austenite phase is just beginning to form.The magnetic field effect does not significantly induce any change in the structure of the sample (the structural contribution to the MCE is practically absent) as the austenite phase is just beginning to form.The presence of inverse MCE in this case is related to the change in magnetocrystalline anisotropy (MCA) energy E a [51], which is determined by equation (2).It is important to note that the MCE contribution due to the paraprocess at the Curie temperature and in a relatively weak magnetic field can be considered negligible.
where C p,H is the specific heat capacity at normal pressure and an applied magnetic field.It is known that the MCA energy of martensite significantly exceeds the MCA energy of austenite [50].As can be seen from equation (1) in this case, the derivative of the MCA energy by temperature is positive, while the MCE determined by equation ( 2) is inverse.At the field of 0.2 T, the maximum value of direct MCE is 0.174 K in the Curie temperature region.The Fig. 6(b, c) illustrates that the inverse MCE maximum after multiple isothermal forge shifts to the region of lower temperatures by 7 K. Comparing to the as-cast state, a decrease in the inverse MCE maximum occurs in the region of magnetostructural transition for measurements taken along and across the drawing axis.The graphs indicate that maximum values of the inverse MCE measured along the drawing axis are slightly higher than those measured across the same axis.This is caused by the influence of induced magnetic anisotropy on the value of MCE.Under the influence of an alternating magnetic field of 1.8 T and at the frequency of 0.2 Hz, the MCE value in the area of martensitic transformation attains 0.8 K in all the three samples, as shown in Fig. 6(d).There is no inverse MCE maximum observed in the region of martensitic transformation anymore.This is due to the considerably higher value of MCE of the paraprocess for both martensite and austenite compared to the inverse MCE bound by the processes of magnetization vector rotation.A step appears on the temperature dependence of the ΔT ad in the region of magnetostructural transition instead of the inverse MCE maximum, which is conditioned by the difference in the value of MCE of the paraprocess for both martensite and austenite states.In this case, the maximum is absent because measurements are taken during the sample's heating process in a relatively low field of 1.8 T. This field is insufficient to significantly alter the structure of sample.The application of a magnetic field above the A s temperature only results in a small fraction of the sample transforming into martensite.Based on our estimates, the minimum field required for complete transformation into martensite at the A s temperature is approximately 10 T. It is evident that increasing the measurement temperature will increase the required field for the return to martensite.Raising the temperature to the A f allows for observing a reversible magnetostructural transition where the sample undergoes a complete transformation from austenite to martensite during field increase and returns to austenite during field deactivation.In order to achieve this, a field of about 36 T and 28 T is required for the as-cast and MIF samples, respectively.
It is apparent that high values of the field of the reversible magnetostructural transition render this alloy unsuitable for use as a material with magnetic shape memory, in both cast and forged states.The main finding of this study is that multiaxial isothermal forging not only enhances the mechanical properties of the materials under investigation, but also shows promise in improving their functional properties, including the magnetic shape memory effect and MCE.Therefore, this approach to functional materials could be applied to other Heusler alloys that have lower hysteresis and higher sensitivity of the magnetostructural transition to a magnetic field.It is expected that significantly lower fields of reversible transitions would be observed in this cases.

Conclusion
In this study, a Ni 54.1 Mn 19.6 Ga 24.6 Si 1.7 alloy was synthesized and subjected to thermo-mechanical treatment by multiple isothermal forging at 953 K and a true degree of deformation of e = 1.9.The results demonstrate that the forging process causes a partly recrystallized microstructure of the necklace type to form from the equiaxed grain structure.This microstructure consists of initial grains of approximately 100 μm, surrounded by an interlayer of fine-grained structure.The substructure formation in the body of coarse grains indicates the presence of internal stresses in the material.The minor oblateness of grains along the drawing axis implies a weak metallographic texture.Electrical resistivity, MCE in alternating magnetic fields up to 1.8 T and in-situ magneto-induced martensitic transformation in a magnetic field up to 12 T were measured on both the as-cast and MIF samples.The analysis of characteristic temperatures of martensitic transformation indicates that after the forging process, these temperatures decrease by approximately 10 K.An increase in defect density in the sample is responsible for this.As is also supported by EBSD analysis data showing a developed low angle boundaries net in the coarse grain matrix in the forged state and electrical resistivity data showing its growth after MIF.This provides an additional barrier to nucleation and propagation of martensite.In addition, the width of the martensitic transformation hysteresis in the forged state decreased significantly (by 6 K) compared to that of the original sample.Twin boundaries mobility and sensitivity of characteristic points of martensitic transformation in this alloy are typical of Ni-Mn-Ga alloys, both in the as-cast and forged states.The conducted evaluation of the sensitivity coefficient, based on the in-situ study of the martensitic transformation in a magnetic field of up to 12 T, showed a value of 0.6 K/T for the two types of samples.In weak magnetic fields up to 0.2 T and in the region of the martensitic transformation, an inverse magnetocaloric effect is observed for the two types of samples.This effect is associated with the difference in the anisotropy energy of martensite and austenite.When the field is increased to 1.8 T (which, according to our assumptions, is much higher than the martensite anisotropy field), the inverse magnetocaloric effect disappears.In the region of magnetostructural transition in the two types of samples, we observe a step that is associated with the difference in the magnetocaloric effect of the paraprocess of martensite and austenite.Thus, based on the foregoing, we assume that multiaxial isothermal forging enhances not only the mechanical characteristics of the investigated materials but also holds the promise of advancing their functional properties.

Declaration of competing interest
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: A. M. Aliev

Fig. 1 .
Fig. 1.Schematic diagrams demonstrating the orientation of the alloy billet in its initial as-cast state (a) and after undergoing MIF at 953 K (b).
I.I.Musabirov et al.

Fig. 4
Fig.4shows temperature dependences of electrical resistivity of the alloy samples in the initial as-cast state (a) and after thermo-mechanical treatment (b).The measurements were made in the region of martensitic transformation during heating and cooling of the sample.From Fig.4it can be seen that the electrical resistivity value of both samples increases in a monotonic manner with the increase in temperature.There is an anomaly in the region of phase transformation that is related to the process of martensitic transformation.Overall, there is a difference in resistivity between the phases.The phase at low temperature exhibits higher resistivity than the one at high temperature.This indicates a reduction of the symmetry in the crystal structure of the martensitic phase during direct martensitic transformation.Additionally, there is a distinct temperature hysteresis effect on electrical resistivity in the phase transformation region.The comparison of electrical resistance in the initial and multiaxial isothermal forged states confirms the EBSD analysis data.As shown in section 3.1, forging results in the formation of an evolved substructure, indicating high levels of internal stresses and defect density.The electrical resistivity also increases due to forging, as evidenced by the ρ(T) curves.At 195 K resistivity increases by approximately 4 %.Based on the measurements taken, we have determined the characteristic temperatures of the martensitic transition as M s = 222 K, M f = 204 K, A s = 209 K, A f = 226 K for the original sample and M s = 210 K, M f = 200 K, A s = 206 K, A f = 216 K for the sample subjected to thermomechanical treatment.The comparison of characteristic temperatures indicates that the martensitic transformation shifted towards the low temperature region due to MIF.The phase transformation range (A f -M f ) reduced significantly from 22 K for the original sample to 16 K for the MIF sample.However, the ρ(T) curves suggest that the martensitic transition is more prominent in the MIF sample.This could be because the structural modifications in the local area of the sample propagate through the crystal volume via internal stress fields, thereby distinctly defining the phase transformation points.

Fig. 3 .
Fig. 3. EBSD and grain boundary maps in the MIF state.The black lines on the Grain boundaries map represent the high-angle boundaries (>15 • ), whilst the red lines signify the low-angle boundaries (<15 • ).

Fig. 4 .
Fig. 4. Temperature dependence of electrical resistivity in the initial as-cast state (a) and MIF one (b).

Fig. 5 .
Fig. 5. Optical images of the microstructure in the initial as-cast state and after being exposed to MIF one.Figure (a) shows the evolution of the microstructure induced by the field at a constant temperature of M s , with magnetic field increasing (from 0 to 12 T) and decreasing (from 12 to 0 T).The microstructure's temperature evolution is shown at temperatures T ≥ A f (austenite) and T ≤ M f (martensite).
reports financial support was provided by Russian Science Foundation No. 22-19-00610.I.I.Musabirov, R. Y. Gaifullin reports equipment, drugs, or supplies was provided by Structural and Physical-Mechanical Studies of Materials Services Center of the Institute for Metals Superplasticity Problems of RAS.E.Dilmieva, Y.S. Koshkid'ko reports financial support and equipment, drugs, or supplies were provided by Laboratoire National des Champs Magnétiques Intenses, member of the European Magnetic Field Laboratory.If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper..