Effect of milling time on the structural, microstructure, and magnetic properties of nanocrystalline Fe90Sb10 powders obtained by high-energy ball milling

Nanocrystalline binary powders Fe90Sb10 (wt.%) have been elaborated by high-energy ball milling in order to study the effect of the milling time on the microstructural and magnetic properties of these alloys. The evolution of structural, morphological, and magnetic properties was investigated, as a function of milling time, using X-ray diffraction (XRD), scanning electron microscopy (SEM) coupled with energy-dispersive X-ray spectrometry (EDX), and the vibrating sample magnetometer (VSM). A disordered Fe (Sb) solid solution with body-centered cubic (bcc) crystal structure is formed after 12 h of milling from XRD results. When the milling time increases, the lattice parameter progressively increases from 0.2861 for the Fe90Sb10 (0 h milling) compound down to 0.2870 nm for 36 h of milling. The sample with the longest milling time has exhibited the lowest value for the mean grain size of 18.16 nm as well as the microstrain of 0.19%. Grain morphology of the powders at different formation stages was examined using scanning electron microscopy (SEM). The chemical composition homogeneity and the powder form Fe90Sb10 (wt.%) were studied with EDX experiments. For Fe-10Sb (wt.%) nanostructured powders, magnetisation saturation, coercive fields, and remnant magnetisation derived from the hysteresis curves were discussed as a function of milling time.


Introduction
The elaboration of nanomaterials has known an evolution these last years, the nanomaterials present more often some originals comportment, which differ considerably from those massifs materials with the same chemical composition [1][2][3][4][5][6].
Mechanical alloying (MA) is a powder metallurgy processing technique that involves repeated coldly welding, fracturing, and rewelding of powder particles in a highenergy ball mill. Due to the specific advantages offered by this technique, MA was used to synthesise a variety of advanced materials [15][16][17][18][19][20][21].
In recent years, nanostructured Fe-Sb alloy powder is fabricated by various methods including heat treatment of rapidly solidified melt and MA [22,23]. In this regard, Wang et al. [22] investigated by rapidly solidified melt the phase formation α-Fe(bcc) in Fe-10%Sb alloy. Kis-Varga et al. [23], after various milling times, obtained the nanocrystalline α-Fe(bcc) phase by stainless steel vibrating mill of Fe 90 Sb 10 powders for milling times above 100 h.
The main objective of our work consists of analysing the nanopowders obtained after transformations by mechanical alloying and studying their physical behaviours. In our work, we have chosen the Fe-Sb system. This last forms a magnetic permanent base from one part, and it is used in various applications, on the other hand.
The first step of our work is the elaboration of the Fe 90 Sb 10 alloy by high-energy ball milling of one powder mixing (composed of iron and antimony). The second step consists of characterising the elements obtained after different milling times by XRD followed by the Rietveld refinement with the aim to study the microstructural variation; the SEM was used to characterise the microstructure such as morphology and the magnetisation measurements by the vibrating sample magnetometry (VSM). These operations allow us to study the behaviour of the magnetisation saturation and the coercive field with the crystalline size.

Materials and methods
High purity (> 99%) and average particle size < 100 μm iron and antimony commercially obtained were used as raw materials. The mechanical alloying process was performed in a planetary high-energy ball mill Retsch PM 400 as shown in Fig. 1a. After ensuring that the milling will be performed in an inert atmosphere, the powders were sealed in a cylindrical vial with stainless steel balls having 12 mm in diameter (Fig. 1b). The ball-to-powder weight ratio is 15:1, and the vial rotation speed was 350 rpm. The milling time ranged from 0 to 36 h (0, 2, 4, 8, 12, 16, 25, and 36 h) to investigate its effect on the properties of the obtained powders. The milling process was carried out with a 1 h sequence of milling followed by 30 min of pause to avoid excessive heating during the milling operation. The powders obtained at different milling times (up to 36 h) are shown in Fig. 2.
The milled powders were analysed by XRD for examining the phase transformations as a function of the alloy composition by a Bruker D8 Advance ECO diffractometer. The diffraction parameters were collected with 2θ ranging from 10 to 130° with a step size of 0.02 and Cu-Kα (λ = 1.5418 Å) radiation. The MAUD software (version 2.22) [24], based on the Rietveld method [25], was adopted to refine the structural and microstructural parameters of nanostructured powders. Each peak was fitted by a formula of the pseudo-Voigt function expressed by a weighted sum of Gaussian (G) and Lorentzian (L) functions: where L and G are, respectively, the Lorentzian and Gaussian components of width at half height, respectively H G and H L . The parameter n, which defines the shape of the diffraction peak, has two limit values: η = 0 or Gaussian limits and η = 1 or limit Lorentzienne.
In the procedures of refining experimental diagrams, the adjustable parameters, apart from the position and the intensity of the peaks, are H and η, respectively. These can be substituted by the two widths H G and H L which are directly related to the average microstructural parameters of the sample, namely the size of the mean grains, <D > [26] and mean level of microstrains, <ε 2 > 1/2 [27], by relations: where K represents the shape factor, which varies with crystal shape, λ is the wavelength of the radiation used, θ is the Bragg angle, and β L is the width of the peak halfway between the continuous bottom background and the top of the peak expressed in radians.  where β G is the breadth of the Gaussian contribution to the peak, which has its origin in the presence of microstrains. Microstructure analysis and morphology observations were carried out using a Quantum 250-FEI electron microscope (SEM) equipped with an EDX. The magnetic properties of the obtained materials, specific magnetisation saturation (M s ), coercivity (H c ), and remanent magnetisation (M r ), were measured using a MicroSense V7 vibrating sample magnetometer (VSM) with a maximum applied field of 18 kOe. After 12 h of milling, we observed that the Sb peaks disappear completely, whereas the peaks related to Fe slightly shift towards small angles (Fig. 4). This proves that Sb atoms dissolve in the Fe lattice leading to the formation of bcc solid

Structural characteristics
solutions (Fe-Sb). The slightly angular shift is attributed to the formation of (Fe-Sb) solid solution and to the first-order internal stress induced by milling. The first-order of angular stress acts as a macroscopic level by modifying the lattice parameter and consequently produces an angular shift of XRD peaks [28,29]. All XRD spectra of the milled powders were analysed by the Rietveld refinement. An example of refinement is presented in Fig. 5 for the powder milling at 12 h. We have shown that the diffraction peaks corresponding to (rhombohedral) Sb and (bcc) α-Fe disappears after 12 h of milling and that only the (bcc) α-Fe (Sb) phase with a group space Im3m is presented. Figure 6 presents the change of lattice parameter (a) versus milling time (t) for Fe 90 Sb 10 samples. As the milling time increases and due to more Sb diffusion, the lattice parameter increases from 0.2861 ± 0.0001 for the pure Fe to 0.2870 ± 0.0001 nm after 36 h of milling (Table 1). Such a variation of the lattice parameter is due to the difference between the atomic radii of Fe and Sb since the atomic radius of Sb (R Sb = 0.145 nm) is greater than the atomic radius of Fe (R Fe = 0.126 nm). Generally, the increase of lattice parameters with milling time is due to the solid solution formation. Moreover, in nanostructured materials produced by mechanical alloying, the increase of lattice parameters may also be due to the defects introduced in the interfaces [30]. Figure 7 shows the evolution of the mean grain sizes < D > (nm) and the mean level of microstrains as a function of the milling time. We have noticed that the mean grain size decreases monotonically with increasing milling time. This decrease in < D > is accompanied by an increase in the rate of microstrain <ε 2 > 1/2 with milling time.
Indeed, the mean grain size decreases from 59.95 (0 h) to 18.16 nm after 36 h, while the rate of microstrain increases from 0.076 (0 h) to 0.19% at 36 h. The decrease of < D > and the increase of <ε 2 > 1/2 can be explained by the hard character that FeSb powders acquire with increasing milling time so that the process of grain fragmentation is favoured and gives rise to smaller crystallite size [31]. We can also cite the work of Kis-Varga et al. [23] who have observed the decrease of the rhombohedral Sb peaks with a slight broadening of all reflections upon milling up to 10 h, and they almost disappear after MA for 100 h and the formation of a solution solide of the (bcc) α-Fe (Sb) phase (the pure crystalline antimony phase is spent) for Fe 90 Sb 10 samples performed in a stainless-steel vibrating mill. The authors calculated from peak widths the grain size value obtained after 200 h of milling was 8.5 nm [23], The value of < D > (nm) = 18.16 nm was obtained in this work after 36 h of milling; it is quite logical well with that reported of Kis-Varga et al. [23] for the vibrating milled Fe 90 Sb 10 alloy.

Microstructure characteristics
Before milling, Fig. 8 shows the SEM image of the starting powder, which is an elemental mixture of primary Fe and the Sb powder of the Fe-10Sb alloy (wt.%). Iron particles have a spherical-like morphology and have an average size of about 6 µm, while antimony particles have an irregularly shaped morphology and have an average size of 20-30 µm. The morphological evolution of the macroscopic powders indicates considerable changes with increasing milling times, as shown by SEM micrographs (Fig. 9). It is well known that the phenomenon of repeated cold welding and fracture is ensured by the action of the balls-powder-balls and balls-powders-wall of the jar during mechanical milling leads to an observable change in the shape and the particle size of the powder obtained [32]. Figure 9 shows SEM images of Fe 90 Sb 10 powder particles mechanically alloyed for 2 h, 4 h, 8 h, 12 h, 16 h, 25 h, and 36 h, of milling. During the milling process (2 and 4 h), the particles of the mixed powders, caught between the balls or between the balls and the walls of the jars, are subjected in a way on a continuous basis, to the repeated effects of fractures and welding (Fig. 9a, b).
During the first milling times (2 and 4 h), the compressive force and the plastic deformations crush the powder particles. The magnification of the particles during this initial stage of milling shows that the phenomenon of cold welding is dominant because the powder is relatively tender at the start of milling. The clusters that form are not yet homogeneous, and the different particles only seem to be stuck to each other. It is noted that the morphological changes of this period are already important after 4 h of milling. This type of behaviour is in good agreement with some previous references that have shown that in the early stages of mechanical alloying, the phenomenon of agglomeration, which changes the morphology, typically the size, and shape of the composites, is started [33,34]. After 8 h of milling (Fig. 9c), you can clearly see the phenomena of fracture and welding of the particles and which are specific to mechanosynthesis. In addition, we have noticed the particle refinement continues and the particle shape changes to a form of laminar structure (multilayered structure) consisting of an overlay of Fe and Sb multilayers. This structure is similar to the materials produced by mechanical grinding from ductile or fragile elements, observed by Davis et al. [35] and Djekoun et al. [36]. The mechanism of formation of this type of lamellar structure is the repetitive result of condensation of powders by cold welding and then fracture, as shown in Fig. 9c by the shape of a relatively large flat particle. Figure 9d represents the micrographs obtained after 12 h of milling. We noted that the majority of the particles possess a lamellar shape and average size between 5 and 15 μm. The decrease in particle size in this stage can be explained by the manner way: The milling process is a balance between fracture and cold   welding. The cold welding process results in an increase in particle size. That information indicates the formation of a phase of the (bcc) α-Fe (Sb) and which corresponds perfectly to the diffraction of X-rays. For milling times between 16 and 25 h (see Fig. 9e, f), it is observed that the ground particles become smaller and that there are fine particles of a size of the order of 5 μm and have a more or less homogeneous aspect characteristic of a balance between the phenomena of fracture and welding. In this stage, the bonding forces of the powder particles are stronger when the size of the grains is small; the deformations are no longer possible because they require a great force to fracture the particles it is noticed that the size of the grains decreases with the time of grinding; this decrease is due to the process of fracture and welding due to the collision between the powder, the balls, and the inner wall of the jar. After 36 h of milling ( Fig. 9g), large agglomerates of very fine particles were observed, these particles being finer and smaller for longer grinding times [37]. These results show that after 36 h of grinding, we produce very small conglomerates compared to the time that preceded it, and their particles are smaller, and more homogeneous than the agglomerates obtained at previous grinding times. It is important to note that the fracture process dominates the mechanosynthesis process in this step, which caused a reduction in particle size. Figure 10 shows the percentage point evolution of iron and antimony in the Fe 90 Sb 10 system by SEM images and EDX analyses performed on all samples, and the values of the chemical composition of Fe 90 Sb 10 powder mixtures after several milling times obtained from the EDX are given in Table 2. SEM and EDX analyses of the mixture without  (Fig. 10a, b) clearly show the iron and Sb particles yet separated from each other and with different morphologies. Selected area 1 (Fig. 10a) corresponding to Fe shows a very high massic percentage of iron (100%). On the other hand, selected area 2 (Fig. 10b) corresponding to Sb shows a very high massic percentage of antimony (95.53%). This confirms the result of the XRD concerning the presence of Fe and Sb elements before the milling process. During the first milling times of 2 to 4 h, it is observed that the morphological changes of Fe and Sb are already significant (Fig. 10c, d). However, we can observe the separate presence of Fe and Sb (the small iron particles are welded to the surface and also become large as well as the antimony particles are reduced by intense breaking), and the FeSb compound already begins to form. With the increase of the times milling from 8 to 36 h, the chemical composition varies slightly; it is close to the nominal composition Fe 90 Sb 10 , as reported in Fig. 10e-i. Indeed, it becomes difficult to distinguish the particles of Fe and the particles of Sb; this indicates a homogeneous distribution of the elements between them and the formation of the solid solution (Fe, Sb). These results are in good agreement with those found by X-ray diffraction [15,34]. It is very important to note that there are no other peaks other than those of the elements present in the powders; this indicates that there is no impurities and no contamination possibly introduced during the grinding operation (the balls and the internal wall of the jars) [38].

Magnetic properties
In our measurements to obtain the hysteresis cycles of the samples, the external magnetic field H is continuously varied between two extreme values, − 1.8 kOe and + 1.8 kOe. These values allow us to reach the magnetisation saturation of the material. With the gradual cancellation of the external magnetic field, the material remains in a stable state of residual magnetisation. Then, with the increase of the external magnetic field applied in the opposite direction, the magnetisation gradually reaches the state of reverse saturation. For a particular value of the applied field, called coercive field H c , the magnetisation is cancelled. Several parameters, such as the coercive field H c , the magnetic moment m, the magnetisation saturation M s , and the remanent magnetisation Mr are extracted from the hysteresis curves. Figure 11 shows the room temperature hysteresis loops (M-H) of Fe 90 Sb 10 powders for different milling times.
We note that all the cycles of hysteresis have a sigmoid shape and are generally observed in nanostructured magnetically soft samples with small magnetic domains (see the box in Fig. 11). This is due to the presence of structural distortions within the grains. Low hysteresis losses are properties generally sought after in soft magnetic materials. The curves of magnetisation-field loops have been used to determine the values of the magnetisation saturation (M S ), coercive fields (H C ), remanent magnetisation (M r ), and squareness ratio (M r /M s ) (see Table 1).
In a ferromagnetic material, the orientation of atomic magnetic moments can occur spontaneously, even in the absence of an external magnetic field, provided that the temperature of the material is lower than the critical temperature called ferromagnetic curie temperature. The region of the material or the magnetic moments have the same orientation, and they are called magnetic domains or Weiss domains. When one passes from the magnetic field to the neighbouring field, the magnetic moments gradually change orientation over a short distance. This interface where occurs this transition is called a block wall.
In a material that is not subjected to any excitatory magnetic field, the vector sum of magnetic moments associated with the Weiss domains is zero; that is to say that the material macroscopically presents no magnetisation.
If the material is subjected to an exciting magnetic field H, the domains whose magnetic orientation is close to that of the exciting field H, enlarge to the detriment of the less well-oriented domains, which gradually disappear when the intensity of the excitatory field increases.
There is a higher value of the excitation field called the saturation field for which the single crystal or the grain will then consist of a single Weiss domain whose magnetisation M will have the same orientation as the exciter field H. The corresponding magnetisation is the magnetisation saturation M s .
The values of M s are also included in Table 1. The evolution in magnetisation saturation M s as a function of the milling time (Fig. 12) shows a decrease from 213.73 after 2 h of milling, then, an increase to about 226.03 emu/g after 4 h of milling. Finally, a rapid decrease is recorded up to 36 h of milling to reach 156.95 emu/g.
The reason for the decrease in magnetisation saturation is attributed to the electronic transfer of the antimony atoms, which fill partially the third band of Fe giving rise to lower values for the magnetic moment of these atoms [39]. This effect results in the reduction of M s linked to the existence of the nonmagnetic elements (Sb) in the vicinity of the Fe atoms. The presence of Sb in the vicinity of Fe causes a decrease in the magnetic moment of iron. We take note that the increase in M s can be attributed to the reduction in magnetocrystalline anisotropy, which leads to an easier rotation of spins [40,41].
The changes in the magnetic properties of nanomaterials ferromagnetic, such as the remanent magnetisation (M r ) and the coercivity (H c ), usually originate from the microstructure and are attributed to the large fraction of atoms present at the grain and the grain boundaries.
Furthermore, the remanence M r represents the resistance of a material to demagnetisation.
The variation of H C and M r as a function of milling time is shown in Fig. 13. It was observed that the residual magnetisation behaves in a similar manner to that of the The decrease of the coercivity H c during the second stage depends on the refinement of the grain size, which leads to an easier rotation of the magnetic vector, as explained in G. Herzer's model [42]. It should be noted that this model indicates that the grain size for all the samples is less than the magnetic exchange length of the iron-based alloys, which is L ex = 20-30 nm [43], which is probably the main cause of saturation observed in the coercive field around 98-121.69 Oe (see in Table 1). In the present study, the grain size of the α-Fe (Sb) alloy is at the second stage of processing approaches. The exchange length (which is between 18 and 25 nm), the average magnetocrystalline anisotropy of the randomly oriented crystallites do not offer resistance to Bloch walls and the coercivity approaches to the low-value characteristic of mild ferromagnetic alloys.
The M r /M s ratio is essentially the square measure of the hysteresis loop (M-H). It is related to the level of inter-grain interaction. The evolution with milling time of remanenceto-saturation ratio, M r /M s of Fe 90 Sb 10 powder mixture is shown in Fig. 14. It is observed that a gradual increase the square ratio M r /M s to reach a value of around 0.057 after 2 h milling, then decreases rapidly from 0.056 at 4 h to 0.042 at 25 h. After 36 h of milling, the M r /M s undergoes a slight increase to reach 0.044 (Table 1). All samples treated by MA have a (M r /M s ) ratio between 0.04 and 0.06, which is much lower than that of a single domain particle. The Stoner-Wolfarth model [44] predicts that in single-field particles with uniaxial anisotropy, the low residual is in the order of M r /M s = 0.5.  Magnetic anisotropy is linked to two microscopic origins: the first is due to the dipolar interaction, which is a long-range interaction (~ r −3 ) and which will lead to shape anisotropy, and the second is the spin-orbit interaction, which is the coupling between magnetic moments and the crystal lattice. These two interactions are going to play a very important role for small particles.
However, the free energy of magnetic anisotropy depends on the macroscopic shape of the material and its crystal axes. Each type of crystal lattice will give The values of the magnetocrystalline anisotropy constant for all the samples are listed in Table 1.
The evolution of anisotropy magnetic constant K and magnetisation saturation M S as a function of milling time is shown in Fig. 15. It was observed that the anisotropy magnetic constant K behaves in a similar manner to that of the magnetisation saturation M S . We can observe three stages: a slight decrease in the magnetic anisotropy constant K during 2 h of grinding, then an increase between 2 and 4 h of milling, a slight decrease in the magnetic anisotropy constant K during 2 h of grinding, then an increase between 2 and 4 h of milling, and finally a rapid decrease until reaching a low value of around 16,021.97 after 36 h of milling ( Table 1). The increase in K is a tributary of the hardening of the system and the introduction of an important density of crystal defects. However, the decrease in K may be related to the decrease of the frome anisotropy due to the decrease in the shape distribution of particles during milling [46][47][48]. Furthermore, it is presumed that the decrease in apparent anisotropy following to grain size refinement cannot produce effectively with the existence of nonmagnetic phases along the joints of grains. This refinement prevents exchange coupling between the grains. With the decrease in dimensionality, the effects related to surfaces become more and more important because the fraction of atoms of surfaces on atoms of volumes is no longer negligible. Thus, it is necessary to hold on to account a term related to the surface of the nanostructure.
The virgin curve (or initial magnetisation curve) reflects the magnetic behaviour of demagnetised samples with increasing applied fields. Figure 16 shows at room temperature the M (H) virgin curves of Fe 90 Sb 10 powders for different milling times. We observe that all the virgin curves pass through the origin and show a linear evolution of the magnetisation for low values of the magnetic excitation, and from a certain value, the magnetisation increases less quickly; the Fe 90 Sb 10 powders for the different milling times begin to saturate. It is also noted that the magnetisation saturation M s as a function of the milling time by increasing the values of the magnetic excitation decrease from 212.46 emu/g after 2 h of milling, then increases to about 224.17 emu/g after 4 h of milling. Finally a rapid decrease up to 36 h of milling to reach 156.36 emu/g. The increase in magnetisation saturation can be correlated with that of the crystalline parameter, which can be influenced by plastic deformations and the density of defects produced by high-energy mechanical milling. On the other hand, the decrease in M s can be related to the change in the magnetic moment following the modification of the electronic configuration of the closest neighbours of the Fe atom. The decrease in M s with the increase in the grinding time can be explained by the antiparallel coupling of iron and antimony spins.

Conclusions
The experimental work presented in this article concerns the preparation of nanostructured Fe 90 Sb 10 (wt.%) powders using high-energy ball milling from pure elemental Fe and Sb powders in a Retsch PM400-type planetary mill for different milling times up to 36 h. The structural, microstructural, and magnetic characterisations were made by X-ray diffraction using a structural refinement program (MAUD) based on the method of Rietveld, SEM coupled to EDX, and VSM. The XRD results reveal the formation of (bcc) α-Fe(Sb) solid solution by the gradual diffusion of Sb atoms into (bcc) α-Fe. After 12 h of milling, only the (bcc) α-Fe(Sb) phase is detected. The results of the lattice parameter calculation show that the latter increases slightly from its initial value corresponding to that of (bcc) α-Fe until reaching a final value of 0.2870 nm after 36 h of milling. In addition, we have noticed that the average grain size decreases with increasing milling time. This decrease in < D > is accompanied by an increase in the rate of micro-distortions < ε > with milling time. In fact, the final values of the mean grain size and of the micro-distortions reached 18.16 nm and 0.19%, respectively. The study of the morphology of the Fe 90 Sb 10 (wt.%) powders allowed us to observe the change of the shape as well as the size of the particles after the grinding. It seems like for long grinding times, the mode used as well as the grinding conditions favour the existence of roundshaped particles. The maps produced by EDX allowed us to follow the evolution of the formation of the alloy according to the grinding time. From the hysteresis curves, we studied the values of the saturation magnetisation (M s ), the coercive field (H c ), remanent magnetisation (M r ), the square ratio M r /M s , and the magnetocrystalline anisotropy constant (K). M s , H c , and M r show a rapid decrease for times of 4 up to 36 h of milling to reach values of 156.95 emu/g, 98Oe, and 6.95 emu/g, respectively. Furthermore, we note that in the M r /M s ratio, the samples produced during 36 h of grinding are multidomain. The values of the M r /M s ratio are between 0.044 and 0.057. These M r /M s values, which are less than 0.1, corresponding to multidomains. The magnetocrystalline anisotropy constant (K) exhibits a behaviour similar to that of M s at room temperature.