Dependence of Magnetic Properties with Structural/Microstructural Parameters of Ball-milled Fe15Co2P3 Powder Mixture

This research work aims to investigate the mechanically alloyed Fe15Co2P3. Parametric Rietveld refinement method, of the obtained X-ray patterns, was performed for qualitative and quantitative phase analysis, structural, microstructural and mechanical properties. The ball-milled powder mixture crystallized within the face-centred cubic α-Fe(P) solid solution in equilibrium with Co75Fe25 phase. The crystallite size decreases reaching 100 and 200 nm respectively after 3h of milling. The highest values of the dislocation density, microstain and stored energy are registered for the α-Fe(P) solid solution. The studied mechanical properties manifest the brittle nature of the α-Fe(P) solid solution compared to the Co75Fe25 phase. The squareness ratio Mr/Ms and the coercivity values of the milled powders increase with increasing milling time and reach steady state after 2 h. The hysteresis loss energy and maximum permeability reach minimal values of 45*10 W/m and 49*10 H/m respectively, after 1 h of milling at the opposite of the switching field distribution.


Introduction
The magnetic nanoparticles Fe-Co based alloys have been the subject of many researches due to their potential applications such as medical hyperthermia and targeted source applied to activate these magnetic nanoparticles lead to the destruction of pathological cells by physic-chemical effect [2]. Moreover, iron oxides and derivative nanoparticles act as an agent for the advancement of clinical regenerative medicine and magnetoresponsive therapy using magnetic resonance imaging tracking or multimodal imaging [3,4]. Other studies reveal that calcium phosphate CaP and indium phosphides InP based alloys have an influence on biocompatibility property [5,6]. The magnetic hyperthermia is a type of thermal treatment of cancer; the ferromagnetic nanoparticles once localized in cancer cells, under external magnetic field will heat up resulting in the death (burn out) of cancer cells. Thus, heat can be used as a support of the therapeutic effects of other treatments by reducing the covering of cancer cells from anti-cancer activities [7,8]. Hence, magnetic Fe-Co-P alloys due to their interesting properties, are considered as promising candidates for wide range of applications, including from media storage as the Fe-Co-P/C [9] to magnetic memory devices to vector probes in the biomedical research and clinical diagnostics and therapeutics [10,11].
Most of Fe-Co-P alloys were produced as amorphous and/or crystalline nanowires by electrochemical deposition process [12] whereas in the biomedical field powder is recommended for the preparation of suspensions that can subsequently be easily administered to the human body. For this purpose, in this study Fe-Co-P alloys will be prepared in the form of powder by mechanical milling technique, which was used frequently to mix powders to achieve a homogeneous alloy through successive welding, fracturing and rewelding processes [13].
Similarly, binary systems such as Fe-P and Fe-Co based alloys were also prepared by mechanical alloying and exhibited interesting properties [14,15]. In one hand, Fe-Co alloys attracted great attention due to their excellent soft magnetic and mechanical properties, which are found to be strongly dependent on the adopted fabrication method and subsequent heating treatment [16,17]. They are widely known by their high specific saturation magnetization, low coercivity, high permeability, and high Curie temperature, making them promising for high temperature applications besides being competitive candidates with other highly magnetic materials [18,19] . In the other   hand, the transition metal phosphides  alloys  and  their  solid  solutions  demonstrated interesting magnetic properties which are greatly influenced by both the type of the crystal structure and the chemical composition; for instance it was reported that the lattice parameters and Curie temperature of Fe2-xP system changes significantly with the presence of small amount of impurities and the deviation of stoichiometry [20]. The role of the compound on the structure stability, phase composition and properties was mostly studied on binary Fe-P alloys that dependent on P concentration with a ferromagnetic ground state [14,21]. In recent years, great attention has been given to the thermal stability of transition metal phosphides nanomaterials [22,23]. Others studies of Co2P encapsulated in N, Pdoped grapheme, CoMnP nanoparticles, nanostructured Fe92P8 and Fe-Co, MnFeP1-yAsy, (Fe1-xMnx)3P, Li-Fe-P and FeP alloys report a robust catalytic activity [24,25], interesting magnetic [26,27], electronic and mechanical properties [28,29], and a good storage energy capacity [30,31]. These properties can be altered by changing the chemical composition, type of crystal structure, and grain size. These nanostructured materials formed by mixing a metal with phosphorus are wellknown by their metalloid characteristics with good electrical conductivity [32], which is important for electrochemical applications.
Moreover, numerous studies report on the fabrication of Fe-Co-P alloys by different techniques such as reacting low-reactive metal-oleates (Co 2+ and Fe 3+ ) with trioctylphosphine [33], electrodeposition [34,12], drop synthesis method [36], organic phase reaction [37,38], phase-solution method [39], and electroless plating method [40]. Herein, it is important to highlight that phosphorus was added to FeCo alloy to improve the soft magnetic performance of the mixture the magnetic permeability as well as provides strengthening to the solid solution within the matrix [41,42].
The present work aims to study the elemental (Fe, Co and P) powder mixture through atomic diffusion during the mechanical alloying process. Particular emphasis will be devoted to the evolution of structural and microstructural as function of milling time, and subsequently the correlation with the mechanical and magnetic properties. This study primarily focuses on the fabrication of nanostructured powder by optimizing their manufacturing protocol and analysis for a future preformulation of active nanosuspensions.

Materials and methods
Pure elemental powders of iron, Fe (97 %, average particle size ~ 325 mesh), cobalt, Co (99.90% average particle size ~ 150 µm), and amorphous red phosphorus, P (99.9%), were mixed in a high energy planetary ball mill Retsch PM 400. The milling process was performed at room temperature under an inert atmosphere using hardened steel balls and vials. The milling speed was fixed at 350 rpm with a ball-to-powder weight ratio of 10:3 while the milling time vas varied from 1 to 3 h with a pause of 30 min/h.
The structure of the milled powder was checked by X-ray diffraction (XRD) using a Bruker-D8 advanced diffractometer in a (θ-2θ) Bragg-Brentano geometry equipped with Cu-Kα radiation source (λCu = 0.15406 nm). Qualitative and quantitative phase analysis of XRD patterns was investigated by the Rietveld method [43] using the MAUD program version 2.26 [44].
The magnetic measurements were carried out at 300 K using the vibrating sample magnetometer (VSM) MicroSence-EZ7 under an applied magnetic field of 20 kOe.
The phase composition, structural, microstructural and mechanical parameters were determined by the refinements of XRD patterns by means of MAUD program [43]. The effective crystallite size and roots mean square (r.m.s) of microstrain were obtained by fitting the peaks profile using the pseudo-voigt function, which is a combination of a Gaussian and a Lorentzian peaks shape [45]. The refinement program minimized, by an algorithm based on the least squares method, the function M called residue where its absolute value is defined by [46]: (1) where yi and yci are, respectively, the observed and calculated intensity; wi = 1/yi is the weight associated to the i th observed count.
The calculated intensity is obtained by summing different contributions of Bragg diffraction peaks and the background [47]: with K the Miller's indices for a reflection (h,k,l); ybi the continuous background intensity; Sϕ the scale factor, proportional to the volume fraction of each refined phase; jϕk the multiplicity factor of the k th reflection peak; LPϕk the Lorentz-Polarization factor; Oϕk the correction factor describing the preferred orientation; A the absorption factor; FK the structure factor; and Ωiϕk the profile shape function.
The quality of the refinement with the MAUD program is characterized by the reliability weighted, Rw, and expected factor, Rexp, or just by the goodness of fit,, defined as follow: where N and P are the number of experimental points and refined parameters, respectively.
The dislocation density, ρ, is one of the important parameter influencing the final microstructure, is calculated by [48]: where B is the Burger's vector, which is equal to a(√2/3) for the <110> direction of the bcc structure, <L> the crystallite size and <σ 2 > 1/2 the root mean square (r.m.s) microstrain, obtained by the Rietveld refinements.
The planar defects expressed in terms of stacking faults probabilities, SFP, are given by [49,50]: Where α', α'' are the intrinsic and extrinsic deformation faults probabilities, respectively, and β is the twin faults one.
To calculate the stored energy, ES, the following formula is used [51]: Where E is Young's modulus and v is Poisson ratio.

Results and discussion
3.1 Structural and microstructural properties The best Rietveld refinements of XRD patterns of the powder mixture Fe15Co2P3 as function of milling time have been obtained using an isotropic fitting model with the combination of different phases. For the un-milled powder mixture, the starting structural model is based on the elementary powders of sc-P, bcc-α-Fe and Co-hexagonal. However, for the XRD pattern of the milled powder mixture, the best Rietveld refinements has been found with two bcc phases only; an α-Fe(P) solid solution and a binary Co75Fe25 phase with Im-3m space group. Figure 1 displays the XRD refined patterns of the un-milled and ball-milled Fe15Co2P3 powder mixture using the MAUD program [44], manifesting the evolution of the alloying as a function of milling time. From Figure  1, one can observe that the variation of peaks relative intensity with milling time indicates the corresponding change of phase's composition, whereas peaks' broadening indicates the occurrence of grain refinement and accumulation of microstrain induced by severe plastic deformations during the milling process.
The initial mixture displays the diffraction peaks characteristics of pure bcc α-Fe and Co-hcp in addition to P, whereas the latter disappears after milling evidenced by the dissolution of P into the α-Fe host lattice by solid state reaction accompanied by the formation of the α-Fe(P) solid solution. Similarly, Co atoms will diffuse and incorporate into α-Fe host lattice leading to the formation of Co75Fe25 phase after 1 h of milling. The formation of this phase is due to its higher thermodynamic stability under the experimental milling conditions compared to other phases present in the binary Fe-Co phase diagram. In fact, it is important to highlight that this phase has been obtained under an ultrahigh-vacuum chamber at a low pressure by molecular beam epitaxy (MBE) [52] and synthesized by DC magnetron sputtering deposition on top of a tunneling barrier of AlOx [53]. Accordingly, the presence of P atoms in the studied mixture facilitates the precipitation of Co75Fe25 into an α-Fe(P) solid solution with lesser energy. This is probably due to the small difference between the atomic radii of the host metal, Fe, and the dissolved P (rFe = 0.125 nm, rP = 0.128 nm), hence preferring a substitutional site within the Fe crystal lattice [54]. The α-Fe(P) solid solution was also obtained at much higher milling time of 9, 12 and 21 h [55] with subsequent annealing at 210°C under argon for 30 min [56].
The relative deviation of the unit cell volume from that of the perfect crystal V0 as defined by ΔV/V0 = (V -V0)/V0, is found to be nearly constant after 1 h of milling (Fig. 2a). The deviation increases after the first hour of milling is due to the deformation of the crystal structure of both α-Fe(P) and Co75Fe25 phases, associated with the repeated fracturing, cold welding and re-welding processes of the newly formed powdered particles and the diffusion of both P and Co atoms within the host lattice of Fe. The obtained results reveal that the unit cell volume expansion of the newly formed Co75Fe25 phase is higher than that of the α-Fe(P) solid solution. In fact, after 3 h of milling, V/V0 of Co75Fe25 is in the order of 5.26±0.02%, which is two times higher than 2.5±0.02% for α-Fe(P), signifying that the structure of the Co75Fe25 phase is more deformed than that of the α-Fe(P) solid solution. These results can be correlated with the values of the internal microstrain <σ 2 > 1/2 deduced from the Rietveld refinements of the XRD patterns; i.e. 0.4 x10 -3 ±0.0002 for Co75Fe25 compared to 0.2 x10 -3 ± 0.0002 for α-Fe(P) solid solution, after 3 h of milling. Figure 2b illustrates the variation of phase composition as a function of milling time. The percentage of the formed Co75Fe25 phase increases rapidly, in the first milling hour, at the expense of pure Co and Fe elements reaching ~ 60 %. In fact, pure α-Fe has the highest percentage before milling of ~75 % then varies with milling time to reach 35% after 3 h milling.
To better understand the pure element diffusion within the host lattice and subsequently the formation mechanism occurring by the mechanical milling process, primarily well-defined planar crystallographic defects playing a key role in solid state reactions has been chosen carefully. Thus, Figure 2c illustrates the evolution of the antiphases' presence probability during the milling in both α-Fe(P) solid solution and Co75Fe25 structures deduced from the XRD Rietveld refinements. The highest probability values are recorded for the newly formed Co75Fe25 phase, which corroborate with the variation of its unit cell volume. Alternatively, the stacking fault probability, SFP, is found to be very weak in the binary Co75Fe25 phase but increases with milling time for the solid solution (Fig. 2d). The increase of SFP, intimately related to the creation and reaction of dislocations, with extensive milling time reflects an important increase in the dislocations density in Fe crystal lattice (Fig. 2e). These results highlight the pathway of the solid state reactions in this compound, occurring by diffusion of both elemental P and Co within Fe host lattice through stacking faults as well as dislocations induced by the milling process into the solid solution and Co75Fe25 phase.
As a host, the bcc -Fe phase can dissolve P atoms thereby creating lattice defects such as dislocations and grain boundaries. The increase of the SFP after 2 h of milling can be attributed to the annihilation of dislocations to minimize their energy. It is clear that the dislocations density of Co75Fe25 phase is steady and reaches the smallest value of about 2.22× 10 10 m -2 .
The accumulation of lattice defects induced during milling, manifested by the variation of the microtrain rate <σ 2 > 1/2 , has a direct influence on the evolution of the crystallite size <L> of the obtained phases in the milled Fe15Co2P3 powder mixture ( Fig. 2f-g). Accordingly, for α-Fe(P) solid solution, the crystallite size decreases drastically from 483 nm to reach an average value of about 100 nm from 1 to 3 h of milling. Meanwhile, the crystallite size of Co75Fe25 phase is found to be nearly stable with milling time and reaches a mean value of 193 nm.

Mechanical properties
The evolution of the simulated mechanical properties such as Young modulus and Poisson ratio, have been deduced from the XRD Rietveld refinements. The highest value of Young modulus, E, in the milled Fe15Co2P3 powder mixture is ~ 200 GPa, which is close to that of coarsed metals but higher than that of other nanomaterials such as FeCoP nanoglass films i.e. 138.85 GPa [57]. However, this estimated value is slightly smaller compared to that of Fe60Co40 alloy of 250 GPa [58] but almost three times lower than the monolithic FeCo alloy setting in the range 611 -536 MPa [59]. The results obtained in this study reflect the influence of the addition of P powder to the Fe-Co system, as consequence a dramatic decrease in the Young modulus values compared to Fe-Co binary alloys. This can be attributed to the precipitation of the Co75Fe25 particles embedded in the α-Fe(P) solid solution during the milling process, resulting in the weakness and rigidness of final powder mixture because the initial powder mixture is ductile (Co, Fe) -brittle (P) type. The Poisson ratio (Fig. 3a) of the Co75Fe25 phase reaches a nearly stable mean value during the milling while for the α-Fe(P) solid solution it has lower values and decreases gradually with milling time. The above results expose the brittle nature of the α-Fe(P) solid solution in comparison with the Co75Fe25 phase. Moreover, the evolution of the calculated stored energy as a function of milling time (Fig. 3b) shows that the prevalent value of the stored energy is observed for the α-Fe(P) solid solution after 1h of milling. The values of the stored energy in the Co75Fe25 phase are very weak and nearly equal to 83×10 -6 J/mol. These results may be attributed to the high rate of microstain and dislocations density in the nanometric α-Fe(P) grains compared to those of Co75Fe25 phase.

Magnetic Properties
The magnetization-field hysteresis (M-H) curves of the Fe15Co2P3 powder mixture recorded at room temperature are displayed in Figure 4a, with the inset representing M-H curves at low fields. All M-H curves exhibit similar soft magnetic features of the powder mixture with an extremely thin hysteresis loops, irrespective of the milling time. This shape is determined by the domain state which can be distinguished by several parameters such as the coercive field, Hc, the squareness ratio Mr/Ms, the switching field distribution, SFD, magnetic permeability, μmax and loss energy Qh.
The maximum energy loss of the hysteresis loop in the 2 nd and 4 th quadrant of the hysteresis loop is presented in Figure 4b. A very small hysteresis loss is implied by the resulting narrow of the hysteresis loop. This type of loss strongly depends on the crystallite size, residual stresses and density of the material. According to the obtained results, for the Fe15Co2P3 compound, the hysteresis loss shows a higher value of 6.94 × 10 -3 W/m 3 in un-milled powder mixture due to the large crystallite size. The hysteresis loss decreases for the first hour of milling following an important reduction of the crystallite size [60], then increases with further milling to reach a steady state between 2 and 3 h. Indeed, the evolution of the coercive field Hc vs. the average grain size of the Fe15Co2P3 powder mixture as a function of milling time (Fig. 4c), manifests a gradual increase up to 2 h of milling while the average grain size decreases then reaches a steady state. The increase of the coercive field is related to the growth of the microstrain ratio introduced during milling and can be explained through the theory of soft magnetic materials [61]. Additionally, one can observe the evolution of the nucleation field Hn of the Fe15Co2P3 powder mixture Hn, which means that a magnetization state becomes unstable and the change in the magnetization configuration begins. However, the nucleation field is nearly close to the coercive field Hc (Hn ≈ Hc, indicating that the milled powder mixture is nearly a perfect magnet. The squareness ratio Mr/Ms (Fig. 4d) increases gradually with the milling time then reaches stability up to 2 h. The rise of the Mr/Ms ratio can be associated with the crystallization process that leads to the increase in the magnetic anisotropy. From the values of the squareness ratio Mr/Ms, it is possible to differentiate between single domain and multi-domain particles. Thus, the obtained values of Mr/Ms ratio in the range of 0.07 to 0.09 are much lower than the expected values [62], which reached 0.95 for the ferromagnetic Co75Fe25 alloy [63]. The switching field distribution, SFD, is an important micromagnetic characteristic curve depending on the degree of alignment of particles along the easy axis. It is supposed that the extracted SFD from macroscopic measurements rely on separating the contributions to the measurements of the intrinsic SFD, the extrinsic effects of magnetostatic and exchange interactions. The characteristic features of interphase exchange coupling are illustrated by switching field distribution via dH/dHc vs. the milling time (Fig. 4e), where dH is the field between 0.5 Mr and -0.5 Mr whereas Hc is the coercivity. The distribution of the switching field shows one peak at 1 h of milling a typical characteristic of soft phases, indicating the magnetization reversal is completed in one-step for this powder mixture. Consequently, the width of the dH/dHc peak can be interpreted as an estimation of the efficiency of hard/soft interphase exchange coupling. Figure 4f shows the maximum magnetic permeability μmax of the Fe15Co2P3 powder mixture as a function of milling time. It can be seen that the maximum permeability decreases after 1 h of milling compared with its value before milling then increases with milling time to reach a maximum permeability value of about 65×10 -3 H/m after 3 h of milling. This can be attributed to the presence of a nonmagnetic P element within the -Fe(P) solid solution in the powder mixtures which acts like an air gap, as a source of demagnetizing field causing the existence of very mobile domain walls. As consequence, the maximum permeability value increases, since it is reported that the permeability is sensitive to the microstructure and thereby can be affected by the shape of the particles, density, porosity and strongly depends on the grain size [64,65]. It is well-known that addition of P increases the permeability while decreases the coercivity [66,67]. This, as suggested by the above magnetic results is due to the higher phosphorus concentration ~ 15 (wt.%) in the α-Fe(P) solid solution. The observed variation in the magnetic properties of the milled Fe15Co2P3 powder mixture may also be correlated indirectly with the fabrication parameters, for instance milling atmosphere, milling speed, rise of the local temperature, and so on. Indeed, it's well established that the effect of temperature on ferromagnetism is very important. When the temperature increases, the thermal energy tends more and more to break the spontaneous alignment of atoms. The increase of the local temperature during the milling process can modify the magnetic properties of materials mainly by an irreversible change in their local chemical composition and homogeneity.

Conclusion
A soft magnetic Fe15Co2P3 alloy was successfully prepared by mechanical alloying from elemental Fe, Co and red P powders. The Rietveld refinements of the XRD patterns revealed that, irrespective of the milling time, only bcc-type structures are formed and present Lorentizien Bragg diffraction peaks, with grain refinement and accumulated microstrain. 60% of the formed compound is a Co75Fe25 phase after 1 h of milling with the highest antiphases boundaries and deformed grains. The crystallite size decreased to 100 -200 nm after 3h of milling. The high values of the SFP reflected an important increase in the dislocations density in Fe host lattice and manifested the solid state reaction pathway which takes place through dislocations and stacking faults. The value of Young modulus in the Fe15Co2P3 powder mixture was found smaller than that obtained in binary Fe-Co alloys, reflecting the effect of P addition. A narrow hysteresis loop suggested a very low hysteresis loss. The coercivity was found to increase with milling time while the average grain size decreases; which is accompanied by an enhancement of the microstrain ratio. Different magnetic properties such as hysteresis loss energy, magnetic susceptibly and switching field distribution are determined, which help in defining the manufacturing protocol with a better preformulation of active magnetic nanosuspensions for biomedical applications.