B Malaman

G Le Caër

B F O Costa

B2 long-range order in mechanically alloyed Fe 53.3-0.6x Co 46.7-0.4x Sn x (2 ≤ x ≤ 26) annealed at moderate temperatures

Keywords: Fe-Co-Sn alloys, Heusler alloys, mechanical alloying, B2 long-range order, Mössbauer spectroscopy

    B2 long-range order in mechanically alloyed Fe 53.3-0.6x Co 46.7-0.4x Sn x (2 ≤ x ≤ 26) annealed at moderate temperatures B Malaman, Gérard Le Caër, B. F.O. Costa

Introduction

Near-equiatomic Fe 100-x Co x alloys, which are body-centered cubic (bcc), denoted as A2, between ~1000K and ~1250K, order to a CsCl type structure (B2) at temperatures below ~1000K for x ranging between ~40 and ~60 [START_REF] Sourmail | Near equiatomic FeCo alloys: constitution, mechanical, magnetic properties[END_REF]. A perfect B2 FeCo alloy may be described as two interpenetrating simple cubic sublattices, in (0,0,0) and in (1/2,1/2,1/2), Fe on one and Co on the other. Ferromagnetism stabilizes the B2 phase of Fe-Co alloys [START_REF] Neumayer | Atomic defects in FeCo: stabilization of the B2 structure by magnetism[END_REF][START_REF] Drautz | Ordering and magnetism in Fe-Co: dense sequence of ground-state structures[END_REF] and the bcc phase of Fe at low temperature [START_REF] Hasegawa | Microscopic theory of the temperature-pressure phase diagram of iron[END_REF]. In addition, magnetism plays a crucial role in the formation of point defects in B2 FeCo. It results in an effective formation energy of thermal antisite defects which is much smaller than those of Fe and Co vacancies [START_REF] Neumayer | Atomic defects in FeCo: stabilization of the B2 structure by magnetism[END_REF]. Cooling rates of at least ∼4000K/s are needed to bypass the order-disorder transformation of equiatomic FeCo, i.e. to retain the hightemperature disordered bcc phase at low temperature [START_REF] Sourmail | Near equiatomic FeCo alloys: constitution, mechanical, magnetic properties[END_REF]. Such rates can only be achieved by ultrafast quenching [START_REF] Fultz | Kinetics of short-range and long-range B2 ordering in FeCo[END_REF].

The B2 unit cell may serve as a basic brick for the construction of other ordered structures, in particular those of ternary alloys like half-Heusler (XYZ, C1b structure) and Heusler (X 2 YZ, L2 1 structure) alloys [START_REF] Yin | A review of phase equilibria in Heusler alloy systems containing Fe, Co or Ni[END_REF], where X and Y are transition metal elements, notably 3d elements, and Z is a sp element. The structures of Heusler and half-Heusler can be described from four interpenetrating fcc sublattices, one being empty in half-Heusler alloys.

Ternary Fe-Co-Sn alloys; Heusler and related alloys

Until recently, the Fe-Co-Sn system was essentially uninvestigated. The compound FeCoSn, with a hexagonal Ni 2 In type structure, was however studied in [START_REF] Buschow | Note on the magnetic and magneto-optical properties of Ni 2 In type 3d transition metal compounds[END_REF]. Splatquenched alloys Fe 75-x Co x Sn 25 (0 ≤ x ≤ 75) were reported to be B2 for any x [START_REF] Singh | Metastable Phases in Fe 75 Sn 25 -Co 75 Sn 25 Alloys[END_REF]. On the contrary, splat-quenched Co 75 Sn 25 was found to be A2 [START_REF] Schluckebier | A New Intermetallic Phase in the Co-Sn System[END_REF]. Further, splat-quenched Fe 35 Co 40 Sn 25 annealed for 12h at 1073K and water quenched was reported to consist of hexagonal Co 3 Sn 2 and of bcc Fe(Sn) [START_REF] Singh | Metastable Phases in Fe 75 Sn 25 -Co 75 Sn 25 Alloys[END_REF], most likely bcc (Fe-Co) as found hereafter for Fe 38 Co 36 Sn 26 (sections 3 and 4). Recent interest in Fe-Co-Sn alloys stems from Heusler alloys because of the magnetic properties of this class of materials and the associated functional properties, for instance, shape memory, magnetocaloric effect, magnetoresistance, thermoelectric power, spintronic [START_REF] Yin | A review of phase equilibria in Heusler alloy systems containing Fe, Co or Ni[END_REF].

Ordered alloys of the ternary systems Co-Mn-Sn and Ni-Mn-Sn are interesting, more particularly in relation with Heusler alloys. The structures of quaternary Co 2 Mn 1-x Fe x Sn alloys, prepared by arc-melting, were studied by Zhang et al. [START_REF] Zhang | Effect of substitution of Mn with Fe or Cr in Heusler alloy of Co 2 MnSn[END_REF]. Heusler alloys are formed for x ranging from 0 to 0.5 while the alloys phase separate into Co 3 Sn 2 , presumably hexagonal, and bcc Fe-Co for x>0.5. A Co 2 FeSn Heusler alloy is concluded to be unstable relative to other phases from ab initio calculations [START_REF] Yin | A review of phase equilibria in Heusler alloy systems containing Fe, Co or Ni[END_REF]. The alloy Co 2 FeSn, formed by high temperature direct synthesis calorimetry, is for instance decomposed into Co 3 Sn 2 and bcc Fe-Co [START_REF] Yin | Enthalpies of formation of selected Co 2 YZ Heusler compounds[END_REF]. The energy difference is however relatively small so that a Co 2 FeSn Heusler phase is concluded to be possibly synthesized by non-equilibrium techniques [START_REF] Yin | A review of phase equilibria in Heusler alloy systems containing Fe, Co or Ni[END_REF]. The latter difference is more unfavorable to the formation of a Fe 2 CoSn Heusler alloy [START_REF] Yin | A review of phase equilibria in Heusler alloy systems containing Fe, Co or Ni[END_REF]. Most recent studies of ternary Fe-Co-Sn alloys concentrate therefore on Co 2 FeSn. Three types of alloy structures have been reported according to the preparation method, bcc (A2), B2 and L2 1 . Ternary Fe-Co-Sn alloys were prepared by electrodeposition: as-prepared alloys, among which Co 2 FeSn and alloys whose compositions are close to those investigated here (section 1.3), were established to be bcc (A2) [START_REF] Duan | Effect of Current Density on the Microstructure and Magnetic Properties of Electrodeposited Co 2 FeSn Heusler Alloy[END_REF][START_REF] Watanabe | Preparation of Co 2 FeSn Heusler alloys by electrodeposition method[END_REF]. Small amounts of Co 3 Sn 2 were observed to form according to the current densities [START_REF] Duan | Effect of Current Density on the Microstructure and Magnetic Properties of Electrodeposited Co 2 FeSn Heusler Alloy[END_REF]. Li et al. used a reduction method of metal chlorides and sulfate, with sodium hypophosphite as a reducing agent, to prepare nanoparticles of B2 Co 2 FeSn [START_REF] Li | Synthesis, microstructure and magnetic properties of Heusler Co 2 FeSn nanoparticles[END_REF]. Finally, L2 1 Co 2 FeSn Heusler alloys films were synthesized by atomically controlled deposition of successive layers of Co, Fe and Sn for substrate temperatures of at most 523K [START_REF] Tanaka | Preparation of Co 2 FeSn Heusler alloy films and magnetoresistance of Fe/MgO/Co 2 FeSn magnetic tunnel junctions[END_REF]. The present work is more particularly focused on metastable ordered alloys prepared by annealing of disordered phases of Sn in near-equiatomic Fe-Co made by mechanical alloying. General characteristics of the latter non-equilibrium technique are summarized below [START_REF] Gaffet | Some recent developments in mechanical activation and mechanosynthesis[END_REF][START_REF] Suryanarayana | Mechanical alloying and milling[END_REF].

Mechanical alloying and grinding

Mechanical alloying of mixtures of powders of pure elements or of powders of already partially combined elements is basically a dry and high-energy milling process used to synthesize all kinds of materials, often with non-equilibrium structures, from metallic to ionic such as extended solid solutions, alloys of immiscible elements, amorphous phases, all sorts of compounds and composites [START_REF] Gaffet | Some recent developments in mechanical activation and mechanosynthesis[END_REF][START_REF] Suryanarayana | Mechanical alloying and milling[END_REF]. Mechanical grinding differs from mechanical alloying in that the chemical composition of the starting powder particles remains the same during milling but their structure is expected to evolve.

In the mechanical alloying process of ductile elemental powder mixtures, particles are trapped between colliding balls or between balls and vial. They are subjected to a severe plastic deformation, which exceeds their mechanical strength, accompanied by a temperature rise. Particles are repeatedly flattened, fractured and welded. A layered structure of the ground elements is formed initially. It is progressively refined and becomes tortuous. Fracture and welding are the two essential events through which matter is permanently exchanged between particles. They ensure mixing of the elements of ground powders down to the atomic scale.

Milled powders of a given composition reach a stationary state, or dynamical equilibrium, through the combined action of plastic deformation and of diffusion for given mechanical and thermal working conditions of the high-energy mill as advocated in the theory of driven systems applied to ball-milling [START_REF] Bellon | Driven alloys[END_REF]. The phases which are expected to form depend on the milling conditions whose parameters for the present study are described in section 2. An example relevant to the present work is that of grinding of B2 FeAl in a Fritsch P0 vibratory mill which consists of a tungsten carbide vial vibrating at 50 Hz [START_REF] Pochet | Order-disorder transformation in Fe-Al under ball milling[END_REF]. The vial contains a single ball either a 1 kg tungsten carbide ball or a 500 g hardened steel ball and powders. The FeAl equilibrium structure is of the B2 type up to its melting temperature which exceeds 1500K. A dynamical diagram gives the steady state value of the LRO parameter S as a function of milling temperature for a given "milling intensity" (figure 7 of [START_REF] Pochet | Order-disorder transformation in Fe-Al under ball milling[END_REF]). The latter is defined by Pochet et al. to be equal to M b V max f/M p with M b the mass of the ball, V max the maximum velocity of the ball, f the impact frequency and M p the mass of powder in the vial. At room temperature (RT) and below, the steady state structure is disordered bcc (figure 7 of [START_REF] Pochet | Order-disorder transformation in Fe-Al under ball milling[END_REF]). Between RT and ~530K, the LRO parameter increases progressively up to S=1. The steady state results from a competition between atomic jumps forced by shear and thermal jumps. Disorder induced by shear dominates at low temperature and explains that B2 FeAl transforms by ball-milling into a disordered bcc phase.

Experiments were not performed at temperatures higher than ~530K.

In all experiments described below, high-energy ball-mills operate at RT. For convenience, we denote hereafter as p-A x B y C z an initial mixture of elemental powders of composition A x B y C z to be milled. The compositions of as-milled powders differ in general from the initial ones as elements from milling tools, notably iron, are incorporated into the milled powders.

Nanocrystalline mechanically alloyed p-Fe 50-y/2 Co 50-y/2 Sn y

In classical milling conditions, similar to those used here (section 2), disordered bcc FeCo forms either by mechanical alloying of initial powder mixtures of elemental Fe and Co at RT [START_REF] Brüning | The mixing of iron and cobalt during mechanical alloying[END_REF][START_REF] Elkakouli | Mechanical and magnetic properties of nanocrystalline FeCo alloys produced by mechanical alloying[END_REF][START_REF] Sorescu | Structural and magnetic properties of Fe50Co50 system[END_REF][START_REF] Moumeni | Structural properties of Fe50Co50 nanostructured powder prepared by mechanical alloying[END_REF][START_REF] Garroni | Mechanistic inferences on the synthesis of Co 50 Fe 50 solid solution by mechanical alloying[END_REF] or by grinding B2 FeCo at RT for only 90 minutes [START_REF] Loureiro | Comparison of disorder induced by annealing and quench and by ball-milling in B2 FeCo[END_REF]. In the latter case, shear-induced disorder dominates, as above, the trend towards ordering. The stationary state of as-milled B2 FeCo consists then of a disordered bcc phase, with a typical crystallite size of ~10 nm [START_REF] Loureiro | Comparison of disorder induced by annealing and quench and by ball-milling in B2 FeCo[END_REF]. This stationary state does not depend on the nature of starting powders (alloyed or not).

The solubility of Sn in FeCo (A2 or B2) is very low at equilibrium, ~ 1 at% [START_REF] Delyagin | Hyperfine magnetic fields for 119 Sn atoms in ferromagnetic CoFe[END_REF][START_REF] Huffman | Hyperfine fields at 119 Sn nuclei in ordered Fe-Co and -Fe-Mn. CoFe[END_REF][START_REF] Campbell | Magnetic hyperfine fields at Fe, Cd and Sn sites in an FeCo alloy[END_REF].

High-energy ball-milling is a possible method to enhance it. Mechanical alloying was employed to synthesize ternary Fe-Co-Sn alloys from p-Fe 50-y/2 Co 50-y/2 Sn y for y ≤ 33 at.% in the milling conditions described in section 2 [START_REF] Loureiro | Mechanosynthesis of supersaturated solid solutions of Sn in near-equiatomic bcc FeCo[END_REF][START_REF] Loureiro | Mechanically driven dissolution of Sn in near-equiatomic bcc FeCo[END_REF][START_REF] Loureiro | Formation stages of bcc (Fe44Co44)Sn12 extended solid solution by mechanical alloying[END_REF]. When tin is added, a supersaturated solid solution of Sn in near-equiatomic bcc FeCo is expected to form. However, there is currently no way to predict theoretically the maximum degree of supersaturation in the given milling conditions and it is necessary to resort to experiment to determine it. The dissolution of Sn in near-equiatomic bcc Fe-Co was unambiguously proven by X-ray diffraction (figure 1) and by 57 Fe and 119 Sn Mössbauer spectroscopy (section 3.1). A disordered bcc phase, with significant amounts of tin dissolved in it, was found to remain the principal constituent of as-milled p-Fe 50-y/2 Co 50-y/2 Sn y alloys (figure 1). The maximum solubility of Sn in near-equiatomic nanocrystalline bcc FeCo, in the milling conditions described in section 2, is at least equal to 15±2 at.%. The difficulty raised by its determination is discussed in section 4.1.

Ordering of mechanosynthesized nanocrystalline alloys and aims

The combination of mechanical alloying and of annealing at moderate temperatures is a possible method to follow the recovery of order in as-milled nanocrystalline alloys when their coarse-grained counterparts are ordered at equilibrium. Some examples, among many, of ordered alloys disordered by ball-milling whose order is re-established by subsequent annealing, are L2 1 Ni 2 MnSn [START_REF] Leonova | Reordering of a Ni 2 MnSn Heusler Alloy after Disordering in a Planetary Ball Mill[END_REF], L1 2 Ni 3 Al [START_REF] Cahn | Disordering and reordering of mechanically milled superlattice alloys[END_REF] and B2 Fe 60 Al 40 [START_REF] Suriñach | Kinetics of reordering in a nanograined FeAl alloy[END_REF].

In addition, mechanical alloying followed by annealing makes possible the formation of metastable ordered alloys from alloys which are not long-range ordered at equilibrium but are prone to ordering. An example is metastable B2 ordering of near-equiatomic bcc Fe-V nanocrystalline alloys [START_REF] Ziller | Metastable and transient states of chemical ordering in Fe-V nanocrystalline alloys[END_REF]. The present study of mechanosynthesized alloys from ternary mixtures p-Fe 50-y/2 Co 50-y/2 Sn y (y ≤ 33) falls within this framework. The sole or preponderant constituent of as-milled powders is a metastable bcc phase ( [START_REF] Loureiro | Mechanosynthesis of supersaturated solid solutions of Sn in near-equiatomic bcc FeCo[END_REF][START_REF] Loureiro | Mechanically driven dissolution of Sn in near-equiatomic bcc FeCo[END_REF][START_REF] Loureiro | Formation stages of bcc (Fe44Co44)Sn12 extended solid solution by mechanical alloying[END_REF] and figure 1). The question then arises as to whether metastable tin-rich bcc phases do order to a B2 structure when annealed as do stable dilute solutions of tin in bcc FeCo [START_REF] Delyagin | Hyperfine magnetic fields for 119 Sn atoms in ferromagnetic CoFe[END_REF][START_REF] Huffman | Hyperfine fields at 119 Sn nuclei in ordered Fe-Co and -Fe-Mn. CoFe[END_REF][START_REF] Campbell | Magnetic hyperfine fields at Fe, Cd and Sn sites in an FeCo alloy[END_REF] and, if so, what is the range of tin content in which B2 ordering occurs. The peculiarities of annealing of nanocrystalline alloys, are essential for this purpose. Their high density of defects, in particular vacancies and grain boundaries, enhance the kinetics of ordering when they are annealed at moderate temperatures. The ordering of nanocrystalline alloys can thus be studied at lower temperatures and more practical times than would coarse-grained alloys [START_REF] Ziller | Metastable and transient states of chemical ordering in Fe-V nanocrystalline alloys[END_REF]. However, the maximum steadystate value of the long-range order (LRO) parameter S they reach is typically ~80% of the maximum value measured in their microcrystalline counterparts ( [START_REF] Ziller | Metastable and transient states of chemical ordering in Fe-V nanocrystalline alloys[END_REF] and references therein).

The present paper aims to study the transformations of p-Fe 50-y/2 Co 50-y/2 Sn y powder mixtures (y ≤ 33) ball-milled at high-energy and then annealed at moderate temperatures. Two techniques, neutron diffraction and 119 Sn Mössbauer spectroscopy, are essential to evidence the emergence of B2 long-range order in annealed powders.

We first recall the main structural features of p-Fe 50-y/2 Co 50-y/2 Sn y (y ≤ 33) blends ballmilled at high energy. Then, we describe and discuss the results of an experimental study of annealed alloys by neutron diffraction and by 57 Fe and 119 Sn Mössbauer spectroscopy.

Experimental

Elemental powder mixtures of Fe (purity: 99.9%), Co (purity: 99.8%) and Sn (purity: 99.5%) were ball-milled in argon atmosphere for 10h in a planetary Fritsch P6 ball-mill operating at RT at a disc rotation speed of 500 rpm. The rotating disc of the mill bears a vial which rotates in the opposite direction. The vial contains seven balls of 15 mm diameter and the powder mixture to be milled. Vials and balls are made of hardened steel. The powder-to-ball weight ratio was 1:20. The chosen milling time of 10h ensures that powders reach a stationary state in these dynamical milling conditions as confirmed for instance by figure 2 (see too section 3.1). Except if otherwise stated, "as-milled" stands hereafter for "milled for 10h under the above-specified conditions".

The compositions of as-milled powders were determined by energy-dispersive X-ray spectroscopy (EDS) in a scanning electron microscope JEOL JSM630, working at 15kV. The library standards provided by the instrument manufacturer (Oxford INCA Energy 350) were used for the quantitative analysis of the EDS data. The compositions of as-milled alloys deviate from their starting compositions. The final Sn content x is a little larger, by less than ~1 at.%, than the nominal content y. It is given by x=1.05y-0.16 with an accuracy better than 0.2 at.% for 2 ≤ y ≤ 25 while x=34 for y=33. As-milled powders were placed in quartz tubes opened at one end. The tubes were first evacuated by a primary pump and were then filled with argon. These two steps were repeated ten times before sealing the tubes under an argon pressure of about 27 kPa at 300K which becomes ~60 kPa at 673K. As-milled alloys were finally annealed at 673K for 15h.

Annealed alloys were characterized by X-ray diffraction (XRD) using CuKα radiation (λ = 0.1542 nm). The precise determination of peak positions was carried out by means of the software Analyze-RayfleX supplied by Agfa Seifert. Lattice parameters of bcc phases (figure 2) were then obtained by least-square fitting using a cell parameter refinement software named U-FIT [START_REF] Evain | U-FIT A cell parameter refinement program[END_REF]. Neutron diffraction (ND) experiments were carried out at Institut Laue Langevin (ILL, Grenoble, France), with the one-dimensional multidetector D1B (λ =0.252 nm). 57 Fe and 119 Sn Mössbauer spectra were recorded at room temperature, in transmission geometry, by a constant acceleration type spectrometer using sources of 57 Co in Rh and 119m Sn in CaSnO 3 both with a strength of ~ 10 mCi. Isomer shifts are not really relevant in the present context. When mentioned they are referenced to α-Fe at RT and to SnO 2 at RT for Fe and Sn respectively. Hyperfine magnetic field distributions (HMFD's), P X (B), were analyzed both for 57 Fe and 119 Sn with a constrained Hesse-Rübartsch method [START_REF] Caër | Evaluation of hyperfine parameter distributions from overlapped Mössbauer spectra of amorphous alloys[END_REF] employing Lorentz lines. In the previous notation, X is either F or S which stand for 57 Fe and 119 Sn respectively. Any HMFD is such that P X (B)dB, represents primarily the fraction of X atoms whose field lies between B and B + dB. The mean HMF is denoted as <B X >. The 'width' of a distribution P X (B) is represented below by a standard-deviation  X = <( B X -<B X >) 2 > 1/2 . Finally, we define B M either as the 57 Fe HMF for which P F (B) is maximum when B ranges between ~20 and 40 T or as the 119 Sn HMF for which P S (B) is maximum when B ranges between ~5 and 30 T where the context makes it clear which is which. Typical errors on <B X > and on B M are respectively of ~0.3 T and ~0.2 T. [START_REF] Loureiro | Formation stages of bcc (Fe44Co44)Sn12 extended solid solution by mechanical alloying[END_REF]. The first stage, for milling times t m ranging from 0.5h to 2h is characterized by the formation of stannides, FeSn 2 and CoSn 5 respectively at the Fe-Sn and Co-Sn interfaces. Solid solutions are formed at Fe-Co interfaces. Tetragonal FeSn 2 , with a CuAl 2 type structure, forms too during the first stage of mechanical alloying of Fe-Sn solid solutions [START_REF] Cabrera | Time and composition dependence of mechanical alloying of Fe 1-x Sn x[END_REF][START_REF] Yelsukov | Structure and magnetic properties of Fe 100-x Sn x ( 3.2 < x < 62) alloys obtained by mechanical milling[END_REF][START_REF] Dorofeev | Thermodynamic modeling of mechanical alloying in the Fe-Sn system[END_REF]. The formation and the structure of a tetragonal stannide, CoSn 5 , prepared via a conversion chemistry route and possibly non-stoechiometric Co 1-z Sn 5 (z=0.1-0.2), were reported only recently [START_REF] Wang | CoSn 5 Phase: Crystal Structure Resolving and Stable High Capacity as Anodes for Li Ion Batteries[END_REF]. It was shown to be non-magnetic [START_REF] Loureiro | Formation stages of bcc (Fe44Co44)Sn12 extended solid solution by mechanical alloying[END_REF].

Results

Previous characterizations of as-milled Fe

Both stannides disappear for longer milling times, only after ~1h for CoSn 5 .The second stage occurs for t m ≥ 2.5h until a stationary state is reached at t m ~ 8h. The lattice parameter a(x) of the supersaturated bcc phase of elemental powder mixtures of composition Fe 53.3-0.6x Co 46.7-0.4x Sn x milled for times ranging from 8h to 16h is shown in figure 2 as a function of x. It varies according to Vegard's law for x ≤ 10 with a(0)=0.2858(1) nm and a slope of 4.61(9)10 -4 nm(at.%) -1 . For larger values of x, a(x) increases steadily but deviates from Vegard's law, being for instance 0.2935(2) nm for x=21. The lattice parameters for a given x remain essentially constant for samples whose milling times range from 8h to 16h. This confirms that a stationary state, i.e. a dynamical equilibrium (section 1.2), has been reached at ~8h of milling.

XRD patterns evidence the formation of a bcc phase while well-separated peaks at ~30° grow progressively when x increases from 21 to 34 (figure 1). As mentioned in [START_REF] Loureiro | Mechanically driven dissolution of Sn in near-equiatomic bcc FeCo[END_REF], the broad additional peaks would be due to nanocrystalline hexagonal Co 3 Sn 2 of the B8 2 type with some iron dissolved in it, denoted hereafter as (Fe,Co) 3 Sn 2 . High-energy ballmilling of Co 3 Sn 2 is known to transform the low-temperature orthorhombic phase into the high-temperature hexagonal phase (P6 3 /mmc) [START_REF] Di | Atomic disorder, phase transformation, and phase restoration in Co 3 Sn 2[END_REF]. However, the XRD pattern (CuKα) of amorphous Co 3 Sn 2 , prepared by a solvothermal route, exhibits also a broad halo at ~32° and a second one at ~43° [START_REF] Xie | Electrochemical performance of nanostructured amorphous Co 3 Sn 2 intermetallic compound prepared by a solvothermal route[END_REF] which corresponds here to the position of the (110) peak of the bcc phase (fig. 1). Haloes are observed as well at 32° and 43° in electro-co-deposited Co 33 Sn 67 [START_REF] Tamura | Mechanical stability of Sn-Co alloy anodes for lithium secondary batteries[END_REF]. The formation of amorphous Co-Sn alloys by solidstate diffusion in multilayers or in granular systems is known to take place at room temperature because cobalt is a fast diffuser when dissolved into tin [START_REF] Guilmin | Amorphization of crystalline cobalt and tin multilayers by solid state reaction at room temperature[END_REF][START_REF] Gaffet | Amorphization by solid state diffusion in granular system[END_REF]. Gaffet et al. [START_REF] Gaffet | Amorphization by solid state diffusion in granular system[END_REF] report that amorphous Co 100-z Sn z decomposes for long diffusion times at RT and forms Co 3 Sn 2 for 0<z≤35. We identified too hexagonal (Fe,Co) 3 Sn 2 from narrower peaks of XRD patterns of as-milled samples annealed in the range 673-773K. The formation of a Co-rich (Fe,Co)-Sn amorphous phase, partly crystallized, provides thus a plausible explanation of the systematic presence, for high tin contents, of diffraction peaks, at ~30°, which are asymmetrical with slowly decreasing right tails (figure 1, x=21,26). The presence of crystalline (Fe,Co) 3 Sn 2 is clearly exhibited by the XRD lines at ~30° for x=21, 26, 34 (figure 1).

As-milled alloys: neutron diffraction and Mössbauer spectroscopy

Representative neutron diffraction patterns of as-milled alloys are shown in figure 3 for four values of x and 2 ranging from 20° to 110°. They focus on the angular range in which superlattice lines are expected to appear clearly in annealed alloys and on the (110) line of the bcc phase. Only very small peaks at ~35° and small bumps are observed at ~50° for x=21, 26. The peak shift towards smaller angles when x increases reflects the associated increase of the lattice parameter (figure 2).

Figure 4 shows representative RT 57 Fe and 119 Sn Mössbauer spectra of as-milled alloys.

The mean 57 Fe hyperfine magnetic field at room temperature <B F (x)> decreases fairly linearly with x, <B F (x)> (T) = 34.7-0.25x. The field <B F (0)>=34.7 T is consistent with the HMF's measured in mechanically alloyed FeCo which are all reported to be close to 35 T [START_REF] Pochet | Order-disorder transformation in Fe-Al under ball milling[END_REF][START_REF] Brüning | The mixing of iron and cobalt during mechanical alloying[END_REF][START_REF] Elkakouli | Mechanical and magnetic properties of nanocrystalline FeCo alloys produced by mechanical alloying[END_REF][START_REF] Sorescu | Structural and magnetic properties of Fe50Co50 system[END_REF][START_REF] Moumeni | Structural properties of Fe50Co50 nanostructured powder prepared by mechanical alloying[END_REF]. The mean 57 Fe isomer shift of as-milled bcc alloys increases rather linearly from 0.06(4) mm/s for x=0 to 0.20(4) mm/s for x=26 [START_REF] Loureiro | Mechanically driven dissolution of Sn in near-equiatomic bcc FeCo[END_REF]. The rate of decrease of the mean 57 Fe HMF is comparable to the one measured in supersaturated bcc Fe 100-x Sn x , <B F (x)> ≈ 33.1-0.30x (T) (0≤x≤30) [START_REF] Cabrera | Time and composition dependence of mechanical alloying of Fe 1-x Sn x[END_REF]. Diamagnetic Sn reduces the average Fe HMF when dissolved in bcc FeCo as it does in bcc Fe. Further, the Curie 57 Fe HMF is ~34.9 T. The latter field reveals that Sn atoms have been expelled from near-equiatomic bcc FeCo as expected from the low equilibrium solubility of Sn in FeCo [START_REF] Delyagin | Hyperfine magnetic fields for 119 Sn atoms in ferromagnetic CoFe[END_REF][START_REF] Huffman | Hyperfine fields at 119 Sn nuclei in ordered Fe-Co and -Fe-Mn. CoFe[END_REF][START_REF] Campbell | Magnetic hyperfine fields at Fe, Cd and Sn sites in an FeCo alloy[END_REF]. 57 Fe Mössbauer spectra (figure 7, [START_REF] Kovacheva | Synthesis and characterization of magnetic nano-sized Fe 3 O 4 and CoFe 2 O 4[END_REF]). For x=34, as-milled samples decompose already when annealed for 30 min. 57 Fe and 119 Sn Mössbauer spectra, the associated HMFD's and two of their characteristics, <H X > (X=F,S) and H M (section 2), are shown in figures 7 to 11.

57 Fe Mössbauer spectra of annealed samples

Only limited changes of 57 Fe Mössbauer spectra occur after annealing for x ≤ 26 (figure 7). Lines are narrower for the annealed alloys than they are for the as-milled ones and the widths of the HMFD's are thus smaller (figure 9 right for x=12). The mean HMF for x=12 increases for instance from 31.7 T in the as-milled state to 32.9 T after annealing while the standard-deviation decreases from 3.0 T to 2.6 T. The average 57 Fe HMF of Fe 53.3-0.6x Co 46.7-0.4x Sn x annealed alloys (4 ≤ x ≤ 26) decreases fairly linearly when the Sn content increases, <B F (x)> = 34.1-0.10x (T) (figure 11 left), but less rapidly than it does for as-milled alloys, <B F (x)> = 34.7-0.25x (T). Concomitantly, the concentration dependence of the 57 Fe HMF B M is well accounted for by B M (x) =35.0-0.19x (T) in the as-milled state and, for annealed alloys, by B M (x) =34.5-0.11x (T) and 32.6 T when 2 ≤ x ≤ 15 and 15 < x ≤ 26 respectively (figure 11 left).

119 Sn Mössbauer spectra of annealed samples

By contrast to 57 Fe HMF's, 119 Sn HMF's show a great sensitivity to chemical order when dissolved in B2 FeCo (section 4.4). The characteristics of Mössbauer spectra of annealed alloys (figure 8) differ strongly from those of their as-milled counterparts

Discussion

The solubility of tin in as-milled bcc Fe 53.3-0.6x Co 46.7-0.4x Sn x

The maximum solubility x S , in our milling conditions, of Sn in near-equiatomic nanocrystalline bcc Fe 53.3-0.6x Co 46.7-0.4x Sn x ought to be defined classically as the Sn content below which as-milled alloys are bcc and single-phase. A tentative estimate of x S would then be 15±2 at.% (figure 1). However, the lattice parameter of the bcc phase increases gently and regularly with the Sn content even when phases co-exist with it. A clear change of slope is observed only for x ≈ 26 (figure 2). Extra peaks become for instance more and more visible on the X-ray diffraction patterns of figure 1 and on the 119 Sn Mössbauer spectra of figure 4 for x ≥ 21. Concomitantly, the 57 Fe and 119 Sn Mössbauer spectra (figure 4) and the derived hyperfine magnetic field distributions of the bcc phase [START_REF] Loureiro | Mechanically driven dissolution of Sn in near-equiatomic bcc FeCo[END_REF] evolve regularly with x. The faster decrease of the mean 57 Fe HMF's observed for x>21 (figure 4, figure 5 of [START_REF] Loureiro | Mechanically driven dissolution of Sn in near-equiatomic bcc FeCo[END_REF]) is due both to the large Sn contents and to the ensuing decrease of the Curie temperature, as observed for instance in bcc Fe-Sn [START_REF] Yelsukov | Structure and magnetic properties of Fe 100-x Sn x ( 3.2 < x < 62) alloys obtained by mechanical milling[END_REF][START_REF] Arzhnikov | Concentration dependence of the magnetization and the Curie temperature in disordered Fe-M alloys (M=AI, Si, Sn)[END_REF] or in amorphous Fe-Sn alloys [START_REF] Rodmacq | Structure and magnetic properties of amorphous Fe x Sn 1-x alloys[END_REF]. The x=34 as-milled alloy seems however to differ from those with x ≤ 26 (see below).

A solubility, x S =15±2 at.%, makes then the aforementioned results puzzling for x > x S . The evolution of the characteristics of the bcc phase beyond the latter content requires to be interpreted from non-equilibrium features of mechanical alloying. A possible explanation relies on the external forcing action of mechanical alloying at low temperatures which drives the milled system toward composition homogenization [START_REF] Ma | Calorimetric Evidence for Polymorphous Constraints on Metastable Zr-Al Phase Formation by Mechanical Alloying[END_REF].

The latter phenomenon is exemplified by mechanically alloyed binary Fe-Ni alloys (negative heat of mixing) and Fe-Cu alloys (positive heat of mixing) which exhibit similar dynamical phase diagrams ( [START_REF] Schilling | Overlapping solid solubility in mechanically alloyed Fe-Ni and Fe-Cu[END_REF] and references therein). These diagrams consist of two terminal solid solutions, bcc on the Fe side and fcc on the Ni (rsp. Cu) side and, in between, of a two-phase region where the bcc and the fcc solutions have everywhere the same composition as the overall alloy. For instance, the solubility of Ni in the bcc Fe-Ni phase is not limited to the maximum Ni content of the bcc terminal solution at 15% Ni, but extends through the two-phase (bcc+fcc) region to the minimum Ni content of the fcc terminal solution at 40% [START_REF] Schilling | Overlapping solid solubility in mechanically alloyed Fe-Ni and Fe-Cu[END_REF].

A transposition of the previous idea to as-milled Fe-Co-Sn might consist of a one-phase bcc region up to ~15 at.% followed by a two-phase region (bcc+amorphous) up to ~26 at.% Sn, in which the two polymorphs would have the same composition. In addition, the amorphous phase would be partly decomposed into hexagonal (Fe,Co) 3 Sn 2 as discussed in section 3.1 and into a bcc Fe-Co alloy. The upper tin content, ~26 at.%, is chosen here because the most marked changes take place between x=26 and x=34: a) for XRD patterns, with the sharpest 30° peak at x=34 (figure 1) b) for the composition dependence of the lattice parameter (figure 2) and c) for 57 Fe and 119 Sn Mössbauer spectra (figure 4). Finally, as-milled Fe 34.7 Co 31.3 Sn 34 decomposes after annealing for 30 min at 673K in contrast to as-milled powders with x ≤ 26.

To conclude, the amount of tin which can be really dissolved in near-equiatomic bcc Fe-Co alloys in our milling conditions is certainly much closer to 26 at.% than to 15 at.%. Consistently, we show below that annealed alloys order to a B2 structure for tin contents as large as 26 at.%. The Sn content of ~15 at.% remains however remarkable in many respects (section 4.4.3).

Neutron diffraction patterns of annealed Fe 53.3-0.6x Co 46.7-0.4x Sn x

The LRO parameter S of B2 Fe 1-z Co z is defined as S= 2([Fe] Fe -1+z) as the vacancy concentration is negligible [START_REF] Neumayer | Atomic defects in FeCo: stabilization of the B2 structure by magnetism[END_REF]. Here [Fe] Fe is the iron concentration on the Fe sublattice and 0 ≤ S ≤ 1-2│z-0.5│( [START_REF] Ziller | Metastable and transient states of chemical ordering in Fe-V nanocrystalline alloys[END_REF] and references therein, [START_REF] Fultz | Transmission Electron Microscopy, Diffractometry of Materials[END_REF]). The intensities of diffraction lines of B2 Fe 1-z Co z are governed by S and by f Fe and f Co which are respectively atomic form factors for X-ray diffraction and neutron coherent scattering lengths for neutron diffraction, generally denoted as b Fe (=9.45 fm) and b Co (=2.49 fm).

Diffraction patterns of disordered bcc Fe-Co alloys include only fundamental (hkl) lines, with h+k+l even, while patterns of B2 ordered Fe-Co alloys include in addition superlattice lines (hkl), with h+k+l odd. The intensities of XRD fundamental lines are proportional to the square of the average form factor while those of superlattice lines are proportional to S 2 (f Fe -f Co ) 2 [START_REF] Fultz | Transmission Electron Microscopy, Diffractometry of Materials[END_REF]. Since the X-ray form factors for iron and cobalt atoms differ only slightly, the intensities of x-ray superlattice lines are nearly zero and long-range order is hardly evidenced by standard XRD. XRD with CoK radiation might be applied to bcc Fe-Co alloys to evidence LRO through anomalous dispersion, as done for instance for B2 FeCo milled for various times [START_REF] Loureiro | Order-disorder phenomena from X-ray diffraction in FeCo alloys annealed and ground at high energy[END_REF], but neutron diffraction remains the most efficient method when accessible. In contrast to XRD, the neutron coherent scattering lengths of Fe and Co, are different enough to enable superlattice lines to appear.

In the ternary case, it would be necessary to define two long-range order parameters to describe the concentrations of Fe, Co and Sn on the two sublattices (see for instance [START_REF] Chapink | Ordered states in ternary B2-type intermetallic alloys including vacancies[END_REF]). The intensities of fundamental and superlattice lines include nuclear contributions which depend on these two LRO parameters and magnetic contributions which vary according to the considered line and represent at most ~15% of the total intensity. We will not discuss this problem further as we did not analyze line intensities. In any case, the previous discussion, valid for B2 FeCo, remains qualitatively correct in the presence of tin (b Sn =6.225 fm) if the Sn repartition on the Fe and Co sublattices is random or if it is short-range ordered with diffuse scattering between Bragg peaks. It is only in the case of a long-range ordered repartition of Sn that the resulting structure would no more be B2 and that extra superlattice lines would emerge.

The presence of superlattice lines (hkl), with h+k+l odd, establishes unambiguously that the bcc phases of as-milled alloys transform, for x ≤ 26, into long-range ordered B2 phases by annealing at moderate temperatures (figure 6). Superlattice lines are broader than fundamental lines. In the as-milled state, the crystallite size is ~6 nm. Using the Scherrer formula, we estimated the mean crystallite size and the mean size of ordered domains in annealed alloys to be respectively ~10 nm and ~4 nm. When annealed at 723K, a mechanically-alloyed bcc Fe 53 V 47 , yields similarly a B2 phase [START_REF] Ziller | Metastable and transient states of chemical ordering in Fe-V nanocrystalline alloys[END_REF]. As-milled Fe 53 V 47 powders annealed for ~20h have sizes of ordered domains, ~5 nm, which are about half those of crystallites, 9 nm (figure 5 of [START_REF] Ziller | Metastable and transient states of chemical ordering in Fe-V nanocrystalline alloys[END_REF]). The latter values are comparable to those we estimate.

4.3 57 Fe Mössbauer spectra of annealed Fe 53.3-0.6x Co 46.7-0.4x Sn x When a transition A2B2 occurs in FeCo, the mean 57 Fe HMF decreases by an amount which depends on the long-range order parameter S [START_REF] Eymery | Ordre atomique et spectrométrie Mössbauer dans l'alliage Fe-Co équiatomique[END_REF] and is ~0.9-1 T for S=1 [START_REF] Demayo | Atomic ordering transition in FeCo[END_REF][START_REF] Hamdeh | Mössbauer spectrometry study of the hyperfine fields and electronic structure of Fe-Co alloys[END_REF]. Consistently, the field <B F (0)>≈ 34.7 T for as-milled alloys is larger than the corresponding field , <B F (0)>≈ 34.1 T (section 3.3.3), for annealed alloys. A change of slope of B M (x) takes place at ~15 at.% for annealed alloys and B M (x) is essentially constant for x ≥ ~15 at.% (figure 11 left), a tin content which plays also a role in the evolution of 119 Sn spectra as discussed below.

The observed evolution of 57 Fe Mössbauer spectra is consistent with long-range ordering observed from neutron diffraction patterns. However, these spectra alone cannot provide convincing evidence of ordering in annealed alloys. The main contribution of 57 Fe Mössbauer spectroscopy is to confirm that, for x ≤ 26, alloys consist essentially of bcc phases when as-milled and of transformed bcc phases when annealed.

119 Sn Mössbauer spectra 4.4.1 119 Sn Mössbauer spectra of equilibrium solid solutions of Sn in B2 FeCo

Only a few 119 Sn Mössbauer studies were devoted to FeCo [START_REF] Delyagin | Hyperfine magnetic fields for 119 Sn atoms in ferromagnetic CoFe[END_REF][START_REF] Huffman | Hyperfine fields at 119 Sn nuclei in ordered Fe-Co and -Fe-Mn. CoFe[END_REF][START_REF] Campbell | Magnetic hyperfine fields at Fe, Cd and Sn sites in an FeCo alloy[END_REF]. Ordered B2 FeCo and near-equiatomic FeCo were doped with at most 1 at.% of 119 Sn enriched tin. The spectra are composed of a magnetically split component and of a central component which appears as a (weak [START_REF] Huffman | Hyperfine fields at 119 Sn nuclei in ordered Fe-Co and -Fe-Mn. CoFe[END_REF]) "doublet". The HMF's of Sn atoms on the Co sublattice, with eight Fe nearest neighbors in perfectly ordered FeCo, are large, B S (Co) ~23-25 T, with a slight decrease of the field when the cobalt content increases beyond 50 at.% (table 1). By contrast, B S (Fe) is rather close to zero, but definitely different from zero, for Sn atoms on the Fe sublattice, with eight Co nearest neighbors in perfectly ordered FeCo (table 1). From the relative intensities of the two spectral components, Sn is concluded to occupy preferentially sites of the Co sublattice in a sample annealed for weeks at a succession of decreasing temperatures down to 673K and then quenched [START_REF] Huffman | Hyperfine fields at 119 Sn nuclei in ordered Fe-Co and -Fe-Mn. CoFe[END_REF]. A long-range order parameter S close to 1 and the low Sn content account for well-resolved and narrow lines of the magnetic sextet seen for instance in figure 1 of [START_REF] Delyagin | Hyperfine magnetic fields for 119 Sn atoms in ferromagnetic CoFe[END_REF]. The "doublet" intensity was found to increase by a factor of ~5 when a 119 Sn doped-FeCo sample was annealed for 15 days at 873K and quenched [START_REF] Huffman | Hyperfine fields at 119 Sn nuclei in ordered Fe-Co and -Fe-Mn. CoFe[END_REF].

From a collection of 119 Sn HMF's measured at 77K, Delyagin and Kornienko [START_REF] Delyagin | Magnetic hyperfine interaction for tin atoms in metallic ferro-and antiferromagnets with bcc structure[END_REF] proposed a relation which expresses mean HMF's <B S > of diamagnetic Sn in various ferro-and antiferromagnetic bcc alloys: <B S > (T) =-21.8<μ 1 >+0.9<μ 2 >+16.5<μ>. It includes the magnetic moments (in µ B ) <μ k > of atoms of the first two coordination shells around the considered tin atom (k=1,2) and an additional contribution from more remote shells whose total effect is taken to be proportional to the average magnetic moment of the alloy, <μ>. As the Curie temperature of B2 FeCo is high, T C =1253K [START_REF] Sundar | Soft magnetic FeCo alloys: alloy development, processing, and properties[END_REF], the decrease of Sn HMF's between 0K and RT is only of the order of 10% [START_REF] Huffman | Hyperfine fields at 119 Sn nuclei in ordered Fe-Co and -Fe-Mn. CoFe[END_REF] which is the expected precision of the estimates obtained from this semi-empirical model. In other words, the precise values of the measurement temperatures of the HMF's between 0K and RT don't need to be considered to get the estimates given below. At 0K, the mean magnetic moments <μ Fe > are 3.02 µ B and 2.92 µ B in disordered A2 FeCo and in ordered B2 FeCo respectively while the moments <μ Co > are respectively 1.81 µ B and 1.62 µ B [64][START_REF] Kulkova | The electronic properties of FeCo, Ni 3 Mn and Ni 3 Fe at the order-disorder transition[END_REF][START_REF] Bhatia | Magnetic moments in the Fe-Co system[END_REF]. The previous model yields then <B S (Co)>= -23.6 T and <B S (Fe)> =+2.5 T.

Table 1 compares mean 119 Sn HMF's measured at RT in various Fe x Co y Sn 100-x-y alloys.

The 119 Sn HMF's in bcc Fe 100-z Sn z alloys reach their maximum for dilute alloys and decrease steadily when z increases [START_REF] Cabrera | Time and composition dependence of mechanical alloying of Fe 1-x Sn x[END_REF][START_REF] Yelsukov | Structure and magnetic properties of Fe 100-x Sn x ( 3.2 < x < 62) alloys obtained by mechanical milling[END_REF]. The maximum HMF in table 1 is by far the field of tin atoms on the Co sublattice of B2 FeCo. The corresponding mean fields are expected to be smaller for Sn-rich near-equiatomic Fe-Co alloys than they are for dilute alloys as explained below. The HMFD's obtained from 119 Sn spectra of annealed alloys differ strongly from their counterparts in as-milled alloys which are approximatively Gaussians with values of The mean and the width of the HMFD P S (B) are related to the characteristics of the distribution P Co (x,n) which evolve both when x increases and when the long-range order parameter decreases. The maximum value of the LRO parameter in various nanocrystalline materials is reduced typically to ~80% of the value expected at equilibrium in bulk samples ( [START_REF] Ziller | Metastable and transient states of chemical ordering in Fe-V nanocrystalline alloys[END_REF] and references therein). Ab initio calculations of the 57 Fe hyperfine magnetic field in B2 FeCo predict fields whose magnitudes are smaller than the experimental fields by ~7.5 T or ~6 T according to the method used [START_REF] Samara | On the magnetic properties and hyperfine fields in Fe-containing alloys: A theoretical study[END_REF]. This constitutes an additional difficulty for trustworthy calculations of 119 Sn HMF's in dilute alloys of Sn in B2 FeCo. Presently, it seems hopeless to account theoretically for 119 Sn HMFD's in the concentrated and partly disordered Fe-Co-Sn alloys we studied and thus to extract from them a detailed information about short-range order. Fortunately, mean HMF's and the two components of HMFD's carry valuable information about the existence of a long-range ordered B2 phase in these alloys and about the repartition of tin between its two sublattices (next section).

                 n where m k    (1) n (2) 2 
To conclude 119 Sn Mössbauer spectra, with a broad component at HMF's much larger than 10 T, prove unambiguously that annealed bcc Fe 53.3-0.6x Co 46.7-0.4x Sn x order to a B2 type structure in agreement with neutron diffraction results. x ≤ 12 (figure 10). To make it more quantitative, we calculated, as a function of x, the fractions of 119 Sn atoms whose hyperfine magnetic fields are either less or equal to 5 T (F S (5)) or less or equal to 7 T (F S ( 7)) (figure 12). These fractions are fairly well representative of the fraction of tin atoms whose number of Co neighbors is large, either equal to eight or close to it (section 4.2). The values of F S (5) and of F S [START_REF] Buschow | Note on the magnetic and magneto-optical properties of Ni 2 In type 3d transition metal compounds[END_REF] at 15K are used for x=21, 26.

Evolution with x of the repartition of tin on the Fe and Co sublattices of the B2 phase

In any case, the latter are equal to or smaller than their corresponding values at RT.

Both F S (5) and of F S (7) display a change of slope at ~15 at.% (figure 12). This suggests that short-range order of tin atoms evolves with x. In annealed alloys, Sn atoms tend then to have much more Fe neighbors than Co neighbors for x below ~15 at.% and vice versa for x beyond ~15 at.%.

The extent of B2 ordering in Fe-Co-Sn alloys

The occurrence of metastable B2 ordering is established with certainty from neutron diffraction patterns and 119 Sn Mössbauer spectra in Fe 53.3-0.6x Co 46.7-0.4x Sn x for x ≤ 26.

As discussed in section 1.1, it exists too for Fe 50 Co 25 Sn 25 and possibly for other alloy compositions such as Fe 75-x Co x Sn 25 (0 ≤ x ≤ 75). Combining all results, we conclude that long-range order of B2 type exists most likely over a significant concentration range for Sn-rich Fe-Co-Sn alloys. This conclusion is not really surprising for the present alloys when their tin contents are small. However, the fact that equiatomic FeCo orders in that way does not imply that bcc Fe 53.3-0.6x Co 46.7-0.4x Sn x solid solutions, with a very high degree of supersaturation, have to order similarly. The association of two 3d

elements with an sp element plays without doubt a role in the observed ordering. Neutron diffraction patterns and 119 Sn Mössbauer spectra prove unambiguously that the bcc phases of as-milled alloys transform into B2 phases for 2 ≤ x ≤ 26 when annealed at 673K. Beyond long-range order, 57 Fe and 119 Sn Mössbauer spectra provides evidence that the previous tin content, ~15 at.%, marks too the separation between domains with different repartitions of tin atoms between the two sublattices of the B2 structure.

Conclusions

Mechanosynthesized ternary alloys with overall composition

Combining our results with published results, we are led to conclude that metastable B2 alloys are formed over a significant concentration range in Sn-rich ternary Fe-Co-Sn alloys.

Figure 1 -

 1 Figure 1-X-ray diffraction patterns of as-milled (10h) Fe 53.3-0.6x Co 46.7-0.4x Sn x for the indicated tin contents (Cu K, λ =0.1542 nm). The most significant peaks of hexagonal (Fe,Co) 3 Sn 2 (B8 2 -type) are shown by asterisks. (color online)

Figure 2 -

 2 Figure 2 -Evolution with tin content of the lattice parameter of the bcc phase of as-milled Fe 53.3-0.6x Co 46.7-0.4x Sn x (milling times range from 8h to 16h).

Figure 3 -

 3 Figure 3 -Neutron diffraction patterns (λ =0.252 nm) of as-milled (10h) Fe 53.3-0.6x Co 46.7-0.4x Sn x for the indicated values of x (x increases from right to left). (color online)

Figure 4 -

 4 Figure 4 -RT 57 Fe Mössbauer spectra (left) and 119 Sn Mössbauer spectra (right) of as-milled (10h) Fe 53.3-0.6x Co 46.7-0.4x Sn x for the indicated values of x.

3. 3

 3 Annealed Fe 53.3-0.6x Co 46.7-0.4x Sn x (x ≤ 34) 3.3.1 Choice of an annealing temperature Various alloys were annealed, most often for short times, at moderate temperatures ranging typically from 673K to 873K to select an annealing temperature valid for all tin contents. For instance, the XRD patterns of Fe 53.3-0.6x Co 46.7-0.4x Sn x annealed at 623K for 15 min remain unchanged for x=10, 12, 21, 34 except for line narrowing due to crystallite growth and for the formation of a small amount of CoFe 2 O 4 . The XRD pattern of Fe 41 Co 38 Sn 21 annealed for 12h at 723K shows the presence of the previous oxide, of an intermetallic compound (Fe,Co)Sn of the B35 type and of a bcc alloy whose

Figure 5 presents

 5 Figure 5 presents XRD patterns of Fe 46 Co 42 Sn 12 in the as-milled state and after annealing for 35 min at 673K and for 15 min at 873K. Only minor changes are noted for the sample annealed at 673K (the peak at 35° is due to CoFe 2 O 4[START_REF] Kovacheva | Synthesis and characterization of magnetic nano-sized Fe 3 O 4 and CoFe 2 O 4[END_REF]). The sample annealed at 873K is decomposed. The XRD lines are due to three intermetallic

Figure 5 -

 5 Figure 5-X-ray diffraction patterns of as-milled (10h) Fe 46 Co 42 Sn 12 annealed at two temperatures (1= hexagonal B35 (Fe,Co)Sn, 2=hexagonal (Fe,Co) 3 Sn 2 , 3=tetragonal C16 (Fe,Co)Sn 2 ). (color online)

Figure 6 -

 6 Figure 6 -Neutron diffraction patterns (λ =0.252 nm) of as-milled Fe 53.3-0.6x Co 46.7-0.4x Sn x (6 ≤ x ≤ 26) annealed at 673K for 15h. (color online)

Figure 7 -

 7 Figure 7 -RT 57 Fe Mössbauer spectra of as-milled (10h) Fe 53.3-0.6x Co 46.7-0.4x Sn x annealed at 673K for 15h.

Figure 8 -

 8 Figure 8 -RT 119 Sn Mössbauer spectra of as-milled (10h) Fe 53.3-0.6x Co 46.7-0.4x Sn x annealed at 673K for 15h.

Figure 9 (

 9 left) compares 119 Sn HMFD's of as-milled and of annealed powders for x=12. The former HMFD is approximatively Gaussian with <B S (12)>≈B M (12)=9.8 T and a standard-deviation of 4.8 T. The latter is split in two main peaks, one at ~1.5 T and a broad peak with B M ~20.6 T. The resulting mean HMF is then 13.6 T for annealed Fe 46 Co 42 Sn 12 .

Figure 9 -

 9 Figure 9 -RT hyperfine magnetic field distributions ( 119 Sn: left, and 57 Fe: right) of Fe 46 Co 42 Sn 12 : in the as-milled state (10h) and after annealing at 673K for 15h. (color online).

4. 4 . 2 119

 42 Sn Mössbauer spectra of annealed Fe 53.3-0.6x Co 46.7-0.4x Sn x

  r =(n Fe[START_REF] Sourmail | Near equiatomic FeCo alloys: constitution, mechanical, magnetic properties[END_REF], 8-n Fe[START_REF] Sourmail | Near equiatomic FeCo alloys: constitution, mechanical, magnetic properties[END_REF],0, 6-n Co[START_REF] Neumayer | Atomic defects in FeCo: stabilization of the B2 structure by magnetism[END_REF],n Co[START_REF] Neumayer | Atomic defects in FeCo: stabilization of the B2 structure by magnetism[END_REF],0) and n Fe (1)=0,..,8, n Co (2)=0,..,6. In contrast to narrow lines of Mössbauer spectra of Sn diluted in FeCo with S≈1[START_REF] Delyagin | Hyperfine magnetic fields for 119 Sn atoms in ferromagnetic CoFe[END_REF], the broad lines of the magnetic component at ~20 T (figures 8 and 10) arise mainly from a variety of atomic environments of Sn atoms on the Co sublattice as quantified by the probability distribution P Co (x,n) discussed above. Part of line broadening comes from ultrafine ordered domains which result in a high density of antiphase boundaries.The environments of Sn atoms located in these boundaries are perturbed as compared to those of Sn atoms inside domains. The evolution with x of < B S (x)> and of B M (x) is shown in figure11(right). Their slow decrease with tin content (x ≤ 21) is first caused by a decrease of the Curie temperature. An additional effect on the Sn HMF's comes from a deviation from 1 of the ratio of Fe content to Co content (table 1,[START_REF] Campbell | Magnetic hyperfine fields at Fe, Cd and Sn sites in an FeCo alloy[END_REF]).

Figure 10 -

 10 Figure 10 -119 Sn hyperfine magnetic field distributions of as-milled (10h) Fe 53.3-0.6x Co 46.7-0.4x Sn x annealed at 673K for 15h (right) : (left) distributions at RT for the indicated values of x) and (right) distributions at 15K for x=21, 26. (color online).

Figure 11 -

 11 Figure 11 -As-milled (10h) Fe 53.3-0.6x Co 46.7-0.4x Sn x annealed at 673K for 15h: 57 Fe (left) and 119 Sn (right) HMF's at RT: < B F > and < B S > (empty circles), and B M (solid circles) as a function of x. For comparison, < B S > is shown for as-milled alloys (right, empty squares) (the associated B M almost coincides with it). (color online).

Figure 12 -

 12 Figure 12 -As-milled (10h) Fe 53.3-0.6x Co 46.7-0.4x Sn x annealed at 673K for 15h: Fraction at RT of 119 Sn atoms whose HMF's are either less or equal to 5 T (empty circles) or less or equal to 7 T (solid circles), as a function of x for x ≤ 19. The values at 15K are plotted for x=21, 26 (empty squares for 5 T and solid squares for 7 T). The dashed lines are guides to the eye.

  Fe 53.3-0.6x Co 46.7-0.4x Sn x (2 ≤ x ≤ 34), are composed of a supersaturated bcc phase for x<~15 at.%. For larger values of x, as-milled powders consist primarily of a bcc phase with steadily increasing tin contents and of extra phases which include hexagonal (Fe,Co) 3 Sn 2 . The tin content which can be really dissolved in near-equiatomic bcc Fe-Co alloys in our milling conditions appears thus to be much closer to 26 at.% than to 15 at.%.

  3. The Fe (rsp. Co) content is larger (rsp. smaller) than its nominal content. A Cr content less than 0.2 at.% is neglected hereafter. The overall composition is well described by Fe 53.3-0.6x Co 46.7-0.4x Sn x where the calculated Fe and Co contents are accurate to within ~0.3 at.% for 2 ≤ x ≤ 26. The alloy composition is Fe 34.7 Co 31.3 Sn 34 for x=34. For the sake of simplicity, while remaining still consistent with the actual precision of composition measurements, any alloy is designated hereafter by Fe, Co and Sn contents rounded to the nearest integers, for instance Fe 35 Co 31 Sn 34 for the latter alloy. Figures are however plotted with tin contents determined by EDS.

  53.3-0.6x Co 46.7-0.4x Sn x alloys (x ≤ 34) The formation of metastable bcc Fe 53.3-0.6x Co 46.7-0.4x Sn x by mechanical alloying takes place in two steps as shown by a study of a representative alloy, Fe 46 Co 42 Sn 12

Table 1 :

 1 Mean119 Sn hyperfine magnetic fields, <B S > (T), measured at RT in Fe x Co y Sn 100-x-y alloys (preparation method: LH= melting+cooling+heat treatment, MA=mechanical alloying, SSD=solid state diffusion).Intense peaks emerge in the 119 Sn hyperfine magnetic field distributions at RT at field values of ~20 T for any x ≤ 21 as expected when annealed bcc Fe 53.3-0.6x Co 46.7-0.4x Sn x phases order to a B2 structure (figures 8 and 10). To get rid of a significant effect of a lower Curie temperature on the RT spectra, 119 Sn Mössbauer spectra were recorded at 15K for x=21 and 26. The associated HMFD's are shown in figure10(right). Although the broad magnetic component shifts downwards when x increases, it is still centered on

	Composition (at.%) <B S > (T) [reference] preparation, structure
	Fe 99.5 Sn 0.5	7.89 [60]	LH, bcc
	Fe 92 Sn 8	5.9 [30]	MA, bcc
	Fe 82 Sn 18	4.5 [30]	MA, bcc
	Fe 80 Sn 20	4.0 [39]	MA, bcc
	Fe 3 Sn	8.3 [61]	SSD, D019
	Co 98 Sn 2	3.6 [62]	quench, hcp
	Co 99.5 Sn 0.5	1.7 [62-63]	LH, fcc
	B2 alloys	Co sublattice	preparation, structure
	Fe 49.9 Co 49.9 Sn 0.2	25.2* [26]	LH, B2
	Fe 49.5 Co 49.5 Sn 1	25.3 [27]	LH, B2
	Fe 47.3 Co 52.4 Sn 0.3	23.1 [28]	LH, B2
	B2 alloy	Fe sublattice	preparation, structure
	Fe 49.5 Co 49.5 Sn 1	0.7* [26]	LH, B2
	* HMF's measured at 77K mentioned to be hardly altered between 77K and RT
	< B S (x)> and B M (x) both close to 10 T (figure 9 left and figure 11). We note in passing
	that the previous semi-empirical relation may be applied to bcc Fe 46 Co 42 Sn 12 alloy
	assuming no changes of the mechanisms which determine the tin hyperfine fields. The
	moments <μ Fe > and <μ Co > are simply replaced by the mean magnetic moment per
	transition metal atom, <μ T > =2.05 μB, which is measured at 5K (figure 3 of [31]). The
	predicted value, <B S (x=12)>=-9 T, is in good agreement with the experimental result
	(9.5 T [30]) as signs cannot be determined from Mössbauer spectra in zero applied
	magnetic field.

Acknowledgements

This paper is dedicated to the memory of Alain Reza Yavari (SIMAP, Grenoble INP).

The financial support of the bilateral Portuguese-French program FCT-CNRS is gratefully acknowledged. We thank ILL for the provision of neutron beam time. We thank P.M. Gordo (Physics Department, University of Coimbra), A. Ramalho (Department of Mechanical Engineering, University of Coimbra) and P. Delcroix (Université de Lorraine) for providing assistance in some aspects of the study. We thank Dr. R. A. Brand (Universität Duisburg-Essen) for useful discussions.