Near equiatomic FeCo alloys: constitution, mechanical and magnetic properties.



T. Sourmail
Department of Materials Science and Metallurgy, University of Cambridge
Pembroke Street, Cambridge CB2 3QZ, U.K.
email:ts228@cus.cam.ac.uk
Prog. Mater. Sci., in press, downloaded from www.thomas-sourmail.org.
Get pdf file.


Abstract
Alloys based on the near-equiatomic FeCo offer exceptional magnetic properties. The equiatomic alloy was `invented' in 1929, it offers a saturation hardly lower than that of the maximum obtained for Fe-0.35Co, with higher permeability and a lower coercivity than the latter. However, this alloy remained without industrial application, mainly because of its extreme brittleness. Only with the addition of a third element did it become possible to impart sufficient ductility for cold-rolling, and develop applications as laminated products. The addition of 2 wt% vanadium (1932) led to the ubiquitous FeCo-2V, or Permendur. It not only imparts, given appropriate heat-treatments, sufficient ductility, but also increases significantly the resistivity of the alloy while having little impact on the saturation.

From a scientific point of view, the FeCo alloys, with their B2 structure below 730 $^{\circ}$C, fall in the interesting category of ordered compounds. The ordering reaction has significant influence on the mechanical and magnetic properties and has therefore prompted a number of investigations. Not surprisingly, the vast majority of the work published to date concerns the FeCo-2V or its variants, rather than the binary alloy or other ternary systems. Recently though, alternative compositions, or improvement on the basic FeCo-2V have been put forward.

This review attempts to summarise the current knowledge about the constitution, mechanical and magnetic properties of these alloys, focussing on the general properties of bulk FeCo and FeCo-X alloys (developped for applications such as rotor or stator laminations in motors). Recent developement of nanocomposite and nanocrystalline materials such as HITPERM are not considered. A review of this developements is available in reference [1]. An overview is given of work undertaken to date on various FeCo-X ternary system, with emphasis on the influence of these ternary additions on microstructure and characteristics of the phase diagram. The problem of the kinetics of ordering is given particular attention. Magnetic and mechanical properties are then discussed with emphasis on the relationship between microstructure and properties, and the main quantitative theories put forward are assessed again data gathered from the literature. It is shown that, while some points are clearly understood, a number of question remains in different areas which are outlined.
Keywords: iron-cobalt alloys; soft magnetic materials, Hiperco, Permendur

Contents

Introduction

Iron-cobalt based alloys exhibit particularly interesting magnetic properties, with high Curie temperatures, the highest saturation magnetisations, high permeability, low losses and are relatively strong. These alloys are expensive, so are, since their discovery by Elmen in 1929 [2], confined to applications where a small volume and high performances were critical. The `invention' of the FeCo-2V alloy in 1932 by White and Wahl [3] was a critical step in achieving an alloy of industrial relevance. Since then and despite much research, few new compositions have emerged. This is because all solute additions tend to reduce the saturation of the alloy and in general increase its coercivity, thereby degrading its magnetic performances.

There has been a resurgence of interest in these alloys, particularly in the context of the more electric engine [4], which poses a challenge for existing magnetic materials. It is envisaged, in the more electric engine concept, that there will be a greater use of embedded electrical generators and electro-magnetic bearings. To date however, a number of aspects of the FeCo-X system also remain elusive, most remarkably perhaps the role of vanadium in improving the ductility of the equiatomic alloy.

As is true for most metallic materials, a good understanding of magnetic or mechanical properties often requires a knowledge of the microstructure. This review therefore covers the microstructural aspects of FeCo alloys, attempting to sum up the knowledge available to date and identifying areas where further work is required. Because of the particular attention the ordering reaction (b.c.c. to B2 structure) has received in the literature, an entire section has been entirely dedicated to its study, detailing the methods of investigation, the influence of ternary additions of heat-treatment and of cold-work. The first section deals with the microstructure of the different alloys which have been investigated to date, that is, essentially, the transition from b.c.c. (body centred cubic) at low temperature to f.c.c. (face centred cubic) at high temperature, and the precipitation phenomena. The last section concerns the strength and ductility of these alloys, many aspects of which remain without clear explanations. Finally, a short overview is given of the most recent areas of interest.

Most of the literature refers to equiatomic alloys as `FeCo', sometimes not specifying the exact composition which can however be off stoichiometry by one or two percent. The units are also frequently omitted when describing a Fe-50%Co, this is of little consequence given the similar atomic masses of Fe and Co but nevertheless introduces an uncertainty of similar amplitude (equiatomic being Fe-51.3Co wt%). In the following, the compositions have been detailed whenever possible.

Constitution of FeCo and FeCo-X alloys

As discussed below, near-equiatomic FeCo alloys are b.c.c. at low temperature and f.c.c. at temperature above $\sim$ 983 $^{\circ}$C. The b.c.c. phase orders to a B2 structure at temperatures below $\sim 730$ $^{\circ}$C. In a first part, the main constituents of the different FeCo based alloys are discussed; the ordering reaction is dealt with separately in the next section.

Thermodynamics of the FeCo system

Phase equilibria in the Fe-Co system are somewhat out of the scope of this review which is mainly concerned with equiatomic (or close to) compositions. It seems nevertheless useful to give a brief reminder of the phase diagram (figure 1).

Figure: The Fe-Co binary diagram as given in [5]. Tc denotes the Curie temperature.
\begin{figure}\centering\epsfig{file=./figures/X60_FeCo_binary_2.eps,width=9cm}\end{figure}

Equiatomic FeCo alloys have a b.c.c structure ($\alpha$ in figure 1) below $\sim 983$ $^{\circ}$C, with a lattice parameter given by [6]:

$\displaystyle a_{\alpha} / {\mathrm{nm}}$ = $\displaystyle 0.28236 + 6.4514\times10^{-5}{\mathrm {[at\% Fe]}}$  
$\displaystyle a_{\alpha_{2}} / {\mathrm{nm}}$ = $\displaystyle 0.28250 + 6.4231\times10^{-5}{\mathrm {[at\% Fe]}}$ (1)

and a f.c.c one ($\gamma$ in figure 1) above this temperature, with a lattice parameter given by:
\begin{displaymath} a_{\gamma} / {\mathrm{nm}} = 0.35438 + 1.0233\times10^{-4}{\mathrm {[at\% Fe]}} \nonumber \end{displaymath}  

There is confusion in the terminology used to refer to the different phases. The high-temperature f.c.c. phase has been referred to as $\gamma$, the disordered b.c.c. phase as $\alpha_{1}$, and its ordered state as $\alpha_{1}'$. (for example, [7]).

If FeCo or FeCoV alloys are quenched from a temperature inside the $\alpha_{1}+\gamma$ region, the remaining $\gamma$ undergoes a martensitic transformation to the b.c.c. phase. The latter has sometimes been referred to as $\alpha_{2}$ [7,8,9].

Ashby et al. have instead used $\alpha_{2}$ to refer to the ordered state of the b.c.c. phase, and $\alpha_{1}'$ for the martensite. They have further distinguished between $\gamma_{1}$, the high-temperature f.c.c. phase, and $\gamma_{2}$, the vanadium, cobalt-rich ordered f.c.c. phase that precipitates during ageing below $\sim 712$ $^{\circ}$C (in FeCo-2V, [10]). We propose to follow a similar terminology, which is consistent with that used for steels, but not stating the index 1 , i.e. $\alpha$, $\alpha_{2}$ (ordered), $\alpha'$ (martensite), $\gamma$ and $\gamma_{2}$ (ordered f.c.c. precipitate).

The binary FeCo system has been the object of detailed studies by Ellis and Greiner (1941,[11]), Normanton et al. (1975,[12]) and more recently by Ohnuma et al. (2002,[6]) and it seems reasonable to state that there is now a good thermodynamic description of it.

A point remains obscure however, which is the so-called `550 $^{\circ}$C anomaly' [13,1,14] corresponding to a secondary peak in heat-capacity below that for the ordering reaction. There is much confusion even about its existence which appears to be strongly sensitive to heat-treatments and measurement conditions. It has been suggested, without further explanation, that this is a kinetic effect as it is not observed in measurements where the temperature is varied slowly enough [15,12], however recent works also have questioned this assumption [13], and in one case, even proposed that this corresponds to a phase-transition [14], as discussed in section 3.3.

The Fe-Co-V system

This section is concerned with the Fe-Co-V system in regions of interest for typical FeCo-2 alloys, i.e. compositions close to equiatomic FeCo with small additions of V.

In spite of the fact that the FeCo-V alloys are the only one to have been industrially produced (FeCo being too brittle), the determination of the phase diagram leaves many areas which need clarification.


$\alpha/\alpha+\gamma$ boundary

A number of studies have focused on the determination of the $\alpha / \alpha+\gamma$ and $\alpha+\gamma / \gamma$ boundary [16,17,8,7,18,9,10]. It is undisputed that vanadium additions reduce both the $\alpha/\alpha+\gamma$ and $\alpha+\gamma/\gamma$ transition temperatures (further denoted $T_{\alpha/\alpha+\gamma}$ and $T_{\alpha+\gamma/\gamma}$).

It has emphasised [19,10] that there exists significant discrepancy between the different estimations of these temperatures. It also appears that no further assessment of the Fe-Co-V system has been undertaken. Figure 2 illustrates the differences between the prediction obtained with the thermodynamic calculation software MT-DATA [20] and different estimations of the two-phase region.

Figure: Isopleth section at 52 at% Co for the FeCoV system. Dotted lines indicate the calculation made using MT-DATA and the SGTE solution database, solid lines and data point are from Koster et al. [21,22]; $\circ$ are points identified as single-phased regions and $\bullet$ as two-phases regions.
\begin{figure}\centering\epsfig{file=./figures/Koster.eps,width=12cm}\end{figure}

Figure 3 illustrate a similar isopleth as determined by Martin and Geisler [16], which suggests a solubility of up to 4 wt% V around 700 $^{\circ}$C. It is also noticeable that ordering is not found past 10 wt% V, this has been also reported by Foutain and Libsch [15].

Figure: Isopleth section at 52% Co in FeCo-V system, after Martin and Geisler [16]. Solid lines indicate boundaries determined by thermal analyses, phases are otherwise identified by X-ray diffraction.
\begin{figure}\centering\epsfig{file=./figures/Martin.eps,width=8cm}\end{figure}

As mentioned above, there is agreement that vanadium lowers $T_{\alpha/\alpha+\gamma}$ and $T_{\alpha+\gamma/\gamma}$, but authors have emphasised the large interval of estimated values. However, it appears that the exact stoichiometry has sometimes been neglected in comparisons. For example, while some of the values obtained by Martin and Geisler [16], or Ashby et al. [10] are for equiatomic content in Fe and Co, other values are for alloys with identical wt% of Fe and Co, which corresponds to an excess of Fe in at% (for example, Bennett and Pinnel, [7]).

Figure 4 superimposes results from a number of studies, and shows that there is reasonable agreement between the values obtained by Martin and Geisler [16] by thermal analysis (lines), and the phases identified by Ashby et al. [10] in materials quenched from high-temperature after 24 h heat-treatment, in equiatomic FeCo-2V. However, data obtained from alloys with excess Fe (empty symbols in figure 4) seem to indicate higher values for $T_{\alpha/\alpha+\gamma}$ and $T_{\alpha+\gamma/\gamma}$, while values for alloys with Co excess (crossed symbols in 4) seem to lie lower than those estimated for equiatomic alloys. From this, it could be proposed that, in composition with excess Fe (empty symbols), vanadium does not depress $T_{\alpha/\alpha+\gamma}$ and $T_{\alpha+\gamma/\gamma}$ as strongly, while it is more efficient in alloys with excess Co.

This may not be the case, though, as the results obtained by Kawahara [23] who reports $T_{\alpha/\alpha+\gamma}$=882 $^{\circ}$C and $T_{\alpha+\gamma/\gamma}$=945 $^{\circ}$C (averaging values measured during heating and cooling) for an alloy with 51Fe-47Co-2V (at%), are in excellent agreement with the results from Martin and Geisler [16] despite the off-stoichiometric composition.

Figure: The $\alpha/\alpha+\gamma$ and $\alpha+\gamma/\gamma$ boundaries as a function of vanadium content in an equiatomic FeCo alloy, as measured by Martin and Geisler [16] by thermal analysis (lines, dotted lines are average of values measured during cooling and heating), and comparison with other published data [16,7,10]. Filled points represent values for equiatomic compositions, empty points indicate alloys with excess Fe (addition of V at the expense of Co) and crossed points indicate alloys with excess Co (addition of V at the expense of Fe).
\begin{figure}\centering\epsfig{file=./figures/comparison.ps,width=12cm}\end{figure}

It has been mentioned above the the $\gamma$ phase may transform to martensite upon quenching to room temperature. The morphology of the martensite has been reported with a varyingly pronounced lath-like morphology [10,8]. While Mahajan et al. [8] suggest that this might be the result of the transformation being partially massive, partially martensitic, Ashby et al. [10] proposed that this is essentially dependent on the vanadium content of the prior $\gamma$ phase: the higher the V-content, the lower the martensite start (Ms) temperature, and the more pronounced is the lath shape.

Additions of vanadium are also reported to lower the ordering temperature (713 $^{\circ}$C for FeCo with 2 wt% V [24]).


Lower temperature phases

There is significant confusion over the phase-diagram at lower temperature. As illustrated in figure 2, Koster and Schmidt (1955,[21,22]) propose that $\gamma$ is found in FeCo alloys with more than 1-2 at% V (it should however be noted that the diagram is not a section through equiatomic FeCo, as wrongly quoted by Chen [17], and that a 2% V addition corresponds to 46Fe-52Co-2V). This section also leaves significant uncertainty about the exact position of the $\alpha/\alpha+\gamma$ boundary at low vanadium content, and proposes that the ordered f.c.c. $\gamma_{2}$ phase only exists at higher vanadium content.

Further investigations, however, do not necessarily support the diagram proposed by Koster and Schmidt, in particular with regard to the formation of $\gamma$ at lower temperatures. For example, Chen (1961, [17]) did not confirm the formation of $\gamma$ phase, after 110 h at 565 $^{\circ}$C, for a FeCo-2V alloy (it must be noted however that many experimental details remain unclarified). Fiedler and Davis (1970, [25]) later reported precipitation of $\gamma$ in a cold-rolled FeCo-2V after 48 h at 680 $^{\circ}$C, and noted that this precipitation was not observed in a sample first recrystallised at higher temperature. They also estimated the composition of the precipitate phase to 22V-65Co-15Fe (wt%). Bennett and Pinnel (1974, [7]) noted the inconsistency between the composition proposed in [25] and the isotherm section of Fe-Co-V proposed by Koster and Schmidt [21], which places the $\gamma$ formed at low temperature in the $\alpha+\gamma+\gamma_{2}$ field. However, the problem remained discussed in terms of $\alpha + \gamma$ equilibrium (for example [8,26]) until the work of Ashby et al. (1976, [10]), who proposed that the phase precipitating at low temperature is not $\gamma$ but a Fe-substituted variant of the Co3V compound, (Fe,Co)3V, with L12 structure (ordered f.c.c.), vanadium occupying the corner of the lattice and (though not stated) Fe and Co mixing on the face centres.

Although they observed the forbidden reflections {001} and {110} in electron diffraction, they were unable to do so using X-ray diffraction and argued that this was a consequence of the very similar X-ray scattering factor of Fe and Co. This argument is frequently put forward to explain the low intensity of the superlattice reflections of ordered b.c.c FeCo, but it is not clear how it would apply here: if one assumes a random distribution of Co and Fe on the face centres and, with Ashby et al., vanadium on the cube corners, the {110} reflection, for example, relates to $[(0.83f_{\mathrm{Co}}+0.17f_{\mathrm{Fe}})-f_{\mathrm{V}}] \sim(f_{\mathrm{Fe}}-f_{\mathrm{V}})$, and it is therefore the similar scattering factor of Fe,Co and V which explain the difficulty in observing the superlattice peaks (the atomic scattering factor of V is intermediate between Fe and Co, leading to an even smaller difference than in of ordered b.c.c. FeCo so that the conclusion remains valid).

The ordered $\gamma_{2}$ phase has also been reported by Pitt and Rawlings (1981, [18]) in Fe-Co-V-Ni, however there is no explanation of how the L12 structure was identified.

Further investigations have usually accepted the hypothesis of a L12 structure for $\gamma_{2}$ (or that $\gamma_{2}$ was the compound (Fe,Co)3V rather than a prolongation of the high-temperature $\gamma$ phase), for example [23,27,19,28], although it appears that none have obtained independent confirmation of the structure. The composition proposed by Fiedler and Davis [25] was confirmed by Kawahara (1983, [23]) who reported 21V-64Co-15Fe (wt%) for $\gamma_{2}$.

Surprisingly, in a recent investigation on the ageing (200 h at 450 $^{\circ}$C) of FeCo-2V, Zhu et al. [29] report the formation of a primitive cubic second phase, of lattice parameter 2.8278 Å, and although refer to past literature on $\gamma_{2}$, do not comment on the discrepancy with the otherwise accepted structure.

In summary, although it seems accepted that the vanadium rich phase precipitating out of $\alpha$ FeCo-2V below $\sim$ 630 $^{\circ}$C is an iron-substituted form of Co3V, with an ordered L12 structure, there have been no attempts to correct the FeCo-V phase diagram proposed by Koster and Schmidt. The ordered nature of the precipitate has been reported in only one work, and most other observations are based on the composition being close to that expected from such a compound.


Kinetics of precipitation

The kinetics of precipitation of $\gamma_{2}$ have been studied by Ashby et al. [10] for FeCo-2V and Pitt and Rawlings [18] for the same alloy with additions of Ni up to 7.4 wt%.

Figure: TTP diagram for intragranular $\gamma_{2}$ formation in FeCo-2%V, after Ashby et al. [10].
\begin{figure}\centering\epsfig{file=./figures/gamma2_ttp.eps,width=10cm}\end{figure}

After verifying that a 10 ks heat-treatment at 850 $^{\circ}$C produced a fully $\alpha$ microstructure, Ashby et al. aged undeformed, 25% and 50% cold-rolled samples. Their results are summarised in a TTP (time temperature precipitation) diagram reproduced in figure 5. Precipitation occurs preferentially on antiphase boundaries in the undeformed samples; it is accelerated by deformation, $\gamma_{2}$ being found mainly on dislocations and subgrain boundaries in cold-rolled samples. The TTP diagram does not include high-angle grain boundary precipitates which are found at early stages of ageing in all samples.

The time required to observe $\gamma_{2}$ on the grain boundaries is not clear in the work of Ashby et al.; a study by Novotny [30] underlines the absence of any $\gamma_{2}$ after 4 h at 845 $^{\circ}$C followed by cooling at 100 $^{\circ}$C/h, suggesting that grain boundary $\gamma_{2}$ does not occur fast enough to be observed after slow cooling.

A number of studies provide measurements of precipitates volume fraction. Yu et al. [31] reported diameter and volume fraction of precipitates in FeCo-2V and FeCo-2V-0.3Nb during ageing at 600 $^{\circ}$C (figure 6).

Figure: Volume percent and diameter of precipitates during ageing of FeCo-2V and FeCo-2V-0.3Nb according to Yu et al. [31].
\begin{figure}\centering\epsfig{file=./figures/X38_vf.ps,width=60mm}\epsfig{file=./figures/X38_diameter.ps,width=60mm}\end{figure}

Although the problem of determining the volume fraction of small particles is notoriously difficult, and require assumptions as to their shape and distribution, the work published in [31] does not provide any detail about the experimental methods used. The measured composition of $\gamma_{2}$ (about 18V at%) means a maximum mole fraction of about 10% if the solubility of vanadium is taken to be 0 ($\alpha$ and $\gamma_{2}$ having similar molar volume, mole fractions are used in this discussion, but it is expected that volume fraction would be very similar), or 5% if a more realistic assumption of 1% solubility is assumed. Large volume fraction of $\gamma_{2}$ have been reported by different authors [24,28], but in alloys containing up to 6V at%; it was verified that these were consistent with the maximum expected from the composition. The large inconsistency between estimated maximum ($\sim 5\%$) and measured volume fractions ($12-18 \%$) in Yu et al.'s study [31] cast some doubts on the validity of these results, all the more that the authors claim to have confirmed a (FeCo)3M type formula for the precipitates.

Unfortunately, although a number of studies report volume fractions of $\gamma_{2}$ after short annealing treatments [32,18], there does not appear to be data other than those discussed above for aged samples.

Results by Zhu et al. [29] suggest the presence of a vanadium-rich phase in 0.3% volume fraction in FeCo-2V, increasing to 0.8% after 200 h at 450 $^{\circ}$C. However, they report a simple cubic structure with a lattice parameter of 2.8278 Å, while $\gamma_{2}$ is usually accepted that $\gamma_{2}$ is an ordered LI2 structure of lattice parameter 3.56 Å.


Influence of quaternary additions

Nickel additions

Pitt and Rawling [18] have investigated the influence of Ni additions to a FeCo-2%V, varying the Ni content from 0 to 7.4 wt%. The results of their investigations show that nickel stabilises $\gamma_{2}$. This implies that larger amounts are obtained (about 7% of $\gamma_{2}$ after 2 h at 750 $^{\circ}$C for nickel contents between 3.5 and 7.4 wt%. The kinetics are also affected, with times to detect precipitation an order of magnitude smaller with additions of 3.5% Ni and more. The authors suggests that nickel substitute for Fe or Co in the compound (Fe,Co)3V, however not providing evidence of its ordered nature, nor of its exact composition, which is only reported to be vanadium and nickel rich. There are a number of problems with these results: It is therefore difficult, for lack of direct evidence, and support from the other observations, to accept the hypothesis of Ni substituting for Fe or Co in (Fe,Co)3V. Furthermore, Orrock [19] reported precipitation of a phase of composition close to (Fe,Co)3Ni in FeCo-5Ni (at%). Such a composition would be consistent with the amount of $\gamma_{2}$ increasing with increasing Ni content, and with the volume fractions larger than calculated on the basis of vanadium solubility alone.

The effect of smaller quantities of nickel (<0.7 wt%), corresponding to contamination rather than deliberate additions has been investigated by Novotny [30]. The author proposes that additions of more than 0.3 wt% Ni lead to a significant decrease of $T_{\alpha/\alpha+\gamma}$ and report the presence of martensite in high Ni sample (0.7 wt%) annealed at 885 $^{\circ}$C and cooled at 100 K/h to room temperature.

Mention is also made of the absence of $\gamma_{2}$. This is not inconsistent with the results of Pitt and Rawlings who indicate no $\gamma_{2}$ in lower Ni alloys following slow cooling from 750 $^{\circ}$C.

Niobium additions

There does not appear to have been any systematic study of Nb additions in FeCo-V. As discussed in a later section, it has been proposed that a compound similar to $\gamma_{2}$ forms in FeCo-Nb the system [24,28], however there is no clear agreement over the phases found in FeCoV-Nb. The most commonly studied alloy in this system is potentially Hiperco H50HS (Carpenter Ltd), which contains typically $\sim2$V and $\sim0.3$Nb (wt%) [33,32,34,31,35]; but few studies have investigated the microstructure of this alloy.

Yu et al. (2000, [31]) have suggested occurrence of a $\gamma_{2}$-type phase (figure 6), however, the problems outlined in section 2.2.2 remain, in particular for the FeCoV-Nb system in which the volume fractions reported are totally inconsistent with the suggested compositions of the precipitates. In addition, the phrasing in [31] makes it difficult to separate the findings of the authors from quoted results. Shang et al. (2000, [33]) have, on the other hand, reported formation of niobium carbonitrides in alloys with additions of 0.06 wt% Nb (and $\sim0.01\%$ C) and Laves-phase (Fe,Co)2Nb in alloys with 0.3 wt% Nb. This behaviour is more consistent with, for example, that of Nb in other Fe-based alloys. In austenitic stainless steels, for example, Nb forms NbC to its solubility limit, excess Nb forming Laves phase at a later stage [36]. It is not clear from the work quoted in [33] whether niobium carbides are observed together with Laves phase in materials containing excess Nb.

Other additions

Orrock [19] investigated the effect of tungsten and copper additions to FeCo-V, and reported the formation of f.c.c. copper precipitates (a=0.3608 nm) in an alloy with 5% Cu annealed at 760 $^{\circ}$C. $\gamma_{2}$ was found in FeCo-V with 3 and 5 wt% W additions after annealing at 850 $^{\circ}$C.

Other Fe-Co-X systems

There is data for a few other ternary systems [37,38,39,40,41,42,43]. However, in a number of cases, no further work appear to have been undertaken since the 30s. In most of these investigations, which concern the entire ternary system, the precision is not sufficient to be of any use in the design of equiatomic FeCo alloys.

Fe-Co-Cr

Although the system has been investigated by a number of authors (for example [44,41,45], a review is given in [46]), data in the area of interest for high-saturation equiatomic FeCo alloys are far from accurate and mostly extrapolated or even guessed. The influence of Cr additions on $T_{\alpha/\alpha+\gamma}$ and $T_{\alpha+\gamma/\gamma}$ is illustrated in figure 7.

Figure: The influence of Cr on the $\alpha/\alpha+\gamma$ and $\alpha+\gamma/\gamma$ boundaries. Constructed from the isotherm section in [46]. These isotherms are largely extrapolated if not guessed in this region.
\begin{figure}\centering\epsfig{file=./figures/FeCoCr.eps,width=8cm}\end{figure}

Fe-Co-Ni

Work on Fe-Co-Ni has been reviewed by Rivlin [46]. Figure 8 is a pseudo-binary diagram constructed from isothermal ternary sections published in the literature [47,48,46]. The phases were determined by long-term ageing at the given temperatures.

Figure: The influence of Ni and Mn on the $\alpha/\alpha+\gamma$ and $\alpha+\gamma/\gamma$ boundaries. FeCo-Ni constructed from the isotherm sections in [46]. FeCo-Mn from isotherm sections in [49]. It should be noted that these isotherms are largely extrapolated if not guessed in this region.
\begin{figure}\centering\epsfig{file=./figures/FeCoNi.eps,width=7cm}\epsfig{file=./figures/FeCoMn.eps,width=7cm}\end{figure}

Fe-Co-Mn

Figure 8 shows a construction of the isopleth FeCo-Mn for equiatomic alloys, constructed from the isothermal ternary sections by Köster and Speidel [49]. The authors also reported a significant influence on Tk, which is lowered to $\sim 685$ $^{\circ}$C for a 3 wt% addition of Mn.

As noted in section 5.2, Mn does not impart enough ductility to obtain a cold-workable alloy [50].

Fe-Co-W

The FeCo-W system has been partially studied by Köster [51] and Köster and Tonn [37], although, as mentioned earlier, there is no reliable assessment of the impact of small additions of W to equiatomic FeCo alloys. Orrock [19] report a significant influence of a 1 wt% addition on $T_{\alpha/\alpha+\gamma}$, lowered from 977 $^{\circ}$C to about 910 $^{\circ}$C, while further additions up to 5 wt% do not affect $T_{\alpha/\alpha+\gamma}$. As discussed in section 5.2, W addition do not, in most cases, lead to a workable alloy, which probably explain the little interest in the system.


Fe-Co-Nb

The FeCo-Nb system has been studied by Rezende et al. [52] and Persiano and Rawlings [24,28]. Nb as limited solubility in equiatomic FeCo alloys, estimated to 0.3 at% [24]. This result was obtained for samples furnace cooled from 760 or 850 $^{\circ}$C, and it is therefore not straightforward to assess which temperature it is representative of, particularly as there is evidence that precipitation occurs even during cooling (table 1). Beyond this limit, increasing amounts of spherical paramagnetic particles are found, of composition 49Co-35Fe-15Nb at% [24].

Table: The volume fraction of second phase identified in equiatomic FeCo annealed 2 h at 850 $^{\circ}$C and furnace cooled (FC) or quenched in iced brine (IBQ). After [24]
Nb / at% FC IBQ  
0.62 7 6  
1.24 11 10  
1.77 14 11  


It must be emphasised that, while the authors suggest that this may be the previously mentioned L12 structure, they do not provide evidence for the structure.

According to differential thermal analysis [24], Nb has no impact, either on $T_{\alpha/\alpha+\gamma}$ or Tk. The former (averaged over heating/cooling) appears to vary by less than 5 $^{\circ}$C with increasing amounts of Nb (up to 1.77 at%), and there is no detectable opening of the $\alpha+\gamma$ field as is the case for V additions. Tk is constant and reported as 731 $^{\circ}$C $\pm 2$.

Fe-Co-Si and Fe-Co-Al

Griest et al. [53] reported the effect of small Si and Al additions in FeCo alloys. In thermal analysis studies, silicon was found to raise the ordering temperature but also reduce the amplitude of the corresponding peak (for example, Tk=805 $^{\circ}$C for 2 wt% Si). It also lowered the $T_{\alpha/\alpha+\gamma}$ and $T_{\alpha+\gamma/\gamma}$ temperature, (in the vicinity of 940 $^{\circ}$C for 2 wt% Si). Al was found to have a similar impact on Tc (Tk=808 $^{\circ}$C for 2 wt% Al), but little effect on $T_{\alpha/\alpha+\gamma}$ and $T_{\alpha+\gamma/\gamma}$.

Recrystallisation and grain-growth

As will be discussed later, many of the mechanical and magnetic properties of FeCo based alloys are conditioned by the grain size. It appeared therefore appropriate to discuss the problem of recrystallisation and grain-growth.

Because of the ordering reaction, recrystallisation and grain-growth do not follow standard behaviour. Using X-ray, Borodkina et al. [54] studied the recovery and recrystallisation of FeCo alloys of different stoichiometries. Their results indicate that, while recovery is detected earliest in the equiatomic alloy, recrystallisation is slowest for this composition. In particular, remainders of the deformation texture are still present even after 1 h at 800 $^{\circ}$C. These authors also suggest that recrystallisation does not begin below Tk, with the argument that recrystallisation below Tk implies the formation of a disordered structure, and might therefore not be thermodynamically advantageous. It is not clear why, however, one would assume that recrystallised grains must be disordered.

In further work, Seliskii and Tolochko [55] and Goldenberg and Seliskii [56] studied the same problem using optical microscopy instead of X-rays, and reported similar conclusions.

Later, Davies and Stoloff [57] studied the kinetics of recrystallisation for a FeCo-2V alloy and reported significantly different results: after similar thickness reductions (90%), complete recrystallisation occurred after 1 h at 650 $^{\circ}$C, while Goldenberg and Seliskii suggested that recrystallisation only started after 8 h at 700 $^{\circ}$C in a FeCo alloy. Furthermore, the grain sizes reported in both studies are vastly different. For example, Davies and Stoloff [57] report a grain size of 12 $\mu$m after 1 h at 750 $^{\circ}$C, while, in Seliskii and Tolochko's work [55], the grain size only reaches $\sim 3$ $\mu$m after 8 h at 750 $^{\circ}$C. This is illustrated in figure 9; the thickness reduction in [58] is not specified, but as the authors used commercial sheets provided by Carpenter Ltd, it seems reasonable to assume that these have been cold-rolled to 90% thickness reduction as usually reported.

Figure: The grain size as a function of time during annealing at varying temperatures following deformation. (A) FeCo-2V, drawn, area reduction 75% [57], (B) FeCo-2V-.05Nb, cold-rolled, thickness reduction presumed 90% [58], (C) FeCo, cold-rolled, thickness reduction 82% [55].
\begin{figure}\centering\epsfig{file=./figures/D_vs_time.ps,width=14cm}\end{figure}

Further studies are also contradictory with regard to the recrystallisation kinetics. Thornburg [59] reported only 10-20% recrystallisation in FeCo-2V, cold-rolled to 90% reduction in thickness and annealed 2 h at 670 $^{\circ}$C, with full recrystallisation only achieved, at 710 $^{\circ}$C. Similarly, Pitt and Rawlings [18] report an equiaxed, recovered structure with subgrain size of about 1 $\mu$m, for FeCo-2V after 2 h at 680 $^{\circ}$C. This appears to be in contradiction with the results of Davies and Stoloff, who, for identical material and conditions, observed full recrystallisation after 1h at 650 $^{\circ}$C.

One possibility is that the latter authors have mistaken the well developed subgrain structure reported by Pitt and Rawlings [18], for a recrystallised structure. In the absence of misorientation measurements, it is difficult to assess these results. Subgrain boundaries are believed to have a similar impact on strength as grain boundaries, which can be modelled by an equation of the type [60] :

\begin{displaymath} \sigma_{y}=\sigma_{0}+cd^{-m} \end{displaymath} (2)

Because of their low misorientation however, their impact is significantly less, that is to say, c is expected to be significantly smaller than typical values as determined for grain boundary strengthening.

Using independent published data on the grain size, the present author showed [61] that the strength measured by Thornburg [59] matched very well that expected from the grain sizes reported by Davies and Stoloff [57], implying that the strengthening effect is as expected for a normal grain structure rather than a subgrain one.

Recent developments have confirmed and exploited (for example [62]) the possibility for these alloys to recrystallise at low temperature. Buckley [63,64] investigated the interactions between the ordering reaction and recrystallisation. Using an FeCo-0.4Cr alloy deformed to about 40%, he distinguished four temperature regions as illustrated in table 2.

Table: Recrystallisation and ordering in FeCo-0.4Cr, after Buckley [63].
Annealing temperature / $^{\circ}$C Observation
>Tc recrystallisation in disordered state, rapid.
600 < T < 725 very fast ordering, recrystallisation slower
475 < T < 600 ordering, recovery
250 < T < 475 ordering and recrystallisation to very fine grains


The authors pointed out that, while at intermediate temperatures (475 < T < 600 $^{\circ}$C), only recovery occurred even after times up to 100 h, recrystallisation was observed at lower temperatures. He proposed that, while the ordering reaction occurs before and independently of recrystallisation at higher temperatures, the ordering proceeds, at lower (T<475 $^{\circ}$C) temperature, through the formation of new ordered grains. However, according to Buckley [63,64], this does not seem to occur in FeCo-V alloys, where no recrystallisation is observed at lower temperatures.

Recent results from Duckham et al. [65] show a 70 % recrystallised structure after 5 h at 438 $^{\circ}$C and almost 100 % after 1 h at 600 $^{\circ}$C, for a FeCo-1.8V-0.3Nb cold-rolled to 93% reduction in thickness. These heat-treatments lead to grain-sizes of 100 and 150 nm respectively. Once again, it is not impossible that this is a misidentification of a well developed subgrain structure.

Kinetics of grain growth

Davies and Stoloff (1966,[57]) studied grain growth in FeCo-2V and used a parabolic growth rate to fit their data:
\begin{displaymath} D^{2}=\sigma V K_{0} \exp\left(\frac{- Q_{g}}{RT}\right) t \end{displaymath} (3)

where D is the grain size, $\sigma$ the grain-boundary energy per unit area, V the molar volume, K0 the pre-exponential factor for the grain boundary mobility $K=K_{0}\exp\left(-\Delta Q/(RT)\right)$, Qg the activation energy, T the temperature and t the duration of the annealing treatment. $K^{\prime}=K_{0}\sigma V$ will be used for further discussion. Part of their results are shown in figure 9.

These authors reported an activation energy of $Q_{g}\sim 238$ kJ/mol in the disordered state (T>Tc), and pointed out the difficulty of fitting a single value of activation energy at lower temperature, where the ordering reaction is expected to continuously modify this value.

More recently, Yu et al. [58,66] studied the grain growth kinetics of FeCo-1.9V-0.05Nb (figure 9). Despite the higher temperature, this alloy exhibits slower grain growth as expected from the addition of a small amount of Nb. It is not clear, however, as to how the authors obtained the value of Qg=240.3 kJ/mol, given that growth was characterised at only one temperature. In these conditions, obtaining Qg implies knowledge of the pre-exponential factor $K^{\prime}$, for which the authors give no value. While it can be worked out that a value of $K^{\prime}\sim8.3\times10^{-4}$ m2 s-1 must have been used by these authors, the only value which may have been available from the literature is $K^{\prime}\sim5.5\times10^{-2}$ m2 s-1 [57].

In conclusion, also there is good agreement concerning the recrystallisation behaviour at high and low temperatures, there is a need for clarification regarding the evolution of deformed structures in FeCo just below Tc (650-720 $^{\circ}$C), in particular, whether only recovery occurs around these temperatures or whether the observations can be explained by a large change in the grain growth rate in the ordered condition.

Ordering of Fe-Co

It is commonly accepted that Fe-Co undergoes an ordering transition around 730 $^{\circ}$C where the b.c.c. structure takes the CsCl (B2) ordered structure (figure 10).

Figure: b.c.c. and ordered B2 structure.
\begin{figure}\centering\epsfig{file=./figures/B2_structure.eps,width=9cm}\end{figure}

Before discussing the characteristics of the ordering reaction in Fe-Co and related alloys, the experimental methods most often used in investigations of the ordering reaction are briefly presented.

The kinetics of the ordering reaction are commonly described in terms of the evolution of the long range order parameter S, defined for this structure, by $S=2(p-\frac{1}{2})$, where p is the fraction of, say, Fe atoms occupying Fe sites. This is 0.5 for a fully disordered alloy (and therefore S=0) and 1 for a fully ordered equiatomic alloy (S=1).

Before presenting the results, the experimental techniques most commonly used for the estimation of the order parameter are briefly reviewed.

Experimental methods

Lattice parameter measurements

Bozorth (1951, [67]), measured the lattice parameter change accompanying the ordering of Fe-Co for Co varying between 0 and 80 at%. The ordering reaction only occurs between 29 and 70 at% Co [12], and causes an increase of lattice parameter, from 2.8485 to . This method has also been used by Clegg and Buckley [68], who report a 0.2% change in lattice parameter between the disordered and ordered phases, with a change from 2.8550 to 2.8570 Å. The order parameter S is assumed to be proportional to the increase of lattice parameter.
Figure: The lattice parameter change caused by ordering as a function of the cooling rate, in equiatomic FeCo, and FeCo-2.5V. The ordering reaction can be avoided with cooling rates greater than $\sim 4000$ $^{\circ}$C/s. After [68].
\begin{figure}\centering\epsfig{file=./figures/x18_fig2.eps,width=8cm}\end{figure}

Superlattice reflections

Upon ordering, the lattice type changes to primitive and the intensity for lines otherwise forbidden in b.c.c. becomes non-zero. However, this intensity remains extremely small if conventional X-ray methods are used, because of the similar atomic factors of Fe and Co. If a wavelength near the absorption edge of one of the scattering elements is used in a diffraction experiment, anomalous scattering effects occur that can enhance the intensity of these lines by an order of magnitude [68]. Most studies have therefore made use of Co or Fe $K_{\alpha}$ radiations in X-ray experiments. The order parameter can be related to the ratio I{100}/I{200} where I{hkl} is the intensity of the line of corresponding indices, more exactly:
\begin{displaymath} S^{2}=R\frac{I_{\{100\}}}{I_{\{200\}}} \end{displaymath} (4)

where R includes Lorentz and polarisation factors.

Most often, this method is used to estimate S/Smax rather than an absolute value of S [68,64,63,18]. Smax refers to the value of S for a fully ordered system. Different references have been used for Smax: although some authors have used ordered binary FeCo for which S is close to one (and I{100}/I{200}=1/66.1) [18], others have used the equilibrium state of the system studied (for example, [68]). In the former case, the values estimated are close to the absolute ones In the latter, and particularly in the study of ternary FeCo-X alloys, they provide an over-estimation of the order parameter, because the absolute value of the equilibrium order parameter in FeCo-X is below one.

In the case of neutron diffraction [69,70,29], the absolute order parameter can be obtained. In ternary FeCo-X systems, this requires assumptions as to the distribution of the X.

Magnetic measurement

Various methods have been used to correlate magnetic properties changes and the disorder-order transition. Measurements of the saturation moment show an increase of about 4% upon ordering [17,68,71,72], as illustrated in figure 12.

Figure: The variation of the saturation magnetisation as a function of temperature, after [68].
\begin{figure}\centering\epsfig{file=./figures/x18_fig6.eps,width=8cm}\end{figure}


Kinetics of ordering

The kinetics of ordering of FeCo and related alloys has been the focus of much attention in the 1970s with particular emphasis on the role of vanadium additions.


Ordering of binary FeCo alloy

Early evidence for ordering were presented by Kussmann et al. [73], Rodgers and Maddocks (1939 [74]) and Shull and Siegel (1949 [70]). Ellis and Greiner [11] provided an accurate measurement of the ordering temperature for equiatomic FeCo, reporting a value of Tk=732 $^{\circ}$C, but values as low as 710 $^{\circ}$C have also been reported [12].

The ordering reaction in equiatomic FeCo is very rapid, so that the cooling rates required to obtain fully disordered samples cannot be achieved in industrial scale processes. Clegg and Buckley [68] investigated the kinetics of the ordering reaction in equiatomic Fe-Co using lattice parameters measurement. Quenching samples of different thicknesses in iced brine (after 30 min at 810 $^{\circ}$C), they estimated that ordering was totally avoided only for quenching rates greater than $\sim 4000$ $^{\circ}$C/s (figure 11). This value was estimated from the specimen thickness (700 $\mu$m).

The equilibrium degree of order depends on temperature, particularly near the critical temperature. Using X-rays, Stoloff and Davies [75] reported the long-range order parameter in FeCo-2V, as a function of temperature and showed that these measures compared well with other results obtained by different techniques, and with theoretical values. This is illustrated in figure 13. It must be noticed that variations of the order parameter occur essentially between 600 $^{\circ}$C and Tk.

Figure: The long range order parameter as a function of temperature in FeCo, after [75].
\begin{figure}\centering\epsfig{file=./figures/S_vs_temperature_2.eps,width=8cm}\end{figure}

An activation energy Qo can be calculated for the kinetics of the ordering reaction, although some studies emphasise the difficulty in giving it a clear physical meaning [68,76]. Particular difficulties arise in the physical interpretation of the ordering rates as the kinetics of quenched-in vacancies annihilation is similar, so that both phenomena must be considered together [76]. Values tend to be in reasonable agreement with each other; for example Qo=188 kJ/mol [76], or 160 kJ/mol [68]. Rajkovic and Buckley [77] report Qo=105 kJ/mol for heterogeneous ordering (see below) at low temperature.

Ordering mechanism:

Clegg and Buckley [68] then Buckley [64] found two distinct ordering mechanisms in binary Fe-Co: The kinetics of domain coalescence in binary FeCo alloys have been studied by Clegg and Buckley [68], and later Rajkovic and Buckley [77]. As mentioned above, when ordering above $\sim 400$ $^{\circ}$C, the process is homogeneous, in which case domains of constant size are observed while the long-range degree of order increases. Once S has reached its equilibrium value, APD coalescence begins [78]. The coalescence stage is generally well fitted to:

d2-d02=kt (5)

where d is the domain size, d0 the domain size at t=0, and k is related to the antiphase boundary mobility and can be written:
\begin{displaymath} k=k^{\prime}\exp{\left(-\frac{Q_{d}}{RT}\right)} \end{displaymath} (6)

A value of Qd=264 kJ/mol for the activation energy of the antiphase boundary mobility has been calculated by the present author from published data [77], while Grosbras et al. [76] report a value of 190 kJ/mol. Both studies have however investigated APD growth in the same range of temperature following similar annealing conditions. This activation energy is in general expected to be identical to that for volume diffusion in the disordered material [68], and although there is no data for the binary alloy, this has been confirmed in FeCo-2V.


Influence of vanadium addition

As will be shown, the agreement over the influence of vanadium additions on the kinetics of ordering remains poor after more than 50 years of investigations.

The FeCo-2V composition was first proposed by White and Wahl [3] in 1932. Through addition of about 2% vanadium and in conjunction with appropriate heat-treatment, equiatomic FeCo alloys become workable (this is further discussed in section 5.2). The ordered $\alpha_{2}$ phase is frequently observed to be very brittle while the disordered $\alpha$ may have some ductility. This lead to the hypothesis that vanadium slows the ordering process and allow ductility to be retained through quenching. The absence of direct evidence was underlined by Stanley (1950 [79]).

A number of investigations followed which cast doubts on this hypothesis. In 1973, Clegg and Buckley [68] showed that the critical cooling rate to avoid ordering was similar in FeCo and FeCo-2.5V. These results were based on lattice parameter measurements (figure 11), but were validated by comparison to magnetic and X-ray diffraction data. As for FeCo, a cooling rate of about 4000 $^{\circ}$C/s, corresponding to a thickness of 700 $\mu$m quenched in iced brine, was required to obtain a fully disordered sample. A similar limit was proposed by Smith and Rawlings in 1976 [69], who used neutron diffraction to study the kinetics of ordering in FeCo-1.8V: while a 600 $\mu$m sample quenched in iced brine from 850 $^{\circ}$C lead to a fully disordered sample, the order parameter in the as-quenched state for a 1 mm sample was about 0.3.

Most studies have concentrated on the kinetics of ordering during reheating after quench. Clegg and Buckley (1973, [68]), then Buckley (1975, [64]), showed that, the kinetics of ordering of FeCo and FeCo-2.5V are similar over a wide range of temperatures. Some of these results are summarised in figure 20, which shows the times to reach S/Smax=0.5 and S/Smax=0.95 during isothermal annealing after quenching from 810 $^{\circ}$C. The same authors also investigated the effect of larger vanadium contents (5.1%) and observed a retardation of the ordering reaction [68].

Figure: The times to reach S/Smax=0.5 (empty symbols) and S/Smax=0.95 (full symbols) in FeCo based alloys with different additions, after quench in iced brine from 810 $^{\circ}$C. After [68,64].
\begin{figure}\centering\epsfig{file=./figures/ordering_kinetics.ps,width=14cm}\end{figure}

Subsequent studies do not completely agree with these results. Eymery et al. (1974,[80]), used X-rays to estimate the evolution of S/Smax during isothermal annealing of FeCo and FeCo-2V after quenching samples of 1 mm thickness from different temperatures. The reference used for Smax is unfortunately not stated As illustrated in figure 15, these authors gave evidence that the vanadium containing alloy orders faster than the binary one, although it appears that the initial degree of order is lower in the vanadium containing alloy.

Figure: Isothermal ordering kinetics at 440 $^{\circ}$C for FeCo and FeCo-2V quenched from 780 $^{\circ}$C. After Eymery et al. [80]. Isothermal domain growth in same conditions, after Grobras et al. [76].
\begin{figure}\centering\epsfig{file=./figures/X57_ordering_Eymery_2.eps,width=7cm}\epsfig{file=./figures/domain_growth_X78.ps,width=7cm}\end{figure}

Eymery et al. (1974,[80]) and later Grobras et al. (1976,[76]) proposed that a higher concentration of quenched-in vacancies in FeCo-V than in FeCo explains the difference; this in turn would be caused by a strong interaction between vacancy and vanadium. The formation of numbers of dislocation loops and helices during low-temperature annealing was taken as evidence for this large concentration of quenched-in vacancies [76].

Measurements of ordering kinetics by Smith and Rawlings (1976, [69]) on FeCo-1.8V are consistent with previous studies, but provide a more reliable estimate of the equilibrium degree of order in this material. The value estimated from neutron diffraction, assuming distribution of V on both Fe and Co sites, was 0.80. The authors further support the hypothesis made by Grosbras et al. [76] on the role of quenched-in vacancies by showing that the activation energy for the ordering evolution increases towards that for diffusion as the process occurs. This can be explained by the rapid disappearance of the excess vacancies.

The results reported above are in clear contradiction with the hypothesis that vanadium slows the ordering kinetics. More recently however, results by Orrock and Major [19] and Orrock [68] provided support for this hypothesis. Using lattice parameters measurements, the authors estimated the degree of order for 2.5 mm samples of various FeCo-X alloys quenched in iced brine from 850 $^{\circ}$C. Their results are illustrated in figure 16.

Figure: The ordering parameter of binary and ternary FeCo alloys as a function of elemental additions, after quenching into ice brine from 730 $^{\circ}$C. After [19,81].
\begin{figure}\centering\epsfig{file=./figures/S_vs_alloying_2.eps,width=7cm}\end{figure}

Although a significant amount of order is to be expected from the thickness of the specimen used in Orrock's work, it is difficult to reconcile the largely different order parameters for FeCo and FeCo-2V with the previous results indicating identical ordering kinetics in these systems. To date, there does not appear to be an explanation for this paradox.

Overall, Orrock's results are the only ones supporting the early hypothesis that vanadium slows ordering and therefore helps obtain a ductile alloy. Most other results indicate no effect or even an acceleration of the ordering reaction by vanadium. It should be emphasised however that few studies [68,19] have compared the order parameter of FeCo and FeCo-V for identical quenching conditions, most work having focused on the ordering kinetics during annealing.

Discarding the Clegg and Buckley [68] study, the results are consistent in as much as measurements by Eymery et al. [80] indicate a lower order parameter for FeCo-2V after quenching (figure 15). There is, however no obvious reason to doubt the work of Clegg and Buckley. Furthermore, if one were to accept that vanadium retards the ordering during quenching but not annealing, it would still be necessary to propose a mechanism explaining this paradoxical behaviour.

It seems therefore reasonable to suggest that measurements and comparisons of the order parameters for FeCo and FeCo-2V following quenching at different rates should be repeated, if possible with a direct method such as neutron diffraction. If such results were are to confirm Orrock's measurements rather than Clegg and Buckley's one, work would be required to understand the `double' effect of vanadium on the ordering reaction.

As for the binary alloy, it is possible to estimate an activation energy for the ordering process. Values are in reasonable agreement with the exception of one study (table 3).

Table: The activation energy for the ordering reaction in FeCo-2V alloys.
Qo / kJ mol-1 Reference
160 Clegg and Buckley [68]
170 Rajkovic and Buckley [77]
154 Grosbras et al. [76]
255 Smith and Rawlings [82]


Ordering mechanism:

Clegg and Buckley (1973, [68]), Buckley (1975, [64]), and Rajkovic and Buckley (1981 [77]) have investigated the ordering mechanisms in FeCo-V alloys of different compositions. As mentioned earlier, the binary alloy has been found to order homogeneously at high temperatures, but by nucleation and growth of an ordered phase at lower temperatures. With increasing vanadium additions however, the transition disappears, and the conventional FeCo-2V alloys exhibit homogeneous ordering at all temperatures. This is illustrated in figure 17.

Figure: The ordering mechanism of FeCo-V alloys as a function of temperature and vanadium content, for samples quenched from 800 $^{\circ}$C, after [77].
\begin{figure}\centering\epsfig{file=./figures/ordering_mechanism.ps,width=7cm}\end{figure}

In the temperature range where mechanisms differ, the FeCo-V alloys are found to order more slowly than FeCo or, as discussed later, FeCo-Cr (figure 14).

A number of studies [83,68,84,85,76,80] have investigated the coalescence of domains in FeCo-V during homogeneous ordering, and reported values for the activation energy as described in section 3.2.1. These include English [83] and Clegg and Buckley [68], whose methods were later criticised by Rogers et al. [84] who recalculated values of Qd based on the data published by the former authors. Results are summarised in table 4 which highlights some discrepancies between different studies. Most of the results fall reasonably close to the activation energy for volume diffusion in the disordered material, estimated to 250-300 kJ/mol.


Table: The activation energy for the APD boundary mobility as estimated by various authors.
Qd / kJ.mol-1 Reference
294 English [83]
337 recalculated by Rogers et al. [84] from data in [83]
284 Clegg and Buckley [68]
213 recalculated by Rogers et al. [84] from data in [68]
178 Rogers et al. [84]
251 Grosbras et al. [76] and Eymery et al. [80]


Influence of chromium additions

Very few studies have dealt with the influence of Cr additions to FeCo [64,63].

Clegg and Buckley [68] compared the kinetics of isothermal ordering of a FeCo-0.4Cr to binary FeCo and FeCo-2.5V, at 435 $^{\circ}$C and 550 $^{\circ}$C and observed significant retardation of the ordering reaction. However, Buckley [64] later concluded the opposite, and showed that ordering kinetics and mechanisms of FeCo-0.4Cr are the same as for the binary system (figure 14) in the temperature range 260-600 $^{\circ}$C.

Influence of niobium additions

Clegg and Buckley [68] first investigated the effect of small niobium addition (0.4%). Measuring the isothermal kinetics of FeCo-0.4Nb at 435 and 550 $^{\circ}$C, they observed a strong retardation compared to FeCo or FeCo-2V, particularly at 435 $^{\circ}$C (more than one order of magnitude).

The impact of Nb on the ability to retain the disordered state of FeCo alloys through quenching is further supported by Major and Orrock [81]. The details of this study have been reviewed earlier (section 3.2.2). As illustrated in figure 16, Nb appears to be the most effective in helping retaining a low degree of order after quench.

In more recent studies, Persiano and Rawlings (1991,[24,28]) have investigated the influence of higher Nb content (1, 2 and 3 wt%). Using 250 $\mu$m thick samples quenched in iced brine from 850 $^{\circ}$C, the authors investigated the isothermal ordering kinetics at 550 $^{\circ}$C with X-rays and showed an 0.62 at% Nb addition results in retardation by one to two order of magnitudes compared to FeCo or FeCoV as measured by Clegg and Buckley [68]. As will be discussed later, the use of a higher quenching temperature than that used by Clegg and Buckley (850 instead of 810 $^{\circ}$C) implies that the difference could be even larger if an identical disordering temperature is used.

Figure: The equilibrium or near-equilibrium degree of order in different FeCo-X alloys, at 550 $^{\circ}$C. After [28].
\begin{figure}\centering\epsfig{file=./figures/max_order_vs_alloying_2.eps,width=7cm}\end{figure}

Yu et al. (1999,[32]) undertook direct measurement of order parameter by neutron diffraction for FeCo-2V-0.3Nb following quench at different rates from 820 $^{\circ}$C, and obtained a negligible order parameter (0.04) for a quenching rate of 30000 $^{\circ}$C/h, i.e. $\sim 8.3$ $^{\circ}$C/s, which is considerably less than the estimated 3000 $^{\circ}$C/s for FeCo-2V [68].

Niobium additions not only have an impact on kinetics, but also on the maximum degree of order that can be reached, as indicated by Persiano and Rawlings [28], who report the equilibrium or near-equilibrium degree of order to be close to only 0.5 with a 2% addition of Nb; this represent a stronger impact than vanadium (figure 18).

Influence of other elements

Very few studies have been found that deal directly with the influence of other elements on the degree of order, although, as will be discussed later, more work has been done on the ductility of the as-quenched state, which seems closely related to the ordering phenomenon.

Orrock [19] used lattice parameter measurements to determine the degree of order in 2.5 mm think strips of various FeCo-X alloys, (and FeCo-2V-X). The results are illustrated in figure 16. Si is found to have little impact, Cu and Ni a mild impact, W and V a stronger impact and Nb the strongest one.

In the FeCo-2V-X system however, Si seems to have an opposite effect and reduce the 'quenchability' of the disordered state, while W and Cu have no effect up to about 2 and 5 at% respectively (figure 19). This shows that the combined effect of different solutes cannot easily be inferred from their individual impact.

Figure: The variation of long-range order parameter for 2.5 mm strips of various compositions, quenched from 850 $^{\circ}$C. After [19].
\begin{figure}\centering\epsfig{file=./figures/S_vs_alloying_quat.eps,width=8cm}\end{figure}

Influence of quenching temperature

The influence of the temperature from which the alloy is quenched before isothermal ordering has been studied by Eymery et al. (1974,[80]) and Smith and Rawlings (1976,[69]). It is illustrated in figure 20. The accelerated ordering kinetics for disordering temperatures in the range 730-850 $^{\circ}$C is explained by the increase of excess vacancies quenched in the material (section 3.2.2). The discontinuity above 850 $^{\circ}$C is attributed to entering the $\alpha+\gamma$ field.

Figure: The degree of order achieved after 500 s at 450 $^{\circ}$C in a 48.4Fe-49.8Co-1.8V wt%, as a function of the prior `disordering' temperature.
\begin{figure}\centering\epsfig{file=./figures/S_vs_annealing_2.eps,width=8cm}\end{figure}

Influence of cold work

Grobras et al. (1973,[78]), Eymery et al. (1974,[80]) and later Smith and Rawlings (1976,[69]) have investigated the effect of cold-work on the isothermal ordering kinetics. The former authors deformed samples at room temperature after quenching 1 mm thick FeCo-2V samples from 780 $^{\circ}$C, then followed the evolution of the long-range order parameter by X-ray diffraction, during annealing at 440 $^{\circ}$C. Their results indicate that for 10 or 20% thickness reduction, ordering is initially accelerated, but hindered towards the end of the reaction, reaching equilibrium order well after the non-deformed samples.

Smith and Rawlings [69] used 0.6 mm thick FeCo-1.8V samples quenched from 850 $^{\circ}$C, deformed by cold-rolling (25-75%), then followed the ordering kinetics using neutron diffraction at 450, 475 and 500 $^{\circ}$C. Their results indicate, on the contrary, that the reaction is slower throughout. Having observed that dislocations sub-structures consist of cells whose size is an order of magnitude larger than that of the domains at the end of the ordering reaction, they conclude that the dislocation obstacle effect can probably not account fully for the retardation. Also, there appears to be no recovery nor recrystallisation at the temperatures investigated (within the duration of the ordering reaction). They propose that the dislocations play an important role both as vacancies sinks during the ordering reaction and by reducing the short-range order (and therefore the number of ordered nuclei) during prior deformation.

An experiment can here be suggested which would provide further support for this hypothesis. A higher quenching temperature implies a higher concentration of quenched in vacancies but lower number density of ordered embryo. If the effect of deformation on the vacancy concentration is more important, the ordering kinetics after deformation, in a sample quenched from a lower temperature will be proportionally less affected than one quenched from a higher temperature. If on the other hand, after quenching from a higher temperature, deformation has less influence, then it might be supposed that the main effect is on the ordered embryos.


Challenging the existence of an ordering reaction

Although the existence of an ordering reaction, together with its implications, have been a working hypothesis for the past 50 years, recent work has challenged up to the existence of an ordered phase in bulk FeCo and emphasised the importance of the 550 $^{\circ}$C anomaly in explaining the magnetic properties of these alloys. The problem has been reviewed in details by the present author [86]. It was found that numerous published results could not be reconciled with the new theory. In addition, some of the results put forward as evidence for this new theory could not be reproduced.

Magnetic and electrical properties

The following section discuss the magnetic properties of FeCo based alloys, essentially with respect to the microstructural features of the alloy.

Overview

Iron-cobalt alloys have the highest magnetisation saturation of all known magnetic alloys (figure 21).

Figure: The Slater-Pauling curve showing the mean atomic moment for a variety of binary alloys as a function of their composition, after [67].
\begin{figure}\centering\epsfig{file=./figures/Slater-Pauling.eps,width=8cm}\end{figure}

Although the maximum saturation is obtained around 35% cobalt, equiatomic compositions offer a considerably larger permeability for a similar saturation, as illustrated in figure 22.

Figure: Initial and maximum permeability for Fe-Co alloys, the annealing temperature influences strongly the maximum permeability, in this case most likely because 1000 $^{\circ}$C lies in the two-phase region. After [67].
\begin{figure}\centering\epsfig{file=./figures/permeability.eps,width=8cm}\end{figure}

As for soft magnetic systems in general, the coercivity of FeCo alloys depends strongly on the microstructure. It is out of the scope of this review to discuss the theories describing this dependency, the focus being on reviewing the impact of composition and thermomechanical treatment on the magnetic properties.

The saturation of FeCo based alloys

The saturation magnetisation is generally regarded as independent of the microstructure. As indicated earlier (figure 12), an increase of saturation has been observed following ordering, which in turns has been used as an indicator of the order parameter. Although the moments of Co atoms does not depend on their environment, that of Fe does, as it increases from 2.2 $\mu_{B}$ in pure Fe to about 3 $\mu_{B}$ (figure 23) in ordered equiatomic FeCo [67,69,87]. This is rather spectacularly illustrated in the measurement of the saturation of FeCo alloys where a solid solution is obtained by mechanical milling of pure Fe and Co particles (figure 23).

Figure: The magnetic moments of Fe and Co on binary alloys of different compositions, after [87]. The saturation magnetisation of Fe1-xCox alloys as a function of composition. The straight line is that for an unmilled mixture of pure elements. The formation of a solution is accompanied by an increase in the saturation magnetisation. After [88].
\begin{figure}\centering\epsfig{file=./figures/moments_vs_compo.ps,height=45mm}\epsfig{file=./figures/saturation_milling.ps,height=45mm}\end{figure}

Typical saturation values for ordered binary FeCo [72] or FeCo-2V [19,24] are about 2.35 T.

Chen [67] investigated the influence of ternary additions on the saturation of FeCo alloys, and found that most (Ti, V, Cr, Ni, Cu) had a detrimental effect, with the exception of Mn. This author also reported that, while Ti, V and Cr order antiferromagnetically, Ni and Mn order ferromagnetically. In addition, Mn displays an atomic moment larger than that the average one for FeCo ($\sim$ 3 $\mu_{B}$). The case of Mn is further complicated by the fact that its atomic moment depends on the exact stoichiometry of the alloy. It has a simple dilution effect if Fe:Co >1, only increasing the saturation in alloys where Fe:Co <1.

This has been further investigated theoretically by Reddy et al. [89] using the cluster variation method. Their results also indicate that the impurities Al, V, Mn and Ru preferentially occupy the Fe site, with the substitution of Fe by V being the only one energetically favourable. Chen reports a solubility limit of 7 at% for Mn in FeCo [67] (Köster [49] reporting about 5.5 at%), and the possibility to achieve an average atomic moment of 2.43 $\mu_{B}$ for a 5 at% addition. Mostly because the addition has to be done with excess of Co, the peak reached at 35% Co is not surpassed by that obtained with Mn additions. Few compositions today are found with more than 0.5 wt% ($\sim 0.48$ at%).

Furthermore, similar if not larger saturations have been reported in other ternary alloys by Major and Orrock [81], with 2.44 T (at 4 x 104 A.m-1) for an equiatomic FeCo with 0.23 wt% Nb and 2.45 T for 0.2 wt% Ta.

Saturation is usually regarded as being independent, to a large extent, of the microstructure. Small variations can however be detected; for example, Fingers and Kozlowski [90] report different values of saturation for the same alloy depending on the exact heat-treatment conditions, as illustrated in table 5. Discussion by the above authors appear to imply that such variations are beyond typical error; it must be noted however that error estimations, when published can reach 0.1 T [19].


Table 5: Saturation magnetisation for a FeCo-2V-0.3Nb alloy after different heat-treatments, after [90].
Temperature / K Time / h Grain size / $\mu$m Saturation induction / T
704 1 1.13 2.37
720 1 1.68 2.40
720 2 2.80 2.43
732 1 2.33 2.40


Increasing further the amount of ternary addition leads to significant reduction in saturation, resulting from the both the dilution effect due to the addition of V or Nb, and from the precipitation of non-magnetic particles [24,28] as illustrated in table 6.


Table 6: Saturation magnetisation for different FeCo based alloys after furnace cooling from 760 $^{\circ}$C, data from [28].
Alloy Saturation induction / T Estimated volume fraction of second phase / %
FeCo-2V 2.32
-
FeCo-3.6V 2.29 not measured
FeCo-1Nb 2.34 7
FeCo-2Nb 2.29 11
FeCo-3Nb 2.2 14


Similar results have been obtained by Orrock [19] for quaternary systems FeCo-2V-Cu and FeCo-2V-W, where it is shown that the saturation as calculated from the dilution caused by the formation of paramagnetic precipitates (table 11) is in good agreement with measurements, as illustrated in figure 24. This is not the case for FeCo-5Ni [19] or the FeCo-Nb alloys in table 6 where the saturation appears to be larger than expected given the amount of second phase. Orrock suggests that this can occur if the removal of solute causes an increase in average moment in the bulk, that is to say, the loss due to the paramagnetic precipitates is compensated by a increase of the bulk average atomic moment as the concentration of atoms in solid solution decreases. This is however not a satisfying explanation, since the calculated reference curve mentioned above does not include the solid solution effect in the first place.

Figure: The saturation of a variety of FeCo based alloy as a function of the volume fraction of paramagnetic second phase, after [19,24]
\begin{figure}\centering\epsfig{file=./figures/saturation_vs_vf.ps,width=9cm}\end{figure}

Error estimates are visible in figure 24 for the data from [19]. Taking into account that some studies have reported saturations up to 2.44 T, it is not evident whether, even for FeCo-Nb, reasons for the differences should be sought elsewhere than in the inaccuracy of the measurements.


Coercivity

The coercivity is often seen as an important parameter if low losses are to be achieved. It is out of the scope of this review to provide a detailed account of theories relating the coercivity to the microstructure of soft magnetic alloys. The coercivity is, in general, affected by most types of defects. This includes dislocations, grain boundaries, and precipitates.

The coercivity depends on the grain size as follows [31]:

\begin{displaymath} H_{c}\sim 3 \sqrt{ \frac {kT_{c}K_{1}}{a M_{s}} } \frac{1}{D} \end{displaymath} (7)

where Hc is the coercivity, D the grain size, Ms the magnetisation saturation, K1 the magnetocrystalline anisotropy, Tc the Curie temperature and a the lattice constant.

The most often quoted relationship between coercivity and non-magnetic particle distribution is due to Kersten [31]:

\begin{displaymath} H_{c} \propto \frac{\delta_{w} K_{1}}{M_{s} \mu_{0} \overline{r}} {V_{f}}^{2/3} \end{displaymath} (8)

where $\delta_{w}$ is the wall thickness, $\mu_{0}$ the permeability of vacuum, $\overline{r}$ the average radius of the particles and Vf their volume fraction. This does not apply if the wall thickness is greater than the particle size. Néel's approach accounts for the presence of free poles associated with the non-magnetic inclusions, and tend to lead to a linear relationship between the coercivity and the volume fraction of precipitate.

Grain size

In the following section, data from a number of publications have been gathered for comparison. Ideally, the different grain sizes should have been obtained by varying the annealing time at the same temperature, as the concentration of quenched-in vacancies may otherwise vary and affect the result. Clearly, the samples should also be well annealed if comparisons are to mean anything. Figure 25 shows a number of measurements made on a variety of FeCo-X alloys.

Figure: Coercivity of a variety of FeCo based alloys as a function of their grain size. (a) Stanley, 1950, for FeCo-2V [79] (b) Yu et al.,