2000 Kluwer Academic Publishers. Printed in the Netherlands.
Structure and magnetic properties of nanocrystalline soft ferromagnets
T. Keménya, D. Kaptása, L.F. Kissa, J. Balogha, I. Vinczea,b, S. Szabóc and D.L. Bekec
aResearch Institute for Solid State Physics and Optics, H-1525, P.O. Box 49, Budapest, Hungary bGeneral Physics Department, Eötvös University, Budapest, Hungary
cDepartment of Solid State Physics, Lajos Kossuth University, H-4010, P.O. Box 2, Debrecen, Hungary
The structure and magnetic properties of soft magnetic nanocrystalline composites crys- tallised from amorphous ribbons are reviewed. The Fe–Early Transition Metal–Boron (Nanoperm-type) nanostructures are discussed in details and compared to the Si containing (Finemet) alloys. The nanocrystallization process was studied by calorimetry; the spatial di- mension, the composition and the relative fraction of the bcc and the residual amorphous phases were investigated by X-ray diffraction and Mössbauer spectroscopy. A small fraction of Fe atoms (about 4%) was found which cannot be assigned either to the residual amorphous or to the bcc phase. It is suggested that the magnetic anisotropy of the bcc phase is decreased due to the dissolved Zr and B impurities. The Curie point and Fe atomic moments in the resid- ual amorphous tissue are determined and compared to that of a macrosized amorphous phase of similar composition. The observed deviations do not scale with the average characteristic size of the amorphous phase and thus cannot be explained in the framework of the existing models. Magnetic dipolar coupling and tensile stresses between the grains of the different phases are suggested for explaining the soft magnetic behaviour of the nanostructures.
1. Introduction
One of the characteristic trends in the study of condensed phases of the last decade is the interest in mesoscopic phenomena, i.e., those between atomic and macroscopic scales. Research in this area is motivated on one hand by practical interest, since the devices used recently gradually approach this scale. It is therefore more and more im- portant to understand the different physical properties in this dimension. On the other hand, it is also motivated by academic interest, as the observation of some unexpected behaviours on this scale (e.g., giant magnetoresistance in multilayers and granular ma- terials [1]) needs a better understanding. Magnetism is a discipline which is stimulated by both basic and practical motivations for the study of different nanostructures. Mi- cromagnetic modelling of magnetic materials on different length scales is a well estab- lished practice [2,3], making obvious the prominent influence of the grain size reduction to the magnetic properties [4]. In this description the magnetocrystalline anisotropy, which limits the magnetic softness, is averaged out (i.e., significantly reduced) when the length scale of the magnetic grains is smaller than the characteristic exchange length. It
was pointed out in a recent review [5] that non-monotonous size dependence of various physical properties is expected and observed when the grain size is reduced below the characteristic scale determining the corresponding property. This characteristic scale is determined by the domain wall width for magnetic properties and by the dislocation cell dimension for microhardness.
One of the intensive stimulations for the research of the nanocrystalline structure thus comes from the magnetic applications. Both hard and soft magnetic materials of significant application potential can be found in different nanostructures. Although some reviews on the different properties of the nanocrystalline state have already been pub- lished [6,7], these works treat soft magnetic properties rather briefly. The present work will focus on the soft magnetic materials, mainly the thermally crystallised Fe–B based amorphous alloys. It has been known since the early crystallisation studies [8–10] that crystallisation starts with the precipitation of a body centred cubic (bcc) phase in low B content samples. These partially crystallised alloys are, however, not suitable for practical applications since the bcc grains attain a large size. Besides that, the forma- tion of the bcc phase is considerably overlapped by the second stage of crystallisation, where the magnetically hard intermetallic compound phase forms. Alloying additives hinder this process, allowing nanocrystalline composites of promising magnetic para- meters to be produced. The alloys are simultaneously doped by Cu, which (according to atomic probe field ion microscopy, APFIM [11] and X-ray absorption fine structure, EXAFS [12]) promotes copious nucleation at low temperatures, and also by one or more refractory metals (Zr, Hf, Ta or Nb). This latter component enhances atomic binding and reduces diffusion; it limits the growth of the bcc grains and delays the second stage of crystallisation. This way nanocrystalline composites can be formed by heat treat- ment until the end of the first of the two well-separated crystallisation stages, where the further growth of the bcc nanograins ceases and these nanograins remain embedded in the residual amorphous tissue. These types of nanostructures are composite (two- phase) materials. Therefore the dimension, composition and fraction of both phases and the role of possible boundary phases must be clarified before delicate questions of the magnetic structure can be answered. For this purpose it is necessary that detailed com- position dependence studies be made in a range wide enough for a reliable identification of characteristic trends.
Two main types of nanocrystalline soft magnetic composites have been studied recently: the Si containing Finemet and the Si-free Nanoperm alloys, both with good permeability and saturation magnetisation characteristics. The Si containing Finemet alloy has the higher permeability and the lower saturation magnetisation value [13], while the saturation magnetisation of the high Fe content Nanoperm alloys is higher and the maximum permeability is lower [14]. The enhanced permeability of the Finemet alloys is partly due to the Si dissolved in the bcc phase which reduces magnetostriction (and also decreases saturation magnetisation). From the point of view of nanostructure studies by nuclear methods the Si-free alloys are simpler. In Si-containing alloys, the hyperfine field pattern of the bcc phase is more complicated due to the dissolved Si. The value of the order parameter between the fully disordered Fe–Si solid solution and the
perfectly ordered DO3-type Fe3Si compound is a matter of intensive studies [15]. This complex behaviour makes it difficult to find clear answers to the more subtle questions related to the nanocrystalline structure. It has been reported [16–20] that the bcc phase of the Nanoperm type materials is almost pure Fe which makes them ideal materials to study the extent to which the nanoscale grain size modifies the magnetic behaviour.
Since the magnetic properties are significantly influenced by atomic volume and lo- cal co-ordinations, the magnetic studies might also contribute to a better understanding of the structure of nanoscale materials. Early models of nanocrystals [21,22] were stimu- lated by results obtained from studies on cold condensed powders. It is now clear that the behaviour of these materials are complicated by light element impurities [23] and poros- ity [24,25]. The early views that relatively wide grain boundaries with a significant den- sity deficit (“gas-like phase”) characterise nanoscale materials are not supported by more recent studies. Besides some early X-ray diffraction works [26], recent EXAFS [27,28]
and high resolution transmission electron microscopy studies [29] made it clear that the width of the grain boundaries are limited to at most two atomic distances. The study of the local magnetic structures by hyperfine interactions (i.e., Mössbauer spectroscopy) indicated a peculiar behaviour for cold condensed Fe [30]. Besides the normal behav- iour characteristic for the bulk of the grains, a spectral component was observed with an enhanced magnetic moment at low temperature and with a faster decrease of magnetisa- tion. These properties were attributed to the grain boundaries. Two different sites were also observed in heavily cold worked Fe [31] and are still interpreted [32] by assuming grain boundaries wider than 1 nm. The limitations of these interpretations are treated in a recent work [33], where ball milled, thermally nanocrystallized and solid state reacted multilayer samples are compared.
The present work is an attempt to review the results of studies on Nanoperm-type (Si-free) soft magnetic materials with emphasis on possible impurity effects. Compari- son to parallel developments in Finemet-like systems is also made in order to explore the origin of the special magnetic behaviour. Results on ball milled materials and solid state reacted multilayers will be referred to very briefly. This treatment is aimed to emphasise that the special features (observed and frequently attributed to interfacial phases) are in- fluenced by contamination effects. This complication is frequently neglected in these materials produced by complex technological routes. A formerly not identified compo- nent with reduced magnetism is found in nanocrystalline composites and is attributed to intergrain sites. When contamination effects are correctly accounted for, the fraction of this boundary phase is much less than the amount usually assumed, a finding which is in line with recent structural investigations.
Our results make it possible to determine the dimension, the composition and the relative fraction of the different phases of the nanocrystalline composite in a wide con- centration range. Both the bcc phase and the residual amorphous tissue will be charac- terised in terms of their composition and spatial dimension. The findings stimulated the production of macroscopic sized amorphous Fe67(ZryB1−y)33 (0 6 y 6 0.55) ribbons of compositions very close to that of the residual amorphous tissue in order to compare the magnetic properties. The results are used to establish whether Curie point changes
and other magnetic modifications are to be explained by grain size effects. The question of magnetic coupling between the different phases is also addressed. Some problems with the exchange penetration model are mentioned, as are theoretical and experimental results pointing to the influence of magnetic dipolar coupling.
2. Process of nanocrystallization
This section investigates the formation of nanocrystalline state by thermal crystalli- sation of the amorphous precursor. Those compositions are of special interest, where the crystallisation of the bcc phase is self-limiting. At those compositions the growth of the bcc phase ceases and leaves a well defined residual amorphous tissue. Crystallisation of this residual tissue (yielding compound phases) is thermally well separated from the bcc phase formation. The process of nanocrystal formation, which is based on copious nucleation and limited growth, will only be treated here to the extent necessary to under- stand the oncoming description of the nanocrystalline state. The thermally crystallised nanostructure will be treated as a metastable state which is largely independent from the technical details of the preparation procedure. The existence of related Finemet type nanocrystalline structures formed by ball milling [34] and by multilayer deposition [35]
is only mentioned here.
It is remarkable that the properties of thermally formed nanocrystals are mostly independent from the properties of the melt quenched precursor phase. The magnetic characteristics of nanocrystals prepared from melt quenched ribbons are independent of the ribbon thickness in the 6–26 µm range [36], even though the precursor was only partially amorphous in the 22–26 µm thickness range. This observation shows that nanocrystallization is a self-limiting process during the ribbon formation, as well. It hints to the existence of a metastable nanocrystalline state.
While the nanocrystal formation process is similar in the two different systems studied (Si-containing Finemet and the Si-free Nanoperm), the role of additive elements seems to be different. It has been shown that the addition of both Nb and Cu to the base Fe–B–Si is necessary for nanostructure formation. A minimum amount of Nb (or other refractory metal) was shown to be necessary in order to suppress dendrite formation [37].
It has also been demonstrated that V, in spite of being an early transition metal (TM), is not suitable for this purpose. This finding might indicate that the limited solubility of the TM component in the Fe-rich bcc phase is a significant factor. The importance of Cu, originally suggested by [38,39], is confirmed recently [40]: the DSC curve of the Cu free Fe74.5Si15.5B7Nb3amorphous alloy shows a sharp single peak crystallisation. In the absence of Cu the crystallisation of the bcc phase is not thermally separated from the intermetallic compound formation. In contrast to this, the Fe–TM–B amorphous al- loys with and without Cu form nanostructures by crystallisation. The most effective TM additives for nanocrystallization are Zr, Nb, Hf and Mo. The nanocrystal formation is demonstrated in case of Cu-free Fe93−xM7Bx[41] and for the Fe86−xB14Nbxalloys [42].
The temperature splitting of the crystallisation peaks increases with increasing Nb con- tent.
However, Cu is found to be advantageous in the Nanoperm-type alloys as well, since the temperature difference between the crystallisation processes increases due to Cu addition in Fe86Zr7B6Cu1as compared to Fe87Zr7B6[41,42]. It is also confirmed for the higher B content range, i.e., for Fe81Zr7B12 in comparison to Fe79Zr7B12Cu2 [43].
As for other nucleating agents, the beneficial influence of Ag [44] and Al [45] is also demonstrated. Cu was confirmed to be the most advantageous nucleating agent when a series of additives (M=Cu, Ag, Au, Pd, Pt, Sb and Ga) to the Fe86Zr7B6M1composi- tion was investigated [46].
The composition trends of nanocrystal formation will be illustrated in case of the Fe92−xZr7BxCu1, 26x 623 alloys. In the whole concentration range two well resolved transformations are detected. The Differential Scanning Calorimetry (DSC) curves of two typical compositions are shown in figure 1. The first stage is the formation of bcc nanocrystals embedded in the residual amorphous phase (see also in the next section).
The DSC results show that the heat of the first transformation (which is proportional to the amount of the bcc phase formed) decreases significantly with increasing B (de- creasing Fe) content, as it is shown in figure 2(a). The composition dependence of the crystallisation temperature is shown in figure 2(b). While the kinetics of the transfor- mation will not be discussed in details, it is evident that the starting and the peak tem- perature follow similar trends. It hints that the kinetics is basically unchanged in a wide composition range: the transformation is limited by the soft impingement of the diffu- sion zones [47,48]. The composition dependence is similar to the general trends found in different amorphous alloy systems [49]. When one of the components is exchanged
Figure 1. Crystallization of amorphous Fe90Zr7B2Cu1(a) and Fe80Zr7B12Cu1(b) alloys in two stages.
The output power versus temperature is measured by Setaram DSC 92 at 5 K/min heating rate.
Figure 2. The composition dependence of the heat of crystallisation of the first transformation stage (a) and the start temperature (Tstart) together with the temperature of the maximum output power (Tmax) of the first crystallisation process (b) for the Fe92−xZr7BxCu1alloys (averaged results from 20 K/min heating rate
Perkin Elmer DSC-2 measurements).
for another chemical element (and the heat of mixing with the other element is nega- tive), the crystallisation temperature first increases, then reaches a maximum followed by a decrease. A new component (with different diameter and different chemical prop- erties) initially makes it possible to achieve a denser packing and more intensive atomic binding. This way the diffusion is slowed down and the crystallisation temperature is enhanced. The variation evidently saturates with increasing concentration and reaches a maximum at a ratio of the two components which is determined by both the diameter and the chemical binding energy relations. In case of the Fe92−xZr7BxCu1system fig- ures 2(a) and (b) show that the crystallisation temperature and the heat of crystallisation changes smoothly with composition and this way verifies the nominal concentrations of the samples in the investigated composition range. Our results agree well with a number of works for the two most intensively studied compositions, Fe90Zr7B2Cu1and Fe86Zr7B6Cu1, and are in good agreement with a recently published work [50] in the 06x612 range.
The above results and several reports in the literature evidence that at the end of the first crystallisation peak the rate of transformation is negligibly low and the two crys- tallisation stages are well separated. It means that the nanocrystalline state formed at the end of the first process is to be treated as a metastable state and this state will be the focus of our studies. We have carefully checked that the end of this first process is well defined in the sense that annealing samples to 20–30 K higher temperatures yields iden- tical nanocrystalline samples within our experimental resolution. The nanocrystalline state of isothermally treated samples [51,52] with good soft magnetic properties, slowly
varying bcc fraction and an almost invariant grain size is also close to this metastable state.
3. The nanocrystalline structure
The magnetic properties of a nanostructured composite are determined by the in- dividual properties of the different phases and their magnetic coupling. This section is thus aimed to determine the size, the composition and the fraction of the nanosized bcc phase and the residual amorphous tissue. The existence of a separate grain boundary phase will also be investigated.
3.1. Properties of the bcc phase 3.1.1. Grain size
The very slow increase of the bcc grain size with heat treatment temperature is a key property of the nanocrystal formation. Figure 3 [53] compares the structural evolu- tion in Fe91Zr7B2compared to Fe86B14. In this latter composition the growth of the bcc phase is overlapped by the compound formation and the continuous increase of the bcc grain size is observed which is absent in the nanocrystal forming Fe91Zr7B2composition.
Reliable quantitative determination of the grain size in the 5–30 nm range – which is the case of nanostructured composites – is a difficult experimental problem. The two
Figure 3. The dependence of the bcc grain size, D on the heat treatment temperature in Fe91Zr7B2 nanocrystals compared to that obtained for the crystallisation of amorphous Fe86B14(from [53]).
most widely used methods, transmission electron microscopy (TEM) and X-ray diffrac- tion (XRD) are rarely used in combination and with high enough care to establish the systematic errors. A few problems are briefly mentioned for both methods. TEM investi- gates a very small surface area and to ensure the statistical significance of the data needs significant efforts. Stereoscopic correction (i.e., re-calculation of the average grain size from the measured two dimensional cross sections) cannot be accurately made as sample thickness and grain size are not simply related, which might be a source of systematic error. In the XRD method much larger sample area is studied. Problems of statistical significance might still arise since a small number of large grains might cause an overes- timation of the grain size and textured growth (which can arise due to the ribbon shape of the amorphous precursor) poses a special problem. Different evaluation methods yield systematically different grain size values. The use of the simple Scherrer formula (when the width of a given reflection is used for the grain size determination) underestimates the grain size since the strains evidently present in nanostructures are not taken into account. More sophisticated problems connected with the effects of dislocations were also pointed out [54]. Comparison with other experimental methods (e.g., small angle scattering) makes it even more explicit that different methods yield different averages for the grain size distribution. The results of standard XRD evaluation yielded a factor of two higher grain size than the findings of a small angle X-ray scattering study for Fe93−y−xCuyZr7Bxalloys [55].
In spite of the above problems, it is established that the grain size is characteristic for the composition studied and only minor changes occur in a wide range of the trans- formed bcc fraction values. (This is valid only for the first stage of transformation. The high level of atomic mobility, which makes the compound formation possible in the sec- ond stage, permits a significant grain growth.) This independence of the grain size from the transformed fraction was shown for both the Fe86Zr7B6Cu1composition [56] and for the lower B content Cu-free Fe91Zr7B2alloy [57]. It was also verified for the Finemet alloy that primary crystals grow to their final size even at 5% crystallised fractions [58].
While the bcc grain size is more or less independent of the transformed fraction, com- position trends obviously exist.
Many studies confirm that the bcc grain size is smaller for Cu containing sam- ples. It was already indicated by the first investigations on Fe91Zr7B2. The Scherrer formula yielded 17 nm for the bcc grain size and it was found to decrease for Cu addi- tion [41]. The reduction of the bcc grain size is verified by a more recent report on the Fe93−x−yZr7BxCuy (y =0, 2;x =4, 6, 8, 12) alloys [55].
Another evident trend concerns the Fe content. The smaller is the Fe content of the precursor amorphous alloy the lower is the estimated bcc grain size. Early results – where different transition metals were used – follow this pattern. For the Fe90Zr7B3, Fe89Hf7B4and Fe84Nb7B9 series the Scherrer formula yields 18, 14 and 9 nm, respec- tively [59]. This trend is confirmed for the F91.5−xBxZr3.75Nb3.75Cu1alloys [60] and is indirectly supported in case of Fe86ZrxNb7−xB6Cu1alloys where an invariant grain size is observed for the constant Fe content alloys [61]. The trend is also confirmed by a recent work on Fe93−x−yZr7BxCuy (y =0, 2;x =4, 6, 8, 12 alloys) [55].
Figure 4. The composition dependence of the bcc grain size,D(filled circles) and the thickness of the resid- ual amorphous tissue,d(empty circles) for the nc Fe92−xZr7BxCu1alloys. The solid line is a calculated
curve as explained in the text. The star (D) and the cross (d) are results from [19].
Our experimental results for the Fe92−xZr7BxCu1alloys heat treated to the end of the first crystallisation stage are in agreement with the above composition trends. The measurements were made with a Phillips X0pert diffractometer by Cu Kαradiation in the Bragg–Brentano geometry. The data were evaluated using Rietveld full-profile match- ing, applying the FULLPROF program for evaluation. This way numerical agreement with literature data obtained by the Scherrer formula is not expected. The X-ray dif- fraction results confirm that in the first transformation stage nanosized bcc grains are formed. Figure 4 shows the composition dependence of the grain size characteristic for this metastable state. While the systematic error of these grain size determinations is significant, the tendency that the size is reduced with increasing B (decreasing Fe) content is evident. The findings were cross checked with different instruments includ- ing a study by synchrotron radiation [52] and were also confirmed in a recent study of (Fe1−xCox)90Zr7B2Cu1by high resolution X-ray diffraction [62]. The results were also compared with transmission electron microscopy measurements for the two most widely investigated compositions Fe90Zr7B2Cu1and Fe86Zr7B6Cu1[51]. The trend is confirmed and the figure shows acceptable agreement with [19]. A high resolution TEM investi- gation of the Fe90Zr7B3alloy heat treated at 923 K for 60 min [63] finds the bcc grain size as 6–18 nm, which is rather close to our results. It is emphasised that especially for the low B content alloys the relatively high grain size makes the size determination by XRD rather inaccurate. We encountered some samples, where only a limiting value (the grain size is above 20 nm) could be reliably established. However, both the trend of the magnetic properties and the TEM results made it evident that these alloys are also nanostructured. In the following when the structural properties will be further studied the bcc grain size values shown in figure 4 will be used. For determination of the fraction and phase composition of the phases Mössbauer spectroscopy results will be utilised.
3.1.2. Impurity content
Standard methods are not suitable for direct determination of the composition of nanometer sized regions. Indirect results (i.e., the discrepancy between the crystallisa-
Figure 5. Atomic probe field ion microscopy results of [63] for Fe90Zr7B3 annealed at 723 K for 60 minutes. The slope indicated is the content of the given component in the different phases.
tion and the Curie temperatures) for the Finemet alloys hinted at the dissolution of 1.5 at% Nb in the bcc Fe–Si phase [64]. The early results based on analytical electron mi- croscopy and electron energy loss spectroscopy made it clear that in the nanocrystalline state of both the low and the high B content Fe–TM–B (TM =Nb and Hf) alloys the Fe content of the bcc phase is enhanced and the composition of other elements is much reduced in comparison with the amorphous precursor [59,65]. The most accurate com- position results are evidently given by the atomic probe field ion microscopy (APFIM) studies. The results, besides confirming the partitioning, give quantitative figures for the impurity content of the bcc phase. Figure 5 shows the results of [63], where the slope indicated is the content of the given component in the different phases. The systematic error of these determinations are significantly higher than the statistical errors denoted in the figure. The average Zr and B concentration values were also determined for the
nanocrystallized Fe87Zr7Si4B2 amorphous precursor. The mean values, averaged for a higher area are found [66] as Zr =8.9 and B=0.8 at%. The authors quote preferen- tial evaporation of Fe and B as the main source of error. The APFIM studies evidently indicate a measurable amount of solutes in the Fe-rich bcc phase.
The measured lattice parameters of different nanocrystals also indicate a non- negligible solute content. It is frequently observed that the lattice parameter value of the nanocrystals formed at low temperature is significantly higher than that of pure bcc- Fe and the difference decreases as the heat treatment temperature increases. It was found for Fe89Hf7B4[59] and for Fe86Zr7B6Cu1[56,67,68]. The same findings are reported for Fe90Zr7B3[69] and also for Fe87Zr7B5Ag1 [70]. These results indicate that the refrac- tory metal dissolved at low temperature increases the lattice parameter and its content is gradually diminished by heat treatment at higher temperatures. Our findings [52], which confirmed this behaviour for Fe86Zr7B2Cu1 but reported a lattice parameter which is independent of the heat treatment temperature for Fe86Zr7B6Cu1, indicated that the be- haviour might be more complex. The dissolution of B (which depends on sample and heat treatment details and decreases the lattice parameter when it occurs) might lead to a compensation, i.e., the absence of the modified lattice parameter does not exclude impurity dissolution. While the equilibrium solubility of both Zr and B is negligible in bcc Fe, supersaturated solid solution in nanocrystals is by no means surprising when the findings for ball milled [71] and evaporated [72] binary Fe–Zr alloys are taken into account. Both type of non-equilibrium treatments yielded Zr dissolution as confirmed by magnetic studies, lattice parameter measurements and Mössbauer spectroscopy. Be- sides that, it was also confirmed that the magnetostriction of the metastable bcc alloy is much reduced, which – taken into account the good soft magnetic properties of the nanocrystals – also indicates that solutes are present in the bcc phase. It was also ob- served for Fe80.5Nb6.9B12.6 alloys that the Curie point of the bcc nanocrystals follows closely the trend described for the lattice parameter: it is lower than that of the pure bcc Fe at low heat treatment temperatures, the deviation is much reduced when the treatment temperature increases [73].
The impurity content of the bcc grains will seriously influence the evaluation and interpretation of the Mössbauer spectra. A typical decomposition is shown in figure 6(a) for Fe80Mo7B12Cu1nanocrystal at room temperature [17]. Assuming no dissolved im- purity in the bcc grains, only the outer sharp lines – whose Mössbauer parameters within the evaluation errors are rather similar to those of α-Fe – are attributed to bcc grains (this is the CR-component). The rest of the spectrum is described by a hyperfine field distribution (HFFD), which is divided into two parts. The low-field part belongs to the amorphous residual phase (AM), the high-field part is attributed to a so-called Interface Zone (IF). The division is arbitrarily done around 20 T in the given case. It is unfor- tunate that the position of the 2nd and 5th lines of the sextet attributed to the CR com- ponent coincides with the given cut-off field. It is known that the correlation between the unknown, i.e., fitted, 2nd and 5th line intensities and the shape of the hyperfine field distribution may cause systematic errors in the evaluation. This correlation may result in a structured hyperfine field distribution of the residual amorphous phase. However,
generally the peaked structure is not observed in the high external magnetic field spectra where the mentioned line overlap is removed (see later). Another problem of this of- ten used decomposition that the whole satellite structure of the CR lines is attributed to the interface phase and no contribution is allowed to the dissolved Mo in the bcc α-Fe structure which is known to exist even in the equilibrium alloy [74].
Another way to describe the characteristic features of the nanocrystalline Möss- bauer spectra is shown in figure 6(b). The outer narrow sextet having parameters at low temperatures similar to pure bcc Fe (main line) is fitted like in the former case. The shoulder on its low field side is attributed to a rather broad sextet and considered as a satellite contribution. The rest of the spectrum is fitted with a hyperfine field distribution which is attributed to the residual amorphous phase. The main difference between the formerly discussed and the present decomposition of the spectra is the use of a broad sextet for the description of the broad shoulder feature instead of a hyperfine field distri- bution of unrestricted shape. In this approximation the line width of the broad sextet in the fitting procedure is determined from the slope of the shoulder. This way the problems originating from the correlation between the overlapping distributions are less important.
This is reflected in the unstructured shape of the hyperfine field distribution attributed to the residual amorphous phase. It is much more similar to that of the macroscopic sized (melt quenched, evaporated, etc.) amorphous alloys than the majority of the results in the literature of nanocrystals [16,75–77] indicate. Measurements in applied magnetic field support this kind of evaluation.
The application of external magnetic field might considerably simplify the Möss- bauer spectra. When the applied magnetic field is parallel to the γ-ray, the 2nd and 5th lines of each sextet should be eliminated if the magnetic moments are fully aligned in this direction. The influence of the external magnetic field to the low temperature Mössbauer spectra of Fe90Zr7B2Cu1 nanocrystals is shown in figure 7. The detailed field dependence shows that the intensity of the 2nd–5th lines, I2−5, is gradually de- creased with the external field and it vanishes above 2 T for the different phases as it is expected in normal ferromagnets. Since the properties of the residual amorphous tissue will be discussed later, the evaluated HFFD for this phase is only shown in the figure to demonstrate the reliability of our fitting procedure: the average hyperfine field of the amorphous nanophase decreases with the value of the applied external field as expected and the shape of the distribution is invariant. Similar behaviour is also found for Fe86Zr7B6Cu1nanocrystals [78]. Our investigation does not support the hypothesis of non-collinear spin arrangement of Fe atoms drawn from measurements at a few ap- plied fields where unsaturated behaviour was reported although in the high external field spectrum the presence of the 2nd and 5th lines cannot be observed [76,77].
In the following the effect of possible dissolved impurity content of the bcc grains for the Mössbauer spectra of nanocrystals will be discussed.
The influence of the dissolved impurities was also observed in some Mössbauer studies [79,80] and it was studied in details in our previous reports [51,52,78,81]. It is known since the early dilute alloy studies [74] that Mössbauer spectroscopy is very sensitive for impurities in the few atomic percents’ range. The hyperfine field of each
Figure 6. (a) Mössbauer spectrum of the Fe80Mo7B12Cu1nanocrystal measured at room temperature with the fitted subspectra and the corresponding hyperfine field distributions fitted according to [17]. (AM, IF and CR stands for the amorphous, interface and crystalline contributions, respectively, see text for details.) (b) Mössbauer spectrum of the Fe88Zr7B4Cu1nanocrystalline composite measured at 12 K and the evalu- ated hyperfine field distribution of the residual amorphous phase. The fitted subspectra are indicated in the
top of the figure, see text for details.
Figure 7. Influence of external magnetic field to the Mössbauer spectra of Fe90Zr7B2Cu1nanocrystals measured at 4.2 K (a) and the evaluated hyperfine field distributions of the residual amorphous tissue (b).
Fe atom which has nearest or next nearest impurity neighbour(s) is perturbed. It means that the number of iron atoms with modified properties has an initial slope of 14 Fe atoms per impurity atom. (The influence of further neighbours and the resolution of different neighbourhoods are also covered in the literature but it evidently goes beyond the scope of the recent review.) These Fe atoms with modified hyperfine parameters are observed in the Mössbauer spectrum as a satellite of the main Fe line (belonging to Fe atoms without nearest and next nearest impurity neighbours). Dissolved impurities in the bcc grains will result in a satellite feature similar to that observed in the nanocrys- talline spectra. The present section will only review the results for the main line. The results for the satellite will be discussed in the next part, after the similar structure in ball milled nanocrystalline Fe is investigated. The proper determination of the atomic frac- tion of the bcc phase (i.e., the assignment of the satellite feature to a different interfacial phase or to the impurity content of the bcc grains) is rather important since its magni- tude influences the estimation of the characteristic size and composition of the residual amorphous tissue.
The temperature dependence of the hyperfine field is characteristic for the different phases. The anomalous temperature dependence of the iron hyperfine field of the bcc phase near the Curie point of the residual amorphous phase is reported and interpreted as a direct evidence for their exchange coupling in Fe66Cr8Nb3Si13B9Cu1[82,83] and in Fe69.5Cr4V5Si13B8Cu0.5[84]. These reports refer to compositions with a significant Si, Cr and/or V content which leads to a broad distribution of Fe environments in the bcc phase. Similar behaviour is also reported for the nanocrystalline Fe73.5Nb4.5Cr5B16Cu1
alloy [85]. The temperature dependence of both the hyperfine field of the nanocrys- talline phase and the assumed grain boundary contribution deviates from that of pure α-Fe and their difference starts to increase near the assumed Curie point of the inter- granular amorphous phase. Similar results are reported [20] for Fe80Nb7Cu1B12. On the contrary, it was found for the Fe87.5Zr6.5B6nanocrystal that the hyperfine field of the bcc grains fairly fits to that of pure bcc-Fe below 600 K [18]. The overlap of the differently assigned wide distributions and the correlations between the fitting parameters make the determination of relatively small changes in the temperature dependence of the hyperfine field unreliable thus explaining the contradictory results.
The temperature dependence of the hyperfine field of the main line of the Fe92−xZr7BxCu1nanocrystals are summarised in figure 8, that of the pure bcc-Fe is also shown for comparison. The temperature range covers the respective Curie temperatures of the different residual amorphous phases (see later) and no anomaly of the temperature dependence in the main line of the bcc phase is observed. The curves practically overlap at low temperatures and gradually deviate at higher temperatures which makes it pos- sible to estimate how the Curie point of the bcc phase is modified due to the dissolved impurities. It is evaluated by using the asymptotic expression for the reduced magneti- sation of the α-Fe, σ ∼ (Tc −T )β, β = 0.38 [86] and attributing the hyperfine field depression (relative to pure bcc-Fe) measured at T = 700 and 750 K to the decreased Curie point. The results are shown in figure 9: the extrapolated Curie point of the bcc phase initially decreases and shows a broad minimum as the Fe content of the precur-
Figure 8. Temperature dependence of the hyperfine field of the main line of the Mössbauer spectra in Fe92−xZr7BxCu1nanocrystals together with this dependence for the hyperfine field of pure bcc-Fe.
Figure 9. Extrapolated Curie point of the nanocrystalline bcc phase as the function of the composition of the precursor amorphous phase. Data (extrapolated from the iron hyperfine field values measured at 700
and 750 K for the main lines) are indicated by circles and dots, respectively.
sor amorphous phase decreases. This behaviour indicates the presence of an increasing amount of impurities in the bcc phase. At least two different kind of impurities should be present to explain the appearance of the minimum.
3.2. Interfaces in nanocrystalline composites
The structure and the boundary range of the nanocrystals is a contradictory issue.
Among many similar studies nanocrystalline Fe was also produced by ball milling and cold surface evaporation. The atomic structure was interpreted by assuming a wide and low density fully disordered (gas-like) grain boundary phase [87]. The hyperfine struc- ture was also attributed to a grain boundary phase which had a higher value of the low temperature magnetisation but decreased faster with temperature than that of the bulk bcc phase [30]. Besides the reported hyperfine field behaviour, early EXAFS results also fit to the trend that wide grain boundaries are detected with a significant density deficit and decreased co-ordination numbers [88]. After the experimental artefacts of the EXAFS measurements had been carefully eliminated for nanocrystalline Cu, it was found [27] that the coordination number was very close to that of the bulk value. The same results have recently been confirmed also for ball milled nanocrystalline Fe [28].
A recent Mössbauer work [89] however claims that in ball milled pure nanostructured Fe a significant fraction of the atoms are located at the surface with a hyperfine pat- tern with a decreased average field. Similar results were published for attritor milled nanostructured Fe [90].
Besides the fact that the two reported structures are by no means close, theoretical and experimental trends also contradict the expectation that the interfacial atoms have a reduced hyperfine field (magnetic moment). It is known for a long time that the Fe atomic moment increases with atomic volume (i.e., with reduced density) [91]. It is confirmed by electronic structure calculations for small clusters that the magnetic mo- ment increases when the co-ordination number is reduced [92] to the extent that for an Fe dimerµ =3.25µBis used. The calculations predict 2.9–2.5µB/Fe for 9–229 atom clusters [93], a result which is verified by the most sophisticated Stern–Gerlach exper- iments for atomic clusters [94]. A similar trend, i.e., increased magnetic moment for the Ni atoms in the grain boundary with reduced density is also observed in polarized neutron reflectivity measurements [95]. While the width of the boundary and the mag- nitude of the enhancement might be overestimated, the trend is also in good agreement with atomic cluster experiments [96]. Theoretical calculations for amorphous Ni [97]
also hint that the magnetic moment is rather insensitive to the amount of disorder. These conclusions are also verified for nanocrystalline iron by the observation that the magne- tization is essentially unchanged when the grain size is reduced to 7 nm [98].
Experimentally iron/non-magnetic material (e.g., Fe/B) multilayers are the most suitable to study the interfacial fraction of pure bcc Fe. A considerable fraction of the alternately deposited Fe and B layers form an amorphous alloy phase [99]. Figure 10 shows our results [33] for thedFe =2.5 nm thick deposited layer, where the amorphous alloy thickness is near 2 nm. The average thickness of the residual bcc layer is near 0.5 nm and it is surrounded by amorphised regions. The applied external magnetic field suppresses the 2nd–5th lines of the spectra enabling a better evaluation of the HFFD of the amorphous region [33]. Comparison of the outmost lines of the 0.5 nm thick (a) and the 1µm thick (b) sample shows, that apart from the somewhat increased linewidth
Figure 10. Mössbauer spectra of a Fe/B multilayer with 2.5 nm thick deposited Fe layers (a) and a 1µm thick Fe sample deposited to Si substrate (b) at 4.2 K and in 3 T external magnetic field. The amorphised Fe–B alloy thickness is near to 2 nm, and the sharp lines at low velocities belong to Fe impurities in the Al
substrate.
(0.36±0.02 mm/s), the hyperfine splitting of the 0.5 nm thick bcc layer (which is exclu- sively interface, based on its thickness) is the same as the bulk value within 0.1 T. The difference between the hyperfine field of iron atoms in the interface and in the bulk is in the order of the experimental Mössbauer linewidth.
It is difficult to exclude that the frequently reported excess structure in the hyperfine pattern of ball milled Fe is dominantly influenced by the impurity content (Cr and C) originating from the used milling tools. Each impurity atom affects the hyperfine field of nearest and next nearest Fe atoms: it is a factor of 14 as discussed before. It was shown [100] that this structure might be caused even by some tenths of an atomic percent of Cr. It was shown independently that the same effect might also be caused by a minor amount of C impurities [101]. Taking into account the observation that mechanically alloyed materials consist of nanometer sized zones [102], the heterogeneous presence of traces of multiple impurities can not be excluded by routine analytical techniques. This finding is of considerable importance for the correct interpretation of our nanocrystal results.
3.2.1. Satellite of the Mössbauer spectra due to dissolved impurities
It was shown in section 3.1.2 that APFIM results and lattice parameter values for nanocrystals indicate dissolved impurities in the bcc phase of the nanocrystal. The tem-
perature dependence of the main line of the Mössbauer spectra was shown to indicate a measurable amount of impurities. This confirmed presence of impurities should in turn yield a corresponding satellite in the Mössbauer spectra near 30 T. It was also discussed in the previous paragraph that the hyperfine features observed in this range for ball milled nanocrystalline Fe cannot be unambiguously associated with interfacial atoms. In the following we will discuss the satellite feature of the Mössbauer spectra in the nanocrystalline composite.
The influence of the external magnetic field on the satellite and the main line is compared first. The Mössbauer spectra of Fe90Zr7B2Cu1nanocrystals in different exter- nal magnetic field was previously shown in figure 7. Since the hyperfine field is oriented antiparallel to the magnetic moment, the quantity which characterise in the simplest way the hyperfine field in external magnetic field is defined asBplus=Bhf+Bext. The results are shown in figure 11 for both, the main line and the satellite. As the external mag- netic field is perpendicular to the plane of the ribbon, the demagnetization field, 4π Ms, should be attained for saturation. Above that, the external magnetic field corrected Bplus
is independent of the external field. The demagnetisation field established this way is in good agreement with the external field where the elimination of the 2nd and 5th lines is observed. The main line and the satellite follow a common dependence on external magnetic field in both the Fe90Zr7B2Cu1 and Fe86Zr7B6Cu1 nanocrystals. The consis- tent fitting of the Mössbauer spectra in several different external applied magnetic fields supports the identification of the satellite as given above.
The ratio of the satellite hyperfine field to the main line is temperature independent as shown in figure 12 for the Fe88Zr7B4Cu1 nanocrystal. It means that both the main line and the satellite follow the temperature dependence determined by the same Curie point [78]. This observation indicates that the satellite belongs to the bcc phase.
The excess features of the Mössbauer spectra (i.e., those beyond pure bcc Fe and the residual amorphous tissue) are frequently attributed to a grain boundary phase
Figure 11. The external magnetic field dependence ofBplus=Bhf+Bextat 4.2 K in Fe90Zr7B2Cu1and Fe86Zr7B6Cu1for both the main line (full and empty circles) and for the satellite (full and empty squares),
respectively.
Figure 12. Temperature dependence of the hyperfine field of the main line,Bm, the satellite,Bs, and their ratio in Fe88Zr7B4Cu1nanocrystal.
Figure 13. (a) Difference between the hyperfine field attributed to pure Fe (CR) and the average of the so-called interface (grain boundary) (IF) contribution for different alloying elements of the FeMBCu (M= Zr, Nb, Mo, Ti) nanocrystals taken from [18] and [103] (empty symbols). The average decrease of the Fe hyperfine field due to single first and second impurity neighbours in bcc dilute iron alloys taken from [74]
and [52] are also shown (filled symbols). (b) The low temperature saturation hyperfine field of the main line (full dots) and the satellite (empty circles) as a function of the composition of the precursor amorphous
phase in Fe92−xZr7BxCu1.
[16–20]. It is argued that the observed features are universal for nanocrystals with dif- ferent alloying elements (e.g., Zr, Nb, Mo, Ti) [103]. Figure 13(a) shows the difference between the hyperfine field attributed to pure Fe and the average of the so-called in- terface (grain boundary) contribution for different alloying elements of the FeMBCu (M = Zr, Nb, Mo, Ti) nanocrystals taken from [16,103]. The data show a consider- able scatter, not only because they are taken at different temperatures (between 373 and 77 K), but even when the same spectra are evaluated on the base of slightly different assumptions [16]. As it was mentioned in section 3.1.2, these differences may be at- tributed to the temperature dependent overlap and arbitrary assignment of the different
contributions together with the problems caused by the correlation with the intensities of the 2nd and 5th lines. However, a trend which reflects the averaged behaviour of a single impurity in the dilute iron based alloys in the first two co-ordination shells seems to be present in these data. Dissolved boron and further impurities in these co- ordination shells will obviously influence the satellite position. In the nanocrystalline Fe90−xZr7BxCu1 alloys similar behaviour is found. The dependence of both, the main line and the satellite (low temperature saturation) hyperfine field on the composition of the precursor amorphous phases is shown in figure 13(b). An independent indication that the satellite is caused by impurities is, that in contrast to the main line whose position is constant, the satellite hyperfine field moves towards the main line with increasing B content. A Zr neighbour causes a higher perturbation of the hyperfine field of a close Fe atom than a B atom does. While the separate B and Zr environments cannot be re- solved in the Mössbauer spectra, the gradual shift from the dominant Zr neighbours at the low B content range to the B richer environments for the higher B content alloys is evident.
The inset of figure 14 shows the amount of impurities in the bcc phase. The es- timate is based on the relative intensity of the satellite in the Mössbauer spectrum as- suming binomial distribution in the first two co-ordination shells. This determination is of limited accuracy. The main source of systematic error is the large linewidth of the satellite since both B and Zr contribute to it. Their ratio (and this way also the width of the satellite contribution in the Mössbauer spectra) changes with the B content. This systematic error may cause an overestimation of the satellite intensity. If the average im- purity content of the bcc grains were proportional to the B+Zr content of the precursor amorphous phase the trend shown in the inset would be obtained. This is not evident in the figure, which is attributed partly to the large systematic errors in the determination of the satellite intensity. The other reason is the binomial assumption, i.e., the assumed ran-
Figure 14. Fraction of the Fe atoms in the bcc phase (the sum of the main line and the satellite contributions) as the function of the composition of the precursor amorphous phase (dots) in nc Fe92−xZr7BxCu1alloys.
The solid line corresponds to the calculated curve for pure Fe grains in the Fe2(B,Zr) residual amorphous tissue. Empty circles: the fraction of the inter-grain atoms (see below in section 3.2.2) as a function of the composition of the precursor amorphous phase. Inset: the amount of impurities in the bcc phase based on the relative intensity of the satellite in the Mössbauer spectrum assuming binomial (i.e., random) distribution in the first two co-ordination shells. The solid line is the linear dependence of the impurity content on the
precursor amorphous phase composition.
Figure 15. bcc fraction values determined in Fe90Zr7B3 by X-ray diffraction, DSC and by Mössbauer evaluation when the satellite intensity is not included to the bcc phase [104].
dom distribution of the B and Zr atoms in the bcc phase. In contrast to this, the pairing of Zr and B, thus the enhancement of Zr solubility at high B content is expected.
Consistent description of our findings is not possible when the satellite is associated with grain boundary atoms. It was shown before (in agreement with related literature re- sults) that the bcc grain size decreases significantly in the broad composition range of the present study. This change is evidently not reflected in the satellite intensity which excludes its association with grain boundaries. The previous observation [52], that a significant satellite intensity is still observed when the grain size reached a consider- able value due to further high temperature annealing, points to the same direction. Our conclusion from the preceding discussion is that according to the line of independent ev- idences (as external magnetic field, temperature and composition dependencies) shown above, the satellite in the Mössbauer spectra must be attributed to the bcc phase. The fraction of Fe atoms in the bcc phase have to be calculated both from the main line and the satellite intensities, their sum is shown in figure 14. The dependence on the com- position of the precursor amorphous phase will be analysed later, when it is used for the estimation of the characteristic size and the composition of the residual amorphous tissue.
Some reports in the literature which associate the satellite to grain boundaries, do not include its contribution to the bcc fraction. Figure 15 shows literature results where bcc fraction values determined by X-ray diffraction, DSC and Mössbauer evaluation as described above are compared [104]. The bcc fraction is systematically underestimated in the evaluations of the Mössbauer spectra when the satellite intensity is not included to it.
3.2.2. Interlayer
While it was elaborated in details in the previous section that the satellite observed in the whole temperature range is not associated with grain boundaries, there is a much smaller fraction of sites with a remarkable magnetic behaviour which might belong to this category. Figure 16(a) [78] shows the Mössbauer spectrum of the nanocrystalline Fe86Zr7B6Cu1alloy determined at 651 K, i.e., above the Curie temperature of the resid- ual amorphous tissue. Figure 16(b) shows the contribution obtained after the subtrac- tion of the fitted bcc (main line plus satellite) contribution from the measured spectrum, the inset denotes the hyperfine field distribution of this residual spectrum. A hyperfine field substantially less than that of the bcc phase is observed besides the contribution of the paramagnetic amorphous tissue. This component belongs to 4–8% of the Fe
Figure 16. Mössbauer spectrum of the nanocrystalline Fe86Zr7B6Cu1alloy at 651 K (above the Curie temperature of the residual amorphous tissue) (a) and the residual spectrum after the subtraction of the fitted bcc (main line plus satellite) contribution from the measured spectrum (b). The inset shows the
corresponding hyperfine field distribution.
Figure 17. Temperature dependence of the hyperfine field of the inter-grain contribution in Fe90Zr7B2Cu1 nanocrystal (a) and the ratio of this value to that of the main line (b).
atoms, which correspond to two atomic layers if it comprises the grain boundary re- gions. The temperature dependence of the hyperfine field of this contribution is shown in figure 17 [105], together with the ratio of this value to that of the main line. The proportionality might indicate, that this very small fraction of Fe atoms is located very close to the bcc grains. The low temperature extrapolation yields about 13 T, i.e., about 1 µB for the magnetic moment of the Fe atoms for these sites. The estimated isomer shift of this contribution is a higher negative value than that of the residual amorphous tissue, which indicates a Zr rich environment. The empty circles in figure 14 show that the fraction of these inter-grain atoms is between 4 and 8% and can only be determined with a considerable scatter. This contribution can only be evaluated above the Curie temperature of the residual amorphous tissue. At lower temperatures the broad magnetic hyperfine field distribution of the residual amorphous phase prevents its observation.
3.3. Residual amorphous tissue
Two aspects will be treated here: besides the characteristic average size, the com- position of the residual amorphous phase will also be discussed.
3.3.1. The composition of the residual amorphous phase
Figure 14 shows the dependence of the bcc atomic fraction (main line plus the satellite) on the composition of the precursor amorphous phase. In order to avoid the use of free parameters, the solid (calculated) line corresponds to the oversimplified crys- tallisation scheme of pure Fe formation with Fe2(B,Zr) residual amorphous tissue. The agreement is satisfactory except for the highest B composition region, where neither ne- glecting B and Zr dissolved in the bcc phase nor the simple crystallisation scheme is fully justified. It was shown in the studies of the crystallisation of melt quenched amorphous Fe2(B,Zr) alloys that an amorphous or nanocrystalline B–Zr phase which is directly not detected either by diffraction or other methods should also be present to conserve mass
Figure 18. The room temperature isomer shift (1IS) of the melt quenched amorphous Fe2(B1−yZry) ribbons (empty circles, plotted asx=7(1−y)/y) and that of amorphous Fe2Zr (square) together with the results for the residual amorphous tissue of the nanocrystalline composites (full dots, the star is from [19]).
All figures are relative toα-Fe.
balance [106]. In the nanocrystalline alloy Mössbauer measurements safely exclude Fe containing compound formation, a B–Zr phase might, however, form in the hetero- geneous composite due to the strong B–Zr interaction at high B contents and remains undetected in X-ray measurements due to its small grain size or amorphous structure.
The transformed bcc fraction is thus successfully described as bcc Fe grains in the residual amorphous tissue of the composition shifted to Fe2(B,Zr). Since no detailed composition dependence studies are reported in the literature, this finding can only be compared to some scattered compositions. The Fe concentration of the residual amor- phous phase at the end of the nanocrystallization of the Fe77B18Nb4Cu1amorphous alloy is predicted [107] as 67 at% Fe content. In case of the Fe87B6Zr6Cu1nanocrystal the Fe fraction is given in the residual amorphous phase at the highest heat treatment tempera- ture; it corresponds to 65 at% Fe content [19]. When the different uncertainties are taken into account these findings are in good agreement with our results. In order to compare the properties of the nanosized amorphous regions to those of the macroscopic amor- phous phases, Fe67(ZryB1−y)33 ribbons were melt quenched and they were found to be fully amorphous in the 06y 60.55 composition range [106]. Figure 18 shows the iso- mer shift of these amorphous alloys together with the results for the residual amorphous tissue of the nanocrystalline composites [81]. The agreement confirms our identification of the composition of the residual amorphous tissue and this way opens the route for the comparison of the nanosized amorphous phase to the macroscopic phase of very close composition as proven by the isomer shift. This comparison of the magnetic properties is the subject of the next section.
3.3.2. The characteristic size of the residual amorphous tissue
In the simplest approximation (of monosized cubes) the thickness (characteristic size) of the residual amorphous phase, d, the bcc grain size, D, and the transformed bcc fraction, p, are related as: d = D(p−1/3−1) [107]. The characteristic size val- ues evaluated from the measured grain size (figure 4) and the transformed bcc fraction values shown in figure 14 (i.e., using atomic fraction for volume fraction neglecting density differences) are indicated in figure 4 by empty circles. The characteristic size of the residual amorphous tissue is found to be independent of the composition of the
amorphous precursor. It is a remarkable feature as it is derived from the bcc grain size and the transformed fraction values both showing marked composition dependencies.
The continuous line which describes (without any fitting parameters) the grain size de- pendence is the same relation using the constant characteristic size value, 4 nm with the transformed fraction resulting from the oversimplified crystallisation scheme of pure Fe grains in the Fe2(B,Zr) residual amorphous tissue. The composition independence of the thickness of the residual amorphous tissue might be an important property of the nanocrystalline composite. The characteristic size of the residual amorphous phase is re- lated to the soft impingement of the diffusion zones which effectively block the further growth possibility of the bcc grains [47,48].
4. Magnetic behaviour of the nanostructure
In this section three closely related topics will be treated. Since the interest in the Fe-rich Fe–Zr–B based nanocrystalline materials is mainly motivated by the soft magnetic properties these will be reviewed first. The emphasis of this treatment is on the comparison with the more studied Finemet-like alloys. The magnetic properties (Curie temperature and hyperfine field) of the bcc phase was extensively discussed in section 3.1.2. The magnetic properties of the residual amorphous tissue will be presented here. Both, the Curie temperature and the atomic magnetic moment distribution (mani- fested in the hyperfine field distribution) will be treated in this section. It is concluded by presenting Mössbauer spectroscopic evidences for magnetic moment relaxation at high temperatures for 10 nm or smaller bcc nanograins. In this context the possible coupling mechanisms between the nanophases will be discussed.
4.1. Soft magnetic properties
Since these properties have already been subject of excellent reviews [4] some re- cent developments will only be mentioned here. According to Herzer’s model, when the grain size is much lower than the exchange length, the crystalline anisotropy is averaged out and soft magnetic behaviour occurs (if the magnetostriction is also low enough). The prediction of the theory is that the coercive field decreases as the 6th power of the grain size, Dwhen the uniaxial anisotropy is negligible in comparison with the random crys- talline anisotropy. This behaviour has been observed in some Finemet type alloys and it is only modified below 1 A/m coercive field. In this extremely soft limit (field- and magnetoelastic) induced anisotropies must also be taken into account [108].
The grain size dependence is different when the long range uniaxial anisotropy is much larger than the random magnetocrystalline anisotropy. In this limit the aver- aged effective anisotropy must be recalculated self-consistently, which yields itsD3de- crease. This dependence was observed both in Cu-containing and Cu-free low B content Fe91−yZr7B2Cuy(y =0, 1, 2) nanocrystals [108]. The same behaviour has also been obtained for Fe73.5Si13.5B9Cu1TM3 (TM= Ta and Nb) alloys [109]. The mechanism causing this uniaxial anisotropy is not yet established. The origin of uniaxial magnetic
