- Email: [email protected]
Mössbauer study of fine structure features of equiatomic FePd alloy after severe plastic deformation and ordering annealing
Journal of Alloys and Compounds 583 (2014) 191–197
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Mössbauer study of fine structure features of equiatomic FePd alloy after severe plastic deformation and ordering annealing N.I. Vlasova a,b,⇑, N.M. Kleinerman a, V.V. Serikov a, A.G. Popov a a b
Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 18 S. Kovalevskoi Str., 620990 Ekaterinburg, Russia Institute of Nature Sciences, Ural Federal University, 48a Kuibysheva Str., 620141 Ekaterinburg, Russia
a r t i c l e
i n f o
Article history: Received 20 June 2013 Received in revised form 15 August 2013 Accepted 16 August 2013 Available online 31 August 2013 Keywords: Intermetallics Nanostructures Crystal structure and symmetry Nuclear resonances Strain High pressure
a b s t r a c t Using Mössbauer spectroscopy based on modern methods of processing spectra, new fine features of the structure of equiatomic alloy FePd, which is formed upon the A1 ? L10 phase transformation in the course of severe plastic deformation by torsion and annealing for ordering at the temperature T = 450 oC, have been studied. It is shown that the structure of the alloy in the as-deformed state cannot be treated as a homogeneous solid solution; it is more likely to consider it as an alternation of disordered regions that are different in composition and in the sign and degree of tetragonal distortions of the initial fcc lattice. Already at early stages of ordering annealing, there are detected low-symmetry regions, inhomogeneous in composition and in the degree of ordering, with tetragonal distortions of the same sign but essentially different in magnitude. These regions can be identified as the structure constituents of the A6 and L10 type with the tetragonal lattice. Such a multi-phase structure is retained even after a long-time (tann = 40 h) annealing. A conclusion is made that the equilibrium tetragonal L10 phase is formed as a result of long-term redistribution of Fe atoms between the initial cubic and newly formed tetragonal components. The effect of the fine-structure peculiarities on the coercivity of the FePd alloys is considered. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction The hard magnetic alloys Co–Pt, Fe–Pt, and Fe–Pd, which possess an L10-type ordered structure, have intensively been studied for the last decades. Nowadays, these materials are paid evergrowing attention as promising magnetic media for high-density recording and storage of information. The FePd alloys, similarly to FePt, exhibit high values of saturation magnetization, magnetic anisotropy constant [1–4], and the theoretical limit of maximal energy product (BH)max = 47 MGOe; yet, the latter can hardly be realized because of low coercivity. In [5–8], data are reported on the realization in this material, when subjected to a severe plastic deformation by cold rolling or by torsion and subsequent annealing, of a coercive force Hc = 1.40–1.75 kOe, which is several times as high as Hc of the annealed nondeformed sample; however, this value makes up no more than 5% of the anisotropy field (35 kOe). The level of magnetic hardness is strongly dependent on the degree of long-range order; therefore, the process of the formation of a structure that provides enhanced magnetic characteristics remains
⇑ Corresponding author at: Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 18 S. Kovalevskoi Str., 620990 Ekaterinburg, Russia. Tel.: +7 343 378 37 82; fax: +7 343 374 52 44. E-mail address: [email protected] (N.I. Vlasova). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.08.110
in the focus of researchers using different experimental techniques. Recently, it has been shown [8–10], employing methods of electron microscopy, X-ray diffraction, and thermomagnetic and polarization-optics analyses, that in single-crystal, polycrystalline, and nanocrystalline samples of equiatomic FePd upon the phase transformation of the initial disordered A1 phase with an fcc crystal lattice (space group Fm3m) into an ordered L10-type structure (space group P4/mmm), a metastable disordered bct phase with a structure of the A6 type (space group I4/mmm) is formed, which can cause a lowering of the coercivity Hc. Clear ideas about the mechanisms of structure formation in these alloys and the relationship between the structure and magnetic properties are urgent for the development of approaches to realizing the potential of these materials. However, structure techniques applied in most researches are lacking the ways of gaining information on the fine features of the structure. The Mössbauer method is a widely employed powerful tool of studying the processes related to the redistribution of atoms in Fe-based alloys. However, the earlier Mössbauer experiments on the kinetics of atomic ordering in single crystals, polycrystalline samples deformed by rolling, and aerosol powder samples of FePd did not show up any signs of formation of metastable phases upon the A1 ? L10 transformation [11–15]. The generally recognized advances of the authors of [12] are the dependence of the hyperfine
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
field (Hhf) on the Fe concentration in the range of 25–75 at.% for the alloys in the disordered state, constructed based on the experimental data; and data on the effect of atomic correlation on Hhf for the alloys subjected to annealing for ordering. However, the methods of analysis of that time did not allow gaining full information from the spectra measured and estimation of the whole bulk of data on the structural changes. Nowadays, currently designed and widely applied computer programs present ample opportunities for analyzing the results of Mössbauer studies. In the later works [16], fitting of the Mössbauer spectra was performed by the method of restoration of probability-density distribution functions for the parameter Hhf. The form of these distributions allows a qualitative description of the dynamics of relative changes for individual contributions at different steps of treatment of massive and film samples; however, no quantitative estimates of the parameters of individual structure components were made, which could give grounds for the construction of a model of the alloy structure. In the work presented, modern possibilities of the Mössbauer spectroscopy are used for the investigation of the process of formation of long-range order in nanocrystalline FePd samples with a composition close to equiatomic. 2. Experimental As-cast polycrystalline coarse-grained samples of the equiatomic FePd alloy in the form of rods 50 mm in length and 6 mm in diameter were homogenized at a temperature of 950 oC for 6 h and quenched into icy water. After quenching, diskshaped samples were cut off from the rods and then deformed by the method of severe plastic deformation by high-pressure torsion (HPT) at the number of revolutions n = 10 and a high quasihydrostatic pressure P = 6 GPa and annealed at a temperature of 450 oC with holdings from 0.5 to 40 h. Under the conditions stated, mechanical and heat treatments result in the formation of a nanocrystalline state (d = 50–200 nm [7,8]) in the FePd samples that are featured by the maximal values of coercivity (Hmax 1760 Oe). The Mössbauer spectra were measured at 300 K in c the mode of constant accelerations with a source of Co57 in the chromium matrix. The measurements were performed on foils 20 lm thick with the use of an MS1101 spectrometer (512 channels, (5–8) 105 counts/channel, quality factor of 70–80). The spectra were analyzed, with allowance for the effects of self-absorption, using the program package MSTOOLS [17] which, along with the direct fitting of spectra with a number of subspectra, allows construction of the co-called multi-core distributions of the probability density for different hyperfine parameters if there are grounds to suppose that different structure components present different correlation relations of at least two Mössbauer parameters. In such a case, several mathematical ‘‘cores’’ are specified to independently restore different distribution functions. The isomeric shifts were taken relative to the spectrum of a–Fe.
3. Results 3.1. Dependence of coercivity for the samples of the FePd alloy on the time of annealing Comparison of the dependences of coercivity on the time of annealing obtained up to now for the FePd samples shows that the maximal values of Hc are the higher, the larger the degree of preliminary plastic deformation and the lower the annealing temperature [5–8]. It also follows from [5–8] that, taking into consideration the duration of annealing required for the achievement of the maximal Hc, the optimal annealing temperature is T = 450 °C. In Fig. 1a there are shown dependences of the coercivity on the time of annealing tann at 450 oC for the as-cast sample that (1) is quenched from 950 °C and (2) is subjected to subsequent HPT with n = 10. Higher values of Hc for the deformed sample and faster kinetics of its growth, as compared to sample 1, are traceable to both finer grains and accelerated process of ordering in a material with the strain energy stored upon HPT. In sample 2, HPT and annealing at 450 oC for 15 h led to the achievement of the value Hc = 1760 Oe. To ascertain the fine structure peculiarities of the deformed FePd that are formed in the course of the A1 ? L10 phase
2
1600
1200
Нс (Oe)
192
800 1
400
0
0
10
20
30
40
Annealing time (h) Fig. 1. Dependence of coercivity Hc of the FePd alloy on the time of annealing at T = 450 oC. 1 – quenched alloy; 2 – after subsequent HPT at P = 6 GPa and n = 10 revolutions.
transformation and could cause low maximal values of Hc, Mössbauer studies of the structure transformations were performed on an alike sample.
3.2. Mössbauer spectra for samples after quenching and HPT Fig. 2 shows a spectrum (a) and its description with the use of one-core distribution of hyperfine fields P(Hhf) (b) for the sample of the FePd alloy after quenching from 950 °C. Both the form of the very distribution and the difference graph between the experimental and calculated values of spectral intensities (at the bottom of Fig. 2a) testify to the presence in the structure, along with the main component whose average hyperfine field coincides with the value (323 kOe) determined in [12] for the equiatomic composition, of an additional contribution with lowered values of hyperfine fields (Fig. 2b), which cannot be associated with regions of disordered equiatomic alloy. Besides, small peaks in the envelope indicate the presence of short-range-ordered regions. Failure to attain a homogeneous disordered state in the equiatomic alloy via quenching was reported on in a number of works, including [12]. After HPT, the relative content of iron in the low-field regions becomes negligibly small and the very distribution for the whole bulk of the sample becomes more homogeneous (Fig. 2d). In this figure, there are also given binominal distributions for three compositions: Fe50Pd50, Fe49Pd51, Fe48Pd52. It is seen that these distributions do not match the one-core curve either in the form or in width, which means that this state cannot be described under an assumption of a homogeneous solid solution close in composition to the equiatomic. At the same time, the simulation of the spectrum with the use of two-core representation involving two binominal distributions resulted in a more exact description (Fig. 2e and f). The average hyperfine fields Hhf of these two-core distributions make up 306 and 340 kOe; the quadrupole shifts Q are small in magnitude and different in sign, 0.068 and 0.13 mm/s; and the relative fractions of these contributions are equal to 55 and 45%, respectively. One can suggest the presence in this sample of disordered regions of two compositions with deviations from the equiatomic one toward higher contents of both iron and palladium. If we again use the dependence of Hhf on the concentration constructed in [12], we can approximately estimate the concentration of elements in these regions, though the very dependence was constructed with no allowance for the deviation of the form of spectral envelope from the Lorenz line; only the centers of gravity being taken into consideration. Such estimation gives compositions differing from equiatomic by approximately ±10%. The same approach turned out valid when describing the spectrum after quenching as well, which means that regions of
193
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
0.02
100
a
98
b
0.01 0.00 0.02
94 100
c
98
d
Fe50Pd50 Fe49Pd51 Fe48Pd52
0.01
P (H)
Intensity (%)
96
96
0.00 0.02
100
e
98
f
0.01
96 -8
-6
-4
-2
0
2
4
6
8
100
150
200
250
300
350
0.00 400
Н (kOe)
V (mm/s)
Fig. 2. Spectra and distribution functions P(H) for the Fe50Pd50alloy: (a, b) after quenching; (c, d) after deformation, in the one-core mode (additional lines - binomial distributions for Fe50Pd50, Fe49Pd51, Fe48Pd52); (e, f) after deformation, in the two-core mode.
different composition are present in the structure already after quenching, though the very compositions and the volume fractions of the constituents are somewhat different. The spectrum is treated most correctly via fitting with eight independent subspectra with equal linewidths determined in the course of iteration process. Based on the results of such computations, there were constructed dependences of the relative area (S) of the subspectra (Fig. 3a) and of the quadrupole shift (Q) (Fig. 3b) on Hhf. Considering approximately equal changes in Hhf for the contributions found, one can ascribe these contributions to particular configurations of neighborhood of iron atoms in the fcc lattice. For the given composition of the binary alloy, the main configurations Pd:Fe in the first coordination shell of an iron atom turn out to be 9:3, 8:4, 7:5, 6:6, 5:7, 4:8, 3:9 and 2:10. If we assume that two contributions with the highest Hhf values are related only to one solid solution (for the distribution with the essentially lower average Hhf the probability of such configurations is negligibly small), then from the ratio of their areas one can construct, using the binominal law, the other relative fractions and subtract them
Number of Fe neigbours 20
3
4
5
6
7
8
9
S (%)
3.3. Mössbauer spectra changes in the course of annealing of the deformed samples
10
a
16 12 8 4
Q (mm/s)
0
b
0.04 0.00 -0.04 280
300
320
340
360
from the total dependence. Then, the remaining intensities can be ascribed to the other solid solution and their dependence on Hhf can be restored. The results of such analysis are shown in Fig. 3a. The relative volume fractions of these two solid solutions, determined in such a way, make up 54 and 46% and the positions of maxima are 310 and 345 kOe, respectively. Moreover, in accordance with the statistic law, the compositions of these regions can be approximately estimated to be 44 and 62% Fe. The data obtained are close to the above estimated contributions from the two-core distributions using data from [12]. Besides, the dependence Q(Hhf) (Fig. 3b) testifies to the presence in the deformed sample of weakly distorted regions with different signs of distortions of the crystal lattice, the maximal positive Q being equal to 0.11 mm/s at Hhf = 281 kOe. It can be concluded that already in this state the sample is featured by local inhomogeneities in composition, which may result in the observed local tetragonal distortions of the fcc lattice. As to the isomeric shift, its value increases with decreasing Heff, i.e., with increasing number of Pd nearest neighbors, linearly from 0.15 to 0.20 mm/s.
380
H (kOe) Fig. 3. Results of description of the experimental spectrum of the deformed sample via fitting with eight subspectra: (a) dependence of the total subspectra intensities and of two separated contributions on H; (b) dependence of Q on H for the eight subspectra.
In Fig. 4, spectra and two-core distribution functions P(Hhf) are given for the states of the sample after different annealing holdings. The spectra were treated under the assumption that the ordering tetragonal regions differ from the initial fcc phase in correlation of the hyperfine parameters. In the graph for the state after 30-min holding, there is already present a contribution in the Hhf range 250–280 kOe, which was absent immediately after deformation (for comparison, the distribution P(Hhf) for the deformed state is shown in this figure by a solid thin line). In accordance with the known results of X-ray and Mössbauer studies [5–8,12,15], this fact testifies to the onset of the formation of a tetragonal structure in this sample. In the course of annealings, the contribution from the regions with the distorted fcc lattice decreases, and the tetragonal regions make two distinct contributions already after the 2.5 h holding, whose ratio changes with the annealing time. Similar distribution functions were constructed in the one-core representation from the Mössbauer spectra of the Fe50Pd50 alloy in the states after different annealings of the quenched sample in [16]. However, since the description was performed on the
194
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
0.02 100
b
1
а
1 0.00 0.02
100
2
2 0.00 0.03
3 3
0.00 0.03
100
4
P (H)
Intensity (%)
100
4 100
0.00 0.03
5 5
100
0.00 0.03
6 6
95 -8
-6
-4
-2
0
2
4
6
8
240
280
V
320
0.00 360
400
Н (kOe)
Fig. 4. (a) Spectra and (b) two-core distributions P(H) for the Fe50Pd50 alloy after annealings for different times: 1–0.5 h; 2–2.5 h; 3–5 h; 4–10 h; 5–20 h; 6–40 h (for comparison, solid thin line in graph 1 shows the distribution function for the deformed state of the sample).
assumption of one linear correlation of the parameters from both the cubic and tetragonal structure components, no detailed analysis of the contributions to the distribution function could be done. In our representation, the contributions from the cubic and tetragonal regions can be separated based on their different correlation functions, but to estimate the individual parts taken by regions with different lattice distortions is impossible in this approach. To more exactly separate all the contributions, the experimental spectra were fitted with 10 subspectra with the linewidth equal to that of the line from pure iron. Fig. 5a presents the examples of such fitting; and Fig. 5b shows histograms of distributions of the relative area (S) of the subspectra (or relative fractions of iron in the corresponding regions) over Hhf. In Fig. 5b, the subspectra are numbered from 1 to 10. The relative fractions of the contributions (No. 7–10) from the regions with a high Fe content (Hhf > 330 kOe) and negative sign of the quadrupole shift Q virtually disappear al-
100
ready after 5 h, and only a small contribution with the Hhf = 330 kOe is retained, which can be ascribed to iron-containing regions with the bcc structure. Their relative fraction is well determined to be 5% just after a 5-h holding. The presence of a small amount (3–5%) of such regions in the structure of the alloy was also discovered in the neutron diffraction study of nanocrystalline Fe100 xPdx (x = 50, 53, and 60) alloy [18]. The isomeric shift for all the lines, except that for bcc iron, becomes closer in value and varies insignificantly in the range of 0.19–022 mm/s at the following steps of annealing. To ascribe lines 1–6 in the histograms in Fig 5b to the corresponding regions in the tetragonal structure, there were constructed dependences of the relative fractions of the contributions S and their quadrupole shifts Q on Hhf, which are shown in Fig. 6a and b, respectively, for several annealing holdings. Taking into consideration the values of Hhf and Q, as well as their changes in
b
a
1
98
2
3
4
5
6
7,8
0.5 h 20 9
10
0.5 h
0 20
96 100
0 20
5h
98
0
5h
96
20
S (%)
Intensity (%)
2.5 h
10 h 0 20
100 98
20 h 0
96
40 h
94 -8
40 h -6
-4
-2
0
2
V (mm/s)
4
6
8
20
0 260 280 300 320 340 360 380 400
Н (kOe)
Fig. 5. (a) Spectra for samples of the Fe50Pd50 alloy annealed for 0.5, 5, and 40 h; and (b) histograms of relative fractions of subspectra for a series of annealing times. Digits in the upper right graph mark the order number of the sextet.
195
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
35
0.5
a
30
0.3
Q (mm/s)
25
S (%)
b
0.4
20 15
0.5h 5h 40 h
0.2 0.1 0.0
10
-0.1 5 -0.2 0
280
320
360
400
280
320
360
400
H (kOe)
H (kOe)
Fig. 6. Dependences of (a) the relative fractions S of the subspectra and (b) the quadrupole shifts Q on H for several stages of annealing.
4. Discussion The experiments conducted and their analysis made it possible to pick out a number of peculiarities in the description of the structure that were absent in the previous Mössbauer studies. Thus, in one of the basic works [12] devoted to studying disordered FePd alloys of different compositions it was discovered that the spectral lines featuring disordered states had an asymmetric shape from both low and high values of Hhf. However, no analysis of such
80
60
S (%)
the course of annealing, three types of regions can be picked out. By the minimal values of Hhf and equal maximal values of Q 0.44 mm/s, two contributions (lines 1 and 2), whose intensities grow with time, though somewhat differently, can be ascribed to the regions of the first type with the highest tetragonal distortions, and (most probably) with the highest degrees of order [2–5,19,20]. To the second type, the structure components with lower (about by a factor of 1.5) quadrupole shifts Q 0.30 mm/s and, consequently, smaller tetragonal distortions can be referred (lines 3 + 4). They appear already at the early stages of annealing, and their intensities are approximately equal and almost independent of the time of annealing. The third type (lines 5, 6) comprises regions of variable composition with low positive distortions (Q = 0.2–0.1 mm/s). With increasing holding time, theirs contributions decrease. In Fig. 7 there are constructed dependences of the sums of individual contributions on the time of annealing. From the analysis of these curves it can be concluded that the summed contribution to the spectral intensity from the lines corresponding to large numbers of Fe atoms in the first coordination shell in the fcc lattice remains low and constant already after 10-h annealing. The contributions from two lines that are related to the regions with the most distorted crystal lattice (lines 1 and 2) grow though the dynamics of growth slows down after the 10-h annealing, whereas the sum of two intensities (lines 3 + 4) from the less distorted regions with higher Hhf starts decreasing. However, if to ascribe to these regions contributions with lower positive Q values (lines 5, 6), their summed fraction starts decreasing already after the 5-h annealing. Thus, already at the early stages of annealing there form regions with tetragonal distortions which are equal in sign but essentially different in magnitude. In the course of annealing there takes place a redistribution of iron atoms between both cubic and tetragonal structure components and over different regions of the tetragonal component proper.
1+2 3+4+5+6
40
3+4 20
0
Rest 0
10
20
30
40
Annealing time (h) Fig. 7. Dependences of spectral contributions from separated regions on the annealing time: 1, 2, lines with Q 0.44 mm/s; 3, 4, lines with Q 0.30 mm/s; 5, 6, lines with variable positive Q; the rest contributions are related to the cubic phase (for designations, see Fig. 5b).
asymmetry was done and the centers of gravity of the spectra were used to construct the concentration dependence of Hhf. The interpretation of the spectra measured in our work showed that the inhomogeneities in the structure of alloys are retained both after quenching and after HPT, and that they are not traceable to any shortcomings of homogenization and quenching modes. (In work [12], for example, the alloys were homogenized at T = 1000 oC for 100 h). Such features should be treated as indications of the presence of disordered regions significantly differing in composition rather than the effects of short-range ordering. This conclusion is supported by quantitative estimates gained from both two-core distribution functions P(Hhf) and fitting of the spectra with a set of subspectra, which are close in values. At the same time, the X-ray and electron microscopy examinations of deformed samples of this alloy [7,8,10] did not reveal any compositional inhomogeneities. One can suggest a model of a periodical arrangement of such regions, most likely nanosized and coherently related, by a kind of spinodal or pseudospinodal mechanism similar to that described in [21–23], which results in an averaging of local parameters. Besides, in [24], the reason for phase separation in nanostructured materials after HPT is stated to be different diffusion mobility of the constituting elements, which may be our case as well. In accordance with the model calculations of
196
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
microstructure upon phase transformations of the cubic-tetragonal type [22,23] and experimental results [8–10], the formation of such nanodomain regions with a distorted crystal lattice can evidently be treated as a precursor of the formation of a tetragonal phase. The description of the structural state of the alloy after different annealings given in [16] with the use of distribution functions allows, at best, quantitative estimations of Hhf and relative fractions of the contributions from the cubic and the tetragonal structure component. Such an approach failed to separate pronounced contributions to the spectra from different tetragonal regions. Similar faulty attempts were made as early as in [25] where conversion Mössbauer spectra of film samples were treated under the assumption of a linear correlation between the Hhf and Q magnitudes, which evidently is not valid in our case. However, the very quality of the conversion spectra together with the processing routines available at that time could not provide a stricter approach. In [15], the spectra were fitted with three subspectra, one of which, in high fields, was ascribed to the initial fcc structure, another, low-field, contribution with the values Hhf = 267 kOe and Q = 0.42 mm s, to the L10 structure with a certain degree of ordering, and the intermediate contribution with Hhf = 288 kOe and Q = 0.29 mm/s, to regions with a twinned structure or, to be more precise, to areas close to the boundaries of the ordered twins, in which the exchange coupling between magnetic moments in the neighboring twins, orientated at an angle to each other, increases Hhf and decreases Q, in accordance with the model calculations made in [15]. However, in the above-mentioned work, no metallographic examinations were performed which could point to the presence of a large volume fraction of the twinned structure. Again, the authors of [25] paid attention to the explanation put forward in [15] and concluded that the contribution from the twin-oriented domains and antiphase boundaries are small and masked by the contributions from disordered fct clusters. A detailed research of the microstructure of the FePd samples deformed by rolling to 97% and annealed at 400, 500, and 600 oC for 7 days was carried out by the method of scanning electron microscopy in [6]. It was revealed that grains-twins do not take more than 5% of the alloy bulk even after annealing at 600 oC. Since regions with an effective interaction at the twin boundaries make up only small part of the sample volume; their influence on the parameters Hhf and Q should be negligibly small. In the approach under consideration, it turned out possible to separate and describe contributions from the regions possessing different configurations of the nearest neighborhood of the resonant atom and different values of the quadrupole shift and to analyze correlations in the changes of the parameters. In the frame of the earlier developed models of the A1 ? L10 transformation, the main differences between the ordered regions of the L10 type (primitive lattice P4/mmm) and initial fcc (Fm3m) phase are absence of Fe atoms in the nearest layer (first coordination shell of a resonant atom) and of Pd atoms in the iron layer (second and third coordination shells) and the appearance of the electric-field gradient and uniaxial magnetocrystalline anisotropy. The equilibrium L10 phase should be represented in the Mössbauer spectra by a single line with the lowest hyperfine field Hhf and highest quadrupole shift Q, its relative volume fraction increasing with the time of annealing. In the spectra presented there are observed two contributions in the histograms (see lines 1 and 2 in Fig. 5b) from the regions with the maximal quadrupole shift Q = 0.44 mm/s and minimal values of Hhf (255 and 263 kOe). Consequently, these two contributions have to be ascribed to an L10 phase in which the resonant atoms in one and the same layer, all having only Pd atoms in the first coordination shell, differ in the number of second-coordination iron atoms because of the presence of excessive Pd atoms in the iron layer. The relative volume fractions S1 and S2 of such contributions, as well as their sum, change slowly already after 10-h annealing; after 40 h, the ratio of S1/
(S1 + S2) is 0.39. This means that about 40% of iron atoms in these regions have one neighboring Pd atom in the Fe layer. As each atom in the Fe sublattice proper has four second neighbors, this could mean that there are 4 times as few Pd atoms in this layer. Supposing one layer being taken by Pd atoms only, with the number of sites being equal in each layer by the bct structure pattern, we reduce our calculation to 100 sites and thus obtain 4.4 Pd atoms to 45.6 Fe atoms in the iron layer. The next step can be a reasoning that if about 95 atoms of 100 match their sites in terms of longrange ordering, this purports a high degree of order. This may serve as a strong indication of the fact that in our case this phase is close to equilibrium state. At the same time, starting from the stage of annealing for 0.5 h, there takes place the formation of regions in which, judging from the higher values of Hhf, there are present more iron atoms in the first coordination shell and their crystal lattice is featured by the constant (though lower but still significant) quadrupole shift (Q = 0.32 mm/s) and, consequently, tetragonal distortions. If to suppose an excessive amount of iron in these regions, the Hhf values of these lines, equal to 270 and 278 kOe, can be treated as corresponding to the configuration with one iron atom in the Pd layer and one Pd atom in the iron layer (line 3) and that with one iron atom in the Pd layer and no Pd atom in the iron layer (line 4). These considerations lead to a suggestion that in this way we have determined the values of the field shift for the second coordination shell to be 8 kOe and for the first coordination shell, 15 kOe (255 and 270, 263 and 278 kOe) in the distorted tetragonal lattice. The ratio of contributions 3 and 4, close to 1, is almost unchanged with time, which purports that the amount of these regions changes without variation of its local composition. The summed volume fraction of iron atoms in such regions starts decreasing after a 10-h annealing. Since the transition from a disordered cubic phase into a layered ordered phase must proceed with a consistent rearrangement of the crystal lattice, and consequently, coordination shells, these regions with equal intensities and quadrupole shifts cannot be ascribed either to highly ordered or fully disordered structure components but to a low-ordered bct phase of the A6 type, whose existence was evidenced by both theoretical conclusions and data of morphological methods [8–10]. Since the changes in the volume fractions of two phases after the 10-h annealing exhibit different tendencies, the scenario of transformations should account for the transition regions with changeable tetragonal distortions, whose part is especially pronounced at the early stages of annealing (lines 5 and 6 in Fig. 5). Moreover, if to estimate the field shifts for the lines from these regions with the positions at 286 and 297 kOe, a supposition can be made that these regions have two atoms of iron in the Pd layer with one and no Pd atoms in the iron layer, respectively, which obviously lowers the degree of tetragonality. Feasibly, these regions, represented by lines 5 and 6, should be assigned to the disordered tetragonal-phase component. By the dependence of the volume fraction of iron in such configurations, an inference should be drawn that the changes are conditioned by diffusion mobility of iron atoms, which continue redistributing between the layers with time, and promote the state of ordering. Thus, based on the results of Mössbauer studies, it can be concluded that in the process of annealing the following changes take place. Already at the early stages of annealing (tann = 0.5 h) of the severely deformed FePd alloy, there forms a tetragonal phase, which is characterized by a set of Hhf values (253–300 kOe) and of Q (0.44–0.11 mm/s) and, consequently, is inhomogeneous in composition and degree of tetragonality. At this stage, the most significant contribution to the spectral intensity comes from regions (lines 3–6) with a quadrupole shift Q 6 0.32 mm/s, which are ascribed, based on the spectra analysis, to the low-ordered bct regions of the A6 type. The formation of the A6 phase is likely
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
to precede the ordering process, since weak tetragonal deformation of the crystal lattice is observed even prior to annealing of the deformed alloy (Fig. 3). At the same type, already after short annealing, the sample contains (in a noticeable amount) structure components 1 and 2 with the highest Q = 0.44 mm/s, which represent the ordered L10 phase. The volume fraction of the most ordered regions increases first sharply and, after the 10-h annealing, smoothly. At this very stage, the growth of the volume fraction of the tetragonal regions with Q 0.30 mm/s terminates and the amount of fcc regions decreases (Fig. 7). The volume fraction of the disordered bct phase in which, judging from the changes of the parameters Hhf b Q, changes in the composition and local symmetry proceed up to 40 h, decreases already after 5 h. These regions may serve as a transition zone for the formation of the main structure constituents and, eventually, equilibrium ordered L10 phase of the hard magnetic alloy Fe50Pd50. As follows from the results obtained, under the chosen annealing conditions the formation of the equilibrium ordered L10 phase in the whole bulk is hampered and proceeds through a series of intermediate tetragonal phases with different degrees of tetragonality and ordering. This result agrees with the conclusions of the earlier X-ray diffraction investigations [26] and suppositions [27]. The observed complicated mode of the A1 ? L10 phase transformation has much in common with that described in [22,23] using methods of computer-assisted simulations of cascade phase cubic-tetragonal transformations. According to these model computations, the composition of the arising tetragonal phase deviates from the initial composition of the cubic matrix because of a contribution from the transformation–induced strain to the total free energy. The equilibrium tetragonal phase is formed as a result of a long-term redistribution of elements between the initial cubic and newly formed tetragonal components of a nonequilibrium composition. In our case, the cubic-tetragonal transition is even more complicated due to internal stresses induced by severe plastic deformation and to the process of atomic ordering in the bct phase. With taking into account recent structure investigations [8–10], the data obtained make it possible to conclude that the A1 ? L10 phase transformation in the deformed nanocrystalline FePd alloy is a complex transition of the cascade type, which involves such processes as decomposition into cubic phases of different compositions, A1 ? A6 transformation of the shear type, and atomic ordering by the L10 type, with continuously changing composition of structure constituents. As is seen from the experiments, the inhomogeneous structure formed in the course of phase transition turns out quite stable and is still retained after a long-term (tann = 40 h) annealing (Fig. 7). If to compare Figs. 1 and 7, one can notice that the coercivity reaches its maximal value Hc = 1.75 kOe at tann = 15 h, but in this state the highly anisotropic L10 phase takes up only less than half of the sample volume. The other part consists of regions of the low-anisotropic bct phase. This apparently results in a significant lowering of the effective magnetic anisotropy in the sample and, as a consequence, in low values of the maximal Hc. Despite the continuous growth of the fraction of the highly distorted regions and decrease of that from the regions with low distortions in the course of annealing, the coercivity Hc, starts decreasing. This behavior has to be ascribed to growing grain size, which has been pointed out to many times earlier [5–7]. 5. Conclusions 1. Quenching of the Fe50Pd50 alloy does not provide a homogeneous disordered state of the structure. This fact, though established in the earliest works [12], is paid strict
197
attention for the first time. High pressure torsion of the quenched alloy results in a change of the rate of separation in composition but does not lead to the formation of homogeneous structure either. Two contributions from the disordered regions with different Hhf and Q purport the presence in the structure of components with different local tetragonal distortions, which distinguish this structure from the pure fcc already at this stage. 2. Annealing of the alloy for ordering results in the formation of tetragonal regions from the initial cubic phase, which are different in composition and degrees of atomic ordering and tetragonal distortions, which can be ascribed to phases of the L10 and A6 type. The volume fractions of such regions change with time of annealing differently. Feasibly, multiphase structure is retained even after the long-term annealing (tann = 40 h). 3. Comparison of the behavior of the dependences of Hc and relative volume fractions of the separated structure components on the time of annealing makes it possible to conclude that, along with the formation of structure components that are inhomogeneous in the degree of tetragonal distortions, there likely occurs grain growth, which negatively affects the coercitivity magnitude.
Acknowledgment The work was supported by the Program of the Ural Branch of the Russian Academy of Sciences, Project No. 12-P-23-2005. References [1] A. Kussman, K. Muller, Z. Angew, Phys. 17 (1964) 509–511. [2] L.M. Magat, A.S. Yermolenko, G.V. Ivanova, G.M. Makarova, Ya.S. Shur, Fiz. Met. Metalloved. 26 (1968) 511–516. [3] A.Ye. Yermakov, V.V. Maikov, Phys. Met. Metallogr. 69 (1990) 198–199. [4] H. Shima, K. Oikawa, A. Fujita, K. Fukamichi, K. Ishida, A. Sakuma, Phys. Rev. B 70 (2004) 224408. [5] G.V. Ivanova, N.N. Shchegoleva, L.M. Magat, Ya.S. Shur, Phys. Met. Metallogr. 34 (1972) 107–113. [6] A.R. Deshpande, J.M.K. Wiezorek, JMMM 270 (2004) 157–166. [7] A. Chbihi, X. Sauvage, C. Genevois, D. Blavette, D. Gunderov, A.G. Popov, Adv. Eng. Mater. 12 (2010) 708–713. [8] N.I. Vlasova, V.S. Gaviko, A.G. Popov, N.N. Shchegoleva, L.A. Stashkova, D.V. Gunderov, X. Sauvage, Solid State Phenom. 168–169 (2011) 392–395. [9] N.I. Vlasova, N.N. Shchegoleva, A.G. Popov, G.S. Kandaurova, Phys. Met. Metallogr 110 (2010) 449–463. [10] N.I. Vlasova, A.G. Popov, N.N. Shchegoleva, V.S. Gaviko, L.A. Stashkova, G.S. Kandaurova, D.V. Gunderov, Acta Mat. 61 (2013) 2560–2570. [11] G. Longworth, Phys. Rev. 172 (1968) 572–576. [12] V.A. Tsurin, E.E. Yurchikov, A.Z. Men’shikov, Solid State Phys. 17 (1975) 2915– 2925. [13] V.A. Tsurin, A.V. Stepanov, Fiz. Met. Metalloved. 46 (1978) 726–732. [14] V.A. Tsurin, A.Ye. Yermakov, Fiz. Met. Metalloved. 50 (1980) 1271–1275. [15] V.A. Tsurin, A.Ye. Yermakov, Yu.G. Lebedev, B.N. Filippov, Phys. Stat. Sol (a) 33 (1978) 325–332. [16] C. Issro, M. Abes, W. Pueschl, B. Sepiol, W. Pfeiler, P.F. Rogl, G. Schmerber, W.A. Soffa, R. Kozubski, V. Pierron-Bohnes, Metall. Mater. Trans. A 37A (2006) 3415– 3422. [17] V.S. Rusakov, Mossbauer spectroscopy of locally inhomogeneous systems, Institute of Nuclear Physics, National Nuclear Center, Alma-Ata, 2000. [18] J. Lyubina, O. Gutfleisch, O. Isnard, J. Appl. Phys. 105 (2009) 07A717. [19] B.W. Roberts, Acta Metall. 2 (1954) 597–608. [20] P.S. Rudman, B.L. Averbach, Acta Metall. 5 (1957) 65–73. [21] W.A. Soffa, D.E. Laughlin, Acta Metall. 37 (1989) 3019–3028. [22] Y. Ni, Y.M. Jin, A.G. Khachaturyan, Acta Mater. 55 (2007) 4903–4914. [23] Y. Ni, A.G. Khachaturyan, Nat. Mater. 8 (2009) 410–414. [24] A.Ye. Yermakov, V.L. Gapontsev, V.V. Kondrat’ev, Yu.N. Gornostyrev, Phys. Met. Metallogr. 88 (1999) 211–218. [25] V. Gehanno, P. Auric, A. Marty, B. Gilles, JMMM 188 (1998) 310–318. [26] G.V. Ivanova, L.M. Magat, Fiz. Met. Metalloved. 39 (1975) 999–1006. [27] W.A. Soffa, W. Puschl, W. Pfeiler, Intermetallics 11 (2003) 161–167.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Mössbauer study of fine structure features of equiatomic FePd alloy after severe plastic deformation and ordering annealing N.I. Vlasova a,b,⇑, N.M. Kleinerman a, V.V. Serikov a, A.G. Popov a a b
Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 18 S. Kovalevskoi Str., 620990 Ekaterinburg, Russia Institute of Nature Sciences, Ural Federal University, 48a Kuibysheva Str., 620141 Ekaterinburg, Russia
a r t i c l e
i n f o
Article history: Received 20 June 2013 Received in revised form 15 August 2013 Accepted 16 August 2013 Available online 31 August 2013 Keywords: Intermetallics Nanostructures Crystal structure and symmetry Nuclear resonances Strain High pressure
a b s t r a c t Using Mössbauer spectroscopy based on modern methods of processing spectra, new fine features of the structure of equiatomic alloy FePd, which is formed upon the A1 ? L10 phase transformation in the course of severe plastic deformation by torsion and annealing for ordering at the temperature T = 450 oC, have been studied. It is shown that the structure of the alloy in the as-deformed state cannot be treated as a homogeneous solid solution; it is more likely to consider it as an alternation of disordered regions that are different in composition and in the sign and degree of tetragonal distortions of the initial fcc lattice. Already at early stages of ordering annealing, there are detected low-symmetry regions, inhomogeneous in composition and in the degree of ordering, with tetragonal distortions of the same sign but essentially different in magnitude. These regions can be identified as the structure constituents of the A6 and L10 type with the tetragonal lattice. Such a multi-phase structure is retained even after a long-time (tann = 40 h) annealing. A conclusion is made that the equilibrium tetragonal L10 phase is formed as a result of long-term redistribution of Fe atoms between the initial cubic and newly formed tetragonal components. The effect of the fine-structure peculiarities on the coercivity of the FePd alloys is considered. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction The hard magnetic alloys Co–Pt, Fe–Pt, and Fe–Pd, which possess an L10-type ordered structure, have intensively been studied for the last decades. Nowadays, these materials are paid evergrowing attention as promising magnetic media for high-density recording and storage of information. The FePd alloys, similarly to FePt, exhibit high values of saturation magnetization, magnetic anisotropy constant [1–4], and the theoretical limit of maximal energy product (BH)max = 47 MGOe; yet, the latter can hardly be realized because of low coercivity. In [5–8], data are reported on the realization in this material, when subjected to a severe plastic deformation by cold rolling or by torsion and subsequent annealing, of a coercive force Hc = 1.40–1.75 kOe, which is several times as high as Hc of the annealed nondeformed sample; however, this value makes up no more than 5% of the anisotropy field (35 kOe). The level of magnetic hardness is strongly dependent on the degree of long-range order; therefore, the process of the formation of a structure that provides enhanced magnetic characteristics remains
⇑ Corresponding author at: Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 18 S. Kovalevskoi Str., 620990 Ekaterinburg, Russia. Tel.: +7 343 378 37 82; fax: +7 343 374 52 44. E-mail address: [email protected] (N.I. Vlasova). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.08.110
in the focus of researchers using different experimental techniques. Recently, it has been shown [8–10], employing methods of electron microscopy, X-ray diffraction, and thermomagnetic and polarization-optics analyses, that in single-crystal, polycrystalline, and nanocrystalline samples of equiatomic FePd upon the phase transformation of the initial disordered A1 phase with an fcc crystal lattice (space group Fm3m) into an ordered L10-type structure (space group P4/mmm), a metastable disordered bct phase with a structure of the A6 type (space group I4/mmm) is formed, which can cause a lowering of the coercivity Hc. Clear ideas about the mechanisms of structure formation in these alloys and the relationship between the structure and magnetic properties are urgent for the development of approaches to realizing the potential of these materials. However, structure techniques applied in most researches are lacking the ways of gaining information on the fine features of the structure. The Mössbauer method is a widely employed powerful tool of studying the processes related to the redistribution of atoms in Fe-based alloys. However, the earlier Mössbauer experiments on the kinetics of atomic ordering in single crystals, polycrystalline samples deformed by rolling, and aerosol powder samples of FePd did not show up any signs of formation of metastable phases upon the A1 ? L10 transformation [11–15]. The generally recognized advances of the authors of [12] are the dependence of the hyperfine
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
field (Hhf) on the Fe concentration in the range of 25–75 at.% for the alloys in the disordered state, constructed based on the experimental data; and data on the effect of atomic correlation on Hhf for the alloys subjected to annealing for ordering. However, the methods of analysis of that time did not allow gaining full information from the spectra measured and estimation of the whole bulk of data on the structural changes. Nowadays, currently designed and widely applied computer programs present ample opportunities for analyzing the results of Mössbauer studies. In the later works [16], fitting of the Mössbauer spectra was performed by the method of restoration of probability-density distribution functions for the parameter Hhf. The form of these distributions allows a qualitative description of the dynamics of relative changes for individual contributions at different steps of treatment of massive and film samples; however, no quantitative estimates of the parameters of individual structure components were made, which could give grounds for the construction of a model of the alloy structure. In the work presented, modern possibilities of the Mössbauer spectroscopy are used for the investigation of the process of formation of long-range order in nanocrystalline FePd samples with a composition close to equiatomic. 2. Experimental As-cast polycrystalline coarse-grained samples of the equiatomic FePd alloy in the form of rods 50 mm in length and 6 mm in diameter were homogenized at a temperature of 950 oC for 6 h and quenched into icy water. After quenching, diskshaped samples were cut off from the rods and then deformed by the method of severe plastic deformation by high-pressure torsion (HPT) at the number of revolutions n = 10 and a high quasihydrostatic pressure P = 6 GPa and annealed at a temperature of 450 oC with holdings from 0.5 to 40 h. Under the conditions stated, mechanical and heat treatments result in the formation of a nanocrystalline state (d = 50–200 nm [7,8]) in the FePd samples that are featured by the maximal values of coercivity (Hmax 1760 Oe). The Mössbauer spectra were measured at 300 K in c the mode of constant accelerations with a source of Co57 in the chromium matrix. The measurements were performed on foils 20 lm thick with the use of an MS1101 spectrometer (512 channels, (5–8) 105 counts/channel, quality factor of 70–80). The spectra were analyzed, with allowance for the effects of self-absorption, using the program package MSTOOLS [17] which, along with the direct fitting of spectra with a number of subspectra, allows construction of the co-called multi-core distributions of the probability density for different hyperfine parameters if there are grounds to suppose that different structure components present different correlation relations of at least two Mössbauer parameters. In such a case, several mathematical ‘‘cores’’ are specified to independently restore different distribution functions. The isomeric shifts were taken relative to the spectrum of a–Fe.
3. Results 3.1. Dependence of coercivity for the samples of the FePd alloy on the time of annealing Comparison of the dependences of coercivity on the time of annealing obtained up to now for the FePd samples shows that the maximal values of Hc are the higher, the larger the degree of preliminary plastic deformation and the lower the annealing temperature [5–8]. It also follows from [5–8] that, taking into consideration the duration of annealing required for the achievement of the maximal Hc, the optimal annealing temperature is T = 450 °C. In Fig. 1a there are shown dependences of the coercivity on the time of annealing tann at 450 oC for the as-cast sample that (1) is quenched from 950 °C and (2) is subjected to subsequent HPT with n = 10. Higher values of Hc for the deformed sample and faster kinetics of its growth, as compared to sample 1, are traceable to both finer grains and accelerated process of ordering in a material with the strain energy stored upon HPT. In sample 2, HPT and annealing at 450 oC for 15 h led to the achievement of the value Hc = 1760 Oe. To ascertain the fine structure peculiarities of the deformed FePd that are formed in the course of the A1 ? L10 phase
2
1600
1200
Нс (Oe)
192
800 1
400
0
0
10
20
30
40
Annealing time (h) Fig. 1. Dependence of coercivity Hc of the FePd alloy on the time of annealing at T = 450 oC. 1 – quenched alloy; 2 – after subsequent HPT at P = 6 GPa and n = 10 revolutions.
transformation and could cause low maximal values of Hc, Mössbauer studies of the structure transformations were performed on an alike sample.
3.2. Mössbauer spectra for samples after quenching and HPT Fig. 2 shows a spectrum (a) and its description with the use of one-core distribution of hyperfine fields P(Hhf) (b) for the sample of the FePd alloy after quenching from 950 °C. Both the form of the very distribution and the difference graph between the experimental and calculated values of spectral intensities (at the bottom of Fig. 2a) testify to the presence in the structure, along with the main component whose average hyperfine field coincides with the value (323 kOe) determined in [12] for the equiatomic composition, of an additional contribution with lowered values of hyperfine fields (Fig. 2b), which cannot be associated with regions of disordered equiatomic alloy. Besides, small peaks in the envelope indicate the presence of short-range-ordered regions. Failure to attain a homogeneous disordered state in the equiatomic alloy via quenching was reported on in a number of works, including [12]. After HPT, the relative content of iron in the low-field regions becomes negligibly small and the very distribution for the whole bulk of the sample becomes more homogeneous (Fig. 2d). In this figure, there are also given binominal distributions for three compositions: Fe50Pd50, Fe49Pd51, Fe48Pd52. It is seen that these distributions do not match the one-core curve either in the form or in width, which means that this state cannot be described under an assumption of a homogeneous solid solution close in composition to the equiatomic. At the same time, the simulation of the spectrum with the use of two-core representation involving two binominal distributions resulted in a more exact description (Fig. 2e and f). The average hyperfine fields Hhf of these two-core distributions make up 306 and 340 kOe; the quadrupole shifts Q are small in magnitude and different in sign, 0.068 and 0.13 mm/s; and the relative fractions of these contributions are equal to 55 and 45%, respectively. One can suggest the presence in this sample of disordered regions of two compositions with deviations from the equiatomic one toward higher contents of both iron and palladium. If we again use the dependence of Hhf on the concentration constructed in [12], we can approximately estimate the concentration of elements in these regions, though the very dependence was constructed with no allowance for the deviation of the form of spectral envelope from the Lorenz line; only the centers of gravity being taken into consideration. Such estimation gives compositions differing from equiatomic by approximately ±10%. The same approach turned out valid when describing the spectrum after quenching as well, which means that regions of
193
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
0.02
100
a
98
b
0.01 0.00 0.02
94 100
c
98
d
Fe50Pd50 Fe49Pd51 Fe48Pd52
0.01
P (H)
Intensity (%)
96
96
0.00 0.02
100
e
98
f
0.01
96 -8
-6
-4
-2
0
2
4
6
8
100
150
200
250
300
350
0.00 400
Н (kOe)
V (mm/s)
Fig. 2. Spectra and distribution functions P(H) for the Fe50Pd50alloy: (a, b) after quenching; (c, d) after deformation, in the one-core mode (additional lines - binomial distributions for Fe50Pd50, Fe49Pd51, Fe48Pd52); (e, f) after deformation, in the two-core mode.
different composition are present in the structure already after quenching, though the very compositions and the volume fractions of the constituents are somewhat different. The spectrum is treated most correctly via fitting with eight independent subspectra with equal linewidths determined in the course of iteration process. Based on the results of such computations, there were constructed dependences of the relative area (S) of the subspectra (Fig. 3a) and of the quadrupole shift (Q) (Fig. 3b) on Hhf. Considering approximately equal changes in Hhf for the contributions found, one can ascribe these contributions to particular configurations of neighborhood of iron atoms in the fcc lattice. For the given composition of the binary alloy, the main configurations Pd:Fe in the first coordination shell of an iron atom turn out to be 9:3, 8:4, 7:5, 6:6, 5:7, 4:8, 3:9 and 2:10. If we assume that two contributions with the highest Hhf values are related only to one solid solution (for the distribution with the essentially lower average Hhf the probability of such configurations is negligibly small), then from the ratio of their areas one can construct, using the binominal law, the other relative fractions and subtract them
Number of Fe neigbours 20
3
4
5
6
7
8
9
S (%)
3.3. Mössbauer spectra changes in the course of annealing of the deformed samples
10
a
16 12 8 4
Q (mm/s)
0
b
0.04 0.00 -0.04 280
300
320
340
360
from the total dependence. Then, the remaining intensities can be ascribed to the other solid solution and their dependence on Hhf can be restored. The results of such analysis are shown in Fig. 3a. The relative volume fractions of these two solid solutions, determined in such a way, make up 54 and 46% and the positions of maxima are 310 and 345 kOe, respectively. Moreover, in accordance with the statistic law, the compositions of these regions can be approximately estimated to be 44 and 62% Fe. The data obtained are close to the above estimated contributions from the two-core distributions using data from [12]. Besides, the dependence Q(Hhf) (Fig. 3b) testifies to the presence in the deformed sample of weakly distorted regions with different signs of distortions of the crystal lattice, the maximal positive Q being equal to 0.11 mm/s at Hhf = 281 kOe. It can be concluded that already in this state the sample is featured by local inhomogeneities in composition, which may result in the observed local tetragonal distortions of the fcc lattice. As to the isomeric shift, its value increases with decreasing Heff, i.e., with increasing number of Pd nearest neighbors, linearly from 0.15 to 0.20 mm/s.
380
H (kOe) Fig. 3. Results of description of the experimental spectrum of the deformed sample via fitting with eight subspectra: (a) dependence of the total subspectra intensities and of two separated contributions on H; (b) dependence of Q on H for the eight subspectra.
In Fig. 4, spectra and two-core distribution functions P(Hhf) are given for the states of the sample after different annealing holdings. The spectra were treated under the assumption that the ordering tetragonal regions differ from the initial fcc phase in correlation of the hyperfine parameters. In the graph for the state after 30-min holding, there is already present a contribution in the Hhf range 250–280 kOe, which was absent immediately after deformation (for comparison, the distribution P(Hhf) for the deformed state is shown in this figure by a solid thin line). In accordance with the known results of X-ray and Mössbauer studies [5–8,12,15], this fact testifies to the onset of the formation of a tetragonal structure in this sample. In the course of annealings, the contribution from the regions with the distorted fcc lattice decreases, and the tetragonal regions make two distinct contributions already after the 2.5 h holding, whose ratio changes with the annealing time. Similar distribution functions were constructed in the one-core representation from the Mössbauer spectra of the Fe50Pd50 alloy in the states after different annealings of the quenched sample in [16]. However, since the description was performed on the
194
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
0.02 100
b
1
а
1 0.00 0.02
100
2
2 0.00 0.03
3 3
0.00 0.03
100
4
P (H)
Intensity (%)
100
4 100
0.00 0.03
5 5
100
0.00 0.03
6 6
95 -8
-6
-4
-2
0
2
4
6
8
240
280
V
320
0.00 360
400
Н (kOe)
Fig. 4. (a) Spectra and (b) two-core distributions P(H) for the Fe50Pd50 alloy after annealings for different times: 1–0.5 h; 2–2.5 h; 3–5 h; 4–10 h; 5–20 h; 6–40 h (for comparison, solid thin line in graph 1 shows the distribution function for the deformed state of the sample).
assumption of one linear correlation of the parameters from both the cubic and tetragonal structure components, no detailed analysis of the contributions to the distribution function could be done. In our representation, the contributions from the cubic and tetragonal regions can be separated based on their different correlation functions, but to estimate the individual parts taken by regions with different lattice distortions is impossible in this approach. To more exactly separate all the contributions, the experimental spectra were fitted with 10 subspectra with the linewidth equal to that of the line from pure iron. Fig. 5a presents the examples of such fitting; and Fig. 5b shows histograms of distributions of the relative area (S) of the subspectra (or relative fractions of iron in the corresponding regions) over Hhf. In Fig. 5b, the subspectra are numbered from 1 to 10. The relative fractions of the contributions (No. 7–10) from the regions with a high Fe content (Hhf > 330 kOe) and negative sign of the quadrupole shift Q virtually disappear al-
100
ready after 5 h, and only a small contribution with the Hhf = 330 kOe is retained, which can be ascribed to iron-containing regions with the bcc structure. Their relative fraction is well determined to be 5% just after a 5-h holding. The presence of a small amount (3–5%) of such regions in the structure of the alloy was also discovered in the neutron diffraction study of nanocrystalline Fe100 xPdx (x = 50, 53, and 60) alloy [18]. The isomeric shift for all the lines, except that for bcc iron, becomes closer in value and varies insignificantly in the range of 0.19–022 mm/s at the following steps of annealing. To ascribe lines 1–6 in the histograms in Fig 5b to the corresponding regions in the tetragonal structure, there were constructed dependences of the relative fractions of the contributions S and their quadrupole shifts Q on Hhf, which are shown in Fig. 6a and b, respectively, for several annealing holdings. Taking into consideration the values of Hhf and Q, as well as their changes in
b
a
1
98
2
3
4
5
6
7,8
0.5 h 20 9
10
0.5 h
0 20
96 100
0 20
5h
98
0
5h
96
20
S (%)
Intensity (%)
2.5 h
10 h 0 20
100 98
20 h 0
96
40 h
94 -8
40 h -6
-4
-2
0
2
V (mm/s)
4
6
8
20
0 260 280 300 320 340 360 380 400
Н (kOe)
Fig. 5. (a) Spectra for samples of the Fe50Pd50 alloy annealed for 0.5, 5, and 40 h; and (b) histograms of relative fractions of subspectra for a series of annealing times. Digits in the upper right graph mark the order number of the sextet.
195
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
35
0.5
a
30
0.3
Q (mm/s)
25
S (%)
b
0.4
20 15
0.5h 5h 40 h
0.2 0.1 0.0
10
-0.1 5 -0.2 0
280
320
360
400
280
320
360
400
H (kOe)
H (kOe)
Fig. 6. Dependences of (a) the relative fractions S of the subspectra and (b) the quadrupole shifts Q on H for several stages of annealing.
4. Discussion The experiments conducted and their analysis made it possible to pick out a number of peculiarities in the description of the structure that were absent in the previous Mössbauer studies. Thus, in one of the basic works [12] devoted to studying disordered FePd alloys of different compositions it was discovered that the spectral lines featuring disordered states had an asymmetric shape from both low and high values of Hhf. However, no analysis of such
80
60
S (%)
the course of annealing, three types of regions can be picked out. By the minimal values of Hhf and equal maximal values of Q 0.44 mm/s, two contributions (lines 1 and 2), whose intensities grow with time, though somewhat differently, can be ascribed to the regions of the first type with the highest tetragonal distortions, and (most probably) with the highest degrees of order [2–5,19,20]. To the second type, the structure components with lower (about by a factor of 1.5) quadrupole shifts Q 0.30 mm/s and, consequently, smaller tetragonal distortions can be referred (lines 3 + 4). They appear already at the early stages of annealing, and their intensities are approximately equal and almost independent of the time of annealing. The third type (lines 5, 6) comprises regions of variable composition with low positive distortions (Q = 0.2–0.1 mm/s). With increasing holding time, theirs contributions decrease. In Fig. 7 there are constructed dependences of the sums of individual contributions on the time of annealing. From the analysis of these curves it can be concluded that the summed contribution to the spectral intensity from the lines corresponding to large numbers of Fe atoms in the first coordination shell in the fcc lattice remains low and constant already after 10-h annealing. The contributions from two lines that are related to the regions with the most distorted crystal lattice (lines 1 and 2) grow though the dynamics of growth slows down after the 10-h annealing, whereas the sum of two intensities (lines 3 + 4) from the less distorted regions with higher Hhf starts decreasing. However, if to ascribe to these regions contributions with lower positive Q values (lines 5, 6), their summed fraction starts decreasing already after the 5-h annealing. Thus, already at the early stages of annealing there form regions with tetragonal distortions which are equal in sign but essentially different in magnitude. In the course of annealing there takes place a redistribution of iron atoms between both cubic and tetragonal structure components and over different regions of the tetragonal component proper.
1+2 3+4+5+6
40
3+4 20
0
Rest 0
10
20
30
40
Annealing time (h) Fig. 7. Dependences of spectral contributions from separated regions on the annealing time: 1, 2, lines with Q 0.44 mm/s; 3, 4, lines with Q 0.30 mm/s; 5, 6, lines with variable positive Q; the rest contributions are related to the cubic phase (for designations, see Fig. 5b).
asymmetry was done and the centers of gravity of the spectra were used to construct the concentration dependence of Hhf. The interpretation of the spectra measured in our work showed that the inhomogeneities in the structure of alloys are retained both after quenching and after HPT, and that they are not traceable to any shortcomings of homogenization and quenching modes. (In work [12], for example, the alloys were homogenized at T = 1000 oC for 100 h). Such features should be treated as indications of the presence of disordered regions significantly differing in composition rather than the effects of short-range ordering. This conclusion is supported by quantitative estimates gained from both two-core distribution functions P(Hhf) and fitting of the spectra with a set of subspectra, which are close in values. At the same time, the X-ray and electron microscopy examinations of deformed samples of this alloy [7,8,10] did not reveal any compositional inhomogeneities. One can suggest a model of a periodical arrangement of such regions, most likely nanosized and coherently related, by a kind of spinodal or pseudospinodal mechanism similar to that described in [21–23], which results in an averaging of local parameters. Besides, in [24], the reason for phase separation in nanostructured materials after HPT is stated to be different diffusion mobility of the constituting elements, which may be our case as well. In accordance with the model calculations of
196
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
microstructure upon phase transformations of the cubic-tetragonal type [22,23] and experimental results [8–10], the formation of such nanodomain regions with a distorted crystal lattice can evidently be treated as a precursor of the formation of a tetragonal phase. The description of the structural state of the alloy after different annealings given in [16] with the use of distribution functions allows, at best, quantitative estimations of Hhf and relative fractions of the contributions from the cubic and the tetragonal structure component. Such an approach failed to separate pronounced contributions to the spectra from different tetragonal regions. Similar faulty attempts were made as early as in [25] where conversion Mössbauer spectra of film samples were treated under the assumption of a linear correlation between the Hhf and Q magnitudes, which evidently is not valid in our case. However, the very quality of the conversion spectra together with the processing routines available at that time could not provide a stricter approach. In [15], the spectra were fitted with three subspectra, one of which, in high fields, was ascribed to the initial fcc structure, another, low-field, contribution with the values Hhf = 267 kOe and Q = 0.42 mm s, to the L10 structure with a certain degree of ordering, and the intermediate contribution with Hhf = 288 kOe and Q = 0.29 mm/s, to regions with a twinned structure or, to be more precise, to areas close to the boundaries of the ordered twins, in which the exchange coupling between magnetic moments in the neighboring twins, orientated at an angle to each other, increases Hhf and decreases Q, in accordance with the model calculations made in [15]. However, in the above-mentioned work, no metallographic examinations were performed which could point to the presence of a large volume fraction of the twinned structure. Again, the authors of [25] paid attention to the explanation put forward in [15] and concluded that the contribution from the twin-oriented domains and antiphase boundaries are small and masked by the contributions from disordered fct clusters. A detailed research of the microstructure of the FePd samples deformed by rolling to 97% and annealed at 400, 500, and 600 oC for 7 days was carried out by the method of scanning electron microscopy in [6]. It was revealed that grains-twins do not take more than 5% of the alloy bulk even after annealing at 600 oC. Since regions with an effective interaction at the twin boundaries make up only small part of the sample volume; their influence on the parameters Hhf and Q should be negligibly small. In the approach under consideration, it turned out possible to separate and describe contributions from the regions possessing different configurations of the nearest neighborhood of the resonant atom and different values of the quadrupole shift and to analyze correlations in the changes of the parameters. In the frame of the earlier developed models of the A1 ? L10 transformation, the main differences between the ordered regions of the L10 type (primitive lattice P4/mmm) and initial fcc (Fm3m) phase are absence of Fe atoms in the nearest layer (first coordination shell of a resonant atom) and of Pd atoms in the iron layer (second and third coordination shells) and the appearance of the electric-field gradient and uniaxial magnetocrystalline anisotropy. The equilibrium L10 phase should be represented in the Mössbauer spectra by a single line with the lowest hyperfine field Hhf and highest quadrupole shift Q, its relative volume fraction increasing with the time of annealing. In the spectra presented there are observed two contributions in the histograms (see lines 1 and 2 in Fig. 5b) from the regions with the maximal quadrupole shift Q = 0.44 mm/s and minimal values of Hhf (255 and 263 kOe). Consequently, these two contributions have to be ascribed to an L10 phase in which the resonant atoms in one and the same layer, all having only Pd atoms in the first coordination shell, differ in the number of second-coordination iron atoms because of the presence of excessive Pd atoms in the iron layer. The relative volume fractions S1 and S2 of such contributions, as well as their sum, change slowly already after 10-h annealing; after 40 h, the ratio of S1/
(S1 + S2) is 0.39. This means that about 40% of iron atoms in these regions have one neighboring Pd atom in the Fe layer. As each atom in the Fe sublattice proper has four second neighbors, this could mean that there are 4 times as few Pd atoms in this layer. Supposing one layer being taken by Pd atoms only, with the number of sites being equal in each layer by the bct structure pattern, we reduce our calculation to 100 sites and thus obtain 4.4 Pd atoms to 45.6 Fe atoms in the iron layer. The next step can be a reasoning that if about 95 atoms of 100 match their sites in terms of longrange ordering, this purports a high degree of order. This may serve as a strong indication of the fact that in our case this phase is close to equilibrium state. At the same time, starting from the stage of annealing for 0.5 h, there takes place the formation of regions in which, judging from the higher values of Hhf, there are present more iron atoms in the first coordination shell and their crystal lattice is featured by the constant (though lower but still significant) quadrupole shift (Q = 0.32 mm/s) and, consequently, tetragonal distortions. If to suppose an excessive amount of iron in these regions, the Hhf values of these lines, equal to 270 and 278 kOe, can be treated as corresponding to the configuration with one iron atom in the Pd layer and one Pd atom in the iron layer (line 3) and that with one iron atom in the Pd layer and no Pd atom in the iron layer (line 4). These considerations lead to a suggestion that in this way we have determined the values of the field shift for the second coordination shell to be 8 kOe and for the first coordination shell, 15 kOe (255 and 270, 263 and 278 kOe) in the distorted tetragonal lattice. The ratio of contributions 3 and 4, close to 1, is almost unchanged with time, which purports that the amount of these regions changes without variation of its local composition. The summed volume fraction of iron atoms in such regions starts decreasing after a 10-h annealing. Since the transition from a disordered cubic phase into a layered ordered phase must proceed with a consistent rearrangement of the crystal lattice, and consequently, coordination shells, these regions with equal intensities and quadrupole shifts cannot be ascribed either to highly ordered or fully disordered structure components but to a low-ordered bct phase of the A6 type, whose existence was evidenced by both theoretical conclusions and data of morphological methods [8–10]. Since the changes in the volume fractions of two phases after the 10-h annealing exhibit different tendencies, the scenario of transformations should account for the transition regions with changeable tetragonal distortions, whose part is especially pronounced at the early stages of annealing (lines 5 and 6 in Fig. 5). Moreover, if to estimate the field shifts for the lines from these regions with the positions at 286 and 297 kOe, a supposition can be made that these regions have two atoms of iron in the Pd layer with one and no Pd atoms in the iron layer, respectively, which obviously lowers the degree of tetragonality. Feasibly, these regions, represented by lines 5 and 6, should be assigned to the disordered tetragonal-phase component. By the dependence of the volume fraction of iron in such configurations, an inference should be drawn that the changes are conditioned by diffusion mobility of iron atoms, which continue redistributing between the layers with time, and promote the state of ordering. Thus, based on the results of Mössbauer studies, it can be concluded that in the process of annealing the following changes take place. Already at the early stages of annealing (tann = 0.5 h) of the severely deformed FePd alloy, there forms a tetragonal phase, which is characterized by a set of Hhf values (253–300 kOe) and of Q (0.44–0.11 mm/s) and, consequently, is inhomogeneous in composition and degree of tetragonality. At this stage, the most significant contribution to the spectral intensity comes from regions (lines 3–6) with a quadrupole shift Q 6 0.32 mm/s, which are ascribed, based on the spectra analysis, to the low-ordered bct regions of the A6 type. The formation of the A6 phase is likely
N.I. Vlasova et al. / Journal of Alloys and Compounds 583 (2014) 191–197
to precede the ordering process, since weak tetragonal deformation of the crystal lattice is observed even prior to annealing of the deformed alloy (Fig. 3). At the same type, already after short annealing, the sample contains (in a noticeable amount) structure components 1 and 2 with the highest Q = 0.44 mm/s, which represent the ordered L10 phase. The volume fraction of the most ordered regions increases first sharply and, after the 10-h annealing, smoothly. At this very stage, the growth of the volume fraction of the tetragonal regions with Q 0.30 mm/s terminates and the amount of fcc regions decreases (Fig. 7). The volume fraction of the disordered bct phase in which, judging from the changes of the parameters Hhf b Q, changes in the composition and local symmetry proceed up to 40 h, decreases already after 5 h. These regions may serve as a transition zone for the formation of the main structure constituents and, eventually, equilibrium ordered L10 phase of the hard magnetic alloy Fe50Pd50. As follows from the results obtained, under the chosen annealing conditions the formation of the equilibrium ordered L10 phase in the whole bulk is hampered and proceeds through a series of intermediate tetragonal phases with different degrees of tetragonality and ordering. This result agrees with the conclusions of the earlier X-ray diffraction investigations [26] and suppositions [27]. The observed complicated mode of the A1 ? L10 phase transformation has much in common with that described in [22,23] using methods of computer-assisted simulations of cascade phase cubic-tetragonal transformations. According to these model computations, the composition of the arising tetragonal phase deviates from the initial composition of the cubic matrix because of a contribution from the transformation–induced strain to the total free energy. The equilibrium tetragonal phase is formed as a result of a long-term redistribution of elements between the initial cubic and newly formed tetragonal components of a nonequilibrium composition. In our case, the cubic-tetragonal transition is even more complicated due to internal stresses induced by severe plastic deformation and to the process of atomic ordering in the bct phase. With taking into account recent structure investigations [8–10], the data obtained make it possible to conclude that the A1 ? L10 phase transformation in the deformed nanocrystalline FePd alloy is a complex transition of the cascade type, which involves such processes as decomposition into cubic phases of different compositions, A1 ? A6 transformation of the shear type, and atomic ordering by the L10 type, with continuously changing composition of structure constituents. As is seen from the experiments, the inhomogeneous structure formed in the course of phase transition turns out quite stable and is still retained after a long-term (tann = 40 h) annealing (Fig. 7). If to compare Figs. 1 and 7, one can notice that the coercivity reaches its maximal value Hc = 1.75 kOe at tann = 15 h, but in this state the highly anisotropic L10 phase takes up only less than half of the sample volume. The other part consists of regions of the low-anisotropic bct phase. This apparently results in a significant lowering of the effective magnetic anisotropy in the sample and, as a consequence, in low values of the maximal Hc. Despite the continuous growth of the fraction of the highly distorted regions and decrease of that from the regions with low distortions in the course of annealing, the coercivity Hc, starts decreasing. This behavior has to be ascribed to growing grain size, which has been pointed out to many times earlier [5–7]. 5. Conclusions 1. Quenching of the Fe50Pd50 alloy does not provide a homogeneous disordered state of the structure. This fact, though established in the earliest works [12], is paid strict
197
attention for the first time. High pressure torsion of the quenched alloy results in a change of the rate of separation in composition but does not lead to the formation of homogeneous structure either. Two contributions from the disordered regions with different Hhf and Q purport the presence in the structure of components with different local tetragonal distortions, which distinguish this structure from the pure fcc already at this stage. 2. Annealing of the alloy for ordering results in the formation of tetragonal regions from the initial cubic phase, which are different in composition and degrees of atomic ordering and tetragonal distortions, which can be ascribed to phases of the L10 and A6 type. The volume fractions of such regions change with time of annealing differently. Feasibly, multiphase structure is retained even after the long-term annealing (tann = 40 h). 3. Comparison of the behavior of the dependences of Hc and relative volume fractions of the separated structure components on the time of annealing makes it possible to conclude that, along with the formation of structure components that are inhomogeneous in the degree of tetragonal distortions, there likely occurs grain growth, which negatively affects the coercitivity magnitude.
Acknowledgment The work was supported by the Program of the Ural Branch of the Russian Academy of Sciences, Project No. 12-P-23-2005. References [1] A. Kussman, K. Muller, Z. Angew, Phys. 17 (1964) 509–511. [2] L.M. Magat, A.S. Yermolenko, G.V. Ivanova, G.M. Makarova, Ya.S. Shur, Fiz. Met. Metalloved. 26 (1968) 511–516. [3] A.Ye. Yermakov, V.V. Maikov, Phys. Met. Metallogr. 69 (1990) 198–199. [4] H. Shima, K. Oikawa, A. Fujita, K. Fukamichi, K. Ishida, A. Sakuma, Phys. Rev. B 70 (2004) 224408. [5] G.V. Ivanova, N.N. Shchegoleva, L.M. Magat, Ya.S. Shur, Phys. Met. Metallogr. 34 (1972) 107–113. [6] A.R. Deshpande, J.M.K. Wiezorek, JMMM 270 (2004) 157–166. [7] A. Chbihi, X. Sauvage, C. Genevois, D. Blavette, D. Gunderov, A.G. Popov, Adv. Eng. Mater. 12 (2010) 708–713. [8] N.I. Vlasova, V.S. Gaviko, A.G. Popov, N.N. Shchegoleva, L.A. Stashkova, D.V. Gunderov, X. Sauvage, Solid State Phenom. 168–169 (2011) 392–395. [9] N.I. Vlasova, N.N. Shchegoleva, A.G. Popov, G.S. Kandaurova, Phys. Met. Metallogr 110 (2010) 449–463. [10] N.I. Vlasova, A.G. Popov, N.N. Shchegoleva, V.S. Gaviko, L.A. Stashkova, G.S. Kandaurova, D.V. Gunderov, Acta Mat. 61 (2013) 2560–2570. [11] G. Longworth, Phys. Rev. 172 (1968) 572–576. [12] V.A. Tsurin, E.E. Yurchikov, A.Z. Men’shikov, Solid State Phys. 17 (1975) 2915– 2925. [13] V.A. Tsurin, A.V. Stepanov, Fiz. Met. Metalloved. 46 (1978) 726–732. [14] V.A. Tsurin, A.Ye. Yermakov, Fiz. Met. Metalloved. 50 (1980) 1271–1275. [15] V.A. Tsurin, A.Ye. Yermakov, Yu.G. Lebedev, B.N. Filippov, Phys. Stat. Sol (a) 33 (1978) 325–332. [16] C. Issro, M. Abes, W. Pueschl, B. Sepiol, W. Pfeiler, P.F. Rogl, G. Schmerber, W.A. Soffa, R. Kozubski, V. Pierron-Bohnes, Metall. Mater. Trans. A 37A (2006) 3415– 3422. [17] V.S. Rusakov, Mossbauer spectroscopy of locally inhomogeneous systems, Institute of Nuclear Physics, National Nuclear Center, Alma-Ata, 2000. [18] J. Lyubina, O. Gutfleisch, O. Isnard, J. Appl. Phys. 105 (2009) 07A717. [19] B.W. Roberts, Acta Metall. 2 (1954) 597–608. [20] P.S. Rudman, B.L. Averbach, Acta Metall. 5 (1957) 65–73. [21] W.A. Soffa, D.E. Laughlin, Acta Metall. 37 (1989) 3019–3028. [22] Y. Ni, Y.M. Jin, A.G. Khachaturyan, Acta Mater. 55 (2007) 4903–4914. [23] Y. Ni, A.G. Khachaturyan, Nat. Mater. 8 (2009) 410–414. [24] A.Ye. Yermakov, V.L. Gapontsev, V.V. Kondrat’ev, Yu.N. Gornostyrev, Phys. Met. Metallogr. 88 (1999) 211–218. [25] V. Gehanno, P. Auric, A. Marty, B. Gilles, JMMM 188 (1998) 310–318. [26] G.V. Ivanova, L.M. Magat, Fiz. Met. Metalloved. 39 (1975) 999–1006. [27] W.A. Soffa, W. Puschl, W. Pfeiler, Intermetallics 11 (2003) 161–167.