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Influence of Nb on the first stage of crystallization in Fe86−xNbxB14 amorphous alloys
Materials Science and Engineering A 382 (2004) 401–406
Influence of Nb on the first stage of crystallization in Fe86−x Nbx B14 amorphous alloys A. Chrobak a , D. Chrobak b , G. Haneczok b,∗ , P. Kwapuli´nski b , Z. Kwolek b , M. Karolus b a
b
Institute of Physics, Silesian University, 40-007 Katowice, 4 Uniwersytecka, Poland Institute of Materials Science, Silesian University, 40-007 Katowice, 12 Bankowa, Poland Received 10 December 2003; received in revised form 4 May 2004
Abstract The kinetics of the first stage of crystallization (nanocrystallization) in the Fe86−x Nbx B14 amorphous alloys was studied by applying differential scanning calorimetry and magnetic balance techniques. It was shown that the nanocrystallization temperature increases with increasing Nb content by more than 80 K. Activation enthalpy of the nanocrystallization process increases from 2 eV for 2 at.% of Nb to 4 eV for 5–8 at.% of Nb. The results obtained by the mentioned experimental techniques are also discussed from the methodological point of view. © 2004 Elsevier B.V. All rights reserved. Keywords: Nanocrystallization; Amorphous alloys; Magnetization; Differential scanning calorimetry
1. Introduction The examined amorphous alloys belong to a widely studied group of modern soft magnetic materials based on iron which are frequently used as precursors of nanostructured materials [1–5]. Indeed, using a suitable thermal annealing at temperatures close to the crystallization temperature one can obtain a microstructure with iron nanograins embedded in the amorphous matrix. Soft magnetic properties of these alloys are found to be superior to those of conventional materials. For instance, the initial magnetic permeability can be of the order of 104 and the coercive field about 1–3 A/m. Moreover, very good magnetic properties are usually correlated with high resistivity (1–3 m) ensuring a low level of eddy current losses. The key to the formation of nanocrystallites in an amorphous solid of an appropriate chemical composition lies in the controlling of the annealing conditions (temperature and time) to ensure a relatively high nucleation rate and a small growth rate [1–4]. Experimental study of the nanocrystallization process as a diffusion controlled phenomenon is usu-
∗ Corresponding author. Tel.: +48 32 359 16 64; fax: +48 32 259 69 29. E-mail address: [email protected] (G. Haneczok).
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.05.013
ally carried out by applying differential scanning calorimetry [1,4–8] or by resistivity measurements [1,5,9] though in some cases magnetic balance is also used [10–12]. For magnetic materials the latter allows for a direct study of the formation of a new ferromagnetic phase. Using these techniques one can determine the activation enthalpy of the nanocrystallization process which allows us to control its kinetics [11,12] and in effect the material properties. The main aim of the present paper is to study the influence of niobium content on the first stage of the crystallization (or nanocrystallization) process in the Fe86−x Nbx B14 (2 ≤ × ≤ 8) group of amorphous alloys. Differential scanning calorimetry and magnetic balance are used as two complementary experimental techniques. The obtained results are discussed from the methodological point of view.
2. Material, experimental procedure and results Amorphous alloys examined in the present paper— Fe86−x Nbx B14 (2 ≤ × ≤ 8)—were produced by the melt spinning technique in form of strips with thickness of about 25 m and width of 10 mm. As-quenched samples were in the amorphous state, confirmed by X-ray and high resolution electron microscopy techniques.
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Kinetics of the nanocrystallization process was examined by applying two experimental techniques: • Magnetic balance (MB, Faraday type)—magnetization in saturation M(T) (magnetic field 0.5 T) was measured in the temperature range of 300–1000 K and heating rates ranged from 2 to 8 K/min. • Differential scanning calorimetry (DSC, Perkin-Elmer DSC-7)—experiments were carried out in the temperature range of 300–850 K and heating rates ranged from 5 to 20 K/min. In order to identify new phases formed during crystallization X-ray diffraction analysis (Philips X’Pert Diffractometer PW 3040/60) and transmission electron microscopy observations (JEM 3010) were used. As-quenched samples were annealed for 1 h in the temperature range from 300 to 900 K (in steps of about 20 K) and X-ray diffraction patterns were measured at room temperature. Application of such a procedure (according to [1,4] a standard annealing procedure) makes it possible to establish thermal treatment conditions (i.e. temperature and time) essential to obtain nanostructured materials. Fig. 1a and b presents a family of magnetization curves M(T) normalized to the value at 300 K (heating rate v = 2.6 K/min) and the corresponding dM/dT curves, respectively. As can be seen magnetization of amorphous phase initially (300–600 K) decreases with temperature up to the Curie point and in the temperature range of 650–800 K strongly increases due to formation of ␣-Fe nanograins confirmed by X-ray diffraction analysis. From the data shown in Fig. 1b the Curie temperature of the amorphous phase TC (position of the first minimum in the dM/dT curve) and the so-called nanocrystallization temperature Tm (position of the maximum of dM/dT) can be determined. The value of Tm deduced in this way corresponds to the highest formation rate of the new ferromagnetic phase. From Fig. 1 it can be deduced that the temperature Tm shifts towards higher temperature with increasing niobium content (for the same heating rate). For v = 2.6 K/min Tm = 690 K for 2 at.% of Nb and Tm = 775 K for 8 at.% of Nb. With increasing heating rate the maxima of dM/dT shift towards higher temperatures which is a characteristic feature of thermally activated (diffusion controlled) processes. It is noteworthy that the Curie temperature of the amorphous phase decreases with increasing Nb content from 524 K for 2 at.% of Nb to 346 K for 8 at.% of Nb (see Fig. 1b). Fig. 2a shows three DSC curves, i.e. heat flow curves obtained for samples with different Nb content (2, 5 and 6 at.%) and the same heating rate 15 K/min. As can be seen the nanocrystallization phenomenon is observed as exothermal heat flow maxima. For two alloys with the low Nb content (i.e. 2 and 3 at.%) the DSC curves consist of two exothermal peaks. For the Fe84 Nb2 B14 alloy and v = 15 K/min the first peak is situated at 735 K and the second one at 795 K (see Fig. 2a). With increasing Nb content both maxima shift towards higher temperature and therefore for higher Nb con-
Fig. 1. (a) Normalized magnetization vs. temperature for different Nb contents, (b) dM/dT curves for the data presented in (a).
centrations we were not able to measure the second maximum (out of range of our apparatus). The peak temperature of the first exothermal maximum, Td , increases from 735 K for 2 at.% of Nb to 820 K for 8 at.% of Nb (v = 15 K/min, see Fig. 2a). The obtained results indicate that the observed nanocrystallization process is a complex phenomenon, which consists of at least two stages. The second DSC maximum related to full crystallization was not analyzed in this paper, since it is focused on the first stage of crystallization, i.e. nanocrystallization. Fig. 2b shows the DSC curves obtained for the Fe81 Nb5 B14 amorphous alloy applying different heating rates (5, 10 and 15 K/min). The shift of Td towards higher temperatures with increasing heating rate is well documented. Fig. 3 shows the DSC curve and normalized magnetization curve M(T) obtained for the Fe84 Nb2 B14 amorphous alloy for the heating rate 5 K/min. It is evident that the first heat flow maximum corresponds to the earlier stages of the magnetization increase, i.e. to nanocrystallization. The second DSC maximum is related to full crystallization of the examined material, i.e. to a growth of ␣-Fe nanograins and
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Fig. 4. Crystallite size vs. 1 h annealing temperature Ta for the Fe80 Nb6 B14 alloy.
Fig. 2. (a) DSC curves obtained for different Nb contents, (b) DSC curves for the Fe81 Nb5 B14 alloy at different heating rates.
the formation of Fe3 B and Fe2 B borides as identified by X-ray diffraction analysis. In order to avoid a possible change of material microstructure due to different heating/cooling rates, X-ray patterns
were measured for samples annealed for 1 h at 300–900 K. The first stage of crystallization was attributed to the 1 h annealing temperature leading to the appearance of the first diffraction lines typical for the ␣-Fe phase. In order to determine the size of ␣-Fe nanocrystallites the line broadening of the 1 1 0, 2 0 0, 2 1 1 reflections was analyzed by applying the Philips software X’Pert Plus and the Williamson–Hall theory [13,14]. The results of this analysis for the Fe80 Nb6 B14 alloy are shown in Fig. 4 where the crystallite size is plotted versus the 1 h annealing temperature Ta . Fig. 5a–c shows the microstructure of the Fe80 Nb6 B14 alloy after annealing at 720, 760 and 840 K/1 h, respectively. As it can be seen from Fig. 5a after annealing at 720 K/1 h the examined material is in the amorphous state. The first nanograins of the order of 2–3 nm were detected in samples annealed at 760 K/1 h (see Fig. 5b), while the first X-ray diffraction lines of the ␣-Fe phase were observed after annealing at 770 K/1 h. Annealing at 840 K/1 h leads to the formation of an ␣-Fe nanostructure which is well documented in Fig. 5c. For this case the mean grain size was estimated as 10 nm.
3. Data analysis Since in the experiments the nanocrystallization temperature Tm exceeds the Curie temperature of the amorphous phase (see Fig. 1a and b) magnetization is a direct measure of the volume fraction of the crystalline phase that has transformed. Hence, one can assume that above the Curie point M(T) is directly proportional to the volume fraction x of the new ferromagnetic phase. As the nanocrystallization process is a diffusion controlled phenomenon the evolution of x with time t can be described by the kinetics rate equation [1,4,9,11,12]: Fig. 3. Normalized magnetization curve and DSC curve for the Fe84 Nb2 B14 alloy.
dx = F(x)K, dt
(1)
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Fig. 6. Plot of ln(Th2 /v) vs. 1/Th (see Eq. (3)) for the Fe82 Nb4 B14 alloy.
Fig. 5. (a) Microstructure of the Fe80 Nb6 B14 alloy after annealing at 720 K/1 h and the corresponding diffraction pattern, (b) microstructure of the Fe80 Nb6 B14 alloy after annealing at 760 K/1 h and the corresponding diffraction pattern, (c) microstructure of the Fe80 Nb6 B14 alloy after annealing at 840 K/1 h and the corresponding diffraction pattern.
where Th is the so-called temperature of an homological point determined for the heating rate v. Taking into account that both characteristic temperatures Tm and Td correspond to the highest formation rate of nano-crystallities one can assign the homological point Th to Tm and Td , respectively. Hence, we assume that Th = Tm for magnetic balance experiments and Th = Td for DSC. According to Eq. (3) a plot of ln(Th2 /v) versus 1/Th should yield a straight line the slope H/kB . An example of such a plot for both methods used is given in Fig. 6 for the Fe82 Nb4 B14 alloy. Activation enthalpies obtained in this way are plotted versus niobium content in Fig. 7. It is easy to notice that both experimental techniques give similar values of H. For low Nb content activation enthalpies are essentially lower (2–2.5 eV for 2 and 3 at.% of Nb) than the values obtained for higher Nb concentrations (approximately 4 eV for 5–8 at.% of Nb). The values of H obtained from both experimental techniques are listed in Table 1, where the characteristic
x where F(x) is any function of x assuring that 0 0 dx/F(x) = const. regardless of the heating rate v; K the effective overall reaction rate obeying an Arrhenius relationship of the form: −H K = K0 exp , (2) kB T where K0 is the so-called pre-exponential factor and H the effective activation enthalpy describing the overall nanocrystallization process (activation enthalpy barrier for nanocrystallization), kB the Boltzmann constant. It is generally accepted that for a reaction rate of the order of γ, F(x) = −xγ . From Eqs. (1) and (2) for T = T0 + vt (T0 ≈ 300 K) and H/kB T 1 one gets [1,12]: 1 kB Th2 H const. ≈ , (3) exp − v H kB T h
Fig. 7. Activation enthalpy vs. Nb content for the Fe86−x Nbx B14 amorphous alloys.
A. Chrobak et al. / Materials Science and Engineering A 382 (2004) 401–406 Table 1 Activation enthalpies and characteristic temperatures Td and Tm determined for the Fe86−x Nbx B14 amorphous alloys (heating rate 5 K/min) Nb content [at.%]
DSC
MB
Td [K]
H [eV]
Tm [K]
H [eV]
2 3 4 5 6 8
718 709 733 768 788 806
2.5 2.4 2.9 4.2 4.2 3.9
706 708 722 753 780 790
1.7 2.8 3.0 4.0 3.7 4.0
temperatures Td and Tm determined for heating rate 5 K/min are also given.
4. Discussion and conclusions The experimental results presented in Figs. 1 and 2 show that the crystallization of the examined amorphous alloys consists of at least two stages (primary and secondary crystallization). Using X-ray diffraction analysis and electron microscopy observations it was shown that in the first stage—at lower temperatures—␣-Fe nanograins are formed in the amorphous matrix. Irrespective of different heating procedures (linear heating and 1 h annealing) used in our experiments we assume that formation of nanograins observed by X-ray diffraction corresponds to the maxima of dM/dT (Fig. 1b) as well as to DSC maxima (Fig. 2). This results from the fact that the nanocrystallization process in both cases is the effect first observed. For the Fe80 Nb6 B14 alloy the evolution of grain size with the 1 h annealing temperature Ta is well documented in Figs. 4 and 5. From these figures it follows that the nanocrystallization takes place in the temperature range of 760–880 K. The DSC- and dM/dT-maxima for all using heating rates are observed in the same temperature range (see Table 1 for the heating rate 5 K/min). Hence, we conclude that using a linear heating with heating rates between 5 and 20 K/min one observes only the nanocrystallization process, i.e. nucleation and grain grow leading to formation of the nanostructure with grains of about 10–20 nm. For thermally activated processes this conclusion is quite obvious. In the second stage the already formed ␣-Fe nanograins grow and a formation of Fe3 B and Fe2 B borides is also observed. These two stages are well separated on the temperature scale only in DSC experiments (see Fig. 2a) which is well demonstrated in Fig. 3. The detailed analysis of our experimental data shows that the temperatures Td obtained form DSC curves are always higher than the temperatures Tm deduced from magnetization measurements (see Table 1). This difference cannot be explained neither by the unavoidable temperature gradient existing in both apparatuses nor by the natural dependence of magnetization on temperature. The latter can be neglected, since Tm is much higher than the Curie temperature of the
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amorphous phase and much lower then the Curie temperature of ␣-Fe crystalline phase (see Fig. 1a and b). According to our estimations at least half of the difference Td − Tm should have a physical meaning. Let us notice that according to Eq. (3) a linear correlation of ln(Th2 /v) versus 1/Th was obtained for both DSC and MB data for all Nb concentrations. A typical example for the Fe82 Nb4 B14 alloy is presented in Fig. 5. As can be seen the straight lines obtained for the same Nb content are shifted parallel to each other. This means that the constant term on the left side of Eq. (3) is slightly different for both experimental methods. In our opinion the problem lies in a definition of a homological point representative for both experimental techniques. It seems that the temperature Tm defined as a position of the maximum of dM/dT does not correspond exactly to the temperature of the heat flow maximum Td . Independent of the above remark, it is necessary to underline that the values of activation enthalpies obtained by applying Eq. (3) to MB and DSC data are similar (the same within error limits except the case of 2 at.% of Nb) for all examined alloys. This fact confirms that the difference in temperatures of homological points determined by the methods used is not very significant. Hence, one can conclude that both experimental methods for ferromagnetic materials can be used alternatively. The experimental results obtained in the present paper show that in the group of the examined amorphous alloys the nanocrystallization phenomenon shifts towards higher temperatures with increasing Nb content. This effect is observed as an increase of the characteristic temperatures Td or Tm and essentially does not depend on any data analysis. The variation of Nb content from 2 to 8 at.% leads to an increase of both temperatures by about 80 K. This means that Nb atoms as an alloying addition cause a slowing down of the diffusion processes. The observed dependence of the activation enthalpy on Nb content (see Fig. 7) reflects this tendency. For low Nb concentration the energetic barrier H for iron diffusion in the amorphous matrix is of about 2 eV whereas for higher concentrations H increases to about 4 eV (see Table 1). According to Fig. 7 a slowing down of the diffusion processes exhibits a saturation effect. This can be explained qualitatively by the diffusion mechanism of iron atoms via free volume frozen in the material during production. On one hand the higher concentration of Nb makes iron atoms diffusion more difficult but on the other hand can cause an increase of the vacancy concentration in the as-quenched state. Similar results were reported in [5] where for the Fe86−x Cu1 Nbx B13 (x = 4, 5, 7) amorphous alloys a slowing down of the diffusion processes was also observed. Based on Mössbauer spectroscopy and electron diffraction analysis it was concluded that Nb atoms segregate to grain boundaries and stop the growth of ␣-Fe nanograins. Such a conclusion is consistent with the data presented in Fig. 7 and with the mechanism of iron diffusion via free volume.
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5. Conclusion
References
The main conclusion of the present paper can be summarized as follows:
[1] M.E. McHenry, M.A. Willard, D.E. Laughlin, Prog. Mater. Sci. 44 (1999) 291. [2] G. Herzer, L.L. Varga, J. Magn. Magn. Mater. 215–216 (2000) 506. [3] P. Kwapuli´nski, J. Rasek, Z. Stokłosa, G. Haneczok, J. Magn. Magn. Mater. 254–255 (2003) 413. [4] T. Kulik, J. Non-Cryst. Solids 287 (2001) 145. [5] T. Girchardt, B. Friedrichs, E. Woldt, J. Hesse, K.G. Efthimiadis, S.C. Chadjivasiliou, Nanostruct. Mater. 12 (1999) 585. [6] J. Moya, M.J. Garcia, M. Vazquez, H. Sirkin, J. Phys. IV 8 (1998) 135. [7] P. Butvin, J. Sitek, B. Butvinova, E. Illekova, J. Phys. IV 8 (1998) 123. [8] C. Gomez-Polo, J.I. Perez-Landazabal, V. Recarte, W. Ciurzy´nska, J. Magn. Magn. Mater. 254–255 (2003) 88. [9] E.J. Illekowa, I. Matko, P. Duhaj, F.A. Kuhnast, J. Mater. Sci. 32 (1997) 4645. [10] P. Kwapuli´nski, A. Chrobak, G. Haneczok, Z. Stokłosa, J. Rasek, J. Lel˛atko, Mater. Sci. Eng. C 23 (2003) 71. [11] A. Chrobak, G. Haneczok, Z. Stokłosa, P. Kwapuli´nski, J. Rasek, G. Chełkowska, Phys. Stat. Sol. (a) 196 (2003) 248. [12] J. Rasek, Some Diffusion Phenomena in Crystalline and Amorphous Metals, Silesian University Press, Katowice, 2000 (in Polish). [13] G.K. Williamson, W.H. Hall, Acta Metall. 1 (1953) 22. [14] M. Karolus, E. Jartych, D. Oleszak, Acta Phys. Polonica A 102 (2002) 253.
1. Crystallization phenomenon in the Fe86−x Nbx B14 (2≤ × ≤8) amorphous alloys proceeds in two stages: (i) formation of ␣-Fe nanograins (nanocrystallization); and (ii) the growth of already formed ␣-Fe nanograins plus formation of borides (Fe3 B and Fe2 B). 2. Niobium as an alloying addition in the Fe86−x Nbx B14 (2≤ × ≤8) amorphous alloys causes a slowing down of the diffusion processes which leads to an increase of the nanocrystallization temperature from 735 for 2 at % of Nb to 820 K for 8 at % of Nb (heating rate 15 K/min). 3. Activation enthalpy of the nanocrystallization phenomenon in the Fe86−x Nbx B14 (2≤ × ≤8) amorphous alloys increases from 2 eV for 2 at % of Nb to 4 eV for 5–8 at % of Nb. Acknowledgements This work was supported by the Polish State Committee for Scientific Research under grant no. PBZ/KBN/013/ T08/47.
Influence of Nb on the first stage of crystallization in Fe86−x Nbx B14 amorphous alloys A. Chrobak a , D. Chrobak b , G. Haneczok b,∗ , P. Kwapuli´nski b , Z. Kwolek b , M. Karolus b a
b
Institute of Physics, Silesian University, 40-007 Katowice, 4 Uniwersytecka, Poland Institute of Materials Science, Silesian University, 40-007 Katowice, 12 Bankowa, Poland Received 10 December 2003; received in revised form 4 May 2004
Abstract The kinetics of the first stage of crystallization (nanocrystallization) in the Fe86−x Nbx B14 amorphous alloys was studied by applying differential scanning calorimetry and magnetic balance techniques. It was shown that the nanocrystallization temperature increases with increasing Nb content by more than 80 K. Activation enthalpy of the nanocrystallization process increases from 2 eV for 2 at.% of Nb to 4 eV for 5–8 at.% of Nb. The results obtained by the mentioned experimental techniques are also discussed from the methodological point of view. © 2004 Elsevier B.V. All rights reserved. Keywords: Nanocrystallization; Amorphous alloys; Magnetization; Differential scanning calorimetry
1. Introduction The examined amorphous alloys belong to a widely studied group of modern soft magnetic materials based on iron which are frequently used as precursors of nanostructured materials [1–5]. Indeed, using a suitable thermal annealing at temperatures close to the crystallization temperature one can obtain a microstructure with iron nanograins embedded in the amorphous matrix. Soft magnetic properties of these alloys are found to be superior to those of conventional materials. For instance, the initial magnetic permeability can be of the order of 104 and the coercive field about 1–3 A/m. Moreover, very good magnetic properties are usually correlated with high resistivity (1–3 m) ensuring a low level of eddy current losses. The key to the formation of nanocrystallites in an amorphous solid of an appropriate chemical composition lies in the controlling of the annealing conditions (temperature and time) to ensure a relatively high nucleation rate and a small growth rate [1–4]. Experimental study of the nanocrystallization process as a diffusion controlled phenomenon is usu-
∗ Corresponding author. Tel.: +48 32 359 16 64; fax: +48 32 259 69 29. E-mail address: [email protected] (G. Haneczok).
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.05.013
ally carried out by applying differential scanning calorimetry [1,4–8] or by resistivity measurements [1,5,9] though in some cases magnetic balance is also used [10–12]. For magnetic materials the latter allows for a direct study of the formation of a new ferromagnetic phase. Using these techniques one can determine the activation enthalpy of the nanocrystallization process which allows us to control its kinetics [11,12] and in effect the material properties. The main aim of the present paper is to study the influence of niobium content on the first stage of the crystallization (or nanocrystallization) process in the Fe86−x Nbx B14 (2 ≤ × ≤ 8) group of amorphous alloys. Differential scanning calorimetry and magnetic balance are used as two complementary experimental techniques. The obtained results are discussed from the methodological point of view.
2. Material, experimental procedure and results Amorphous alloys examined in the present paper— Fe86−x Nbx B14 (2 ≤ × ≤ 8)—were produced by the melt spinning technique in form of strips with thickness of about 25 m and width of 10 mm. As-quenched samples were in the amorphous state, confirmed by X-ray and high resolution electron microscopy techniques.
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Kinetics of the nanocrystallization process was examined by applying two experimental techniques: • Magnetic balance (MB, Faraday type)—magnetization in saturation M(T) (magnetic field 0.5 T) was measured in the temperature range of 300–1000 K and heating rates ranged from 2 to 8 K/min. • Differential scanning calorimetry (DSC, Perkin-Elmer DSC-7)—experiments were carried out in the temperature range of 300–850 K and heating rates ranged from 5 to 20 K/min. In order to identify new phases formed during crystallization X-ray diffraction analysis (Philips X’Pert Diffractometer PW 3040/60) and transmission electron microscopy observations (JEM 3010) were used. As-quenched samples were annealed for 1 h in the temperature range from 300 to 900 K (in steps of about 20 K) and X-ray diffraction patterns were measured at room temperature. Application of such a procedure (according to [1,4] a standard annealing procedure) makes it possible to establish thermal treatment conditions (i.e. temperature and time) essential to obtain nanostructured materials. Fig. 1a and b presents a family of magnetization curves M(T) normalized to the value at 300 K (heating rate v = 2.6 K/min) and the corresponding dM/dT curves, respectively. As can be seen magnetization of amorphous phase initially (300–600 K) decreases with temperature up to the Curie point and in the temperature range of 650–800 K strongly increases due to formation of ␣-Fe nanograins confirmed by X-ray diffraction analysis. From the data shown in Fig. 1b the Curie temperature of the amorphous phase TC (position of the first minimum in the dM/dT curve) and the so-called nanocrystallization temperature Tm (position of the maximum of dM/dT) can be determined. The value of Tm deduced in this way corresponds to the highest formation rate of the new ferromagnetic phase. From Fig. 1 it can be deduced that the temperature Tm shifts towards higher temperature with increasing niobium content (for the same heating rate). For v = 2.6 K/min Tm = 690 K for 2 at.% of Nb and Tm = 775 K for 8 at.% of Nb. With increasing heating rate the maxima of dM/dT shift towards higher temperatures which is a characteristic feature of thermally activated (diffusion controlled) processes. It is noteworthy that the Curie temperature of the amorphous phase decreases with increasing Nb content from 524 K for 2 at.% of Nb to 346 K for 8 at.% of Nb (see Fig. 1b). Fig. 2a shows three DSC curves, i.e. heat flow curves obtained for samples with different Nb content (2, 5 and 6 at.%) and the same heating rate 15 K/min. As can be seen the nanocrystallization phenomenon is observed as exothermal heat flow maxima. For two alloys with the low Nb content (i.e. 2 and 3 at.%) the DSC curves consist of two exothermal peaks. For the Fe84 Nb2 B14 alloy and v = 15 K/min the first peak is situated at 735 K and the second one at 795 K (see Fig. 2a). With increasing Nb content both maxima shift towards higher temperature and therefore for higher Nb con-
Fig. 1. (a) Normalized magnetization vs. temperature for different Nb contents, (b) dM/dT curves for the data presented in (a).
centrations we were not able to measure the second maximum (out of range of our apparatus). The peak temperature of the first exothermal maximum, Td , increases from 735 K for 2 at.% of Nb to 820 K for 8 at.% of Nb (v = 15 K/min, see Fig. 2a). The obtained results indicate that the observed nanocrystallization process is a complex phenomenon, which consists of at least two stages. The second DSC maximum related to full crystallization was not analyzed in this paper, since it is focused on the first stage of crystallization, i.e. nanocrystallization. Fig. 2b shows the DSC curves obtained for the Fe81 Nb5 B14 amorphous alloy applying different heating rates (5, 10 and 15 K/min). The shift of Td towards higher temperatures with increasing heating rate is well documented. Fig. 3 shows the DSC curve and normalized magnetization curve M(T) obtained for the Fe84 Nb2 B14 amorphous alloy for the heating rate 5 K/min. It is evident that the first heat flow maximum corresponds to the earlier stages of the magnetization increase, i.e. to nanocrystallization. The second DSC maximum is related to full crystallization of the examined material, i.e. to a growth of ␣-Fe nanograins and
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Fig. 4. Crystallite size vs. 1 h annealing temperature Ta for the Fe80 Nb6 B14 alloy.
Fig. 2. (a) DSC curves obtained for different Nb contents, (b) DSC curves for the Fe81 Nb5 B14 alloy at different heating rates.
the formation of Fe3 B and Fe2 B borides as identified by X-ray diffraction analysis. In order to avoid a possible change of material microstructure due to different heating/cooling rates, X-ray patterns
were measured for samples annealed for 1 h at 300–900 K. The first stage of crystallization was attributed to the 1 h annealing temperature leading to the appearance of the first diffraction lines typical for the ␣-Fe phase. In order to determine the size of ␣-Fe nanocrystallites the line broadening of the 1 1 0, 2 0 0, 2 1 1 reflections was analyzed by applying the Philips software X’Pert Plus and the Williamson–Hall theory [13,14]. The results of this analysis for the Fe80 Nb6 B14 alloy are shown in Fig. 4 where the crystallite size is plotted versus the 1 h annealing temperature Ta . Fig. 5a–c shows the microstructure of the Fe80 Nb6 B14 alloy after annealing at 720, 760 and 840 K/1 h, respectively. As it can be seen from Fig. 5a after annealing at 720 K/1 h the examined material is in the amorphous state. The first nanograins of the order of 2–3 nm were detected in samples annealed at 760 K/1 h (see Fig. 5b), while the first X-ray diffraction lines of the ␣-Fe phase were observed after annealing at 770 K/1 h. Annealing at 840 K/1 h leads to the formation of an ␣-Fe nanostructure which is well documented in Fig. 5c. For this case the mean grain size was estimated as 10 nm.
3. Data analysis Since in the experiments the nanocrystallization temperature Tm exceeds the Curie temperature of the amorphous phase (see Fig. 1a and b) magnetization is a direct measure of the volume fraction of the crystalline phase that has transformed. Hence, one can assume that above the Curie point M(T) is directly proportional to the volume fraction x of the new ferromagnetic phase. As the nanocrystallization process is a diffusion controlled phenomenon the evolution of x with time t can be described by the kinetics rate equation [1,4,9,11,12]: Fig. 3. Normalized magnetization curve and DSC curve for the Fe84 Nb2 B14 alloy.
dx = F(x)K, dt
(1)
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Fig. 6. Plot of ln(Th2 /v) vs. 1/Th (see Eq. (3)) for the Fe82 Nb4 B14 alloy.
Fig. 5. (a) Microstructure of the Fe80 Nb6 B14 alloy after annealing at 720 K/1 h and the corresponding diffraction pattern, (b) microstructure of the Fe80 Nb6 B14 alloy after annealing at 760 K/1 h and the corresponding diffraction pattern, (c) microstructure of the Fe80 Nb6 B14 alloy after annealing at 840 K/1 h and the corresponding diffraction pattern.
where Th is the so-called temperature of an homological point determined for the heating rate v. Taking into account that both characteristic temperatures Tm and Td correspond to the highest formation rate of nano-crystallities one can assign the homological point Th to Tm and Td , respectively. Hence, we assume that Th = Tm for magnetic balance experiments and Th = Td for DSC. According to Eq. (3) a plot of ln(Th2 /v) versus 1/Th should yield a straight line the slope H/kB . An example of such a plot for both methods used is given in Fig. 6 for the Fe82 Nb4 B14 alloy. Activation enthalpies obtained in this way are plotted versus niobium content in Fig. 7. It is easy to notice that both experimental techniques give similar values of H. For low Nb content activation enthalpies are essentially lower (2–2.5 eV for 2 and 3 at.% of Nb) than the values obtained for higher Nb concentrations (approximately 4 eV for 5–8 at.% of Nb). The values of H obtained from both experimental techniques are listed in Table 1, where the characteristic
x where F(x) is any function of x assuring that 0 0 dx/F(x) = const. regardless of the heating rate v; K the effective overall reaction rate obeying an Arrhenius relationship of the form: −H K = K0 exp , (2) kB T where K0 is the so-called pre-exponential factor and H the effective activation enthalpy describing the overall nanocrystallization process (activation enthalpy barrier for nanocrystallization), kB the Boltzmann constant. It is generally accepted that for a reaction rate of the order of γ, F(x) = −xγ . From Eqs. (1) and (2) for T = T0 + vt (T0 ≈ 300 K) and H/kB T 1 one gets [1,12]: 1 kB Th2 H const. ≈ , (3) exp − v H kB T h
Fig. 7. Activation enthalpy vs. Nb content for the Fe86−x Nbx B14 amorphous alloys.
A. Chrobak et al. / Materials Science and Engineering A 382 (2004) 401–406 Table 1 Activation enthalpies and characteristic temperatures Td and Tm determined for the Fe86−x Nbx B14 amorphous alloys (heating rate 5 K/min) Nb content [at.%]
DSC
MB
Td [K]
H [eV]
Tm [K]
H [eV]
2 3 4 5 6 8
718 709 733 768 788 806
2.5 2.4 2.9 4.2 4.2 3.9
706 708 722 753 780 790
1.7 2.8 3.0 4.0 3.7 4.0
temperatures Td and Tm determined for heating rate 5 K/min are also given.
4. Discussion and conclusions The experimental results presented in Figs. 1 and 2 show that the crystallization of the examined amorphous alloys consists of at least two stages (primary and secondary crystallization). Using X-ray diffraction analysis and electron microscopy observations it was shown that in the first stage—at lower temperatures—␣-Fe nanograins are formed in the amorphous matrix. Irrespective of different heating procedures (linear heating and 1 h annealing) used in our experiments we assume that formation of nanograins observed by X-ray diffraction corresponds to the maxima of dM/dT (Fig. 1b) as well as to DSC maxima (Fig. 2). This results from the fact that the nanocrystallization process in both cases is the effect first observed. For the Fe80 Nb6 B14 alloy the evolution of grain size with the 1 h annealing temperature Ta is well documented in Figs. 4 and 5. From these figures it follows that the nanocrystallization takes place in the temperature range of 760–880 K. The DSC- and dM/dT-maxima for all using heating rates are observed in the same temperature range (see Table 1 for the heating rate 5 K/min). Hence, we conclude that using a linear heating with heating rates between 5 and 20 K/min one observes only the nanocrystallization process, i.e. nucleation and grain grow leading to formation of the nanostructure with grains of about 10–20 nm. For thermally activated processes this conclusion is quite obvious. In the second stage the already formed ␣-Fe nanograins grow and a formation of Fe3 B and Fe2 B borides is also observed. These two stages are well separated on the temperature scale only in DSC experiments (see Fig. 2a) which is well demonstrated in Fig. 3. The detailed analysis of our experimental data shows that the temperatures Td obtained form DSC curves are always higher than the temperatures Tm deduced from magnetization measurements (see Table 1). This difference cannot be explained neither by the unavoidable temperature gradient existing in both apparatuses nor by the natural dependence of magnetization on temperature. The latter can be neglected, since Tm is much higher than the Curie temperature of the
405
amorphous phase and much lower then the Curie temperature of ␣-Fe crystalline phase (see Fig. 1a and b). According to our estimations at least half of the difference Td − Tm should have a physical meaning. Let us notice that according to Eq. (3) a linear correlation of ln(Th2 /v) versus 1/Th was obtained for both DSC and MB data for all Nb concentrations. A typical example for the Fe82 Nb4 B14 alloy is presented in Fig. 5. As can be seen the straight lines obtained for the same Nb content are shifted parallel to each other. This means that the constant term on the left side of Eq. (3) is slightly different for both experimental methods. In our opinion the problem lies in a definition of a homological point representative for both experimental techniques. It seems that the temperature Tm defined as a position of the maximum of dM/dT does not correspond exactly to the temperature of the heat flow maximum Td . Independent of the above remark, it is necessary to underline that the values of activation enthalpies obtained by applying Eq. (3) to MB and DSC data are similar (the same within error limits except the case of 2 at.% of Nb) for all examined alloys. This fact confirms that the difference in temperatures of homological points determined by the methods used is not very significant. Hence, one can conclude that both experimental methods for ferromagnetic materials can be used alternatively. The experimental results obtained in the present paper show that in the group of the examined amorphous alloys the nanocrystallization phenomenon shifts towards higher temperatures with increasing Nb content. This effect is observed as an increase of the characteristic temperatures Td or Tm and essentially does not depend on any data analysis. The variation of Nb content from 2 to 8 at.% leads to an increase of both temperatures by about 80 K. This means that Nb atoms as an alloying addition cause a slowing down of the diffusion processes. The observed dependence of the activation enthalpy on Nb content (see Fig. 7) reflects this tendency. For low Nb concentration the energetic barrier H for iron diffusion in the amorphous matrix is of about 2 eV whereas for higher concentrations H increases to about 4 eV (see Table 1). According to Fig. 7 a slowing down of the diffusion processes exhibits a saturation effect. This can be explained qualitatively by the diffusion mechanism of iron atoms via free volume frozen in the material during production. On one hand the higher concentration of Nb makes iron atoms diffusion more difficult but on the other hand can cause an increase of the vacancy concentration in the as-quenched state. Similar results were reported in [5] where for the Fe86−x Cu1 Nbx B13 (x = 4, 5, 7) amorphous alloys a slowing down of the diffusion processes was also observed. Based on Mössbauer spectroscopy and electron diffraction analysis it was concluded that Nb atoms segregate to grain boundaries and stop the growth of ␣-Fe nanograins. Such a conclusion is consistent with the data presented in Fig. 7 and with the mechanism of iron diffusion via free volume.
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5. Conclusion
References
The main conclusion of the present paper can be summarized as follows:
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1. Crystallization phenomenon in the Fe86−x Nbx B14 (2≤ × ≤8) amorphous alloys proceeds in two stages: (i) formation of ␣-Fe nanograins (nanocrystallization); and (ii) the growth of already formed ␣-Fe nanograins plus formation of borides (Fe3 B and Fe2 B). 2. Niobium as an alloying addition in the Fe86−x Nbx B14 (2≤ × ≤8) amorphous alloys causes a slowing down of the diffusion processes which leads to an increase of the nanocrystallization temperature from 735 for 2 at % of Nb to 820 K for 8 at % of Nb (heating rate 15 K/min). 3. Activation enthalpy of the nanocrystallization phenomenon in the Fe86−x Nbx B14 (2≤ × ≤8) amorphous alloys increases from 2 eV for 2 at % of Nb to 4 eV for 5–8 at % of Nb. Acknowledgements This work was supported by the Polish State Committee for Scientific Research under grant no. PBZ/KBN/013/ T08/47.