Microstructural observations of the crystallization of amorphous Fe Si B based magnetic alloys

Transcription

1 Thin Solid Films 505 (2006) Microstructural observations of the crystallization of amorphous Fe Si B based magnetic alloys Y.R. Zhang, R.V. Ramanujan * School of Materials Science and Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, , Singapore Available online 21 November 2005 Abstract The effect of Cu and Nb alloying additions on the crystallization of Fe Si B based alloys were studied. DSC, XRD, TEM, EELS and VSM techniques were used to study the thermal properties, phase formation during primary crystallization, morphological transitions and magnetic properties. The additions of individual Cu or Nb alloying additions changed the crystallization temperature as well as the activation energy for primary crystallization. The phases formed during primary crystallization for the Fe 77.5 Si 13.5 B 9,Fe 76.5 Si 13.5 B 9 Cu 1 and Fe 74.5 Si 13.5 B 9 Nb 3 Cu 1 alloys are the same, however the morphologies are significantly different. Alloying additions of 3 at.% Nb induced a change in the crystallization mechanism and the type of phases formed. The combined additions of Cu and Nb resulted in the formation of nanocrystals. B atoms were found to be rejected around dendrites formed during primary crystallization of the Fe 77.5 Si 13.5 B 9 alloy. The highest saturation magnetization and the lowest coercivity is obtained in the Fe 77.5 Si 13.5 B 9 and Fe 74.5 Si 13.5 B 9 Nb 3 Cu 1 alloy respectively after annealing at 550 -C for 1 h. D 2005 Elsevier B.V. All rights reserved. Keywords: Alloying addition; Crystallization; Electron microscopy; Magnetism 1. Introduction The Fe Si B Nb Cu alloy with the commercial name Finemet is a soft magnetic alloy with saturation magnetization of 1.2 T and small coercivity [1]. Its good magnetic properties are due to nanocrystals about 15 nm in size in an amorphous matrix, this microstructure is attained by heat treatment at 550 -C for 1 h. According to Herzer s model, since the radius of the nanocrystals is less than the exchange length, the magnetic anisotropy is spatially averaged, and the high saturation magnetization is obtained as the coercivity remains almost zero [2]. Concerning the mechanism of nanostructure formation it has been shown that Cu and Nb alloying additions play a crucial role in the formation of the nanostructure. The formation of Cu clusters is expected to serve as the nucleation sites, enhancing the nucleation rate of the nanocrystallization process. The Nb atoms are expected to hinder the growth of the nanocrystals thus decreasing its growth rate [3 5]. Combined alloying additions of Cu and Nb resulted in nanocrystal formation, which resulted in good soft magnetic properties. * Corresponding author. address: RAMANUJAN@NTU.EDU.SG (R.V. Ramanujan). Regarding the role of Cu in this alloy there have been several contradictory reports: Yoshizawa and Yamauchi suggested that Cu clusters form prior to nanocrystallization leading to an increase in the local concentration of Fe in the vicinity of these clusters, thus leading to the formation of a-fe crystals [6] By means of atom probe field ion microscopy (APFIM) Hono et al. found that after short annealing at 550 -C clusters of Cu of few nanometers in size were formed which acted as heterogeneous nucleation sites for the a-fe particles [3,7]. Ayers et al. suggested that, due to the similarity of the crystal structure of f.c.c Cu and the DO 3 phase of a-fe, rather than f.c.c Cu formation acted as the catalyst for the formation of a-fe with the DO 3 crystal structure [8,9]. Duhaj et al. suggested that the decisive factor in the process of the primary crystallization of nanocrystalline microstructure from amorphous alloy is the short range order in the amorphous structure, which strongly depends on the mixing enthalpy of constituents [10]. Concerning the role of Nb in the Finemet alloy Yavari and Negri assumed a sharp concentration gradient of Nb at the crystal matrix interface, this gradient would hinder the diffusion of Fe and Si thus reducing the growth of the nanocrystal [11]. However a different model has suggested that soft impingement by overlapping fields surrounding the /$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi: /j.tsf

2 98 Y.R. Zhang, R.V. Ramanujan / Thin Solid Films 505 (2006) h in a vacuum furnace (10 5 Torr). A JEOL 2010 Transmission Electron Microscope (TEM) with an accelerating voltage of 200 kv was employed for micrograph studies. Philips 300 kv TEM with EELS attachment was used for element mapping. The samples prepared for TEM observation were cut into 3 mm discs before heat-treatment and subsequently ion-milled. Measurements of the magnetic properties were made using a LakeShore 7300 vibrating sample magnetometer. All the measurements were conducted three times to minimize errors. 3. Results Fig. 1. DSC measurements of different samples with heating rate at 10 K/min: Fe 77.5 Si 13.5 B 9 (A); Fe 74.5 Nb 3 Si 13.5 B 9 (B); Fe 76.5 Cu 1 Si 13.5 B 9 (C); Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 (D). precipitates can lead to the observed retardation of crystal growth [12]. By means of Mossbauer spectrometry Gupta et al. suggested that there was very little segregation of Nb atoms at the crystal matrix interface. Nb diffuses out of the crystal but it does not just get segregated at the interface, rather it diffuses into the amorphous matrix giving rise to a Nb concentration gradient [13]. Thus up to now the crucial role of Cu and Nb alloying additions in the Finemet alloy is not yet clear. In this study four alloys compositions were selected: Fe 77.5 Si 13.5 B 9, Fe 76.5 Si 13.5 B 9 Cu 1, Fe 74.5 Si 13.5 B 9 Nb 3 and Fe 74.5 Si 13.5 B 9 Nb 3 Cu 1. Comparison of the thermal properties, phase formation, the microstructure and the magnetic properties after crystallization of these alloys facilitates the understanding of the effect of Cu and Nb alloying addition in the Finemet alloy. Although previous work has been carried out in these compositions [14 19], no report has combined this information to facilitate a comprehensive understanding of the effect of Cu and Nb alloying additions on the crystallization process of the amorphous Fe Si B alloy. Differential scanning calorimetry (DSC), X-ray diffractometry (XRD), transmission electron microscopy (TEM) attached with electron energy loss spectroscopy (EELS) and vibrating sample magnetometer (VSM) techniques were utilized in this investigation. 2. Experimental procedure Fe 77.5 Si 13.5 B 9, Fe 76.5 Si 13.5 B 9 Cu 1, Fe 74.5 Si 13.5 B 9 Nb 3 and Fe 74.5 Si 13.5 B 9 Nb 3 Cu 1 alloys were prepared in the form of 20 Am thick and 25 mm wide ribbons, all the alloys are amorphous in the as received condition. A NETZSCH DSC- 404C was employed for calorimetry, at heating rates of 5 K/ min, 10 K/min and 20 K/min were utilized. All the DSC experiments were performed in vacuum using ceramic sample pans. X-ray diffraction studies were carried out in a RIGAKU DMAX 2200 with Cu Ká radiation. Heat treatment conditions were selected according to the DSC results: all alloys were annealed at 550 -C for 5 min, 30 min, 1 h, 4 h, 8 h, 16 h and Fig. 1 showed the DSC curves of the selected alloys. For the Fe Si B alloy two peaks were observed which indicated that two crystallization processes occurred during crystallization. With Cu alloying additions there are two peaks in the DSC curve the first one occurred at lower temperatures compared to the Fe Si B alloy, this result suggested that Cu alloying additions made primary crystallization earlier. With Nb alloying additions only one peak was observed at a higher temperature compared to the Fe Si B alloy, which indicated that the amorphous matrix was stabilized in the Fe Si B Nb alloy. With both Cu and Nb alloying additions three peaks were observed which indicated that besides primary and secondary crystallization, processes such as decomposition of the Fe 3 B phase to the Fe 2 B phase and a-fe also occurred at higher temperatures. By using the Doyle Ozawa Method the activation energies can be calculated by means of the following equation [20]: Logb ¼ Log½AE=RFðaÞŠ 2:315 0:4567E= ðrtþ where b is the heating rate, A is a constant, F(a) is the crystallized fraction, T is the temperature corresponding to the crystallized fraction, E is the activation energy and R is gas constant: J/K. Plotting Logb as the y-axis and 1/T as the x-axis a straight line can be obtained, the slope of which is E/R, thus the activation energy can be calculated (Table 1). This table showed that activation energy for primary crystallization of the Table 1 Calculated activation energy of different alloys Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 Fe 76.5 Cu 1 Si 13.5 B 9 Heating rate (K/min) First peak (K) Activation energy (kj/mol) Second peak (K) Activation energy (kj/mol) Third peak (K) Activation energy (kj/mol) 381 Fe 74.5 Nb 3 Si 13.5 B 9 Fe 77.5 Si 13.5 B 9 Heating rate (K/min) First peak (K) Activation energy (kj/mol) Second peak (K) Activation energy (kj/mol) 342

3 Y.R. Zhang, R.V. Ramanujan / Thin Solid Films 505 (2006) Fig. 2. XRD results for the alloy heat treatment at 550 -C for 30 min: (1) Fe 77.5 Si 13.5 B 9 ; (2) Fe 76.5 Cu 1 Si 13.5 B 9 ; (3) Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 ; (4) Fe 74.5 Nb 3 Si 13.5 B 9 :Fe 3 Si (4), Fe 23 B 6 (?), and Fe 3 B(>)(y-axis is plotted on a log scale). Fe Si B Cu alloy is the lowest (267 kj/mol) while that of the Fe Si B Nb alloy is the highest (421 kj/mol). The phases formed after annealing at 550 -C for 30 min were identified by XRD results (Fig. 2). Due to the low intensity of the peaks of the Fe Si B Nb alloy a logarithmic scale was used for the y-axis. For the Fe Si B alloy, Fe Si B Cu alloy and Fe Si B Nb Cu alloys only the Fe 3 Si phase was identified. In the case of the Fe Si B Nb alloy three phases were formed: Fe 3 Si, Fe 23 B 6 and Fe 3 B. Transmission Electron Microscopy is a useful technique for microstructure observation. Fig. 3(a) to (d) shows the TEM microstructures of the alloys after heat treatment at 550 -C for 30 min. For the Fe Si B alloy the dendritic morphology was observed (Fig. 3(a)). On the other hand, with Cu alloying addition, instead of the dendritic morphology, an equiaxed morphology with rough interface was observed (Fig. 3(b)), the crystal size varies from 50 nm to 100 nm. With Nb alloying additions an equiaxed morphology with smaller crystal size was observed (Fig. 3(c)), the crystal size is in the range from 30 nm to 50 nm. With both Cu and Nb alloying additions equiaxed nanocrystals about 15 nm in size was observed in the matrix (Fig. 3(d)). It has been suggested that during primary crystallization of the Fe Si B alloy B was rejected due to the formation of the Fe 3 Si phase. However, no report has provided detailed EELS observations. The B element mapping in the Fe Si B alloy by EELS was obtained in order to show the distribution of boron during crystallization (Fig. 4). The white area indicated regions with higher B concentration and the dark areas indicated regions with less B distribution, regions around the dendrite are rich in B element compared Fig. 3. BF TEM micrographs of the (a) Fe 77.5 Si 13.5 B 9, (b) Fe 76.5 Si 13.5 B 9 Cu 1, (c) Fe 74.5 Si 13.5 B 9 Nb 3 and (d) Fe 74.5 Si 13.5 B 9 Nb 3 Cu 1 alloys heat treatment at 550 -C for 30 min.

4 100 Y.R. Zhang, R.V. Ramanujan / Thin Solid Films 505 (2006) Fig. 4. B element mapping for the Fe Si B alloy after heat treatment at 550 -C for 30 min. with the region within the dendrite. Thus it could be inferred that the B was rejected due to the formation of the Fe 3 Si phase during primary crystallization in the Fe Si B alloy. VSM was used to measure the magnetic properties as a function of annealing time when the heat treatment temperature is 550 -C (Figs. 5 and 6). The saturation magnetization was highest (1.65 T) for the Fe Si B alloy and the coercivity is smallest: (30 A/m) for the Fe Si B Cu Nb alloy respectively after heat treatment for 1 h. Following crystallization the coercivity of the Fe Si B and Fe Si B Cu alloy increased dramatically to more than 3000 A/m. Annealing time had only a small effect on the coercivity of the Fe Si B Nb and Fe Si B Nb Cu alloys. 4. Discussion 4.1. Thermal properties The curve 1 for the Fe Si B alloy (Fig. 1) exhibits two exothermic peaks which is consistent with the previous report that the first peak corresponds to the formation of the Fe 3 Si phase while the second one corresponds to the formation of the Fe B compound [21 24]. With Cu alloying additions the amorphous matrix was destabilized and the first peak occurs at lower temperature compared with that of the Fe Si B alloy [25]. As expected, the activation energy in the case of Fe Si B Cu alloy is 267 kj/mol, lower than that of the Fe Si B alloy: 376 kj/mol, which also indicated the crystallization occurred more easily with Cu alloying additions. With Nb alloying additions, if the Nb concentration is less than 3 at.%, two peaks can be observed in the DSC curve [26]. With 3 at.% Nb alloying additions the crystallization mechanism is changed from primary crystallization to eutectic crystallization. The Nb concentration influences the onset of crystallization, when 3 at.% Nb was added its peak shifts to a value of 863 K, which showed that Nb will stabilize the amorphous phase and make it difficult to crystallize compared to the other alloys [27]. The activation energy is the highest: 421 kj/mol of the four alloys which also indicated that the crystallization is more difficult with Nb alloying additions. For the Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloy the DSC curve exhibits a highly intense exothermic peak. This peak can be attributed to the primary crystallization of the nanocrystalline phase which was followed by two other exothermic peaks. The second and third peaks partly split, this could be attributed either to further crystallization of the residual amorphous phase, or to phase transformation of existing metastable phases (such as Fe 3 B), occurring after primary crystallization. With both Cu and Nb alloying additions, the first DSC exotherm of Fe 73.5 Cu 1 Nb 3- Si 13.5 B 9 alloy is flatter and wider than those found in other alloys, suggesting lower crystallization kinetics which may be due to a substantial decrease in the crystal growth rate. The Fig. 5. Magnetization dependence on annealing time at 550 -C. Fig. 6. Coercivity dependence on annealing time at 550 -C.

5 Y.R. Zhang, R.V. Ramanujan / Thin Solid Films 505 (2006) observed large separation of the two crystallization stages (about 150 K) in Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 is another feature of alloys exhibiting easy nanocrystallization. It is well known that Cu additions to Fe Si B Nb glasses sharply increases DT x, which is the difference between T x1, the temperature of the a- Fe crystal formation and T x2, the crystallization temperature of the Nb and B-enriched amorphous phase [18,19]. This is because there is no attractive interaction between Cu and Nb atoms and no driving force for alloying or compound formation. Thus Cu additions to amorphous Fe-based alloys containing Nb atoms will have tendency to phase-separate out of the matrix facilitating a high density of crystal formation [28]. Additions of Cu and Nb together with higher DT x are thus favorable to soft magnetic properties Phase formation and microstructral evolution Although the same Fe 3 Si phase is identified in the Fe Si B alloy, Fe Si B Cu and Fe Si B Nb Cu alloys, the morphologies are significantly different. In the Fe Si B alloy the dendritic morphology was observed. With individual Cu and Nb alloying additions the equiaxed morphology was observed, while with combined Cu and Nb alloying additions the nanocrystals were observed. Mullins and Sekerka suggested that spheres undergoing diffusion controlled growth into a supersaturation matrix are unstable above a critical size [29,30]. The critical value of the crystal size is just seven times of the critical radius of nucleation theory [29,30]. That means there is a critical value for the crystal size, exceeding this value the crystal can grow into a dendrite, while smaller than that critical value the dendrite cannot develop. Cu alloying additions increased the nucleation rate which made the nucleation process dominate once crystallization began, the crystal growth was reduced. Thus the size of the original crystal formed cannot reach the critical value and the dendrites do not form in the Fe Si B Cu alloy. With both Cu and Nb alloying additions Nb will reduce the solubility of Cu in the alloy so as to promote formation of the Cu clusters on a much finer scale than in the Nb-free alloy [28]. Thus the nucleation rate was further increased, and the growth rate was further decreased due to the slow atomic diffusivity of Nb alloying addition. Hence the crystal size can not reach the critical value and dendrites cannot develop in the Fe Si B Nb Cu alloy. The phases formed in the Fe Si B Nb alloy are Fe 3 Si, Fe 23 B 6 and Fe 3 B, detailed structural analysis has been reported earlier [31]. The rationale for the addition of Nb to the Fe B Si alloy originates from the application of empirical guidelines [32 34], i.e., (1) multi-component alloys consisting of more than three constituent elements (or three groups), (2) significant atomic size ratios above 12% among the main three elements, and (3) suitable negative heats of mixing among their elements. The addition of Nb enables us to satisfy these three rules for the Fe B Si base alloys. It has previously been reported that if these rules are satisfied a glassy structure with highly dense random packing, new local atomic configuration and longrange homogeneity with attractive interaction is expected to form, leading to an increase in interfacial energy, low atomic diffusivity and the necessity of long-range atomic rearrangements for the progress of crystallization [34]. It is therefore suggested that nucleation and growth reactions for crystallization are significantly suppressed in the supercooled liquid phase with the above described features, resulting in an increase in stability of the supercooled liquid against crystallization. Thus the dendritic morphology can be avoided by Nb alloying addition, promoting the formation of the equiaxed morphology, as was observed in the case of the Fe Si B Nb alloy. Concerning the crystallization behavior at lower or higher annealing temperature it has been reported that increase of annealing temperature resulted in much greater increase of nucleation rate than growth rate. Thus the increase of the nucleation rate will lead to much finer scale of the crystal which can not reach the critical value of the dendrite formation. And at lower annealing temperature more quenched clusters can serve as nuclei or nucleation site which increase the nucleation rate, thus the critical value can not be reached [14] Magnetic properties From Figs. 5 and 6 it can be seen that the saturation magnetization (Ms) of the Fe 77.5 Si 13.5 B 9 alloy is highest at 550 -C for 60 min while the coercivity is as high as 4000 A/m. Compared with that of the Fe 79 Si 7 B 14 alloy (1.9 A/m) after flash annealing the coercivity is much higher in this alloy after conventional annealing [35]. The saturation magnetization of the Fe Si B alloy is higher than that of the Fe Si B Nb Cu alloy after heat treatment at 550 -C for 30 min (1.3 T); it may be possible to improve the soft magnetic properties if coercivity could be decreased. With Cu alloying addition coercivity is lower than that of the Fe Si B alloy for annealing times less than 480 min (Fig. 6). In the case of the Fe Si B alloy a dendritic morphology was observed while with Cu alloying addition a spheroidal morphology with rough interfaces was observed. From shape anisotropy considerations the coercivity of the dendritic morphology can be higher than that of the spheroidal morphology [36], thus the coercivity is higher in the Fe Si B alloy compared with that of the Fe Si B Cu alloy. With Nb alloying additions Ms showed little difference as the annealing time was increased. The coercivity in the case of the Fe Si B Nb alloy remained at 1000 A/m as the annealing time was increased, which may be due to a compromise between the soft magnetic phases Fe 3 Si and Fe 23 B 6 and hard magnetic Fe 3 B phase. With both Cu and Nb alloying additions the saturation magnetization was about 1.3 T while the coercivity remained at 100 A/m until 480 min, it then increased due to the formation of the Fe B compound which leads to an increase of magnetocrystalline anisotropy, as a result of which magnetic hardening takes place [37].

6 102 Y.R. Zhang, R.V. Ramanujan / Thin Solid Films 505 (2006) Conclusions The effect of individual and combined Cu and Nb alloying additions in Fe Si B alloys was studied by DSC, XRD, TEM, EELS and VSM techniques. Combining the results obtained, the following conclusions can be drawn. The primary crystallization temperatures and activation energy for the selected alloys were: 772 K and 376 kj/mol, 720 K and 236 kj/mol, 844 K and 421 kj/mol, 795 K and 301 kj/mol for the Fe 77.5 Si 13.5 B 9, Fe 76.5 Cu 1 Si 13.5 B 9, Fe 74.5 Nb 3- Si 13.5 B 9 and Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloys respectively. The phase formed after primary crystallization of the Fe 77.5 Si 13.5 B 9, Fe 76.5 Cu 1 Si 13.5 B 9 and Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloys was Fe 3 Si phase. However, Fe 3 Si, Fe 23 B 6 and Fe 3 B phases were induced in the Fe 74.5 Nb 3 Si 13.5 B 9 alloy. For the Fe 77.5 Si 13.5 B 9 alloy the morphology after primary crystallization is dendritic. B atoms were found by EELS measurements to be rejected to the inter-dendritic region following primary crystallization. With Cu alloying additions the equiaxed morphology, with crystal size in the range from 50 nm to 100 nm was observed. With Nb alloying additions the equiaxed morphology, with crystal size in the range from 30 nm to 50 nm, was observed. With both Cu and Nb alloying additions nanocrystals about 15 nm in size were observed. The highest saturation magnetization was 1.7 T after the Fe 77.5 Si 13.5 B 9 alloy was annealed at 550 -C for 1 h. The lowest coercivity was 30 A/m which was measured after Fe 73.5 Cu 1 Nb 3 Si 13.5 B 9 alloy was heat treated at 550 -C for 1 h. Acknowledgement The ribbons used in this study were kindly supplied by Dr. Y. Yoshizawa of Hitachi Metals, Japan. References [1] Y. Yoshizawa, S. Oguma, K. Yamaguchi, J. Appl. Phys. 64 (1988) [2] G. Herzer, IEEE Trans. Magn. 26 (1990) [3] K. Hono, K. Hiraga, Q. Wang, A. Inoue, T. Sakurai, Acta Metall. Mater. 40 (1992) [4] K. Hono, Acta Mater. 47 (1999) [5] K. Hono, D.H. Ping, M. Ohnuma, H. Onodera, Acta Mater. 47 (1999) 997. [6] Y. Yoshizawa, K. Yamauchi, Mater. Sci. Eng., A 114 (1991) 176. [7] K. Hono, Y. Zhang, A. Inoue, T. Sakurai, Mater. Trans., JIM 36 (1995) 909. [8] J.D. Ayers, V.G. Harris, J.A. Sprague, W.T. Elam, H.N. Jones, Nanostruct. Mater. 9 (1997) 931. [9] J.D. Ayers, V.G. Harris, J.A. Sprague, W.T. Elam, H.N. Jones, Acta Mater. 46 (1998) [10] P. Duhaj, P. Sveca, J. Sitek, D. Janickovic, Mater. Sci. Eng., A (2001) 178. [11] A.R. Yavari, D. Negri, Nanostruct. Mater. 8 (1997) 969. [12] J.S. Blazquez, V. Franco, A. Conde, J. Phys., Condens. Matter 14 (2002) [13] A. Gupta, S.N. Kane, N. Bhagat, T. Kulik, J. Magn. Magn. Mater (2003) 492. [14] T. Kulik, J. Non-Cryst. Solids 287 (2001) 145. [15] T. Kulik, Mater. Sci. Eng., A 159 (1992) 95. [16] T.H. Noh, M.B. Lee, H.J. Jim, I.K. Kang, J. Appl. Phys. 67 (1990) [17] W.T. Kim, P.W. Jang, Mater. Sci. Eng., A 179/180 (1994) 309. [18] I. Matko, P. Duhaj, P. Svec, D. Janickovic, Mater. Sci. Eng., A 179/180 (1994) 557. [19] F. Zhou, K.Y. He, M.L. Sui, Mater. Sci. Eng., A 181/182 (1994) [20] T. Ozawa, J. Therm. Anal. 2 (1970) 301. [21] A.R. Bhatti, B. Cantor, J. Mater. Sci. 29 (1994) 816. [22] K. Chrissafis, M.I. Maragakis, K.G. Efthimiadis, E.K. Polychroniadis, J. Alloys Compd. 28 (2004) 375. [23] K.G. Efthimiadis, E.K. Polychroniadis, S.C. Chadjivasiliou, I.A. Tsoukalas, Mater. Res. Bull. 35 (2000) 937. [24] K.G. Efthimiadis, G. Stergioudis, S.C. Chadjivasiliou, I.A. Tsoukalas, Cryst. Res. Technol. 37 (2002) 827. [25] P. Marin, M. Vazquez, A.O. Olofinjana, H.A. Davies, Nanostruct. Mater. 10 (1998) 293. [26] A. Inoue, B. Shen, Mater. Sci. Eng., A (2004) 302. [27] N. Mattern, A. Danzig, M. Muller, Mater. Sci. Forum (1995) 539. [28] J.D. Ayers, V.G. Harris, J.A. Sprague, W.T. Elam, Appl. Phys. Lett. 64 (1994) 974. [29] W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 35 (1964) 444. [30] W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 34 (1963) 323. [31] Y.R. Zhang, R.V. Ramanujan, J. Alloys Compd. 403 (2005) 197. [32] A. Inoue, Mater. Trans., JIM 36 (1995) 866. [33] A. Inoue, Acta Mater. 48 (2000) 279. [34] A. Inoue, Mater. Sci. Eng., A (2001) 1. [35] Z.H. Lai, H. Conrad, G.Q. Teng, Y.S. Chao, Mater. Sci. Eng., A 287 (2000) 238. [36] R.B. Schwarz, T.D. Shen, U. Harms, T. Lillo, J. Magn. Magn. Mater. 283 (2004) 223. [37] M.A. Hakim, S.M. Hoque, J. Magn. Magn. Mater. 284 (2004) 395.