Detection of the onset of nanocrystallization by calorimetric and magnetic measurements

Detection of the onset of nanocrystallization by calorimetric and magnetic measurements J. S. Blázquez, V. Franco, C. F. Conde, A. Conde, and S. Roth Citation: Journal of Applied Physics 97, 044308 (2005); doi: 10.1063/1.1849826 View online: http://dx.doi.org/10.1063/1.1849826 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/97/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetic permeability of Si-rich (FeCoNi)-based nanocrystalline alloy: Thermal stability in a wide temperature range J. Appl. Phys. 113, 17A310 (2013); 10.1063/1.4794718 Magnetic field driving custom assembly in (FeCo) nanocrystals Appl. Phys. Lett. 89, 033508 (2006); 10.1063/1.2222254 Structural, magnetic, and magnetostriction behaviors during the nanocrystallization of the amorphous Ni 5 Fe 68.5 Si 13.5 B 9 Nb 3 Cu 1 alloy J. Appl. 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Box 1065, 41080 Sevilla, Spain and Leibniz Institute for Solid State and Materials Research Dresden (IFW-Dresden), Institute for Metallic Materials, Helmholtzstrasse 20, 01069 Dresden, Germany V. Franco, C. F. Conde, and A. Condea兲 Departamento de Física de la Materia Condensada, Instituto de Ciencia de Materiales de Sevilla–Consejo Superior de Investigaciones Cientifícas (ICMSE-CSIC), Universidad de Sevilla, P.O. Box 1065, 41080 Sevilla, Spain S. Roth Leibniz Institute for Solid State and Materials Research Dresden (IFW-Dresden), Institute for Metallic Materials, Helmholtzstrasse 20, 01069 Dresden, Germany 共Received 13 July 2004; accepted 22 November 2004; published online 24 January 2005兲 It is generally accepted that measurements of the magnetic properties are more sensitive than measurements of the enthalpy changes in the detection of the onset of crystallization of ferromagnetic phases emerging from a paramagnetic amorphous alloy. In this work, it is shown that the formation of a very fine nanocrystalline microstructure can make this assumption incorrect. Under some circumstances, the nanocrystallization onset temperature obtained from magnetic techniques is higher than the one obtained from enthalpy changes. The phenomenon is explained in terms of the superparamagnetic behavior of the uncoupled nanocrystals at the very early stages of nanocrystallization. © 2005 American Institute of Physics.关DOI: 10.1063/1.1849826兴 I. INTRODUCTION A widespread technique to obtain nanocrystalline alloys is the controlled partial crystallization of a precursor amorphous alloy with a suitable composition. The optimization of the material properties requires an accurate determination of the onset temperature of nanocrystallization, TX. This parameter, which depends on the heating rate due to the thermally activated character of the devitrification process, can be directly measured from enthalpy changes. However, indirect measurements, like changes in the electrical resistivity or in the magnetic properties due to the formation of a new phase, are claimed to be more sensitive than calorimetric measurements for the detection of the emerging crystals.1This attributed higher sensitivity is in agreement with the fact that the onset temperature extracted from magnetic techniques 共TX mag兲 is usually lower than the one obtained from differential scanning calorimetry 共TX DSC兲.1Magnetization measurements are especially useful when TXis above the Curie temperature TC of the amorphous phase. In this case, a zero signal is obtained previous to the onset of crystallization and the signal increases as the crystalline volume fraction Xincreases, allowing detailed kinetic studies of the transformation.2 In this paper we report experimental results indicating that, under some circumstances, the assumption TX mag艋TX DSC is no longer true. For this purpose, Fe-based nanocrystalline alloys have been studied. Their characteristic microstructure consists of randomly dispersed crystallites 共⬃10 nm兲of a ferromagnetic phase 共 ␣ -Fe-type兲embedded in a residual amorphous matrix, also ferromagnetic but with a lower TC.3 This microstructure facilitates the averaging of the magnetocrystalline anisotropy due to the exchange coupling of the nanocrystals via the ferromagnetic amorphous matrix. The reduced value of the overall anisotropy is responsible for the outstanding soft magnetic properties exhibited by these alloys.4The difference in the nanocrystallization onset temperatures obtained from the calorimetric and magnetic techniques will be analyzed taking into account the possibility of a superparamagnetic behavior of the emerging monodomain nanoparticles embedded in the paramagnetic amorphous matrix. II. EXPERIMENT Samples of Fe60Co18Nb6B15Cu1,Fe 60Co18Nb6B16 共Hitperm-type alloys兲, and Fe74Si16Nb3B6Cu1共Finemet-type兲 were studied. They will be denoted in the following as Cu-HT, HT, and FM, respectively. Ribbons 5–10 mm wide and 10–20 ␮ m thick were produced by melt spinning. TX DSC was measured by differential scanning calorimetry 共DSC兲in a Perkin–Elmer DSC7 calorimeter; TX mag was measured by thermomagnetic gravimetry 共TMG兲in a Perkin–Elmer TGA7 thermobalance using a small magnet 共maximum field ⬃20 mT兲. Both measurements were performed at heating rates of 10 K/min. A vibrating-sample magnotemeter 共VSM兲 was used to study quantitatively the dependence of the magnetic signal with the applied magnetic field B=0.002, 0.02, and 0.2 T, using a heating rate of 5 K/min. a兲Author to whom correspondence should be addressed; FAX: ⫹34-95/4612097; electronic mail: [email protected] JOURNAL OF APPLIED PHYSICS 97, 044308 共2005兲 0021-8979/2005/97共4兲/044308/4/$22.50 © 2005 American Institute of Physics97, 044308-1 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.182.116 On: Fri, 22 Jan 2016 15:34:58 III. RESULTS The microstructure of the Cu-HT and HT alloys is similar. Both develop a nanocrystalline ␣ -Fe,Co phase and present the same crystalline volume fraction at the end of the nanocrystallization process 共X⬃0.65兲.5However, the addition of 1 at. % of Cu in the Cu-HT alloy with respect to the HT alloy provokes a strong refinement of the microstructure through an enhancement of the heterogeneous nucleation due to the formation of Cu clusters before nanocrystallization.6 Consequently, the mean grain sizes are very different: D ⬃5 nm for Cu-HT and ⬃20 nm for HT.7In the case of the FM alloy, the Cu-clustering phenomenon is also present, and the mean grain size of the ␣ -Fe,Si phase at the end of nanocrystallization is ⬃15 nm.2Although the Cu-clustering phenomenon occurs in both the FM and Cu-HT alloys, a larger grain size is obtained in the case of FM.8A lower Nb content 共3 at. %兲with respect to that of Cu-HT 共6 at. %兲and the presence of Si in the ␣ -Fe crystals could be the origin of this larger grain growth in the FM alloys. In order to calculate the crystalline volume fraction, both calorimetric and magnetic measurements can be used. In the first case, the crystalline volume fraction Xcan be associated with the enthalpy change 共X⬀⌬H兲, while for magnetic measurements it is connected to the magnetization 共X⬀M兲.In fact, the magnetization of the nanocrystals depends on the temperature but, in the case of isothermal experiments or for small temperature ranges 共provided that the Curie temperature of the phase is distant enough兲, reasonable results can be obtained by considering a temperature-independent magnetization of the phase. Under these conditions it can be assumed that the crystalline fraction is directly proportional to the magnetization signal. Nevertheless, the relationship involving enthalpy and crystalline fraction is also not exempt from criticisms,9as it disregards the continuous compositional change of the amorphous matrix along the nanocrystallization process. The signal measured in a DSC run corresponds to the time variation of the enthalpy of the system during the transformation, dH/dt. Both techniques, TMG and DSC, allow a very good control of the heating rate. Therefore, a comparison between TX obtained at the same heating rate will give an idea of the sensitivity of the technique without being affected by the thermally activated character of the process. Figure 1 shows the normalized DSC plots 共peak area=1兲of the three as-cast alloys, together with the normalized first derivative of the TMG curves 共at a field of ⬃20 mT兲with respect to the temperature 共the noise in these curves is due to the numerical derivatives兲. The onset of crystallization is detected at a lower temperature by TMG than by DSC. However, whereas the difference in TXbetween both techniques is only of 3 K for the Cu-HT alloy, that difference clearly increases for the other two alloys, being ⬎10 K. To explain this effect, the Cu-clustering process before nanocrystallization in the alloys with Cu could be taken into account. The formation of this Cu-rich nonmagnetic phase implies that an extra amount of enthalpy change would be observed at a lower temperature. This could make the onset temperatures detected from DSC and TMG closer, as found for the Cu-HT alloy. However, it cannot explain the difference between the TXvalues observed by DSC and TMG for the FM alloy, for which an even higher density of Cu clusters than for the Cu-HT alloy is expected.10 To investigate these differences in the crystallization onset detected by DSC and TMG techniques for the studied alloys, the applied magnetic field in the TMG measurements was changed to test its influence on the observed value of TX mag. Table I shows TXvalues obtained by DSC and by TMG using two applied fields controlled by the position of the magnet at the thermobalance: the maximum achievable field 共high兲and a field which supplies a signal equal to 10% of the maximum signal 共low兲. It can be observed that whereas for the HT and FM alloys TX mag is almost independent of the field, for the Cu-HT alloy, TX mag is higher for low-field measurements than for high-field ones. In the case of low-field measurement, TX mag is even higher than that observed from the DSC measurements. A quantitative study of the field dependence of TX mag was done using a VSM. Figure 2 shows Mversus temperature plots for the Cu-HT and HT alloys obtained for different FIG. 1. Thermomagnetic gravimetry 共TMG兲共dM/dt兲and differential scanning calorimetry 共DSC兲共dH/dt兲plots at a heating rate of 10 K/min. The TMG signal is obtained as the derivative of the experimental M共T兲data for an applied field of ⬃0.02 T. TABLE I. Values of TXmeasured from DSC and TMG techniques at the same heating rate, 10 K/min. High field corresponds to the positioning of the magnet to obtain the maximum signal at room temperature 共⬃20 mT兲. Low field is obtained for a signal equal to 10% of that maximum. Alloy Composition 共at. %兲TX DSC 共±1 K兲 TX mag 共±2 K兲 共high field兲 TX mag 共±2 K兲 共low field兲 Cu-HT Fe60Co18Nb6B15Cu1727 724 731 HT Fe60Co18Nb6B16 759 741 740 FM Fe74Si16Nb3B6Cu1784 771 769 044308-2 Blázquez et al. J. Appl. Phys. 97, 044308 共2005兲 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.182.116 On: Fri, 22 Jan 2016 15:34:58 applied magnetic fields. Samples were heated at ⬃5 K/min. For the highest field 共B=0.2 T兲, even the paramagnetic matrix gives a nonzero signal. However, it is possible to distinguish a temperature at which the signal rises due to the onset of nanocrystallization. In the case of the alloy without Cu, TX mag=730±1 K and is independent of the applied field. On the other hand, for the alloy with Cu, TX mag increases as the applied field is decreased: TX mag=707, 712, and 722±1 K for B=0.2, 0.02, and 0.002 T, respectively. At first sight, this increase could be related to the sensitivity of the measuring equipment. However, this can be ruled out as the signal level for a given field value is the same for both the Cu-HT and HT samples and the TXincrease as the applied field decreases is only observed for the Cu-HT samples. IV. DISCUSSION An explanation of this effect may be found in the differences observed in the microstructure of the studied alloys. At the very beginning of nanocrystallization, very small crystals are formed, which can be considered isolated and, therefore, in a superparamagnetic state. The magnetization produced by a monodispersed superparamagnetic system is described by M=N ␯ mL共mB/kBT兲,共1兲 where N ␯ is the numerical density of particles, mthe magnetic moment of the individual particles, Bthe magnetic field, Tthe temperature, kBthe Boltzmann constant, and L the Langevin function. Several assumptions may be made to have a view of the existing microstructure at the very early stages of nanocrystallization. A first approximation would be to consider instantaneous nucleation regime, i.e., the number of nanocrystals remains constant during the nanocrystallization. After this, it is easy to obtain the value of N ␯ for each alloy: 0.01 and 0.00016 nm−3 for the Cu-HT and HT alloys, respectively, which yields X⬃65% for a value of Dof 5 and 20 nm, respectively. The value of mcan be obtained as the number of atoms in the nanocrystal times its atomic magnetic moment, which can be estimated as 2.2 ␮ B. The bcc unit cell contains two atoms in a volume equal to a3, where a =0.28625 nm is the lattice parameter,10 therefore, m共D兲= 2.2 ␮ B2 a3 ␲ D3 6.共2兲 At this point, magnetization can be obtained as a function of the grain size using Eq. 共1兲, where N ␯ would characterize the microstructure of each particular case. The next step will be to relate the grain size Dto the temperature. This can be done using the known kinetic parameters of these alloys11,12 and the Avrami equation. Although this equation is valid for isothermal regimes, we are only interested in a very small temperature range, just after the onset of crystallization. Therefore, kinetic parameters will be used in the following without considering their thermal dependence. The Avrami equation establishes a relationship between the fraction of the process, X*, and the time, t, X*=1−exp关−共Kt兲n兴,共3兲 where Kis the frequency factor and nis the Avrami exponent. The Avrami exponent is approximately 1 and is independent of the temperature at the early stages of nanocrystallization.12 Kfollows an Arrhenius-type dependence with the temperature, K=K0exp共−Q/kBT兲,共4兲 where K0is a constant and Qis an activation energy. From the kinetic results, K0⬃1013 s−1 and Q⬃2.4 eV.12 In the aim of simplifying the calculations and taking into account that we are interested in a very small temperature range, the thermal dependence of Khas been neglected and a value of ⬃0.0004 s−1 共at T=725 K兲has been used. X*=X/0.65 for both the studied alloys, thus X*=1 at the end of the nanocrystallization. From t=共T−TX兲/ ␤ , and taking into account 共2兲and 共3兲, T=TX− ␤ Kln 冉 1− 1 0.65N ␯ ␲ 6D3 冊 ,共5兲 where TXis 710 K for the Cu-HT alloy and 730 K for the HT alloy, and ␤ =5 K/min, the same value as used in the VSM experiments. Considering a sensitivity of the VSM device of 0.1 memu, the detection limit of the magnetization will be about 0.1 mT in the case of the studied samples 共sample mass ⬃8 mg, density ⬃7.8 g/cm3兲. Figure 3 shows the effect of the applied field on the detected crystallization onset as is expected under the assumptions indicated above; experimental values from Fig. 2 are also included. It can be seen that the observed behavior is qualitatively reproduced. An important effect of the applied magnetic field is found for FIG. 2. Magnetization M共T兲curves for Fe60Co18Nb6B16−yCuy共y=0,1兲alloys at a heating rate of ⬃5 K/min registered in the vibrating-sample magnetometer 共VSM兲at the early stages of nanocrystallization using different applied fields. 044308-3 Blázquez et al. J. Appl. Phys. 97, 044308 共2005兲 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.182.116 On: Fri, 22 Jan 2016 15:34:58 the Cu-HT sample 共with a much lower grain size than HT兲: the detection limit for 0.2 T is overcome at a temperature 18 K lower than for 0.002 T. However, for the HT sample this difference is smaller than 2 K. In terms of crystalline volume fraction, for the HT sample the detection limit would be overcome for X⬍2% even for the lowest applied field 共0.002 T兲. However, in the case of the Cu-HT alloy at B =0.002 T, the detection limit would be overcome only for X⬎15%, which could explain why the apparent onset of crystallization is detected in this case even later than using DSC 共Table I兲. Although strong assumptions were made to model the M signal, the trends observed experimentally are described with a fairly good qualitative agreement. It must be taken into account that the approximations used above lose their validity as the difference in temperature between the detected onsets becomes larger: the isothermal kinetic parameters will be modified and, at a high crystalline volume fraction, superparamagnetic particles will interact.13 These effects could explain the overestimated modeled value of the crystallization onset for the Cu-HT alloy at 0.002 T with respect to the experimental value. As the range of temperatures is extended, the temperature dependence of Kshould be taken into account. On the other hand, as the crystalline volume fraction increases, the interaction among the particles will modify the magnetic response of the system from the simple Langevin function used in this work. Nevertheless, the observed trend is successfully described. V. CONCLUSIONS In conclusion, for a comparison of calorimetric and magnetic techniques as tools for detecting the crystallization onset, it has to be taken into account that the sensitivity of the latter can be dependent, in some cases, on the applied magnetic field. The generally accepted idea that magnetic techniques have a higher sensitivity than the calorimetric ones is not necessarily true in presence of a very fine microstructure, which can produce a superparamagnetic behavior. ACKNOWLEDGMENTS This work was supported by the CICYT of the Spanish Government and EU FEDER 共Project MAT 2001-3175兲, and the PAI of the Regional Government of Andalucía. One of the authors 共J.S.B.兲acknowledges a research contract of that regional government. 1W. Hofstetter, H. Sassik, R. Grössinger, R. Trausmuth, G. Vertesy, and L. F. Kiss, Mater. Sci. Eng., A 226–228,213共1997兲. 2C. F. Conde and A. Conde, Mater. Lett. 21, 409 共1994兲. 3M. E. McHenry, M. A. Willard, and D. E. Laughlin, Prog. Mater. Sci. 44, 291 共1999兲. 4A. Hernando, M. Vázquez, T. Kulik, and C. Prados, Phys. Rev. B 51, 3581 共1995兲. 5J. S. Blázquez, V. Franco, C. F. Conde, and A. Conde, J. Magn. Magn. Mater. 254–255, 460 共2003兲. 6Y. Zhang, J. S. Blázquez, A. Conde, P. J. Warren, and A. Cerezo, Mater. Sci. Eng., A 353, 158 共2003兲. 7J. S. Blázquez, V. Franco, and A. Conde, J. Phys.: Condens. Matter 14, 11717 共2002兲. 8J. S. Blázquez, J. M. Borrego, C. F. Conde, A. Conde, and J. M. Greneche, J. Phys.: Condens. Matter 15, 3957 共2003兲. 9J. M. Barandiarán, I. Tellería, J. S. Garitaonandia, and H. A. Davies, J. Non-Cryst. Solids 329,57共2003兲. 10M. Ohnuma, D. H. Ping, T. Abe, H. Onodera, K. Hono, and Y. Yoshizawa, J. Appl. Phys. 93, 9186 共2003兲. 11J. S. Blázquez, C. F. Conde, and A. Conde, J. Non-Cryst. Solids 287,187 共2001兲. 12J. S. Blázquez, C. F. Conde, and A. Conde, Appl. Phys. A: Mater. Sci. Process. 76, 571 共2003兲. 13V. Franco, L. F. Kiss, T. Kemény, I. Vincze, C. F. Conde, and A. Conde, Phys. Rev. B 66, 224418 共2002兲. FIG. 3. Experimental TX mag obtained by vibrating-sample magnotemeter 共VSM兲measurements 共solid symbols兲and results of the modellization 共hollow symbols兲of Fe60Co18Nb6B16−yCuy共y=0,1兲alloys as noninteracting monodispersed superparamagnetic particles 共numerical densities N ␯ =0.01 and 0.00016 nm−3 and crystallization onset temperature TX=710 and 730 K for the alloys with and without Cu, respectively兲. The experimental symbols are joined by lines as a guide to the eye. 044308-4 Blázquez et al. J. Appl. Phys. 97, 044308 共2005兲 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.182.116 On: Fri, 22 Jan 2016 15:34:58