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Modelling of nanocrystallization in Finemet-type alloy from enthalpy measurements
Journal of Magnetism and Magnetic Materials 160 (1996) 263-265
ELSEVIER
Journalof magnetism ~ i ~ and magnetic ~ H materials
Modelling of nanocrystallization in Finemet-type alloy from enthalpy measurements N. Lecaude, J.C. Perron * lxzboratoire de Gdnie Electrique de Paris, URA 0127, ESE, Plateau du Moulon, 91192 Gtf-sur-Ycette Cedex, France
Abstract We have studied the enthalpy changes in Fe73.sCutNb3Si13.sB9 alloy along isothermal DSC runs and performed X-ray diffraction (XRD) on annealed samples. The average grain size of nanograins presents a limit nearly independent of temperature ( = 12 nm). Modelling of the enthalpy variations was performed and good agreement with experiments is observed in the low temperature range. When the temperature is increased, steady-state nucleation seems to be invalid for long annealing times. A plausible explanation is presented involving the formation of a Nb diffusion layer around the nanograins. Keywords: Calorimetry; XRD; Modelling; Nanocrystallization
1. Introduction The good magnetic properties of Finemet-type alloy are mainly ascribed to the small average grain size resulting from nanocrystallization. In the temperature range from 750 to 850 K, several studies have shown that the crystal size in Fey3.sNb3CulSi135B9 saturates, for sufficiently long times and various temperatures, in the range from 10 to 15 nm [1-3]. We take this into account to model the enthalpy evolution along the isotherms. Previously we had analyzed our DSC results using the JMA formula [4] for the 763 K isotherm, but the fitting of the experimental curve was poor, especially for long times.
2. Experimental We have performed isothermal annealing of asquenched Fe73.5Nb3Cu i Si k3.5B9 samples in a DSC apparatus. The heating and cooling rates (respectively 200 and 320 K / m i n ) were chosen to preserve, as far as possible, the thermodynamic state of the samples before and after the isotherms. The temperature range extends from 750 to 830 K and the isotherm duration varies from 30 s to 18 ks depending on the temperature. The time response of the apparatus was checked and the baseline was subtracted from all data. At the beginning of the low temperature isotherms we observed a contribution due to the enthalpy of relaxation of the amorphous samples. So before the
* Corresponding author. Fax: + 33-1-6941-8318.
isotherms and to reduce this effect, we performed a quick preannealing (up and down) at 763 K leaving the sample in a fully amorphous state. After the isotherms, samples were analyzed by X-ray diffraction (XRD), mainly in the first peak region, using FeK~ radiation and a low scan rate to improve the signal-to-noise ratio. The spectra were corrected for strain and instrumental broadening. The separation of contributions from the amorphous and nanocrystalline phases was performed using pseudo-Voigt functions. From this deconvolution and using the Scherrer formula we obtained the average grain sizes.
3. Results and discussion Fig. l gives the time variation of the average grain radius along the 763 K isotherm. We assume primary crystallization with grains always spherical. Modelling is performed using the following law for the evolution of average grain radius:
ra,.(t) =
[
ro+(r2-ro)c+(t_to)
,
(1)
where r 0, the grain radius at the end of incubation time t o, will be assumed to be zero in the nucleation and growth process (critical radius), r m is the limit of the radius for long times, chosen here as a constant (6 nm). c is a parameter depending only on the temperature, an order of magnitude of which comes from the fit of the time dependence of the radius (Fig. 1, Table 1). Eq. (1) is similar to the equation given by Chen and Spaepen [Eq. (8) in Ref.
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0304-8853(96)00 191 -6
N. Lecaude, J.C. Perron / Journal of Magnetism and Magnetic Materials 160 (1996) 263-265
264 r
, ~
,
i
i
i
6
i5
i ° -
~3 .~2
0.005
-0.010
"~4r
• Experimentalpoints .......... Calculatedcurve
< 1 o
"''"
t
o'o
5 0
10000 ' Time (s)
[ 0
2 0
15000 '
D.S.C signal "......... Nucleationand growth (NG) I
I
4000 6000 Time (s)
I
I
8000
Fig. 1. r~, versus time. Endo l
,~0 [5]] but, here, the diffusion coefficient is time-dependent• Along the isotherm we assume, after t o, steady-state nucleation at constant rate 1~. Using the concept of extended volume and taking into account the impingement between grains (or overlap of diffusion fields), the DSC signal for the nucleation and growth process is: dx 4~[ 4zr -t ] h N G ~ -/ = h N G ~ - - ! ~ r 3 ( t ) e x p [ - - - - I s / r 3 ( z ) d r / ,
T (K)
763
798
to (s) c (s) l~(nm 3s i) hNG (J/g) r o (nm) h G (J/g) h t = h G + hNG (J/g)
300 900 9.5X10 -7 25.1 0 0 25.1
0 120 1.655<10 5 53 0.8 25.9 78.9
]f...[2.z.= z~
-0.2
(b)
-0.4
D.S.C signal .......... Nucleation and growth (NG) ...... G ~ n ~owth (G) ............ NG+G
(2)
where hNG is the total enthalpy difference between the transformed and untransformed states and r(t) is the isothermal change of the instantaneous grain radius calculated from r~v. Modelling was performed by using I~ and c as fitting parameters; typical values are given in Table 1. The results, corresponding to the 763 K isotherm, are plotted in Fig. 2a, where good agreement with experiment is shown. After about 2 h the calorimetric signal coincides with the apparatus noise so it is difficult to assert that the process is fully complete at this time. At 798 K, to fit the results corresponding to shorter times more accurately, we had to add a small contribution given by the growth of the nucleus existing at the start of the isotherm. The fitting of XRD data and modelling of the temperature dependence of parameter c (to be published) suggest an order of magnitude of about 1 nm for r o. The signal growth is obtained
Table 1 Modelling parameters
• - - ..........
I
I
200
400
I
I
600
800
Time (s)
1000
Fig. 2. DSC signal versus time.
by modifying the equation given by Chen and Spaepen [Eq. (13) in Ref. [5]]:
G
= ho
1 -
r° dt
-2" Fay
(3)
The total enthalpy is the sum of the contributions given by Eq. (2) and Eq. (3) balanced by a choice of hNG and h~. The results obtained at 798 K are plotted in Fig. 2b. The calculated curve is in good agreement with experimental data up to about 200 s. Above this time the model gives a signal that goes to zero too quickly. The explanation for this may be that, at this temperature, the nucleation rate is no longer constant along the isotherm but decreases as a result of the saturation of nucleation centers• From Eq. (1) the behaviour at short times of the average radius is given by ray = [ rZ(t - to)/C] 1/2, therefore r,21c- I is analogous to diffusion coefficient D. As discussed by Yavari and Drbohlav [6], during the formation of a-FeSi nanocrystals, boron atoms move rapidly away from the grain boundaries in the amorphous phase, whereas niobium atoms diffuse more slowly and settle as a diffusion barrier around the nanograins. The niobium enrichment of the amorphous phase stabilizes it. This barrier is the main reason for the decrease in growth rate for long times and also for the rapid saturation of nucleation sites at sufficiently high
N. Lecaude, J.C. Perron / Journal of Magnetism and Magnetic Materials 160 (1996) 263-265 temperature. At 763 K the calculated value o f rrn2 C- I is 4 × 10 20 m 2 s - J. In FeB-based amorphous alloys [6], at 773 K, the diffusivity o f boron is D B > 10 15 m 2 s l and Dre = 10 Is m 2 s - l, whereas DNb for a - F e is 5 × 10 -~° m 2 s l, close to our calculated value. W e believe that our model gives further evidence of the main role played by niobium atoms in the limitation o f grain size in this alloy. Acknowledgement: The authors would like to thank Dr. A.R. Yavari for performing the X R D measurements.
265
References [1] G. Hampel et al., J. Phys. Condensed Matter 4 (1992) 3195. [2] K.Y. He et al., J. Appl. Phys. 75 (1994) 3684. [3] M. Baricco and L. Battezzati, Mater. Sci. Forum 179-181 (1995) 597. [4] J. Bigot et al., J. Magn. Magn. Mater. 133 (1994) 299. [5] L.C. Chen and F. Spaepen, J. Appl. Phys. 69 (1991) 679. [6] A.R. Yavari and O. Drbohlav, Mater. Trans. JIM 36 (1995) 896.
ELSEVIER
Journalof magnetism ~ i ~ and magnetic ~ H materials
Modelling of nanocrystallization in Finemet-type alloy from enthalpy measurements N. Lecaude, J.C. Perron * lxzboratoire de Gdnie Electrique de Paris, URA 0127, ESE, Plateau du Moulon, 91192 Gtf-sur-Ycette Cedex, France
Abstract We have studied the enthalpy changes in Fe73.sCutNb3Si13.sB9 alloy along isothermal DSC runs and performed X-ray diffraction (XRD) on annealed samples. The average grain size of nanograins presents a limit nearly independent of temperature ( = 12 nm). Modelling of the enthalpy variations was performed and good agreement with experiments is observed in the low temperature range. When the temperature is increased, steady-state nucleation seems to be invalid for long annealing times. A plausible explanation is presented involving the formation of a Nb diffusion layer around the nanograins. Keywords: Calorimetry; XRD; Modelling; Nanocrystallization
1. Introduction The good magnetic properties of Finemet-type alloy are mainly ascribed to the small average grain size resulting from nanocrystallization. In the temperature range from 750 to 850 K, several studies have shown that the crystal size in Fey3.sNb3CulSi135B9 saturates, for sufficiently long times and various temperatures, in the range from 10 to 15 nm [1-3]. We take this into account to model the enthalpy evolution along the isotherms. Previously we had analyzed our DSC results using the JMA formula [4] for the 763 K isotherm, but the fitting of the experimental curve was poor, especially for long times.
2. Experimental We have performed isothermal annealing of asquenched Fe73.5Nb3Cu i Si k3.5B9 samples in a DSC apparatus. The heating and cooling rates (respectively 200 and 320 K / m i n ) were chosen to preserve, as far as possible, the thermodynamic state of the samples before and after the isotherms. The temperature range extends from 750 to 830 K and the isotherm duration varies from 30 s to 18 ks depending on the temperature. The time response of the apparatus was checked and the baseline was subtracted from all data. At the beginning of the low temperature isotherms we observed a contribution due to the enthalpy of relaxation of the amorphous samples. So before the
* Corresponding author. Fax: + 33-1-6941-8318.
isotherms and to reduce this effect, we performed a quick preannealing (up and down) at 763 K leaving the sample in a fully amorphous state. After the isotherms, samples were analyzed by X-ray diffraction (XRD), mainly in the first peak region, using FeK~ radiation and a low scan rate to improve the signal-to-noise ratio. The spectra were corrected for strain and instrumental broadening. The separation of contributions from the amorphous and nanocrystalline phases was performed using pseudo-Voigt functions. From this deconvolution and using the Scherrer formula we obtained the average grain sizes.
3. Results and discussion Fig. l gives the time variation of the average grain radius along the 763 K isotherm. We assume primary crystallization with grains always spherical. Modelling is performed using the following law for the evolution of average grain radius:
ra,.(t) =
[
ro+(r2-ro)c+(t_to)
,
(1)
where r 0, the grain radius at the end of incubation time t o, will be assumed to be zero in the nucleation and growth process (critical radius), r m is the limit of the radius for long times, chosen here as a constant (6 nm). c is a parameter depending only on the temperature, an order of magnitude of which comes from the fit of the time dependence of the radius (Fig. 1, Table 1). Eq. (1) is similar to the equation given by Chen and Spaepen [Eq. (8) in Ref.
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0304-8853(96)00 191 -6
N. Lecaude, J.C. Perron / Journal of Magnetism and Magnetic Materials 160 (1996) 263-265
264 r
, ~
,
i
i
i
6
i5
i ° -
~3 .~2
0.005
-0.010
"~4r
• Experimentalpoints .......... Calculatedcurve
< 1 o
"''"
t
o'o
5 0
10000 ' Time (s)
[ 0
2 0
15000 '
D.S.C signal "......... Nucleationand growth (NG) I
I
4000 6000 Time (s)
I
I
8000
Fig. 1. r~, versus time. Endo l
,~0 [5]] but, here, the diffusion coefficient is time-dependent• Along the isotherm we assume, after t o, steady-state nucleation at constant rate 1~. Using the concept of extended volume and taking into account the impingement between grains (or overlap of diffusion fields), the DSC signal for the nucleation and growth process is: dx 4~[ 4zr -t ] h N G ~ -/ = h N G ~ - - ! ~ r 3 ( t ) e x p [ - - - - I s / r 3 ( z ) d r / ,
T (K)
763
798
to (s) c (s) l~(nm 3s i) hNG (J/g) r o (nm) h G (J/g) h t = h G + hNG (J/g)
300 900 9.5X10 -7 25.1 0 0 25.1
0 120 1.655<10 5 53 0.8 25.9 78.9
]f...[2.z.= z~
-0.2
(b)
-0.4
D.S.C signal .......... Nucleation and growth (NG) ...... G ~ n ~owth (G) ............ NG+G
(2)
where hNG is the total enthalpy difference between the transformed and untransformed states and r(t) is the isothermal change of the instantaneous grain radius calculated from r~v. Modelling was performed by using I~ and c as fitting parameters; typical values are given in Table 1. The results, corresponding to the 763 K isotherm, are plotted in Fig. 2a, where good agreement with experiment is shown. After about 2 h the calorimetric signal coincides with the apparatus noise so it is difficult to assert that the process is fully complete at this time. At 798 K, to fit the results corresponding to shorter times more accurately, we had to add a small contribution given by the growth of the nucleus existing at the start of the isotherm. The fitting of XRD data and modelling of the temperature dependence of parameter c (to be published) suggest an order of magnitude of about 1 nm for r o. The signal growth is obtained
Table 1 Modelling parameters
• - - ..........
I
I
200
400
I
I
600
800
Time (s)
1000
Fig. 2. DSC signal versus time.
by modifying the equation given by Chen and Spaepen [Eq. (13) in Ref. [5]]:
G
= ho
1 -
r° dt
-2" Fay
(3)
The total enthalpy is the sum of the contributions given by Eq. (2) and Eq. (3) balanced by a choice of hNG and h~. The results obtained at 798 K are plotted in Fig. 2b. The calculated curve is in good agreement with experimental data up to about 200 s. Above this time the model gives a signal that goes to zero too quickly. The explanation for this may be that, at this temperature, the nucleation rate is no longer constant along the isotherm but decreases as a result of the saturation of nucleation centers• From Eq. (1) the behaviour at short times of the average radius is given by ray = [ rZ(t - to)/C] 1/2, therefore r,21c- I is analogous to diffusion coefficient D. As discussed by Yavari and Drbohlav [6], during the formation of a-FeSi nanocrystals, boron atoms move rapidly away from the grain boundaries in the amorphous phase, whereas niobium atoms diffuse more slowly and settle as a diffusion barrier around the nanograins. The niobium enrichment of the amorphous phase stabilizes it. This barrier is the main reason for the decrease in growth rate for long times and also for the rapid saturation of nucleation sites at sufficiently high
N. Lecaude, J.C. Perron / Journal of Magnetism and Magnetic Materials 160 (1996) 263-265 temperature. At 763 K the calculated value o f rrn2 C- I is 4 × 10 20 m 2 s - J. In FeB-based amorphous alloys [6], at 773 K, the diffusivity o f boron is D B > 10 15 m 2 s l and Dre = 10 Is m 2 s - l, whereas DNb for a - F e is 5 × 10 -~° m 2 s l, close to our calculated value. W e believe that our model gives further evidence of the main role played by niobium atoms in the limitation o f grain size in this alloy. Acknowledgement: The authors would like to thank Dr. A.R. Yavari for performing the X R D measurements.
265
References [1] G. Hampel et al., J. Phys. Condensed Matter 4 (1992) 3195. [2] K.Y. He et al., J. Appl. Phys. 75 (1994) 3684. [3] M. Baricco and L. Battezzati, Mater. Sci. Forum 179-181 (1995) 597. [4] J. Bigot et al., J. Magn. Magn. Mater. 133 (1994) 299. [5] L.C. Chen and F. Spaepen, J. Appl. Phys. 69 (1991) 679. [6] A.R. Yavari and O. Drbohlav, Mater. Trans. JIM 36 (1995) 896.