J. Mater. Sci. Technol. ›› 2019, Vol. 35 ›› Issue (1): 118-126.DOI: 10.1016/j.jmst.2018.09.010
• Orginal Article • Previous Articles Next Articles
L.Y. Guoa, X. Wanga, K.C. Shena, K.B. Kimb, S. Lanc, X. WangL.d, W.M. Wanga*()
Received:
2018-01-03
Revised:
2018-03-05
Accepted:
2018-04-10
Online:
2019-01-04
Published:
2019-01-15
Contact:
Wang W.M.
L.Y. Guo, X. Wang, K.C. Shen, K.B. Kim, S. Lan, X. WangL., W.M. Wang. Structure modification and recovery of amorphous Fe73.5Si13.5B9Nb3Cu1 magnetic ribbons after autoclave treatment: SAXS and thermodynamic analysis[J]. J. Mater. Sci. Technol., 2019, 35(1): 118-126.
Fig. 2. (a) SAXS data and fitting results for Fe73.5Si13.5B9Nb3Cu1 amorphous ribbons under different autoclave treatments, (b) the pair distance distribution function p(r) curve deduced from the SAXS by indirect Fourier transformation.
Fig. 3. DSC curves for Fe73.5Si13.5B9Nb3Cu1 amorphous ribbons under different autoclave treatments at a heating rates of (a) 20?°C/min and (b) 40?°C/min; inset in (a) gives the Curie temperature of samples.
Sample | β (oC/min) | Tx1 (oC) | Tx2 (oC) | Tp1 (oC) | Tp2 (oC) | Tc (oC) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(oC) | ||||||||||||||
R0 | 10 | 518 | 663 | 536.3 | 682.5 | 322.6 | 320.9 | |||||||
20 | 526 | 669 | 546.1 | 692.6 | 320.6 | |||||||||
30 | 531 | 676 | 551.6 | 699.4 | 321.3 | |||||||||
40 | 534 | 678 | 554.2 | 702.0 | 319.4 | |||||||||
R1 | 10 | 518 | 662 | 537.0 | 682.8 | 323.6 | 321.9 | |||||||
20 | 526 | 668 | 546.7 | 693.2 | 321.3 | |||||||||
30 | 531 | 675 | 551.6 | 698.8 | 321.8 | |||||||||
40 | 535 | 678 | 553.9 | 701.3 | 320.9 | |||||||||
R2 | 10 | 517 | 660 | 536.0 | 682.1 | 322.3 | 321.3 | |||||||
20 | 526 | 669 | 544.8 | 692.6 | 321.6 | |||||||||
30 | 533 | 677 | 551.3 | 699.7 | 321.1 | |||||||||
40 | 536 | 679 | 554.2 | 701.7 | 320.2 |
Table 1 Characteristic temperatures of exothermic peak in the DSC patterns for Fe73.5Si13.5B9Nb3Cu1 amorphous ribbons under different autoclave treatments.
Sample | β (oC/min) | Tx1 (oC) | Tx2 (oC) | Tp1 (oC) | Tp2 (oC) | Tc (oC) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(oC) | ||||||||||||||
R0 | 10 | 518 | 663 | 536.3 | 682.5 | 322.6 | 320.9 | |||||||
20 | 526 | 669 | 546.1 | 692.6 | 320.6 | |||||||||
30 | 531 | 676 | 551.6 | 699.4 | 321.3 | |||||||||
40 | 534 | 678 | 554.2 | 702.0 | 319.4 | |||||||||
R1 | 10 | 518 | 662 | 537.0 | 682.8 | 323.6 | 321.9 | |||||||
20 | 526 | 668 | 546.7 | 693.2 | 321.3 | |||||||||
30 | 531 | 675 | 551.6 | 698.8 | 321.8 | |||||||||
40 | 535 | 678 | 553.9 | 701.3 | 320.9 | |||||||||
R2 | 10 | 517 | 660 | 536.0 | 682.1 | 322.3 | 321.3 | |||||||
20 | 526 | 669 | 544.8 | 692.6 | 321.6 | |||||||||
30 | 533 | 677 | 551.3 | 699.7 | 321.1 | |||||||||
40 | 536 | 679 | 554.2 | 701.7 | 320.2 |
Fig. 4. Kissinger plot for calculation of activation energies for Fe73.5Si13.5B9Nb3Cu1 amorphous ribbons. The activation energie corresponds to the first exothermic peak: (a) the onset temperature and (b) the peak temperature; the second exothermic peak: (c) the onset temperature and (d) the peak temperature.
Fig. 5. DSC data and crystallized volume fraction (α) curves related to the first exothermic peak for as-quenched Fe73.5Si13.5B9Nb3Cu1 amorphous ribbons at different heating rates.
Fig. 6. Dependence of local activation energy E(α) on the crystalline fraction α for the primary crystallization process of Fe73.5Si13.5B9Nb3Cu1 amorphous ribbons under different autoclave treatments.
Fig. 7. Normalized z(α) function curves obtained by transformation of non-isothermal data at different heating rate for the primary crystallization process of as-quenched Fe73.5Si13.5B9Nb3Cu1 amorphous ribbons.
Fig. 8. (a) Suri?ach representations of non-isothermal DSC curves for the primary crystallization process of Fe73.5Si13.5B9Nb3Cu1 amorphous ribbons under different autoclave treatments at the heating rate of 20?°C/min. Scatter plots is the experimental results. Continuous lines are the plots for the theoretical NGG kinetics with different m value. (b) Local Avrami exponent n(α) vs crystallized volume fraction for the first stage which fits JMA model.
Sample | Stages | α | lnA0 | m |
---|---|---|---|---|
R0 | Stage I-NGG | 0.41-0.87 | 60.0 | 1.1(mI) |
Stage II-NGG | 0.87-0.97 | 58.8 | 0.5(mII) | |
R1 | Stage I-NGG | 0.40-0.86 | 63.5 | 1.4(mI) |
Stage II-NGG | 0.86-0.97 | 61.5 | 0.4(mII) | |
R2 | Stage I-NGG | 0.41-0.87 | 59.1 | 1.1(mI) |
Stage II-NGG | 0.87-0.97 | 57.8 | 0.5(mII) |
Table 2 Parameters of NGG stages for the primary crystallization reaction of different samples at the heating rate of 20?°C/min.
Sample | Stages | α | lnA0 | m |
---|---|---|---|---|
R0 | Stage I-NGG | 0.41-0.87 | 60.0 | 1.1(mI) |
Stage II-NGG | 0.87-0.97 | 58.8 | 0.5(mII) | |
R1 | Stage I-NGG | 0.40-0.86 | 63.5 | 1.4(mI) |
Stage II-NGG | 0.86-0.97 | 61.5 | 0.4(mII) | |
R2 | Stage I-NGG | 0.41-0.87 | 59.1 | 1.1(mI) |
Stage II-NGG | 0.87-0.97 | 57.8 | 0.5(mII) |
Case No. | α | E(α) | n | ω | a | b | Roots of Eq. (13) (kJ/mol) | Roots of Eq. (14) (kJ/mol) | Standard Deviation (kJ/mol) |
---|---|---|---|---|---|---|---|---|---|
1 | 0.15 | 420.51 | 2.00 | 0.5 | 1.50 | 1 | En?=?442.23 Eg?=?355.12 | En?=?442.13 Eg?=?355.44 | σn?=?0.11 σg?=?0.32 |
0.25 | 414.74 | 1.58 | 0.5 | 1.08 | 1 | ||||
0.35 | 408.31 | 1.28 | 0.5 | 0.78 | 1 | ||||
2 | 0.15 | 420.51 | 2.00 | 0.5 | 1.50 | 1 | En?=?442.23 Eg?=?355.12 | En?=?426.24 Eg?=?403.26 | σn?=?15.99 σg?=?48.14 |
0.25 | 414.74 | 1.58 | 0.5 | 1.08 | 1 | ||||
0.35 | 408.31 | 1.28 | 0.5 | 0.28 | 2 | ||||
3 | 0.15 | 420.51 | 2.00 | 0.5 | 1.50 | 1 | En?=?424.27 Eg?=?409.17 | En?=?426.24 Eg?=?403.26 | σn?=?1.97 σg?=?5.91 |
0.25 | 414.74 | 1.58 | 0.5 | 0.58 | 2 | ||||
0.35 | 408.31 | 1.28 | 0.5 | 0.28 | 2 | ||||
4 | 0.15 | 420.51 | 2.00 | 0.5 | 1.00 | 2 | En?=?442.23 Eg?=?398.68 | En?=?442.13 Eg?=?398.78 | σn?=?0.10 σg?=?0.10 |
0.25 | 414.74 | 1.58 | 0.5 | 0.58 | 2 | ||||
0.35 | 408.31 | 1.28 | 0.5 | 0.28 | 2 |
Table 3 Values of a, b and ω when α?=?0.15, 0.25 and 0.35, and the roots of Eqs. (13) and (14) for as-quenched sample when heating rate is 20?°C/min. The bold case 4 has the lowest standard deviation.
Case No. | α | E(α) | n | ω | a | b | Roots of Eq. (13) (kJ/mol) | Roots of Eq. (14) (kJ/mol) | Standard Deviation (kJ/mol) |
---|---|---|---|---|---|---|---|---|---|
1 | 0.15 | 420.51 | 2.00 | 0.5 | 1.50 | 1 | En?=?442.23 Eg?=?355.12 | En?=?442.13 Eg?=?355.44 | σn?=?0.11 σg?=?0.32 |
0.25 | 414.74 | 1.58 | 0.5 | 1.08 | 1 | ||||
0.35 | 408.31 | 1.28 | 0.5 | 0.78 | 1 | ||||
2 | 0.15 | 420.51 | 2.00 | 0.5 | 1.50 | 1 | En?=?442.23 Eg?=?355.12 | En?=?426.24 Eg?=?403.26 | σn?=?15.99 σg?=?48.14 |
0.25 | 414.74 | 1.58 | 0.5 | 1.08 | 1 | ||||
0.35 | 408.31 | 1.28 | 0.5 | 0.28 | 2 | ||||
3 | 0.15 | 420.51 | 2.00 | 0.5 | 1.50 | 1 | En?=?424.27 Eg?=?409.17 | En?=?426.24 Eg?=?403.26 | σn?=?1.97 σg?=?5.91 |
0.25 | 414.74 | 1.58 | 0.5 | 0.58 | 2 | ||||
0.35 | 408.31 | 1.28 | 0.5 | 0.28 | 2 | ||||
4 | 0.15 | 420.51 | 2.00 | 0.5 | 1.00 | 2 | En?=?442.23 Eg?=?398.68 | En?=?442.13 Eg?=?398.78 | σn?=?0.10 σg?=?0.10 |
0.25 | 414.74 | 1.58 | 0.5 | 0.58 | 2 | ||||
0.35 | 408.31 | 1.28 | 0.5 | 0.28 | 2 |
Sample | ω | α?=?0.15 | α?=?0.25 | α?=?0.35 | En (kJ/mol) | Eg (kJ/mol) | |||
---|---|---|---|---|---|---|---|---|---|
a | b | a | b | a | b | ||||
R0 | 0.5 | 1.00 | 2 | 0.58 | 2 | 0.28 | 2 | 442.2 | 398.7 |
R1 | 0.5 | 1.49 | 1 | 0.55 | 2 | 0.24 | 2 | 410.4 | 403.7 |
R2 | 0.5 | 1.17 | 2 | 0.74 | 2 | 0.43 | 2 | 424.5 | 375.6 |
Table 4 Nucleation and growth activation energies of Fe73.5Si13.5B9Nb3Cu1 amorphous ribbons under different autoclave treatments.
Sample | ω | α?=?0.15 | α?=?0.25 | α?=?0.35 | En (kJ/mol) | Eg (kJ/mol) | |||
---|---|---|---|---|---|---|---|---|---|
a | b | a | b | a | b | ||||
R0 | 0.5 | 1.00 | 2 | 0.58 | 2 | 0.28 | 2 | 442.2 | 398.7 |
R1 | 0.5 | 1.49 | 1 | 0.55 | 2 | 0.24 | 2 | 410.4 | 403.7 |
R2 | 0.5 | 1.17 | 2 | 0.74 | 2 | 0.43 | 2 | 424.5 | 375.6 |
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