- Email: [email protected]
Effect of Copper and Niobium Addition on Crystallization Kinetics in Fe-Cu-Nb-Si-B Alloys
Rare Metal Materials and Engineering Volume 42, Issue 7, July 2013 Online English edition of the Chinese language journal Cite this article as: Rare Metal Materials and Engineering, 2013, 42(7): 1352-1355.
ARTICLE
Effect of Copper and Niobium Addition on Crystallization Kinetics in Fe-Cu-Nb-Si-B Alloys Li Guangmin,
Li Deren,
Ni Xiaojun,
Li Zhun,
Lu Zhichao
Advanced Technology & Materials Co., Ltd., China Iron & Steel Research Institute Group, Beijing 100081, China
Abstract: The activation energies of amorphous Fe78Si11B9 and nanocrystalline Fe73.5Cu1B7Si15.5Nb3 alloys were tested by a high-sensitivity differential scanning calorimeter with different heating rates. Kissinger equation was adopted to calculate the activation energies of the primary phase of Fe73.5Cu1B7Si15.5Nb3 alloy (295±5) kJ and the crystal phase of Fe78Si11B9 alloy (370±3) kJ. The low activation energy of the primary phase for Fe73.5Cu1B7Si15.5Nb3 alloy is related to the precipitation of Cu clusters. The precipitation kinetics of Cu clusters was analyzed. The calculated result of the mean radius R m of Cu cluster is 3 nm after aging for 3600 s at 773 K in Fe73.5Cu1B7Si15.5Nb3 glass alloy and the maximum value of number density is 3.7 ×1024 /m3 after aging for 2.5 h at 773 K, which accords with K. Hono’s observation (approximately 3 nm after annealing at 673 K or 3600 s). The density of Cu is in the order of 1024 m-3). Key words: nanocrystalline alloys; Fe-Cu-Nb-Si-B alloy; crystallization kinetics; Cu cluster
Nanocrystalline soft magnetic alloys have a great potential for electromagnetic applications due to their excellent soft magnetic properties. The Fe73.5Cu1B7Si15.5Nb3 alloy is one of amorphous Fe-Si-B family alloys and first examined by Yoshizawa et al. in 1988 [1]. The addition of Cu and Nb in some Fe-Si-B based alloys promotes a two-phase structure material coming into being which consists of small nanocrystals embedding in a residual amorphous matrix. Copper is a necessary element for initializing crystallization at lower temperature, and niobium stabilizes the nanostructure during crystallization process and limits the growth of the grains [2]. Cu cluster in the early crystallization stage of Fe73.5Cu1B7Si15.5Nb3 amorphous alloy was studied by K.hono et al.[3,4], and Cu cluster stimulates nucleation of the nanocrystalline soft magnetic alloys[5-9]. Copper particles were observed spatially separated from the α–Fe particle in the one-dimensional atom probe concentration depth profile, and the density of Cu enriched particles is in the order of 1024/m3. There are two models to explain how the Cu clusters stimulate nucleation in nanocrystalline alloys. One model is that the interfaces of Cu precipitates adjoin directly the primary phase. The other model is that Cu
clusters are entirely enveloped by primary phase[10]. Currently, no theory research on precipitation kinetics of Cu clusters was reported. This paper is in an attempt to introduce cluster models to make clear Cu clusters precipitation in amorphous matrix, and to study the effect on primary phase in crystallization process by addition of Cu and Nb elements.
1
Experiment
Amorphous Fe78Si9B13 and Fe73.5Cu1B7Si15.5Nb3 soft magnetic alloys ribbons were prepared by single-roller melt spinning. The thickness measured by thickness gauge and width of the ribbon were 24 µm and 30 mm, respectively, shown in Fig.1. High-sensitivity differential scanning calorimeter (DSC, NETZSCH404) measurements were taken for Fe78Si9B13 and Fe73.5Cu1B7Si15.5Nb3 soft magnetic alloys at different heating rates of 10, 15, 20, 25, 30, 40 K/min to observe the crystallization temperature.
2 2.1
Results and Discussions Activation energy of the alloys
Fig.2 shows the crystallization temperatures of Fe73.5Cu1B7Si15.5Nb3 alloy measured by DSC with different
Received date: July 29, 2012 Foundation item: National High Technology Research and Development Program of China “863 Program”(2009AA03Z214) Corresponding author: Li Guangmin, Ph. D., Advanced Technology & Materials Co., Ltd., China Iron & Steel Research Institute Group, Beijing 100081, P. R. China, Tel:0086-10-58742808, E-mail: [email protected] Copyright © 2013 Northwest Institute for Nonferrous Metal Research. Published by Elsevier BV. All rights reserved.
1352
Li Guangmin et al. / Rare Metal Materials and Engineering, 2013, 42(7): 1352-1355 Thickness b Tester
a
Amorphous Ribbon
Table 1
Fe73.5Cu1B7Si15.5Nb3 alloys
Fe73.5Cu1B7Si15.5Nb3 Thr/K·min-1 Tp1/K 10 797.2 15 803.8 20 808.8 25 813.4 30 813.5 40 821.4
ln(
Heat Flow/mW·mg-1
24 µm measured by thickness gauge (b)
3 2 1
o Peak: 714.3 oC Peak: 540.440 CK/min o Exo Peak:548.4 C Peak:709.3 oC
Peak:540.5 oC 30 K/min
Peak: 704.0 oC Peak: 535.8 oC
20 K/min Peak: 707.4 oC
Peak: 698.9 oC Peak: 530.8 oC
25 K/min 15 K/min 10 K/min Peak: 524.2 oC Peak: 692.1 oC
0 100
300
500
700
o
Temperature/ C Fig.2
Crystallization temperatures of Fe73.5Cu1B7Si15.5Nb3 alloy with different heating rates measured by DSC
heating rates. The crystallization peaks and onsets temperature are postponed with increasing of the heating rate. There are two distinct crystallization peaks which are different from Fe78Si9B13 alloys. Table 1 shows the crystallization temperatures of Fe78Si9B13 and Fe73.5Cu1B7Si15.5Nb3. The addition of Cu and Nb in Fe-Si-B alloy produces two crystallization phases. Tp1 and Tp2 are the peak temperatures of the first crystallization and the second crystallization of Fe73.5Cu1B7Si15.5Nb3 alloy, respectively. Tx is the unique temperature of the crystallization peak of Fe78Si9B13 alloy. It is clear to see that Tx is slightly higher than Tp1, but lower than Tp2. The addition of Cu in Fe-Si-B alloy produces a large number of Cu clusters which provide nucleation sites for approaching primary phase. These nucleation sites can decrease crystallization activation energy. In the crystallization process, Nb atoms are pushed into the residual amorphous phase and increase its temperature[11]. But, with increasing of the heating rate, Nb and B elements have no sufficient time for diffusion, and lead to secondary crystallization peak shifting towards the high temperature district. The apparent activation energy E a for the crystallization process is usually determined with the Kissinger equation [12-14]
Fe78Si11B9 Tx/K 792.4 825 / 835 / 846.3
(1)
where Thr is the heating rate, R is the gas constant, T is characteristic temperature and C is a constant. In Fig.3, the activation energies calculated by Kissinger plots in Fe73.5Cu1B7Si15.5Nb3 and Fe78Si11B9 alloys are (295 ±5) kJ and (370±3) kJ, respectively. Copper and niobium elements in Fe-Si-B alloys decrease crystallization temperature and activation energy. Two models of Cu clusters provide nucleation sites for the primary phase as shown in Fig.4. The first model is the interfaces of Cu precipitates adjoining directly the primary phase. The primary phase nucleation only depends on a the interface little and extends the amorphous matrix. Another model is that Cu clusters are entirely enveloped by primary phase. The primary phase firstly annexes the whole Cu cluster and then extends toward the three-dimensional direction. The driving force of primary phase nucleation is decreased because of their lower interface energy connection which creates favorable conditions α-Fe phase crystallization. 2.2 Mean radius of Cu cluster The growth velocity of Cu cluster in radius R is given by [15]
dR KDα (C∞ − CR ) = dt α D + K
(2)
Where, K is the transfer velocity through the interface of thickness b; D is the diffusion coefficient, b=D/K, and α=(R+b)/R2; CR is the solute concentration in equilibrium with a precipitate of radius R. The value of thickness b is 13.6 12.8
Fe73.5Cu1B7Si15.5Nb3 first peak Tp1 Fe78Si9B11
12.0
2
Width of the ribbon is 30 mm (a) and the thickness is
Tp2/K 965.1 971.9 977 980.4 982.3 987.3
E Thr ) = − a +C 2 T RT
ln(T /Thr)
Fig.1
Crystallization temperatures of Fe78Si9B13 and
11.2 10.4 9.6
0.142 0.144 0.146 0.148 0.150 0.152 -1
-3
-1
(TR) ×10 /K Fig.3
Kissinger plots of the heating rate in DSC crystallization temperature in Fe73.5Cu1B7Si15.5Nb3 and Fe78Si11B9 alloys
1353
Li Guangmin et al. / Rare Metal Materials and Engineering, 2013, 42(7): 1352-1355
a
6 5
Rm/nm
4
2 1 0
Fig.5
Fig.4
Primary phase
0
7200 t/s
10800
14400
Mean radius of Cu cluster versus time at T=773 K for nanocrystalline
alloy
with
KCu=1.5×10-8cm/s-1, DCu=9.4×10-16 m2/s
Np =
3 4 π (3σ
fp 2
(3)
+ R m2 ) R m
fp is the volume fraction of precipitates, σ is the interface energy, and Rm is the mean radius. Symmetrical radius distribution h(R) is given by Lifshitz-Slyosov-Wagner coarsenning theory h(R ) =
⎡ ( R − Rm )2 ⎤ 1 exp ⎢ − ⎥ 2σ 2 2 πσ ⎣ ⎦
(4)
The half-width of the size distribution at half maximum ΔR is given by σ =ΔR/1.177. The values of parameters ΔR and fp are given by Ref.[16]. After aging at 773 K for 2.5 h, fp is about 0.7 %. After aging at 773 K for 4.5 h, fp is about 1.1 %. Number density as a function of Rm of Cu precipitates in Fe73.5Cu1B7Si15.5Nb3 nanocrystalline alloy after aging for different time, is shown in Fig.6. There are sharp peaks of the number density functions at different aging time for Cu precipitate diameter. The precipitate diameter is less than 0.5 nm while the maximum value of number density is 3.7 ×1024 /m3 after aging for 2.5 h 4
b
Cu
Two models of Cu clusters providing nucleation sites for the primary phase: (a) the interfaces of Cu precipitates adjoining
3600
Fe73.5Si13.5B9Nb3Cu1
Primary phase Cu
3
24 24 m-3-3 Number Density/ ×10 Number Density 10 m
about 0.15 nm, because of Cu atom must transfer some distance in amorphous structure to reach clusters. The distance must be more than a half regular bcc. Fe lattice ao=0.2866 nm. During thermal annealing, these vacancies are mobile and thus give rise to a contribution of self-diffusion by exchanging their sites with adjacent atoms [16]. Molecular dynamics simulation reveals the unstableness of vacancies or plenty of interstices. Activation energy Q and pre-exponential factors D0 of Cu in amorphous alloys are 1.8 -8 eV and 5×10 m2/s respectively, at 653 K [17]. According to Arrhenius equation DCu(T)=D0exp(–Ea/kT) (k is Boltzmann constant), the value of copper diffusion coefficient is -20 DCu=9.4×10 m2/s, which is less than the value of copper -19 diffusion coefficient DCry-Cu=4 × 10 m2/s in Fe-Cu(1.35at%) crystalline alloys at 773 K. The order of the values are closely related with other elements diffusion in amorphous matrix such as Fe (DFe, 10-21~10-22 m2/s in amorphous alloys Fe80B2) and B (DB, 10-19 m2/s in Fe40N40B20 alloy at 625 K). Fig.5 shows that the calculated mean radius Rm of Cu cluster grown up nonlinearly with heat treatment time. The mean radius Rm is about 3 nm for Fe73.5Si13.5B9Nb3Cu1 nanocrystalline alloy aged for 3600 s at 773 K. The mean radius of Cu cluster which is so small and will be covered by approaching primary phase can not be found easily by the microscopy. But, these nano-particles write firstly prologue of nanocrystalline precipitation on amorphous matrix and play an important role on stimulating primary phase precipitates. The Cu cluster is coarsened sharply in early aging stage, and grows up tardily in later aging time. The reason is that the solute concentration of Cu concentration in matrix decreases with precipitating of volumes of Cu cluster. The result of calculation accords with K. Hono’s observation (approximately 3 nm after annealing at 673 K for 3600 s and approximately 5 nm after annealing at 823 K for 3600 s in Fe73.5Si13.5B9Nb3Cu1 alloys)[18]. 2.3 Number density of Cu cluster The number density of Cu cluster Np is given by [19]
Fig.6
3 aging 2 .5 h aging 4 .5 h
2 1 0
0
1
2
3 Rm/nm
4
5
Number density as functions of Rm of Cu precipitates in alloy
directly the primary phase; (b) Cu clusters entirely enveloped
with the cluster model for Fe73.5Si15.5B9Nb3Cu1 nanocrystalline
by primary phase
alloy
1354
Li Guangmin et al. / Rare Metal Materials and Engineering, 2013, 42(7): 1352-1355
at 773 K, and the precipitate diameter is more than 0.5 nm while the maximum value of number density is 2.5×1024 /m3 after aging for 4.5 h at 773 K. The Cu element precipitates a large number of nano-clusters in amorphous matrix after aging for 2.5 h, but it has no sufficient time to coarsen. But the Cu clusters start to coarsen in the form of mergence which causes the number density of Cu nano-clusters dwindling. It is the reason that the average diameter of precipitates of Cu cluster after aging for 4.5 h is bigger than that after aging for 2.5 h, and the number density of Cu clusters decreases. The calculation results also provide well guidance for our industrial test, which means a reasonable heating treatment time can precipitate the maximum density nano-clusters to stimulate more homogeneous nano primary phase precipitation. The calculated results of the number density of Cu precipitate diameter are in agreement with experimental analysis in Ref.[3].
3
Conclusions
1) In crystallization process, elements Nb and B have no sufficient time for diffusion with increasing of the heating rate, and such a case leads secondary crystallization peak to shift towards the high temperature district. 2) The addition of Cu and Nb into Fe-Si-B alloys decreases the first crystallization activation energy. It is closely related to Cu cluster serving as heterogeneous nucleation sites for the α-Fe primary phase.
References 1
Yoshizawa Y, Oguma Y, Yamauchi S. Journal of Applied Physics[J], 1988, 64: 6044
2
3
Hono K, Ping H D, Ohnuma et al. Acta Materialia[J], 1999, 47: 997
4
Hono K, Hiraga K, Wang Q. Acta Metallurgica and Materialia[J],
5
Ohnuma M, Hono K, Linderoth S et al. Acta Materialia[J], 2000,
1993, 40: 2137 48: 4783
6
Chen Y M, Ohkubo T, Ohta M et al. Acta Materialia[J], 2009, 57: 4463
7
Makino A, Men H, Kubota T et al. Journal of Applied Physics[J], 2009, 105: 07A308
8
Ohta M, Yoshizawa Y. Journal Applied Physics[J], 2008, 103:
9
Ohta M, Yoshizawa Y. Journal Magnetism and Magnetic
07E722 Materials[J], 2008, 320: e750
10
Ayers D J, Harris G V, Sprague A J et al. Acta Materiallia[J],
11
Yoshizawa Y, Yamauchi K. Materials Science and Engineering[J],
1998, 46: 1861 1993, a133: 176
12
Yifang Y O, Jie Z, Hongmei C et al. Jourmal of Alloys and Compounds[J], 2008, 454: 359
13
Ye F, Lu K. Journal of Non-Crystalline Solids[J], 2000, 262: 228
14
Rho I C, Yoon C S, Kim C K et al. Journal of Non-Crystalline
15
Mathon M H. Nuclear Materials[J], 1997, 245: 224
16
Hung P K, Vinh L T, Kien P H. Journal of Non-Crystalline
Solids[J], 2003, 316: 289
Solids[J], 2010, 356: 1213
17
Flege S, Fecher U, Hahn H. Journal of Non-Crystalline Solids[J],
18
Hono K, Ping D H. Materials Characterization[J], 2000, 44: 203
19
Golubov S I, Serra A, Osetsky Y N et al. Nuclear Materials[J],
2000, 270: 123
2000, 277: 113
Graf T, Hampel G, Korus J et al. Nanostructured Materials[J], 1995, 6: 469
1355
ARTICLE
Effect of Copper and Niobium Addition on Crystallization Kinetics in Fe-Cu-Nb-Si-B Alloys Li Guangmin,
Li Deren,
Ni Xiaojun,
Li Zhun,
Lu Zhichao
Advanced Technology & Materials Co., Ltd., China Iron & Steel Research Institute Group, Beijing 100081, China
Abstract: The activation energies of amorphous Fe78Si11B9 and nanocrystalline Fe73.5Cu1B7Si15.5Nb3 alloys were tested by a high-sensitivity differential scanning calorimeter with different heating rates. Kissinger equation was adopted to calculate the activation energies of the primary phase of Fe73.5Cu1B7Si15.5Nb3 alloy (295±5) kJ and the crystal phase of Fe78Si11B9 alloy (370±3) kJ. The low activation energy of the primary phase for Fe73.5Cu1B7Si15.5Nb3 alloy is related to the precipitation of Cu clusters. The precipitation kinetics of Cu clusters was analyzed. The calculated result of the mean radius R m of Cu cluster is 3 nm after aging for 3600 s at 773 K in Fe73.5Cu1B7Si15.5Nb3 glass alloy and the maximum value of number density is 3.7 ×1024 /m3 after aging for 2.5 h at 773 K, which accords with K. Hono’s observation (approximately 3 nm after annealing at 673 K or 3600 s). The density of Cu is in the order of 1024 m-3). Key words: nanocrystalline alloys; Fe-Cu-Nb-Si-B alloy; crystallization kinetics; Cu cluster
Nanocrystalline soft magnetic alloys have a great potential for electromagnetic applications due to their excellent soft magnetic properties. The Fe73.5Cu1B7Si15.5Nb3 alloy is one of amorphous Fe-Si-B family alloys and first examined by Yoshizawa et al. in 1988 [1]. The addition of Cu and Nb in some Fe-Si-B based alloys promotes a two-phase structure material coming into being which consists of small nanocrystals embedding in a residual amorphous matrix. Copper is a necessary element for initializing crystallization at lower temperature, and niobium stabilizes the nanostructure during crystallization process and limits the growth of the grains [2]. Cu cluster in the early crystallization stage of Fe73.5Cu1B7Si15.5Nb3 amorphous alloy was studied by K.hono et al.[3,4], and Cu cluster stimulates nucleation of the nanocrystalline soft magnetic alloys[5-9]. Copper particles were observed spatially separated from the α–Fe particle in the one-dimensional atom probe concentration depth profile, and the density of Cu enriched particles is in the order of 1024/m3. There are two models to explain how the Cu clusters stimulate nucleation in nanocrystalline alloys. One model is that the interfaces of Cu precipitates adjoin directly the primary phase. The other model is that Cu
clusters are entirely enveloped by primary phase[10]. Currently, no theory research on precipitation kinetics of Cu clusters was reported. This paper is in an attempt to introduce cluster models to make clear Cu clusters precipitation in amorphous matrix, and to study the effect on primary phase in crystallization process by addition of Cu and Nb elements.
1
Experiment
Amorphous Fe78Si9B13 and Fe73.5Cu1B7Si15.5Nb3 soft magnetic alloys ribbons were prepared by single-roller melt spinning. The thickness measured by thickness gauge and width of the ribbon were 24 µm and 30 mm, respectively, shown in Fig.1. High-sensitivity differential scanning calorimeter (DSC, NETZSCH404) measurements were taken for Fe78Si9B13 and Fe73.5Cu1B7Si15.5Nb3 soft magnetic alloys at different heating rates of 10, 15, 20, 25, 30, 40 K/min to observe the crystallization temperature.
2 2.1
Results and Discussions Activation energy of the alloys
Fig.2 shows the crystallization temperatures of Fe73.5Cu1B7Si15.5Nb3 alloy measured by DSC with different
Received date: July 29, 2012 Foundation item: National High Technology Research and Development Program of China “863 Program”(2009AA03Z214) Corresponding author: Li Guangmin, Ph. D., Advanced Technology & Materials Co., Ltd., China Iron & Steel Research Institute Group, Beijing 100081, P. R. China, Tel:0086-10-58742808, E-mail: [email protected] Copyright © 2013 Northwest Institute for Nonferrous Metal Research. Published by Elsevier BV. All rights reserved.
1352
Li Guangmin et al. / Rare Metal Materials and Engineering, 2013, 42(7): 1352-1355 Thickness b Tester
a
Amorphous Ribbon
Table 1
Fe73.5Cu1B7Si15.5Nb3 alloys
Fe73.5Cu1B7Si15.5Nb3 Thr/K·min-1 Tp1/K 10 797.2 15 803.8 20 808.8 25 813.4 30 813.5 40 821.4
ln(
Heat Flow/mW·mg-1
24 µm measured by thickness gauge (b)
3 2 1
o Peak: 714.3 oC Peak: 540.440 CK/min o Exo Peak:548.4 C Peak:709.3 oC
Peak:540.5 oC 30 K/min
Peak: 704.0 oC Peak: 535.8 oC
20 K/min Peak: 707.4 oC
Peak: 698.9 oC Peak: 530.8 oC
25 K/min 15 K/min 10 K/min Peak: 524.2 oC Peak: 692.1 oC
0 100
300
500
700
o
Temperature/ C Fig.2
Crystallization temperatures of Fe73.5Cu1B7Si15.5Nb3 alloy with different heating rates measured by DSC
heating rates. The crystallization peaks and onsets temperature are postponed with increasing of the heating rate. There are two distinct crystallization peaks which are different from Fe78Si9B13 alloys. Table 1 shows the crystallization temperatures of Fe78Si9B13 and Fe73.5Cu1B7Si15.5Nb3. The addition of Cu and Nb in Fe-Si-B alloy produces two crystallization phases. Tp1 and Tp2 are the peak temperatures of the first crystallization and the second crystallization of Fe73.5Cu1B7Si15.5Nb3 alloy, respectively. Tx is the unique temperature of the crystallization peak of Fe78Si9B13 alloy. It is clear to see that Tx is slightly higher than Tp1, but lower than Tp2. The addition of Cu in Fe-Si-B alloy produces a large number of Cu clusters which provide nucleation sites for approaching primary phase. These nucleation sites can decrease crystallization activation energy. In the crystallization process, Nb atoms are pushed into the residual amorphous phase and increase its temperature[11]. But, with increasing of the heating rate, Nb and B elements have no sufficient time for diffusion, and lead to secondary crystallization peak shifting towards the high temperature district. The apparent activation energy E a for the crystallization process is usually determined with the Kissinger equation [12-14]
Fe78Si11B9 Tx/K 792.4 825 / 835 / 846.3
(1)
where Thr is the heating rate, R is the gas constant, T is characteristic temperature and C is a constant. In Fig.3, the activation energies calculated by Kissinger plots in Fe73.5Cu1B7Si15.5Nb3 and Fe78Si11B9 alloys are (295 ±5) kJ and (370±3) kJ, respectively. Copper and niobium elements in Fe-Si-B alloys decrease crystallization temperature and activation energy. Two models of Cu clusters provide nucleation sites for the primary phase as shown in Fig.4. The first model is the interfaces of Cu precipitates adjoining directly the primary phase. The primary phase nucleation only depends on a the interface little and extends the amorphous matrix. Another model is that Cu clusters are entirely enveloped by primary phase. The primary phase firstly annexes the whole Cu cluster and then extends toward the three-dimensional direction. The driving force of primary phase nucleation is decreased because of their lower interface energy connection which creates favorable conditions α-Fe phase crystallization. 2.2 Mean radius of Cu cluster The growth velocity of Cu cluster in radius R is given by [15]
dR KDα (C∞ − CR ) = dt α D + K
(2)
Where, K is the transfer velocity through the interface of thickness b; D is the diffusion coefficient, b=D/K, and α=(R+b)/R2; CR is the solute concentration in equilibrium with a precipitate of radius R. The value of thickness b is 13.6 12.8
Fe73.5Cu1B7Si15.5Nb3 first peak Tp1 Fe78Si9B11
12.0
2
Width of the ribbon is 30 mm (a) and the thickness is
Tp2/K 965.1 971.9 977 980.4 982.3 987.3
E Thr ) = − a +C 2 T RT
ln(T /Thr)
Fig.1
Crystallization temperatures of Fe78Si9B13 and
11.2 10.4 9.6
0.142 0.144 0.146 0.148 0.150 0.152 -1
-3
-1
(TR) ×10 /K Fig.3
Kissinger plots of the heating rate in DSC crystallization temperature in Fe73.5Cu1B7Si15.5Nb3 and Fe78Si11B9 alloys
1353
Li Guangmin et al. / Rare Metal Materials and Engineering, 2013, 42(7): 1352-1355
a
6 5
Rm/nm
4
2 1 0
Fig.5
Fig.4
Primary phase
0
7200 t/s
10800
14400
Mean radius of Cu cluster versus time at T=773 K for nanocrystalline
alloy
with
KCu=1.5×10-8cm/s-1, DCu=9.4×10-16 m2/s
Np =
3 4 π (3σ
fp 2
(3)
+ R m2 ) R m
fp is the volume fraction of precipitates, σ is the interface energy, and Rm is the mean radius. Symmetrical radius distribution h(R) is given by Lifshitz-Slyosov-Wagner coarsenning theory h(R ) =
⎡ ( R − Rm )2 ⎤ 1 exp ⎢ − ⎥ 2σ 2 2 πσ ⎣ ⎦
(4)
The half-width of the size distribution at half maximum ΔR is given by σ =ΔR/1.177. The values of parameters ΔR and fp are given by Ref.[16]. After aging at 773 K for 2.5 h, fp is about 0.7 %. After aging at 773 K for 4.5 h, fp is about 1.1 %. Number density as a function of Rm of Cu precipitates in Fe73.5Cu1B7Si15.5Nb3 nanocrystalline alloy after aging for different time, is shown in Fig.6. There are sharp peaks of the number density functions at different aging time for Cu precipitate diameter. The precipitate diameter is less than 0.5 nm while the maximum value of number density is 3.7 ×1024 /m3 after aging for 2.5 h 4
b
Cu
Two models of Cu clusters providing nucleation sites for the primary phase: (a) the interfaces of Cu precipitates adjoining
3600
Fe73.5Si13.5B9Nb3Cu1
Primary phase Cu
3
24 24 m-3-3 Number Density/ ×10 Number Density 10 m
about 0.15 nm, because of Cu atom must transfer some distance in amorphous structure to reach clusters. The distance must be more than a half regular bcc. Fe lattice ao=0.2866 nm. During thermal annealing, these vacancies are mobile and thus give rise to a contribution of self-diffusion by exchanging their sites with adjacent atoms [16]. Molecular dynamics simulation reveals the unstableness of vacancies or plenty of interstices. Activation energy Q and pre-exponential factors D0 of Cu in amorphous alloys are 1.8 -8 eV and 5×10 m2/s respectively, at 653 K [17]. According to Arrhenius equation DCu(T)=D0exp(–Ea/kT) (k is Boltzmann constant), the value of copper diffusion coefficient is -20 DCu=9.4×10 m2/s, which is less than the value of copper -19 diffusion coefficient DCry-Cu=4 × 10 m2/s in Fe-Cu(1.35at%) crystalline alloys at 773 K. The order of the values are closely related with other elements diffusion in amorphous matrix such as Fe (DFe, 10-21~10-22 m2/s in amorphous alloys Fe80B2) and B (DB, 10-19 m2/s in Fe40N40B20 alloy at 625 K). Fig.5 shows that the calculated mean radius Rm of Cu cluster grown up nonlinearly with heat treatment time. The mean radius Rm is about 3 nm for Fe73.5Si13.5B9Nb3Cu1 nanocrystalline alloy aged for 3600 s at 773 K. The mean radius of Cu cluster which is so small and will be covered by approaching primary phase can not be found easily by the microscopy. But, these nano-particles write firstly prologue of nanocrystalline precipitation on amorphous matrix and play an important role on stimulating primary phase precipitates. The Cu cluster is coarsened sharply in early aging stage, and grows up tardily in later aging time. The reason is that the solute concentration of Cu concentration in matrix decreases with precipitating of volumes of Cu cluster. The result of calculation accords with K. Hono’s observation (approximately 3 nm after annealing at 673 K for 3600 s and approximately 5 nm after annealing at 823 K for 3600 s in Fe73.5Si13.5B9Nb3Cu1 alloys)[18]. 2.3 Number density of Cu cluster The number density of Cu cluster Np is given by [19]
Fig.6
3 aging 2 .5 h aging 4 .5 h
2 1 0
0
1
2
3 Rm/nm
4
5
Number density as functions of Rm of Cu precipitates in alloy
directly the primary phase; (b) Cu clusters entirely enveloped
with the cluster model for Fe73.5Si15.5B9Nb3Cu1 nanocrystalline
by primary phase
alloy
1354
Li Guangmin et al. / Rare Metal Materials and Engineering, 2013, 42(7): 1352-1355
at 773 K, and the precipitate diameter is more than 0.5 nm while the maximum value of number density is 2.5×1024 /m3 after aging for 4.5 h at 773 K. The Cu element precipitates a large number of nano-clusters in amorphous matrix after aging for 2.5 h, but it has no sufficient time to coarsen. But the Cu clusters start to coarsen in the form of mergence which causes the number density of Cu nano-clusters dwindling. It is the reason that the average diameter of precipitates of Cu cluster after aging for 4.5 h is bigger than that after aging for 2.5 h, and the number density of Cu clusters decreases. The calculation results also provide well guidance for our industrial test, which means a reasonable heating treatment time can precipitate the maximum density nano-clusters to stimulate more homogeneous nano primary phase precipitation. The calculated results of the number density of Cu precipitate diameter are in agreement with experimental analysis in Ref.[3].
3
Conclusions
1) In crystallization process, elements Nb and B have no sufficient time for diffusion with increasing of the heating rate, and such a case leads secondary crystallization peak to shift towards the high temperature district. 2) The addition of Cu and Nb into Fe-Si-B alloys decreases the first crystallization activation energy. It is closely related to Cu cluster serving as heterogeneous nucleation sites for the α-Fe primary phase.
References 1
Yoshizawa Y, Oguma Y, Yamauchi S. Journal of Applied Physics[J], 1988, 64: 6044
2
3
Hono K, Ping H D, Ohnuma et al. Acta Materialia[J], 1999, 47: 997
4
Hono K, Hiraga K, Wang Q. Acta Metallurgica and Materialia[J],
5
Ohnuma M, Hono K, Linderoth S et al. Acta Materialia[J], 2000,
1993, 40: 2137 48: 4783
6
Chen Y M, Ohkubo T, Ohta M et al. Acta Materialia[J], 2009, 57: 4463
7
Makino A, Men H, Kubota T et al. Journal of Applied Physics[J], 2009, 105: 07A308
8
Ohta M, Yoshizawa Y. Journal Applied Physics[J], 2008, 103:
9
Ohta M, Yoshizawa Y. Journal Magnetism and Magnetic
07E722 Materials[J], 2008, 320: e750
10
Ayers D J, Harris G V, Sprague A J et al. Acta Materiallia[J],
11
Yoshizawa Y, Yamauchi K. Materials Science and Engineering[J],
1998, 46: 1861 1993, a133: 176
12
Yifang Y O, Jie Z, Hongmei C et al. Jourmal of Alloys and Compounds[J], 2008, 454: 359
13
Ye F, Lu K. Journal of Non-Crystalline Solids[J], 2000, 262: 228
14
Rho I C, Yoon C S, Kim C K et al. Journal of Non-Crystalline
15
Mathon M H. Nuclear Materials[J], 1997, 245: 224
16
Hung P K, Vinh L T, Kien P H. Journal of Non-Crystalline
Solids[J], 2003, 316: 289
Solids[J], 2010, 356: 1213
17
Flege S, Fecher U, Hahn H. Journal of Non-Crystalline Solids[J],
18
Hono K, Ping D H. Materials Characterization[J], 2000, 44: 203
19
Golubov S I, Serra A, Osetsky Y N et al. Nuclear Materials[J],
2000, 270: 123
2000, 277: 113
Graf T, Hampel G, Korus J et al. Nanostructured Materials[J], 1995, 6: 469
1355