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The internal stresses dependence of the magnetic properties of cast amorphous microwires covered with glass insulation
~ l ~ Journalof magnetism ELSEVIER
Journal of Magnetism and Magnetic Materials 196-197 (1999) 835-836
~
and
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malerlals
magnetic
The internal stresses dependence of the magnetic properties of cast amorphous microwires covered with glass insulation A.V. Torcunov*, S.A. Baranov, V.S. Larin 'AmoTec' S.R.L. 78, 15 b-d, Dacia, 2038 Kishinev, Republic of Moldova, Moldavia
Abstract The anisotropy field of cast amorphous microwires covered with glass is determined by internal stress distribution. Both quenching and thermoelastic stresses are present in microwires. All presented experimental data permit to conclude that thermoelastic stresses determine the magnetic behaviour of the microwires and that the quenching stresses must be taken into account only in the case of small glass thicknesses. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Amorphous microwire; Anisotropy field; Internal stress
The internal stresses, arising in the metal core of cast amorphous microwires covered with glass insulation (produced by Taylor-Ulitovsky technique) during manufacturing, determine the magnetic behaviour of such kind of microwires. Both quenching stresses and stresses resulting from the difference between the expansion coefficients of metal and glass (thermoelastic stresses) are present in glass covered microwires. The thermoelastic stresses was first calculated by the authors of Ref. [1,2]. The thermoelastic internal stresses depend on the mechanical, thermal properties and the cross-section ratio of glass and metal, X = (dw/dm) 2 - 1, where dw and dm are the wire and metal core diameters, respectively. The typical X dependence of the thermoelastic stresses calculated by this method is presented in Fig. I. The quenching stresses are not taken into account because its less contribution is less when compared with thermoelastic stresses which can reach up to 1 GPa. Thermoelastic stress depends on the mechanical and thermal properties of glass and metal such as: the Young's modulus (E~, Era), the Poisson's coefficients (vg, Vm),and the expansion coefficients (%, 0~m). Assuming
* Corresponding author. Titulescu str. 47 ap. 3, MD 2032, Kishinev, Republic of Moldova, Moldavia. Fax: + 3732731359; e-mail: [email protected].
that: Vg~ Vr~-,~½, a simple equation for stress components (cylindrical coordinate) can be obtained: a,r = a ~ = eEmkX/((k/3 + 1)X + 4/3),
(la)
or= = arr((k + 1)X + 2)/(kX + 1),
(lb)
c%)(T* - T),
(lc)
F, =
(~m --
where T is the temperature, T* the minimum (glass or metal) solidification temperature, and k = Eg/Em. It is useful to note that in this model the stress component does not depend on the radial coordinate, a,, -- ao~ is 2-3 times smaller than o.-z. On assuming that the quenching stress distribution has the same character as in the 'in-rotating-water' wire, where err > a ~ , the following stress component relation o= > a,r > ao~ in the entire microwire's volume can be supposed. In this case, the circular magnetization for a negative magnetostriction constant alloy and the axial magnetization for positive ones must be obtained. The anisotropy field, Hk, must linearly depend on the internal stress value in the case of a negative magnetostriction constant value microwire. An attempt to take into account both the quenching stresses and the thermoelastic ones was performed in Ref. [3]. But the calculation was based on the simple addition of both kinds of the stresses. This assumption is not correct. A more correct procedure was performed in
0304-8853/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 85 3(9 8 ) 0 0 9 6 2 - 7
836
A. I4 Torcunov et al. /Journal o f Magnetism and Magnetic Materials 196-197 (I 999) 835-836 T hermoelastic stress
150
eoeoe
125
1200 1000
g- 8oo IE
a481
qle°eee
100
I 0e
e
75
-r-
50
radial
25
2170,
0 50 10
2O
100
30
!50
X
Fig. 1. The X dependence of thermoelastic stress.
Fig. 3. The temperature dependence of Hk.
600
450
500
In D
35O
400 E
•
3oo
iimQ u
II
E
ee 00
• samF31ea
2~o
= sam pie b
O
I 20O 100
200
Temperature
a,:"'.°
OO
150
e4
OO
50 0
200
400
0
600
Fig. 2. The thermoelastic stress dependence of Hk.
Ref. [4], where it was found that the stress distribution is very sensitive to the value of the axial extraction stress. Co~sMnTBxsSilo and C06vMn8B15Silo composed amorphous microwires covered with glass insulation were produced by the Ulitovsky-Taylor method. The axial M z - H z hysteresis loops were measured at room temperature by means of a conventional induction method at 50 Hz. The following experimental results were obtained for the alloy composed of Co68MnTB15Sixo with a small negative magnetostriction constant value: X dependence of Hk is the same as X dependence of a, calculated by assuming the contribution of only thermoelastic stresses (see Fig. 1). As a result, Hk linearly depends on axial thermoelastic stresses, a, (see Fig. 2). Only when the value of X i s less than 1, corresponding to small glass thickness values, A, (in this case, the glass thickness to metal core diameter ratio is smaller than 0.2) the quenching stresses begin to play an important role, changing the obtained dependencies of Hk. It means, as one can see from Fig. 2, that the quenching stresses are less than approximately 100 M P a for the investigated microwire. Hk linearly depends on temperature too. The thermoelastic stresses, as predicted by Eqs. (la)-(lc), must decrease the anisotropy field to zero with temperature up to T*, corresponding to the solidification temperature of glass (approximately 550°C). The linear approximation
2000
1000 Totals~ess,
Axial stress, MPa
MPa
Fig. 4. Total stress dependence of H~, sample a - dw = 17 pro, dm = 16 ~tm, sample b - dw = 14 ~tm, dm = 6 lam.
of the experimental data presented in Fig. 3 shows the same value of temperature at which Hk reaches zero. The applied external stresses have the same influence on Hk and the coercive force. He, as the internal ones. The total stress (external and thermoelastic) dependence of Hc for the alloy Co67MnsB15Silo with a small positive magnetostriction constant value is presented in Fig. 4. In summary, all the presented experimental data permit to conclude that thermoelastic stresses determine the magnetic behaviour of cast amorphous microwires covered with glass and that the quenching stresses must be taken into account only in case of small glass thicknesses (when X < 1).
References
[1] S.A. Baranov, V.N. Berzhanski, S.K. Zotov, V.L. Kokoz, V.S. Larin, A.V. Torcunov, Fizika Metall. Metalloved. (Soy.) 67 (1989) 73. [2] A.N. Antonenko, S.A. Baranov, V.S. Larin, A.V. Torcunov, Material Science and Engineering, A, Rapidly quenched & Metastable Material (Suppl.) 1997 pp. 248-250. [3] H. Chiriac, T.A. Ovari, Gh. Pop, Phys. Rev. B 52 (1995i 10104. [4] J. Velazquez, M. Vazquez, A.P. Zhukov, J. Mater. Res. 11 (1996) 2499.
Journal of Magnetism and Magnetic Materials 196-197 (1999) 835-836
~
and
,~
malerlals
magnetic
The internal stresses dependence of the magnetic properties of cast amorphous microwires covered with glass insulation A.V. Torcunov*, S.A. Baranov, V.S. Larin 'AmoTec' S.R.L. 78, 15 b-d, Dacia, 2038 Kishinev, Republic of Moldova, Moldavia
Abstract The anisotropy field of cast amorphous microwires covered with glass is determined by internal stress distribution. Both quenching and thermoelastic stresses are present in microwires. All presented experimental data permit to conclude that thermoelastic stresses determine the magnetic behaviour of the microwires and that the quenching stresses must be taken into account only in the case of small glass thicknesses. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Amorphous microwire; Anisotropy field; Internal stress
The internal stresses, arising in the metal core of cast amorphous microwires covered with glass insulation (produced by Taylor-Ulitovsky technique) during manufacturing, determine the magnetic behaviour of such kind of microwires. Both quenching stresses and stresses resulting from the difference between the expansion coefficients of metal and glass (thermoelastic stresses) are present in glass covered microwires. The thermoelastic stresses was first calculated by the authors of Ref. [1,2]. The thermoelastic internal stresses depend on the mechanical, thermal properties and the cross-section ratio of glass and metal, X = (dw/dm) 2 - 1, where dw and dm are the wire and metal core diameters, respectively. The typical X dependence of the thermoelastic stresses calculated by this method is presented in Fig. I. The quenching stresses are not taken into account because its less contribution is less when compared with thermoelastic stresses which can reach up to 1 GPa. Thermoelastic stress depends on the mechanical and thermal properties of glass and metal such as: the Young's modulus (E~, Era), the Poisson's coefficients (vg, Vm),and the expansion coefficients (%, 0~m). Assuming
* Corresponding author. Titulescu str. 47 ap. 3, MD 2032, Kishinev, Republic of Moldova, Moldavia. Fax: + 3732731359; e-mail: [email protected].
that: Vg~ Vr~-,~½, a simple equation for stress components (cylindrical coordinate) can be obtained: a,r = a ~ = eEmkX/((k/3 + 1)X + 4/3),
(la)
or= = arr((k + 1)X + 2)/(kX + 1),
(lb)
c%)(T* - T),
(lc)
F, =
(~m --
where T is the temperature, T* the minimum (glass or metal) solidification temperature, and k = Eg/Em. It is useful to note that in this model the stress component does not depend on the radial coordinate, a,, -- ao~ is 2-3 times smaller than o.-z. On assuming that the quenching stress distribution has the same character as in the 'in-rotating-water' wire, where err > a ~ , the following stress component relation o= > a,r > ao~ in the entire microwire's volume can be supposed. In this case, the circular magnetization for a negative magnetostriction constant alloy and the axial magnetization for positive ones must be obtained. The anisotropy field, Hk, must linearly depend on the internal stress value in the case of a negative magnetostriction constant value microwire. An attempt to take into account both the quenching stresses and the thermoelastic ones was performed in Ref. [3]. But the calculation was based on the simple addition of both kinds of the stresses. This assumption is not correct. A more correct procedure was performed in
0304-8853/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 85 3(9 8 ) 0 0 9 6 2 - 7
836
A. I4 Torcunov et al. /Journal o f Magnetism and Magnetic Materials 196-197 (I 999) 835-836 T hermoelastic stress
150
eoeoe
125
1200 1000
g- 8oo IE
a481
qle°eee
100
I 0e
e
75
-r-
50
radial
25
2170,
0 50 10
2O
100
30
!50
X
Fig. 1. The X dependence of thermoelastic stress.
Fig. 3. The temperature dependence of Hk.
600
450
500
In D
35O
400 E
•
3oo
iimQ u
II
E
ee 00
• samF31ea
2~o
= sam pie b
O
I 20O 100
200
Temperature
a,:"'.°
OO
150
e4
OO
50 0
200
400
0
600
Fig. 2. The thermoelastic stress dependence of Hk.
Ref. [4], where it was found that the stress distribution is very sensitive to the value of the axial extraction stress. Co~sMnTBxsSilo and C06vMn8B15Silo composed amorphous microwires covered with glass insulation were produced by the Ulitovsky-Taylor method. The axial M z - H z hysteresis loops were measured at room temperature by means of a conventional induction method at 50 Hz. The following experimental results were obtained for the alloy composed of Co68MnTB15Sixo with a small negative magnetostriction constant value: X dependence of Hk is the same as X dependence of a, calculated by assuming the contribution of only thermoelastic stresses (see Fig. 1). As a result, Hk linearly depends on axial thermoelastic stresses, a, (see Fig. 2). Only when the value of X i s less than 1, corresponding to small glass thickness values, A, (in this case, the glass thickness to metal core diameter ratio is smaller than 0.2) the quenching stresses begin to play an important role, changing the obtained dependencies of Hk. It means, as one can see from Fig. 2, that the quenching stresses are less than approximately 100 M P a for the investigated microwire. Hk linearly depends on temperature too. The thermoelastic stresses, as predicted by Eqs. (la)-(lc), must decrease the anisotropy field to zero with temperature up to T*, corresponding to the solidification temperature of glass (approximately 550°C). The linear approximation
2000
1000 Totals~ess,
Axial stress, MPa
MPa
Fig. 4. Total stress dependence of H~, sample a - dw = 17 pro, dm = 16 ~tm, sample b - dw = 14 ~tm, dm = 6 lam.
of the experimental data presented in Fig. 3 shows the same value of temperature at which Hk reaches zero. The applied external stresses have the same influence on Hk and the coercive force. He, as the internal ones. The total stress (external and thermoelastic) dependence of Hc for the alloy Co67MnsB15Silo with a small positive magnetostriction constant value is presented in Fig. 4. In summary, all the presented experimental data permit to conclude that thermoelastic stresses determine the magnetic behaviour of cast amorphous microwires covered with glass and that the quenching stresses must be taken into account only in case of small glass thicknesses (when X < 1).
References
[1] S.A. Baranov, V.N. Berzhanski, S.K. Zotov, V.L. Kokoz, V.S. Larin, A.V. Torcunov, Fizika Metall. Metalloved. (Soy.) 67 (1989) 73. [2] A.N. Antonenko, S.A. Baranov, V.S. Larin, A.V. Torcunov, Material Science and Engineering, A, Rapidly quenched & Metastable Material (Suppl.) 1997 pp. 248-250. [3] H. Chiriac, T.A. Ovari, Gh. Pop, Phys. Rev. B 52 (1995i 10104. [4] J. Velazquez, M. Vazquez, A.P. Zhukov, J. Mater. Res. 11 (1996) 2499.