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Disaccomodation phenomenon in Fe82B18-xCx and Fe82B18-xSix metallic glasses
Journal of Magnetism and Magnetic North-Holland, Amsterdam
Materials
68 (1987) 145-150
DISACCOMMODATION PHENOMENON AND Fe,B,,_,Si, METALLIC GLASSES
145
IN Fe, B 18_ $2,
ZHANG Yan Zhong Shanghai Iron and Steel Research Institute, Received
23 December
IO5 Tai-He Road, Wu-song. Shanghai,
1986; in revised form 17 March
P.R. China
1987
The isochronal disaccommodation (DA) of the initial permeability was measured in Fe,,B,,_,C, and Fes,B,,_,Si, metallic glasses in the temperature range from 77 to 600 K. An asymmetric isochronal spectrum with a single relaxation peak was observed on each studied glassy alloy. The peak shifts to the lower temperature side with increasing C content in Fe,,BIs_XC,, whereas the influence of Si on the peak in Fes,B,s_XSi, is opposite to the effect of C. The kinetic behavior of DA was examined and the activation energy spectrum was evaluated. The replacement of B by C gives rise to the reduction of the activation energy, whereas the addition of Si increases the energy. A clearly annealing effect on DA was observed on each examined alloy.
1. Introduction
2. Experiments
Metallic glasses prepared by melt quenching are in a thermodynamically metastable state. Annealing at lower temperatures well below the glass transition temperature will give rise to relaxation in various physical properties. Of these relaxations the magnetic permeability relaxation is of great importance to practical applications. The experiments have shown that the total permeability relaxation consists of ordinary DA and continuous permeability decay [l-3]. The former is reversible with respect to demagnetization and the relaxation process can reproducibly be excited. This phenomenon is the ordinary magnetic after-effect which was earlier observed in metallic soft magnetic materials and ferrites. The latter is irreversible with respect to demagnetization, i.e. the original value of the permeability can not be recovered by demagnetization and decreases continuously. In this paper we report the experimental results of the ordinary DA in as-quenched Fe,,B,,_,C, (x = O-S) and Fes2B,,_,Si, (x = 0, 3, 5 and 8) metallic glasses, the evaluated activation energy spectrum as well as the observed annealing effect on DA.
Glassy allows were fabricated in a ribbonform using a single roller rapid quenching technique. The shape of the ribbon was 1 cm in width and about 35 pm in thickness. The diffraction pattern obtained by the conventional X-ray diffraction technique exhibited a diffused halo. The toroidal samples made of the ribbons were used for measuring the permeability relaxation. The relative change in reluctivity, r = 4a/p, between t, = 1 s and t, = 120 s after demagnetization was measured by using an automatic DA apparatus controlled by a microcomputer. The measurements of DA during heating were performed at various temperatures with interval of 5-10 K in the range from 77 to 60 K. This type of measurements is equivalent to a temperature scanning measuring. The frequency of demagnetization and magnetization were 1 and 10 kHz, respectively. The maximum amplitude of the demagnetization field and the intensity of the ac field were 4000 and 0.08 A/m, respectively. At t2 = 120 s after the first demagnetization, the repetitious demagnetization and the measurement of the reluctivity, r(t;), at ti = 1 s after the second demagnetization were
0304-8853/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
146
Y.Z. Zhang / Disaccommodation in Fea,Bls_ .C, and Fe,?B,,_ Ji,
carried out. In the case of the presence of permeability decay, r(l) # r(t;), therefore, generally speaking the ordinary DA should be defined as Ar/r, = ((r(tz) - r(Q) - (r(G) - rtt))l/r(M = (r( t2) - t( ti)]/r( ti) in order to separate DA from the total relaxation. In order to examine the kinetic process of DA, the time dependence of permeability after dema~etization was measured at 273 K, until an equilibrium value of permeability was reached. The irreversible permeability decay was not observed within the measuring time limit, thus indicating that the total relaxation only consists of DA at 273 K. In order to examine the annealing effect on DA, as-quenched samples were first annealed at various temperatures, which did not exceed 700 K, and then quenched into ice water. For a given and examined alloy the annealing temperature was below the Curie temperature of the alloy. The subsequent measurements of DA were performed in the way of temperature scanning at various temperatures up to 600 K.
Fig. 1. Isochronal DA spectrum of Fes,B,s_ $, 8) (t2 = 120 s).
(x = 2, 6 and
effect of C on DA spectrum is different from the effect of Si. 3.2. Kinetic behavior of DA and activation energy spectrum
3. Results and discussion 3.1. Isochronai DA spectrum
As a typical example, fig. 1 shows the isochronal DA spectra for as-quenched Fe,,B,,C,, Fe,,B,,C, and Fe,,B,,C,, and fig. 2 shows the The spectra spectra for Fe,,B,, and Fe,,B,,Si,. similar to those shown in figs. 1 and 2 were obtained for the other examined alloys. These spectra with a single relaxation peak are asymmetric. The spectra were broadened by increasing C and Si content, i.e. the full widths of half maximum (fwhm) of the spectra were increased. The peak temperature, TP, corresponding to the maximum DA decreases with increasing C content, i.e. the relaxation peak shifts to lower temperature. When x in Fe,,B,,_,C, increases from 6 to 8, the m~mum DA, (Ar/rt),, decreases from 0.175 to 0.1. On the contrary, the increase in x in Fe,,B,,_,Si, gives rise to the increase in TP and the change in (Ar/r,), from 0.175 to 0.33. Fig. 3 shows TP as a function of C or Si content. The facts mentioned above have indicated that the
3.2.1. Kinetic cw+veof DA A norm~~ed variation _X(7’, t ) = (FL’ cl;9/(G’ - &I) was introduced to describe the kinetic behavior of DA, wher e p,, pt and pm are the permeability at initial moment and time t after demagnetization and the equilibrium permeability, respectively. As a typical example, fig. 4 shows the kinetic curve of DA obtained at 273 K for Fe,,B,,. & cevl Q6
a72
108
f&
l&l
2.15
20
Fig. 2. Isochronal DA spectrum of Fes2B1s_xSix (x = 0 and 8) (tl = 120 s).
Y. Z. Zhang / Disaccommodation
Fig. 3. Composition dependence of peak temperature DA spectrum. (0) Fe,,B,8_xSi,, (0) Fe,,B,,_,C,.
TP on
The part of the curve for longer time than 104s is not shown in fig. 4. The curves similar to that shown in fig. 4 were obtained on the other examined glassy alloys. These curves shift right and left as a function of C or Si content. As can be seen from fig. 4, the main part of the kinetic curve nearly exhibits lnt kinetic behavior. 3.2.2, Activation kinetic data
enera
spectrum
evaluated
by
Such curves as that shown in fig. 4 can be fitted making use of the following equation: X(T, t) = /P(ln
~)[l-
exp(-t/T)]
(1)
d In 7,
where P(ln 7) is a distribution function for relaxation time 7. Taking account of the equation In 7 = E/kT - In v,, for thermal activation process, we can write eq. (1) as
x(T, ~)=JQ(E)[~-exp(-ho X exp( - E/kT))]
dE/kT,
in Fe,B,,_
,C, and Fe,B,,
_ xSi,
147
Debye frequency. However v. was found to be of order of 10’5-10’7 s-l by fitting the isochronal DA spectra for Fe-B metallic glasses [4,5]. It is considered that a large frequency factor is attributed to a small entropy factor exp( - S/k), i.e. to a large hopping entropy [4,5]. Regarding v, as a fitting constant and carefully choosing it in the range of 10’2-1017 s-l, we can obtain a numerical solution of eq. (2) by using Hesse-Rubartsch’s method [6], thus evaluating activation energy spectrum. The detailed account can be found elsewhere [1,2]. Careful calculations have shown that the satisfactory results for all examined glassy alloys were obtained by choosing v, of (1.64-4.83) X 10’6s-‘. The activation energy spectrum obtained for Fe,,B,, by choosing v. of 2.67 x 10’6s-’ is shown in fig. 5 as a typical example. The most probable activation energy Em, of Fe,,B,, obtained from fig. 5 approximately is 1.4 eV, which approximates the energy for and Fe,,B,, obtained by Rettenmeier Fess,Bi4.s [5]. The spectra similar to that in fig. 5 were obtained for all the examined alloys. The features of these spectra are the asymmetry and the more clear probability distribution in lower energy range. The most probable activation energy, Em, obtained from the spectrum are shown in fig. 6 as a function of C or Si content. The difference in the effects of C and Si on E,,, can be seen from fig. 6. E, decreases with increase in C, whereas the effect of Si is opposite to that of C.
(2)
where Q(E) represents an activation energy spectrum; k is Boltzmann’s constant; v. is a frequency factor, in general, which should be of order of the
IOr
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P
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10'
I
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IN11111
4
IO'
11111,1
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,
,,,,,L
Id
Fig. 4. Kinetic curve of DA in Fe,,B18 measured at 2.73 K.
lo’
0.4
cl8
1.2
E Lew
I
,_I
1.6
Fig. 5. Activation energy spectrum of DA process in Fe,,B18.
148
Y. 2. Zhang / Disaccommodation in Fee2 Bl 8 _ ,C, and Fe,, B,, _ x Si,
(3) can approximately
I.7
Ar/rl = 0.0359( Ar,/r,)q(
-1.6 -15 - 14
1.0 0
I 2
I 4
X
I 6
I r3
10
Fig. 6. Composition dependence of the most probable activation energy of DA process. (a) Fes2B,s_,Cx, Si,.
(0)
Fes2BIs_,
3.2.3.
Evaluation by activation energy spectrum model We assume that the relaxation center responsible for DA approximately are independent of one another and their contribution, Arm/r,, to DA is independent of activation energy. This assumption is similar to assuming the independence of the shear transformation originating from isolated relaxation center on activation energy [7]. According to the activation energy spectrum model proposed by Gibbs et al. (8) the following equation can be used for describing DA dependence on temperature obtained at given t and T in the way of temperature scanning,
J
Ar/rl = Arm/r1 q(E) x [l - exp( - tv, exp( - E/kT))]
be re-written as
(3)
where q(E) may be regarded as the number density of the local relaxation centers with the activation energy, E, i.e. q(E) represents an activation energy spectrum. By means of a good approximation to the characteristic function, 1 - exp( - t v, exp( -E/kT)), by a step function at an energy, E, = kT ln(vat,), inducted by Gibbs et al. [8] eq.
(4)
In the derivation of eq. (4) we took into account the order of v,, obtained by Rettenmeier et al. [5] and our fitting the kinetic curves and took AT = 10 K, rr, = lo’%-‘, t2 = 120 s and dE = 0.0359 eV. The formula, E, = kT In(&) = 0.00359 T (eVK_‘) obtained by choosing Q, = 10’6s-’ and t, = 120 s has given the temperature dependence of the characteristic energy E,,. Eq. (4) implies that the temperature scanning measurement may be considered to simply produce a temperature dependent energy spectrum. This is similar to those results obtained by measuring internal friction in the way of temperature scanning [7]. Therefore, using the characteristic energy, E,, as abscissa instead of temperature coordinate, the activation energy spectrum can be evaluated through DA spectrum as a first approximation. The abscissa using E0 are shown above figs. 1 and 2. The most probable activation energy, E,, can be evaluated by the following formula: E, = kTP ln(vat,),
(5)
where TP is the temperature corresponding to the peak of the isochronal DA spectrum. As is well known, a definite most probable activation energy was obtained self-consistently by fitting isochronal spectra, as done by Rettenmeier et al. [5], and by our fitting of the kinetic curves of DA. However, noting the fact that the isochronal DA spectrum shifts to higher temperatures with decreasing t2 [4,5], we can understand that evaluating eq. (5) should bring in the following relative deviation due to small changes, ATr and At,, in TP and t,. AEJE,
dE,
E,).
= dE,,,/E, = ATP/TP + At/[
t, ln( v,&)] .
(6)
when At,= t;- t, ~0, the case of AT,>0 will appear as shown by Rettenmeier [5]. As well known from data reported by Kronmiiller [4] and Rettenmeier et al. [5], for a small change in t, ATr is a small quantity which is almost neglected. Therefore, according to eq. (6), AE,,,/E,,, also is a small quantity to be almost neglected. According
Y. Z. Zhang / Disaccommodation in Fe,, Ble _ J,
to Rettemneier’s data [5], even if a larger change, ]At, ) = 178, in t, from 180 s to 2 s, AT, for Fe,,&, and Fe7,B,, only and apFe85.zB14.89 proximately are 10, 20 and 20 K, respectively. Using these data and taking r+,= 1015 s-l we can find the relative deviation, AE,,,/E,, corresponding to this change in t, only an approximately to be 9.00, 7.31 and 7.79%, respectively. On the other hand, according to Rettenmeier’s data for f2 = 180 Fe&%, and Fe,,ks aPs [51, TP for Fe,,.,B,,,, proximately are 380, 440 and 500 K, respectively. Taking Y,,= 10” s-l and r, = 180 s we can find E, = O.O0342T, (eVK_‘). E, for these three alloys evaluated by this formula nearly are 1.30, 1.51 and 1.71 eV, respectively, which may be considered to agree with the results obtained selfconsistently by fitting isochrones [5]. Comparing the present figs. 1 and 2 with fig. 6 we can also find that E, evaluated by eq. (5) better agrees with that obtained by fitting the kinetic curve. These facts mentioned above have shown that carefully choosing v0 obtained self-consistently we may use eq. (5) for simply estimating the most probable activation energy, though the estimation will lead to a small deviation.
3. Annealing effect on DA As typical examples, the maximum relaxation intensity, (87/r,),, for Fe,,B,,C, and FegzB&, are shown in fig. 7 as a function of annealing temperature. The annealing effect similar to that shown in fig. 7 was observed on all examined alloys. As is seen, annealing below the Curie temperature, especially annealing at high enough temperature, apparently gives rise to the reduction in DA as compared to the as-quenched state. This annealing effect does not appear to be attributed to the annihilation of free volume according to analyses made in the literature [2]. This effect seems to be understood by a two-level system model (TLS) for DA proposed by Kronmtiller [9]. According to the TLS model DA is considered to results from the reorientations of the mobile atom pairs in localized relaxation centers within domain walls. In as-quenched glassay alloys, we may assume that an equidistribution exists for all two-
149
and Fe,, B,, _ x Si,
0
Fig. 7. Annealing temperature dependence of maximum DA in Fe,, BIB-,C, (x = 2,g)
level configurations of the atom pairs. The annealing below the Curie temperature would result in the re-distribution of the pair on these two levels through magnetic interactions, and this is a kinetic process. In the equilibrium distribution the population of the pairs on lower level is much more than that on higher level. Since DA results from the transition of the pairs from higher level to lower level, the reduction in the pairs on higher level is equivalent to the freezing of local degrees of freedom responsible for DA, thus leading to the obvious annealing effect.
4. Conclusions
DA in Fe,,Big_,C, and Feg,B,g_,Si, meta& glassy alloys exhibits an asymmetric spectrum with a single relaxation peak. The increase in C content gives rise to shifting of the peak temperature towards lower temperature and the reduction in the maximum relaxation intensity, whereas the effect of the replacement of B by Si is opposite to the effect of C. The activation energy for DA process exhibits an asymmetric spectrum. The most probable activation energy decreases with increasing C content, whereas the effect of the addition of Si on the energy is opposite to the effect of C. For all the examined glassy alloys DA apparently decreases due to annealing below the Curie temperature.
150
Y. Z. Zhang / Disaccommodation in Fe,, B,8 _ ,C, and Fe,,B,,
References [l] Y.Z. Zhang, Acta Metallurgica Sinica, 21 (1985) B189 (in Chinese). [2] Y.Z. Zhang, Scientia Sinica, Series A 30 (1987) 317 (in English). [3] K. Ohta and T. Matsuyama, J. Magn. Magn. Mat. 19 (1980) 165.
[4] HKronmbller,
_ $3,
J. Magn. Magn. Mat. 41 (1984) 366. [5] F. Rettenmeier, K. Kisdi-Koszo and H. Kronmiiller, Phys. Stat. Sol. (a) 93 (1986) 597. [6] J. Hesse and A. Rtibarsch, J. Phys. E 7 (1974) 526. [7] N. Morito and T. Egami, Acta Metall. 32 (1984) 603. [8] M.R.J. Gibbs, E. Evetts and J.A. Leake, J. Mater. Sci. 18 (1983) 278. [9] H. Kronmtiller, Phys. Stat. Sot. (b) 127 (1985) 531.
Materials
68 (1987) 145-150
DISACCOMMODATION PHENOMENON AND Fe,B,,_,Si, METALLIC GLASSES
145
IN Fe, B 18_ $2,
ZHANG Yan Zhong Shanghai Iron and Steel Research Institute, Received
23 December
IO5 Tai-He Road, Wu-song. Shanghai,
1986; in revised form 17 March
P.R. China
1987
The isochronal disaccommodation (DA) of the initial permeability was measured in Fe,,B,,_,C, and Fes,B,,_,Si, metallic glasses in the temperature range from 77 to 600 K. An asymmetric isochronal spectrum with a single relaxation peak was observed on each studied glassy alloy. The peak shifts to the lower temperature side with increasing C content in Fe,,BIs_XC,, whereas the influence of Si on the peak in Fes,B,s_XSi, is opposite to the effect of C. The kinetic behavior of DA was examined and the activation energy spectrum was evaluated. The replacement of B by C gives rise to the reduction of the activation energy, whereas the addition of Si increases the energy. A clearly annealing effect on DA was observed on each examined alloy.
1. Introduction
2. Experiments
Metallic glasses prepared by melt quenching are in a thermodynamically metastable state. Annealing at lower temperatures well below the glass transition temperature will give rise to relaxation in various physical properties. Of these relaxations the magnetic permeability relaxation is of great importance to practical applications. The experiments have shown that the total permeability relaxation consists of ordinary DA and continuous permeability decay [l-3]. The former is reversible with respect to demagnetization and the relaxation process can reproducibly be excited. This phenomenon is the ordinary magnetic after-effect which was earlier observed in metallic soft magnetic materials and ferrites. The latter is irreversible with respect to demagnetization, i.e. the original value of the permeability can not be recovered by demagnetization and decreases continuously. In this paper we report the experimental results of the ordinary DA in as-quenched Fe,,B,,_,C, (x = O-S) and Fes2B,,_,Si, (x = 0, 3, 5 and 8) metallic glasses, the evaluated activation energy spectrum as well as the observed annealing effect on DA.
Glassy allows were fabricated in a ribbonform using a single roller rapid quenching technique. The shape of the ribbon was 1 cm in width and about 35 pm in thickness. The diffraction pattern obtained by the conventional X-ray diffraction technique exhibited a diffused halo. The toroidal samples made of the ribbons were used for measuring the permeability relaxation. The relative change in reluctivity, r = 4a/p, between t, = 1 s and t, = 120 s after demagnetization was measured by using an automatic DA apparatus controlled by a microcomputer. The measurements of DA during heating were performed at various temperatures with interval of 5-10 K in the range from 77 to 60 K. This type of measurements is equivalent to a temperature scanning measuring. The frequency of demagnetization and magnetization were 1 and 10 kHz, respectively. The maximum amplitude of the demagnetization field and the intensity of the ac field were 4000 and 0.08 A/m, respectively. At t2 = 120 s after the first demagnetization, the repetitious demagnetization and the measurement of the reluctivity, r(t;), at ti = 1 s after the second demagnetization were
0304-8853/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
146
Y.Z. Zhang / Disaccommodation in Fea,Bls_ .C, and Fe,?B,,_ Ji,
carried out. In the case of the presence of permeability decay, r(l) # r(t;), therefore, generally speaking the ordinary DA should be defined as Ar/r, = ((r(tz) - r(Q) - (r(G) - rtt))l/r(M = (r( t2) - t( ti)]/r( ti) in order to separate DA from the total relaxation. In order to examine the kinetic process of DA, the time dependence of permeability after dema~etization was measured at 273 K, until an equilibrium value of permeability was reached. The irreversible permeability decay was not observed within the measuring time limit, thus indicating that the total relaxation only consists of DA at 273 K. In order to examine the annealing effect on DA, as-quenched samples were first annealed at various temperatures, which did not exceed 700 K, and then quenched into ice water. For a given and examined alloy the annealing temperature was below the Curie temperature of the alloy. The subsequent measurements of DA were performed in the way of temperature scanning at various temperatures up to 600 K.
Fig. 1. Isochronal DA spectrum of Fes,B,s_ $, 8) (t2 = 120 s).
(x = 2, 6 and
effect of C on DA spectrum is different from the effect of Si. 3.2. Kinetic behavior of DA and activation energy spectrum
3. Results and discussion 3.1. Isochronai DA spectrum
As a typical example, fig. 1 shows the isochronal DA spectra for as-quenched Fe,,B,,C,, Fe,,B,,C, and Fe,,B,,C,, and fig. 2 shows the The spectra spectra for Fe,,B,, and Fe,,B,,Si,. similar to those shown in figs. 1 and 2 were obtained for the other examined alloys. These spectra with a single relaxation peak are asymmetric. The spectra were broadened by increasing C and Si content, i.e. the full widths of half maximum (fwhm) of the spectra were increased. The peak temperature, TP, corresponding to the maximum DA decreases with increasing C content, i.e. the relaxation peak shifts to lower temperature. When x in Fe,,B,,_,C, increases from 6 to 8, the m~mum DA, (Ar/rt),, decreases from 0.175 to 0.1. On the contrary, the increase in x in Fe,,B,,_,Si, gives rise to the increase in TP and the change in (Ar/r,), from 0.175 to 0.33. Fig. 3 shows TP as a function of C or Si content. The facts mentioned above have indicated that the
3.2.1. Kinetic cw+veof DA A norm~~ed variation _X(7’, t ) = (FL’ cl;9/(G’ - &I) was introduced to describe the kinetic behavior of DA, wher e p,, pt and pm are the permeability at initial moment and time t after demagnetization and the equilibrium permeability, respectively. As a typical example, fig. 4 shows the kinetic curve of DA obtained at 273 K for Fe,,B,,. & cevl Q6
a72
108
f&
l&l
2.15
20
Fig. 2. Isochronal DA spectrum of Fes2B1s_xSix (x = 0 and 8) (tl = 120 s).
Y. Z. Zhang / Disaccommodation
Fig. 3. Composition dependence of peak temperature DA spectrum. (0) Fe,,B,8_xSi,, (0) Fe,,B,,_,C,.
TP on
The part of the curve for longer time than 104s is not shown in fig. 4. The curves similar to that shown in fig. 4 were obtained on the other examined glassy alloys. These curves shift right and left as a function of C or Si content. As can be seen from fig. 4, the main part of the kinetic curve nearly exhibits lnt kinetic behavior. 3.2.2, Activation kinetic data
enera
spectrum
evaluated
by
Such curves as that shown in fig. 4 can be fitted making use of the following equation: X(T, t) = /P(ln
~)[l-
exp(-t/T)]
(1)
d In 7,
where P(ln 7) is a distribution function for relaxation time 7. Taking account of the equation In 7 = E/kT - In v,, for thermal activation process, we can write eq. (1) as
x(T, ~)=JQ(E)[~-exp(-ho X exp( - E/kT))]
dE/kT,
in Fe,B,,_
,C, and Fe,B,,
_ xSi,
147
Debye frequency. However v. was found to be of order of 10’5-10’7 s-l by fitting the isochronal DA spectra for Fe-B metallic glasses [4,5]. It is considered that a large frequency factor is attributed to a small entropy factor exp( - S/k), i.e. to a large hopping entropy [4,5]. Regarding v, as a fitting constant and carefully choosing it in the range of 10’2-1017 s-l, we can obtain a numerical solution of eq. (2) by using Hesse-Rubartsch’s method [6], thus evaluating activation energy spectrum. The detailed account can be found elsewhere [1,2]. Careful calculations have shown that the satisfactory results for all examined glassy alloys were obtained by choosing v, of (1.64-4.83) X 10’6s-‘. The activation energy spectrum obtained for Fe,,B,, by choosing v. of 2.67 x 10’6s-’ is shown in fig. 5 as a typical example. The most probable activation energy Em, of Fe,,B,, obtained from fig. 5 approximately is 1.4 eV, which approximates the energy for and Fe,,B,, obtained by Rettenmeier Fess,Bi4.s [5]. The spectra similar to that in fig. 5 were obtained for all the examined alloys. The features of these spectra are the asymmetry and the more clear probability distribution in lower energy range. The most probable activation energy, Em, obtained from the spectrum are shown in fig. 6 as a function of C or Si content. The difference in the effects of C and Si on E,,, can be seen from fig. 6. E, decreases with increase in C, whereas the effect of Si is opposite to that of C.
(2)
where Q(E) represents an activation energy spectrum; k is Boltzmann’s constant; v. is a frequency factor, in general, which should be of order of the
IOr
I
I
P
Uil
10'
I
f.5
IN11111
4
IO'
11111,1
1
,
,,,,,L
Id
Fig. 4. Kinetic curve of DA in Fe,,B18 measured at 2.73 K.
lo’
0.4
cl8
1.2
E Lew
I
,_I
1.6
Fig. 5. Activation energy spectrum of DA process in Fe,,B18.
148
Y. 2. Zhang / Disaccommodation in Fee2 Bl 8 _ ,C, and Fe,, B,, _ x Si,
(3) can approximately
I.7
Ar/rl = 0.0359( Ar,/r,)q(
-1.6 -15 - 14
1.0 0
I 2
I 4
X
I 6
I r3
10
Fig. 6. Composition dependence of the most probable activation energy of DA process. (a) Fes2B,s_,Cx, Si,.
(0)
Fes2BIs_,
3.2.3.
Evaluation by activation energy spectrum model We assume that the relaxation center responsible for DA approximately are independent of one another and their contribution, Arm/r,, to DA is independent of activation energy. This assumption is similar to assuming the independence of the shear transformation originating from isolated relaxation center on activation energy [7]. According to the activation energy spectrum model proposed by Gibbs et al. (8) the following equation can be used for describing DA dependence on temperature obtained at given t and T in the way of temperature scanning,
J
Ar/rl = Arm/r1 q(E) x [l - exp( - tv, exp( - E/kT))]
be re-written as
(3)
where q(E) may be regarded as the number density of the local relaxation centers with the activation energy, E, i.e. q(E) represents an activation energy spectrum. By means of a good approximation to the characteristic function, 1 - exp( - t v, exp( -E/kT)), by a step function at an energy, E, = kT ln(vat,), inducted by Gibbs et al. [8] eq.
(4)
In the derivation of eq. (4) we took into account the order of v,, obtained by Rettenmeier et al. [5] and our fitting the kinetic curves and took AT = 10 K, rr, = lo’%-‘, t2 = 120 s and dE = 0.0359 eV. The formula, E, = kT In(&) = 0.00359 T (eVK_‘) obtained by choosing Q, = 10’6s-’ and t, = 120 s has given the temperature dependence of the characteristic energy E,,. Eq. (4) implies that the temperature scanning measurement may be considered to simply produce a temperature dependent energy spectrum. This is similar to those results obtained by measuring internal friction in the way of temperature scanning [7]. Therefore, using the characteristic energy, E,, as abscissa instead of temperature coordinate, the activation energy spectrum can be evaluated through DA spectrum as a first approximation. The abscissa using E0 are shown above figs. 1 and 2. The most probable activation energy, E,, can be evaluated by the following formula: E, = kTP ln(vat,),
(5)
where TP is the temperature corresponding to the peak of the isochronal DA spectrum. As is well known, a definite most probable activation energy was obtained self-consistently by fitting isochronal spectra, as done by Rettenmeier et al. [5], and by our fitting of the kinetic curves of DA. However, noting the fact that the isochronal DA spectrum shifts to higher temperatures with decreasing t2 [4,5], we can understand that evaluating eq. (5) should bring in the following relative deviation due to small changes, ATr and At,, in TP and t,. AEJE,
dE,
E,).
= dE,,,/E, = ATP/TP + At/[
t, ln( v,&)] .
(6)
when At,= t;- t, ~0, the case of AT,>0 will appear as shown by Rettenmeier [5]. As well known from data reported by Kronmiiller [4] and Rettenmeier et al. [5], for a small change in t, ATr is a small quantity which is almost neglected. Therefore, according to eq. (6), AE,,,/E,,, also is a small quantity to be almost neglected. According
Y. Z. Zhang / Disaccommodation in Fe,, Ble _ J,
to Rettemneier’s data [5], even if a larger change, ]At, ) = 178, in t, from 180 s to 2 s, AT, for Fe,,&, and Fe7,B,, only and apFe85.zB14.89 proximately are 10, 20 and 20 K, respectively. Using these data and taking r+,= 1015 s-l we can find the relative deviation, AE,,,/E,, corresponding to this change in t, only an approximately to be 9.00, 7.31 and 7.79%, respectively. On the other hand, according to Rettenmeier’s data for f2 = 180 Fe&%, and Fe,,ks aPs [51, TP for Fe,,.,B,,,, proximately are 380, 440 and 500 K, respectively. Taking Y,,= 10” s-l and r, = 180 s we can find E, = O.O0342T, (eVK_‘). E, for these three alloys evaluated by this formula nearly are 1.30, 1.51 and 1.71 eV, respectively, which may be considered to agree with the results obtained selfconsistently by fitting isochrones [5]. Comparing the present figs. 1 and 2 with fig. 6 we can also find that E, evaluated by eq. (5) better agrees with that obtained by fitting the kinetic curve. These facts mentioned above have shown that carefully choosing v0 obtained self-consistently we may use eq. (5) for simply estimating the most probable activation energy, though the estimation will lead to a small deviation.
3. Annealing effect on DA As typical examples, the maximum relaxation intensity, (87/r,),, for Fe,,B,,C, and FegzB&, are shown in fig. 7 as a function of annealing temperature. The annealing effect similar to that shown in fig. 7 was observed on all examined alloys. As is seen, annealing below the Curie temperature, especially annealing at high enough temperature, apparently gives rise to the reduction in DA as compared to the as-quenched state. This annealing effect does not appear to be attributed to the annihilation of free volume according to analyses made in the literature [2]. This effect seems to be understood by a two-level system model (TLS) for DA proposed by Kronmtiller [9]. According to the TLS model DA is considered to results from the reorientations of the mobile atom pairs in localized relaxation centers within domain walls. In as-quenched glassay alloys, we may assume that an equidistribution exists for all two-
149
and Fe,, B,, _ x Si,
0
Fig. 7. Annealing temperature dependence of maximum DA in Fe,, BIB-,C, (x = 2,g)
level configurations of the atom pairs. The annealing below the Curie temperature would result in the re-distribution of the pair on these two levels through magnetic interactions, and this is a kinetic process. In the equilibrium distribution the population of the pairs on lower level is much more than that on higher level. Since DA results from the transition of the pairs from higher level to lower level, the reduction in the pairs on higher level is equivalent to the freezing of local degrees of freedom responsible for DA, thus leading to the obvious annealing effect.
4. Conclusions
DA in Fe,,Big_,C, and Feg,B,g_,Si, meta& glassy alloys exhibits an asymmetric spectrum with a single relaxation peak. The increase in C content gives rise to shifting of the peak temperature towards lower temperature and the reduction in the maximum relaxation intensity, whereas the effect of the replacement of B by Si is opposite to the effect of C. The activation energy for DA process exhibits an asymmetric spectrum. The most probable activation energy decreases with increasing C content, whereas the effect of the addition of Si on the energy is opposite to the effect of C. For all the examined glassy alloys DA apparently decreases due to annealing below the Curie temperature.
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Y. Z. Zhang / Disaccommodation in Fe,, B,8 _ ,C, and Fe,,B,,
References [l] Y.Z. Zhang, Acta Metallurgica Sinica, 21 (1985) B189 (in Chinese). [2] Y.Z. Zhang, Scientia Sinica, Series A 30 (1987) 317 (in English). [3] K. Ohta and T. Matsuyama, J. Magn. Magn. Mat. 19 (1980) 165.
[4] HKronmbller,
_ $3,
J. Magn. Magn. Mat. 41 (1984) 366. [5] F. Rettenmeier, K. Kisdi-Koszo and H. Kronmiiller, Phys. Stat. Sol. (a) 93 (1986) 597. [6] J. Hesse and A. Rtibarsch, J. Phys. E 7 (1974) 526. [7] N. Morito and T. Egami, Acta Metall. 32 (1984) 603. [8] M.R.J. Gibbs, E. Evetts and J.A. Leake, J. Mater. Sci. 18 (1983) 278. [9] H. Kronmtiller, Phys. Stat. Sot. (b) 127 (1985) 531.