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Hydrogen mobility in the amorphous alloy Fe40Ni40P14B6 as studied by induced magnetic anisotropy measurements
Scripta
METALLURGICA
Vol. 18, pp. P r i n t e d in
29-33, 1984 the U . S . A .
P e r g a m o n P r e s s Ltd. All rights reserved
HYDROGEN MOBILITY IN THE AMORPHOUS ALLOY F e Ni P B AS STUDIED BY INDUCED MAGNETIC ANISOTROPY t ~ S U ~ M ~ T ~ W. CHAMBRON, F. LAN~ON AND A. CHAMBEROD Centre d'Etudes Nucl~aires de Grenoble, D~partement de Recherche Fondamentale, Section de Physique du Solide, 85 X - 38041 - Grenoble Cedex (France) ( R e c e i v e d J u l y 17, 1 9 8 3 ) ( R e v i s e d O c t o b e r 31, 1 9 8 3 )
Introduction As it has been shown by several authors (I-4), hydrogen can be dissolved in various amorphous metallic alloys and causes an internal friction peak. This phenomenon has been explained in terms of stress-induced dipole reorientation in analogy to the well known Snoek-effect in crystalline metals and alloys. On the other hand, Berry and Pritchet (5) have pointed out that the very large "AE-effect" observed in the ferromagnetic amorphous alloys disappears when these alloys are charged with hydrogen. That denotes, according to the authors, a strong interaction of the hydrogen atoms with the Bloch walls. This pinning suggests the existence of a magnetic anisotropy induced locally by a redistribution of the hydrogen "interstitials", according to the mechanism well established in crystals (6). Let us remember here that an induced magnetic anisotropy (IMA) of that type has been observed in the amorphous alloy Fe~.B.~ ~Si^ ~C_, due to the redistribution of the • 3 J D Z . . carbon interstitial a t o m s ( 7 ) . T h l s p a p e r s h o w s ~ a ~ t~e s~me p h e n o m e n o n I s d u e t o h y d r o g e n ~n t h e amorphous alloy Fe4oNi4oPI4B6. Experimental I. S a m p l e s . We h a v e u s e d t h e a m o r p h o u s a l l o y F e . N i . P B. s u p p l i e d by A l l i e d C h e m i c a l C o r _.40 40,14 o .. poration~as 2826) as a thin ribbon (50 ~m). ~ne samples are clscs cut from the ribbon. To evaluate the influence of the structural relaxation, two series of experiments have been performed the first one with the alloy in the as-received condition, and the other one after an anneal of 30 min at 633 K, just below the crystallisation temperature. For comparison, we have also studied the crystalline alloy Fe2oNiso ; the ingot was rolled at room temperature down to O.Z mm, then recrystallised by anneali~g ~Br l h at l[48 K. 2. Hydrogen charging. Two methods have been used : a) with gaseous hydrogen. After an anneal at 593 K under hydrogen at atmospheric pressure, the samples contain a hydrogen concentration, CH, of about IO-4 per atom (C is expressed in comparison with both metal and metalloldatoms as a whole). Such a concentratio H corresponds to the limit of detection by IMA measurements. On the other hand, no significant hydrogen penetration has been observed in an annealed sample kept under 16 MPa for a week at 300 K. But, if the sample has been etched or mechanically polished, a concentration of about 6 x |O-2 at % was observed. Therefore, there exists at the surface of the as-received amorphous ribbon a barrier which inhibits hydrogen penetration, a phenomenon already reported (4). b) by cathodic charging. Electrolysis was made in a solution of H2S04, 0.9 N, at 313 K, saturated with CS~, which is a poison for the recombination of H ions. The current density was from l to 6 mA/~m 2 and charging time from ] to 6 hours. With this method the hydrogen concentration can reach 2 at. %. 3. H~drogen concentration measurements. Hydrogen introduced by either method goes slowly out of the sample at room temperature (time-constant about ]OO hours). But, as soon as the sample is heated, hydrogen goes out quickly - a few minutes at 440 K, for instance. Then, it is easy to measure the hydrogen concentration by heating the sample in a small cavity of about I cm 3 connected with a mercury column initiall~ under vacuum. Volume and pressure of the desorbed gas are measured. The accuracy is about lO-I mole, corresponding to a hydrogen concentration of lO-2 at. % with the samples used.
29 0036-9748/84 $ 3 . 0 0 + .00 Copyright (c) 1984 P e r g a m o n P r e s s
Ltd.
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HYDROGEN MOBILITY IN AHORPHOUS Fe40Ni40P14B6
Vol.
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4. Magnetic anisotropy measurement. The magnetic anisotropy is measured by means of an automatic torque magnetometer, with an accuracy of 0.| J/m 3. It is deduced from the curve F(e), being the torque acting on the sample when the magnetic field (0.34 T) is applied in the direction e (the angle e is referred to a fixed direction on the sample). F ( ~ is the derivative of the magnetic anisotropy energy : r(e)
: - ~w(e)
/ ~e.
The F measurements are performed at ]03 K. The thermomagnetic treatments (TMT) are performed in situ, in the torque magnetometer. Results I. Induced magnetic anisotropy. When a hydrogen-charged sample is cooled in a magnetic field from room temperature to 103 K,.the IMA, measured at 103 K, is of the form dF(e) = - K
sin 2 ( G - O
) = AA sin 2 0 +
U
AB cos 2e,
(I)
O
with AA = - K u cos 20 o I
AB = K u sin 28 o.
(2)
e characterizes the position of the magnetic field applied during cooling, and O defines its O . . posztlon during the torque measurement. A and B are the coefficients of sin 28 and cos 20 in the Fourier series development of F(O) ; AA and AB are the variations of these coefficients because of the IMA. This IMA is uniaxial with the axis of easy magnetization along the direction e . O
Fe4oNi4oP~ I ~
Fe4o Ni4ol:~. Be A As- received
Mo
180 _o Anneoled
-50
A . ,
/ ~
~zOmin, 6 3 3 K / /
I0
'E
m
50
v
i
IO
B(; -
M1
? E
-I00
v
-150
I 200
Aoll 250
I 500 A (J.m-3)
FIG. I Representation of the figurative point M whose coordinates, A and B, are the coefficients of sin 2e and cos 2@, respectively, in the Fourier series development of the anisotropy torque. The experimental points (open circles) correspond to different directions of the magnetic field applied during TMT : for instance, M is the representative point of the IMA o~tained after cooling under magnetic field set along G^ = 40 °, and M|oiS the asymptotic value after anneaYing when ~ = .
14(
0
0.01 OH
0.02 (at.)
o
FIG. 2 Plot of the IMA energy, K , and • U of the temperature, T _ . , at whlch ~ = 0.5 " U.D (C .f. Fig. 3), VS hydrogen concentration, CH •
If the sample is further heated at 233 K (a temperature too low to modify the hydrogen concentration), then cooled again under a magnetic field directed along another direction, one
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observes a new IMA, still of the form (]). This shows the perfect reversibility of the phenomenon. Thus, for example, we have plotted (Fig. |) the coordinates A and B of the point M when the experiment was repeated with different values of ~ . The sample used was as-received. When • . • O. . O changes, the flguratlve polnt clearly describes a czrcle of center (A , B ) and of radlus K = V A A 2 + AB 2 (c.f. equations (2)). Therefore, the anisotropy energ~ density, K (radius of the . . . . . . . . U clrcle), Is independent of the dlrectlon e of the fleld applled durlng the coollng ; thls property is true also for the annealed sample~. No meaning is attached to the values A and Bo, • O coordinates of the circle center, because they include not only the alloy anlsotropy in the absence of IMA but also all the parasite anisotropies, in particular that of the sample holder. Fig. 2 represents the variation of K u with CH. It appears that, for the same concentration, ~u is the same in the as-received and annealed samples. This curve can be used to deduce CH from u for measurements made in situ in the torque magnetometer, without removing hydrogen from the sample. 2. IMA rotation kinetics. The IMA magnitude due to hydrogen does not depend on the TMT direction. Thus it is possible to study the IMA rotation. The principle of the method is the same as the one used to study the directional order (8) or the carbon mobility (7). The initial state is obtained by cooling from 233 K to |30 K under a magnetic field oriented along C (in general 40°). The IMA is then described by equation (|) and represented by M on Fig. l°i O
_1.0
Fe4o Ni4.o P14 Be
~ d
~0.50 h
~
0
.
4
30rain,633 K
5
O
<
OAO 100
150
200 Temper~ure (K)
0
I
0.005
0.010 C.
FIG. 3
I
0.015
(at.)
FIG. 4
Kinetics of variations of B (the coefficient of cos 2C in the torque Fourier series development) during an isochronal TMT (5 K/IO min) : a) crystalline alloy Fe2oNiso ; b) amorphous alloy Fe4oNi4oP|4B6 (as-received) ; c)d)e) same amorphous alloy annealed 30 min, 633 K ; f) calculated curve with a unique time-constant T = T exp (AE/kT) o (T = ]O-IJs, AE = 0.5 eV).
Activation energy variation of hydrogen mobility, AE, as a function of hydrogen concentration, CH ; these values are de duced from Fig. 2, assuming that AE is proportional to TO. 5.
o
We have B. = B 1
+ K O
sin 2@ . U
O
Afterwards, isochronal (5K/|O min) TMT are performed under a magnetic field set along the direction Cof = O ; the asymptotic state is then represented by the point M] (Fig. l), and we have B = B° . Fig. 3 shows the evolution of the parameter ~ = (B - B i) / ( B
- Bi).
The variation of ~ characterizes the IMA rotation kinetics. Considering the curves o(T), we can deduce that : a) In both crystalline Fe2oNiso and amorphous Fe4oNi4oPI4B 6 (as-received or anneale~ alloys the IMA rotation takes place in one stage only, but this stage is much wider in the amorphous material than in the crystal, indicating a large distribution of time-constants. b) In the amorphous alloy, the curve ~(T) shifts towards low temperatures when C H increases,
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showing that the IMA rotation is faster ; in the crystalline alloy, the curve depends very little on CHc) F o r t h e same CH, t h e r o t a t i o n amorphous alloy.
is
slightly
faster
in the as-received
These results a r e s u m m a r i z e d on F i g . 2 w h e r e t h e v a r i a t i o n o ffi 0 . 5 ) a r e r e p o r t e d a s a f u n c t i o n o f CH-
than in the annealed
o f TO. 5 ( t e m p e r a t u r e
at which
Discussion The correlation between K and C. (Fig. 2) shows that the IMA observed is due to hydrogen d ~ solved in the amorphous alloyU; on t~e other hand, the proportionality of K to CH, as observed for the small values of CH, means that the effect ought to be attributed toUhydrogen atoms considered separately ; if IMA were due to hydrogen di-interstitials we should have K u % C~. The analogy with the crystalline alloy (Fig. 3) leads us to propose a similar model (6). According to that model, the introduced hydrogen atoms go into interstitial sites with a low symmetry. In crystalline Fe-Ni alloys, hydrogen interstitials fill octahedral sites, the anisotropy of which is related essentially to the nature of each of the 6 nearest neighbour atoms (6). In the amorphous alloy, an "interstitial" site presents the same kind of anisotropy, so-called "chemical" or "compositional", but it presents also an anisotropy of "topological" origin, due to the geometric position of the neighbours. Let us consider an interstitial site with a well defined chemical or topological environment ; such sites exist in the amorphous material with all the possible "orientations". The energy of an interstitial located in such a site depends a little on the site orientation with respect to the magnetization. If temperature is high enough so that interstitials jump from one site to another, they occupy preferably the sites with the orientation corresponding to a lower energy and that causes the IMA. Therefore, the time required for the setting up of the IMA is practically the time necessary for an interstitial to jump from one site to another. The study of the amorphous alloy shows the following peculiarities
:
• a) One can infer from the broadening of the curves (Fig. 3) that the IMA sets up a wide time-constant distribution in the amorphous alloy. For comparison, we have drawn on the same figure the Gurve O(T) which we obtained with a unique time-constant T ffi T exp (AE/kT), taking T ffi lO-13s and AE ffi0.5 eV. The AE distribution which accounts for theUcurves o(T) measured in t~e amorphous alloy is ± 0.08 eV, while in the crystalline alloy Fe2oNi80 , ± 0.035 eV is sufficient (not taking into account a possible distribution of the preexpo-nential factors, To). This distribution of the potential barriers in an amorphous alloy is not surprising. b) In the amorphous alloy, the curve ~(T) shifts towards low temperatures when C H increases, while this effect does not exist in the crystalline alloy. Assuming that only a variation of the mean activation energy, AE, is responsible for the effect, and that AE is proportional to T O ~, AE can be estimated in the amorphous material by comparison to the value in the crystalline a ~ o y , 0.35 eV (6). Fig. 4 shows the dE variations vs C H. These results are in qualitative agreement with prior works : - Berry and Pritchet have estimated the hydrogen migration energy in the amorphous alloy Fe4oNi4oPI4B 6 to be 0.5 eV, from the internal friction peak location (5). This value is comparable t o ours. - Lin and Johnson (9) have determined the hydrogen solubility and diffusivity in this same alloy. Thus, under a pressure of 105 Pa, the solubility C H is between 3 and 5 x 10 -5 ; it does not depend significantly on temperature. Between |03 and |O 5 Pa, it obeys Sievert's law. Extrapolating this law to the pressure which we have used (16 MPa), C H would be between 3.8 and 6.3xI0-~ values quite in agreement with our result (6 x IO-4). Also, Lin and Johnson firda diffusivity activation energy of 0.49 eV, a value close to our result for small C H (Fig. 4). - From the width of the internal friction peak, Berry and Pritchet have estimated the distribution of the activation energies to be (+ 0.057/-0.092 eV) for the alloy Pd8oSi20 (4). Such a width is quite comparable with the one we find in Fe4oNi4oP|4B 6. - All the authors observe a shift of the internal friction peak with C H (|,3), whatever the amorphous alloy studied. To explain the increase in hydrogen mobility when C H increases, Agyeman et el. (|) have suggested that the energy of a dissolved hydrogen atom depends strongly cnthetypeofsite where it is
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located (i.e. composition and topology of the neighbourhood). When C~ increases, the sites of lower energy are first filled. Kirchheim et al. (I0, 11) have used thi~ model quantitatively, showing that the hydrogen interstitials have an energy distributed according to Fermi-Dirac statistics (considering that an interstitial site can contain only one hydrogen atom) ; thus, after (10, 11), ~(E) being the concentration of sites where an interstitial would have the energy E, the concentration of hydrogen atoms (occupied sites) having the energy E is written : F(E) = ~(E) /(I + exp ~ k - ~ ) is the "Fermi energy" of the interstitials. It rises with C H as hydrogen fills in the interstitial sites• Clearly the interstitials having E << D do not contribute to the IMA, because the sites are all occupied, whatever their orientation is, and the magnetic coupling cannot modify the interstitial distribution on these sites• Also, those with E >> ~ have too small a concentration. Thus, only the interstitials with an energy close to ~ contribute to the IMA. The kinetics of establishment, or rotation, of the IMA, are governed by a potential barrier the height of w h ~ h is, on the average, AE = E - ~ (E is the mean energy of an interstitial in saddle position) ; S . S therefore, AE decreases when ~ increases. c) Influence of the structural relaxation: Fig. 2 shows that K (CH) is identical for both • U ° the as-received and annealed alloys. Thls result suggests that the structural relaxatlon should modify only slightly the local arrangement of the atoms around the interstitial sites. But the hydrogen mobility, at equal concentration, is a little weaker in the annealed alloy. Lin and Johnson have obtained a similar result (9). This may result from a very small increase in the saddle point energy (+ O.O1 eV). Conclusion The hydrogen mobility in the amorphous alloy Fe. Ni. PI.B- has been studied by following the . . . . 4 40 4 6 . . . IMA kinetics• It increases slgnlflcantly when the hydrogen concentratlon increases. Thls effect is well accounted for by assuming that hydrogen locates in "interstitial" sites having widely distributed energies, and that the filling starts with the deepest ones. The neighbourhood of active sites is not much affected by the structural relaxation, since the IMA energy is practically unchanged by the annealing. References I. 2.
3. 4. 5. 6. 7. 8. 9. I0. 11.
K. Agyeman, E. Armbruster, H.U. KGnzi, A. Das Gupta and H.J. G~ntherodt, J. Phys. 42, C5-535 (1981) H.U. KHnzi, E. Armbruster and H.J. G~ntherodt, Proceedings of the 4th International Conference on Rapidly Quenched Metals, ed. by T. Masumoto and K. Suzuki (The Japan Institute of Metals, Sendal) p. 1653 (1982) B.S. Berry and W.C. Pritchet, Scripta Met. 15, 637 (1981) B.S. Berry and W.C. Pritchet, Phys. Rev. B, 24, 2299 (1981) B.S. Berry and W.C. Pritchet, J. Appl. Phys. 52, 1865 (1981) E. Adler and C. Radeloff, J. Appl. Phys. 40, 1526 (1969) W. Chambron, F. LanGon and A. Chamberod, J. Phys. Lettres 43, L-55 (1982) W. Chambron and A. Chamberod, Solid State Con~mum. 33, 157 (]-980) R.W. Lin and H.H. Johnson, J. Non-crystalline SolTds 51, 45 (1982) R. Kirchheim, F. Sormer and G. Schluckebier, Acta Met. 30, 1059 (1982) R. Kirchheim, Acta Met. 30, 1069 (1982)
METALLURGICA
Vol. 18, pp. P r i n t e d in
29-33, 1984 the U . S . A .
P e r g a m o n P r e s s Ltd. All rights reserved
HYDROGEN MOBILITY IN THE AMORPHOUS ALLOY F e Ni P B AS STUDIED BY INDUCED MAGNETIC ANISOTROPY t ~ S U ~ M ~ T ~ W. CHAMBRON, F. LAN~ON AND A. CHAMBEROD Centre d'Etudes Nucl~aires de Grenoble, D~partement de Recherche Fondamentale, Section de Physique du Solide, 85 X - 38041 - Grenoble Cedex (France) ( R e c e i v e d J u l y 17, 1 9 8 3 ) ( R e v i s e d O c t o b e r 31, 1 9 8 3 )
Introduction As it has been shown by several authors (I-4), hydrogen can be dissolved in various amorphous metallic alloys and causes an internal friction peak. This phenomenon has been explained in terms of stress-induced dipole reorientation in analogy to the well known Snoek-effect in crystalline metals and alloys. On the other hand, Berry and Pritchet (5) have pointed out that the very large "AE-effect" observed in the ferromagnetic amorphous alloys disappears when these alloys are charged with hydrogen. That denotes, according to the authors, a strong interaction of the hydrogen atoms with the Bloch walls. This pinning suggests the existence of a magnetic anisotropy induced locally by a redistribution of the hydrogen "interstitials", according to the mechanism well established in crystals (6). Let us remember here that an induced magnetic anisotropy (IMA) of that type has been observed in the amorphous alloy Fe~.B.~ ~Si^ ~C_, due to the redistribution of the • 3 J D Z . . carbon interstitial a t o m s ( 7 ) . T h l s p a p e r s h o w s ~ a ~ t~e s~me p h e n o m e n o n I s d u e t o h y d r o g e n ~n t h e amorphous alloy Fe4oNi4oPI4B6. Experimental I. S a m p l e s . We h a v e u s e d t h e a m o r p h o u s a l l o y F e . N i . P B. s u p p l i e d by A l l i e d C h e m i c a l C o r _.40 40,14 o .. poration~as 2826) as a thin ribbon (50 ~m). ~ne samples are clscs cut from the ribbon. To evaluate the influence of the structural relaxation, two series of experiments have been performed the first one with the alloy in the as-received condition, and the other one after an anneal of 30 min at 633 K, just below the crystallisation temperature. For comparison, we have also studied the crystalline alloy Fe2oNiso ; the ingot was rolled at room temperature down to O.Z mm, then recrystallised by anneali~g ~Br l h at l[48 K. 2. Hydrogen charging. Two methods have been used : a) with gaseous hydrogen. After an anneal at 593 K under hydrogen at atmospheric pressure, the samples contain a hydrogen concentration, CH, of about IO-4 per atom (C is expressed in comparison with both metal and metalloldatoms as a whole). Such a concentratio H corresponds to the limit of detection by IMA measurements. On the other hand, no significant hydrogen penetration has been observed in an annealed sample kept under 16 MPa for a week at 300 K. But, if the sample has been etched or mechanically polished, a concentration of about 6 x |O-2 at % was observed. Therefore, there exists at the surface of the as-received amorphous ribbon a barrier which inhibits hydrogen penetration, a phenomenon already reported (4). b) by cathodic charging. Electrolysis was made in a solution of H2S04, 0.9 N, at 313 K, saturated with CS~, which is a poison for the recombination of H ions. The current density was from l to 6 mA/~m 2 and charging time from ] to 6 hours. With this method the hydrogen concentration can reach 2 at. %. 3. H~drogen concentration measurements. Hydrogen introduced by either method goes slowly out of the sample at room temperature (time-constant about ]OO hours). But, as soon as the sample is heated, hydrogen goes out quickly - a few minutes at 440 K, for instance. Then, it is easy to measure the hydrogen concentration by heating the sample in a small cavity of about I cm 3 connected with a mercury column initiall~ under vacuum. Volume and pressure of the desorbed gas are measured. The accuracy is about lO-I mole, corresponding to a hydrogen concentration of lO-2 at. % with the samples used.
29 0036-9748/84 $ 3 . 0 0 + .00 Copyright (c) 1984 P e r g a m o n P r e s s
Ltd.
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HYDROGEN MOBILITY IN AHORPHOUS Fe40Ni40P14B6
Vol.
18, No. 1
4. Magnetic anisotropy measurement. The magnetic anisotropy is measured by means of an automatic torque magnetometer, with an accuracy of 0.| J/m 3. It is deduced from the curve F(e), being the torque acting on the sample when the magnetic field (0.34 T) is applied in the direction e (the angle e is referred to a fixed direction on the sample). F ( ~ is the derivative of the magnetic anisotropy energy : r(e)
: - ~w(e)
/ ~e.
The F measurements are performed at ]03 K. The thermomagnetic treatments (TMT) are performed in situ, in the torque magnetometer. Results I. Induced magnetic anisotropy. When a hydrogen-charged sample is cooled in a magnetic field from room temperature to 103 K,.the IMA, measured at 103 K, is of the form dF(e) = - K
sin 2 ( G - O
) = AA sin 2 0 +
U
AB cos 2e,
(I)
O
with AA = - K u cos 20 o I
AB = K u sin 28 o.
(2)
e characterizes the position of the magnetic field applied during cooling, and O defines its O . . posztlon during the torque measurement. A and B are the coefficients of sin 28 and cos 20 in the Fourier series development of F(O) ; AA and AB are the variations of these coefficients because of the IMA. This IMA is uniaxial with the axis of easy magnetization along the direction e . O
Fe4oNi4oP~ I ~
Fe4o Ni4ol:~. Be A As- received
Mo
180 _o Anneoled
-50
A . ,
/ ~
~zOmin, 6 3 3 K / /
I0
'E
m
50
v
i
IO
B(; -
M1
? E
-I00
v
-150
I 200
Aoll 250
I 500 A (J.m-3)
FIG. I Representation of the figurative point M whose coordinates, A and B, are the coefficients of sin 2e and cos 2@, respectively, in the Fourier series development of the anisotropy torque. The experimental points (open circles) correspond to different directions of the magnetic field applied during TMT : for instance, M is the representative point of the IMA o~tained after cooling under magnetic field set along G^ = 40 °, and M|oiS the asymptotic value after anneaYing when ~ = .
14(
0
0.01 OH
0.02 (at.)
o
FIG. 2 Plot of the IMA energy, K , and • U of the temperature, T _ . , at whlch ~ = 0.5 " U.D (C .f. Fig. 3), VS hydrogen concentration, CH •
If the sample is further heated at 233 K (a temperature too low to modify the hydrogen concentration), then cooled again under a magnetic field directed along another direction, one
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observes a new IMA, still of the form (]). This shows the perfect reversibility of the phenomenon. Thus, for example, we have plotted (Fig. |) the coordinates A and B of the point M when the experiment was repeated with different values of ~ . The sample used was as-received. When • . • O. . O changes, the flguratlve polnt clearly describes a czrcle of center (A , B ) and of radlus K = V A A 2 + AB 2 (c.f. equations (2)). Therefore, the anisotropy energ~ density, K (radius of the . . . . . . . . U clrcle), Is independent of the dlrectlon e of the fleld applled durlng the coollng ; thls property is true also for the annealed sample~. No meaning is attached to the values A and Bo, • O coordinates of the circle center, because they include not only the alloy anlsotropy in the absence of IMA but also all the parasite anisotropies, in particular that of the sample holder. Fig. 2 represents the variation of K u with CH. It appears that, for the same concentration, ~u is the same in the as-received and annealed samples. This curve can be used to deduce CH from u for measurements made in situ in the torque magnetometer, without removing hydrogen from the sample. 2. IMA rotation kinetics. The IMA magnitude due to hydrogen does not depend on the TMT direction. Thus it is possible to study the IMA rotation. The principle of the method is the same as the one used to study the directional order (8) or the carbon mobility (7). The initial state is obtained by cooling from 233 K to |30 K under a magnetic field oriented along C (in general 40°). The IMA is then described by equation (|) and represented by M on Fig. l°i O
_1.0
Fe4o Ni4.o P14 Be
~ d
~0.50 h
~
0
.
4
30rain,633 K
5
O
<
OAO 100
150
200 Temper~ure (K)
0
I
0.005
0.010 C.
FIG. 3
I
0.015
(at.)
FIG. 4
Kinetics of variations of B (the coefficient of cos 2C in the torque Fourier series development) during an isochronal TMT (5 K/IO min) : a) crystalline alloy Fe2oNiso ; b) amorphous alloy Fe4oNi4oP|4B6 (as-received) ; c)d)e) same amorphous alloy annealed 30 min, 633 K ; f) calculated curve with a unique time-constant T = T exp (AE/kT) o (T = ]O-IJs, AE = 0.5 eV).
Activation energy variation of hydrogen mobility, AE, as a function of hydrogen concentration, CH ; these values are de duced from Fig. 2, assuming that AE is proportional to TO. 5.
o
We have B. = B 1
+ K O
sin 2@ . U
O
Afterwards, isochronal (5K/|O min) TMT are performed under a magnetic field set along the direction Cof = O ; the asymptotic state is then represented by the point M] (Fig. l), and we have B = B° . Fig. 3 shows the evolution of the parameter ~ = (B - B i) / ( B
- Bi).
The variation of ~ characterizes the IMA rotation kinetics. Considering the curves o(T), we can deduce that : a) In both crystalline Fe2oNiso and amorphous Fe4oNi4oPI4B 6 (as-received or anneale~ alloys the IMA rotation takes place in one stage only, but this stage is much wider in the amorphous material than in the crystal, indicating a large distribution of time-constants. b) In the amorphous alloy, the curve ~(T) shifts towards low temperatures when C H increases,
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showing that the IMA rotation is faster ; in the crystalline alloy, the curve depends very little on CHc) F o r t h e same CH, t h e r o t a t i o n amorphous alloy.
is
slightly
faster
in the as-received
These results a r e s u m m a r i z e d on F i g . 2 w h e r e t h e v a r i a t i o n o ffi 0 . 5 ) a r e r e p o r t e d a s a f u n c t i o n o f CH-
than in the annealed
o f TO. 5 ( t e m p e r a t u r e
at which
Discussion The correlation between K and C. (Fig. 2) shows that the IMA observed is due to hydrogen d ~ solved in the amorphous alloyU; on t~e other hand, the proportionality of K to CH, as observed for the small values of CH, means that the effect ought to be attributed toUhydrogen atoms considered separately ; if IMA were due to hydrogen di-interstitials we should have K u % C~. The analogy with the crystalline alloy (Fig. 3) leads us to propose a similar model (6). According to that model, the introduced hydrogen atoms go into interstitial sites with a low symmetry. In crystalline Fe-Ni alloys, hydrogen interstitials fill octahedral sites, the anisotropy of which is related essentially to the nature of each of the 6 nearest neighbour atoms (6). In the amorphous alloy, an "interstitial" site presents the same kind of anisotropy, so-called "chemical" or "compositional", but it presents also an anisotropy of "topological" origin, due to the geometric position of the neighbours. Let us consider an interstitial site with a well defined chemical or topological environment ; such sites exist in the amorphous material with all the possible "orientations". The energy of an interstitial located in such a site depends a little on the site orientation with respect to the magnetization. If temperature is high enough so that interstitials jump from one site to another, they occupy preferably the sites with the orientation corresponding to a lower energy and that causes the IMA. Therefore, the time required for the setting up of the IMA is practically the time necessary for an interstitial to jump from one site to another. The study of the amorphous alloy shows the following peculiarities
:
• a) One can infer from the broadening of the curves (Fig. 3) that the IMA sets up a wide time-constant distribution in the amorphous alloy. For comparison, we have drawn on the same figure the Gurve O(T) which we obtained with a unique time-constant T ffi T exp (AE/kT), taking T ffi lO-13s and AE ffi0.5 eV. The AE distribution which accounts for theUcurves o(T) measured in t~e amorphous alloy is ± 0.08 eV, while in the crystalline alloy Fe2oNi80 , ± 0.035 eV is sufficient (not taking into account a possible distribution of the preexpo-nential factors, To). This distribution of the potential barriers in an amorphous alloy is not surprising. b) In the amorphous alloy, the curve ~(T) shifts towards low temperatures when C H increases, while this effect does not exist in the crystalline alloy. Assuming that only a variation of the mean activation energy, AE, is responsible for the effect, and that AE is proportional to T O ~, AE can be estimated in the amorphous material by comparison to the value in the crystalline a ~ o y , 0.35 eV (6). Fig. 4 shows the dE variations vs C H. These results are in qualitative agreement with prior works : - Berry and Pritchet have estimated the hydrogen migration energy in the amorphous alloy Fe4oNi4oPI4B 6 to be 0.5 eV, from the internal friction peak location (5). This value is comparable t o ours. - Lin and Johnson (9) have determined the hydrogen solubility and diffusivity in this same alloy. Thus, under a pressure of 105 Pa, the solubility C H is between 3 and 5 x 10 -5 ; it does not depend significantly on temperature. Between |03 and |O 5 Pa, it obeys Sievert's law. Extrapolating this law to the pressure which we have used (16 MPa), C H would be between 3.8 and 6.3xI0-~ values quite in agreement with our result (6 x IO-4). Also, Lin and Johnson firda diffusivity activation energy of 0.49 eV, a value close to our result for small C H (Fig. 4). - From the width of the internal friction peak, Berry and Pritchet have estimated the distribution of the activation energies to be (+ 0.057/-0.092 eV) for the alloy Pd8oSi20 (4). Such a width is quite comparable with the one we find in Fe4oNi4oP|4B 6. - All the authors observe a shift of the internal friction peak with C H (|,3), whatever the amorphous alloy studied. To explain the increase in hydrogen mobility when C H increases, Agyeman et el. (|) have suggested that the energy of a dissolved hydrogen atom depends strongly cnthetypeofsite where it is
Vol.
18,
No.
1
HYDROGEN
MOBILITY
IN A M O R P H O U S
Fe40Ni40PI4B6
33
located (i.e. composition and topology of the neighbourhood). When C~ increases, the sites of lower energy are first filled. Kirchheim et al. (I0, 11) have used thi~ model quantitatively, showing that the hydrogen interstitials have an energy distributed according to Fermi-Dirac statistics (considering that an interstitial site can contain only one hydrogen atom) ; thus, after (10, 11), ~(E) being the concentration of sites where an interstitial would have the energy E, the concentration of hydrogen atoms (occupied sites) having the energy E is written : F(E) = ~(E) /(I + exp ~ k - ~ ) is the "Fermi energy" of the interstitials. It rises with C H as hydrogen fills in the interstitial sites• Clearly the interstitials having E << D do not contribute to the IMA, because the sites are all occupied, whatever their orientation is, and the magnetic coupling cannot modify the interstitial distribution on these sites• Also, those with E >> ~ have too small a concentration. Thus, only the interstitials with an energy close to ~ contribute to the IMA. The kinetics of establishment, or rotation, of the IMA, are governed by a potential barrier the height of w h ~ h is, on the average, AE = E - ~ (E is the mean energy of an interstitial in saddle position) ; S . S therefore, AE decreases when ~ increases. c) Influence of the structural relaxation: Fig. 2 shows that K (CH) is identical for both • U ° the as-received and annealed alloys. Thls result suggests that the structural relaxatlon should modify only slightly the local arrangement of the atoms around the interstitial sites. But the hydrogen mobility, at equal concentration, is a little weaker in the annealed alloy. Lin and Johnson have obtained a similar result (9). This may result from a very small increase in the saddle point energy (+ O.O1 eV). Conclusion The hydrogen mobility in the amorphous alloy Fe. Ni. PI.B- has been studied by following the . . . . 4 40 4 6 . . . IMA kinetics• It increases slgnlflcantly when the hydrogen concentratlon increases. Thls effect is well accounted for by assuming that hydrogen locates in "interstitial" sites having widely distributed energies, and that the filling starts with the deepest ones. The neighbourhood of active sites is not much affected by the structural relaxation, since the IMA energy is practically unchanged by the annealing. References I. 2.
3. 4. 5. 6. 7. 8. 9. I0. 11.
K. Agyeman, E. Armbruster, H.U. KGnzi, A. Das Gupta and H.J. G~ntherodt, J. Phys. 42, C5-535 (1981) H.U. KHnzi, E. Armbruster and H.J. G~ntherodt, Proceedings of the 4th International Conference on Rapidly Quenched Metals, ed. by T. Masumoto and K. Suzuki (The Japan Institute of Metals, Sendal) p. 1653 (1982) B.S. Berry and W.C. Pritchet, Scripta Met. 15, 637 (1981) B.S. Berry and W.C. Pritchet, Phys. Rev. B, 24, 2299 (1981) B.S. Berry and W.C. Pritchet, J. Appl. Phys. 52, 1865 (1981) E. Adler and C. Radeloff, J. Appl. Phys. 40, 1526 (1969) W. Chambron, F. LanGon and A. Chamberod, J. Phys. Lettres 43, L-55 (1982) W. Chambron and A. Chamberod, Solid State Con~mum. 33, 157 (]-980) R.W. Lin and H.H. Johnson, J. Non-crystalline SolTds 51, 45 (1982) R. Kirchheim, F. Sormer and G. Schluckebier, Acta Met. 30, 1059 (1982) R. Kirchheim, Acta Met. 30, 1069 (1982)