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High temperature hydrogen diffusion in Zr0.33Ni0.67Hx amorphous alloys
Journal of
ALLOY5 A N D COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 231 (1995) 334-336
High temperature hydrogen diffusion in Zr0.33Ni0.67-H x amorphous alloys J. T6th, K. Tompa, A. Lovas, P. B~inki Research Institute for Solid State Physics" of Hungarian Academy of Sciences, P.O.B. 49, Budapest, H-1525, Hungary
Abstract
The proton content in Zr0.33Ni~.67-Hx amorphous alloy was monitored by changes in electrical resistivity and with the extraplated spin echo amplitude measured by the Carr-Purcell-Meiboom-Gill (CPMG) nuclear magnetic resonance pulse sequence in the temperature interval 300 to 450K. Both methods show that the hydrogen desorption processes can be approximately divided into two ranges. The first is a fast process which is at present not interpretable. In the second stage, the process is thermally activated, and the activation energy calcualted from the resistivity changes is equal to 0.32 _+0.04eV. The CPMG spin echo measurements also give the spin-spin relaxation time of diffusing protons and the activation energy of this process, 0.34 _+0.02 eV, is exactly the same as extracted from the resistivity measurements. Keywords: Hydrogen diffusion; Activation energy; Resistivity; Nuclear magnetic resonance; Amorphous alloy
1. Introduction The purpose of this work was an examination of what kind of information could be obtained from two inherently different experimental methods for investigation of the hydrogen motion in metal-hydrogen systems. The two methods are electrical resistivity measurements and pulsed nuclear magnetic resonance (NMR) of protons. The processes under investigation are (i) the discharge of hydrogen from a fully charged amorphous alloy at moderately high temperatures and (ii) the microscopically observable diffusion events in this temperature range, For monitoring the hydrogen discharge of Zr0.33Ni0.67-H x amorphous alloys, measurements of the time dependence of the decrease in electrical resistivity could be used, following hydrogen charging. Ifthere is no hydride formation, then the resistivity is proportional to the number of atomically distributed hydrogen atoms. The decrease in resistivity is proportional to the amount of hydrogen desorbed. If the desorption is not hindered at the surface and if the distribution of hydrogen atoms at the beginning is homogeneous, then the process is clearly diffusion controlled. The characteristic length of the diffusion is the half thickness value of the ribbon. The fact that the hydrogen diffusion coefficient depends on the 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(95)01810-7
hydrogen concentration [1] in our case too will complicate the interpretation. The characterization of the discharge with a single activation energy is possible only at the last stage of the process. The mechanism which is responsible for the rapid decrease in the hydrogen concentration at the beginning of the discharge is not completely known at present, but is probably connected with the hydrogen concentration dependent diffusion. In contrast to the macroscopic measurements, N M R is also sensitive to atomic motion. The Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence (see [2] and references therein) was selected because two parameters can be used to follow the above mentioned processes. The first is the determination of the hydrogen concentration from measurements of proton magnetization M 0 in a relative scale. The second is a really microscopic quantity, the spinspin relaxation time T 2. T 2 offers a microscopic sampling of the atomic motion. The more detailed motivation for the application of the CPMG sequence to metal-hydrogen systems will be given in [3].
2. Experimental details The Zr0.33Ni0.67 glassy metal alloys were prepared by melt-spinning in Ar atmosphere from 99.9% pure
J. T6th et al. / Journal of Alloys and Compounds 231 (1995) 334-336
335
3. D i s c u s s i o n
4
~
~
F-i]o.
-
T=454.5K
~-
-
For the mathematical modelling of the resistivity measurements the method of Baranowski and Bochenska [4] was applied. For the hydrogenating process of Ni foils under high pressure they used the following formula:
~
. -4
-~ 0
2
4
i ......... --+---Time [11] 6
8
~
P' _ P~ Po - P~
8-2 exp ( - ~2Dt'~ ~r 412 )
(1)
10
Fig. 1. The resistivity decrease of H charged Zro.33Ni0.67 amorphous ribbon in the discharging process at 454.5 K.
Zr and 99.99% pure Ni metals after electron beam melting, and the non-clqystalline state was checked by X-ray diffraction. The thickness of the ribbons was approximately 30/am. The H charging was accomplished in most cases in medium pressure H 2 atmosphere and in one case electrolytically. The surface state of the sample plays an important role in both filling methods. Charging in H 2, the sample could be filled even at room temperature at low H pressure after a thorough grindirtg, The H content was determined immediately after the charging process, by weighing and by measurement of the electrical resistance and the thermoelectric power. In the electrochemical charging method the standard electrolyte 1 part phosphoric acid + 2 parts glycerine was used. The H uptake was monitored by the usual four point contact method, using in situ impulse resistance measurement inside the electrolyte. The process was stopped when the increase in resistivity reached the typicalt value of gaseous charging, approximately 0.7 H/Ivl. Resistance vs. time curves were recorded at 295, 373.5 and 454.5 K; a typical curve is shown in Fig. 1. The NMR measurements and data acquisition were accomplished on a SMIS and partly on a BRUKER NMR spectrometer of about 1 0 _6 resolution. The initial hydrogen content was measured by the weight increase and the CPMG pulse sequence was used for in situ determination of the relative proton content H / M during the measurements (for details see [3]).The extrapolated anzplitude of the echo-train gives the equilibrium value of the proton magnetization which is the hydrogen content free from any field inhomogenity and after r.f.-pulse transient effects. So application of the CPMG pulse sequence allows in situ measurement of the relative proton content. Typical results are shown in Fig. 3. This pulse sequence also gives the method for the spin-spin relaxation time T2 measurements.
or on logarithmic scale log(pt - p~) = - a t + c o n s t
(2)
where P0 is the resistivity of the H-free sample, p~ is the resistivity of the charged sample, D is the diffusion constant, l = d/2 where d is the thickness of the ribbon and a = ~r2D/412. As working hypothesis, we applied Eq. (2) for the reverse process, for the spontaneous discharge of samples at different temperatures. In this case p(0) refers to the resistivity of the charged sample and instead of p~ the last measured resistivity value of the discharge process p(e) was used. (This notation is used in the figures.) The exponential time dependence is valid only for the very late stage of the desporption process. Thus the slope of log(p(0)-p(e)) vs. t allows calculation of the diffusion coefficient for the later stages, that is for low H concentrations. Using this formalism the diffusion coefficient was evaluated. The results are given in Fig. 2 as a function of inverse temperature. The nearly linear dependence can be used for determination of the motional activation energy. The measured value is E a = 0.32 _+0.04 eV. In the interpretation of NMR results the standard formalism was used [2]. Here the nucler magnetization M at time 2r in the CPMG sequence is M(2z) = Mof(D, r)exp(-2r/T2)
(3)
where f(D, ~') is a term depending explcitly on diffu-
10oo ....................................................................... •
E,--0.32:1: O.04eV
~100 ...............................................................................
~',~ • a ~o .................................................. • 1
I
I
za
2.4
I
~
2.6 zs 10~rr [KII
I
3
--I
I
3.2
34
Fig. 2. Temperature dependence of the H diffusion constant in Zro.33Nio.67 amorphous alloy measured by the resistivity change.
J. T6th et al. / Journal of Alloys and Compounds 231 (1995) 334-336
336
sion constant D. The well known checking in [2] proves that this term does not influence the echo amplitudes and can be taken as unity in our case [3]. So, the measurements give M o on a relative scale, and T 2. In the motionally averaged state [2] omitting the life time contribution of lower than 10% to T~ 1 we can write T~ 1 = const r o
(4)
3~ • 1 30 2s ~ 20 ~ 1s ~ ~o
k , ° ~
s . . . . .
and
o+
2.4
7"0 = 7"~ e x p ( E a / k
where k B is the Boltzmann constant, 7"0 and 7"~ are the proper correlation times for the diffusion motion and E a is the activation energy of the motion. The results in Figs. 2 and 4 give the results of activation energy evaluated using Eqs. (3) and (5). Figs. 3(a) and 3(b) show a qualitative comparison in the H / M values measured by N M R and with the resistivity decrease. The probable explanation of the fast stage is that in amorphous metals the diffusion coefficient of H strongly depends on the H concentration [2]. The higher the H concentration, the faster is the diffusion. This dependence is connected with the site energy distribution for the different types of tetrahedral site ( Z r 4 , ZrNi 3, Zr2Ni 2. . . . ) [5]. The
(a)
0.6,0I~"7
u45 ~
0.5
[K"]
3.4
Fig. 4. Proton spin-spin relaxation time-temperature curve in Zro.33Ni0.67-H x alloys and the activation energy for hydrogen diffusionevaluated by Arrhenius fitting.
greater diffusion rate at high H concentration may be the reason for the faster resistivity decrease (see Fig. 1). The agreement between the activation energy of the second stage by measurement of resistivity and that measured by T 2 is reassuring, but the questions connected with fast hydrogen discharge on a microscopic scale remain open.
Acknowledgements
References
_~"~
o Ii -+-~
0
lo3rr
3.2
~.3
"~ 0.3
0.0
3
T=373.5 K
~
0.1
j 2.6
This work was supported by the Hungarian Academy of Sciences and by the National Science Foundation under the Grant OTKA-2949.
(b)
T=370K
0.4 0.2
~2.6
(5)
B T)
~u--o.26 E.--0.a4~0.02,V--.
\o
10
o
1
I
,
=
I
20
30
40
50
Time [h]
0
o I 10
~20
=
=
30
40
~ 50
Time [hi
Fig. 3. (a) Time dependence of H / M values measured by the C a r r - P u r c e l l - M e i b o o m - G i l l sequence after extrapolating the proton spin echo amplitude to zero time [1], and (b) the electrical resistivity change in amorphous Zr033Ni0.67-n x alloys.
[1] J.O. Str6m-Olsen, Y. Zhao and D.H. Ryan, J. Less-Common Met., 172-174 (1991) 922. [2] C.P. Slichter, Principles of Magnetic Resonance, Springer, 1990, p. 367.
[3] K. Tompa, P. B~nki, C. Hargitai, G. Lasanda and L.K. Varga,
this conference. [4] B. Baranowski and K. Bochenska, Atomic Transport in Solids and Liquids, Proc. Marstrand, Ttibingen, 1970. [5] T. Araki, T. Abe and K. Tanaka, Mater. Trans., JIM, 30 (1989) 748.
ALLOY5 A N D COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 231 (1995) 334-336
High temperature hydrogen diffusion in Zr0.33Ni0.67-H x amorphous alloys J. T6th, K. Tompa, A. Lovas, P. B~inki Research Institute for Solid State Physics" of Hungarian Academy of Sciences, P.O.B. 49, Budapest, H-1525, Hungary
Abstract
The proton content in Zr0.33Ni~.67-Hx amorphous alloy was monitored by changes in electrical resistivity and with the extraplated spin echo amplitude measured by the Carr-Purcell-Meiboom-Gill (CPMG) nuclear magnetic resonance pulse sequence in the temperature interval 300 to 450K. Both methods show that the hydrogen desorption processes can be approximately divided into two ranges. The first is a fast process which is at present not interpretable. In the second stage, the process is thermally activated, and the activation energy calcualted from the resistivity changes is equal to 0.32 _+0.04eV. The CPMG spin echo measurements also give the spin-spin relaxation time of diffusing protons and the activation energy of this process, 0.34 _+0.02 eV, is exactly the same as extracted from the resistivity measurements. Keywords: Hydrogen diffusion; Activation energy; Resistivity; Nuclear magnetic resonance; Amorphous alloy
1. Introduction The purpose of this work was an examination of what kind of information could be obtained from two inherently different experimental methods for investigation of the hydrogen motion in metal-hydrogen systems. The two methods are electrical resistivity measurements and pulsed nuclear magnetic resonance (NMR) of protons. The processes under investigation are (i) the discharge of hydrogen from a fully charged amorphous alloy at moderately high temperatures and (ii) the microscopically observable diffusion events in this temperature range, For monitoring the hydrogen discharge of Zr0.33Ni0.67-H x amorphous alloys, measurements of the time dependence of the decrease in electrical resistivity could be used, following hydrogen charging. Ifthere is no hydride formation, then the resistivity is proportional to the number of atomically distributed hydrogen atoms. The decrease in resistivity is proportional to the amount of hydrogen desorbed. If the desorption is not hindered at the surface and if the distribution of hydrogen atoms at the beginning is homogeneous, then the process is clearly diffusion controlled. The characteristic length of the diffusion is the half thickness value of the ribbon. The fact that the hydrogen diffusion coefficient depends on the 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(95)01810-7
hydrogen concentration [1] in our case too will complicate the interpretation. The characterization of the discharge with a single activation energy is possible only at the last stage of the process. The mechanism which is responsible for the rapid decrease in the hydrogen concentration at the beginning of the discharge is not completely known at present, but is probably connected with the hydrogen concentration dependent diffusion. In contrast to the macroscopic measurements, N M R is also sensitive to atomic motion. The Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence (see [2] and references therein) was selected because two parameters can be used to follow the above mentioned processes. The first is the determination of the hydrogen concentration from measurements of proton magnetization M 0 in a relative scale. The second is a really microscopic quantity, the spinspin relaxation time T 2. T 2 offers a microscopic sampling of the atomic motion. The more detailed motivation for the application of the CPMG sequence to metal-hydrogen systems will be given in [3].
2. Experimental details The Zr0.33Ni0.67 glassy metal alloys were prepared by melt-spinning in Ar atmosphere from 99.9% pure
J. T6th et al. / Journal of Alloys and Compounds 231 (1995) 334-336
335
3. D i s c u s s i o n
4
~
~
F-i]o.
-
T=454.5K
~-
-
For the mathematical modelling of the resistivity measurements the method of Baranowski and Bochenska [4] was applied. For the hydrogenating process of Ni foils under high pressure they used the following formula:
~
. -4
-~ 0
2
4
i ......... --+---Time [11] 6
8
~
P' _ P~ Po - P~
8-2 exp ( - ~2Dt'~ ~r 412 )
(1)
10
Fig. 1. The resistivity decrease of H charged Zro.33Ni0.67 amorphous ribbon in the discharging process at 454.5 K.
Zr and 99.99% pure Ni metals after electron beam melting, and the non-clqystalline state was checked by X-ray diffraction. The thickness of the ribbons was approximately 30/am. The H charging was accomplished in most cases in medium pressure H 2 atmosphere and in one case electrolytically. The surface state of the sample plays an important role in both filling methods. Charging in H 2, the sample could be filled even at room temperature at low H pressure after a thorough grindirtg, The H content was determined immediately after the charging process, by weighing and by measurement of the electrical resistance and the thermoelectric power. In the electrochemical charging method the standard electrolyte 1 part phosphoric acid + 2 parts glycerine was used. The H uptake was monitored by the usual four point contact method, using in situ impulse resistance measurement inside the electrolyte. The process was stopped when the increase in resistivity reached the typicalt value of gaseous charging, approximately 0.7 H/Ivl. Resistance vs. time curves were recorded at 295, 373.5 and 454.5 K; a typical curve is shown in Fig. 1. The NMR measurements and data acquisition were accomplished on a SMIS and partly on a BRUKER NMR spectrometer of about 1 0 _6 resolution. The initial hydrogen content was measured by the weight increase and the CPMG pulse sequence was used for in situ determination of the relative proton content H / M during the measurements (for details see [3]).The extrapolated anzplitude of the echo-train gives the equilibrium value of the proton magnetization which is the hydrogen content free from any field inhomogenity and after r.f.-pulse transient effects. So application of the CPMG pulse sequence allows in situ measurement of the relative proton content. Typical results are shown in Fig. 3. This pulse sequence also gives the method for the spin-spin relaxation time T2 measurements.
or on logarithmic scale log(pt - p~) = - a t + c o n s t
(2)
where P0 is the resistivity of the H-free sample, p~ is the resistivity of the charged sample, D is the diffusion constant, l = d/2 where d is the thickness of the ribbon and a = ~r2D/412. As working hypothesis, we applied Eq. (2) for the reverse process, for the spontaneous discharge of samples at different temperatures. In this case p(0) refers to the resistivity of the charged sample and instead of p~ the last measured resistivity value of the discharge process p(e) was used. (This notation is used in the figures.) The exponential time dependence is valid only for the very late stage of the desporption process. Thus the slope of log(p(0)-p(e)) vs. t allows calculation of the diffusion coefficient for the later stages, that is for low H concentrations. Using this formalism the diffusion coefficient was evaluated. The results are given in Fig. 2 as a function of inverse temperature. The nearly linear dependence can be used for determination of the motional activation energy. The measured value is E a = 0.32 _+0.04 eV. In the interpretation of NMR results the standard formalism was used [2]. Here the nucler magnetization M at time 2r in the CPMG sequence is M(2z) = Mof(D, r)exp(-2r/T2)
(3)
where f(D, ~') is a term depending explcitly on diffu-
10oo ....................................................................... •
E,--0.32:1: O.04eV
~100 ...............................................................................
~',~ • a ~o .................................................. • 1
I
I
za
2.4
I
~
2.6 zs 10~rr [KII
I
3
--I
I
3.2
34
Fig. 2. Temperature dependence of the H diffusion constant in Zro.33Nio.67 amorphous alloy measured by the resistivity change.
J. T6th et al. / Journal of Alloys and Compounds 231 (1995) 334-336
336
sion constant D. The well known checking in [2] proves that this term does not influence the echo amplitudes and can be taken as unity in our case [3]. So, the measurements give M o on a relative scale, and T 2. In the motionally averaged state [2] omitting the life time contribution of lower than 10% to T~ 1 we can write T~ 1 = const r o
(4)
3~ • 1 30 2s ~ 20 ~ 1s ~ ~o
k , ° ~
s . . . . .
and
o+
2.4
7"0 = 7"~ e x p ( E a / k
where k B is the Boltzmann constant, 7"0 and 7"~ are the proper correlation times for the diffusion motion and E a is the activation energy of the motion. The results in Figs. 2 and 4 give the results of activation energy evaluated using Eqs. (3) and (5). Figs. 3(a) and 3(b) show a qualitative comparison in the H / M values measured by N M R and with the resistivity decrease. The probable explanation of the fast stage is that in amorphous metals the diffusion coefficient of H strongly depends on the H concentration [2]. The higher the H concentration, the faster is the diffusion. This dependence is connected with the site energy distribution for the different types of tetrahedral site ( Z r 4 , ZrNi 3, Zr2Ni 2. . . . ) [5]. The
(a)
0.6,0I~"7
u45 ~
0.5
[K"]
3.4
Fig. 4. Proton spin-spin relaxation time-temperature curve in Zro.33Ni0.67-H x alloys and the activation energy for hydrogen diffusionevaluated by Arrhenius fitting.
greater diffusion rate at high H concentration may be the reason for the faster resistivity decrease (see Fig. 1). The agreement between the activation energy of the second stage by measurement of resistivity and that measured by T 2 is reassuring, but the questions connected with fast hydrogen discharge on a microscopic scale remain open.
Acknowledgements
References
_~"~
o Ii -+-~
0
lo3rr
3.2
~.3
"~ 0.3
0.0
3
T=373.5 K
~
0.1
j 2.6
This work was supported by the Hungarian Academy of Sciences and by the National Science Foundation under the Grant OTKA-2949.
(b)
T=370K
0.4 0.2
~2.6
(5)
B T)
~u--o.26 E.--0.a4~0.02,V--.
\o
10
o
1
I
,
=
I
20
30
40
50
Time [h]
0
o I 10
~20
=
=
30
40
~ 50
Time [hi
Fig. 3. (a) Time dependence of H / M values measured by the C a r r - P u r c e l l - M e i b o o m - G i l l sequence after extrapolating the proton spin echo amplitude to zero time [1], and (b) the electrical resistivity change in amorphous Zr033Ni0.67-n x alloys.
[1] J.O. Str6m-Olsen, Y. Zhao and D.H. Ryan, J. Less-Common Met., 172-174 (1991) 922. [2] C.P. Slichter, Principles of Magnetic Resonance, Springer, 1990, p. 367.
[3] K. Tompa, P. B~nki, C. Hargitai, G. Lasanda and L.K. Varga,
this conference. [4] B. Baranowski and K. Bochenska, Atomic Transport in Solids and Liquids, Proc. Marstrand, Ttibingen, 1970. [5] T. Araki, T. Abe and K. Tanaka, Mater. Trans., JIM, 30 (1989) 748.