- Email: [email protected]
Electrical transport properties of ZrFe2−xCrxHy
Journal of
ALLOVS AND COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 231 (1995) 176-181
Electrical transport properties of ZrFe2_xCrxHy Y.S. Choi, D.J. Lee, Y.W. Park Department of Physics, Seoul National University, Seoul 151-742, South Korea
Abstract
We have measured the electrical resistivity for ZrFe 2 ~Crx as a function of temperature between 20 K and 300 K. We have found that the dominant scattering mechanism for conduction electrons is changed from scattering by phonons to that due to the disordered atomic potentials as Cr composition is increased. We have also measured the thermoelectric power (TEP) for ZrFe 2 xCrx and the hydrides of x = 0.6 and 1.5 as a function of temperature in the same range of temperature. For the alloys before hydrogenation, the non-linear temperature dependence of TEP is changed into the linear temperature dependence as Cr composition is increased. TEP for the hydride of x = 0.6 and 1.5 exhibits a positive hump at low temperatures. From these results, we have found that the hydrogen plays the role of an attractive scattering centre for the conduction electrons. Keywords: Electrical transport properties; Scattering mechanisms; Hydrogen
1. Introduction The dissolution of hydrogen in a metal lattice and the formation of a metal hydride perturb considerably the electrons and phonons of the host metal. Accordingly, the study of the electronic properties of a metalhydrogen system is not only of fundamental interest in understanding the hydrogen-metal interaction but also of importance in technological point of view. Many theoretical and experimental studies of the electronic properties have been conducted [1]. In particular, the magnetic properties have been the subject of extensive studies. For ZrFe2_xCr x, both the ferromagnetic transition temperature and the magnetic moment are reported to become larger in the hydride phase [2]. The enhancement of the magnetic moment has been interpreted by the suggestion that the hydrogen behaves as if it is an anion, an electron acceptor, This suggestion is tending toward the anionic model, one of two classical competing descriptions of the metal-hydrogen bond which are (a) the proton model, in which the hydrogen loses its electron to electronic states of the metal, and (b) the anion model, in which the hydrogen atom, with the larger electronegativity than the metal, becomes negatively charged. Neither the proton model or anion model is, however, known to be a good description of the hydrides [1]. With the expectation that the charge state of the dissolved H atoms would influence the scattering 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(95)01796-8
process of conduction electrons, we have studied the electrical transport properties of the ZrFe2_xCrx and their hydrides in order to investigate how the dissolved hydrogen atoms influence the scattering mechanisms of conduction electrons and to obtain information on the charge state of dissolved hydrogen atoms. The electrical transport properties that we have studied are the electrical resistivity p and the thermoelectric power (TEP) denoted by S(T). The electrical resistivity is measured to investigate the dominant scattering mechanism. TEP is an extremely useful probe to investigate the intrinsic electronic conduction mechanism since it is a zero current transport coefficient. Furthermore, TEP is a very sensitive probe of the scattering mechanisms of charge carriers with static disorder such as vacancies and impurities, or with dynamic disorder such as phonons since it depends on delicate quantities such as the energy derivative of the scattering of the electrons. TEP of a metal and metal alloys have been studied both experimentally and theoretically. It is extremely difficult to complete any realistic calculation encompassing all the currently suggested contributions such as phonon drag, virtual recoil [3], electron-phonon renormalization [4], intrinsic multiphonon scattering, and many-body corrections to the electron velocity [5]. Recently, Durczewski and Ausloos [6] calculated the TEP for a magnetic metal by considering both magnetic scattering and scattering by phonons. Applying
177
Y.S. Choi et al. / Journal of Alloys and Compounds 231 (1995) 176-181
the obtained result to the rare earth intermetallic compounds such as REAl 2, they showed that their calculations are in good agreement with the experiment. Although a satisfactory theory for metal alloys has not been completed yet, TEP measurements with a reasonable interpretation might be useful for obtaining information on the charge state of the dissolved hydrogen atoms. In this paper, we present the study of electrical transport properties, electrical resistivity and TEP, for ZrFe 2 xCrx and their hydrides.
300
.
.
.
.
.
.
250
~" oE i
200
~ ~ ~ ~ l u l l ~ J
150
~
dm~~-x__0.6 X=0.45
5] 0.3
2. Experimental details The alloys were prepared by arc melting. The starting elements were Zr chips (99.99% purity), Fe chips (99.99% purity) and Cr chunks (99.99% purity). They were weighed appropriately for the stoichiometry of Z r F e e _ x C r x. They were then arc melted under Ar on a standard water-cooled copper hearth. We remelted the initially melted button-type sample four or five times, turning it over between each melt. The prepared ingots were annealed to obtain single-phase crystal at 1000 °C for about 20 h. The hydrogenation is carried out in the gaseous phase. The quantity of absorbed hydrogen is measured as the weight difference between before and after hydrogenation, Electrical resistivity was measured using the fourprobe method with silver paint contacts. TEP was measured using a technique described previously [7].
3. Results and discussion Fig. 1 shows the electrical resistivities of the pseudobinary alloys ZrFe2_xCr x before hydrogenation as a function of temperature between 20 K and 300 K. The noticeable features in the electrical resistivity are summarized as follows. (1) The magnitude of the resistivity at 20 K, which we call the residual resistivity, gradually increases as Cr composition is increased. (2) The quite linear temperature dependence of electrical resistivity is changed into a weak temperature dependence as Cr composition is increased. Most of the residual resistivities of these pseudobinary alloys are very high compared with that of the elemental metal or that of the related binary compounds ZrF% and ZrCr 2. Another feature of the magnitude of residual resistivity is that it is satnrated when the Cr composition x is larger than 0.6 as can be seen in Fig. 1. The increase in residual resistivity could originate in the fact that the increasing randomness of the atomic potentials due to the substitution of Fe by Cr might be the strong scattering sonrces making the mean free
.25
50
--0.2
0 0
, 50
r 100
, 150
, 200
r 250
, 300
350
T(K) Fig. 1. Resistivityof ZrFe2 xCr. path of the metal alloys shorter. Similar trends in the resistivity have been found in binary solid solutions such as the C u - A u system [8]. In our system, Fe and Cr atoms can be assumed to be randomly distributed in the B sublattice and to form a type of disordered solid solution although zirconium and iron (or chromium) form the ordered Laves-type crystal AB 2. Thus the effect on the electrical resistivity of the substitution of Fe with Cr could be regarded as equivalent to that in the binary solid solution. In the present pseudobinary alloys, it can be imagined that there are two dominant conduction electron scattering mechanisms, scattering by the random atomic potentials in the B sublattice due to alloying and that by the lattice vibrations (phonons). It is well known that the scattering by the phonons gives a linearly increasing resistivity on increasing temperature. On the contrary, the scattering from the disordered atomic potential, a static imperfection, would give an electrical resistivity which is independent of temperature. The resistivity of the alloy with a Cr composition of 0.2 reveals a quite linear temperature dependence as found in Fig. 1. As the Cr composition is increased, this linear temperature dependence is gradually changed into a weak dependence. The high absolute value and the weak temperature dependence of the electrical resistivity for the alloys having higher Cr composition indicate that the scattering by the disordered atomic potential becomes dominant and the phonon scattering becomes comparatively less
178
Y.S. Choi et al. / Journal o f Alloys and Compounds 231 (1995) 176-181
important as Cr composition is increased. F r o m the t e m p e r a t u r e dependence of the electrical resistivity, we have found that the conduction electron scattering in the present alloys with x lower than 0.35 is mainly due to the phonons, while for the alloys with x higher than 0.35 the scattering due to the disordered atomic potential is dominant. Fig. 2 shows the T E E S ( T ) , for the present pseudobinary alloys as a function of t e m p e r a t u r e between 20 K and 300 K. T E P for the alloys with x = 0.2 and 0.25 exhibits a positive sign in the whole t e m p e r a t u r e range of measurement. The t e m p e r a t u r e dependence of T E P has a broad m a x i m u m around a certain temperature. A non-linear t e m p e r a t u r e dependence below r o o m t e m p e r a t u r e is often found in T E P of the transition metals or alloys. This non-linear temperature dependence of T E P might be discussed in terms of the scattering by phonons, Analysis of T E P data usually begins with the Boltzmann equation, which results in
S ( T ) = - - 1 T - K~ tel
(1)
K0
where
f dk -~ (
Kn
e2 3
Of~
2,
4,rr3 \ - - ~ } r v x I , e -- Ix)"
In the above equation, f is the Fermi function, vx is the velocity in the direction of the t e m p e r a t u r e gra-
18
,
,
14 12 10
d~ g"n" "
a 8
v ~t
4
,
,
, , • :0.2 ~ :0.25 • :0.3 o :0.* • ****•• • :0.6 • :1.5 •• • • ~ * , ~h • ~ * gl~ • [] []
|
2 o -2 -4 0
I
,50
'
100
~
150
~
200
~
250
T(K) Fig. 2. TEP of ZrF%_~Cr~ before hydrogenation,
'
300
350
dient, T is the relaxation time, /x is the chemical potential, and e is the electron energy. For the free electron case, the above equation reduces to a familiar form, the so-called Mott formula [9]:
S(T)-
7r2k 2B - T( 31elE v '
0 In o- 3 (= - 0 In e 2
0 In r -~ (2) 0 In e
~ is called a thermoelectric parameter. The second term of sc is usually neglected by assuming energyindependent scattering of conduction electrons. However, we cannot explain the non-linear t e m p e r a t u r e dependence which is often found in T E P of the metals or metal alloys with only the first term of ( which gives a linear t e m p e r a t u r e dependence for T E R In particular, for the alloys with x = 0.2 and 0.25, the second term would be important since the scattering of conduction electrons by the phonons is expected to depend very strongly on the energy. The importance of e l e c t r o n - p h o n o n interaction in T E P was given by Nielson and Taylor [10]. T h e y ascribed the deviation from the linearity in the electron diffusion thermopower to a new contribution which they called " p h o n y p h o n o n drag" ( P P D ) because its shape is closely similar to that of p h o n o n drag. However, the deviation due to PPD has the shape of a positive h u m p while the p h o n o n drag has the shape of a negative hump. This P P D arises as a natural consequence of the inclusion of intrinsic two-phonon processes in a second-order treatment of the electron scattering probability due to e l e c t r o n - p h o n o n interaction. Comparing this argument with our data, we can say that the non-linear t e m p e r a t u r e - d e p e n d e n c e of T E P for the alloys with low Cr composition originates from the conduction electron scattering by phonons. T E P at r o o m t e m p e r a t u r e is negative and almost the same ( - 2 pN K - ~) for the alloys with x = 0.3, 0.4. T E P of the alloy with x = 0.3 exhibits a non-linear temperature dependence with a zero crossing at 150 K and a broad m a x i m u m at 70 K. T E P s of the alloys with x = 0.4 are negative in the whole t e m p e r a t u r e range of measurement. Unlike for the alloy with x = 0.3, its t e m p e r a t u r e dependence is almost linear. It can be suggested that the dominance of the scattering mechanism is transferred from the scattering by phonons to that by the disordered atomic potential in this range of Cr compositions. Fig. 3 shows the t e m p e r a t u r e dependence of T E P for the alloys of x = 0 . 6 , 1.5 in m o r e detail. It is noticeable that the T E P of both alloys of x = 0.6, 1.5 varies quite linearly with the t e m p e r a t u r e and has a negative sign in the whole range of temperature. This indicates that the scattering by phonons which is supposed to cause the nonlinear t e m p e r a t u r e dependence becomes less important. This argument is con-
Y.S. Choi et al. / Journal of Alloys and Compounds 231 (1995) 176-181
0
,
,
,
,
,
,
0.5
,
o
-1
0.0
"-"% "/'• ~"*'**i.=***.
o°
00
~, >
-2
%:.:..
•. ==
,,=08
,
:. +=%
5
I=
=0*
.,** ** =-. **
:t
..•
(n
*
=t~== ooo= . * =nats=P. .
>
"..
-1.0
=°°°
." ..,,. --3
+
o8
x=1.5 •
-1.5
%
I 0
50
I 100
I 150
nm
°*o°0,
• ,,=,
--4.
,
**
X=0.6
~"
,
%0 o
-o5
"%..
=t
;
t~l%=.-=q% o%0o o X = I . D
•
,
179
I
I
I
200
250
300
--2.0 3,50
I 0
T(K)
50
I 100
I 150
I
I
I
200
250
300
350
T(K)
Fig. 3. TEP of ZrFe 2 xCrx (x = 0.6, 1.5) before hydrogenation.
Fig. 4. TEP of ZrFe2_xCrx (x = 0.6, 1.5) after hydrogenation.
sistent with that for the resistivity results as mentioned above, In the absence of inelastic scattering, e.g. scattering by phonons, the scattering by the disordered atomic potentials will yield the T E P parameter ~: of magnitude
temperatures. We will explain these two features by considering the T E P parameter ~ for the hydrides. The thermoelectric power parameter ~: can be divided into two parts C0 and ~H, where ~:0 is that before hydrogenation and #H is that yielded by dissolved hydrogen atoms, ~:0, as shown above, equals
5 2
5 2
o In IUI a In e
(3)
where IUI is the Fourier transform of the difference between the actual atomic potential and the average potential of the constituent atom. This leads to the linear temperature dependence of T E P for the alloys of x = 0.6 and 1.5. We have also measured the T E P for the alloys ZrFee_xCrxHy with x = 0.6 and 1.5 as a function of temperature to investigate the charge state of the hydrogen atom in the alloys. The reasons for choosing these alloys is the T E P of host alloys is so simple that the change after hydrogenation is easily found. The temperature dependence of T E P after hydrogenation is presented in Fig. 4. The hydrogen compositions y are 1.5 for the present alloys with x = 0.6 and 2.0 for the alloy with x = 1.5. The overall features of the change in T E P due to hydrogenation can be summarized as follows. (1) In the high temperature range (100 K and above), T E P exhibits an almost linear temperature dependence but its absolute value is lowered. (2) A positive hump is displayed at lower
0 In IUI 8 In e
(4)
It is not easy to obtain sen and also difficult to find literature to deal with that subject. T E P of palladium hydride ( P d H ) at low temperature was reported [11]. As hydrogen atoms are dissolved, the negative T E P becomes positive at low temperatures, as in our case. Nielson et al. [12] interpreted the results according to their suggestion that the hydrogen atoms could be treated as impurities and the scattering by a virtual recoil of hydrogen atom must be included. They did not, however, consider the terms caused by mixed scattering of a hydrogen atom and a p h o n o n since the motion of the impurities is treated as an independent excitation of the host metal, not connected to the p h o n o n modes of the host lattice. It has not been well established whether the dissolved hydrogen must be treated as an intercalated atom having motion independent of host lattice or as a constituent atom of an alloy, so-called hydride, having a motion connected with the metal lattice. As mentioned just above, Nielson et al. treated the dissolved hydrogen in P d H
180
Y.S. Choi et al. / Journal of Alloys and Compounds 231 (1995) 176-181
as an intercalated atom having a motion independent of the host metal and calculated the contribution to ~ by the hydrogen. This contribution gives a positive value to TEP which is consistent with the experimental results for PdH. Since this contribution to ~: is temperature independent and so gives a linear temperature dependence to T E E their treatment is not applicable to our results which reveal a non-linear temperature dependence of T E E the positive hump. To obtain the temperature-dependent thermoelectric parameter giving the positive hump in T E E we assume the hydride to be an alloy and the hydrogen as its constituent atom having motion connected with the metal lattice. Nielson et al. [10] calculated the contribution to ~: of a dilute alloy by the solute atoms as well as PPD contribution. To interpret the results summarized above, we will use their calculation for TEP of an alloy. They considered double scattering at the solute atoms and mixed scattering by a solute atom and a phonon. If we treat the hydrogen as a solute atom of the hydride, the thermoelectric parameter (H can be, as described in Ref. [10], written as 0 In IVHI N' (H = 1 -- 2 - - + 0 1 n e 6VH N A ~ ( T ) 2N)l/3 + Vo ~ A~(T)
A
-
(5)
Ev m (k B0 ) 2 M -
-
where VH is the Fourier transform of the difference between the potentials due to hydrogen and host alloy, V0 is the Fourier transform of the potential of the host alloy and the ratio N ' / N is the valence. For the exact form of the two functions ~ and ~3, one can refer to Ref. [10]. The first two terms in Eq. (5) represent the prediction of first-order theory, giving linear temperature dependence of TEP. The third term is due to double scattering at a hydrogen site and the fourth term is due to the mixed scattering by a hydrogen atom and a phonon. VH is the Fourier transform of the difference between the potentials of hydrogen and host alloy. It equals to V(H) (the potential due to hydrogen) minus V0. We suppose that the magnitude of N ' / N is 0.5 which is characteristic of the transition metal. The last two terms can be rewritten as 3 V ( H ) A ~ ( T ) +VoA[1.6~3(T ) -31F2(T)]
(6)
~3 is almost the same as 9t2. Thus ~:H becomes approximately 0 In IVHI - + [3V(H) - 1.4Vo]A~(T) (7) 1 2 0 In e The scattering mechanisms by both the disordered atomic potentials of the host alloy and the hydrogen -
potential must be considered. The resultant TEP parameter can be given by the Nordheim-Gorter rule [13] as follows: ~:_ Po~0 + ,OH~'H (8) P0 + PH In the present alloys, P0 is of the order of 200 t~f~ cm. In the hydrogenated Fe91Zrg, we have found that the resistivity due to hydrogen atoms is of the same order [14]. Thus we can assume ('~(~:0 + ~:H)/2" The corresponding TEP can be written as ¢r2kZT S ( T ) - - 31elE------~~:L 2"rr2k~3T - IciEr
[3V(H) - 1.4Vo]A~z(T )
(9)
The first term in Eq. (9) is TEP linearly dependent on temperature. ~:L of the first term is the modified TEP parameter for the linear temperature-dependent part of T E E Ev, the Fermi energy, as well as the thermoelectric parameter are changed by band filling after hydride formation. It seems that the mixed effect of these changes is the origin of the increase in the linear part of TEP at higher temperatures. The second term comes from the double scattering of conduction electrons at the hydrogen site and the mixed scattering by an H atom and a phonon. This second term seems to represent the scattering process leading to the positive hump at low temperature. We extract the linear part A T of TEP, of which A is determined by the measured value of TEP around 300 K, from the total TEP and present the result in Fig. 5. The positive hump is clearly observed. It can be said that the remaining part after extraction corresponds to the second term of the above equation. The second term reduces to a simple form at low temperature as follows: 2 7r M m [3V(H) - 1.4V0] OT L [ 1 - ~4 ~ 2{~--~} T'~ 2]j S H - 2~O (10) We have fitted this equation to our results at low temperature. The full lines shown in Fig. 5 are the curves fitted to the experimental results. We could obtain the Debye temperature OD to be 350 and 420 for the hydrides with x =0.6 and 1.5 respectively. Secondly, it is found that 3 V ( H ) - 1 . 4 V 0 must be negative to explain the observed positive hump. Since V0, the potential due to the transition metal, is originally negative, the hydrogen potential V(H) must be negative. This means that the hydrogen atoms have an attractive potential for the conduction electrons. We have found that the positive humps exhibited after hydrogenation can be well described in terms of the
Y.S. Choi et al. / Journal of Alloys and Compounds 231 (1995) 176-181
0.6
.
.
.
.
• " .
.
o
.
basis of knowledge of the dominant scattering mechanism obtained from the electrical resistivity measurement, T E P for the hydride of the alloys shows that the hydrogen plays the role of an attractive scattering centre for the conduction electrons.
.• x--1.5
0.4
•
•
181
•e
oo
"
•
• e"
"
"
o
Acknowledgment
o
o
o
o ° 0.2
•
°
o~o
s
o°
o.0
o
o
The authors thank Dr. K.Y. Kim at Korea Institute of Science and Technology (KIST) for sharing his arc melter for sample preparation. This work was supported by the Korea Science and Engineering Foundation ( K O S E F ) and the Ministry of Education ( M O E ) as well as the Hyundai M o t o r Company, Korea.
.o
O°o o o o o o o• o oo oo .o " .o o o o
o
•
ooo
o ee o
References
U --0.2
I
0
50
i
1 00
I
150
I
200
f
250
t
300
150
[1] M. Gupta and L. Schlapbach, L. Schlapbach (ed.), Hydrogen in Intermetallic Compounds 1, Springer, Berlin, 1988, pp. 139-218. [2] I. Jacob, D. Davidov and D. Shaltiel, J. Magn. Magn. Mater., 20
Fig. 5. The change in TEP of ZrFez_xCrx (x = 0.6, 1.5) after hydrogenation due to the scattering by the hydrogen atoms.
(1980) 226. [3] P.E. Nielson and P.L. Taylor, Phys. Rev. B, 10 (1974) 4061. [4] A. Hasegawa, Solid State Commun., 15 (1974) 1361. J.L. Opsal, B.J. Tharler and J. Bass, Phys. Rev. Lett., 36 (1976)
T(K)
conduction electron scattering by the hydrogen atoms and the dissolved hydrogen atoms play a role as attractive scattering centres for conduction electrons. In conclusion, we have measured the electrical
[5] S.K. Lyo, Phys. Rev. Lett., 39 (1977) 363.
resistivity of ZrFez_xCr x as a function of temperature between 20 K and 300 K. The residual resistivity increases and the linear temperature dependence of resistivity changes into a weak temperature dependence as Cr composition is increased. From these
[7] Y~W.Park, Synth. Met., 45 (1991) 173. [8] C. Kittel, Introduction to Solid State Physics, Wiley, New York, 1986, p. 582. ]9] N.F. Mott and H. Jones, The Theory of the Properties of Metals
results, we have found that the dominant scattering mechanism for conduction electrons is changed from scattering by the phonons to that by the disordered atomic potentials as Cr composition is increased. We haste also measured the T E P for ZrFez_xCr x and the hydrides with x = 0.6 and 1.5 as a function of temperature. T E P results for each alloy are interpreted on the
1211. S.K. Lyo, Phys. Rev. B, 17(1978)2545. A. Vilenkin and P.L. Taylor, Phys. Rev. B, 18 (1978) 5280. [6] K. Durczewski and M. Ausloos, J. Magn. Magn. Mater., 51 (1985) 230.
and Alloys, Clarendon, London, 1936.
[10] P.E. Nielson and P.L. Taylor, Phys. Rev. B, 15 (1974) 4061. [11] R. Fletcher, N.S. Ho and F.D. Manchester, J. Phys. C, 1 (Suppl.) (1970)$59. [12] P.E. Nielson, EL. Taylor and F.D. Manchester, Phys. Lett., 29
(1970) 161.
[13] L. Nordheim and C.J. Gorter, Physica, 2 (1935) 383. [14] Y.S. Choi, S,S. Choi, Y.W. Park, M. Hirscher and H. Kronmiiller, Mater. Sci. Eng. A, 181-182 (1994) 1035.
ALLOVS AND COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 231 (1995) 176-181
Electrical transport properties of ZrFe2_xCrxHy Y.S. Choi, D.J. Lee, Y.W. Park Department of Physics, Seoul National University, Seoul 151-742, South Korea
Abstract
We have measured the electrical resistivity for ZrFe 2 ~Crx as a function of temperature between 20 K and 300 K. We have found that the dominant scattering mechanism for conduction electrons is changed from scattering by phonons to that due to the disordered atomic potentials as Cr composition is increased. We have also measured the thermoelectric power (TEP) for ZrFe 2 xCrx and the hydrides of x = 0.6 and 1.5 as a function of temperature in the same range of temperature. For the alloys before hydrogenation, the non-linear temperature dependence of TEP is changed into the linear temperature dependence as Cr composition is increased. TEP for the hydride of x = 0.6 and 1.5 exhibits a positive hump at low temperatures. From these results, we have found that the hydrogen plays the role of an attractive scattering centre for the conduction electrons. Keywords: Electrical transport properties; Scattering mechanisms; Hydrogen
1. Introduction The dissolution of hydrogen in a metal lattice and the formation of a metal hydride perturb considerably the electrons and phonons of the host metal. Accordingly, the study of the electronic properties of a metalhydrogen system is not only of fundamental interest in understanding the hydrogen-metal interaction but also of importance in technological point of view. Many theoretical and experimental studies of the electronic properties have been conducted [1]. In particular, the magnetic properties have been the subject of extensive studies. For ZrFe2_xCr x, both the ferromagnetic transition temperature and the magnetic moment are reported to become larger in the hydride phase [2]. The enhancement of the magnetic moment has been interpreted by the suggestion that the hydrogen behaves as if it is an anion, an electron acceptor, This suggestion is tending toward the anionic model, one of two classical competing descriptions of the metal-hydrogen bond which are (a) the proton model, in which the hydrogen loses its electron to electronic states of the metal, and (b) the anion model, in which the hydrogen atom, with the larger electronegativity than the metal, becomes negatively charged. Neither the proton model or anion model is, however, known to be a good description of the hydrides [1]. With the expectation that the charge state of the dissolved H atoms would influence the scattering 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(95)01796-8
process of conduction electrons, we have studied the electrical transport properties of the ZrFe2_xCrx and their hydrides in order to investigate how the dissolved hydrogen atoms influence the scattering mechanisms of conduction electrons and to obtain information on the charge state of dissolved hydrogen atoms. The electrical transport properties that we have studied are the electrical resistivity p and the thermoelectric power (TEP) denoted by S(T). The electrical resistivity is measured to investigate the dominant scattering mechanism. TEP is an extremely useful probe to investigate the intrinsic electronic conduction mechanism since it is a zero current transport coefficient. Furthermore, TEP is a very sensitive probe of the scattering mechanisms of charge carriers with static disorder such as vacancies and impurities, or with dynamic disorder such as phonons since it depends on delicate quantities such as the energy derivative of the scattering of the electrons. TEP of a metal and metal alloys have been studied both experimentally and theoretically. It is extremely difficult to complete any realistic calculation encompassing all the currently suggested contributions such as phonon drag, virtual recoil [3], electron-phonon renormalization [4], intrinsic multiphonon scattering, and many-body corrections to the electron velocity [5]. Recently, Durczewski and Ausloos [6] calculated the TEP for a magnetic metal by considering both magnetic scattering and scattering by phonons. Applying
177
Y.S. Choi et al. / Journal of Alloys and Compounds 231 (1995) 176-181
the obtained result to the rare earth intermetallic compounds such as REAl 2, they showed that their calculations are in good agreement with the experiment. Although a satisfactory theory for metal alloys has not been completed yet, TEP measurements with a reasonable interpretation might be useful for obtaining information on the charge state of the dissolved hydrogen atoms. In this paper, we present the study of electrical transport properties, electrical resistivity and TEP, for ZrFe 2 xCrx and their hydrides.
300
.
.
.
.
.
.
250
~" oE i
200
~ ~ ~ ~ l u l l ~ J
150
~
dm~~-x__0.6 X=0.45
5] 0.3
2. Experimental details The alloys were prepared by arc melting. The starting elements were Zr chips (99.99% purity), Fe chips (99.99% purity) and Cr chunks (99.99% purity). They were weighed appropriately for the stoichiometry of Z r F e e _ x C r x. They were then arc melted under Ar on a standard water-cooled copper hearth. We remelted the initially melted button-type sample four or five times, turning it over between each melt. The prepared ingots were annealed to obtain single-phase crystal at 1000 °C for about 20 h. The hydrogenation is carried out in the gaseous phase. The quantity of absorbed hydrogen is measured as the weight difference between before and after hydrogenation, Electrical resistivity was measured using the fourprobe method with silver paint contacts. TEP was measured using a technique described previously [7].
3. Results and discussion Fig. 1 shows the electrical resistivities of the pseudobinary alloys ZrFe2_xCr x before hydrogenation as a function of temperature between 20 K and 300 K. The noticeable features in the electrical resistivity are summarized as follows. (1) The magnitude of the resistivity at 20 K, which we call the residual resistivity, gradually increases as Cr composition is increased. (2) The quite linear temperature dependence of electrical resistivity is changed into a weak temperature dependence as Cr composition is increased. Most of the residual resistivities of these pseudobinary alloys are very high compared with that of the elemental metal or that of the related binary compounds ZrF% and ZrCr 2. Another feature of the magnitude of residual resistivity is that it is satnrated when the Cr composition x is larger than 0.6 as can be seen in Fig. 1. The increase in residual resistivity could originate in the fact that the increasing randomness of the atomic potentials due to the substitution of Fe by Cr might be the strong scattering sonrces making the mean free
.25
50
--0.2
0 0
, 50
r 100
, 150
, 200
r 250
, 300
350
T(K) Fig. 1. Resistivityof ZrFe2 xCr. path of the metal alloys shorter. Similar trends in the resistivity have been found in binary solid solutions such as the C u - A u system [8]. In our system, Fe and Cr atoms can be assumed to be randomly distributed in the B sublattice and to form a type of disordered solid solution although zirconium and iron (or chromium) form the ordered Laves-type crystal AB 2. Thus the effect on the electrical resistivity of the substitution of Fe with Cr could be regarded as equivalent to that in the binary solid solution. In the present pseudobinary alloys, it can be imagined that there are two dominant conduction electron scattering mechanisms, scattering by the random atomic potentials in the B sublattice due to alloying and that by the lattice vibrations (phonons). It is well known that the scattering by the phonons gives a linearly increasing resistivity on increasing temperature. On the contrary, the scattering from the disordered atomic potential, a static imperfection, would give an electrical resistivity which is independent of temperature. The resistivity of the alloy with a Cr composition of 0.2 reveals a quite linear temperature dependence as found in Fig. 1. As the Cr composition is increased, this linear temperature dependence is gradually changed into a weak dependence. The high absolute value and the weak temperature dependence of the electrical resistivity for the alloys having higher Cr composition indicate that the scattering by the disordered atomic potential becomes dominant and the phonon scattering becomes comparatively less
178
Y.S. Choi et al. / Journal o f Alloys and Compounds 231 (1995) 176-181
important as Cr composition is increased. F r o m the t e m p e r a t u r e dependence of the electrical resistivity, we have found that the conduction electron scattering in the present alloys with x lower than 0.35 is mainly due to the phonons, while for the alloys with x higher than 0.35 the scattering due to the disordered atomic potential is dominant. Fig. 2 shows the T E E S ( T ) , for the present pseudobinary alloys as a function of t e m p e r a t u r e between 20 K and 300 K. T E P for the alloys with x = 0.2 and 0.25 exhibits a positive sign in the whole t e m p e r a t u r e range of measurement. The t e m p e r a t u r e dependence of T E P has a broad m a x i m u m around a certain temperature. A non-linear t e m p e r a t u r e dependence below r o o m t e m p e r a t u r e is often found in T E P of the transition metals or alloys. This non-linear temperature dependence of T E P might be discussed in terms of the scattering by phonons, Analysis of T E P data usually begins with the Boltzmann equation, which results in
S ( T ) = - - 1 T - K~ tel
(1)
K0
where
f dk -~ (
Kn
e2 3
Of~
2,
4,rr3 \ - - ~ } r v x I , e -- Ix)"
In the above equation, f is the Fermi function, vx is the velocity in the direction of the t e m p e r a t u r e gra-
18
,
,
14 12 10
d~ g"n" "
a 8
v ~t
4
,
,
, , • :0.2 ~ :0.25 • :0.3 o :0.* • ****•• • :0.6 • :1.5 •• • • ~ * , ~h • ~ * gl~ • [] []
|
2 o -2 -4 0
I
,50
'
100
~
150
~
200
~
250
T(K) Fig. 2. TEP of ZrF%_~Cr~ before hydrogenation,
'
300
350
dient, T is the relaxation time, /x is the chemical potential, and e is the electron energy. For the free electron case, the above equation reduces to a familiar form, the so-called Mott formula [9]:
S(T)-
7r2k 2B - T( 31elE v '
0 In o- 3 (= - 0 In e 2
0 In r -~ (2) 0 In e
~ is called a thermoelectric parameter. The second term of sc is usually neglected by assuming energyindependent scattering of conduction electrons. However, we cannot explain the non-linear t e m p e r a t u r e dependence which is often found in T E P of the metals or metal alloys with only the first term of ( which gives a linear t e m p e r a t u r e dependence for T E R In particular, for the alloys with x = 0.2 and 0.25, the second term would be important since the scattering of conduction electrons by the phonons is expected to depend very strongly on the energy. The importance of e l e c t r o n - p h o n o n interaction in T E P was given by Nielson and Taylor [10]. T h e y ascribed the deviation from the linearity in the electron diffusion thermopower to a new contribution which they called " p h o n y p h o n o n drag" ( P P D ) because its shape is closely similar to that of p h o n o n drag. However, the deviation due to PPD has the shape of a positive h u m p while the p h o n o n drag has the shape of a negative hump. This P P D arises as a natural consequence of the inclusion of intrinsic two-phonon processes in a second-order treatment of the electron scattering probability due to e l e c t r o n - p h o n o n interaction. Comparing this argument with our data, we can say that the non-linear t e m p e r a t u r e - d e p e n d e n c e of T E P for the alloys with low Cr composition originates from the conduction electron scattering by phonons. T E P at r o o m t e m p e r a t u r e is negative and almost the same ( - 2 pN K - ~) for the alloys with x = 0.3, 0.4. T E P of the alloy with x = 0.3 exhibits a non-linear temperature dependence with a zero crossing at 150 K and a broad m a x i m u m at 70 K. T E P s of the alloys with x = 0.4 are negative in the whole t e m p e r a t u r e range of measurement. Unlike for the alloy with x = 0.3, its t e m p e r a t u r e dependence is almost linear. It can be suggested that the dominance of the scattering mechanism is transferred from the scattering by phonons to that by the disordered atomic potential in this range of Cr compositions. Fig. 3 shows the t e m p e r a t u r e dependence of T E P for the alloys of x = 0 . 6 , 1.5 in m o r e detail. It is noticeable that the T E P of both alloys of x = 0.6, 1.5 varies quite linearly with the t e m p e r a t u r e and has a negative sign in the whole range of temperature. This indicates that the scattering by phonons which is supposed to cause the nonlinear t e m p e r a t u r e dependence becomes less important. This argument is con-
Y.S. Choi et al. / Journal of Alloys and Compounds 231 (1995) 176-181
0
,
,
,
,
,
,
0.5
,
o
-1
0.0
"-"% "/'• ~"*'**i.=***.
o°
00
~, >
-2
%:.:..
•. ==
,,=08
,
:. +=%
5
I=
=0*
.,** ** =-. **
:t
..•
(n
*
=t~== ooo= . * =nats=P. .
>
"..
-1.0
=°°°
." ..,,. --3
+
o8
x=1.5 •
-1.5
%
I 0
50
I 100
I 150
nm
°*o°0,
• ,,=,
--4.
,
**
X=0.6
~"
,
%0 o
-o5
"%..
=t
;
t~l%=.-=q% o%0o o X = I . D
•
,
179
I
I
I
200
250
300
--2.0 3,50
I 0
T(K)
50
I 100
I 150
I
I
I
200
250
300
350
T(K)
Fig. 3. TEP of ZrFe 2 xCrx (x = 0.6, 1.5) before hydrogenation.
Fig. 4. TEP of ZrFe2_xCrx (x = 0.6, 1.5) after hydrogenation.
sistent with that for the resistivity results as mentioned above, In the absence of inelastic scattering, e.g. scattering by phonons, the scattering by the disordered atomic potentials will yield the T E P parameter ~: of magnitude
temperatures. We will explain these two features by considering the T E P parameter ~ for the hydrides. The thermoelectric power parameter ~: can be divided into two parts C0 and ~H, where ~:0 is that before hydrogenation and #H is that yielded by dissolved hydrogen atoms, ~:0, as shown above, equals
5 2
5 2
o In IUI a In e
(3)
where IUI is the Fourier transform of the difference between the actual atomic potential and the average potential of the constituent atom. This leads to the linear temperature dependence of T E P for the alloys of x = 0.6 and 1.5. We have also measured the T E P for the alloys ZrFee_xCrxHy with x = 0.6 and 1.5 as a function of temperature to investigate the charge state of the hydrogen atom in the alloys. The reasons for choosing these alloys is the T E P of host alloys is so simple that the change after hydrogenation is easily found. The temperature dependence of T E P after hydrogenation is presented in Fig. 4. The hydrogen compositions y are 1.5 for the present alloys with x = 0.6 and 2.0 for the alloy with x = 1.5. The overall features of the change in T E P due to hydrogenation can be summarized as follows. (1) In the high temperature range (100 K and above), T E P exhibits an almost linear temperature dependence but its absolute value is lowered. (2) A positive hump is displayed at lower
0 In IUI 8 In e
(4)
It is not easy to obtain sen and also difficult to find literature to deal with that subject. T E P of palladium hydride ( P d H ) at low temperature was reported [11]. As hydrogen atoms are dissolved, the negative T E P becomes positive at low temperatures, as in our case. Nielson et al. [12] interpreted the results according to their suggestion that the hydrogen atoms could be treated as impurities and the scattering by a virtual recoil of hydrogen atom must be included. They did not, however, consider the terms caused by mixed scattering of a hydrogen atom and a p h o n o n since the motion of the impurities is treated as an independent excitation of the host metal, not connected to the p h o n o n modes of the host lattice. It has not been well established whether the dissolved hydrogen must be treated as an intercalated atom having motion independent of host lattice or as a constituent atom of an alloy, so-called hydride, having a motion connected with the metal lattice. As mentioned just above, Nielson et al. treated the dissolved hydrogen in P d H
180
Y.S. Choi et al. / Journal of Alloys and Compounds 231 (1995) 176-181
as an intercalated atom having a motion independent of the host metal and calculated the contribution to ~ by the hydrogen. This contribution gives a positive value to TEP which is consistent with the experimental results for PdH. Since this contribution to ~: is temperature independent and so gives a linear temperature dependence to T E E their treatment is not applicable to our results which reveal a non-linear temperature dependence of T E E the positive hump. To obtain the temperature-dependent thermoelectric parameter giving the positive hump in T E E we assume the hydride to be an alloy and the hydrogen as its constituent atom having motion connected with the metal lattice. Nielson et al. [10] calculated the contribution to ~: of a dilute alloy by the solute atoms as well as PPD contribution. To interpret the results summarized above, we will use their calculation for TEP of an alloy. They considered double scattering at the solute atoms and mixed scattering by a solute atom and a phonon. If we treat the hydrogen as a solute atom of the hydride, the thermoelectric parameter (H can be, as described in Ref. [10], written as 0 In IVHI N' (H = 1 -- 2 - - + 0 1 n e 6VH N A ~ ( T ) 2N)l/3 + Vo ~ A~(T)
A
-
(5)
Ev m (k B0 ) 2 M -
-
where VH is the Fourier transform of the difference between the potentials due to hydrogen and host alloy, V0 is the Fourier transform of the potential of the host alloy and the ratio N ' / N is the valence. For the exact form of the two functions ~ and ~3, one can refer to Ref. [10]. The first two terms in Eq. (5) represent the prediction of first-order theory, giving linear temperature dependence of TEP. The third term is due to double scattering at a hydrogen site and the fourth term is due to the mixed scattering by a hydrogen atom and a phonon. VH is the Fourier transform of the difference between the potentials of hydrogen and host alloy. It equals to V(H) (the potential due to hydrogen) minus V0. We suppose that the magnitude of N ' / N is 0.5 which is characteristic of the transition metal. The last two terms can be rewritten as 3 V ( H ) A ~ ( T ) +VoA[1.6~3(T ) -31F2(T)]
(6)
~3 is almost the same as 9t2. Thus ~:H becomes approximately 0 In IVHI - + [3V(H) - 1.4Vo]A~(T) (7) 1 2 0 In e The scattering mechanisms by both the disordered atomic potentials of the host alloy and the hydrogen -
potential must be considered. The resultant TEP parameter can be given by the Nordheim-Gorter rule [13] as follows: ~:_ Po~0 + ,OH~'H (8) P0 + PH In the present alloys, P0 is of the order of 200 t~f~ cm. In the hydrogenated Fe91Zrg, we have found that the resistivity due to hydrogen atoms is of the same order [14]. Thus we can assume ('~(~:0 + ~:H)/2" The corresponding TEP can be written as ¢r2kZT S ( T ) - - 31elE------~~:L 2"rr2k~3T - IciEr
[3V(H) - 1.4Vo]A~z(T )
(9)
The first term in Eq. (9) is TEP linearly dependent on temperature. ~:L of the first term is the modified TEP parameter for the linear temperature-dependent part of T E E Ev, the Fermi energy, as well as the thermoelectric parameter are changed by band filling after hydride formation. It seems that the mixed effect of these changes is the origin of the increase in the linear part of TEP at higher temperatures. The second term comes from the double scattering of conduction electrons at the hydrogen site and the mixed scattering by an H atom and a phonon. This second term seems to represent the scattering process leading to the positive hump at low temperature. We extract the linear part A T of TEP, of which A is determined by the measured value of TEP around 300 K, from the total TEP and present the result in Fig. 5. The positive hump is clearly observed. It can be said that the remaining part after extraction corresponds to the second term of the above equation. The second term reduces to a simple form at low temperature as follows: 2 7r M m [3V(H) - 1.4V0] OT L [ 1 - ~4 ~ 2{~--~} T'~ 2]j S H - 2~O (10) We have fitted this equation to our results at low temperature. The full lines shown in Fig. 5 are the curves fitted to the experimental results. We could obtain the Debye temperature OD to be 350 and 420 for the hydrides with x =0.6 and 1.5 respectively. Secondly, it is found that 3 V ( H ) - 1 . 4 V 0 must be negative to explain the observed positive hump. Since V0, the potential due to the transition metal, is originally negative, the hydrogen potential V(H) must be negative. This means that the hydrogen atoms have an attractive potential for the conduction electrons. We have found that the positive humps exhibited after hydrogenation can be well described in terms of the
Y.S. Choi et al. / Journal of Alloys and Compounds 231 (1995) 176-181
0.6
.
.
.
.
• " .
.
o
.
basis of knowledge of the dominant scattering mechanism obtained from the electrical resistivity measurement, T E P for the hydride of the alloys shows that the hydrogen plays the role of an attractive scattering centre for the conduction electrons.
.• x--1.5
0.4
•
•
181
•e
oo
"
•
• e"
"
"
o
Acknowledgment
o
o
o
o ° 0.2
•
°
o~o
s
o°
o.0
o
o
The authors thank Dr. K.Y. Kim at Korea Institute of Science and Technology (KIST) for sharing his arc melter for sample preparation. This work was supported by the Korea Science and Engineering Foundation ( K O S E F ) and the Ministry of Education ( M O E ) as well as the Hyundai M o t o r Company, Korea.
.o
O°o o o o o o o• o oo oo .o " .o o o o
o
•
ooo
o ee o
References
U --0.2
I
0
50
i
1 00
I
150
I
200
f
250
t
300
150
[1] M. Gupta and L. Schlapbach, L. Schlapbach (ed.), Hydrogen in Intermetallic Compounds 1, Springer, Berlin, 1988, pp. 139-218. [2] I. Jacob, D. Davidov and D. Shaltiel, J. Magn. Magn. Mater., 20
Fig. 5. The change in TEP of ZrFez_xCrx (x = 0.6, 1.5) after hydrogenation due to the scattering by the hydrogen atoms.
(1980) 226. [3] P.E. Nielson and P.L. Taylor, Phys. Rev. B, 10 (1974) 4061. [4] A. Hasegawa, Solid State Commun., 15 (1974) 1361. J.L. Opsal, B.J. Tharler and J. Bass, Phys. Rev. Lett., 36 (1976)
T(K)
conduction electron scattering by the hydrogen atoms and the dissolved hydrogen atoms play a role as attractive scattering centres for conduction electrons. In conclusion, we have measured the electrical
[5] S.K. Lyo, Phys. Rev. Lett., 39 (1977) 363.
resistivity of ZrFez_xCr x as a function of temperature between 20 K and 300 K. The residual resistivity increases and the linear temperature dependence of resistivity changes into a weak temperature dependence as Cr composition is increased. From these
[7] Y~W.Park, Synth. Met., 45 (1991) 173. [8] C. Kittel, Introduction to Solid State Physics, Wiley, New York, 1986, p. 582. ]9] N.F. Mott and H. Jones, The Theory of the Properties of Metals
results, we have found that the dominant scattering mechanism for conduction electrons is changed from scattering by the phonons to that by the disordered atomic potentials as Cr composition is increased. We haste also measured the T E P for ZrFez_xCr x and the hydrides with x = 0.6 and 1.5 as a function of temperature. T E P results for each alloy are interpreted on the
1211. S.K. Lyo, Phys. Rev. B, 17(1978)2545. A. Vilenkin and P.L. Taylor, Phys. Rev. B, 18 (1978) 5280. [6] K. Durczewski and M. Ausloos, J. Magn. Magn. Mater., 51 (1985) 230.
and Alloys, Clarendon, London, 1936.
[10] P.E. Nielson and P.L. Taylor, Phys. Rev. B, 15 (1974) 4061. [11] R. Fletcher, N.S. Ho and F.D. Manchester, J. Phys. C, 1 (Suppl.) (1970)$59. [12] P.E. Nielson, EL. Taylor and F.D. Manchester, Phys. Lett., 29
(1970) 161.
[13] L. Nordheim and C.J. Gorter, Physica, 2 (1935) 383. [14] Y.S. Choi, S,S. Choi, Y.W. Park, M. Hirscher and H. Kronmiiller, Mater. Sci. Eng. A, 181-182 (1994) 1035.