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The thermopower of the amorphous alloys Co80P20, Ni76Si12B12, Ni78Si8B14 and Ni80Si10B10 as a function of temperature
Journal of Non-CrystallineSolids 74 (1985) 259-269 North-Holland, Amsterdam
259
T H E T H E R M O P O W E R OF T H E A M O R P H O U S A L L O Y S CosoP20, Ni76Si12B12 , NiTsSisBt4 AND NisoSiloBlo AS A FUNCTION O F TEMPERATURE G. F R I T S C H *, W. P O L L I C H , W. D Y C K H O F F , A. S C H U L T E , A. E C K E R T and E. L U S C H E R Physik-Department, TU Mfmchen, D-8046 Garching, Munich, Fed. Rep. Germany
Received 5 December 1984
We report on thermopowerdeterminationsof the ferromagneticalloys CosoP20 and Ni soSiloBl0 as well as of the superparamagnetic alloys Ni76SilEB12 and Ni7sSisB14. The temperature range covered extends from 4.5 K up to 380 K. The effects of magnetism on the thermopower are discussed with respect to the electrical resistivity and theoretical predictions.
1. Introduction The thermopower of non-magnetic alloys is known to be dominated by a linear T dependence at high temperatures [1]. At low temperatures a non-linear behaviour appears which is tentatively ascribed to electron-phonon enhancement [2]. Otherwise, the Ziman theory for electronic transport together with Mott's diffusion-thermopower equation provides a good description of the data [1]. In the magnetic case, the thermopower is non-linear [3,4] and larger than in the non-magnetic case yielding values up to 5 /~V K -1. Such a behaviour is believed to be due to the magnetic part of the thermopower. If the various scattering mechanisms act additively to the resistivity (within the limits of the W i e d e m a n n - F r a n z law), the thermopower can be calculated with the aid of the N o r d h e i m - G o r t e r rule [4] S = E ( PJPtota! )" S,. i
Here, Ptotal = ~iPi is the total resistivity whereas the Pi and S, are the resistivity and the thermopower associated with the ith scattering mechanism,'respectively. However, if there are different groups of charge carriers, such as spin-up and spin-down electrons, then the respective thermopowers S, may be added directly to give the total S [3]. * FB Bau V/I 1, Universit~t der Bundeswehr Mianchen, D-8014 Neubiberg, Fed. Rep. Germany. 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
260
G. Fritsch et al. / Thermopower of amorphous alloys
We would like to compare thermopowers and resistivities of the NiSiB and CoP alloys with one another. This is interesting since within the three NiSiB alloys the transition from non-magnetic to superparamagnetic to ferromagnetic behaviour can be studied. Coa0P20 on the contrary is a typical ferromagnet.
2. Experimental details and results The experimental method to determine the thermopower S(T) has already been described elsewhere [5]. Briefly, it consists in measuring the thermopower voltages of the pairs copper-amorphous alloy and constantan-amorphous alloy, subject to the same temperature gradient. The thermopower of the amorphous alloy can then be derived from the ratio of these two voltages and from the knowledge of the absolute thermopower of copper Scu and constantan Scon without a knowledge of the temperature gradient. Therefore, calibration is an important point in S(T) determinations, since Scu and Scon must be known accurately as a function of temperature. We used high-purity lead (99.9999%) as a reference substance. The Pb data are taken from published values given by Roberts [6]. Using the differential method of measurement the Cu wires were calibrated with respect to Pb. The results are shown in fig. la. The scatter of the data points stemming from various runs is about + 0.05 #V K -1. Critical regions are around 60-70 K, where the phonon-drag peak in Cu occurs and around 18 K where the one of Pb shows up. In the case of Cu we finally used an average over several measurements, indicated as a full line in fig. l(a) for the analysis of the data. This leaves us with a possible systematic error of about 0.05/~V K-1 in Scu at maximum. Since the height of the phonon drag peak of the Pb reference sample may depend on preparation, we used the superconductor Nb3Sn (Tc = 18 K) to check the Cu data in the relevant T range. The result is displayed in fig. lb..The data points up to 18 K indicate that a systematic correction of about 0.02 #V K -1 had to be applied in the region from 10 to 18 K and probably also above. The final calibration curve adopted is given by the full line in fig. l(b). We consider this to be accurate to ± 0.01/xV K -1 at least. The constantan wire was calibrated with respect to Cu. We applied both an integral and a differential method to accomplish this. The integral-data were differentiated numerically. The result is summarized in fig. lc together with literature data [7]. The agreement is good. In view of this we used the literature values for the final data analysis. From the procedure described above, we derive the following error limits. Systematic errors should be smaller than 0.02 /~V K -1, except for the range 60-70 K, where values of 0.05/tV K-1 may apply. Statistical errors are to be expected around 0.01 to 0.06/zV K-1 for 10 and 300 K, respectively [8]. The samples are measured as received. All the alloys were produced by melt-spinning techniques. Rectangular specimens with dimensions 20 × 2 I n l T l2 (NiSiB) and 20 × 0.3 mm 2 (COP) were cut with the help of a razor blade out of
G. Fritsch et al. / Thermopower of amorphous alloys
261
2.5 a
2
1.5
•
Bo
•
0.5
0 0
50
100
150
200
T
250
300
350
(K]
Fig. 1. Calibration curves for thermopower measurements. (a) Cu calibration as measured (points) and as used (full line).
O.S
b
0.3
0.2
"f
0.1
.
5
.
.
.
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IO
.
.
.
.
J"
@@ @ o@ •
I
t
l
15
i
l
J
l
i
A
20
i
25
T [K] Fig. 1. (b) Low-temperature Cu calibration curve. Full points: as derived from Pb calibration; full triangles: as derived from superconducting Nb3Sn calibration; full line: calibration as used.
G. Fritsch et al. / Thermopower of amorphous alloys
262
5o
40 C
\ > ~L
30
,~
2o
0
f
o'
* ~°
•
°
lO
o
T CK~ Fig. 1. (c) Cu-Constantan calibration curve as measured (points) and as given in the literature (full line). The literature values were applied in the data analysis.
the ribbons. The NiSiB samples were delivered by Vakuumschmelze Hanau (Vitrovac), showing a thickness of 40 #m. The Co80P20 samples were given to us by Prof. Steeb from Stuttgart. Their thicknesses amount to (9.5 + 1) /~m. The results of our measurements are given in figs. 2 and 3 for the NiSiB- as well as for the Co80P2o alloys, respectively, as a function of temperature. The data for Co8oP20 consist of three data sets taken between 77-320 K as well as between 4.8-77 K and 300-380 K. The latter two were determined approximately 1 year after the first one. All sets have been corrected separately. The smooth overall appearance is an indication of the stability of this amorphous alloy and of our experimental set-up. In the case of Ni76Si12B12 two runs were performed in the T range from 4.4 to 84 K. They are both included in fig. 2(a).
3. Discussion
3.1. General behaviour The thermopower S(T) of all four alloys examined is negative in sign. S(T) of C080P20 is approaching zero strictly linear for T tending towards zero. This is not the case for the NiSiB alloys. Despite of this behaviour, the linear portions of S(T) can well be extrapolated through the origin for the alloys Ni80 BloSilo and Ni 78Si 8 B14- However, for Ni 75 Sil2 B12 a non-linearity must be assumed, since the extrapolation of the linear part shows a positive offset of about 0.10 /~V K -1. In addition, all the results exhibit a nonlinear S(T) in some T range, which will be discussed below. Since the alloys Ni8oSil0Bl0 and
G. Fritsch et al. / Thermopowerof amorphous alloys T 0
(K)
100
0 •
263
200
300
\
a
-0.2
-0.4
-0.6
-0.8
-1
Ni ~s
Si
12
B
12
-1.2
T 0
i00
(K) 200
300
b -0.5
"\N. \ oO
-1.5
Ni
Si 78
B @
14
-2
Fig. 2. Thermopower S for Ni76Si12BI2 (a) and Ni78SisB14 as a function of temperature. The dashed lines are only guides to the eye. C080 P20 seem to behave similarly as seem the alloys Ni76BI2Si12 and Ni78Si8Bl4 , b o t h of these pairs will be analyzed together. 3.2. L o w T-behaviour
The t h e r m o p o w e r of Co80P20 is linear in T up to about 120 K with a slope o f - 1 . 2 . 1 0 -2 /tV K -2. Small deviations a r o u n d 70 to 80 K m a y be traced
G. Fritsch et al. / Thermopower of amorphous alloys
264
T
0
0
(K)
100
200
500
C -1
-2 0")
-5 ee% oo
-4
Ni
60
Si
10
B
°Ooo
10
OOOo000OO• OOoI9
-5
Fig. 2. (c) Thermopower S for Nis0SiloBlo. The dashed line is only a guide to the eye.
T
0
0
100
CK)
300
200
Co
-1
|0
400
P 20
% -2
o%~°°o e°%%'t, " " i t - . . , , . o . s ~'~
-3i Fig. 3. Thermopower S for CoaoP2o as a function of temperature. The dashed lines are only guides to the eye.
G. Fritsch et al. /Thermopower of amorphous alloys
265
b a c k to s y s t e m a t i c errors in the t h e r m o p o w e r c a l i b r a t i o n in this range as well as in the t e m p e r a t u r e m e a s u r e m e n t (liquid n i t r o g e n b o i l i n g point). Nis0Sil0B10 shows a similar b e h a v i o u r with a slope of - 2.1 • 10 -2/~V K - 2 up to a b o u t 125 K. H o w e v e r , there seems to b e an a d d i t i o n a l c o n t r i b u t i o n up to 30 K of a b o u t 0.1/~V K -1. This figure is b e y o n d the s y s t e m a t i c error in this T range. N o such effect is seen in Co80P20. In the case of Ni76Si12B12 a n d Ni78Si8B14 we see a linear T d e p e n d e n c e a b o v e 60 K with slopes of - 0 . 4 2 . 1 0 -2 /~V K - 2 a n d - 0 . 6 3 - 10 -2 #V K - 2 respectively. Below a b o u t 50 K n o n - l i n e a r b e h a v i o u r can be d e t e c t e d clearly (fig. 2). T h e a d d i t i o n a l c o n t r i b u t i o n is negative in sign. T h e m a g n i t u d e o f this effect with respect to linear e x t r a p o l a t i o n s of the high T b e h a v i o u r is a b o u t 0.2 a n d 0.12 /zV K -1 for Ni76Si12B12 a n d Ni78Si8B14, respectively. However, o n e s h o u l d keep in m i n d that it is n o t clear w h e t h e r a linear e x t r a p o l a t i o n is m e a n i n g f u l for the Ni76SilEB12 alloy, b e c a u s e of the offset t h e r m o p o w e r observed. Hence, a smaller value of a b o u t 0.1 #V K - 1 is likely for this alloy also.
3.3. Relation between thermopower and resistivity D a t a o n the electrical resistivity, m a g n e t o r e s i s t i v i t y a n d H a l l effect of the N i S i B alloys have b e e n p u b l i s h e d earlier [9]. Resistivity d a t a of C080P20 are also available [10,11]. A l l four alloys are c h a r a c t e r i z e d b y a positive T coefficient of resistivity at high T a n d a negative one at low T, thus f o r m i n g resistivity m i n i m a . The l o c a t i o n s of the resistivity m i n i m a together with o t h e r d a t a are c o m p i l e d in table 1. T h e alloy C080P20 is k n o w n to b e f e r r o m a g n e t i c w i t h Tc = (730 __ 30) K [11]. W e have shown that Ni80SiloBlo possesses a C u r i e t e m p e r a t u r e Tc = (110 ± 20) K [9]. T h e alloys Ni76SilEB12 as well as Ni78Si8B14 are s u p e r p a r a m a g n e t s with Tc ~ 0 K. Such b e h a v i o u r is d e m o n -
Table 1 Some data for the NiSiB- and CoP-alloys. Train: temperature of the resistivity minimum; iOadd//Pmin: additional resistivity contribution below Tmin at Tmin / T = 4, with respect to the resistivity Prnin at the minimum; TnHa: temperature below which non-linearities in the Hall-coefficient R H occur; RHo: ordinary Hall-coefficient; Tsa: temperature below and above which nonlinearities in the thermopower occur; dS[dTh: linear slope of the thermopower S(T), and To: Curie-temperature Property
Ni76Si12B12
NiTsSiaB14
T~n/K
23 b) 1.0 X 10 -3b) 40 b) -7.7 b) < 40 a) +0.42 1.1 -
20.9 b) 1.0× 10 -3b ) 40 b) --8.7 b) < 40 a) 0.63 1.9 -
Padd//Pmin
TnHa/K RH0(300 K)×1011/m 3 Cb -1
Tsa/K - d S [ d T ] j × 102//~V K -2 - S ( 3 0 0 K ) / ~ V K -1
Tc/K a) Ref. 10; b) ref. 9; c) ref. 11.
NisoSiloBlo 15.8 b) 1.5 × 10 -3b ) 200 b) --10.1 b) > 120 a) 2.1 5.0 110±20 b)
Co8oP2o 38 a) 1.0× 10 -3a ) _ -> 120 1.2 2.7 730+30 c)
266
G. Fritschet al. / Thermopowerof amorphousalloys
strated by analysing the Hall effect (oH(B), RH(T)). Characteristic values are reproduced in table 1. Let us discuss the superparamagnetic alloys Ni76SilEB12 and Ni78Si8B14 first. Their thermopower is linear above 50 K in both cases, indicating a behaviour to be expected for non-magnetic alloys. This interpretation is supported by Hall-resistivity data, showing PH to be proportional to the magnetic field B in this T range [9]. Hence, the positive T coefficient of resistivity is not correlated to magnetism. It is most probably caused by inelastic potential scattering from thermal vibrations similar to the case of diamagnetic Pd80Si20 [12]. The magnitudes of S at 300 K amount t o - 1.1 as well as - 1.9 #V K-1 for Ni 76Si12B12 and Ni 78Si8B14, respectively. The moduli of these numbers are similar to the ones observed for CuZr- or CuTi alloys. The strong variation of a factor of 1.8 in changing the Ni concentration by only 2% may be caused by the influence of the varying B concentration [3]. The on(B, T) as well as the RH(T ) data [9] show that magnetic behaviour develops below 40 K. Simultaneously, an additional contribution to the linear thermopower is seen. Hence, we attribute this effect to a magnetic scattering mechanism. The resistivity minima for both the alloys (table 1) are around 22 K. Hence, the low T contribution of the resistivity ApadO starts already above that temperature. Assuming that the electrons are now scattered additionally by magnetic order (magnetic dusters) or some other magnetic effect, we use the Nordheim-Gorter rule to estimate the magnitude of the superparamagnetic thermopower Ssp. The relative additional resistivity is about Apadd//Pmin ~---10-3 (see table 1) and the additional thermopower ASsp amounts to about 0.12/~V K -1 (fig. 2). Therefore, we get Ssp --- 120/~V K -1. Such a large value may be explained taking a Kondo-like scattering mechanism into account as given by Grest et al. [13]. The situation is more complicated considering the ferromagnetic alloys. Whereas the resistivity data look similar (fig. 4), as do the thermopower data (figs. 2 and 3), the magnetic behaviour is quite different. The Curie temperature of Co80P20 is very high (730 K), the one of Nis0Sil0B10 is low (110 K). Hence, Cos0P20 is observed in the ferromagnetic state throughout the T range examined, whereas Nis0Six0B10 is non-magnetic above 200 K [9]. The Prt(B) curves are straight lines up to B = 1.2 T, ruling out any B-dependent magnetic effects. Thus, we are forced to conclude that the nonlinear T dependence of the thermopower S is not magnetic in origin at all or different types of magnetism are operating. In addition, the magnitude of the thermopower at 300 K is large, being - 2.7 as well as - 5.0 #V K -1 for Co80P20 and Ni80Sil0B10, respectively. Due to the Nordheim-Gorter rule, an enormous magnetic contribution to the resistivity should be present, in order to explain the large and non-linear thermopower by a magnetic effect. The resistivity of both alloys is 100/x$2cm and 119 /~2cm for Ni8oSiloB10 and Co8oP2o, respectively. These values are close to the resistivity of PdsoSi20 of 88 #~2cm, which is diamagnetic. Hence, a large magnetic resistivity contribution is not plausible. Finally, only a small change in slope in the p ( T ) curve of Ni8oSiloBlo is seen at about 170 K.
G. Fritsch et al. / Thermopowerof amorphous alloys
267
1.0t,5 1.0/,0
1.035 1.030 A
1.025 1.020
,mr"
I'--
1.015 1.010 1.005 1.000
j
j N,7os,12 2
1.0001 1.000 i
i
100
200
300
T[K] Fig. 4. Electrical resistivity data for the NiSiB alloys as a function of temperature. The change in slope at about 170 K is indicated by an arrow in case of NisoSil0Ba0. The straight lines are only meant as guides to the eye. The data are normalized with respect to their values at 4.2 K.
Above this temperature all magnetism should have disappeared [9]. This resistivity argument, however, does not hold, if we have several groups of electrons contributing independently to the conductivity [3]. In this situation the question arises if theories such as proposed by Korenblit [14] and Str0m-Olsen et al. [3] yielding S ( T ) of disordered ferromagnetic alloys as S = ( k B / e ) ( T r -- r~ ) / t ,
where the %'s are the elastic relaxation time for spin-up and spin-down scattering and t represents the mean energy-relaxation time of the system [14] (the other symbols having the usual meaning), are applicable at all in the case of NisoSil0B]0. The origin of the small additional contribution to the thermopower of NiaoSiloBao at low temperature may be similar to the effects observed in the other NiSiB alloys. We do not see such an effect in Co8oP2o. Since the magnitude of the resistivity due to the additional scattering mechanism for the same ratio Tmin/T (see table 1) are roughly equivalent, this difference could be due to a different size of the thermopower associated.
268
G. Fritsch et al. / Thermopower of amorphous alloys
3.4. Comparison with literature values Various authors have published thermopower measurements on magnetic amorphous alloys such as Feloo_xBx [1,3,4], Fea0Ni4oP14B6 [1,4], Fe32Ni36Cr14P12B6 [1,4], FeTaMO2B20 [1,4], Fe82Si6B12 [1], Fe29Nia9P14B6Si 2 [4], Fe39Ni39MoaSi6B12 [16], FexNis0_xB18Si 2 and Fet0o_~Zrx [15,17]. Among them, only the Metglas 2826A (Fe32Ni36Cr14P12B6) offers a Curie temperature below 300 K (Tc = 249 K). However, the T range covered by these experiments is too small to allow for a detailed comparison as was possible in the case of Nia0Sil0B10 . The other results look all very similar to the ones observed for the Co80P20- or the Nis0Sil0B~0-alloys.
4. Conclusions
The results of S(T) reported for the NiSiB alloys permit to study the effect of magnetism on the thermopower in the temperature range below 300 K. Whereas the interpretation of the behaviour seems to be straightforward for the superparamagnetic alloys Ni76Si12B12 and Ni78Si8B14, the ferromagnetic alloy Ni80SiloBlo showing a Tc of 110 K documents that an explanation of its non-linear S(T) by ferromagnetism alone is not sufficient. Hence, the usual interpretation of the S(T) curves for ferromagnetic alloys has to be re-examined in this case. The authors would like to thank Professor Steeb, Stuttgart and Vakuumschmelze Hanau for supplying the samples.
References [1] J.P. Carini, S. Basak and S.R. Nagel, J. de Phys. C8 (1980) 463; S. Basak, S.R. Nagel and B.C. Giessen, Phys. Rev. B21 (1980) 4049. [2] B.L. Gallagher and D. Greig, J. Phys. F12 (1982) 1721; B.L. Gallagher, J. Phys. F l l (1981) L 207; J. J~lckle, J. Phys. F10 (1980) L43. [3] J.O. Str6m-Olsen, M. Olivier, Z. Altounian, W.B. Muir and R.W. Cochrane, J. Non-Crystalline Solids 61/62 (1984) 1391. [4] M.N. Baibich, W.B. Muir, G. B61anger, J. Destry, H.S. Elzinga and P.A. Schroeder, Phys. Lett. 73A (1979) 328. [5] G. Fritsch, W. Dyckhoff, J. Willer and E. Li~scher, Z. Physik B53 (1983) 191. [6] R.B. Roberts, Phil. Mag. 36 (1977) 91; 43 (1981) 1125. [7] L.L. Sparks and R.L. Powell, Cryogenics 12 (1972) 40. [8] W. Dyckhoff, diploma work, TU Munich (1982) unpublished; W. Pollich, diploma work, TU Munich (1984) unpublished. [9] A. Schulte, A. Eckert and G. Fritsch, Solid St. Commun. 50 (1984) 799; G. Fritsch, E. Liischer, A. Schulte, A. Eckert, J. Wilier and W. Dyckhoff, J. Non-Crystalline Solids 61/62 (1984) 1225; A. Schulte, G. Fritsch and E. Lt~scher, Proc. LT-17 Karlsruhe, 1984, eds., U. Eckern, A. Schmid, W. Weber, H. Wahl (North-Holland, Amsterdam, 1984) Part I, p. 369. [10] G. Fritsch, W. Dyckhoff, W. Pollich and E. Ltischer, J. Phys. F, to be published.
G. Fritsch et al. / Thermopower of amorphous alloys [11] [12] [13] [14] [15] [16]
269
G. Dietz and R. Sonneberger, Z. Physik B46 (1982) 213. S.B. Dierker, H. Gudmundsson and A.C. Anderson, Solid St. Commun. 33 (1980) 527. G.S. Grest and S.R. Nagel, Phys. Rev. B19 (1979) 3571. J.Ya. Korenblit, J. Phys. F12 (1982) 1259. J. Ivkov, Z. Marohni6, E. Babi6, M. Miljak and H.H. Liebermann, J. Phys. F13 (1983) 2137. A.K. Bhatnagar, B. Bhanu Prasack and N.R. Runi Rathnam, J. Non-Crystalline Solids 61/62 (1984) 1201. [17] W.B. Muir, Z. Altounian, M. From, J.O. Str6m-Olsen and R.W. Cochrane, J. Non-Crystalline Solids 61/62 (1984) 1115.
259
T H E T H E R M O P O W E R OF T H E A M O R P H O U S A L L O Y S CosoP20, Ni76Si12B12 , NiTsSisBt4 AND NisoSiloBlo AS A FUNCTION O F TEMPERATURE G. F R I T S C H *, W. P O L L I C H , W. D Y C K H O F F , A. S C H U L T E , A. E C K E R T and E. L U S C H E R Physik-Department, TU Mfmchen, D-8046 Garching, Munich, Fed. Rep. Germany
Received 5 December 1984
We report on thermopowerdeterminationsof the ferromagneticalloys CosoP20 and Ni soSiloBl0 as well as of the superparamagnetic alloys Ni76SilEB12 and Ni7sSisB14. The temperature range covered extends from 4.5 K up to 380 K. The effects of magnetism on the thermopower are discussed with respect to the electrical resistivity and theoretical predictions.
1. Introduction The thermopower of non-magnetic alloys is known to be dominated by a linear T dependence at high temperatures [1]. At low temperatures a non-linear behaviour appears which is tentatively ascribed to electron-phonon enhancement [2]. Otherwise, the Ziman theory for electronic transport together with Mott's diffusion-thermopower equation provides a good description of the data [1]. In the magnetic case, the thermopower is non-linear [3,4] and larger than in the non-magnetic case yielding values up to 5 /~V K -1. Such a behaviour is believed to be due to the magnetic part of the thermopower. If the various scattering mechanisms act additively to the resistivity (within the limits of the W i e d e m a n n - F r a n z law), the thermopower can be calculated with the aid of the N o r d h e i m - G o r t e r rule [4] S = E ( PJPtota! )" S,. i
Here, Ptotal = ~iPi is the total resistivity whereas the Pi and S, are the resistivity and the thermopower associated with the ith scattering mechanism,'respectively. However, if there are different groups of charge carriers, such as spin-up and spin-down electrons, then the respective thermopowers S, may be added directly to give the total S [3]. * FB Bau V/I 1, Universit~t der Bundeswehr Mianchen, D-8014 Neubiberg, Fed. Rep. Germany. 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
260
G. Fritsch et al. / Thermopower of amorphous alloys
We would like to compare thermopowers and resistivities of the NiSiB and CoP alloys with one another. This is interesting since within the three NiSiB alloys the transition from non-magnetic to superparamagnetic to ferromagnetic behaviour can be studied. Coa0P20 on the contrary is a typical ferromagnet.
2. Experimental details and results The experimental method to determine the thermopower S(T) has already been described elsewhere [5]. Briefly, it consists in measuring the thermopower voltages of the pairs copper-amorphous alloy and constantan-amorphous alloy, subject to the same temperature gradient. The thermopower of the amorphous alloy can then be derived from the ratio of these two voltages and from the knowledge of the absolute thermopower of copper Scu and constantan Scon without a knowledge of the temperature gradient. Therefore, calibration is an important point in S(T) determinations, since Scu and Scon must be known accurately as a function of temperature. We used high-purity lead (99.9999%) as a reference substance. The Pb data are taken from published values given by Roberts [6]. Using the differential method of measurement the Cu wires were calibrated with respect to Pb. The results are shown in fig. la. The scatter of the data points stemming from various runs is about + 0.05 #V K -1. Critical regions are around 60-70 K, where the phonon-drag peak in Cu occurs and around 18 K where the one of Pb shows up. In the case of Cu we finally used an average over several measurements, indicated as a full line in fig. l(a) for the analysis of the data. This leaves us with a possible systematic error of about 0.05/~V K-1 in Scu at maximum. Since the height of the phonon drag peak of the Pb reference sample may depend on preparation, we used the superconductor Nb3Sn (Tc = 18 K) to check the Cu data in the relevant T range. The result is displayed in fig. lb..The data points up to 18 K indicate that a systematic correction of about 0.02 #V K -1 had to be applied in the region from 10 to 18 K and probably also above. The final calibration curve adopted is given by the full line in fig. l(b). We consider this to be accurate to ± 0.01/xV K -1 at least. The constantan wire was calibrated with respect to Cu. We applied both an integral and a differential method to accomplish this. The integral-data were differentiated numerically. The result is summarized in fig. lc together with literature data [7]. The agreement is good. In view of this we used the literature values for the final data analysis. From the procedure described above, we derive the following error limits. Systematic errors should be smaller than 0.02 /~V K -1, except for the range 60-70 K, where values of 0.05/tV K-1 may apply. Statistical errors are to be expected around 0.01 to 0.06/zV K-1 for 10 and 300 K, respectively [8]. The samples are measured as received. All the alloys were produced by melt-spinning techniques. Rectangular specimens with dimensions 20 × 2 I n l T l2 (NiSiB) and 20 × 0.3 mm 2 (COP) were cut with the help of a razor blade out of
G. Fritsch et al. / Thermopower of amorphous alloys
261
2.5 a
2
1.5
•
Bo
•
0.5
0 0
50
100
150
200
T
250
300
350
(K]
Fig. 1. Calibration curves for thermopower measurements. (a) Cu calibration as measured (points) and as used (full line).
O.S
b
0.3
0.2
"f
0.1
.
5
.
.
.
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IO
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.
.
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T [K] Fig. 1. (b) Low-temperature Cu calibration curve. Full points: as derived from Pb calibration; full triangles: as derived from superconducting Nb3Sn calibration; full line: calibration as used.
G. Fritsch et al. / Thermopower of amorphous alloys
262
5o
40 C
\ > ~L
30
,~
2o
0
f
o'
* ~°
•
°
lO
o
T CK~ Fig. 1. (c) Cu-Constantan calibration curve as measured (points) and as given in the literature (full line). The literature values were applied in the data analysis.
the ribbons. The NiSiB samples were delivered by Vakuumschmelze Hanau (Vitrovac), showing a thickness of 40 #m. The Co80P20 samples were given to us by Prof. Steeb from Stuttgart. Their thicknesses amount to (9.5 + 1) /~m. The results of our measurements are given in figs. 2 and 3 for the NiSiB- as well as for the Co80P2o alloys, respectively, as a function of temperature. The data for Co8oP20 consist of three data sets taken between 77-320 K as well as between 4.8-77 K and 300-380 K. The latter two were determined approximately 1 year after the first one. All sets have been corrected separately. The smooth overall appearance is an indication of the stability of this amorphous alloy and of our experimental set-up. In the case of Ni76Si12B12 two runs were performed in the T range from 4.4 to 84 K. They are both included in fig. 2(a).
3. Discussion
3.1. General behaviour The thermopower S(T) of all four alloys examined is negative in sign. S(T) of C080P20 is approaching zero strictly linear for T tending towards zero. This is not the case for the NiSiB alloys. Despite of this behaviour, the linear portions of S(T) can well be extrapolated through the origin for the alloys Ni80 BloSilo and Ni 78Si 8 B14- However, for Ni 75 Sil2 B12 a non-linearity must be assumed, since the extrapolation of the linear part shows a positive offset of about 0.10 /~V K -1. In addition, all the results exhibit a nonlinear S(T) in some T range, which will be discussed below. Since the alloys Ni8oSil0Bl0 and
G. Fritsch et al. / Thermopowerof amorphous alloys T 0
(K)
100
0 •
263
200
300
\
a
-0.2
-0.4
-0.6
-0.8
-1
Ni ~s
Si
12
B
12
-1.2
T 0
i00
(K) 200
300
b -0.5
"\N. \ oO
-1.5
Ni
Si 78
B @
14
-2
Fig. 2. Thermopower S for Ni76Si12BI2 (a) and Ni78SisB14 as a function of temperature. The dashed lines are only guides to the eye. C080 P20 seem to behave similarly as seem the alloys Ni76BI2Si12 and Ni78Si8Bl4 , b o t h of these pairs will be analyzed together. 3.2. L o w T-behaviour
The t h e r m o p o w e r of Co80P20 is linear in T up to about 120 K with a slope o f - 1 . 2 . 1 0 -2 /tV K -2. Small deviations a r o u n d 70 to 80 K m a y be traced
G. Fritsch et al. / Thermopower of amorphous alloys
264
T
0
0
(K)
100
200
500
C -1
-2 0")
-5 ee% oo
-4
Ni
60
Si
10
B
°Ooo
10
OOOo000OO• OOoI9
-5
Fig. 2. (c) Thermopower S for Nis0SiloBlo. The dashed line is only a guide to the eye.
T
0
0
100
CK)
300
200
Co
-1
|0
400
P 20
% -2
o%~°°o e°%%'t, " " i t - . . , , . o . s ~'~
-3i Fig. 3. Thermopower S for CoaoP2o as a function of temperature. The dashed lines are only guides to the eye.
G. Fritsch et al. /Thermopower of amorphous alloys
265
b a c k to s y s t e m a t i c errors in the t h e r m o p o w e r c a l i b r a t i o n in this range as well as in the t e m p e r a t u r e m e a s u r e m e n t (liquid n i t r o g e n b o i l i n g point). Nis0Sil0B10 shows a similar b e h a v i o u r with a slope of - 2.1 • 10 -2/~V K - 2 up to a b o u t 125 K. H o w e v e r , there seems to b e an a d d i t i o n a l c o n t r i b u t i o n up to 30 K of a b o u t 0.1/~V K -1. This figure is b e y o n d the s y s t e m a t i c error in this T range. N o such effect is seen in Co80P20. In the case of Ni76Si12B12 a n d Ni78Si8B14 we see a linear T d e p e n d e n c e a b o v e 60 K with slopes of - 0 . 4 2 . 1 0 -2 /~V K - 2 a n d - 0 . 6 3 - 10 -2 #V K - 2 respectively. Below a b o u t 50 K n o n - l i n e a r b e h a v i o u r can be d e t e c t e d clearly (fig. 2). T h e a d d i t i o n a l c o n t r i b u t i o n is negative in sign. T h e m a g n i t u d e o f this effect with respect to linear e x t r a p o l a t i o n s of the high T b e h a v i o u r is a b o u t 0.2 a n d 0.12 /zV K -1 for Ni76Si12B12 a n d Ni78Si8B14, respectively. However, o n e s h o u l d keep in m i n d that it is n o t clear w h e t h e r a linear e x t r a p o l a t i o n is m e a n i n g f u l for the Ni76SilEB12 alloy, b e c a u s e of the offset t h e r m o p o w e r observed. Hence, a smaller value of a b o u t 0.1 #V K - 1 is likely for this alloy also.
3.3. Relation between thermopower and resistivity D a t a o n the electrical resistivity, m a g n e t o r e s i s t i v i t y a n d H a l l effect of the N i S i B alloys have b e e n p u b l i s h e d earlier [9]. Resistivity d a t a of C080P20 are also available [10,11]. A l l four alloys are c h a r a c t e r i z e d b y a positive T coefficient of resistivity at high T a n d a negative one at low T, thus f o r m i n g resistivity m i n i m a . The l o c a t i o n s of the resistivity m i n i m a together with o t h e r d a t a are c o m p i l e d in table 1. T h e alloy C080P20 is k n o w n to b e f e r r o m a g n e t i c w i t h Tc = (730 __ 30) K [11]. W e have shown that Ni80SiloBlo possesses a C u r i e t e m p e r a t u r e Tc = (110 ± 20) K [9]. T h e alloys Ni76SilEB12 as well as Ni78Si8B14 are s u p e r p a r a m a g n e t s with Tc ~ 0 K. Such b e h a v i o u r is d e m o n -
Table 1 Some data for the NiSiB- and CoP-alloys. Train: temperature of the resistivity minimum; iOadd//Pmin: additional resistivity contribution below Tmin at Tmin / T = 4, with respect to the resistivity Prnin at the minimum; TnHa: temperature below which non-linearities in the Hall-coefficient R H occur; RHo: ordinary Hall-coefficient; Tsa: temperature below and above which nonlinearities in the thermopower occur; dS[dTh: linear slope of the thermopower S(T), and To: Curie-temperature Property
Ni76Si12B12
NiTsSiaB14
T~n/K
23 b) 1.0 X 10 -3b) 40 b) -7.7 b) < 40 a) +0.42 1.1 -
20.9 b) 1.0× 10 -3b ) 40 b) --8.7 b) < 40 a) 0.63 1.9 -
Padd//Pmin
TnHa/K RH0(300 K)×1011/m 3 Cb -1
Tsa/K - d S [ d T ] j × 102//~V K -2 - S ( 3 0 0 K ) / ~ V K -1
Tc/K a) Ref. 10; b) ref. 9; c) ref. 11.
NisoSiloBlo 15.8 b) 1.5 × 10 -3b ) 200 b) --10.1 b) > 120 a) 2.1 5.0 110±20 b)
Co8oP2o 38 a) 1.0× 10 -3a ) _ -> 120 1.2 2.7 730+30 c)
266
G. Fritschet al. / Thermopowerof amorphousalloys
strated by analysing the Hall effect (oH(B), RH(T)). Characteristic values are reproduced in table 1. Let us discuss the superparamagnetic alloys Ni76SilEB12 and Ni78Si8B14 first. Their thermopower is linear above 50 K in both cases, indicating a behaviour to be expected for non-magnetic alloys. This interpretation is supported by Hall-resistivity data, showing PH to be proportional to the magnetic field B in this T range [9]. Hence, the positive T coefficient of resistivity is not correlated to magnetism. It is most probably caused by inelastic potential scattering from thermal vibrations similar to the case of diamagnetic Pd80Si20 [12]. The magnitudes of S at 300 K amount t o - 1.1 as well as - 1.9 #V K-1 for Ni 76Si12B12 and Ni 78Si8B14, respectively. The moduli of these numbers are similar to the ones observed for CuZr- or CuTi alloys. The strong variation of a factor of 1.8 in changing the Ni concentration by only 2% may be caused by the influence of the varying B concentration [3]. The on(B, T) as well as the RH(T ) data [9] show that magnetic behaviour develops below 40 K. Simultaneously, an additional contribution to the linear thermopower is seen. Hence, we attribute this effect to a magnetic scattering mechanism. The resistivity minima for both the alloys (table 1) are around 22 K. Hence, the low T contribution of the resistivity ApadO starts already above that temperature. Assuming that the electrons are now scattered additionally by magnetic order (magnetic dusters) or some other magnetic effect, we use the Nordheim-Gorter rule to estimate the magnitude of the superparamagnetic thermopower Ssp. The relative additional resistivity is about Apadd//Pmin ~---10-3 (see table 1) and the additional thermopower ASsp amounts to about 0.12/~V K -1 (fig. 2). Therefore, we get Ssp --- 120/~V K -1. Such a large value may be explained taking a Kondo-like scattering mechanism into account as given by Grest et al. [13]. The situation is more complicated considering the ferromagnetic alloys. Whereas the resistivity data look similar (fig. 4), as do the thermopower data (figs. 2 and 3), the magnetic behaviour is quite different. The Curie temperature of Co80P20 is very high (730 K), the one of Nis0Sil0B10 is low (110 K). Hence, Cos0P20 is observed in the ferromagnetic state throughout the T range examined, whereas Nis0Six0B10 is non-magnetic above 200 K [9]. The Prt(B) curves are straight lines up to B = 1.2 T, ruling out any B-dependent magnetic effects. Thus, we are forced to conclude that the nonlinear T dependence of the thermopower S is not magnetic in origin at all or different types of magnetism are operating. In addition, the magnitude of the thermopower at 300 K is large, being - 2.7 as well as - 5.0 #V K -1 for Co80P20 and Ni80Sil0B10, respectively. Due to the Nordheim-Gorter rule, an enormous magnetic contribution to the resistivity should be present, in order to explain the large and non-linear thermopower by a magnetic effect. The resistivity of both alloys is 100/x$2cm and 119 /~2cm for Ni8oSiloB10 and Co8oP2o, respectively. These values are close to the resistivity of PdsoSi20 of 88 #~2cm, which is diamagnetic. Hence, a large magnetic resistivity contribution is not plausible. Finally, only a small change in slope in the p ( T ) curve of Ni8oSiloBlo is seen at about 170 K.
G. Fritsch et al. / Thermopowerof amorphous alloys
267
1.0t,5 1.0/,0
1.035 1.030 A
1.025 1.020
,mr"
I'--
1.015 1.010 1.005 1.000
j
j N,7os,12 2
1.0001 1.000 i
i
100
200
300
T[K] Fig. 4. Electrical resistivity data for the NiSiB alloys as a function of temperature. The change in slope at about 170 K is indicated by an arrow in case of NisoSil0Ba0. The straight lines are only meant as guides to the eye. The data are normalized with respect to their values at 4.2 K.
Above this temperature all magnetism should have disappeared [9]. This resistivity argument, however, does not hold, if we have several groups of electrons contributing independently to the conductivity [3]. In this situation the question arises if theories such as proposed by Korenblit [14] and Str0m-Olsen et al. [3] yielding S ( T ) of disordered ferromagnetic alloys as S = ( k B / e ) ( T r -- r~ ) / t ,
where the %'s are the elastic relaxation time for spin-up and spin-down scattering and t represents the mean energy-relaxation time of the system [14] (the other symbols having the usual meaning), are applicable at all in the case of NisoSil0B]0. The origin of the small additional contribution to the thermopower of NiaoSiloBao at low temperature may be similar to the effects observed in the other NiSiB alloys. We do not see such an effect in Co8oP2o. Since the magnitude of the resistivity due to the additional scattering mechanism for the same ratio Tmin/T (see table 1) are roughly equivalent, this difference could be due to a different size of the thermopower associated.
268
G. Fritsch et al. / Thermopower of amorphous alloys
3.4. Comparison with literature values Various authors have published thermopower measurements on magnetic amorphous alloys such as Feloo_xBx [1,3,4], Fea0Ni4oP14B6 [1,4], Fe32Ni36Cr14P12B6 [1,4], FeTaMO2B20 [1,4], Fe82Si6B12 [1], Fe29Nia9P14B6Si 2 [4], Fe39Ni39MoaSi6B12 [16], FexNis0_xB18Si 2 and Fet0o_~Zrx [15,17]. Among them, only the Metglas 2826A (Fe32Ni36Cr14P12B6) offers a Curie temperature below 300 K (Tc = 249 K). However, the T range covered by these experiments is too small to allow for a detailed comparison as was possible in the case of Nia0Sil0B10 . The other results look all very similar to the ones observed for the Co80P20- or the Nis0Sil0B~0-alloys.
4. Conclusions
The results of S(T) reported for the NiSiB alloys permit to study the effect of magnetism on the thermopower in the temperature range below 300 K. Whereas the interpretation of the behaviour seems to be straightforward for the superparamagnetic alloys Ni76Si12B12 and Ni78Si8B14, the ferromagnetic alloy Ni80SiloBlo showing a Tc of 110 K documents that an explanation of its non-linear S(T) by ferromagnetism alone is not sufficient. Hence, the usual interpretation of the S(T) curves for ferromagnetic alloys has to be re-examined in this case. The authors would like to thank Professor Steeb, Stuttgart and Vakuumschmelze Hanau for supplying the samples.
References [1] J.P. Carini, S. Basak and S.R. Nagel, J. de Phys. C8 (1980) 463; S. Basak, S.R. Nagel and B.C. Giessen, Phys. Rev. B21 (1980) 4049. [2] B.L. Gallagher and D. Greig, J. Phys. F12 (1982) 1721; B.L. Gallagher, J. Phys. F l l (1981) L 207; J. J~lckle, J. Phys. F10 (1980) L43. [3] J.O. Str6m-Olsen, M. Olivier, Z. Altounian, W.B. Muir and R.W. Cochrane, J. Non-Crystalline Solids 61/62 (1984) 1391. [4] M.N. Baibich, W.B. Muir, G. B61anger, J. Destry, H.S. Elzinga and P.A. Schroeder, Phys. Lett. 73A (1979) 328. [5] G. Fritsch, W. Dyckhoff, J. Willer and E. Li~scher, Z. Physik B53 (1983) 191. [6] R.B. Roberts, Phil. Mag. 36 (1977) 91; 43 (1981) 1125. [7] L.L. Sparks and R.L. Powell, Cryogenics 12 (1972) 40. [8] W. Dyckhoff, diploma work, TU Munich (1982) unpublished; W. Pollich, diploma work, TU Munich (1984) unpublished. [9] A. Schulte, A. Eckert and G. Fritsch, Solid St. Commun. 50 (1984) 799; G. Fritsch, E. Liischer, A. Schulte, A. Eckert, J. Wilier and W. Dyckhoff, J. Non-Crystalline Solids 61/62 (1984) 1225; A. Schulte, G. Fritsch and E. Lt~scher, Proc. LT-17 Karlsruhe, 1984, eds., U. Eckern, A. Schmid, W. Weber, H. Wahl (North-Holland, Amsterdam, 1984) Part I, p. 369. [10] G. Fritsch, W. Dyckhoff, W. Pollich and E. Ltischer, J. Phys. F, to be published.
G. Fritsch et al. / Thermopower of amorphous alloys [11] [12] [13] [14] [15] [16]
269
G. Dietz and R. Sonneberger, Z. Physik B46 (1982) 213. S.B. Dierker, H. Gudmundsson and A.C. Anderson, Solid St. Commun. 33 (1980) 527. G.S. Grest and S.R. Nagel, Phys. Rev. B19 (1979) 3571. J.Ya. Korenblit, J. Phys. F12 (1982) 1259. J. Ivkov, Z. Marohni6, E. Babi6, M. Miljak and H.H. Liebermann, J. Phys. F13 (1983) 2137. A.K. Bhatnagar, B. Bhanu Prasack and N.R. Runi Rathnam, J. Non-Crystalline Solids 61/62 (1984) 1201. [17] W.B. Muir, Z. Altounian, M. From, J.O. Str6m-Olsen and R.W. Cochrane, J. Non-Crystalline Solids 61/62 (1984) 1115.