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Thermoelectric power and resistivity of dilute Ag-Yb alloys at low temperatures
t’hvsica 77 (1974) 609- 614 0 North-Holland Publishing Co
LETTER
TO THE EDITOR
THERMOELECTRIC OF DILUTE
Ag-Yb
POWER AND RESISTIVITY
ALLOYS
F. F. BEKKER Natuurkundig
AT LOW TEMPERATURES
and C. J. A. VAN DUREN
Laboratorium, University of‘ Amsterdam, Amsterdam, The Netherlands Received
3 December
1974
Synopsis Thermoelectric force and resistivity of some dilute Ag-Yb alloys have been measured and analysed in terms of a d-like contribution to the scattering from divalent nonmagnetic Yb. Kondo behaviour is exclusively attributed to traces of iron.
From susceptibility and thermopower measurements on dilute alloys of Yb in Agl -*Au, Allali et al. ’ ) concluded that there is no Kondo effect for x’ < 0.05. In a recent paper Muran? ) reports Kondo behaviour in the resistivity of AgYb (x = 0). To resolve this contradiction we have measured the temperature dependence of the thermoelectric power for a series of Ag-Yb samples. Experiments on the magnetic properties of Yb in Ag are very difficult; due to the low solubility of Yb in Ag3 >* traces of other magnetic impurities may seriously influence the results. The samples were prepared from 6N Cominco Ag and 3N Koch Light Yb by high frequency induction melting in vacua in quartz ampullas; the ingots were rolled to bars (1 X 1 mm’ ), the bars drawn to wires of 0.25 mm diameter in diamond dies. Between each step in the rolling and drawing processes the bars or wires were etched to prevent iron contamination. Thermoelectric force E measurements were done between 1.4 K and 16 K against superconducting Nb3Sn, one end of the sample was held at the temperature of the helium bath Tb, the other end at a controllable temperature T:
* In this ref. 3 the authors quote this number should be much lower.
a s‘olubility
609
of about
1 at.% at 800 C; we think
F. F. BEKKER
610
E=
AND C. J. A. VAN DUREN
T JSdT
Tb The thermoelectric power S is the sum of a diffusion part (Sd) and a phonon drag part (Ss - r3). “Kondo” scattering leads to a peak in the temperature dependence of Sd, the peak value is usually of the order of /_lVK-', the part of the peak in the ncighbourhood of the Kondo temperature TK canbe described as T/(To + T) where To is related to TK and characteristic for solute and solvent (for Fc in Ag 4 ): To = 0.15K). Nonmagnetic impurities as well as lattice defects give a contribution to S, linear in temperature. Different contributions to S, must be weighted with with their relative contribution to the resistivity (Nordheim-Gorter rule5 )). So we obtain:
Fig. 1 shows as an example the thermoelectric force E data points for sample 3, a least squares computer program fits these points to a power series in T and then calculates and plots the thermoelectric power S(T). The values of about --0.1 pVK_ ’ at the lowest temperatures for the unannealed samples 1, 2 and 3 are rather small for a Kondo effect; there is a weak concentration dependence (see fig. 1). From formula (1) is it clear that with only one scattering mechanism in the diffusion part Sd, the thermopower S should be concentration independent. By annealing (one hour, 8OO”C, 1 0m4 - 1O- ’ torr) we strongly reduced the scattering on lattice defects; however, a strong concentration dependence appeared (l”, 2” and 3a in fig. 1). So after annealing there still is a now relatively more important second scattering mechanism. We are forced to believe that our samples contain some iron. Using value? > PFe = 1.5 tla cIn/ppm, SFe = 9 1-1VK- l (these values in ref. 6 are preliminary) and To = 0.15K and analysing the curves with a least squares computer program following expression (I), we find the values cFe (S) given in table 1. in samples 1 From the ~4.2K values, it is clear that the Yb contribution and 3 decreased, in 2 increased during annealing (a reasonable value for pdef. is about 0.1 pfl cm). The exceptional increase in S for sample 3” must be understood as an increase of the iron content (we suppose this sample was not etched carefully enough before annealing). As a check we measured the temperature dependence of the resistivity p (T)of the annealed samples (see fig. 2) and found the depths of the Kondo minimum to be related to the iron concentration cFe(S) (and not to the Yb resist-
THERMOELECTRIC
POWER AND RESISTIVITY
OF Ago-Yb ALLOYS
6 1I
ivity). The data points were fitted up till 10 K to p (r) = a0 + al log T + a2 T3 + a3 T5.
(2)
Comparing our al values with the value ( l/cFe) (Ap/A log T) = - 0.28 nS1cm/decade of T. ppm Fe for Ag-Fe6 >, we found somewhat lower iron concentrations; however, the trend is the same as for the concentrations
+600
400
l200
3
-20001 0
2
200 1
L
6
8
1
10
I
12
1
lb
,
16
-TK
Fig. 1. Thermoelectric power S for unannealed and annealed Ag-Yb samples. S is for all samples deduced from a thermoelectric force E measurement. For sample 3 the E data points are also given; the curve through the data points is a fit by means of eq. (1). For Murani’s sample, see second footnote.
1
0.18
0.29
0.14
0.17
0.08
2
3
la
2a
3a
7 12
7 12
I 12
7 12
7 12
7 12
(K)
(Pflcm)
0.32
Tlim
Ptot = P4.2
-ml460 -1455
92 -101
154 -172
89 -90
-77 m-81
-56 -56
(nVK_’ ) ~ .~__
PA,/Ptot
+16.2 +13.2
+2.7 +5.2
PO.8 +6.0
+14.3 +14.1
+12.3 +13.9
+13.0 +12.a
+0.09 +0.18
+0.14 +o. 12
+0.21 +O.lO
+0.01 +0.03
+0.06 +0.03
+0.02 +0.02
(nVKm4)
(nVK-*
)
R
A2
12.2 12.9
1.6 2.9
1.7 2.6
1.8 1.8
0.8 1.2
0.9 1.1
Stand dev. (nV)
~ 1.64
-0.23
PO.53
8.6
1.3
1.8
1.9
1.1
1.3
(wm)
CFe
(S)
and
5.9
0.8
1.9
_
_
(mm)
CFe (P)
of eqs. (1) and (2), CFc(S) and CF~(P) are the iron concentrations as deduced from the thermopower the resistivity. respectively; Tlim is the upper limiting value of the fit. to eq. (1).
1
Samples
Parameters
TABLE
THERMOELECTRIC
POWER AND RESISTIVITY
OF Ag-Yb
ALLOYS
6
13
P
nRcm ,
4 1 16550
\
8560
"\ i
Fig. 2. Resistivity
I
p for annealed
Ag-Yb
samples.
deduced from the thermopower”. This we consider as convincing evidence that the weak Kondo behaviour in thermopower and resistivity in Ag-Yb samples is due to traces of iron. The nonmagnetic contribution from Yb to the thermopower can be obtained as follows: Rumbo has shown that heavy cold working reduces B practically to zero; this is the case for our unannealed samples. An important part of the resistivity in these samples is due to the defects introduced by cold working; these defects give a positive characteristic contribution to Sd with an upper limit’) of about + 17T nVK_’ However, for the annealed samples nearly the whole resistivity is due to Yb. The A2 and B values for sample 3a are unreliable because of the high A 1 value; the average A, value for samples la and 2a of about +3 nVK_’ we assume to be characteristic for Yb in Ag. * Dr. Murani’s2) sample (a) stage 2, which he was so kind to send us for thermopower measurements, shows p A 1/ptot= - 1990 nVK-‘, which leads to CFe = 0.7 ppm. The high thermopower is explained by the very low Yb concentration: ptot z 0.005 @&m.
614
F. F. BEKKER
AND C. J. A. VAN DUREN
From this positive value for A and the rather high resistivity8) p - 2 ps2 cm/at. % for a divalent impurity in Ag (compare Ag-Cd, p = 0.38 p52ccm/at.% Cd) one can conclude that for Yb in Ag there is a considerable contribution with d character. For trivalent Yb in Au9) we measured even bigger resistivity and positive diffusion thermopower, so compared with divalent Yb in Ag the d-phase shift must increase. Acknowledgements. We want to thank Dr. J. Bijvoet, Dr. P. F. de Chatel and Professor Dr. G. de Vries for critical reading the manuscript and N. Zuiderbaan for assistance in the measurements.
REFERENCES 1) Allali, V., Donze, P., Gainon, D. and Sierro, J., J. Appl. Phys. 41 (1970) 1154. 2) Murani, A. P., Sol. State Comm. 14 (1974) 199. 3) Gschneidner, K. A., Mc.Masters, 0. D., Alexander, D. G. and Venteicher, R. F., Metal. Transactions 1 (1970) 1961. 4) Gut&nault, A. M., Phil. Mag. 15 (1967) 17. 5) Barnard, R. D., Thermoelectricity in Metals and Alloys, Taylor and Francis (London, 1972). 6) Van Duren, C. J. A. and Bekker, F. F., to be published. 7) Rumbo, E. R., Phil. Mag. 22 (1970) 953. 8) Boes, J., Van Dam, A. J. and Bijvoet, J., Physics Letters 28A (1968) 101. 9) Bekker, F. F. and Van Duren, C. J. A., to be published.
LETTER
TO THE EDITOR
THERMOELECTRIC OF DILUTE
Ag-Yb
POWER AND RESISTIVITY
ALLOYS
F. F. BEKKER Natuurkundig
AT LOW TEMPERATURES
and C. J. A. VAN DUREN
Laboratorium, University of‘ Amsterdam, Amsterdam, The Netherlands Received
3 December
1974
Synopsis Thermoelectric force and resistivity of some dilute Ag-Yb alloys have been measured and analysed in terms of a d-like contribution to the scattering from divalent nonmagnetic Yb. Kondo behaviour is exclusively attributed to traces of iron.
From susceptibility and thermopower measurements on dilute alloys of Yb in Agl -*Au, Allali et al. ’ ) concluded that there is no Kondo effect for x’ < 0.05. In a recent paper Muran? ) reports Kondo behaviour in the resistivity of AgYb (x = 0). To resolve this contradiction we have measured the temperature dependence of the thermoelectric power for a series of Ag-Yb samples. Experiments on the magnetic properties of Yb in Ag are very difficult; due to the low solubility of Yb in Ag3 >* traces of other magnetic impurities may seriously influence the results. The samples were prepared from 6N Cominco Ag and 3N Koch Light Yb by high frequency induction melting in vacua in quartz ampullas; the ingots were rolled to bars (1 X 1 mm’ ), the bars drawn to wires of 0.25 mm diameter in diamond dies. Between each step in the rolling and drawing processes the bars or wires were etched to prevent iron contamination. Thermoelectric force E measurements were done between 1.4 K and 16 K against superconducting Nb3Sn, one end of the sample was held at the temperature of the helium bath Tb, the other end at a controllable temperature T:
* In this ref. 3 the authors quote this number should be much lower.
a s‘olubility
609
of about
1 at.% at 800 C; we think
F. F. BEKKER
610
E=
AND C. J. A. VAN DUREN
T JSdT
Tb The thermoelectric power S is the sum of a diffusion part (Sd) and a phonon drag part (Ss - r3). “Kondo” scattering leads to a peak in the temperature dependence of Sd, the peak value is usually of the order of /_lVK-', the part of the peak in the ncighbourhood of the Kondo temperature TK canbe described as T/(To + T) where To is related to TK and characteristic for solute and solvent (for Fc in Ag 4 ): To = 0.15K). Nonmagnetic impurities as well as lattice defects give a contribution to S, linear in temperature. Different contributions to S, must be weighted with with their relative contribution to the resistivity (Nordheim-Gorter rule5 )). So we obtain:
Fig. 1 shows as an example the thermoelectric force E data points for sample 3, a least squares computer program fits these points to a power series in T and then calculates and plots the thermoelectric power S(T). The values of about --0.1 pVK_ ’ at the lowest temperatures for the unannealed samples 1, 2 and 3 are rather small for a Kondo effect; there is a weak concentration dependence (see fig. 1). From formula (1) is it clear that with only one scattering mechanism in the diffusion part Sd, the thermopower S should be concentration independent. By annealing (one hour, 8OO”C, 1 0m4 - 1O- ’ torr) we strongly reduced the scattering on lattice defects; however, a strong concentration dependence appeared (l”, 2” and 3a in fig. 1). So after annealing there still is a now relatively more important second scattering mechanism. We are forced to believe that our samples contain some iron. Using value? > PFe = 1.5 tla cIn/ppm, SFe = 9 1-1VK- l (these values in ref. 6 are preliminary) and To = 0.15K and analysing the curves with a least squares computer program following expression (I), we find the values cFe (S) given in table 1. in samples 1 From the ~4.2K values, it is clear that the Yb contribution and 3 decreased, in 2 increased during annealing (a reasonable value for pdef. is about 0.1 pfl cm). The exceptional increase in S for sample 3” must be understood as an increase of the iron content (we suppose this sample was not etched carefully enough before annealing). As a check we measured the temperature dependence of the resistivity p (T)of the annealed samples (see fig. 2) and found the depths of the Kondo minimum to be related to the iron concentration cFe(S) (and not to the Yb resist-
THERMOELECTRIC
POWER AND RESISTIVITY
OF Ago-Yb ALLOYS
6 1I
ivity). The data points were fitted up till 10 K to p (r) = a0 + al log T + a2 T3 + a3 T5.
(2)
Comparing our al values with the value ( l/cFe) (Ap/A log T) = - 0.28 nS1cm/decade of T. ppm Fe for Ag-Fe6 >, we found somewhat lower iron concentrations; however, the trend is the same as for the concentrations
+600
400
l200
3
-20001 0
2
200 1
L
6
8
1
10
I
12
1
lb
,
16
-TK
Fig. 1. Thermoelectric power S for unannealed and annealed Ag-Yb samples. S is for all samples deduced from a thermoelectric force E measurement. For sample 3 the E data points are also given; the curve through the data points is a fit by means of eq. (1). For Murani’s sample, see second footnote.
1
0.18
0.29
0.14
0.17
0.08
2
3
la
2a
3a
7 12
7 12
I 12
7 12
7 12
7 12
(K)
(Pflcm)
0.32
Tlim
Ptot = P4.2
-ml460 -1455
92 -101
154 -172
89 -90
-77 m-81
-56 -56
(nVK_’ ) ~ .~__
PA,/Ptot
+16.2 +13.2
+2.7 +5.2
PO.8 +6.0
+14.3 +14.1
+12.3 +13.9
+13.0 +12.a
+0.09 +0.18
+0.14 +o. 12
+0.21 +O.lO
+0.01 +0.03
+0.06 +0.03
+0.02 +0.02
(nVKm4)
(nVK-*
)
R
A2
12.2 12.9
1.6 2.9
1.7 2.6
1.8 1.8
0.8 1.2
0.9 1.1
Stand dev. (nV)
~ 1.64
-0.23
PO.53
8.6
1.3
1.8
1.9
1.1
1.3
(wm)
CFe
(S)
and
5.9
0.8
1.9
_
_
(mm)
CFe (P)
of eqs. (1) and (2), CFc(S) and CF~(P) are the iron concentrations as deduced from the thermopower the resistivity. respectively; Tlim is the upper limiting value of the fit. to eq. (1).
1
Samples
Parameters
TABLE
THERMOELECTRIC
POWER AND RESISTIVITY
OF Ag-Yb
ALLOYS
6
13
P
nRcm ,
4 1 16550
\
8560
"\ i
Fig. 2. Resistivity
I
p for annealed
Ag-Yb
samples.
deduced from the thermopower”. This we consider as convincing evidence that the weak Kondo behaviour in thermopower and resistivity in Ag-Yb samples is due to traces of iron. The nonmagnetic contribution from Yb to the thermopower can be obtained as follows: Rumbo has shown that heavy cold working reduces B practically to zero; this is the case for our unannealed samples. An important part of the resistivity in these samples is due to the defects introduced by cold working; these defects give a positive characteristic contribution to Sd with an upper limit’) of about + 17T nVK_’ However, for the annealed samples nearly the whole resistivity is due to Yb. The A2 and B values for sample 3a are unreliable because of the high A 1 value; the average A, value for samples la and 2a of about +3 nVK_’ we assume to be characteristic for Yb in Ag. * Dr. Murani’s2) sample (a) stage 2, which he was so kind to send us for thermopower measurements, shows p A 1/ptot= - 1990 nVK-‘, which leads to CFe = 0.7 ppm. The high thermopower is explained by the very low Yb concentration: ptot z 0.005 @&m.
614
F. F. BEKKER
AND C. J. A. VAN DUREN
From this positive value for A and the rather high resistivity8) p - 2 ps2 cm/at. % for a divalent impurity in Ag (compare Ag-Cd, p = 0.38 p52ccm/at.% Cd) one can conclude that for Yb in Ag there is a considerable contribution with d character. For trivalent Yb in Au9) we measured even bigger resistivity and positive diffusion thermopower, so compared with divalent Yb in Ag the d-phase shift must increase. Acknowledgements. We want to thank Dr. J. Bijvoet, Dr. P. F. de Chatel and Professor Dr. G. de Vries for critical reading the manuscript and N. Zuiderbaan for assistance in the measurements.
REFERENCES 1) Allali, V., Donze, P., Gainon, D. and Sierro, J., J. Appl. Phys. 41 (1970) 1154. 2) Murani, A. P., Sol. State Comm. 14 (1974) 199. 3) Gschneidner, K. A., Mc.Masters, 0. D., Alexander, D. G. and Venteicher, R. F., Metal. Transactions 1 (1970) 1961. 4) Gut&nault, A. M., Phil. Mag. 15 (1967) 17. 5) Barnard, R. D., Thermoelectricity in Metals and Alloys, Taylor and Francis (London, 1972). 6) Van Duren, C. J. A. and Bekker, F. F., to be published. 7) Rumbo, E. R., Phil. Mag. 22 (1970) 953. 8) Boes, J., Van Dam, A. J. and Bijvoet, J., Physics Letters 28A (1968) 101. 9) Bekker, F. F. and Van Duren, C. J. A., to be published.