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Thermoelectric measurements on tungsten at ultra low temperatures
Volume 58A, number 4
PHYSICS LETTERS
6 September 1976
TkIERMOELECTRIC MEASUREMENTS ON TUNGSTEN AT ULTRA LOW TEMPERATURES~ E.L. STONE, M.D. EWBANK, W.P. PRATT, Jr. and J. BASS Department of Physics, Michigan State University, East Lansing, Michigan 48824, USA Received 20 July 1976 Measurements are reported of the thermoelectric ratio G for three zone-refined tungsten samples at temperatures down to 45 mK. For the purest sample (R~OK/ROK= 44000), G behaves simply and in accord with expectations. For two less pure samples (R 300K/ROK = 34 000 and 22000), G behaves anomalously, becoming increasingly more negative with decreasing temperature down to at least 45 mK. This anomalous behavior is tentatively attributed to trace amounts of iron.
The development of dilution refrigerators [1] for reaching ultra-low temperatures and of SQUIDs [2] for measuring very small voltages has recently opened up the field of transport in metals at ultra-low temperatures. In this letter we describe the first ultra-low temperature measurements of the thermoelectric ratio, G, for tungsten. We report the observation of a large, new ultralow temperature thermoelectric anomaly, in which both G and the “pseudo-thermopower” GL0beT 8W-f2/K2 is the Lorentz number) (L0= 2.45X10— come increasingly more negative with decreasing temperature down to at least 45 mK. Results are described for three samples, two of which display the new anomaly. A more comprehensive report will follow when additional experiments have been completed. The thermoelectric ratio G is related to the more widely measured thermopower S by the equation [3]
G=S/LT,
(1)
where T is the absolute temperature, L is the Wiedemann—Franz ratio and a term is omitted which in metals is negligibly small. Garland and Van Harlingen [3] have recently discussed in detail what G is, how it is measured, and why it can often be measured more accurately than S. At very low temperatures, where elastic scatteringnormally predominates, L should approach the Lorentz number L0, and S should increase linearly with T [4, 5]. In such a case, G would be expected to approach a constant value G0 as T-+OK. ~Supported in part by the N.S.F. under grants DMR-7514138 and DMR-75-01584.
.0
.8 .6 G(V )
4
.20
• w,GARLAND - PRESENT STUDY eVANHARLINGEN
—
I
0.05 0.1
I
0.5
Fig. 1. The variation with temperature of the thermoelectric ratio G for sample W-1 (RRR = 44000) and for a comparable purity sample (RRR = 63000) as measured by Garland and
VanHarlingen [3]. Fig. 1 shows the variation with temperature of G for our “purest” sample, sample W-1, a three-pass zonerefmed single crystal having 1.4mm diameter and a Residual Resistance Ratio (RRR = R 3~K/RoK)of 44000. Indeed, below 0.5 K, G is constant to within experimental uncertainty down to 0.07 K, the lowest temperature studied with this sample. The data shown in fig. 1 were obtained during three different measuring runs, the first and last occurring three months apart. For comparison with our data, the solid curve in fig. 1 indicates the behavior of G for a sample with RRR = 60000 as reported by Garland and VanHarlingen [3]. The similarity between this curve and our data in the 239
Volume 58A, number 4 +1
PHYSICS LETTERS
‘‘i
_______________
W
1 llRR~44,OOO)
-2 G~
0.01
~—~---
+5
~~--
-
llRR~4OOO)
(RRR~2.oOo)~
I
TK)
T(K) 0.1
Fig. 2. The variation with temperature of the thermoelectric ratio G below 1K for sample W-1 (dashed line) and samples W-2 and W-3 (solid curves). The error bars indicate the outer limits of the experimental data for each sample. Individual data points for samples W-1 and W-3 are given in figs. 1 and 3 respectively.
region of overlap provides support for the basic validity
of both sets of measurements. In view of its agreement with the simple form expected, we believe that the low temperature behavior of sample W-1 is representative of high purity tungsten in which the scattering of electrons is dominated below 1K by impurities for which simple potential scattering applies, In contrast, we observe quite a different behavior for G in two 1.4mm diameter “less pure” samples: W-2, a two-pass zone.refmed single crystal having RRR= 34000; and W-3, a one-pass zone-refmed single crystal having RRR = 22000. In fig. 2, G for samples W-2 and W.3 (solid curves) is compared with G for sample W-1 (dashed line) at temperatures below 1K. Whereas for sample W-1, G is constant below 1 K; for samples W-2 and W-3, G becomes increasingly more negative with decreasing temperature to the lowest temperatures reached. At these lowest temperatures, the accuracy of the data is limited by the fact that the measured thermal voltages are comparable to the Johnson noise in the system (approximately 10—15 volts), According to the third law of thermodynamics, the thermopower of a sample must approach zero as T-+ OK. To investigate whether this is occurring in our temperature range, we multiply G by L 0 T to form a pseudo-thermopower Fig. 3 shows GL0T for samples W-1 and W-3 at temperatures below 0.3 K (sample W-2 .
240
6 September 1976
Fig. 3. The variation with temperature of the “pseudo-thermoper” GL0Tbelow 0.3K for samples W-1 and W-3. For sample W-1 the data shown are from one of three independent measuring runs. The ordinate is in units of 10—8 V/K.
has been omitted in the interests of clarity). For sample W-l, GL0T is positive at 0.3 K and decreases toward zero linearly with decreasing temperature. For samples W-2 and W-3, on the other hand, GL0 Tis initially positive, but then passes through zero and becomes increasingly negative with decreasing temperature. At 45 mK the magnitude of GL0 T for sample W-3 is about 20 times larger than that for sample W-1. Because of the third law, GL0 T cannot continue to become more negative indefinitely as T decreases. At some temperature it must reach a peak negative value and then begin to decrease in magnitude back toward zero. To locate this peak will require stifi lower temperatures than we have reached, perhaps even temperatures lower than the superconducting transition temperature of tungsten 12—16 mK [6,7]). In such a case, it will be necessary to apply a small magnetic field (H~1G) to suppress the superconducting transition. Both the negative sign and the large magnitude of the anomaly in GL0 Tfor sample W-3 are reminiscent of the behavior of the thermo-electric anomalies produced by dissolved impurities whose magnetic properties are important [5,8] Such anomalies are usually (i~i
~.
* The magnitudes of the anomalous values of GL0T at the lowest temperatures probably underestimate the magnitudes of S, since theoretical and experimental work on systems with magnetic impurities mdicate that L > L0 for temperatures near the Kondo temperature TK. Presumably, TK for our samplesis below 45 mK. Seeref. [9].
Volume 58A, number 4
PHYSICS LETTERS
accompanied by the appearance of a resistance minimum [8]. Indeed, upon investigation, we did discover a very small resistance minimum for sample W-3 a fractional increase in resistivity of about 1 part in 1O~between 0.2K and 5OmK [10]. No minimum was found for sample W-1. To follow up this evidence, we had all three samples analyzed by spark source mass spectrometry [11]. A search for over 50 elements revealed only three with apparent concentrations greater than 100 atomic ppm: C, Si, and Fe. Of these three, the only one known to produce magnetically related anomalies is Fe, which has been found to produce giant thermopowers and resistance minima in a number of metals [5, 8, 12]. In tungsten, evidence of magnetic properties of Fe has been obtained from measurements of magnetic susceptibility [13] and from MOssbauer measurements [14]. From all this information, we infer that Fe is the most likely candidate for the source of the observed anomalous behavior. However, neither the reported concentrations of Fe, nor those of any of the other impurities detected, correlate with the magnitudes of the thermoelectric anomalies. This lack of correlation may result from different properties of Fe ions in different states. There is evidence for host metals such as Cu, that Fe ions in solution produce anomalous thermoelectric behavior, whereas Fe ions bound in oxides do not [15].If this is also true in tungsten, then the total concentration of Fe would not necessarily correlate with the magnitude of the thermoelectric anomaly. We conclude that we have observed a new ultra-low temperature thermoelectric anomaly in tungsten, which may be plausibly attributed to Fe ions in very dilute solution. However, a defmitive determination of the source of this anomaly will require further studies, including: ultra-low temperature transport measurements on carefully prepared and well characterized W(Fe) alloys; magnetic susceptibility measurements —
6 September 1976
to search for direct evidence of magnetic behavior; and studies of effects of oxidation on the magnetic behavior and the thermoelectric properties of the alloys. The authors would like to thank FJ. Blatt and C.L. Foiles for helpful comments and criticisms, and C.W. Lee and B. Shumaker for assistance with crystal preparation.
References [1] 0.V. Lounasmaa, Experimental principles and methods below 1K (Acadmic Press, New York 1974). [2] R.P. Giffard, R.A. Webb and J.C. Wheatley, J. Low Temp. Phys. 6 (1972) 533. [3] J.C. Garland and D.J. VanHarlingen, Phys. Rev. lOB
(1974) 4825. [4] F.J. Blatt, Physics of electronic conduction in solids (McGraw-Hill Inc., New York 1968). [5] RD. Barnard, Thermoelectricity in metals and alloys (Taylor and Francis Ltd., London 1972). [6] W.C. Black, R.T. Johnson and J.C. Wheatley, 1. Low Temp. Phys. 1(1969) 641. [7] B.B. Triplett et aL, J. Low Temp. Phys. 12 (1973) 499. [8] D.K.C. MacDonald, Thermoelectricity: an introduction
to thePoo, principles (John Wiley and 451; Sons, 1962). [9] G.S. Phys. Rev. B13 (1976) R.G. Sharma and M.S.R. Chari, J. of Low Temp. Phys. 15 (1974) 79. [10] E.L. Stone, III, M.D. Ewbank, I. Bass and W.P. Pratt, Jr., submitted for publication. [11] Analytical Laboratory, Material Science Center, Cornell University, New Physics York. 23 (1969) 284. [12] AJ. Heeger,Ithaca, Solid State [13] L.K. Thomas and D.J. Sellmyer, 18th Annual Conf. on Magnetism and magnetic materials, Denver, Colorado (November 1972), AlP Conf. Proc. Vol. 10 (1972) p 806. [14] T.A. Kitchens, W.A. Steyert and R.D. Taylor, Phys. Rev. 138 (1965) A467. [15] A.V. Gold, D.K.C. MacDonald, W.B. Pearson and .I.M. Templeton, Phil. Mag. 5 (1960) 765.
241
PHYSICS LETTERS
6 September 1976
TkIERMOELECTRIC MEASUREMENTS ON TUNGSTEN AT ULTRA LOW TEMPERATURES~ E.L. STONE, M.D. EWBANK, W.P. PRATT, Jr. and J. BASS Department of Physics, Michigan State University, East Lansing, Michigan 48824, USA Received 20 July 1976 Measurements are reported of the thermoelectric ratio G for three zone-refined tungsten samples at temperatures down to 45 mK. For the purest sample (R~OK/ROK= 44000), G behaves simply and in accord with expectations. For two less pure samples (R 300K/ROK = 34 000 and 22000), G behaves anomalously, becoming increasingly more negative with decreasing temperature down to at least 45 mK. This anomalous behavior is tentatively attributed to trace amounts of iron.
The development of dilution refrigerators [1] for reaching ultra-low temperatures and of SQUIDs [2] for measuring very small voltages has recently opened up the field of transport in metals at ultra-low temperatures. In this letter we describe the first ultra-low temperature measurements of the thermoelectric ratio, G, for tungsten. We report the observation of a large, new ultralow temperature thermoelectric anomaly, in which both G and the “pseudo-thermopower” GL0beT 8W-f2/K2 is the Lorentz number) (L0= 2.45X10— come increasingly more negative with decreasing temperature down to at least 45 mK. Results are described for three samples, two of which display the new anomaly. A more comprehensive report will follow when additional experiments have been completed. The thermoelectric ratio G is related to the more widely measured thermopower S by the equation [3]
G=S/LT,
(1)
where T is the absolute temperature, L is the Wiedemann—Franz ratio and a term is omitted which in metals is negligibly small. Garland and Van Harlingen [3] have recently discussed in detail what G is, how it is measured, and why it can often be measured more accurately than S. At very low temperatures, where elastic scatteringnormally predominates, L should approach the Lorentz number L0, and S should increase linearly with T [4, 5]. In such a case, G would be expected to approach a constant value G0 as T-+OK. ~Supported in part by the N.S.F. under grants DMR-7514138 and DMR-75-01584.
.0
.8 .6 G(V )
4
.20
• w,GARLAND - PRESENT STUDY eVANHARLINGEN
—
I
0.05 0.1
I
0.5
Fig. 1. The variation with temperature of the thermoelectric ratio G for sample W-1 (RRR = 44000) and for a comparable purity sample (RRR = 63000) as measured by Garland and
VanHarlingen [3]. Fig. 1 shows the variation with temperature of G for our “purest” sample, sample W-1, a three-pass zonerefmed single crystal having 1.4mm diameter and a Residual Resistance Ratio (RRR = R 3~K/RoK)of 44000. Indeed, below 0.5 K, G is constant to within experimental uncertainty down to 0.07 K, the lowest temperature studied with this sample. The data shown in fig. 1 were obtained during three different measuring runs, the first and last occurring three months apart. For comparison with our data, the solid curve in fig. 1 indicates the behavior of G for a sample with RRR = 60000 as reported by Garland and VanHarlingen [3]. The similarity between this curve and our data in the 239
Volume 58A, number 4 +1
PHYSICS LETTERS
‘‘i
_______________
W
1 llRR~44,OOO)
-2 G~
0.01
~—~---
+5
~~--
-
llRR~4OOO)
(RRR~2.oOo)~
I
TK)
T(K) 0.1
Fig. 2. The variation with temperature of the thermoelectric ratio G below 1K for sample W-1 (dashed line) and samples W-2 and W-3 (solid curves). The error bars indicate the outer limits of the experimental data for each sample. Individual data points for samples W-1 and W-3 are given in figs. 1 and 3 respectively.
region of overlap provides support for the basic validity
of both sets of measurements. In view of its agreement with the simple form expected, we believe that the low temperature behavior of sample W-1 is representative of high purity tungsten in which the scattering of electrons is dominated below 1K by impurities for which simple potential scattering applies, In contrast, we observe quite a different behavior for G in two 1.4mm diameter “less pure” samples: W-2, a two-pass zone.refmed single crystal having RRR= 34000; and W-3, a one-pass zone-refmed single crystal having RRR = 22000. In fig. 2, G for samples W-2 and W.3 (solid curves) is compared with G for sample W-1 (dashed line) at temperatures below 1K. Whereas for sample W-1, G is constant below 1 K; for samples W-2 and W-3, G becomes increasingly more negative with decreasing temperature to the lowest temperatures reached. At these lowest temperatures, the accuracy of the data is limited by the fact that the measured thermal voltages are comparable to the Johnson noise in the system (approximately 10—15 volts), According to the third law of thermodynamics, the thermopower of a sample must approach zero as T-+ OK. To investigate whether this is occurring in our temperature range, we multiply G by L 0 T to form a pseudo-thermopower Fig. 3 shows GL0T for samples W-1 and W-3 at temperatures below 0.3 K (sample W-2 .
240
6 September 1976
Fig. 3. The variation with temperature of the “pseudo-thermoper” GL0Tbelow 0.3K for samples W-1 and W-3. For sample W-1 the data shown are from one of three independent measuring runs. The ordinate is in units of 10—8 V/K.
has been omitted in the interests of clarity). For sample W-l, GL0T is positive at 0.3 K and decreases toward zero linearly with decreasing temperature. For samples W-2 and W-3, on the other hand, GL0 Tis initially positive, but then passes through zero and becomes increasingly negative with decreasing temperature. At 45 mK the magnitude of GL0 T for sample W-3 is about 20 times larger than that for sample W-1. Because of the third law, GL0 T cannot continue to become more negative indefinitely as T decreases. At some temperature it must reach a peak negative value and then begin to decrease in magnitude back toward zero. To locate this peak will require stifi lower temperatures than we have reached, perhaps even temperatures lower than the superconducting transition temperature of tungsten 12—16 mK [6,7]). In such a case, it will be necessary to apply a small magnetic field (H~1G) to suppress the superconducting transition. Both the negative sign and the large magnitude of the anomaly in GL0 Tfor sample W-3 are reminiscent of the behavior of the thermo-electric anomalies produced by dissolved impurities whose magnetic properties are important [5,8] Such anomalies are usually (i~i
~.
* The magnitudes of the anomalous values of GL0T at the lowest temperatures probably underestimate the magnitudes of S, since theoretical and experimental work on systems with magnetic impurities mdicate that L > L0 for temperatures near the Kondo temperature TK. Presumably, TK for our samplesis below 45 mK. Seeref. [9].
Volume 58A, number 4
PHYSICS LETTERS
accompanied by the appearance of a resistance minimum [8]. Indeed, upon investigation, we did discover a very small resistance minimum for sample W-3 a fractional increase in resistivity of about 1 part in 1O~between 0.2K and 5OmK [10]. No minimum was found for sample W-1. To follow up this evidence, we had all three samples analyzed by spark source mass spectrometry [11]. A search for over 50 elements revealed only three with apparent concentrations greater than 100 atomic ppm: C, Si, and Fe. Of these three, the only one known to produce magnetically related anomalies is Fe, which has been found to produce giant thermopowers and resistance minima in a number of metals [5, 8, 12]. In tungsten, evidence of magnetic properties of Fe has been obtained from measurements of magnetic susceptibility [13] and from MOssbauer measurements [14]. From all this information, we infer that Fe is the most likely candidate for the source of the observed anomalous behavior. However, neither the reported concentrations of Fe, nor those of any of the other impurities detected, correlate with the magnitudes of the thermoelectric anomalies. This lack of correlation may result from different properties of Fe ions in different states. There is evidence for host metals such as Cu, that Fe ions in solution produce anomalous thermoelectric behavior, whereas Fe ions bound in oxides do not [15].If this is also true in tungsten, then the total concentration of Fe would not necessarily correlate with the magnitude of the thermoelectric anomaly. We conclude that we have observed a new ultra-low temperature thermoelectric anomaly in tungsten, which may be plausibly attributed to Fe ions in very dilute solution. However, a defmitive determination of the source of this anomaly will require further studies, including: ultra-low temperature transport measurements on carefully prepared and well characterized W(Fe) alloys; magnetic susceptibility measurements —
6 September 1976
to search for direct evidence of magnetic behavior; and studies of effects of oxidation on the magnetic behavior and the thermoelectric properties of the alloys. The authors would like to thank FJ. Blatt and C.L. Foiles for helpful comments and criticisms, and C.W. Lee and B. Shumaker for assistance with crystal preparation.
References [1] 0.V. Lounasmaa, Experimental principles and methods below 1K (Acadmic Press, New York 1974). [2] R.P. Giffard, R.A. Webb and J.C. Wheatley, J. Low Temp. Phys. 6 (1972) 533. [3] J.C. Garland and D.J. VanHarlingen, Phys. Rev. lOB
(1974) 4825. [4] F.J. Blatt, Physics of electronic conduction in solids (McGraw-Hill Inc., New York 1968). [5] RD. Barnard, Thermoelectricity in metals and alloys (Taylor and Francis Ltd., London 1972). [6] W.C. Black, R.T. Johnson and J.C. Wheatley, 1. Low Temp. Phys. 1(1969) 641. [7] B.B. Triplett et aL, J. Low Temp. Phys. 12 (1973) 499. [8] D.K.C. MacDonald, Thermoelectricity: an introduction
to thePoo, principles (John Wiley and 451; Sons, 1962). [9] G.S. Phys. Rev. B13 (1976) R.G. Sharma and M.S.R. Chari, J. of Low Temp. Phys. 15 (1974) 79. [10] E.L. Stone, III, M.D. Ewbank, I. Bass and W.P. Pratt, Jr., submitted for publication. [11] Analytical Laboratory, Material Science Center, Cornell University, New Physics York. 23 (1969) 284. [12] AJ. Heeger,Ithaca, Solid State [13] L.K. Thomas and D.J. Sellmyer, 18th Annual Conf. on Magnetism and magnetic materials, Denver, Colorado (November 1972), AlP Conf. Proc. Vol. 10 (1972) p 806. [14] T.A. Kitchens, W.A. Steyert and R.D. Taylor, Phys. Rev. 138 (1965) A467. [15] A.V. Gold, D.K.C. MacDonald, W.B. Pearson and .I.M. Templeton, Phil. Mag. 5 (1960) 765.
241