The electrical resistivity of protactinium

Journal of the Less-Common

THE ELECTRICAL

Metals, 102 (1984)

RESISTIVITY

41

41 - 52

OF PROTACTINIUM

R. BETT*, J. C. SPIRLET and W. MfJLLER Commission of the European Communities, Joint Research Centre, Karlsruhe Establishment, European Institute for Transuranium Elements, Postfach 2266, D-7500 Karlsruhe (F.R.G.) (Received

November

4,1983)

Summary The electrical resistivity of protactinium metal was measured in the temperature range 2 - 295 K. It rises from a residual resistivity of 0.92 ~.tsZ cm through a power law region with an exponent of 1.7. A transition which shows some fine structure, the origin of which is not understood, occurs at about 100 K. Above 110 K the electrical resistivity rises linearly to a room temperature value of 10 /.,G cm. This value is less than the value for thorium, suggesting a dip in the density of states for actinide metals between thorium and uranium.

1. Introduction In the actinide series of the periodic table an inner electron shell is being filled. The 5f electrons have no effect on the properties of actinium and thorium, but their influence increases steadily from protactinium to uranium and neptunium and produces many anomalous features in plutonium. In the elements beyond plutonium the 5f electrons are localized, i.e. confined to particular atoms, and no longer contribute to bonding. Thus these later elements more clearly resemble the rare earths. Protactinium is the third element in the series, and occurs in uranium ore to the extent of about 0.3 ppm because *ziPa is in the *$J radioactive decay chain. It decays by (IIparticle emission with a half-life of 3.28 X lo4 years, which gives rise to a self-heat of 1.2 mW g-i. The results of the first measurements of its electrical resistivity were published in 1968 [l], and were reported in greater detail in 1977 [ 21. These data were obtained for a metal which had been produced by the calcium reduction of protactinium fluoride. Its purity was unknown, and confidence in the absolute value of *Permanent Harwell, Didcot, 0022-5088/84/$3.00

address: Chemistry Division, Atomic Oxon. OX11 ORA, Gt. Britain. @ Elsevier

Energy

Research

Sequoia/Printed

Establishment,

in The Netherlands

42

the resistivity was further limited by the estimated uncertainty in the form factor of the specimen. The development [3] of a preparation route employing a Van Arkel process [4] provided the opportunity of measuring the resistivity of samples of known, and probably greater, purity than was formerly possible. We report here the results obtained over the temperature range from 2 K to room temperature.

2. Experimental

details

2.1. Specimen preparation A ‘small tungsten sphere was suspended in an evacuated sealed quartz tube above a mixture of protactinium carbide and iodine. The sphere was heated to 1500 K using radiofrequency induction, and the mixture was heated to 825 K in a resistance furnace. The iodide vapour produced at the lower temperature was dissociated at the higher temperature, and protactinium was deposited on the sphere. Table 1 shows the composition of a specimen produced by this method. A disc about 0.5 mm thick was cut from the protactinium deposit using a diamond-impregnated slitting wheel, and three slices about 0.5 mm wide and 5.5 mm long were cut from it. Four Pt-Rh alloy wires were spot welded to each slice, and the copper leads of the low temperature probe were attached to these by means of low thermal solder. TABLE 1 Spark source mass spectrometer Element

Content

W Th Si Ti U Fe Zr AC I Ta Sn Al

160 97 73 36 30 24 16 12 9 8 7 6

analysis of Van Arkel protactinium (ppm)

Element K Ni Mg Cl cu Ca Na Zn S Cr P Total

Content

(ppm)

6 5 6 2 2
2.2. Electrical form factor The form factor of the specimen, which is defined as the ratio of the cross-sectional area to the spacing of the voltage contacts, is the largest source of uncertainty in the absolute resistivity. The width and thickness

43

were measured using a micrometer. To obtain the length accurately, the specimens were taped to calibrated graph paper and photographed. The total uncertainty due to measurement errors was probably less than 4%. However, there were two further sources of error arising from the deformation which occurred on welding the leads to the highly ductile specimens and these are difficult to quantify. The cross section may have been reduced and the contact spacing made uncertain because the leads were embedded in the specimen; these two error sources lead to a possible overestimate of the form factor by up to 10%. 2.3. Equipment Radioactivity control considerations required the equipment to be designed to provide complete separation of the radioactive specimen from the vacuum and cooling systems of the cryostat. This imposed the selection of a continuous flow cryostat installed (Fig. 1) so that its specimen chamber opened into the inner argon-filled compartment of a double glove-box. The specimen chamber was cooled by a flow of either liquid or gaseous helium,

I Cryoresistor

Fig. 1. The glove-box,

continuous

flow cryostat

and specimen

holder.

44

delivered under pressure, which avoided direct contact with either the specimen or the glove-box atmosphere. The specimen was lacquered and was clamped to a copper specimen carrier by a copper plate (Fig. 1). A screw thread at the top of the specimen probe pressed the tapered specimen carrier into a correspondingly tapered copper can soldered into the specimen chamber of the cryostat. The temperature was measured using either an (Au-O.O3at.%Fe)chrome1 thermocouple clamped to the specimen or a germanium cryoresistor clamped under the specimen holder. All leads were thermally anchored to the specimen carrier. The use of a continuous flow cryostat precluded the adoption of the boiling point of liquid helium as the thermocouple reference temperature. The thermocouple wires were therefore taken in a continuous length to a junction with copper wires within a copper block contained in a covered vacuum-insulated flask whose temperature was measured using a calibrated thermistor. The remaining leads had one break which was linked by goldplated contacts to which they were attached using low thermal solder. The resistance of the specimens was measured using the four-probe technique (Fig. 2). Semiautomated equipment was used which enabled a cycle of ten sequential measurements to be made followed by ten measurements for which the direction of the current was reversed so that measurements involving currents were unaffected by thermally generated voltages. Measurements of the resistance were accurate to better than O.l%, measurements of the temperature using the cryoresistor were accurate to f 0.1 K, and measurements of the temperature using the thermocouple were accurate to +0.25 K. There was an additional source of error below 10 K, particularly at the lowest temperatures where an interaction between the gas produced in

Thermistor

-

Fig. 2. Resistance-measuring

circuit.

,

Standard Fksistancc

)

Polarity Signal

45

the cryostat heat exchanger and that produced by the heat load of the long flexible liquid helium delivery hose caused rapid temperature oscillations.

3. Results 3.1. The complete temperature range Measurements on the first specimen were performed on many occasions over a period of 3 months, and its room temperature resistance was found to increase slowly and linearly at a mean rate of 0.026% day-‘. The origin of this drift is not known, but it may be due to radiation damage at 2% of the low temperature rate [l] or to a small amount of corrosion caused by the soldering flux, the insulating lacquer or, less probably, the glove-box atmosphere. Whatever its origin, it was consistent with a reducing form factor, and the resistivity was compensated by adjusting to the starting value. The maximum adjustment made to any result was less than 2.5%. Measurements on a second specimen were all made within a few days, and no adjustment was required. The resistivity results obtained for both specimens over the complete temperature range studied are shown in Fig. 3. The data are too numerous to be individually plotted on this scale but are listed as measured for the range 2 - 20 K in Table 2 and as interpolated at 5 K intervals for the range 25 295 K in Table 3. The resistivities of specimens 1 and 2 at 273.15 K were, by interpolation, 10.91 ~s2 cm and 9.57 ps2 cm respectively. The difference of 14% is within the measurement error discussed above. Assuming that the true value lies within the overlap of the area of uncertainty, we conclude that the resistivity of protactinium at 273.15 K is 10.0 f 0.3 /.LZ cm. The low temperature results are discussed in detail below. The best estimates that can be made of the residual resistivity p. are 1,204 /.~a cm for specimen 1 and 0.879 /.LZ cm for specimen 2, giving resistance ratios of 9.06 and 10.88 respectively which indicate that specimen 2 was rather more pure than specimen 1. This can also be seen from Fig. 4, which shows that the ratio of resistivities has an almost constant value of 1.15 above about 170 K, owing to the form factor error, but that the ratio changes rapidly below 170 K as the impurity effect becomes dominant. If we assume as above that the absolute resistivity at 273.15 K is 10.0 + 0.3 r.cC?cm, then the best estimate for the absolute value of p. is 0.92 f 0.02 pSl cm. 3.2. Low temperature results The low temperature resistivity of metals has both temperature-dependent and temperature-independent components which are additive according to Matthiessen’s rule. The temperature-dependent component pi is the ideal behaviour due to the interaction of conduction electrons with phonons. The temperature-independent component p. is constant and is due to electron scattering by impurities, dislocations, defects and grain boundaries.

Temperature

.K

Fig. 3. The temperature dependence of the electrical resistivity of two protactinium specimens. The data are given in detail in Tables 2 and 3. TABLE 2 Low temperature resistivity data (specimen 1) Temperature WI

Resistivity (Pa cm 1

Temperature WI

Resistivity (E.cQcm)

2.4 2.0 2.2 2.26 2.28 3.99 3.87 3.72 3.61 3.59 3.63

1.201 1.201 1.201 1.205 1.202 1.220 1.216 1.213 1.218 1.210 1.214

4.16 9.75 13.40 14.80 16.20 17.52 18.7 19.8 20.6

1.213 1.238 1.254 1.268 1.273 1.290 1.302 1.317 1.332

41

TABLE3 Interpolated resistivity data Temperature (K)

Resistivity (pa cm) for the following specimens Specimen

25 30 35 40 45

50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165

1

Specimen

1.412 1.528 1.681 1.856 2.037

1.303 1.465 1.633

2.230 2.429 2.634 2.838 3.043 3.250 3.456 3.675 3.889 4.085 4.281 4.478 4.674 4.865 5.050 5.238 5.426 5.614 5.802 5.988 6.180 6.371 6.569 6.751

1.810 1.990 2.170 2.353 2.537 2.721 2.905 3.088 3.263 3.440 3.623 3.795 3.965 4.138 4.311 4.484 4.656 4.830 5.000 5.171 5.340 5.511 5.684 5.856

Temperature (W

Resistivity @C! cm) for the following specimens Specimen

2

1

Specimen

170 175 180 185

6.942 7.133 7.326 7.520

190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295

7.710 7.901 8.089 8.278 8.466 8.654 8.844 9.041 9.237 9.431 9.622 9.816 10.007 10.198 10.391 10.587 10.786 10.987 11.188 11.391 11.595 11.799

6.705 6.876 7.045 7.216 7.390 7.563 7.733 7.901 8,075 8.242 8.415 8.588 8.761 8.933 9.107 9.283 9.460 9.626 9.793

273.15

10.913

9.566

2 _

6.023

6.196 6.367 6.536

pi for ideal metals is proportional to the temperature T at temperatures above half the Debye temperature 8, for the resistivity. For temperatures less than en/lo, however, pi is proportional to T5. The behaviour of actinide metals is far from classical, and at low temperatures pi a T” with n < 5. Thus at low temperatures

The exponent n for actinide metals is usually about 3 (Table 4). 8, is given approximately by

48 15 4' k? 0

0 .u L p

I,

,

I

1

,

,

,

,

,

I

I.

_ 13\(

5 B

,

lL-

2 T

,

. 12-

.*..

. .

.

a.....

..*....

ll-

w 1-o 0

'

1

‘1

” 100

”

”

200

’

“1

300

Temperoturc.K

Pig. 4. The temperature dependence of the ratio of electrical resistivities of the protactinium specimens showing the distinction between form factor error and impurity effects as a function of temperature. TABLE 4 The low temperature resistivity exponent n and 6~ for the actinide metals [ 2, 51 Element

n

Th Pa U NP Pu Am

3 1.7 (2.8) 2.8 - 4 2-3 2 - 2.8 2.8 - 4.4

OR

144 147 121 137 110

On substituting the values for protactinium presented values of 149 K (specimen 1) and 145 K (specimen 2). 3.3. The exponent n The exponent can be obtained data available, and since

by estimating

here we obtain

8,

a value for p. from the

p -po=AT” a plot of ln(p - p,-J as a function of temperature provides n directly as the slope. In these experiments it was not clear that the resistivity had reached a constant value at the lower temperature. The need to assume a value for p. was removed by drawing a smooth curve through the data and then taking several pairs of values (p, T) from the curve and solving for n, p. and A for each pair. In this way the best line, which is plotted in Fig. 5, was found to be p = 1.204 + (700 X 10P6)0 1*675~.cs2cm which fits well up to 15 K or 8a/lO.

49

Fig. 5. The low temperature electrical resistivity of protactinium as a function of temperature.

A similar procedure was used to obtain p. = 0.880 pS2 cm for specimen 2. There were insufficient reliable low temperature data to obtain the exponent with confidence for this specimen. The complete low temperature data for specimen 1 are presented in Table 2.

3.4. Slope dp/dT of the resistivity curve The slope of the resistivity curve was determined in several ways, depending on the temperature range. The differential of the equation derived for p was used for the results up to 15 K, the slope of successive 1 K increments of the curve was taken for temperatures between 15 and 55 K and for the remainder of the temperature range investigated the slope of the least-squares line fitted to eight consecutive data pairs was taken to be that at the mean temperature of the set of data pairs. The slope is shown in Fig. 6.

4. Discussion The principal results obtained by Hall et al. [2] and in this work are summarized in Table 5. There are considerable differences, and we begin by considering the common ground.

50

5oLO -

:

specimen .“’_-._ .d.......,....... _V.’ ,I’ .m--, ,,,.,. -. ,_I.‘._....__~ )__-,__,.. .

1

Specimen

2

30-

O'.. 0

,I,, 50

. ,I.. 100

. .I.. 150

. .I ..a * * 1.. 250 200

. 300

Temperature,K

Fig. 6. The slope dp/dT of the electrical resistivity curve as a function of temperature.

Hall et al. observed a change in slope at 103 K, but rather sparse data made it impossible to determine whether this was an isolated event or whether other similar changes occurred. In this work the slope can be examined over the whole temperature range (Fig. 6). It can clearly be seen that the change in slope observed by the earlier workers occurs in both our specimens over the temperature range 98 - 104 K. For specimen 1 the slope at temperatures above the transition is reduced by 2.5’S, and for specimen 2 the reduction is 4%. There is evidence of a similar change at 90 K.

TABLE 5 The electrical resistivity of protactinium Parameter

P273.1tpacm) PO

Wcm)

P273.1iPO

Low temperature exponent n Temperature of anomaly (K) BR(K)

Values from the following sources Hall et al. [ 21

This work

17.80 1.92 9.27 2.8 103 108

10.0 0.92 9.06, 10.88 1.7 98 - 103 (100.7) 147

The plots of the deviation from the least-squares line fitted to the data for the temperature range 80 - 120 K from four experiments show that the mean temperature of the transition is 100.7 f 1.3 K. The nature of the transition is not known, but a change in crystal structure [6] and a magnetic transition [ 71 have both been rejected as possibilities. Above 110 K the slope is constant within the resolution of the results, which is evidence that the 5f electron contribution manifested as a curved

51

resistivity dependence (negative d*p/dT*) in uranium and higher actinides is not present in protactinium. in this work is only The absolute value of the resistivity determined about half that reported by the earlier workers, a difference which is outside the expected experimental error. Since the previous sample was smaller than ours and was wedge shaped, it appears probable that their form factor errors were greater than they estimated [ 81. A more surprising feature is that our measurement moves the protactinium curve from its expected position between thorium and uranium to below that of thorium. This is seen in Fig. 7 which includes results from Hall et al. [ 21 and Schenkel [9]. Thorium has a resistivity of 15.4 pCJ cm at 295 K; our preferred value for protactinium is 10.8 /..& cm at the same temperature, and even the addition of the maximum error yields only 13 ~.ts2cm. The exponent for the low temperature dependence which best fits our data is 1.7, compared with the value of 2.8 derived in the previous work. It is difficult to obtain II because it is very sensitive to the value assumed or implied for po. A value of n = 2.5 fits the published results of Hall et al. very well in the temperature region up to 5 K, and if their isolated measurement at 20.3 K is included a value of n as low as 1.5 is possible. Values for the other actinides taken from Schenkel [ 51 are given in Table 4. Our value of 147 K for OR contrasts with the value of 108 K calculated in the previous work, which, as noted by Hall et al., was “rather low” for the position of protactinium in the actinide series. The difference is largely accounted for by the difference in po. Values for the other actinides are given in Table 4 which shows that our value is close to that of 144 K quoted for thorium.

I

0

100

,

200

I

300

Tempcrature.K

Fig. 7. The temperature

dependence

of the electrical

resistivities

of the actinide

metals.

52

5. Conclusions This redetermination of the low temperature electrical resistivity of protactinium has confirmed the slope anomaly previously observed. The absolute resistivity measured here is lower than that previously reported, so that the resistivity of protactinium lies below that of thorium and a lower density of states is suggested.

Acknowledgments The authors are indebted to Mr. Bednarczyck, Mr. Bottini and Mr. Maino for extensive practical contributions to this work, and to J. A. Lee and M. J. Mortimer for discussions and comments. R. Bett is grateful for the opportunity to carry out this research which was provided by cooperation between the Atomic Energy Research establishment, Harwelf, and the European Transuranium Institute, Karlsruhe.

References 1 2 3 4 5 6 7 8 9

C. S. Griffin, K. Mendelssohn and M. J. Mortimer, Cryogenics, 8 (1968) 110. R. 0. A. Hall, J. A. Lee and M. J. Mortimer, J, Low Temp. P&s., 27 (1977) 305. J. Bohet and W. Miiller, J. Less-Common Met., 57 (1978) 185. J. C. Spirlet, J. Phys. (Paris], Colloq. C4, 40 (1979) 87. R. Schenkel, Rep. Eur 5674d, 1977, pp. 72, 136 (Joint Nuclear Research Centre, Karlsruhe). U. Benedict, C. Dufour and K. Mayne, J. Phys. (Paris), Colloq. C4, 40 (1979) 103. B. M. Bansal, Thesis UCRL 16782, University of California, Berkeley, CA, 1966. J. A. Lee, Atomic Energy Research Establishment, Harwell, personal communication, 1980. R. Schenkel, Solid State Commun., 23 (1977) 389.