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ELECTRICAL RESISTIVITIES OF LIQUID TRANSITION METALS
J. van Zytveld
To cite this version:
J. van Zytveld. ELECTRICAL RESISTIVITIES OF LIQUID TRANSITION METALS. Journal de
Physique Colloques, 1980, 41 (C8), pp.C8-503-C8-506. �10.1051/jphyscol:19808126�. �jpa-00220223�
ELECTRICAL RESISTIVITIES
O FLIQUID TRANSITION METALS
J.B. Van Zytveld
Physics Department, Calvin College, Grand Rapids, Michigan, U. S. A.
Abstract.- A method is described which permits direct measurement of the electrical resistivity, p, of liquid metals to temperatures above 1900°C. The method is applied to the measurement of p and d p / d ~ for liquid Fe and liquid Pt. For liquid Fe we find p = 137.6
+_
1.0 and d p / d ~ = .018+_
.003 ;for liquid Pt the results are p = 82.6
+
2.0 and dp/dT = 0.00+
.01. The units are VR-cm and U R - ~ ~ ~ / ~ C , respectively.~ntroduction very scanty. In the present paper we describe an
The past decade has seen growing interest in experimental method which can be used to obtain the electronic properties of the liquid transition values of p for liquid transition metals to above metals, both from a theoretical and from an experi- 1900°c, and apply this to a measurement of p for mental standpoint. On the theoretical side, liquid (and solid) Fe and Pt. This resistivity Harrison [l] made the first major attempt to apply data is the first to be obtained for liquid Pt by pseudopotential methods to the transition metals; conventional means on a contained sample.
Moriarty [2,3] adapted this to study the metals Sample materials and experimental methods
Cu, Ag and Au, as well as the alkaline earth The Fe sample material, in the form of a rod of metals, Ca, Sr, and Ba. The theoretical treatment nominal purity 99.998%, was obtained from the that has received the most attention, however, has Atomergic Chemetals Corporation. The platnum been that of Evans and his co-workers at Bristol sample material was composed of "VP-grade1' slugs
(cf; Evans e t a2 [4]. This method, employing the obtained from Materials Research Corporation. This single-site t matrix, has been used by Evans to latter material w d s of nominal purity 99.95%; 1st calculate the resistivity, p , and thermopower, S, analysis showed the major impurity to be Si (about of several of the liquid transition metals. 100 ppm), and no other element was detected in Hirata e t a2 [5] have also taken this approach to excess of 13 ppm.
the calculation of p and S for a larger number of During the time measurements were being made, the liquid transition metals, and Khanna and Jain the samples were held in alumina crucibles under [6] have applied it to a calculation of p for an argon atmosphere. Electrical contact was made several solid transition metals. Other authors to the liquid (and also to the solid) by drawing (notably Mott [7], Grieg and Morgan
[a],
Ballentine some of the liquid sample UP into each of four [9], and Espositio e t a l [lo]) have examined the alumina tubes. This sample material made contact limits of validity of Evans' formalism. And with molybdenum wires several inches above the Dunleavy and Jones [ll] have recently suggested actual sample. The liquid material in this contact that multiple-scattering effects may make signifi- area was then immediately frozen by lowering its cant contributions to p for these liquid metals. temperature, thereby immobilizing any impurities In addition, Fujiwara [12] has developed a model introduced by contact with the molybdenum. The due to Mott [7], permitting calculations of p and impurity that was introduced into the main sample S with considerable success. by this process did not exceed 0.005 at. %.On the experimental side, the high melting The sample region of the apparatus was heated temperatures and extreme reactivities of these by a muffle furnace to 1400-1600°C; additional metals have greatly hampered measurements of p and internal molybdenum windings raised the sample S. Several measurements of p for liquid Fe, Co, core region to a maximum of 1950°C. The tempera- and Ni have been reported, however ([13], [14], ture of the sample was measured by a tungsten-
[15], [16]). Measurements of S for liquid Fe, Co, rhenium thermocouple (W5% Re-W26% Re), insulated and Ni have also been made (Enderby and Dupree with Be0 and sheathed with tantalum; this thermo-
[17]). Aside from these three metals and liquid couple was placed alongside the sample crucible.
Pd, a liquid for which both p and S have also been The measurement method which was employed was reported (Dupree et a2 1181, GUntherodt e t a2 basically a four-probe, d c technique. To elimi-
[14]), data on the liquid transition metals is nate thermoelectric effects, however, the d c
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808126
c8-504 JOURNAL DE PHYSIQUE
current was a very-low-frequency square wave, and data acquisition and analysis were automated Essential to the successful measurement of electri- cal resistivities of liquid metals held in ceramic alumina containers at very high temperatures, is the choice of a geometrical configuration that minimizes the effect of the increasing conductivity of the alumina itself at these temperatures. The success of our arrangement can be seen in the com- plete absence of any contribution to the measured liquid resistivity that has an exponential temper- ature-dependence, as is characteristic of alumina.
The geometrical calibration constant for the sample-crucible arrangement (needed for extraction of the sample resistivity from the measured resis- tance) was obtained by finding a single multiplica- tive factor that would fit our data for the solid metal to the best available literature data over
the same temperature range. This temperature range was 0-1500°C for iron and 0-1200°C for platinum.
Results and Discussion
The resuits of our measure~ucnts of 9 for Fe and Pt from room temperature to wel1,above their melting temperatures are shown in Figures 1 and 2 respectively. The measured resistivities of liquid
I I I t
I
400 800 1200 1630
TCC)
Figure 1: Electrical resistivity of pure Fe.
A
-
Powell [13];-
Giintherodt e t a2 [14];---
Cezairliyan e t a2 [24] ;-- -
Kierspe e t a2 [23]; 0 , O -present data. Different symbols indicate data taken at different times.and solid Fe and Pt near their melting temperatures are shown on an expanded scale in Figures 3 and 4.
These figures also display measurements reported by other authors for comparison. A summary of the
data is displayed in Table 1, as well.
The measurement of p for liquid Fe was attempted in part to test our apparatus and measurement technique. We also wished to extend
O(
I ("W
Figure 2: Electrical resistivity of pure Pt.
---Flynn e t a2 [ 2 5 ] ;--- Laubitz e t a2 [26];
o,m,o,. -present data. Different shaped symbols
indicate different samples. Open symbols imply data taken with decreasing temperature; closed symbols, with increasing temperature.
data on p to higher temperatures than previously available in an attempt to obtain a better value for d p / d ~ in the liquid. We find that our data yields p = 137.6
+
luQcm at the meltingliq
temperature (1535"C), and dp/dT = i.018
+
.003pQ-cm/OC. The value for p agrees well with earlier
160-
150-
-
E 140C: P 2 130-
a I20
110-
-
-
- -
z:
-
- -
-
I I I
1500 1600 1700 1800
T(OC1
Figure 3: Electrical resistivity of Fe near the melting temperature. A -Powell [13] ;
---Giintherodt e t a2 [14] ;
---
Cezairliyan e t a2 [24] ;---
Erskov e t a2 [I51 ;------
-Kitae t a2 [16];o,~,o -present data. Different symbols indicate data taken at different times.
the value of .015uQcm/"C measured recently by Kita
e t a2 1161, and also to the value of .017pQcm/oC
inferred from the data of Guntherodt e t a2 [14].
1
1600 1 1700 I I600 I 19W I 1TCO
Figure 4: Electrical resistivity of Pt near the melting temperature. o,m,o,e -present data.
Different shaped symbols indicate different samples. Open symbols imply data taken with de- creasing temperature; closed symbols, with in- creasing temperature.
The temperature-dependence of the solid resis- tivity also follows previously-published values rather closely. These values of p imply that the ratio pliq/esol at the melting temperature is about 1.08. We conclude that our method is capable of measuring p for liquid metals to very high temperatures with reasonable accuracy.
The measurement of p for solid Pt above about 1400°C is the first to be reported, with the exception of the work of Lebedev [19] and of Martynyuk e t a2 [20], both of whom used the tech- nique of exploding wires. Lebedev [19] quotes a value for p liq/psol at the melting temperature
(1770°C) of l.4; Martynyuk e t a2 [20] obtain psol (1770°C) = 62.lpQcm and pliq (1770°C) = 92.6pRcm, yielding p liq/psol = 1.49. Our measure- ments indicate that p (1770°C) = 58
+
lpQcmsol
and pliq (1770°C) = 82.6
+
2.0uQcm, giving pliq/pSo1 = 1.42+
.04. We also note that dp/dT for both liquids is small, a fact consistent with Mott's [7] analysis of liquid transition metal resistivities.A number of calculations of p for liquid Fe and liquid Pt have been reported. (Table 1). The method of Evans e t a2 has been applied by several authors, yielding values for liquid Fe ranging from 182pQcm (Hirata e t a2 [5])~to193pQcm
(Dreirach e t a2 [lo]) and 276pQcm (Evans e t a2 [4]),.
Hirata e t a2 [5] have also calculated p for liquid
tures.
Melting
Temp(Tmp) P O l p P (T )
("0
~ ~ c m ) t i 8 c m ~Experimental
127.5[13,24] 137.651.0 .018f.003 129[14] (present) (present)
139 1131 .015 [16
1
138 [I51 .017[141 136.5 [14]
136 [I61 Theoretical
Experimental 58fl 82.6k2.0 O.OOf.01 (present) (present) (present) 62.1[20] 92.6[20]
Theoretical
94.6[5]
146,200[11]
Pt on this model, obtaining a value of 94.6pQcm.
Cne of t h e great difficulties in this calculation is knowing what effective valence, Z*, to assign to the liquid metal, making the Fermi energy also uncertain. This uncertainty has a great effect on the value calculated for p. Esposito e t a2 [Zl]
have extended the single-site approximation to a calculation of the density of states, permitting an evaluation of Z*, and thus removing this qource of ambiguity. Their calculations yield Z*
4
1 for the liquid transition metals Fe, Co, and Ni3 these values result in a gross overestimate of p for the metals nearest the center of the transition metal series, where the scattering is strongest. The question of the applicability of the Evans forma- lism to metals in which the d band is approximate- ly half-filled must therefore be seriouslyaddressed. (See also Ballentine [9] on this matter.)
Dunleavy and Jones (1978) have looked at the effect of multiple scattering on p for liquid Fe and Pt as well as for several other liquid tran- sition metals. They find that the result of adding multiple scattering effects is to lower the calculated p considerably, bringing it more nearly into line with measured values in many cases. (In Table 1, two values are listed for these authors for each metal; the larger value is calculated assuming single-site scattering, and the smaller
34
c8-506 JOURNAL DE PHYSIQUE
value incorporates multiple scattering.)
Fujiwara [12] has taken a different approach to the problem of calculating p and S for these liquid metals. He has taken a method suggested by :'~ott [7] involving differing s and d electron mean
free paths, and, on the basis of a calculated density of states, has estimated p for liquid Fe to be 129pflcm. This is in good agreement with experiment. In addition, his calculated values for the thermopowers of these liquid metals fall close to the measured ones. This method certainly warrants further attention.
Now that we successfully have tested our apparatus to 1950°C, and are satisfied that we can make measurements of resistivities of liquid metals to that temperature, we can begin to examine other liquid transition metals as well.
Asano and Yonezawa [22] have recently calculated the d-density of states, nd(E), for solid and liquid Cr. They find a minimum in n (E) at Ef for d solid Cr, a minimum which does not exist for liquid Cr. Thus the resistivity of Cr may in- crease perhaps as much as 100 to 200% upon melt- ing. There have been no measurements of p for liquid Cr to-date, making a test of this predic- tion impossible. We are therefore presently be- ginning measurements of the resistivity of this liquid metal.
Acknowledgments
We are happy to acknowledge the financial support of Research Corporation (via a Cottrell College Science Grant) and of the National Science Foundation (via Grants DMR77-05213 and
DMR79-09969).
References
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