JOURNAL OF THE LESS-COMMON METALS
R. V. COLVIN
AND M. J. MARCINKOWSKI
Edgar C. Bain Laboratory,for Fundamental Research, United States Steel Corporation Research Center, Monroeuille, Pa. (U.S.A.) (Received
August Ioth, 1961)
SUMMARY The electrical resistivity parallel to the [IOO] axis of a chromium single crystal has been measured from 4 to 330°K. Considerable hysteresis in electrical resistivity exists in the neighborhood of the Nobelpoint. It is suggested that this effect results from variations in the degree of spin ordering which depend on both temperature and time. The present investigation in contrast to some recent measurements of other properties shows no anomalies in the electrical resistivity at low temperatures. The temperature dependence of the intrinsic resistivity at low temperatures is identical to that found in a pure polycrystalline sample. This suggests that s-d scattering is predominant over other scattering mechanisms. INTRODUCTION
Recently there has been considerable interest in the nature of the magnetic behavior of chromiuml-10. It has been clearly established that the antiferromagnetic-paramagnetic transition temperature (NCel point) for high purity ductile chromium is 312~K2~10~11. Most impurities lower the NCel pointl2.13; however, manganese is an exception. It raises this temperature. Various investigators have observed, in addition to the NCel point, anomalous behavior in certain physical properties of chromium at lower temperatures. FINE et aZ.14 have reported a small minimum in Young’s modulus at 121’K in polycrystalline chromium. Recently, BOLEF et aZ.15have also found an anomaly at 121’K in the elastic constants of single crystal chromium. On the other hand, BYKOV et al.9 have found in a chromium single crystal anomalies in the thermal expansion and in the neutron diffraction data at 115°K. The inferred transition has been confirmed by BACONSusing neutron diffraction. His study also supports an anisotropy transition involving a change of spin direction from a parallel arrangement to one perpendicular to the antiphase domain wall as suggested by HASTING+. According to HASTINGS,this occurs at IIO’K. Conclusions similar to those of HASTINGShave also been obtained by WILKINSONet al.3 from neutron diffraction studies with a powdered chromium sample. However, the magnetic susceptibility measurements obtained with a chromium single crystal by MCGUIRE~indicate that the susceptibility is almost constant over the temperature range from 77 to 673”K, that no anisotropy exists in [IOO] and [III] directions, and that the susceptibility changes associated with the above-mentioned anomalies are less than 0.05 -10-s e.m.unit/g. The most recent contribution on this subject is by COLLINGSet al.10 who J. Less-Common Metals, 4 (1962) 46-51
OF A CHROMIUM SINGLE CRYSTAL
have found a small peak characteristic of a NCel point at 312’K in the susceptibility vs. temperature curve. They have eliminated the possibility that this anomaly is due to small amounts of chromium sesquioxide (NCel point at about 312°K) by making additional measurements on their samples using electron spin resonance techniques. In light of the apparent discrepancies and complexities in these experimental observations in chromium, we decided to investigate the electrical resistivity of a chromium single crystal from liquid helium temperatures to slightly above the NCel point. The potential utility of this measurement is shown by the fact that electrical resistivity studies have been helpful in establishing the magnetic transformations in rare earth metals 16-19. In this paper we shall describe the results of our initial experimental study made with the chromium single crystal.
A single crystal of chromium was grown using a technique described elsewhere8920. The starting material was chromium used in a study of plastic deformation at low temperatures20. This work and ref. 21 describe details concerning the melting and fabricating procedures. The polycrystalline chromium has been analyzed in our laboratory with the following results: oxygen 0.055 wt.%, nitrogen < 0.001 wt.%. A sample of dimensions 0.254 cm x 0.235 cm x 0.900 cm was cut from the original crystal using a diamond wheel. The long axis of this crystal was parallel to the [IOO] axis. The crystallographic orientation of this axis was determined within I’ from Laue back-reflection photographs. The sample was mounted in a specially designed cryogenic apparatus similar to that described previouslyi6. With this equipment, it has been possible to obtain any temperature between liquid helium temperatures and 380°K. The temperatures were kept constant within f o.oY’K by means of an electronic controller. Carbon and copper resistors were used as temperature-sensing elements which determined the amount of heat to be supplied to a manganin heater. The electrical resistivities were determined by comparing the electrical potential across a known length of the crystal with the potential across a standard resistor. Solid copper blocks pressing against the ends of the sample were used as current contacts. Small stainless steel cones separated by a fixed distance and lightly pressed against the sample provided the potential contacts. The voltages across these contacts were measured with a Rubicon six-dial thermofree potentiometer. A Rubicon photoelectric galvanometer combined with a Leeds and Northrup d.c. microvolt amplifier was used as the null indicator. Thermoelectric effects in the electrical circuit were minimized by the method of reversing current and by using Tinsley reversing switches immersed in mineral oil. With this equipment, it was possible to measure reliably & 0.01 ,uV. The electrical current through the sample and the standard resistor was kept constant to I part in 105 by means of an electronic stabilizer. This current was determined with a Rubicon type B potentiometer. The temperatures of the sample over the whole temperature range were determined using a copper-constantan thermocouple whose junction was glued on the sample with GE adhesive 7031. The thermoelectric voltages were measured using a Tinsley J.
S. ARAJS, R. V. COLVIN, M. J. MARCINKOWSKI
Diesselhorst potentiometer. This thermocouple was calibrated at the boiling point of liquid helium. The temperatures were determined to the nearest o.L’K. The probable error in the geometrical form factor (ratio of cross sectional area to the distance between potential contacts) was estimated to be about 1%. RESULTS AND DISCUSSION
The electrical resistivity measurements obtained from the single crystal of chromium parallel to the [IOO] axis are shown in Figs. I and 2. Here e exhibits a striking hysteresis
< 12.4 ¶c a
12.2 i l2.0ll.8-
TA.P=311% Cr SINGLE CRYSTAL, I II [IOO] p,=l.04
280 Fig. I. Electrical
x 10e6 ahm cm
of chromium single crystal in neighborhood
of the Nobeltemperature.
T I’KI Fig. z. Electrical resistivity of chromium single crystal from liquid helium temperatures
in the neighborhood of the NCel temperature. A detailed description of the measurements is as follows: After the sample was cut to the desired orientation, it was placed in the cryostat at room temperature and the resistivity measurements were J. I.ess-Common
4 (1962) 46-51
ELECTRICAL RESISTIVITY OF A CHROMIUM SINGLE CRYSTAL
made giving the results I, 2,. . ., 12 (Fig. I). At the last point corresponding to 309.6”K the sample was left overnight and the experiment was continued the next day (from a to b). Keeping the sample overnight at this temperature did not produce, within experimental error, any change in the electrical resistivity. The region a-b on the e vs. T curve was obtained over the period of an eight-hour day by changing temperatures slowly. A minimum in the Q vs. T curve occurs at about 31PK and is associated with the N6el temperature, in good agreement with the experimental results of previous investigators2,10~11, obtained with a somewhat higher purity ductile polycrystalline sample. The residual resistivity of our single crystal was found to be 1.04.10-6 ohm cm while that cm reflecting
for the above-mentioned
sample was 0.055.10-6
higher purity of the latter material.
At point b on the e vs. T curve of Fig. I, the sample was again left overnight with no effect on the value of Q, and the experiment was continued the next day (from b to c). Temperatures were slowly increased up to the point A. After measuring the resistivity at this point the sample was cooled in a single step to a temperature near the NCel temperature, i.e. point c. Leaving the crystal at this temperature overnight did not change the value of the resistivity. Following this treatment the sample was heated to 373”K, cooled rapidly to 78”K, and left there for two days giving point d in Fig. 2. Measurements were again taken with increasing temperatures (see the small triangles in Fig. 2). After this run, the crystal was cooled to 78°K (e) and left overnight. The next day helium was transferred into the cryostat and the sample cooled to 4.2”K (f). Measurements were taken with increasing temperatures. The intervals f-g, g-h, h-i, i-k, k-l, 1-F represent the Q vs. T measurements on each successive day. At pointsg, h, i, k and 1 the sample was left overnight in the cryostat. The experiment was discontinued after the sample reached the point F. This initial study of the electrical resistivity of a single crystal of chromium clearly indicates that considerable hysteresis occurs in the neighborhood of the NCel temperature. However, the detailed features of this hysteresis are not known at the present time. According to our best knowledge, such an effect has not been noticed before. We are planning to examine this problem in the near future using a purer single crystal and also employing magnetic fields. Another observation is that the location of the minimum in the Q vs. T curve appears to be independent of the thermal history of the sample. The electrical resistivity p(T) of a pure metal can be approximated as being made up of the residual resistivity eo and the intrinsic resistivity &T) due to the scattering
electrons by static imperfections
e(T) = eo + edV In this approximation eo is independent of temperature. The quantity et(T) approaches zero when T goes to zero. Figure 3 shows the temperature dependence of pi(T). In order to eliminate the possible error in the geometrical form factor, in Fig. 3 we have plotted [e(T) - p]/e(8o) vs. T, where Q(T) and ~(80) are the measured resistivities at the temperature T and 80”K, respectively. Our results are in good agreement with those of WHITE AND Woo~P.23 up to about IOOOK. At higher temperatures small deviations ferromagnetic
due to the hysteresis effects associated
Figure 3 also show some possible
with the antidependences
J. Less-Common Metals, 4 (1962) 46-51
S. ARAJS, R. V. COLVIN, M. J. MARCINKOWSKI
expected on theoretical grounds. The intrinsic resistivity Q$ of the single crystal of chromium determined experimentally, varies approximately as T3-2 up to IOO’K. This may possibly indicate that the quantity et results primarily from the s-d scattering24 due to lattice vibrations which should vary as T3. The lattice resistivity associated with the s-s scattering would have a T5 dependence. Electron-electron scattering in a transition metal should follow a 1‘2 law 25.26. Additional complications in the temperature dependence of the electrical resistivity of chromium may arise due to the existence of antiferromagnetism27,2*.
d” ,d Q /
dependence of electrical resistivity of chromium. ---, (polycrystal); 0, A, 0, this investigation (single crystal).
Concerning the hysteresis effects observed in the electrical resistivity of the chromium single crystal shown in Figs. I and 2, it appears that these result from variations in the degree of spin ordering which in turn depend on both temperature and time. The maximum decrease in resistivity occurs when the sample is kept just below the NCel point for a. considerable period of time. After this, a Q vs. T curve which abpears to be independent of time can be obtained by slowly increasing the temperature. If, however, the sample has been kept at some sufficiently elevated temperature (and hence its antiferromagnetic ordering destroyed) and then rapidly cooled to say room temperature before perfect order can be obtained, then the electrical resistivity in this condition will be higher than in the ordered state. If held at this temperature, however, the electrical resistivity will slowly decrease with respect to time to some equilibrium value as the ordering becomes more perfect. Figure I clearly shows that there are no anomalies in Q U.S.T curve at low temperatures corresponding to the magnetic transformations briefly mentioned at the beginning of this paper. It is quite possible that the variety of results obtained by previous J, Less-Common
ELECTRICAL investigators results
is due to the different
in this temperature
ture between function
IOO to 200”K,
of time in order
OF A CHROMIUM SINGLE CRYSTAL of their
a somewhat a better
purer is being
as a function
of the kinetics planned
as a in
for the near future.
ACKNOWLEDGEMENTS The authors
to E. J. FASISKA the
and L. ZWELL
for their painstaking
to J. C. RALEY
the crystal. REFERENCES
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