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Electrical resistivity studies of chromium rich chromium-germanium alloys between 4 and 320°K
J. Phys.
Pergamon
Chem. Solids
ELECTRICAL
Press 1967. Vol. 28, pp. 1459-1564.
RESISTIVITY
CHROMIUM-GERMANIUM
Printed in Great Britain.
STUDIES ALLOYS
OF CHROMIUM
RICH
BETWEEN 4 AND 320°K
SIGURDS ARAJS and W. E. KATZENMEYER* Edgar
C. Bain Laboratory for Fundamental Research, United States Steel Corporation Research Center, Monroeville, Pennsylvania (Receiwed
9 Jumuwy
1967)
Abstract-Electrical resistivity of chromium-germanium alloys, containing 0.35, 0.72, 1 .Os, 1~4~, and 2.1s at.% germanium, have been studied between 4 and 320°K. The NQI temperatures are observable from the resistivity curves for alloys with 0.3s and 0.7s at.% germam ‘um but not for those with higher germanium concentrations. Germanium markedly lowers the N&l temperature of chromium. A minimum in the electrical resistivity vs. temperature curve is observable for all chromium-germanium alloys at low temperatures. This behavior is essentially similar to that noticed previously in chromiurn~obalt and chromium-nickel systems. The increase in the electrical resistivity at 4*2”K due to 1 at. y0 germanium and the longitudinal magnetoresistivity data up to 60 kOe magnetic fields further accents the similarity of germanium with cobalt, nickel and, to some extent, iron as solute in chromium.
INTROKXXTION
have initiated extensive studies of the electrical resistivity of different chromium-rich binary alloys. These investigations have been undertaken, primarily, because the electrical resistivity is a useful method for exploring certain features of antiferromagnetic behaviour and it was used in our previous determinations of the concentration dependence of the Neel temperature of chromium alloys containing iron,(lma)cobalt, t3) nickel and manganese.(*) Furthermore, we also have observed for the first time the occurrence of a minimum in the electrical resistivity vs. temperature curves at low temperatures in chromium alloys containing cobalt and nickel. These results indicate that this phenomenon may be more widespread than previously recognized and that it can also occur in an antiferromagnetic alloy system. The present paper deals with new electrical resistivity measurements on some chromium-germanium alloys between 4 and 320°K which support our expectation that quite interesting behavior can be found in certain chromium RECENTLY
we
* Now at the Department of Physics, Carnegie Institute of Technology, Pittsburgh, Pennsylvania 15213.
alloys. According to our best knowledge the electrical resistivity of chromium-germanium alloys has not been studied before.
-AL
CONSIDERATIONS
The chromium-germanium alloys, containing 0*3,, O-7,, l*Os, 1*4,, and 2.1, at. y0 germanium, were prepared by arc melting chromium and germanium in the same manner as was done with chromium and iron described elsewhere.@) The initial stock of chromium (Iochrome) was obtained from Chromalloy Corporation. The analysis of the impurities found in this material have been recorded previously. (5) Germanium (99*99+ per cent purity), added as a solute to chromium, was supplied by Eagle Picher Company. After the melting, the ingots were sealed into silica capsules filled with 150 Torr of argon at 298”K, homogenized at 1370°K for 120 hr, and then rapidly cooled by removing the capsules from the furnace. The samples for the electrical resistivity measurements were cut from the homogenized ingots using a wafering machine with a high speed carborundum disk. The size of the resistivity samples was about 0.3 cm x q-3 cm x 3 cm.
1459
1460
SIGURDS
ARAJS
and W. E. KATZENMEYER
The electrical resistivity of each sample was determined using the standard four-probe method. The potential leads were spot-welded copper wires of 0.0’2 cm dia. The electrical current leads were attached to the ends of the sample in a conventional manner by means of indium solder. This was possible because the sample ends, after the sample was cut, were covered with pure indium using an ultrasonic soldering technique. Four samples, connected in series, were mounted in a sample holder which was located in a cryostat capable of producing temperatures between 1.2 and 350“K, constant to +O*Ol”K, using a specially designed control system. ~3)The electrical measuring current, provided by 12 V storage batteries, was kept constant to 1 part in lo5 by means of a servosystem. It was measured with a Rubicon potentiometer (Model 2781) and a 0.01 P standard resistor. The voltages between the potential leads, which did not exceed 100 c;V, were measured with a Type 9174 four-figure potentiometer of Guildline Instruments, Ltd. The null detecting system consisted of a Type 5214/9460 photocell galvanometer amplifier together with a Type 9461A galvanometer (both units made by Guildlme Instruments) which allowed us to detect at least rf:0.01 pV. The voltages larger than 100 ~.LVwere determined with a Rubicon six-dial potentiometer (Model 2768) using a Rubicon photoelectric galvanometer (Model 3550) and a Leeds and Northrup d.c. microvolt amplifier (Model 9835B) as the null indicator. It was possible to switch from one potentiometric system to another at any time by means of Guildline Instruments’ selector switches (Type 914541) whose internal thermoelectric voltages, generated at the contacts, were less than 0.01 I_~V.Thermoelectric effects in the external sample circuit were eliminated by a Guildline reversing switch (Type 9600-L) immersed in mineral oil. The temperatures of the samples were measured with two different thermometers. Below 20°K calibrated germanium cryogenic sensors (Minneapolis-Honneywell Regulator Company, Model MHSP 2404, Series II), accurate to + O.l”K, were used. Above 20°K a platinum resistance thermometer (Engelhard Industries, Inc., Model 2070713A) previously checked against a Leeds and Northrup platinum resistance thermometer (calibrated by the National Bureau of Standards) was
used as the temperature indicator, being accurate within &-O*l”K. The absolute values of the electrical resistivity of different chromium-germanium samples are believed to be correct to f 2 per cent, this error resulting primarily from the uncertainties in the geometrical form factor. No corrections due to the thermal expansion were applied to the measured data of the electrical resistivity. Longitudinal electrical magnetoresistivity studies at 4.2°K were made on pure chromium and chromium-germanium alloys containing 0*3s, 0*7s, and l-4* at.% germanium using a compensated Westinghouse superconducting solenoid with the inside diameter of 2 in., outside dia. 6 in., and length 16 in. With this solenoid it was possible to obtain magnetic fields up to 60 kOe. Because of the 2 in. inside dia., four samples could be studied simultaneously. The solenoid current, provided by a Westinghouse power supply capable of controlling the electrical current to 1 part in 105, was determined by using a O$lOl P standard resistor in series with the solenoid. RESULTS AND bISCUSSION The electrical resistivity b(T)] of chromium and chromium-germanium alloys, containing 0*3,, O-7,, l-O,, l-4,, and 2.1, at.% germanium, as a function of absolute temperature (T) between 4 and 320°K is shown in Fig. 1. The curve for chromium is that already published before.‘5) All these curves were obtained with increasing temperatures starting at 4.2°K. From Fig. 1 it can be observed that the NCel temperature (TN) of chromium, appearing as a small minimum in the p(T) vs. T curve at 313”K, is markedly lowered by small additions of germanium. In fact, this rate of decrease is the most drastic one produced by any solute in chromium according to the presently available information. The role of small amounts of different solutes on TN of chromium is demonstrated in Fig. 2. The curve associated with manganese is due to BOOTH.(~)The other curves have been obtained from our electrical resistivity studies on different chromium alloys containing iron,(l) cobalt,(3) tantalum,(8) nickel,(8) and silicon.(g) From Fig. 2 one can notice some similarity between germanium and silicon with respect to their influence on TN of chromium, i.e. the initial decrease in TN is small at low solute
RESISTIVITY
STUDIES
OF
CHROMIUM
RICH
CHROMIUM-GERMANIUM
AI;LOYS
1461
FIG. 1. Electrical resistivity of chromium-germanium alloys between 4 and 320°K. 350
fdll/-+-
/--@
1
I
4*
300 L
C
250 -
To
s 200 -
68
#i +=
150 ~
si
loo
I
1
.
.
0
Z&E
COtKXNlW&
1.5
[at.%]
FIG.2. The variation of the Nkel temperature with solute concentration
of different binary chromium
concentration but then increases rapidly with higher solute percentages. It may be mentioned that ~e.anorn~y in the p(T) vs. T curve in chromium and chromium-O.3, at.% germanium alloy at T,is barely noticeable in the sample containing 007~ at.% germanium and is completely absent in the data for higher composition samples. The most spectacular feature in the curves of p(T) vs. T is the occurrence of a minimum at 10~ temperatures. Because of its smallness this
alloys.
minimum cannot be seen in the curves shown in Fig. 1, but it can be clearly observed in the enlarged plots presented in Fig. 3. This minimum, which does not occur in pure chromium, appears when germanium is added to chromium. The temperature at which the minimum occurs (Tmin), shown by arrows in Fig. 3, first increases with increasing germanium concentration, reach a maximum for about 1 *44 at.% germanium concentration, and then decreases. The exact value
1462
SIGURDS
to determine of TIllin is difficult electrical resistivity minima are, small. Usually the depth of the characterized by the quantity Ap p(Tmin) which, for example, for 0.3, ium sample is about 0.008 ps2 cm.
ARAJS
and
because the indeed, very minimum is = p(4*2”K)at.% germanEven for the
FIG. 3. Electrical resistivity of chromium alloys contain-. ing different amounts of germanium below 40°K.
chromium-germanium alloy containing l-4, at.% germanium, for which Tmin w 28”K, Ap = O@O ~0 cm, which is small in comparison with the maximum values of Ap observed for chromiumcobaW3) (Ap = 0.260 pa cm for 6.2 at.% cobalt content) and even chromium-nickel(*) (Ap = 0.070 @cm for 0.8 at.% nickel content) alloys. At first sight it appears that the origin of the minimum is of the KONDO type (lo), in spite of the fact that the variation of Tmin and Ap with germanium concentration is more complicated than predicted
w.
E.
KATZENMEYER
by the simple Kondo theory. This expectation is based on the observation that the minimum is clearly observable in chromium-cobalt alloys(s) for which the magnetic susceptibility data bySuzur&l) suggest the existence of localized magnetic moments due to cobalt atoms. In this system the quantities T,,, and Ap also do not behave exactly as expected from the Kondo model. However, since the original Kondo theory is based on quite a few idealizations, it should not be surprising that some disagreements may exist between the simple theory and observed localized moment bahaviour in an antiferromagnetic metal such as chromium. The occurrence of the resistivity minimum in thechromium-germanium alloys is a more startling effect than in the cobalt alloys because it is difficult to associate magnetic moments with germanium atoms. There is, however, another possible explanation for the occurrence of the minimum in these alloys at low temperatures. This explanation comes from the recent theoretical work by KIM who suggests that localized nonmagnetic states, associated with certain impurities in a pure metal, may cause a minimum in the p(T) vs. T curves. KIM believes that resistivity minima observed in titanium alloys containing for, example, 0.2 at.% iron or chromium’i3) are due to this cause. Magnetic susceptibility measurements on chrtimium-germanium alloys at low temperatures should be helpful for distinguishing between these two possible mechanisms. Such studies are being planned for the near future in this laboratory. Another feature of the electrical resistivity data, which appears to be interesting from the viewpoint of the minimum phenomenon, is the increase in the electrical resistivity of chromium due to different dissolved impurities in the chromium lattice. Up to this time we have observed the following facts. Elements such as iron, cobalt, and nickel, when added to chromium, produce resistivity increases of about 7.1, 8.5 and 16.0 pCJ cm/ at.% solute, respectively, at 4*2”K.(*) These elements are believed to exist as localized magnetic moments in the chromium matrix. The associated resistivity increases are considerably larger than the corresponding values found when, for example, vanadium or manganese is dissolved in chromium. These latter elements give only about 0.3 &I cm/ at.% solute resistivity increase at 4*2”K.(14) Furthermore, it has been established that neither
RJZSISTIVITY
STUDIES
OF CHROMIUM
RICH
IO
O-5
. f Go tO&TENTRATld~
20
z5
[ot.%f
1 4. Electrical resistivity of chromium-germanium alloys as a function of gctrmanium concentration at 4.2 and 300.O”K.
0
10
ALLOYS
1463
effects on the electrical resistivity in these two materials. That is, the data in Fig. 4 at 3OO.O”K represent the resistivity behavior of paramagnetic chro~~~e~~iurn alloys as a function of germanium-concentration. The fact that one can draw a straight line through these points demonstrates the alloys are homogeneous as was expected. The curve in Fig. 4, associated with 4*2”K, shows an anomaly at about 1 at.% germanium due to the inthtence of TN on the electrical resist&&y. However, one can clearly estimate from Fig. 4 that 1 at.% germanium at 4.2°K increases the electrical resistivity of chromium by about 16.7 &J cm. This value is quite close to that found when nickel is dissolved in chromium. It may be remarked that large increase in the electrical resistivity due to 1 at.% solute, capable of producing localized magnetic moments, has been predicted theoretically by WOLFF. Usually the alloys, which exhibit anomalies in the electrical resistivity at low temperatures, also
vanadium(l*) nor manganese”) is able to produce a minimum in the p(T) vs. T curves at low temperatures. Also, the magnetic susceptibility studiesP on c~o~~-rn~~~e alloys indicate
0
CHROMIUM-GERMANIUM
20
fit@]
40
50
60
H,
FIG. 5. Longitudinal electrical magnetoresistivity of some chromium-germanium alloys as a function of HE at 4*2”K.
that no localized moments exist on manganese atoms in chromium. The behavior of chromiumgermanium alloys, from the viewpoint of the resistivity increase due to 1 at.?; germanium at say, 4*2”K, is very similar to that of binary chromium alloys cont~~ng iron, cobalt, and nickel. Figure 4 shows the electrical resistivity of these alloys as a function of germanium concentration at 4.2 and 3OO*O”K.The points associated with pure chromium and 0.3, at.% germaniumchromium alloy at 3OO*O”Kwere determined from the ~(2’) vs. T plots (Fig. 1) by extrapolating the resistivity curves above TN to 3OO.O”K. This was done in order to eliminate the antiferromagnetic
show some anomalous behavior in magnetic fields.‘le’ Figure 5 presents the total change in the electrical resistivity of some chromiumgermanium alloys due to an applied longitudinal magnetic field, H,, at 4*2”K, defined by Ap s(4~2°K) = p(4*2”K, H,) -p(4*2”K, 0 Oe). The curves were obtained with increasing magnetic fields. The open and closed points, associated with the curve for pure chromium, represent two separate runs indicating good reproducibility of the magnetoresistivity data. From Fig. 5 one can observe that additions of Geoff to chromium cause a decrease in the quantity Ap ,(4*2”K). However, this quantity remains positive for all
1464
SIGURDS
ARAJS
and
alloys up to at least 1.4, at.% germanium level. The decrease in Ap,(4*2’K) with increasing germanium concentrations is similar to that observed in chromium-cobalt and chromiumnickel alloys for which the quantity Ap ,(4*2’K) eventually becomes slightly negative for larger solute contents. Such a behavior is quite distinct from that seen in chromium-manganese alloys(*) in which manganese is quite incapable of significantly lowering the value of Ap , (4*2”K) of pure chromium. These facts give an additional accent to the quite distinct behavior of germanium in solid solution with chromium. Acknowledgements-The authors are grateful to the following xknbers of this laboratory: G. R. DIJNMYRE, G. P. WRAY. and J. W. CONROY for their technical assistance wiih this -&e&p&on and R. M. FISHER for his critical review of this piper. Stimulating discussions with P. A. BECK of the University of Illinois are very much appreciated.
REFERENCES 1. ARAJS S. and G. R. D~YRE, 1017 (1966).
J. appl.
Phys.
37,
W.
E.
KATZENMEYER
2. ARAJSS. and D~NMYRE G. R., EIcctricaZ Magneto-
3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
15. 16.
resistivity of Chromium-Iron Alloys, to be published in J. appl. Phys. ARAJS S., DUNMYRE G. R. and DECHTER S. J., Phys. Rew. 154,448 (1967). AIWJS S. and DUNNIYRE G. R., J. appl. Phys. 38, 1157 (1967). ARAJS ,% and DUNMYRE G. R., J. appl. Phys. 36, 3555 (1965). COLVIN~. VI and bJS S., Phys. Rev. 133, A1076 (1964). BOOTH J. G., phys. status solidi, 7, K157 (1964). ARAJS S. and DIJNMYRE G. R., unpublished studies. ARAJS S. and KATZENMEYERW. E., unpublished studies. KONDO J., Prog. theor. Phys., Kyoto 32, 37 (1964). SUZUKI T:, J. phys. Sot. Japan 21,442 (1966). KIM D.-J.. Phvs. Rev. 146.455 (1966). CAPE J. A: anh IiAKE R. k., Phys. Rev. 139, 455 (1966). TREGO A. L., Antifewomagnetism in Dilute Chromium Alloys, Ph.D. Thesis, Iowa State University of Science and Technology (1965). (University Microfilms, Inc., Ann Arbor, Michigan). WOLFF P. A., Phys. Reu. 124, 1030 (1961). VW DEN BERG 6. J., Anomalies in Dilute Metallic Solutions of Transition Elements, Vol. 4. v. 194, in Progress Low Temperature Physics, e&ted by C. J. GORTER,North-Holland, Amsterdam(1964).
in
Pergamon
Chem. Solids
ELECTRICAL
Press 1967. Vol. 28, pp. 1459-1564.
RESISTIVITY
CHROMIUM-GERMANIUM
Printed in Great Britain.
STUDIES ALLOYS
OF CHROMIUM
RICH
BETWEEN 4 AND 320°K
SIGURDS ARAJS and W. E. KATZENMEYER* Edgar
C. Bain Laboratory for Fundamental Research, United States Steel Corporation Research Center, Monroeville, Pennsylvania (Receiwed
9 Jumuwy
1967)
Abstract-Electrical resistivity of chromium-germanium alloys, containing 0.35, 0.72, 1 .Os, 1~4~, and 2.1s at.% germanium, have been studied between 4 and 320°K. The NQI temperatures are observable from the resistivity curves for alloys with 0.3s and 0.7s at.% germam ‘um but not for those with higher germanium concentrations. Germanium markedly lowers the N&l temperature of chromium. A minimum in the electrical resistivity vs. temperature curve is observable for all chromium-germanium alloys at low temperatures. This behavior is essentially similar to that noticed previously in chromiurn~obalt and chromium-nickel systems. The increase in the electrical resistivity at 4*2”K due to 1 at. y0 germanium and the longitudinal magnetoresistivity data up to 60 kOe magnetic fields further accents the similarity of germanium with cobalt, nickel and, to some extent, iron as solute in chromium.
INTROKXXTION
have initiated extensive studies of the electrical resistivity of different chromium-rich binary alloys. These investigations have been undertaken, primarily, because the electrical resistivity is a useful method for exploring certain features of antiferromagnetic behaviour and it was used in our previous determinations of the concentration dependence of the Neel temperature of chromium alloys containing iron,(lma)cobalt, t3) nickel and manganese.(*) Furthermore, we also have observed for the first time the occurrence of a minimum in the electrical resistivity vs. temperature curves at low temperatures in chromium alloys containing cobalt and nickel. These results indicate that this phenomenon may be more widespread than previously recognized and that it can also occur in an antiferromagnetic alloy system. The present paper deals with new electrical resistivity measurements on some chromium-germanium alloys between 4 and 320°K which support our expectation that quite interesting behavior can be found in certain chromium RECENTLY
we
* Now at the Department of Physics, Carnegie Institute of Technology, Pittsburgh, Pennsylvania 15213.
alloys. According to our best knowledge the electrical resistivity of chromium-germanium alloys has not been studied before.
-AL
CONSIDERATIONS
The chromium-germanium alloys, containing 0*3,, O-7,, l*Os, 1*4,, and 2.1, at. y0 germanium, were prepared by arc melting chromium and germanium in the same manner as was done with chromium and iron described elsewhere.@) The initial stock of chromium (Iochrome) was obtained from Chromalloy Corporation. The analysis of the impurities found in this material have been recorded previously. (5) Germanium (99*99+ per cent purity), added as a solute to chromium, was supplied by Eagle Picher Company. After the melting, the ingots were sealed into silica capsules filled with 150 Torr of argon at 298”K, homogenized at 1370°K for 120 hr, and then rapidly cooled by removing the capsules from the furnace. The samples for the electrical resistivity measurements were cut from the homogenized ingots using a wafering machine with a high speed carborundum disk. The size of the resistivity samples was about 0.3 cm x q-3 cm x 3 cm.
1459
1460
SIGURDS
ARAJS
and W. E. KATZENMEYER
The electrical resistivity of each sample was determined using the standard four-probe method. The potential leads were spot-welded copper wires of 0.0’2 cm dia. The electrical current leads were attached to the ends of the sample in a conventional manner by means of indium solder. This was possible because the sample ends, after the sample was cut, were covered with pure indium using an ultrasonic soldering technique. Four samples, connected in series, were mounted in a sample holder which was located in a cryostat capable of producing temperatures between 1.2 and 350“K, constant to +O*Ol”K, using a specially designed control system. ~3)The electrical measuring current, provided by 12 V storage batteries, was kept constant to 1 part in lo5 by means of a servosystem. It was measured with a Rubicon potentiometer (Model 2781) and a 0.01 P standard resistor. The voltages between the potential leads, which did not exceed 100 c;V, were measured with a Type 9174 four-figure potentiometer of Guildline Instruments, Ltd. The null detecting system consisted of a Type 5214/9460 photocell galvanometer amplifier together with a Type 9461A galvanometer (both units made by Guildlme Instruments) which allowed us to detect at least rf:0.01 pV. The voltages larger than 100 ~.LVwere determined with a Rubicon six-dial potentiometer (Model 2768) using a Rubicon photoelectric galvanometer (Model 3550) and a Leeds and Northrup d.c. microvolt amplifier (Model 9835B) as the null indicator. It was possible to switch from one potentiometric system to another at any time by means of Guildline Instruments’ selector switches (Type 914541) whose internal thermoelectric voltages, generated at the contacts, were less than 0.01 I_~V.Thermoelectric effects in the external sample circuit were eliminated by a Guildline reversing switch (Type 9600-L) immersed in mineral oil. The temperatures of the samples were measured with two different thermometers. Below 20°K calibrated germanium cryogenic sensors (Minneapolis-Honneywell Regulator Company, Model MHSP 2404, Series II), accurate to + O.l”K, were used. Above 20°K a platinum resistance thermometer (Engelhard Industries, Inc., Model 2070713A) previously checked against a Leeds and Northrup platinum resistance thermometer (calibrated by the National Bureau of Standards) was
used as the temperature indicator, being accurate within &-O*l”K. The absolute values of the electrical resistivity of different chromium-germanium samples are believed to be correct to f 2 per cent, this error resulting primarily from the uncertainties in the geometrical form factor. No corrections due to the thermal expansion were applied to the measured data of the electrical resistivity. Longitudinal electrical magnetoresistivity studies at 4.2°K were made on pure chromium and chromium-germanium alloys containing 0*3s, 0*7s, and l-4* at.% germanium using a compensated Westinghouse superconducting solenoid with the inside diameter of 2 in., outside dia. 6 in., and length 16 in. With this solenoid it was possible to obtain magnetic fields up to 60 kOe. Because of the 2 in. inside dia., four samples could be studied simultaneously. The solenoid current, provided by a Westinghouse power supply capable of controlling the electrical current to 1 part in 105, was determined by using a O$lOl P standard resistor in series with the solenoid. RESULTS AND bISCUSSION The electrical resistivity b(T)] of chromium and chromium-germanium alloys, containing 0*3,, O-7,, l-O,, l-4,, and 2.1, at.% germanium, as a function of absolute temperature (T) between 4 and 320°K is shown in Fig. 1. The curve for chromium is that already published before.‘5) All these curves were obtained with increasing temperatures starting at 4.2°K. From Fig. 1 it can be observed that the NCel temperature (TN) of chromium, appearing as a small minimum in the p(T) vs. T curve at 313”K, is markedly lowered by small additions of germanium. In fact, this rate of decrease is the most drastic one produced by any solute in chromium according to the presently available information. The role of small amounts of different solutes on TN of chromium is demonstrated in Fig. 2. The curve associated with manganese is due to BOOTH.(~)The other curves have been obtained from our electrical resistivity studies on different chromium alloys containing iron,(l) cobalt,(3) tantalum,(8) nickel,(8) and silicon.(g) From Fig. 2 one can notice some similarity between germanium and silicon with respect to their influence on TN of chromium, i.e. the initial decrease in TN is small at low solute
RESISTIVITY
STUDIES
OF
CHROMIUM
RICH
CHROMIUM-GERMANIUM
AI;LOYS
1461
FIG. 1. Electrical resistivity of chromium-germanium alloys between 4 and 320°K. 350
fdll/-+-
/--@
1
I
4*
300 L
C
250 -
To
s 200 -
68
#i +=
150 ~
si
loo
I
1
.
.
0
Z&E
COtKXNlW&
1.5
[at.%]
FIG.2. The variation of the Nkel temperature with solute concentration
of different binary chromium
concentration but then increases rapidly with higher solute percentages. It may be mentioned that ~e.anorn~y in the p(T) vs. T curve in chromium and chromium-O.3, at.% germanium alloy at T,is barely noticeable in the sample containing 007~ at.% germanium and is completely absent in the data for higher composition samples. The most spectacular feature in the curves of p(T) vs. T is the occurrence of a minimum at 10~ temperatures. Because of its smallness this
alloys.
minimum cannot be seen in the curves shown in Fig. 1, but it can be clearly observed in the enlarged plots presented in Fig. 3. This minimum, which does not occur in pure chromium, appears when germanium is added to chromium. The temperature at which the minimum occurs (Tmin), shown by arrows in Fig. 3, first increases with increasing germanium concentration, reach a maximum for about 1 *44 at.% germanium concentration, and then decreases. The exact value
1462
SIGURDS
to determine of TIllin is difficult electrical resistivity minima are, small. Usually the depth of the characterized by the quantity Ap p(Tmin) which, for example, for 0.3, ium sample is about 0.008 ps2 cm.
ARAJS
and
because the indeed, very minimum is = p(4*2”K)at.% germanEven for the
FIG. 3. Electrical resistivity of chromium alloys contain-. ing different amounts of germanium below 40°K.
chromium-germanium alloy containing l-4, at.% germanium, for which Tmin w 28”K, Ap = O@O ~0 cm, which is small in comparison with the maximum values of Ap observed for chromiumcobaW3) (Ap = 0.260 pa cm for 6.2 at.% cobalt content) and even chromium-nickel(*) (Ap = 0.070 @cm for 0.8 at.% nickel content) alloys. At first sight it appears that the origin of the minimum is of the KONDO type (lo), in spite of the fact that the variation of Tmin and Ap with germanium concentration is more complicated than predicted
w.
E.
KATZENMEYER
by the simple Kondo theory. This expectation is based on the observation that the minimum is clearly observable in chromium-cobalt alloys(s) for which the magnetic susceptibility data bySuzur&l) suggest the existence of localized magnetic moments due to cobalt atoms. In this system the quantities T,,, and Ap also do not behave exactly as expected from the Kondo model. However, since the original Kondo theory is based on quite a few idealizations, it should not be surprising that some disagreements may exist between the simple theory and observed localized moment bahaviour in an antiferromagnetic metal such as chromium. The occurrence of the resistivity minimum in thechromium-germanium alloys is a more startling effect than in the cobalt alloys because it is difficult to associate magnetic moments with germanium atoms. There is, however, another possible explanation for the occurrence of the minimum in these alloys at low temperatures. This explanation comes from the recent theoretical work by KIM who suggests that localized nonmagnetic states, associated with certain impurities in a pure metal, may cause a minimum in the p(T) vs. T curves. KIM believes that resistivity minima observed in titanium alloys containing for, example, 0.2 at.% iron or chromium’i3) are due to this cause. Magnetic susceptibility measurements on chrtimium-germanium alloys at low temperatures should be helpful for distinguishing between these two possible mechanisms. Such studies are being planned for the near future in this laboratory. Another feature of the electrical resistivity data, which appears to be interesting from the viewpoint of the minimum phenomenon, is the increase in the electrical resistivity of chromium due to different dissolved impurities in the chromium lattice. Up to this time we have observed the following facts. Elements such as iron, cobalt, and nickel, when added to chromium, produce resistivity increases of about 7.1, 8.5 and 16.0 pCJ cm/ at.% solute, respectively, at 4*2”K.(*) These elements are believed to exist as localized magnetic moments in the chromium matrix. The associated resistivity increases are considerably larger than the corresponding values found when, for example, vanadium or manganese is dissolved in chromium. These latter elements give only about 0.3 &I cm/ at.% solute resistivity increase at 4*2”K.(14) Furthermore, it has been established that neither
RJZSISTIVITY
STUDIES
OF CHROMIUM
RICH
IO
O-5
. f Go tO&TENTRATld~
20
z5
[ot.%f
1 4. Electrical resistivity of chromium-germanium alloys as a function of gctrmanium concentration at 4.2 and 300.O”K.
0
10
ALLOYS
1463
effects on the electrical resistivity in these two materials. That is, the data in Fig. 4 at 3OO.O”K represent the resistivity behavior of paramagnetic chro~~~e~~iurn alloys as a function of germanium-concentration. The fact that one can draw a straight line through these points demonstrates the alloys are homogeneous as was expected. The curve in Fig. 4, associated with 4*2”K, shows an anomaly at about 1 at.% germanium due to the inthtence of TN on the electrical resist&&y. However, one can clearly estimate from Fig. 4 that 1 at.% germanium at 4.2°K increases the electrical resistivity of chromium by about 16.7 &J cm. This value is quite close to that found when nickel is dissolved in chromium. It may be remarked that large increase in the electrical resistivity due to 1 at.% solute, capable of producing localized magnetic moments, has been predicted theoretically by WOLFF. Usually the alloys, which exhibit anomalies in the electrical resistivity at low temperatures, also
vanadium(l*) nor manganese”) is able to produce a minimum in the p(T) vs. T curves at low temperatures. Also, the magnetic susceptibility studiesP on c~o~~-rn~~~e alloys indicate
0
CHROMIUM-GERMANIUM
20
fit@]
40
50
60
H,
FIG. 5. Longitudinal electrical magnetoresistivity of some chromium-germanium alloys as a function of HE at 4*2”K.
that no localized moments exist on manganese atoms in chromium. The behavior of chromiumgermanium alloys, from the viewpoint of the resistivity increase due to 1 at.?; germanium at say, 4*2”K, is very similar to that of binary chromium alloys cont~~ng iron, cobalt, and nickel. Figure 4 shows the electrical resistivity of these alloys as a function of germanium concentration at 4.2 and 3OO*O”K.The points associated with pure chromium and 0.3, at.% germaniumchromium alloy at 3OO*O”Kwere determined from the ~(2’) vs. T plots (Fig. 1) by extrapolating the resistivity curves above TN to 3OO.O”K. This was done in order to eliminate the antiferromagnetic
show some anomalous behavior in magnetic fields.‘le’ Figure 5 presents the total change in the electrical resistivity of some chromiumgermanium alloys due to an applied longitudinal magnetic field, H,, at 4*2”K, defined by Ap s(4~2°K) = p(4*2”K, H,) -p(4*2”K, 0 Oe). The curves were obtained with increasing magnetic fields. The open and closed points, associated with the curve for pure chromium, represent two separate runs indicating good reproducibility of the magnetoresistivity data. From Fig. 5 one can observe that additions of Geoff to chromium cause a decrease in the quantity Ap ,(4*2”K). However, this quantity remains positive for all
1464
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ARAJS
and
alloys up to at least 1.4, at.% germanium level. The decrease in Ap,(4*2’K) with increasing germanium concentrations is similar to that observed in chromium-cobalt and chromiumnickel alloys for which the quantity Ap ,(4*2’K) eventually becomes slightly negative for larger solute contents. Such a behavior is quite distinct from that seen in chromium-manganese alloys(*) in which manganese is quite incapable of significantly lowering the value of Ap , (4*2”K) of pure chromium. These facts give an additional accent to the quite distinct behavior of germanium in solid solution with chromium. Acknowledgements-The authors are grateful to the following xknbers of this laboratory: G. R. DIJNMYRE, G. P. WRAY. and J. W. CONROY for their technical assistance wiih this -&e&p&on and R. M. FISHER for his critical review of this piper. Stimulating discussions with P. A. BECK of the University of Illinois are very much appreciated.
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2. ARAJSS. and D~NMYRE G. R., EIcctricaZ Magneto-
3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
15. 16.
resistivity of Chromium-Iron Alloys, to be published in J. appl. Phys. ARAJS S., DUNMYRE G. R. and DECHTER S. J., Phys. Rew. 154,448 (1967). AIWJS S. and DUNNIYRE G. R., J. appl. Phys. 38, 1157 (1967). ARAJS ,% and DUNMYRE G. R., J. appl. Phys. 36, 3555 (1965). COLVIN~. VI and bJS S., Phys. Rev. 133, A1076 (1964). BOOTH J. G., phys. status solidi, 7, K157 (1964). ARAJS S. and DIJNMYRE G. R., unpublished studies. ARAJS S. and KATZENMEYERW. E., unpublished studies. KONDO J., Prog. theor. Phys., Kyoto 32, 37 (1964). SUZUKI T:, J. phys. Sot. Japan 21,442 (1966). KIM D.-J.. Phvs. Rev. 146.455 (1966). CAPE J. A: anh IiAKE R. k., Phys. Rev. 139, 455 (1966). TREGO A. L., Antifewomagnetism in Dilute Chromium Alloys, Ph.D. Thesis, Iowa State University of Science and Technology (1965). (University Microfilms, Inc., Ann Arbor, Michigan). WOLFF P. A., Phys. Reu. 124, 1030 (1961). VW DEN BERG 6. J., Anomalies in Dilute Metallic Solutions of Transition Elements, Vol. 4. v. 194, in Progress Low Temperature Physics, e&ted by C. J. GORTER,North-Holland, Amsterdam(1964).
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