the impurity resistivity and resistivity minima in alcr and almn alloys

Solid StateCommunications, Vol. 13,pp. 1027—1030,1973. PergamonPress. Printedin GreatBritain

THE IMPURITY RESISTIVITY AND RESISTWITYMINIMA IN AICr ANDAIMn ALLOYS

E. Babic* and R. Krsnik

Institut zaFiziku Sveu~iIi~ta,Zagreb,Yugoslavia

and

C. Rizzuto

Istituto di ScienzeFisichee G.N.S.M.del C.N.R,1 Genova,Italy

(Received25 June1973 byL. Hedin)

The impurity resistivity of AICr between1 .5 and50°Kwas determinedwith a characteristictemperaturefor theT2 variationO~= 960 ±40°K.The behaviourof theresistivityminimumboth in AlCr and A1Mn alloyswith impurity concentrationprovidesevidencethat a T3 phononresistivityis foundalsoin aluminiumwith anomalousimpurity resistivity.

IN A PREVIOUScommunication1we havediscussed I 4~i 0

in somedetail the resultsof measurementson thetemperaturevariationof the impurity resistivity Pimpin A1Mn alloys: we also reportedsomequalitative 3.resultson theresistivity observedfor AICr alloys.The observationof the impurity resistivity variationin 30.000

AlCr is considerablymoredifficult than in AlMn be-causethesize of the effect is smaller,andthereforethe subtractionof the phononcontributionneedsto 29.980 •~ 3.6

be performedwith higheraccuracy,on theotherhandit is quite interestingto havesomemorereliabledataon this systemwhichis, at themoment,thedilutealloy with thehighestmeasuredcharacteristictem-perature(Or) for a quadratictemperaturedependence 2~00

due to LocalizedSpin fluctuations. 25.495 - 3.0

Wewishhere to reportbriefly on more accuratedeterminationsof the impurity resistivity obtainedinA1Cr andAIMn, sincereference1 waswritten,while— — 16~000-•~. 2~0we are performinga comprehensivesearchon the

16.4980 -

10.09901-_____________ I I I I20 40 T°K* Presentaddressdo G.N.S.M.del C.N.R.,Genova.

FIG. I. Total resistivity p, of four AICr alloysasa~ GruppoNazionaledi StrutturadellaMateria del function of Tbelow 70~K(concent~tionsin at.%

ConsiglioNazionaledelle Ricerche. written aboveeachcurve).

1027

1028 THE IMPUTITY RESISTIVITY IN A1Cr AND AlMn ALLOYS Vol. 13, No. 7

33.0C ~

32.96~ _____

0 1 2 3c(at%i

0 1000 2000 3000- - . -- - 2 0

FIG. 2. The impurity resistivity,PImp~of thesameAlCr alloys from Fig. I as a functionof T below60 K. (concen-tration in at.%).In the insertis showntheslopeof theresistivity at high temperature(dp/dT)273,n~cm/°Kfor thesealloys asa functionof the concentrationc (in at.%).

transportpropertiesof theAl — transition+ rare impurity resistivity is predominantat leastin the lowearthmetalsalloy system:thecompleteresultsof temperatureregion, and canthereforebe observedthis researchwill bereportedelsewhere. directly.

We referto referenceI for the generaldiscussionof thesealloy systemsand the theoreticalinterpre- We report,in fact, in Fig. 1 the dataasobtained,tationandproposedformulas.Our presentdataon beforesubstractingthe phononcontributionandweAICr shouldbe comparedalsowith thosepreviously observethat the impurity contributionovertakesatreportedin reference2 and 3. low temperaturesthephononcontributiongiving rise

to a minimum.At the lowest temperaturesthe be-Thesamplesmeasured,have,asin reference1, been haviour is clearly proportionalto T

2. If we subtractpreparedby rapid quenching4and measurementswere thephononcontributionup to 50°Kaswasdonemadewith the sametypeof apparatus.5Fourcon- in referenceI usingalso themorerecentdataofcentrationsof Cr, rangingbetween1.2 and3.6 at.% reference6 we obtainthevaluesreportedin Fig. 2.havebeenmeasured;they havebeendeterminedto here the quadratictemperaturedependences(straightwithin few percentaccuracyby microprobeanalysis. lines)are obtainedfrom the ‘rough’ data(beforeThe temperaturerangemeasuredis between1.5 and subtractingphonons)below6 ÷I 0°K.(Dependingon350°K,but thedatawe will considerin more detail theconcentration)andare found to fit thecorrectedherearethosebelow50 K. Also for thesealloys the valuesup to 50 K. Above50 K theuncertaintiesinconsiderationsof referenceI hold in that we have thephononcorrectionbecomebigger(aspointed inhere a higheraccuracythanin all previousmeasure- 1) and the scatterin thecorrectedvaluesdoesnotmentsbecausethe higherconcentrationattainable allow usto follow reliably the detailedbehaviourofwith our methodallows usto havealloyswherethe the resistivityat higher temperatures.

Vol. 13, No.7 THE IMPURITY RESISTIVITY IN A1Cr AND AIMn ALLOYS 1029

20 40 60 ___________________________________________I I

- 13.58

~l~Cr

- / ®~iMn

1.70 - 13.54 —60--

::..::5ii•~.~:~.. *

4.480 - .~0.56 P 9IQcm)

FIG. 4. Temperaturesof the resistivityminima ofAIMn andAlCr alloysasa functionof the residual0.193 1.4502 resistivityPo. (Pois proportionalto the concentration).

consideringwhethertheslopestakenat differentI I I 1.4498 temperatureintervalsand their concentrationde-

20 T°K 60 pendencevary with temperature:we find that there

FIG. 3. Total resistivity,p, of AIMu alloys asa function is a variationup to about250°Kabovewhich tern-ofT up to ~0K. peraturea constantvalueof dp/dTvsc equalto that

reportedaboveseemsto getestablished.From thesedatawe cantentativelyconcludethat above250°K

Thevaluesof 0~so obtained(0~ 970 ±50; the impurity resistivity varieslinearly [asin equation960 ±30; 960±20 and 890±60°Krespectivelyfor (2) of reference1] with a slope(1/c)dp/dT 3.01.2; 2; 3 and3.6at.% samples)give anaverageof 0~= n�lcm/at.%°Kcorrespondingto a = 3000±300°K,960±40°K.This valueis lower than thosequotedin ascomparedto(l/c)dp/dT~’5.5 ±Snllcm/at.%of(2 and 3) (1200±400 and 1370±50°Krespectively). AIMn.

Thedetailedbehaviourof the impurity resistivity In comparingour resultswith thoseof referenceat highertemperaturesis coveredby uncertaintiesin 3 we seethat our parametersdiffer from theirs: thethephononcontribution,it is howeverpossibleto get differencein 0~is probablydue to thefact that onlyanindicationat room temperature,wherethephonon temperaturesabove78°Kwere considered,andif weresistivity is nearlylinearanddeviationsfrom remindthat in generalthe T2 behaviouris well ob-Matthiessens’mie are,as far aswe know,constant servedbelow0.1 ~ this is obviouslythecauseforwith T. In the insetto Fig. 2 we havereportedthe anoverestimationof 0~(seee.g. reference8). be-slopeof the resistivity at room temperaturefor all causeof the vicinity of the transitional(linear) regionsamples,(dp/dT)

273togetherwith thatof pureAl, to a slower temperaturedependence.andwe find that,as it wasthecasefor AlMn, it de-creaseslinearly with concentration,the negative The differencefoundbetweenour valueof 02 andcontributionto theslope,due to the impurities, thatof reference3 is oppositeto that found for0~,beingof 3.0 ±0.3 n~cm/at.%°K. thismay,in turn,as also theyobserve,be dueto the

overestimateof theregion.wherethe linear T behaviourWe cannotdeducefrom this whetherthe behaviour is established(above450°K,while our dataindicate

of pimp(T) is linear,butwe cancheckfor this by this behaviourto be observedalreadyabove250°K).

1030 THE IMPURITY RESISTIVITY IN AICr ANDA1Mn ALLOYS Vol. 13, No. 7

In Fig. 3 we reportdataavailableon AIMn alloys, of theminimum for eachconcentrationof alloy: thiswhich includealso somepreviousmeasurementsfrom gives additionalevidencefor thetemperaturereference2 and our morerecentones,all thesesamples variationof thephononresistivity found in impurecoveringaboutone decadein concentrations, alloys,and moreover,it showsthat this type of

variationis the samebothwith normal impurities,asWe look now at thetemperaturevariationof the thoseexploredin references6 and9 and with im-

resistivityminima bothof AlCr andAlMn, which is puritieswith a temperaturevariationof Pimp’ Thisreportedin Fig. 4: it is interestingto note that the fact allows usto confirm thecorrectnessof thetemperatureof theminimum(Tmm)varieslinearly hypothesisusedto substractthephononpartbywith P0 in bothcases:if we now takeinto account usingthe resultsobtainedon nonanomalousalloys.the factthat Pimp varies as T2, at leastup to 80°K(in AlMn, and probablyto higherT in AICr), and Acknowledgements— We havehadusefuldiscussionsthat theminimum indicatesa balancebetweenphonon with Profs.G. Bobel and B. Leontid. The technicalandimpurity resistivity we find that thephonon help of Mr. G. Massariand the samplepreparationby

A. Hamzic andZ. Vucic are acknowledged.resistivitymust varyas T in thetemperaturerange

REFERENCES

I. BABI( E., FORDP.J.,RIZZUTO C. and SALAMONI E., SolidStateCommun.11, 519 (1972).

2. CAPLIN A.D. and RIZZUTO C.,Phys.Rev.Lett. 21, 746 (1968).

3. KEDVES F.J.,HORDOSM. andGERGELY L., SolidStateCommun.11, 1067 (1972).

4. BABIC F., GIRT E., KRSNIK R. and LEONTIC B., J.Phys.E 3, 1014 (1970).

5. RIZZUTO C.,SALAMONI E. andZANI P.E.,Cryogenics11,306(1971).

6. KRSNIK R.,BABIC E. andRIZZUTO C.,SolidStateCommun.12,891(1973).

7. RIZZUTO C., (Rev.paper)Rep.Frog. Phys., to bepublished.

8. PILOT A., VACCARONE R. and RIZZUTO C.,Phys.Lett. 40A, 405 (1972).

9. CAPLIN A.D. and RIZZUTO C.,Aust..1. Phys.24,309 (1971).

Iloxa3aHbI PC3YJ1bTBTbI Jl3MO~~HJ451ripi~~ecnoroconpoTnB.ieHMslA1CrB i4HT~~BBJ1CTOMFIB~~TY~b!OT 1,5 ~Ito50°K; COOTB~TCTB~IOIUBMxapaKTepHaiI ~eunepa~ypa cBu3aHa C 3aBI4CI4MOCTHO OT T2,01 = 960 ±40°K.

I13MeHOHMC KoHi~eiiTpaIjr1ei1 npuMeceti M~1HI1M~MBCOfl~OTHBJiOHWHB criiiauax A1Cr C ~Mn noKa3biBaeT, ‘-ITO 3aBL4cnMocTb OT T3I~iOHOHHOCOCOHPOTHBJ1OHHMHBXO~MTC~B a~1.1IoMBHMMTOX(~ B c~iy~aealloMa.m1-loro H~I4MBCHOFOCOiIpoTi4BJIeHI4~I.