RESISTIVITY OF AMORPHOUS METALLIC ALLOYS

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RESISTIVITY OF AMORPHOUS METALLIC ALLOYS

R. Cochrane

To cite this version:

R. Cochrane. RESISTIVITY OF AMORPHOUS METALLIC ALLOYS. Journal de Physique Collo-

ques, 1978, 39 (C6), pp.C6-1540-C6-1544. �10.1051/jphyscol:19786597�. �jpa-00218090�

JOURNAL DE PHYSlQUE

Collogue C6, supplhmenr au no 8, Tome 39, aoit 1978, page

R E S I S T I V I T Y OF AMORPHOUS METALLIC ALLOYS

R.W. Cochrane

Rutherford Physics B u i l d i n g , McCilZ U n i v e r s i t y , 3600 U n i v e r s i t y St., Montreal H3A 2T8, Canada

Rdsum6.- Nous Etudions les aspects les plus importants de la rEsistivit6 de divers alliages de mE- t a w amorphes. En g6nbral la r6sistivit6 est grande, se situant entre 100 et 300 uR-cm, avec des va- riations d'au plus 10 % pour des tempEratures allant de moins de 0.05 K jusqu'au point de cristal- lisation. La magn6torbsistivit6 dans la plupart des alliages est trSs petite et ne dEpend que fai- blement de la tempdrature, mGme 1 des temperatures trPs basses. Le comportement de la resistivit6 B des rdgimes differents de temperature suggPre l'existence de trois importants processus de diffusion.

Une brPve description de ces trois processus est presentEe

B

la fin de l'article.

Abstract.- The main features of the resistivity of amorphous metallic alloys are reviewed. In gene- ral the resistivity is large, typically 100-300 uR-cm, with a temperature variation from below 0.05 K to the crystallization point being no more than 10 percent of the total. The magneto-resis- tivity in most alloys is very small and only weakly temperature dependent even at low temperatures.

The resistivity behaviour in different temperature regimes suggest at least three distinct scatte- ring processes areimportant.The paper concludes with a brief description of these processes.

I. GENERAL CHARACTERISTICS.- Amorphous materials are characterized by the lack of long range crystal- line order although the degree of short range order may be very high as in the case for covalently bon- ded semiconductors and insulators. For metallic al- loys the requirement of high density to achieve me- tallic binding necessitates very close packing com- parable to that of crystalline metals. As a result there is a great structural similarity among the various amorphous metals which has been modeled af-

ter the dense random packing of hard spheres /1,2/

or variants which might include chemical constraints or structural relaxations.

The most common amorphous alloys can be di- vided into two classes / 3 / . The first comprises tho- se syscems which combine a transition or noble me- tal with a metalloid element of group IV or V. Most of these alloys have been rapidly quenched from

the melt or deposited from a liquid solution. In addition the concentration usually lies in a narrow range around the eutectic point in the correspon- ding equilibrium phase diagram. The second class contains no metalloid components and are formedfrom an early transition metal with a 'less than half fil- led d-shell (Ti, Zr, Nb, Y ...) and a late transi- tion or. noble metal with filled or a nearly full d shell (Cu, Ni,

...).

Such materials have been pro- duced over wide composition ranges by vapour depo- sition (sputtering, evaporation) onto suitably coo-

led substances.

With the strong emphasis on transition metal

components it is not surprising that these alloys have attracted strong interest for their magnetic properties / 2 , 4 / . Certainly structural and magnetic studies are the most extensive. At the same timethe electrical properties of these alloys have also been thoroughly examined, partly because of the ex- perimental simplicity, partly because the general characteristics of the resistivity give a clear in- dication of the onset of crystallization and partly in the hope of determining the underlying scattering processes in these higly disordered systems. Theaim of this brief review is to summarize the main fea- tures of the resistivity in an attempt to shed some light on this last point.

The most obvious resistivity characteristics are the hlgh values, typically 100-300 pa-an and small temperature dependence. Indeed the high resis- tivity values for alloys such as Nip /5/ are consis- tent with scattering by transition metal elements in a very disordered structure. The weak temperatu- re dependence applies to many magnetic, as well as non-magnetic materials even in the vicinity of well defined magnetic transitions or in the presence of strong magnetic fields

1 6 1 .

Given the high resisti- vity values corresponding to mean free paths of the order of one or two atomic spacings, it is only a rearrangement of the short range order, i.e. crys- tallization, which causes a significant change ig the resistivity. In this sense the electrical con- ductivity is an excellent indicator of crystalliza- tion and is the simplesttechnique for detecting its

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786597

o n s e t . F i n a l l y , i t s h o u l d b e n o t e d t h a t i n many ca- s e s t h e r e s i s t i v i t y o f amorphous a l l o y s e x t r a p o l a t e s v e r y c l o s e t o t h a t of t h e l i q u i d a l l o y / 7 / , l e n d i n g s u p p o r t t o t h e i d e a of t h e amorphous m a t e r i a l a s a f r o z e n l i q u i d .

2 . TEMPERATURE DEPENDENCE.- The d e t a i l s o f t h e con- d u c t i o n p r o c e s s e s have b e e n sought b o t h experimen- t a l l y and t h e o r e t i c a l l y i n s t u d i e s o f t h e temperatu- r e d e p e n d e n t p a r t o f t h e r e s i s t i v i t y / 3 , 5 - 1 3 / . These measurements s p a n f o u r o r d e r s o f magnitude on t h e

t e m p e r a t u r e s c a l e from t h e d i l u t i o n r e f r i g e r a t o r r a n g e below 5 0 mK t o c r y s t a l l i z a t i o n s e v e r a l hundred d e g r e e s above room t e m p e r a t u r e . F o r most s a n p l e s t h e t o t a l change i n r e s i s t i v i t y r a r e l y e x c e e d s 10 p e r c e n t o f t h e t o t a l and i n many c a s e s may b e c o n s i - d e r a b l y l e s s . Assuming i s o t r o p i c t h e r m a l e x p a n s i o n c o e f f i c i e n t s s i m i l a r t o c r y s t a l l i n e a l l o y s t h e mea- s u r e d t e m p e r a t u r e c o e f f i c i e n t s o f r e s i s t a n c e (TCR) have a n e g a t i v e c o n t r i b u t i o n from t h e volume expan- s i o n of t h e m a t r i x . U s u a l l y t h i s i s a s m a l l c o r r e c - t i o n e x c e p t when t h e i n t r i n s i c t e m p e r a t u r e v a r i a t i o n o f t h e r e s i s t i v i t y i s i t s e l f much s m a l l e r t h a n nor- mal.

S e v e r a l common f e a t u r e s of t h e t e m p e r a t u r e dependence of t h e r e s i s t i v i t y h a v e emerged and a r e suuunarized i n t h e d a t a of f i g u r e 1 and 2. S t a r t i n g f r o m t h e l o w e s t t e m p e r a t u r e t h e r e i s a v e r y g r a d u a l d e c r e a s e up t o 1 K f o l l o w e d by a more r a p i d f a l l t h r o u g h t h e l i q u i d h e l i u m regime p r o p o r t i o n a l t o l n T . Above 10 K where normal phonon p r o c e s s e s become i m - p o r t a n t t h e d a t a d i v i d e i n t o two broad c a t e g o r i e s . F o r t h e m a j o r i t y t h e r e s i s t i v i t y p a s s e s t h r o u g h a minimum n e a r 20 K and t h e n i n c r e a s e s f i r s t a s T~

/8.11/ f o l l o w e d by a l i n e a r t e m p e r a t u r e dependence up t o t h e c r y s t a l l i z a t i o n t e m p e r a t u r e . Most o f t h e t r a n s i t i o n m e t a l - m e t a l l o i d a l l o y s of t h e f i r s t c l a s s f a l l i n t o t h i s c a t e g o r y a s i l l u s t r a t e d i n f i g u r e 2 f o r t h e N i r i c h a l l o y s . At t h e same t i m e t h e r e i s a c o n s i d e r a b l e number o f a l l o y s o f t e n from t h e second c l a s s o f e a r l y - l a t e t r a n s i t i o n m e t a l m i x t u r e s f o r which t h e TCR i s n e g a t i v e a t a l l t e m p e r a t u r e s . Ge- n e r a l l y t h e a l l o y s i n t h i s c a t e g o r y e x h i b i t v e r y h i g h r e s i s t i v i t i e s , p > 200 pn-un, a s p o i n t e d o u t o r i g i n a l l y by Mooij / 1 4 / . As i s e v i d e n t from f i g u r e 2 , s e v e r a l of t h e m e t a l - m e t a l l o i d s y s t e m s s u c h a s Nip / 5 / and NiPdP 1 9 1 c r o s s o v e r from t h e f i r s t t o t h e second c a t e g o r y w i t h i n c r e a s i n g m e t a l l o i d con- t e n t . Such a c o n c e n t r a t i o n dependence i s o b s e r v e d i n t h e r e s i s t i v i t i e s of t h e l i q u i d a l l o y s of t h i s t y p e .

-

I I I I I I

0.03 0.1 0.3 1 3 10 30 TEMPERATURE ( K )

F i g . I : Normalized r e s i s t i v i t y a s a f u n c t i o n of log T . The lower t h r e e c u r v e s have been z e r o s h i f t e d a s i n d i c a t e d by t h e h o r i z o n t a l a r r o w s . The f u l l c u r v e i s a . f i t t o l o g ( T ~ + h 2 ) w i t h A = 0.45 K 1131.

Two e x p e r i m e n t a l o b s e r v a t i o n s s h o u l d b e ad- ded t o t h i s g e n e r a l o u t l i n e . The f i r s t c o n c e r n s d a t a on a few a l l o y s , n o t a b l y s p l a t c o o l e d P d S i 1151 and s e v e r a l quench condensed ( F e , Co, Ni) / I 6 1 samples whose low t e m p e r a t u r e r e s i s t i v i t y shows o n l y p o s i t i - v e t e m p e r a t u r e s l o p e s even a t 1 K. T h i s i s t o b e c o n - t r a s t e d w i t h t h e l a r g e number of a l l o y s c o n t a i n i n g t r a n s i t i o n and r a r e e a r t h e l e m e n t s w i t h n e g a t i v e t e m p e r a t u r e c o e f f i c i e n t s i n t h e l i q u i d h e l i u m r a n g e , i n c l u d i n g t h e o r i g i n a l PdSi samples. The u b i q u i t y o f t h e -1nT v a r i a t i o n o v e r many samples p r e p a r e d i n many d i f f e r e n t e n v i r o n m e n t s would seem t o r u l e o u t a p a r t i c u l a r i m p u r i t y . The g r e a t s i m i l a r i t y i n t h e m a g n i t u d e o f t h i s t e r m a s shown i n f i g u r e 1 would a l s o r u l e o u t a n i m p u r i t y e f f e c t and p o i n t t o t h e common f e a t u r e s o f a d i s o r d e r e d s t r u c t u r e and s t r o n - g l y s c a t t e r e d e l e c t r o n i c s t a t e s a s t h e most l i k e l y

C6-

1542 JOURNAL DE PHYSIQUE

of this effect. Indeed this implies that the low

-

_Y

temperature anomaly is an intrinsic property and the absence of this behaviour indicates a structural or electronic change as yet undefined.

TEMPERATURE ( K )

Fig. 2 : Resistivity versus temperature for amor- phous (Pd50-Ni50)100tx Px alloys normalized to the room temperature reslstrvity 191.

The second comment relates to the negative temperature coefficients which persist above 20 K.

For many of these alloys, particularly those without metalloid components such as YFe /17/ ZrCu 1181 and TiZrBe 16,191, there is never an extended range li- near in temperature but a decreasingly negative TCR with increasing temperature. The intermediate cases

such as FeNiCrPB (Allied Chemical metglas 2826A) 16,191 exhibit very high temperature minima. One coumon feature here is the presence of atoms with less than half filled d shells. Even in alloys with metalloid components the substitution of small amounts of elements such as Cr or Mo alters the TCR far more than comparable amounts,of Fe or Ni. The study of transition metals in PdSi/20/ or NiPdB 1211 is an excellent example : the addition of several percent of Cr leads to crossover from positive to negative TCRs at room temperature without altering the total resistivity any more than similar amounts of Fe or Co which have v'irtually no effect on the TCR. In a similar vein the addition of only 2 per- cent Mo to FegOBZO drastically alters the TCR without

rig. 3 : Concentration dependence of the resistivity minimum temperature for amorphous PdSi alloys con-

taining Cr, Mn. Fe or Co. 1201.

changing the overall resistivity. Figure

4

plots the relative resistivity change as measured by us 1221 and by Levy and Rayne 1191 on samples from different batches. Both sets of data show two different nega- tive and two positive regions of TCR ; the differen- ce between the two curves would appear to underscore the sensitivity of the resistivity to small changes in Mo concentration. Reference to figure 1 on the other hand shows that the behaviour in the liquid helium range and below is completely independent of the Mo. The elements Cr and Mo make a resonant like contribution to the high temperature resistivity without affecting the low temperature variation.

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TEMPERATURE ( K )

Fig. 4 : Normalized resistivity of Fe Mo B as a function of temperature. Ref. 1191, re?.

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3. MAGNETORESISTIV1TY.- In view of the wide variety of magnetic behaviour reported for the amorphous alloys 121 it is perhaps surprising that the magne- to-resistivity is always small ; the disorder scat- tering is a much larger effect in every case. Even among ferromagnetic alloys there is at most a small change in the TCR at Tc /6,17,19/. The only consis- tent feature in the magnetoresistivity occurs at low fields in soft ferromagnets and correlates directly with the approach to saturation of the magnetization 1171. This effect is observed in crystalline alloys as well as the amorphous ones and would appear to be a classical interaction of the electric field with the orientation of the magnetic moments of the material.

At low temperatures most alloys including many strongly magnetic ones show a positive magne-

toresistivity at high fields 161. Moreover, this contribution is usually only weakly temperature de- pendent as in the ferromagnetic COP alloy shown in figure 5 ; fields a's high as 50 kOe do not change the temperature dependence below 10 K. This proper- ty implies that the resistivity variation is non magnetic in origin and has led to the suggestion of

structural tunnelling states as a possible mechanism for this temperature dependence 1131.

Fig.

10 K

-

^fi

5 : Normalized resistivity change of COP below as a function of log T. 0 H = 0 , @ H = 45 KOe, .t to log ( T ~ + A ~ ) with A = 0 . 8 K 161.

Fina1,ly there are several examples of signi- ficant magnetic field effects on the resistivity minimum in a number of rare earth alloys 123,241.

DyNi3 data of Asomoza et al. 1231 are presented in figure 6. In this case the resistivity minimum is

an order of magnitude deeper than the usual effect (Cf. scale in figure 5 ) and occurs in the vicinity of the ferromagnetic Curie temperature. The authors consequently relate the minimum'in their alloys to the s-f scattering during the onset of magnetic or- der. In fact they point out that YNi3 shows a resis- tivity minimum of the usual size which is unaffected by an applied magnetic field. The LaCdAu alloys 1241 exhibit a resistivity minimum at a temperature, Tm, which increases with the mictomagnetic or spin glass

ordering temperature in the ragne 15 - 50 K . Outside of this range the resistivity appears to be unaffec- ted by the magnetic order although the significance of this particular temperature range is unknown.

Fig. 6 : Resistivity of DyNi3 as a function of tem- perature. H = 0 , A H = 8 kOe, X H = 20 kOe,

H = 30 kOe /23/.

4. CONCLUSION.- The data presented in the previous sections suggest at least three scattering mecha- nisms in addition to the purely magnetic s-f term observed in the rare earth alloys. There is a very low temperature regime characterized by a slow fall from saturation followed by a -1nT variation through the liquid helium range. This behaviour is indepen- dent of the magnetic order and even composition to a certain extent leading to speculation that it is related to the highly disordered structure common

C6- 1 544 JOURNAL DE PHYSIQUE

t o a l l t h e a l l o y s . I n t h e r e g i o n a b o v e h e l i u m tempe- r a t u r e s t h e s i m i l a r i t y between t r a n s i t i o n metal-me- t a l l o i d a l l o y s and many l i q u i d m e t a l s l e n d s s u p p o r t t o t h e Ziman o r d i f f r a c t i o n t h e o r y / 8 / a s a r e a l i s - t i c d e s c r i p t i o n of t h e r e s i s t i v i t y , b o t h t h e tempe- r a t u r e d e p e n d e n c e and t h e s i g n of t h e TCR. The em- p h a s i s i s o n t h e s t r u c t u r e f a c t o r and i t s v a r i a t i o n a t w a v e v e c t o r s n e a r 2kF. I n t h i s a p p r o a c h t h e e l e c - t r o n i c d e t a i l s c o n t r i b u t e t o t h e o v e r a l l s c a l e o f t h e r e s i s t i v i t y b u t t o d o n o t c o n t r o l t h e TCR d i r e c - t l y . O t h e r t h e o r i e s s u c h a s t h e m u l t i p l e s c a t t e r i n g model o f H a r r i s e t a l . 1 2 5 1 p l a c e more e m p h a s i s on t h e e l e c t r o n i c s c a t t e r i n g . I n d e e d , t h e s t r o n g depen- d e n c e o f t h e TCR on a d d i t i o n o f C r and Mo l e a d t o t h e c o n c l u s i o n t h a t t h e s p e c i f i c e l e c t r o n i c s c a t t e - r i n g a t t h e s e p a r t i c u l a r s i t e s m u s t b e d e a l t w i t h s e p a r a t e l y . T r y i n g t o f o r c e s u c h a l l o y s i n t o t h e s a - me scheme a s Nip i s n o t c o n s i s t e n t w i t h t h e l a r g e c h a n g e s o b s e r v e d f o r q u i t e s m a l l C r o r Mo c o n c e n t r a - t i o n s .

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