Electrical resistivity of FeCr- and NiCr-based amorphous alloys

Materials Science and Engineering, 99 (1988) 207-210

207

Electrical Resistivity of Fe-Cr- and Ni-Cr-Based Amorphous Alloys* D. F. JONES, G. STROINK, Z. M. STADNIKt and R. A. DUNLAP

Department o[' Physics, Dalhousie Unit,ersiO', Hali[ax, Nova Scotia, B3H 3J5 (Canada)

Abstract

We have measured the resistivity of amorphous Fe8l, ~Cr~B~2Si8 and Niso xCr~Bi2Si8 as function of temperature in the temperature range of 4.2 to 300 K. Although the absolute change in the resistivity is small, adding chromium to the base alloys results in large changes in the temperature dependence of the resistivity in these alloys. This temperature dependence is markedly different for these two alloy systems, with the largest changes measured for the Ni C r - M (M--metalloid) glasses. The results are explained qualitatively using existing theoretical models.

Niso xCr:B:2Sis (x = 0, 2, 4, 7, 10, 12, 14) were prepared. This latter series of alloys may contain a few parts per million of iron. Sections of all ribbons were examined by X-ray diffraction using a Siemens scanning diffractometer with Cu K~ radiation and showed no detectable crystalline lines. The electrical resistivity of 8 to 14 cm long ribbons was measured quasi-continuously at slowly changing temperatures by means of a four-probe d.c. technique. Changes in resistance with temperature of about 1 part in 105 could be detected. 3. Results and discussion

I. Introduction Although the electrical resistivity of many metallic glasses has been measured as a function of temperature, the mechanism behind its behavior in the various temperature ranges is not well understood. Empirically the sign of the room temperature coefficient is well described by the Mooij correlation [ 1], whereas at very low temperatures the resistivity data of many systems can be described by a - T ~/2 dependence [2]. In between these regions a wide variety of curves, ascribed to several magnetic and/or structural scattering mechanisms [3], have been observed. To distinguish between the various theories put forward to explain at least some of the observed temperature dependences of the resistivity in amorphous alloys systematic studies are needed. We report here on the results of resistivity measurements of amorphous alloys Fe~o ~Cr~B:,Si~ and Niso ~Cr~Bj2Sis. 2. Experimental method Amorphous alloys were prepared by the meltspinning technique. The ribbons produced were approximately 1 mm wide and 0.03 mm thick. Ribbons of F%o ~Cr~Bj2Si8 ( x = 0 , 3.5, 6, 8, 18) and

*Paper presented at the Sixth International Conference on Rapidly Quenched Metals, Montreal, August 3 7, 1987. "tOn leave from the Institute of Physics, Jagiellonian University, 30-059 Cracow, Poland. 0025-5416/88/$3.50

Figure 1 shows the resistance ratio r, normalized to the room temperature resistance Ro, of the base alloys FesoB~2Si8 and NisoB~2Si8 as a function of temperature. For comparison we also show the measured normalized resistance ratio of F%oB2o. The temperature dependence of the resistivity of these base alloys is characteristic for a wide variety of glassy metallic alloys. It exhibits a Kondo-like minimum at low temperatures, varies as T 2 in the intermediate temperature region and exhibits a linear temperature dependence at high temperatures. The data can be well described by the relation

r ( T ) = a + b ln T + c T 2 + d T

(l)

A non-linear least-squares algorithm was used to fit the data to this expression, if we let the temperature parameters T1 and T2 (T~ < T2) separate the three regions given by (i) l n T at T~ 7"2. The results of this analysis are presented in Table 1. For ferromagnetic FesoB2o the coeffÉcients of the various temperature dependences, the temperature region in which they apply and the location of the temperature minimum ( 15 K) agree reasonably well with values published in the literature for this well-studied alloy (e.g. refs. 4 and 5). The temperature coefficient and location of the minima of the base alloys, ferromagnetic F%oB~2Si8 and paramagnetic NisoB~2Si8, are consistent with Values published for alloys of similar composition [6, 7]. % Elsevier Sequoia/Printed in The Netherlands

208

R

1"0001-

'

'

'

|

R°

o ¢e

Io oo

..... °..%0 a

0 °

b °o

I~ , . ~ " "

l` ~

o

~,......

°oX.8

1.004 R Ro

00 %;0%

I

"+

•

eo

o o

0-960F

o

°+*"*~*#°*"

I

L

l

o"**'-

'

Oo

x=6

eo

o

• •

o °

•

o

+

o

o o

oO°

Co***° I

• •

1.00(3 I

120

I

o •

*

*

-8' o

I

o+ .

240

T(K)

~%,

Fig. I. The temperature dependence of the normalized resistance for FesoBl2Si8(curve a), F%0B2o(curve b) and NiaoBi2Si8 (curve c).

° °0,**

x=3.5

%o

,

0o0 %%

, 00~

•

* o

,

o a o o

*

*

*

*

o

el

x=18

."

0.996

"*

coo

The temperature dependence of the resistivity in the intermediate and high temperature regions, that is above the minimum, are predicted by models that take into account the structural disorder of the alloys [8, 9]. No attempt was made to fit the data to a T 3/2 term expected from electron-magnon scattering in the ferromagnetic alloys [5, 9]. The logarithmic upturn of the resistivity at low temperatures is, at least in part, of magnetic origin [3, 5]. In Fig. 2 we show the results of the normalized resistance of the Fe-Cr-Si-B series and in Figs. 3 and 4 that of the Ni-Cr-Si-B series. All Fe-Cr-Si-B alloys studied here are ferromagnetic over the temperature range measured, with the exception of the sample with x = 18 which, based on magnetization measurements on similar systems [10], probably has a ferromagnetic to paramagnetic transition in the temperature range measured here. As can be seen in Fig. 2 the temperature dependence of the resistivity of the Fe-Cr-based alloys is strongly dependent on the chromium content. These alloys show a resistivity minimum at low temperatures and a second minimum at relatively high temperatures. The temperature at which this second minimum, Tmi,, occurs increases linearly with the concentration x of chromium atoms, peaks around x = 8 and then decreases for the alloy with the highest con-

TABLE

1

e•

+ +•

I

•

•

+ ,

I

+ + I

I

120

240

T(K)

Fig. 2. The temperature dependence of the normalized resistance of Fe8o ~,CrxBa2Sis. centration of chromium (x -- 18). A similar concentration dependence of Tmi. has also been observed in the Fe-Ni amorphous series [11]. The low temperature minimum at about 11 K is essentially independent of x. The temperature dependence observed here is practically the same as has been observed by Olivier e t al. [12] in Fe8o_ xCrxB2o, and by Gudmundsson e t al. [13] in (Fe] _xfrx)75P]6B6A13. Both these groups extended the resistivity measurements to the millikelvin range and concluded that the low temperature minimum finds its origin in the T ~/2 dependence observed in a wide variety of alloys. This behavior is generally believed to be due to electron-electron interactions in a disordered system [2, 12]. Our data differ somewhat from the very similar series F e - C r - B in that, for a similar concentration x, the second minimum is more pronounced and occurs at a substantially higher temperature. This sensitivity of the concentration dependence of Tmin on the metalloid (M) has been observed

Fitted values o f the p a r a m e t e r s

AIloy

a

b

c

d

(×10 4K-I)

(K)

(K)

FesoB2o FesoB]2Si8 NisoBi2Si8

0.962 0.967 0.955

-7.23 - 5.09 - 14.5

7.61 6. l I 14.6

1.58 1.39 1.74

18 20 20

I07 114 35

(×10 5)

( x l 0 7K 2)

Tl

T2

209 i

i

.oq,=~.~.. • . o o

°e °

o:~'. °°

•

° °,

i

1.000

•

o"O'o

• . •

•

o°°.°

OOo

°,

x=7

1.000

ii:o.o. ° °

°°•°°

×:10

o o•

°**~

.

•

. . . .

•

•

o,,g

8

o°°

o

o°

° . ~

o,

R

Ro

o°x:14

"x:4

"'. ........

o o*

0.990 g

I

I

I

120

0.99~

I

240 T(K)

Fig. 4. The temperature dependence of the normalized resistance of Nis0 ~CrxBi2Si 8.

,

x:2

099f

o o

0.994

o o o

oo

oo

240

120 T(K)

Fig. 3. The temperature dependence of the normalized resistance of Ni~0 ~Cr,B=2Si s.

in the various Fe-Ni series as well [l 1]. The appearance of two minima in the F e - C ~ M series is not unique to this system. A very similar temperature dependence of the resistivity has been observed in Feso _,Mo~B2o (x = 2, 4, 6) [14]. Using magnetoresistivity measurements on the F e - C r - B alloy series Olivier et al. [ 12] have identified the In T dependence which, together with the T 2 behavior at the higher temperatures, gives rise to the second minimum, as having a magnetic origin. Possible scattering mechanism is of the modified Kondo type [15], which is consistent with the results of M6ssbauer measurements that show a distribution of hyperfine magnetic fields in similar alloys that extend to zero field [16]. Scattering by spin fluctuations is probably more dominant in the alloy with the higher concentration of chromium (x = 18). Such a mechanism has also been proposed for the resistivity in Fe85 xCr, Bj5 for samples with a comparable, relatively large, concentration of chromium [ 16]. Adding chromium to the base alloy NisoB~zSi8 resuits in variations in the temperature dependence that are even more dramatic than those observed in

the F e - C r - M systems (Fig. 4). The minimum at low temperatures and a positive temperature coefficient at room temperature for relatively low concentrations of chromium (x = 2) changes respectively into a maximum at low temperatures and a negative temperature coefficient at room temperature for higher concentrations. Finally, for the largest concentrations of chromium measured (x = 12, 14), the resistivity shows a positive temperature coefficient at all temperatures. The magnetic phase diagram of this system is not well known. The appearance of a distinct maximum for 12 > x > 2 indicates that this system undergoes a paramagnetic to spin-glass transition at low temperatures. The dependence of Tmax on x with a power less than one, as predicted by theory, seems to confirm this. Resistivity measurements by Park and Sostarich [7] on very similar alloys with x < 11 show that the - I n T temperature dependence extends till well above room temperature and that these alloys show a Tmin at relatively high temperatures that is extremely sensitive to the concentration of chromium. High field magnetization measurements on Ni73CrsSiloB~ 2 [17] show the existence of magnetic clusters, some of which order below about 17 K. The maximum in the resistivity for this alloy near 17 K can then be explained as a freezing out of part of the free spins and the corresponding weakening of the Kondo-type scattering when the temperature is lowered through this ordering temperature. The change in the positive slope of the alloy with x = 12 and 14, similar to that observed in the Niso xFexM [18], suggests a magnetic phase transition in these alloys at T ~ 30 K. A further analysis of this alloy system must await systematic magnetization measurements to clarify its magnetic properties.

210

Acknowledgment T h i s w o r k was f u n d e d t h r o u g h the s u p p o r t o f the N a t u r a l Sciences a n d E n g i n e e r i n g C o u n c i l o f C a n a d a .

References 1 J. H. Mooij, Phys. Status Solidi A, 17(1973) 521. 2 R. W. Cochrane and J. O. Strom-Olsen, Phys. Rev. B, 29 (1984) 1088. 3 R. Harris and J. O. Strom-Olsen, in H. Beck and H.-J. Giintherodt (eds.), Glassy Metals II, Springer, Berlin, 1983, p. 325. 4 N. Banerjee, R. Roy, A. K. Majumdar and R. Hasegawa, Phys. Rev. B, 24(1981) 6801. 5 S. N. Kaul, W. Kettler and M. Rosenberg, Phys, Rev. B, 33 (1986) 4987. 6 T. K. Kim, C. O. Kim, Y. E. Ihm and B. W. Lau, J. Magn. Magn. Mater., 31-34 (1983) 1477. 7 T. S. Park and M. J. Sostarich, J. Appl. Phys., 53(1982) 8251.

8 R. Evans, D. A. Greenwood and P. Lloyd, Phys. Lett. A, 35 (1971) 57. 9 A. Mogro-Campero, J. L. Walter and T. E. Coan, Phys. Rev. B, 24(1981) 3579. I0 M. Olivier, J. O. Strom-Olsen, Z. Altounian and G. Williams, J. AppL Phys., 53 (1982) 7696. 11 K. V. Rao, T. Egami, H. Gudmundsson, H. U./~mstr6m, H. S. Chert and W. N~igele, J. Appl. Phys., 52(1981) 2187. 12 M. Olivier, J. O. Strom-Olsen and Z. Altounian, Phys. Rev. B, 35(1987) 333. 13 H. Gudmundsson, H. J. Hannesson and H. U./~mstr6m, J. Appl. Phys., 57 (1985) 3523. 14 D. F. Jones, M. Sc. Thesis, Dalhousie University, 1985. 15 G. S. Grest and S. R. Nagel, Phys. Rev. B, 19 (1979) 3571. 16 G. L. Whittle, A. M. Stewart, and A. B. Kaiser, Phys. Status Solidi A, 97(1986) 199. 17 H. Sadate-Akhavi, G. Hadjipanayis and D. J. Sellmyer, Phys. Rev. B, 24(1981) 5318. 18 Z. Marohni6 and E. Babi6, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, North-Holland, Amsterdam, 1985, p. 1063.