THE ELECTRICAL RESISTIVITY OF MOLTEN AND GLASSY Mg-Zn ALLOYS

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THE ELECTRICAL RESISTIVITY OF MOLTEN AND GLASSY Mg-Zn ALLOYS

J. Hafner, E. Gratz, H. Güntherodt

To cite this version:

J. Hafner, E. Gratz, H. Güntherodt. THE ELECTRICAL RESISTIVITY OF MOLTEN AND GLASSY Mg-Zn ALLOYS. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-512-C8-515.

�10.1051/jphyscol:19808129�. �jpa-00220226�

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JOURNAL DE PHYSIQUE CoZZoque C8, suppldment au n08, Tome 41, aou'k 1 9 8 0 , page C8-512

THE ELECTRICAL R E S I S T I V I T Y OF MOLTEN AND GLASSY Mg-Zn ALLOYS*

J . Hafner, E . ~ r a t z + and H . J . Giintherodt ++

I n s t i t u t fiir Theoretische Physik, Technische UniversiMt Wien, Austria.

+ ~ n s t i t u t fiir ExperimentaZphysik, Technische Universitift Wien, Austria.

++ I n s t i t u t fiir Physik, Uniuersitift Base 2, Suisse.

INTRODUCTION liquid Mg-Zn alloys.

~lthough there has recently been con-

siderable interest in the electronic trans- EXPERIMENT

port properties of glassy alloys, there is We measured the electrical resisti- still an open controversy as to their cor- vity of a melt-spun Mgo.7Zno.3 glass bet- rect theoretical description. One of the ween T=4.2 K and room temperature (results current approaches relies upon an extension for higher temperatures and for the liquid of the Faber-Ziman-Baym (FZB) liquid-metal phase have been reported by Oberle et al.) 8

the other one uses the coherent using a quasi-continous four-probe techni- potential approximation to sum all the w e . The reproducibility of the measure- multiple scattering contributions to the ment on one sample is better than 0.5%.

resistivity, but ignores the effect of to- The temperature was measured using an pological disorder 6

.

Scattering due to to- Au-Fe/Chromel thermocouple, the amorphous pological as well as to substitutional dis- character of the sample was checked before

order is taken into account in the FZB and after the experiment by X-ray diffrac- theory for alloys. However, a quantitative tion. The accuracy of the absolute value assessment of it's validity is hampered by Of the resistivity is restricted by the the fact that the theory is primarily devi- difficulty of measuring the cross-section

sed to the weak-scattering limit and that of the sample, an investigation of eight it's extensions to strong-scattering situ- different sample resulted in values of

atioqs necessitate a number of assumptions f (4.2~) varying between 55.5 and 61 .I ~ R c m . of doubtful validity7. Most glass-forming The temperature variation of the resisti- alloys contain strong scatterers, thus an vity is known to much better accuracy, the application of the extended FZB-theory to error bars in Figs.1 and 2 represent typi- simple-metal glasses seems to be of pri- cal mean square deviations. Up to about mary interest. JBckle and ~ r o b 6 s e ~ applied 80 K the resistivity is constant to within their calculations to Cu-Sn alloys, but 0.05p.km, for higher temperatures the tem- neglected the effect of substitutional dis- perature coefficient of the resistivity order. In this work we present new experi- (TCR) becomes increasingly negative. At

mental and theoretical results for the room temperature, we obtain

2;

^%=-3.^3x1

^{o - ~}

electrical resistivity of amorphous and ⁸ ^7'

3

K-',whereas Oberle et al. quote dT =

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808129

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-4. 7x1

o - ~

K-I

.

Electrical resistivities for structure factors. They are given by the amorphous Mg-Zn alloys prepared by getter- following integrals over the partial dyna- sputtering have been reported by Hauser and mica1 structure factors Sij(k,@)

00

~auc'. Their results are characterized by

S! .(k) =

- \

^kBTn(~3)s. .(k,d) d*

very high absolute values of the resistivi- ^{l J} ^{2 0}_-00 ¹^J

ty (about twice as large as in the present with the Bose-Einstein distribution func- experiment) and by a large scatter in sign tion n(3).

and magnitude of the TCR (from -3.4~10- 4

to +2.6x1

o - ~

K" )

,

thus establishing the LIQUID PHASE

importance of scattering by structural de- In the limit of high temperatures,

f ects. n(o).vl and the resistivity structure

factor is identical to the static struc-

THEORY ture factor. The structure and the thermo-

Within the framework of the FBZ-theo- dynamic properties (here we need specifi- cally the volume and the thermal expansion ry, the electrical resistivity of a binary

coefficient) may be successfully calculated alloy is given by

2 k ~ using the Gibbs-Bogoljubov variational

p

⁼^c

5

wi(k)w .(k)S! .(k)k dk 3

J 1 J technique based on the pseudopotential ap-

0 i,j=1,2

proach to the interatomic forces and on the Here wi (k) is the self -consistent pseudop0- Percus-Yevick description of haramsphere tential of the component i in the alloy ^'I⁰ mixtures1'. In this approach, the tempera- and *he

s;

j (k) are the partial ture dependence of the partial structure

1 iqu.

L L

Cr

^<A--⁹

---

20.

4-

,---'-

_cryst

Fig.1: Electrical resistivity of amorphous and liquid Mg-Zn alloys. Experiment: open circles present work, full dots Oberle et al. ( ~ g ~ ~ n ~ ) 8 and Roll and ~otz"(~ure liquid Mg and ~n). Theory: full lines liquid, resp. supercooled liquids in the GB-method, triangles and squares amorphous alloys in the Einstein- resp. plane- wave approximations.

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JOURNAL DE PHYSIQUE

factors comes from the temperature variation of the effective hard-sphere diame- ters

Ci= Gi(~),

which is calculated from a minimum principle for the Gibbs free enthalpyl

.

Both the absolute values of the resistivity and the TCR are calculated in very good agreement with experiment, for the pure liquid metals as well as for the liquid Mg7Zn3 alloy. Two things should be noted: (a) the calculated TCR depends very sensitively on thermal expansion effects, the volume variation of the pseudopotential cannot be ignored. (b) The resistivity minimum in liquid Zn is correctly re- produced (though at a somewhat higher temperature). The cross-over from negative to positive TCR1s depends on the difference between the peak positions Qij of the partial structure.factors and 2kF. If the value of the structure factor at 2kF is smaller than unity, S

. .

(2kF)

<

1, there is

1 J

a negative contribution to the TCR from k-Qij and a positive one from k=2kF, at higher temperatures the second effect do- minates. Since QNg-Mg<QZn-Zn, the TCR of Mg is already positive at the melting temperature.

cooled liquid state 14 ,

AMORPHOUS PHASE

Jzckle and Frob8se5 have shown that within the harmonic and the one-phonon approximations the dynamic structure factors may be formulated in terms of the static structure factors Sij(k), the Debye- Waller factors Wij(k,T) and of amplitude correlation functions ~:g(k,u)) as

the difficult problem being the calculation of the temperature dependent correlation functions ciJ(k,d). In the limit of

o(P

uncorrelated atomic vibrations(the Ein- stein model), the resulting resistivity structure factor is

The approach may be extended to the

-

⁰

supercooled liquid state, yielding a very E

&

^-1

realistic result for the temperature depen-

L Y -2,

dence of the amorphous alloy in the region

2

-&-3..

between the crystallization temperature Tc

I

se random packing and the structure factors

Fig.2 Temperature dependence of the elec- diverge at k=Qij, indicating a low-tempera- trical resistivity of amorphous

1

---2---_____ -4 k

QYh

-\, "a

'-\Oh

"Qkq.

- ax-\\

kt,

and room temperature. Near T=260 K, the

2

-4..

L

*

packing

fraction^(^)

of the supercooled -5

ture limit to the existence of a super- Mg7Zn3. Symbols see Fig.1.

0 100 m 300

liquid reaches the limiting value for den- T f K )

p h

\ , .

..

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for high T,

in the high temperature limit this is the simple form of the Einstein-model of Na- gel 4

.

In the limit of plane-wave phonons and omitting the Brillouin-scattering contributions to Sij(k,d), one obtains the model resistivity structure factor of Meisel and Cote 3

This is corroborated by the different resistivities observed in liquid-quenched and vapour-quenched samples. (b) The observed TCR is better described by the-plane wave model (Fig.2). This is in agreement with the results of Meisel and Cote, but in contrast to the conclusions of Jgckle and Frobase. However, both the Einstein- and the plane wave models are certainly oversimplifications and should be replaced by a realistic calculation of the amplitude correlation function. We are presently doing such a calculation.

References

(1 ) T.E.Faber and J.M.Ziman, Phil.Mag.

where Debye dispersion relationsW=cq have

-

11,153(1965)

been assumed. In our calculations we used ( 2 ) G.Baym, Phys.Rev. =,I691 (1964) (3) P.J.Cote and L.V.Meise1, Phys.Rev.Lett.

the partial static structure factors Sij

-

39,1.02(1977) ; ~,v.Meisel and P. J.Cote, calculated by von ~eimendahl' using a Phys.Rev. =,4652(1978).

(4) S.R.Nage1, Phys.Rev. =,1694(1978) ; cluster-relaxation method and two diffe-

S.R.Nage1, J.Vassiliou, P.M.Horn and rent models for the phonon spectrwn N [ r ~ ) : B.C .Giessen, Phys.Rev. =,462(1978).

(a) a Debye model with 8=297 K derived (5) K.Frob6se and J.J&ckle, J.Phys. F7, from the elastic part of von Heimendahls 2331(1977); J.Jackle and K.Frobijse,

J.Phys. 2,967(1979).

dispersionrelati~n~ and (b) vonHeimen- (6) R.Harris, M.Shalmon, andM.Zuckeman, dahls Einstein spectrum N(t3). We find that Phys.Rev. =,5906(1978).

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E.Esposito, H.Ehrenreich, and C.D.Ge- the shape of the phonon spectrum has little

latt, Phys.Rev. B s , 391 3(1978).

influence on the results. The effect of (8) ~.oberle, ~ . ~ . ~ i i ~ ~ i , ~ . ~ , ~ m t h ~ ~ ~ d t thermal expansion upon the TCR has been in- and B.C.Giessen, preprint.

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hauser user

and J,Tauc, Phys.Rev. ,J'B vestigated using ~iinzi s1 experimental

3371 (I 978).

value of the thermal expansion coefficient (70) J.Hafner, j.phys

.g,

12~+3(1976).

and was found to be much smaller than in (11 ) J.Hafner, Phys.Rev. u,351(1977).

(12) A.Roll and H.Motz, Z.Metallkunde the liquid phase. The results may be sum-

48,272(1956).

marized as follows: (a) The calculated re- (13) J.Hafner and L.von Heimendahl, Phys.

-

sidual resitivity is smaller than the ex- Rev.Lett. 42,386(1979); J.Hafner, perimental one by a factor of 1.5. Since Phys.Rev. B20,406(1980).

(14) J.M.Gordon, Phys.Rev.

E,

1272(1978);

the calculated resistivity for 'the liquid J.Hafner, unpublished.

phase is very accurate, we believe that (I 5) L.von Heimendahl, J.Phys.~,161(1979).

the difference is due $0 structural defect (16) H.U.Kiinzi, private communication.

scattering.