ELECTRICAL RESISTIVITY AND THERMOELECTRIC POWER OF LIQUID Ge-Sb AND Pb-Sb ALLOYS

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ELECTRICAL RESISTIVITY AND

THERMOELECTRIC POWER OF LIQUID Ge-Sb AND Pb-Sb ALLOYS

A. Bath, J. Gasser, J. Bretonnet, R. Bianchin, R. Kleim

To cite this version:

A. Bath, J. Gasser, J. Bretonnet, R. Bianchin, R. Kleim. ELECTRICAL RESISTIVITY AND THER-

MOELECTRIC POWER OF LIQUID Ge-Sb AND Pb-Sb ALLOYS. Journal de Physique Colloques,

1980, 41 (C8), pp.C8-519-C8-523. �10.1051/jphyscol:19808131�. �jpa-00220229�

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ELECTRICAL RESISTIVITY

AND

THERMOELECTRIC POWER O F LIQUID Ge-Sb

AND

Pb-Sb ALLOYS

A.

Bath, J.G. Gasser, J.L. Bretonnet, R. ~ianchin and R. Kleim

Laboratoire de Physique des Milieux Condens&s, FacuZtQ des Sciences, IZe du SauZcy, 57000 Metz, France.

Abstract.- The resistivity p and the thermoelectric power S have been measured for the system Pb-Sb from the liquidus to 800°c, and S for the system Ge-Sb up to 950°c. The whole phase diagram has been explored. For the two systems P is a smooth function of concentration and the overall behaviour of S is the same, with very small values for Ge-Sb. The dp/dT is always positive for Pb-Sb, and no anomalous behaviour is observed near the eutectic composition as for Ge-Sb. The results are inter-

preted in terms of the empty core model potential and hard-sphere interference functions, with different dielectric screening functions.

1. Introduction

-

Althoug the electronic transport

properties of liquid polyvalent metals and their al-- 125 loys have received considerable attention, there

h?ve been only few studiec on systems containing antimony like Ge-Sb and Pb-Sb. The aim of this work is to give complete experimental data on resistivity and thermoelectric power (T.E.P.) for these two systems, and to discuss them within the N.F.E.

approximation.

2. Experimental results Resistivity measurements on the Pb-Sb system were performed by the four:

point probe method using a quartz cell fitted with tungsten electrodes as described in ref.

[I] ,

^where

the corresponding resistivity results for Ge&b have been reported. The accuracy of the d.c, resistivity measurements is estimated to be 0.2 %. We must also take into account the effect of the uncer-

tainty in composition which does not exceed 0.5 at. %.

The thermoelectric power of the two binary alloys has been measured by using the small AT-method.

The experimental procedures are essentially those used previously by BATH and KLEIM [ 2 ] with some improvements : i) the electrical contact between

Fig. 1. v Electrical resistivity of liquid Pbl-x~bx alloys as a function of temperature.

the liquid sample and the thermocouples are secured by a tungsten wire sealed to quartz, ii) the small voltages are measured by Keithley model 180 voltme- ters and a X-Y recorder. The T.E.P. of the liquid alloys were measured against copper [3]. The absolute uncertainty is estimated to be of the order of

1

0.4pv.~- in the high temperature range (lOOOOc)

.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808131

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C8-520 ^JOURNAL^DE^PHYSIQUE

I I copper. Antimony, germanium and lead were quoted as

d t % S b

Fig. 2.

-

Electrical resistivity of liquid Pb-Sb alloys at 660°C and Ge-Sb alloys at 950°C.

.-=-.

experimental results.

---

theoretical results calculated using hard- sphere interference functions and empty core model potentials.

at%sb

Fig. 3. - Resistivity isotherms for liquid Pb-Sb alloys

X results of MATUYAMA (1927) at 660°C.

-..-..-a

....-. ....

results of ROLL and BISWAS (1964) at 660°C.

We did not extrapolate from [4] a possible small correction of the values of the absolute T.E.P. of

99.999 % pure.

The resistivity of some Pb-Sb alloys are plotted against temperature in figure 1. Figure 2 shows the concentration dependence of the resistivity of the two liquid alloys. The values of the system Ge-Sb are taken from GASSER and MULLER [ I ] . These authors found positive temperature coefficients over the whole phase diagram, but noticed the existence of small negative values around the eutectic composition (83 at% of antimony) just above the liquidus temperature. For Pb-Sb the temperature coefficient remains everywhere positive. The eutectic (17.5 at%

of antimony) region was investigated with special care but no perceptible irregularity was detected

(Fig. 3).

For comparison, we have also reported in figure 3 the values obtained by MATUYAMA

[s]

and ROLL and BISWAS [6]. At 660aC the differences do not exceed 3 %, and are slightly smaller at higher temperature.

Within the limit of accuracy we did not observe the maxima occuring in the work of ROLL and BISWAS [ 6 ] who used an electrodeless method.

ZOO

300

400

UW) 600 700 boo T (OC)

Fig. 4.

-

Thermoelectric power of liquid Pbl-xSbx alloys as a function of temperature.

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are plotted against temperature in figure 4. The values for the Ge-Sb system, nearly temperature in-

1

dependent, lie between -0.5 and

+

O.~UV.K- (Fig. 5).

The temperature dependence is linear for the two systems. The concentration dependences of the T.E.P. are reported in figure 6 at different tem- peratures. For the pure metals good accordance is achieved with former results [2] [7] [8]

,

for the alloys there exists no previous work at our know- ledge.

Fig. 5.

-

Thermoelectric power of liquid Gel-xSbx alloys as a function of temperature.

3. Discussion

-

Our results are consistent with the general discussion given in FABER'S book [9]. FABER introduced a mean interference function which is reasonably close to unity for our.systems, giving then a more or less linear dependence, versus concentration, for the resistivity p as well as for the term (3-C)p, where

5

is the usual thermoelectric parameter. These trends are particulary well observed for the Ge-Sb system.

everth he less

the small negative temperature coefficients for the

the FABER-ZIMAN theory [lo], because the mean valen- ce is well greater than 2. A plausible interpreta- tion may be based on a structural rearrangement as suggested by DUTCHAK et al.

[I

11 on the ground of their X-ray investigations.

We have calculated p and S, using the FABER- ZIMAN formalism, with the following assumptions :

i) the structure of the alloys is approximated by the hard-sphere solution of the Percus-Yevick equa- tion [12] ; ii) the electron-ion interaction is described by the volume dependent model potential of ASHCROFT and LANGRETH [13]

,

The resistivity of a binary alloy is given by the formula

with R being the mean atomic volume, Vf the Fermi velocity and x stands for q/2kf where q is the scattering vector. The a.

.

(i, j = 1 or 2) are the

1 I

set of hard-sphere partial interference functions and the model potential is given by

2Ef

X~

cos S.x Zi ui(x) =

-

^-'³ _x2

E (XI I - Z (i = 1 or 2) (2)

1

where Si = 2kfRi, = (va,kf)- a, being the Bohr radius, Ei is the Fermi energy,Z is the mean valen- ce and E ( x l is the dielectric screening function.

The T.E.P. may be written in the form

where kg is the Boltzmann constant, and the thermoelectric parameter

5

is defined as

resistivity, around the eutectic composition of

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C8-522 ^JOURNAL^DE^PHYSIQUE

I I I I

I

0 20 40 60 80 100

at%Sb

F i g . 6 . - Thermoelectric power of l i q u i d Pb-Sb a l - l o y s a t 660°C and Ge-Sb a l l o y s a t 950°C.

-

+experimental r e s u l t s .

-,,----theoretical r e s u l t s ( s e e parameters i n t a b l e 1 )

.

...

t h e o r e t i c a l r e s u l t s w i t h parameters Ti= 0

The c o r e parametersRi e n t e r i n g i n t h e model po- t e n t i a l have been f i t t e d on t h e experimental r e - s i s t i v i t y v a l u e s of t h e p u r e m e t a l s , e i t h e r with H a r t r e e s c r e e n i n g ( E ~ ) o r with improved Vashista- Singwi s c r e e n i n g ( E V - S - ) . The hard-sphere d i a m e t e r s

u i

a r e deduced from t h e packing f r a c t i o n s qi g i v e n by WASEDA [14] and t h e experimental d e n s i t i e s com- p i l e d by CRAWLEY [15]. The r e s u l t s a r e summarized i n Table 1 . The c o r e parameters and t h e hard-sphere d i a m e t e r s a r e h e l d c o n s t a n t throughout t h e whole phase diagrams f o r t h e c a l c u l a t i o n s . F u r t h e r it i s supposed t h a t t h e mean atomic volume of t h e a l l o y s f o l l o w s t h e i d e a l law of mixing. For t h e system Pb-Sb, t h i s i s s t r o n g l y supported by t h e d e n s i t y measurements performed by CRAWLEY [16] f o r r i c h Pb c o n c e n t r a t i o n s . The c a l c u l a t e d c u r v e s a r e r e p o r t e d i n f i g u r e 2 (broken l i n e s ) and o v e r a l l agreement i s o b t a i n e d w i t h t h e experimental r e s u l t s .

TO e v a l u a t e numerically t h e thermopower we need

Table 1.

which e n t e r s t h e t h e o r y t h r o u g h a n e x p l i c i t energy dependence of t h e c o r e p a r a m e t e r s Ri [17]. The t h e r - m o e l e c t r i c parameter ( 4 ) i s t h e n w r i t t e n i n terms of

ri

^{w i t h}

The parameters

ri

a r e f i t t e d on t h e e x p e r i m e n t a l T.E.P. v a l u e s of t h e p u r e m e t a l s ( s e e Table I ) , with t h e same s c r e e n i n g f u n c t i o n s . They were h e l d c o n s t a n t t o c a l c u l a t e t h e T.E.P. over t h e whole con- c e n t r a t i o n range. The r e s u l t s o b t a i n e d i n t h i s way a r e r e p o r t e d i n f i g u r e 6 (broken l i n e s ) . F a i r agreement i s achieved f o r t h e T.E.P. of t h e Ge-Sb a l - l o y s , b u t t h e T.E.P. f o r t h e Pb-Sb system i s n o t s a t i s f a c t o r y reproduced.

We n o t i c e t h a t t h e r e s u l t s d o n o t vary s i g n i f i - cantlywether we i n c l u d e o r n o t exchange and c o r r e - l a t i o n i n t h e s c r e e n i n g f u n c t i o n . The r e s u l t i n g c u r v e s a r e t o o c l o s e from one a n o t h e r t o b e d i s t i n - guished i n f i g u r e 6 ( t h e d i f f e r e n c e s do n o t exceed

1

0.6vQ.cm f o r p, and O.IUV.K- f o r S ) . The energy dependence i s s m a l l f o r Ge-Sb and has o n l y l i t t l e e f f e c t on t h e f i n a l r e s u l t . For Pb-Sb t h i s i s n o t t h e c a s e because Tpb i s n o t s m a l l a s may be seen i n Table 1 . The r e s u l t s w i t h t h e parameters Ti t a k e n t o be z e r o a r e r e p o r t e d i n f i g u r e 6 ( d o t t e d l i n e s ) and show t h a t f o r a n element l i k e l e a d , a s d i s c u s s e d by COHEN and HEINE [18], t h e energy dependence may be o f some importance.

t h e energy d e r i v a t i v e o f t h e model p o t e n t i a l ,

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[I] GASSER, J . G . a n d MULLER, J . D . , P r o c e e d i n g s of t h e N.A.T.O. A d v a n c e d S t u d y I n s t i t u t e

" L i a u i d a n d A m o r ~ h o u s M e t a l s " Z w i e s e l ( 1 9 7 9 ) [2] BATH,

i.

^andKLEIM,-R., R e v u e ~ h y s . ~ p p l .

4

( 1 9 7 9 ) 5 9 5

[3] CUSACK, N.E., R e p . P r o g . P h y s .

2

( 1 9 6 3 ) 361 [4] ROBERTS, R . B . , P h i l . M a g .

36

( 1 9 7 7 ) 91

[5] MATUYAMA, Y . , S c i . R e p t . T o h o k u U n i v .

16

( 1 9 2 7 ) 4 4 7

161 ROLL, A. and BISWAS, T . K . , Z. E l e t a l l k .

55

( 1 9 6 4 ) 7 9 4

[ 7 ] MARWAHA, A . S . a n d CUSACK, N . E . , P h y s . L e t t .

22

( 1 9 6 6 ) 556

[8] ZIMMERMANN, A . , J. P h y s i q u e C o l l o q .

22

( 1 9 7 4 ) C 4 - 3 4 3

[9] FABER, T . E .

,

A n I n t r o d u c t i o n t o t h e T h e o r y of L i q u i d M e t a l s ( C a m b r i d g e U n i v e r s i t y P r e s s , L o n d o n ) 1 9 7 2 , pp. 4 5 6 - 4 5 9

[lo] FABER, T . E . a n d ZIMAN, J . M . , P h i l . M a g . - 11 ( 1 9 6 5 ) 153

[ l l ] DUTCHAK, Y.I., FRENCHKO, V . S . a n d VOZNYAK, o.M., I n o r g . M a t e r .

13

( 1 9 7 7 ) 3 3 7 l 1 2 ] ASHCROFT, N.W. a n d LANGRETH, D . C . , P h y s . R e v

1 5 6 ( 1 9 6 7 ) 685

[13] A S H ~ F T , N.W. and LANGRETH, D . C . , P h y s . R e v 159 ( 1 9 6 7 1 5 0 0

[14] WAS=, Y . , L i q u i d M e t a l s 1 9 7 6 : I n s t . P h y s . C o n f . S e r . N 0 3 0 ( 1 9 7 7 ) 2 3 0

[IS] CRAWLEY, A . F .

,

I n t e r n a t i o n a l M e t a l l u r g i c a l - - R e w i e w s , R e v . 1 8 0

19

( 1 9 7 4 ) 3 2

[16] CRAWLEY, A . F . , T r a n s . M e t . S o c . A . I . M . E . - 2 4 2 ( 1 9 6 8 ) 859

[ 1 7 ] ASHCROFT, N.w., J. ~ h y s . C . ( P r o c , ~ h y s . S O C . ) 1 ( 1 9 6 8 ) 2 3 2

[ls]

C O H ~ N , M.L. a n d H E I N E , V . , S o l i d S t a t e P h y s . 2 4 ( 1 9 7 0 ) 3 7

-