THERMODYNAMIC AND ELECTRON TRANSPORT PROPERTIES OF INDIUM-AMALGAMES IN THE DENSITY RANGE OF METAL-NONMETAL TRANSITION

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THERMODYNAMIC AND ELECTRON TRANSPORT PROPERTIES OF INDIUM-AMALGAMES IN THE

DENSITY RANGE OF METAL-NONMETAL TRANSITION

G. Schönherr, F. Hensel

To cite this version:

G. Schönherr, F. Hensel. THERMODYNAMIC AND ELECTRON TRANSPORT PROPERTIES OF INDIUM-AMALGAMES IN THE DENSITY RANGE OF METAL-NONMETAL TRANSITION.

Journal de Physique Colloques, 1980, 41 (C8), pp.C8-8-C8-11. �10.1051/jphyscol:1980802�. �jpa- 00220186�

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JOURNAL DE PHYSIQUE CoZZoque C8, suppZdment au n08, Tome 41, aoat 1980, page (3-8

THERMODYNAMIC A N D ELECTRON T R A N S P O R T PROPERTIES OF INDIUM-AMALGAMES IN T H E DENSITY RANGE OF METAL-NONMETAL TRANSITION

G. Schonherr and F. Hensel

Fachbereich PhysikaZische Chemie, PhiZipps-UniversitBt. Hans-Meerwein-Strasse, 0-3550 Marburg, R.F.A.

I INTRODUCTION

The first investigation of the effect of a solute on the metal-nonmetal transition in expanded liquid mercury was that of Zillgitt et a1 (1) and a number of subsequent papers have demonstrated that a few atomic percent of In greatly affects the conductivity a(2) the thermopower S (1) and the equation of state (3) ,(4) in the transition range. An example of the effect on a is given in fig.

1. It is only in the semiconducting region at pressures smaller than 2000 bars and con- ductivities smaller than 300 ohm-'cm-' that

bars and the conductivity a was measured simultaneously by conventional potentiome- try in the form of a four terminal arrange- ment. The measurements were performed in a

specially constructed high pressure-high temperature apparatus consisting of a steel pressure vessel with an internal electric resistance furnace with three independently

I I

controled heating elements made of molybde-

d num wire. The pressure medium was argon gas.

0 1 2 3

In [at%] ---+ Details of the experimental set up are gi- a becomes strongly concentrations dependent The purpose of the present short note is to present new simultaneous measurements of the pVT-data and of a for mercury-indium amalgams with up to 2.8 at% In. These measurements are intended to separate the effects of temperature and volume expansion on a and to supplement the existing infor- mation on the effect of solutes on thether- modynamic properties of mercury in the me-

tal-nonmetal transition region.

I1 RESULTS AND DISCUSSION

The dilatrometric method described previous- ly (5) was employed to determine the density p of the amalgams up to 1 7 0 0 ~ ~ and 2700

ven in refs. (4), (5). Results for p and 0

Fig.1 Electrical conductivity of Hg-In alloys as a

were taken in the above mentioned pressure- function of In-concentration at 1 5 0 0 ~ ~ and

and temperature range for 0.2, 0.4, 0.8, constante pressures.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980802

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ween 1 1 and 9 g/cm3 the a results are con-

&

sistent with the assumption that L is about

In [at%]

-

Fig.2 Electrical conductivity of Hg-In alloys as a function of In-concentration at constant temperature and number density.

1.8 and 2.8 at% Indium (4) . A few selected data are shown in fig.2 in form of plots of o versus the In-concentration at constant number density.

For pure mercury the electrical transport properties can be well described in terms of three distinct transport regimes. At high densities between 13.5 g/cm5 and 1 1 g/cm5 o varies from to 3-10+~0hm-'cm-~. Here the electron mean free path exceeds the mean interatomic distance and the different transport properties can described by Ziman's nearly-free-electron model. For p smaller than 1 1 g/cm3 a pseudogap opens and accor- ding to Mott (6) a is given by

1 2 s F ~ g 2

6 =

1 2.rr3ih ⁽¹1

where g = N(EF)

free, N(EF) free is the free electron density of states and SF is the free electron fermi surface area. Bet-

equal the interatomic distance and g drops from 1 to 0.3 For p smaller than 9 g/cm 3

- ¹ falls to values smaller than 300 ohm-'cm and fluid mercury shows then the characte- ristics of a fluid semiconductor. We now attend to interpret the change in o with increasing In-concentration assuming that formula (1) is applicable to the expanded amalgam system. In addition it is supposed that adding a small amount of In at constant temperature and number density (fig.2) leaves the density of states unaffected and chan- ges only the electron density N. Then one can write for g:

alnE free alnE

s = C 7 ) /(-I

E=EF E=EF

Together with the thermoelectric power pa- alno

rameter X = (T)E=EF one gets:

Using the X-values from the literature (9) we find with eq. (3) values for g (fig.3) which are in surprisingly good agreement with those derived from measurements of the Hall-constant (7) and conducting of pure expanded mercury (5).

From a comparison of fig.1 and fig.2 it is obvious that a few atomic percent of In greatly affects the thermodynamic properties near the metal-nonmetal transitionden- sity of pure Hg; e.g. In increases the number density of atoms at constant pressure.

This is demonstrated by fig.4 which shows the excess volume of mixing, vEX, defined

3

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JOURNAL DE PHYSIQUE

C8-10

I Î Î Î Î I

13 12 11 10 9 8

d Lg/om)l

-

Fig.3 g-factor for dilute Hg-In alloy as a function of density.

Fig.4 Isothermal compressibility of pure Hg and excessvolume of Hg with 2.8 at% In for seve- ral pressures as a function of temperature.

as VHgIn - ⁽¹ - x)VHg - xVIn for the alloy with 2.8 at% In in comparison with the isothermal compressibility xT of pure mercury.

Both quantities are plotted in form of iso- bars as a function of temperature. The most interesting result seems to be, that xT and

vEx (a similar behaviour is observed for the thermal expansion coefficient a ) rise quite

P

sharply for temperatures larger than 1400°c,

tion density of 9 g/cm3 which is not too

far from twice the critical density ~ ~ ~ 5 . 3 g/cmS. It is necessary to point out that

the turnover in the slopes of the different quantities is generally observed for liquids at densities smaller than about 2pc. It is difficult to separate the effects due to the metal-nonmetal transition from thosedue to the normal divergence of the above mentioned properties as the critical point is approached. This is also demonstrated by the results of fig.5 which shows the partial molar volume VIn = aV/acIn for the mole fraction of In XI, + 0 as a function of pressure at a constant temperature which is very close to the critical temperature Tc = 1 4 9 0 ~ ~ of pure Hg. As the critical pressure is approached the partial molar volume at infinite dilution diverges. The highest negative value observed in our ex- periments is -1500 cm /mole. Such high ne- 3 gative values of the partial molar volumes

Fig.5 Partial molar volume of In in Hg-In alloys i.e. as the density falls below the transi- for XI^ ⁺0.

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of the solute are generally observed close to the critical point of the pure solvent for mixtures with strong attractive forces between the solute- and solvent molecules

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ACKNOWLEDGEMENT

Thanks are due to the Fonds der chemischen Industrie for financial support of this work.

REFERENCES

1 Zillgitt,M., Schmutzler, R.W. and Hensel, F., 1972, Phys.Letters 5, 419

2 Neale, F.E., Cusack, N.E. and Jahusan, R.D., 1979, J.Phys.F. - 9, 113

3 Even, U., Levin, M., Magen, J. and Jort- ner, J., 1973, J.Appl.Phys. 44, ¹⁶⁰⁴

4 Schonherr, G., 1978, Thesis University of Marburg

5 Schonherr, G., Schmutzler, R.W., Hensel, F., 1979, Phil.Mag. 40, ⁴¹¹

6 Mott, N.E., 1966, Phil.Mag. 13, 989 7 Even, U. and Jortner, J., 1972, Phys.Rev.

Lett. 28, 31 -

8 Wheeler, J.C., 1972, Ber.Bunsenges.phys.

Chem. 76, 308 -

9 Schmutzler, R.W. and Hensel, F., 1972, Ber.Bunsenges.phys.Chem. 3, ^531.