Thermotransport studies in liquid alkali metal alloys

T~ER~QTRA~SPORT S. P. MURARK_I,~$

STUDIES T.

Y.

IN LIQUID KIM,5

M.

ALKALI

E’. HSIEHS

and

METAL R.

A.

ALLOYS*!

S-ctALIN$

Thermotransport has been studied as a function of composition in the Sa-fi. liquid alloy system. Thermotransport of trace concentrations of Rb inK, Rb in?ia and% in Rb have also been investigated. A reversal in direction of specie migration occurred at an intermediate composition in the Sa-P system. In 6 rich alloys Sa for esampie migrated toward the hot end of the capillary whereas in Sa rich alloys, Sa migrated to the cold end. At some intermediate composition (between 64.6 at % Sa and 76.6 at % Aa) a crossover occurred and conaequentIy no thermotransport occurred at that composition. This study compares with electrom~~tion studies by other investigators which indicate that a sign reversal m direction of electromigration occurs in both the Sa-K and Sa-Rb systems. TheomtiaaI~aloulations of the heats of transport in the alloy systems studied yield quitegood agreement with the observed sign of the heat transport for most of the alloys investigated. ETUDE

DC

THERXOTRASSPORT

DhXS DES ALCALISS

ALLIAGES

LIQUIDES

DE

METAGS

Le thermotransport a et& Btudie en fonction de la composition dans ie @&me Sa-K liquide. Les thermotransports de traces de Rb dens K, de Rb dsns Na et de Sa dans Rb ont Btb tigalement btudies. Dens le systeme Xa-K, il eriste une composition intermediaire pour laquelle ii se produit une inversion de Is direction de migration. Dans les a&ages riches en B, par exemple, Sa migre vers pestremit chaude du capiflaire alors que dsns les alliages riches en SF, Sa migre vers i’extmmite froide Pour une composition interm&diaire (entre 6t,6 % at.Xa et 76,6 y? at. &a), il se produit une inversion et aucun thermotransport n’a lieu pour cette composition, Cette etude comparee aus etudes d’~lectromig~t,ion effectu&s par d’autres chercheurs, qui montrent qu’il se produit une inversion de la direct,ion d’~le~tromi~ation dans ies deu.. sytemes &-Ii et Na-Rb. Les calculs theoriques des chaleurs de transport dans les systemes cl’alliages etudies sont en t&s bon accord avea le signe ovserve pour is chaleur de transport de la plupart des alliages etudies. THERJLOTRANSPORT

IN FL%SSIGEK

ALEALIJIIETXLL-LEGIERUXGES

Im fliissigen Legierungssystem Sa.E wurde der Thermotransport als Funktion der Zusammensetzung untersucht. AuBerdem wurde der Thermotransport von Spu~~onzentrationen von Rb in Ii, Rb in Sa und XT&in Rb gemeusen. Bei einer mit,tlerenZu~mmensetzung des Systems Ss-K erfoigt eine Richtung. sumkehr des The~ot.~nsports. In K-reichen Legierungen wandert Sa z.b. zum h&Ben Ende der Kapoltarriihre, wahrend es in Sa-reichen Legierungen zum kalten Ende wandert. Bei einer mittleren Zusammensetzung (zwischen 6-1,1 At. % Ea und ‘i6,6 At. % Sa) erfolgt ein Crossover und somit kein Thermotransport bei dieser Zusammensetzunp. Diese Untersuchung ist vergleichbar mit Xessungen des Elektrotransports durch andere Autoren, die in den Systemen Sa-K und Sa-Rb eine Richtungsumkehr des Elektrotransports beobaohteren. Theoretische Bereohungen der TransportwBrmen in den untersuchten Legierungssystemen ergeben fur die meisten Legierungen eine recht gute Ubereinstimmung mit der beobachteten Richtung des Wiirmetransports.

INTRODUCTION

Recently t,he~otr~~port studies of Au, Sb and S in liquid Ag(ri and of Ag in liquid AU(~) were reported. Experimental values of Q&r, the net heat of transport defined as

were obtained. In equation (I), the subscripts I and 2 refer to solvent and solute respectively. The term B, refers to the partial molal volume of component i. In Refs. (1) and (2) classical theories of diffusion in liquid metals were found to be inadequate in interpreting Dheexperimental results. An approach bssed on the sum of tfvo contributions -as developed. The two contributions are, (i) an electronic contri* Received June 11, 1973. Revised-August 10, 1973. t This research was supported by the U.S. Atomic Energy Commission. 2 Now with Bell Telephone Laboratories, Xurrar Hill, Xew Jersey. 8 Department of Chemical Engineering and Yateriats Science, University of Xnnesota, Minneapolis, Jfinnesota 55&5, U.S.A.

bution due to the charge difference between solute and the solvent, and (ii) a contribution due to mass difference between two species in the alloy. The first contribution was calculated by extending Gerl’s caleulations~3~ for solids to liquids and the second was estimated by use of the theories of tmnsport applicable to a dense gas.“’ This approach yielded numbers which compared reasonably Tell with experimental findings for Ag base systems. Some interesting work has been reported on electromigration in alkali metal dlo~3. In Sa-EL alloys for example a reversal in direction of migration of each species occurs at sn alloy composition of about 39-40 at. % IV-” and of 32.1 et.% li: at 140”C.@~ Tn Sa-Rb this occurs at 30 at. % Rb.‘s) Various theoretical attempts have been made to explain this behavior. The most successful is the phase shift approach used by Epstein d al.“) which has been extended by Olson et ai. to various binary liquid alloys of Li, Sa, K, Rb, Cu, Ag and Au. This approach predicts correctly the cross-over in eIectrotransport but fails to yield accurate values

BCT.1

1Yti

JIETALLL-RGIC-4,

of composition at which this reversal should occur. For example in the case of Sa-K alloys, the cross-over is predicted to occur at about 62 at. ‘A K whereas the experimental value is in the region of 40 at. % K. Fundamentally both the processes of thermotransport and electrotransport may be considered to have the same origin(rl) and correlation between them may be expected. Thus, corresponding to the cross-over phenomenon in electrotransport, a reversal in the direction of migration of each species could possibly occur in thermotransport in alkali metal alloys. This means that the species going to the hot end of the thermal-gradient at one extreme alloy composition, will go to the cold end at the other extreme alloy composition. This conclusion has an important consequence-namely: if reversal occurs, for each temperature gradient there will be a time invarient alloy composition. In view of the above experiments, investigation of thermotransport in liquid alkali metal alloys was initiated. This paper reports some of t’he \vork done on Sa-K, Na-Rb and K-Rb alloys together with the results of theoret’ical calculations by use of Bhat and Swalin’s”) approach. EXPERIMENTAL

Sa-K, Sa-Rb and K-Rb alloys were investigated. Esperimental procedure consisted of four major steps: (i) preparation of liquid alloys in fine bore capillaries ; (ii) annealings in a given thermal gradient and (iii) sectioning of the capillaries and determination of the concent’ration in each section. Full description of each of these steps is reported elsemhere”^) and only a brief summary is described here. Alloys of the desired composit,ion were prepared in the laboratory. The radio-isotopes Sa** and Rbs6 were obtained in the form of carrier free Sa?’ Cl and Rbss Cl in solution respectively, whereas K42 was obtained by thermal neutron irradiation of pure potassium metal encapsulated in a fused quartz tube. Capillary tubes of 0.5 mm diameter precision bore were filled to a length of about 7 cm with alloys of the desired compositions and subsequently sealed. Samples were then placed in a temperature gradient in a vertical tube furnace, closed at one end. The furnace could be evacuated to a pressure of < 1,~ of Hg to minimize air convection currents. The thermotransport samples were fastened to the end of a fused quartz tube closed at the bottom end which contained a chromel-alumel thermocouple. The thermocouple could be moved, along the axis of the furnace during the progress of the experiment. This enabled a temperature profile to be determined

VOL.

21,

1974

DISTANCE

FIG. 1. A

FROM

COLD

END

km1

typical temperature profile transport apparatus.

of

thermo-

before, during or after the experimental anneal. The controlling thermocouples were placed outside the main tube on the windings. Figure 1 shows a typical temperature profile of the The temperature difference was about furnace. 100°K over the i cm sample length. -4 sample was held in this gradient for several days in order to ensure achievement of the stationary state. After the diffusion treatment anneal, samples were sliced into lo-15 sections, dissolved in distillecl water and analyzed. The radioactive tracer concentration was determined in each section by use of a well-type scintillation counting set up. y-Rays of energies 1.27, 1.52 and 1.08 MeV were monitored for “Sa, UK and *sRb respectivelv. A problem existed however with 42Ii since the short half-life (12.4 hr) precluded long annealing times. In order to employ long annealing times, an alternative method of analysis was employed. This technique was based on absorption spectroscopy and was satisfactory for alloys which For contained appreciable concentrations of K. dilute alloys, the presence of high concentrations of Sa resulted in interference and thus the less desirable radioisotope technique was employed for Sa-rich alloys. Sormally the experimental configuration was such that the high temperature n-as at the top, although several experiments were performed which had the gradient inverted. EXPERIMENTAL

RESULTS

Table 1 shows the list of alloys studied. For a two component system in a thermal gradient, one can derive the folloning expression for the stationary state.“*?)

JlUR_kRKA

THERMOTRASSPORT

et al.:

TABLE

K_Sa”’

Rb-Se?” &_Ki’ Sa-RbJG K-Rb*d sa-K sa-K

IS

t.he Gibbs-Duhem equation, x1 dp, + ~rnb~n~~ xs dp, = 0 and equations (2) and (3f, one obtains

Qn*

Q,*

‘x is defined as

tvhere xi is the mole fraction of component i, and the gradient dx:,/dT is determined at the steady state. If the definition(14*15)

one obtains

(6)

where U,czX,?

dLLOYS

1Si

equat,ions

I 25

I 24

I 23

I

103/T(‘K, Fm.

2.

Ln C VB the reciprocal of absolute temperature for Sa in Rb.

Thus Q&

=

2

‘!

0

zz

df-

i

Q2* -

i&‘; .

@I

1

T

Figure 2 shows a typical plot of ln x2 vs f/T for a very dilute alloy and Fig. 3 shows a plot of In (xs/xy) vs l/T for 8 concentrated alloy. The slopes of these plots are equal to Q*erp

(4)

d~ffusiou factor

I 22

I 2.1

(3)

Combining

XET_iL


where pi, Qi* and vi are the chemical potential, the heat of transport and the partial molar volume of component i respectively. The symbol ,r represents distance. From the relation ,u+ = f~o,)r,p f RI’ In ai, one obtains

is employed,

ALKALI

wt s<

20’

The thermal

LIQUID

1

Composition

AllO>-

STUDIES

according to equation (6). For bhe very dilute alloys this term corresponds to Q&JR according to equation (8). For concentrated h’a-K allowys, the mole fractions of each component in the sections were determined by use of absorption spectroscopy and the slope of In a, vs In x2 was calculated by use of the activity data obtained by Cafasso et aZ.(rs) fn Table 2 are listed the experimental values of with their standard deviation for the alloy Q* em systems investigated.

0.0 -

f&)-(6), \ve find, that

f = (x1 8, + x26,).

For

very

dilute

I,

pc

r*.

alloys,

1,

dlna,

dlna = ?N d In x1 d In x2

tC?/TPKf

WO. 3. Ln zzlxI vs the reciprocal of absolute temper. ature for a 35.4 at. %K, 64.0 at. %Sa alloy.

ACTA

lY8

METALLGRGICA,

VOL.

“2,

1974

Heat of transport, System Trace cont. of Sa** in K Trace cont. of K’* in Na Trace cone . of A Xaz2 in Rb Trace cont. of Rbsr in Sa Trace cont. of Rbn6 in K 23.3 at % K-76.7 at. % Xa 34.4 at. % K-64.6 at. % Xa

Qf, (cab4 1080 + 600 negative? -4570 & 590 +-lo70 & 670 +-I%0 * 540 -6300 & 490 +-IO10 * -“SO

0.2($

-

+?,]

(11)

-

t The J*K-Na thermotransport experiments were carried out only for a few days because of short half-life of **K isotope. Thus accurate results could not be obtained and the purpose of these experiments was to obtain the the migration direction of K in Na.

where K is a factor involving three integrals evaluated from the law of force between atoms. K has been evaluated from the results of isotope thermotransport experiments and lies in a rather narrow range for alkali metals. The terms m, and 'rn2 are the mass of solvent and solute atoms respectively and s1 and s2 are their equivalent molecular diameters. The term s13 is given by (sl + s2)/2. For very dilute alloys (x2 < z1 E l), and thus

DISCUSSION

The investigation of thermotransport in liquid alkali metal alloys, namely Na-Ii, Sa-Rb and K-Rb, at the extreme ends of phase diagram (Iv-here one of t,he elements is present in tracer form) n-as carried out to determine the heat of kansport values at these concentrations. These values will be then compared with the values calculated from the procedure of Bhat and Smalin. Bhat and Swalin(1*2) considered the heat of transport Q* to consist of two terms:

Qi*=RTK[(.;:+;:)

-O.L($1)].

(12)

From substitution of the appropriate quantities into equations (11) and (12) Qe* and Qi* may be calculated. Table 3 lists calculated values of Qe*, Qi* and Q,:,, for Sa”* in K, Kc2 in Sa, Sa** in Rb Rb@ in Na, Rbss in K. Calculations for AgIl in Ai and Aulg5 in Ag as reported in Refs. (1) and (2) are shown for comparison. It is interesting to see that the overall agreement between calculated and experimental values is reasonably good. Qc*alc = Q,*+ Qi* (9) One of the purposes of these investigations was to find out if there is a reversal in migration direction where Q,* represents the extrinsic contribution which of each species in binary alkali metal alloys when arises from, (a) electrostatic fields created in a metal placed in a thermal gradient. due to the presence of the temperature gradient, For this temperature gradient, in the Sa-K alloy and (b) interaction of the diffusing ion with charge system, there is reversal in the direction of thermocontribution carriers. Qi* re p resents t,he intrinsic migration of K somewhere in the concentration range due to interaction among the ions themselves. Q,* 23.3 at.% K and 36.4 at.% K. K migrates toward was calculated by use of the method of Gerlt3) and the hot end on the Na rich side and to the cold end Qi* was estimated by use of C!hapman’s(2*4) expression on the K rich side. This concenkation range of the for thermotransport in dense gases. These quantities reversal is to be compared wit,h the value of 32.1 at. % are given by following expressions : K at which a cross-over in direction of electromiK,T m* '~2 gration occurs.(8) Ed%, Qe*= For t,he Na-Rb system, Bhat and Swalin’s apJ2 (1m proach predicts a reversal in the direction of migration of each species between two extreme ends of composition. Experimental results at these two where points of Na-Rb alloy are contrary to the calculation K, = electronic contribution to thermal since Na migrates to the hot end in both cases, conductivity of solvent although study of intermediate compositions is m and m* = rest mass and effective mass of necessary to confirm that a non-reversal exists. electron respectively In the case of Ag-Au alloys, the direction of migration Z = effective charge on the diffusing ion is correctly predicted by Bhat and Smalin’s approach A, = resistivity scattering cross-section of for both composition extremes. solute atoms for electrons One may compare these data with the results of electromigration studies of the same liquid alloys. E = Energy of electrons Electromigration experiments indicate that. a reversal EF = Fermi level.

>IUR_%RK_%

THERXOTRASSPORT

et aE.:

TABLE 3. Comparison

_Woys Temp. range employed (>K)

-950 -850

Q"* Q“

Q,‘,k

-18”o

QZX,

-

Tracer goes to

between calculated

1080

Hot end

IS

and experimental

LIQI;ID

_%LK_kLI

XEThL

ALLOTS

189

results of Q* for dilute alloys (cal/mol)

Sa-Rb Sazz in Rb Rbss in Sa

K-Rb RbSB in K

(423-523)

(373-473)

(373-473)

(323-423)

- 1070 + 880

-910 -1260

-2050 + 1210

-130 + 640

-500 -1S60

f 1770

-190

--5170

-860

+?I10

-2360

+1-‘90

negative

-43iO

+ 1070

+ 1280

-1530

f 1690

Hot end

Hot end

Cold end

Cold end

Se-K Sa?” in K K’f in ss

(423-523)

STL-DIES

_1g--1l.l _igl10 in Au AUGER in dg

(1338-143s)

Hot end

(l%s-1345)

-480

Cold end

* Q.* and Qi* are calculated at the midpoint temperature of temperature range employed for each system. occurs in direction of species migration in both the Ka-K and Sa-Rb systems. These results are consistent with theoretical calculations.(lO) Our thermomigration studies on the other hand show a reversal for only the Sa-K system. Electromigration studies have not been performed for the Au-Ag system however, theoretical calculations of Olson et ~1.~~~) indicate that no reversal is espected. Our earlier thermomigration studies for the Au-Ag system indicat’es that no reversal of sign of migration occurs at the composition estremities. SUMMARY

Thermotransport has been studied as a function of composition in the Na-K liquid alloys systems. Thermotransport of trace concentration of Rb in K, Rb in Sa and Xa in Rb was also investigated. A reversal in direction of species migration occurred at an intermediate composition in the Xa-K system. That is to say that in K rich alloys Na migrated to the hot end of the capillary whereas in Na rich alloys, Na migrated to the cold end. At some intermediate composition (between 64.6 at. % Na and 76.6 at. % Ka) a crossover occurred and no thermotransport Electromigration occurred at that composition.

studies by other investigators indicate that a sign reversal occurs in both the ;?ia-K and Sa-Rb systems. Theoretical calculations of the heats of transport in the alloy systems studied yield good agreement with the observed sign of the heat of transport for most of the alloys investigated. REFERENCES 1. 2. 3. 4.

B. S. BHAT and R. -1. Sma~rs, 2. Salur. 28A, 45 (1971). B. S. BH~T and R. .i. SW~LIS, dcta Xet. 20, 1387 (1952). &I. GERL, J. Phys. Chem. Solids 23, i25 (196;). S. CA~PJUX and T. G. COWLISG, The Mathematical Theory of Xon-Uniform Bases. Cambridge (1952). 5. S. I. DR~KIS and -4. K. JIALTSEV, Zh. Pi:. Khim. 31, 2036 (1937). 6. J. C. JOCSSET and H. B. HLTTISGTOS, Phys. Statue Solidi. 31,775 (1969). 7. S. G. EPSTEIS and J. 31. DICKEY, Phys. Rev. Bl, 2442 (1970). 8. J. L. BLOUGH, D. L. OLSES and D. A. RIGJET, Mat. Std. Engng 11,73 (1973). 9. T. S. LAKSHJIA~AJ, D. L. OLSOS and D. 8. RIGXEY, Scrip& Met. 5,1099 (1971). 10. D. L. OLSOS, J. L. BLOGH and D. h. ROG~XY, Acta Met. 20.305 (1972). 11. O.-D. G&&Ez and R. A. ORIAX, Trans. BIME 223, 1878 (1965). 12. T. Y. KIX, XS. Thesis, University of Xnnesota (1973). 13. F. A. CAFASSO. V. 31. K~asra and H. 11. FEDER. Ado. Phys. 16, 536 (1967). 14. K. F. ALEWDER, Fortechr. Phys. 8, 1 (1960). 15. A. LCYDEN, Atomic Transport in Solida and Liquida. (Proc. Europhys Conf.). edited by A. LODDISG and T. LAGERWALL (1971).