A thermoelectric device based on beta-alumina solid electrolyte

Energy Conversion.

Vol. 14, pp. 1-8.

Pergamon

Press, 1974.

Printed in Great Britain

A Thermoelectric DeviceBasedon Beta-Alumina SolidElectrolyte NEILL

WEBERt

(Received 25 May 1973)

the membrane. Electrons left behind leave the Pe region via the negative electrode. On passing through the solid electrolyte membrane, sodium ions are recombined with electrons at the electrode-electrolyte interface, the electrons meanwhile having passed through the electrical load. Neutral sodium evaporates from the porous electrode at pressure PI and temperature TZ passing in the gas phase to a condenser at temperature TI(TI < Tz). Condensed liquid sodium is returned to the high pressure region by the pump, thus completing the cycle. The process occurring in the membrane and at its interfaces is equivalent to an isothermal expansion of sodium from pressure Ps to PI at temperature Ts. No mechanical parts move, and the work output of the process is electrical only. The beta-alumina TEG possesses several attractive features. Under ideal no load conditions the thermodynamic efficiency approaches the Carnot limit. Electrical power outputs of 500 mW/cms appear achievable. If an electromagnetic pump or wick is used, the only moving part is circulating sodium. Engineering of a practical device can take advantage of current technologies for fabrication of beta-alumina ceramic and for handling of molten alkali metals.

1. Introduction The use of beta-alumina type solid electrolytes in experimental high energy density storage batteries is well known [l-3]. Less well known is their application to a device which has been described only in the patent literature [4]. This is a device for the direct conversion of thermal to electrical energy. This paper presents a theoretical analysis and describes the construction of a model beta-alumina thermoelectric generator. We have also tried to identify difficulties in further development of a practical device. To understand the operation of the thermoelectric generator (TEG) consider the diagram in Fig. 1. A closed container is divided into two regions by a pump and a septum consisting of a solid electolyte membrane and porous electrode. The generator contains a working fluid, sodium, whose pressure Ps, in the upper region is greater than PI, the pressure in the lower region. During operation of the device, the working fluid travels a closed cycle around the TEG. Starting in the high pressure region a heat input raises the incoming liquid sodium to temperature Ta. Sodium then migrates through the solid electrolyte as Na+ ions (NaO+Na++e) as a result of the pressure differential (Pa - PI) across

2. Theoretical Analysis of Operation

--------------

1

TEMPERATURE

T2

i

~-___?p:RATURE T’__ J Fig. 1. Schematic diagram of

A. EfJiciency under no load The maximum efficiency under no load can be calculated as the ratio of net useful electrical work to heat abstracted from the high temperature reservoir when the fluid (sodium in this example) is cycled around the cell. Thus, efficiency

?

Where, for unit amount of sodium, Wi is the maximum work obtained by isothermal expansion of gas from pressure PZ to PI at temperature Ts, La the heat of vaporization at Tz, q2 the heat absorbed during isothermal expansion, and q3 the enthalpy difference of the liquid between Ta and TI. W:! is the work in pumping liquid at TZ against a pressure difference P2 - PI. If the vapor is an ideal gas, employing the ClausiusClapeyron equation and ignoring the small term WZ gives

f

thermoelectricgenerator.

(T2

t Scientific Research Staff, Ford Motor Company, P.O. Box 2053, Dearborn,

’=

Michigan 48121, U.S.A.

I

(T2

-

TW”z[l

-

TI)ITz

+

C~TIILI + Tl/Tz

(2)

2

NE&L WEBER

where C, is the heat capacity of the liquid. For sodium, the efficiency calculated with Equation (2) for Ts= 1000 K and Tl = 500 K is 46.7 per cent, compared to Carnot efficiency of 50.0 per cent. A more exact calculation based on Equation (1) and tabulated thermodynamic properties [5] gives 48.6 per cent for sodium and 44.8 per cent for potassium. These calculated efficiencies neglect heat flow by conduction and radiation through the container walls, the metal vapor, electrical leads, and the return line. In principle, these losses can be controlled relative to heat transported during current flow by means of large separation of the heat reservoirs, radiation shielding, etc. B. Current-voltage relationship with a porous electrode A useful current-voltage relationship for the cell can be obtained without the need for considering the detailed structure of the porous electrode. The derivation proceeds from a presumption that the equilibrium potential difference E at zero current obeys the Nernst equation and from the fact that in the steady state, current flow is limited by evaporation of sodium from the outer surface of the porous electrode into the low pressure chamber. At zero current, the voltage, E = RTa ln (J&i)

(3)

nF

where fa and fl are the fugacities at pressures PZ and PI, and Fis the Faraday, PI is the vapor pressure assumed

at the electrode-electrolyte interface and Ps is the vapor pressure of liquid at Ts. When n = 1 and the vapor obeys the perfect gas laws, the open circuit voltage

Following Langmuir [6], the rate of evaporation of metal into a vacuum from the electrode at temperature T is related to the local vapor pressure Ps at the outer surface of the electrode by the equation R = CIP~(T/M)-~/~

Equation (8) expresses the relation between current and voltage under the most favorable conditions possibJe for this cell. At least five sources of polarization or efficiency have been neglected so far. They are: charge transfer, overvoltage at the liquid sodium-electrolyte and porous electrode-electrolyte interfaces; higher effective ohmic resistance in the electrolyte when the electrode is discontinuous; ohmic resistance of the electrode itself; and resistance to mass transfer through the porous electrode. Before taking account of these effects, which will introduce several unknown parameters, it is instructive to examine further Equation (8) in which all of the terms are known. Of particular interest are the conditions for obtaining maximum power, and the variation of maximum power with temperature and Ro. If Equation (8) is multiplied by i to give power and differentiated with respect to i, then the condition for maximum power is

Assigning various values for i and T in Equation (9) and solving for Ro, E and maximum power, graphical relationships among these variables can be found. Figure 2 shows variation of maximum power with temperature for several values of Ro. The importance of maximizing temperature and minimizing Ro for obtaining high power density is evident. We can now use Equation (9) to calculate the performance of the TEG for realistic values of Ro and Ts. If T2 is 700°C and RO is 0.2 ohm cm2, then E is 0.374 V, i is 1.43 amp/cm2, maximum power is 0.535 W/cm2 and PI is 3.93 x lO-2 torr. The pressure PI corresponds to the vapor pressure of sodium at a temperature slightly over 325°C. At interesting levels of power, then, condenser temperature may be in the range of 200-250°C. No advantage is gained by having the condenser below this range. The coefficients A and

(5)

where R is the evaporation rate in g/set ems, M is the molecular weight, and Cl a constant. Since in the steady state the current density i is proportional to evaporation rate, i = C2R = C3P3 (MT)-l12

(6)

where CZ and Cs are constants. For the case where there is no pressure gradient through the porous electrode, and where its sheet resistance is small enough to be neglected, Pa = PI, and -_iR

0

(7)

where X = C;l (MT)112 and Ro is the surface electrical resistivity of the solid electrolyte. Rearranging and using common logarithms, E = A - B log i - iRo.

2 600-

(8)

TEMPERATURE

OC

Fig. 2. Calculated maximum power vs temperature for ideal porous electrode.

A Tbermoeleclric Device Based on Beta-Alumina Solid Electrolyte Tablel.E=A-BZogi-iR~.ForEinvolts and i in amps/cm2 T”C

A

B

400 500 600 700 800

0.160 0.340 0.516 0.693 0.875

0.133 0,153 0.173 0.193 0.213

3

Tin appears to be one of the few metals applicable. Still another electrode type is a thin layer of a solid which has both ionic and electronic conductivity. Operationally, such an electrode behaves like a permeation electrode. As with the latter, the effective area for charge transfer can be the whole interfacial area. Possible materials for this electrode are the alkali ferrites and the tungsten bronzes.

B are tabulated vs temperature in Table 1. The pressure

D. D@ision and electrode polarization

PI can also be used to calculate the mean free path of vapor atoms in the porous electrode. For the conditions cited above, the mean free path is 1.5 mm. For any solid electrode whose pores are smaller than this, transport in the vapor phase will occur by molecular flow.

Resistance to flow of neutral sodium electrode results in a pressure (activity) at electrolyte interface higher than that at where evaporation takes place. Equation the form

C. Porous electrode design Stimulated by interest in fuel cells, many studies have been made of gas supporting electrodes on solid electrolytes, chiefly zirconia. The subject has been reviewed recently by Raleigh [7]. Many of the processes relevant to the zirconia-gas system also apply to the sodium-beta-alumina system. Aside from the necessity of being an electronic conductor, the choice of electrode material depends on the mechanism of transport of sodium atoms away from the electrode-electrolyte interface. Transport can occur by porous flow in the gas phase, permeation through a solid or liquid, or by surface diffusion as an adsorbed species. In the zirconia-gas system, porous metal electrodes are generally employed since porous flow is undoubtedly an important part of the electrode process and the effective three-phase contact area (pore-metal-electrolyte) is maximized. In the sodium-beta-alumina case, the vapor pressure is low and transport in the vapor will be by molecular flow as shown above. As the effective triple interface area is increased, the pore size becomes smaller and the flow per unit area of surface is diminished. For example, in the case of molecular flow in cylindrical channels, for a given differential pressure and channel length, the flow per unit area is proportional to the diameter of the channels. In contrast, flow by surface diffusion is inversely proportional to the channel area. Surface diffusion coefficients of alkali metals on refractory metals are known to be high. A good electrode for the sodium-beta-alumina system might therefore be a thin layer of fine-grained relatively dense metal which is chemically inert to sodium. The triple interface near which charge transfer takes place would be poremetal-electrolyte. Another possible electrode is a thin layer of a liquid or a dense solid metal through which sodium is transported by solution and diffusion (permeation). The effective area for charge transfer would in this case be the whole area of the interface between metal and electrolyte. Such an electrode should have a low vapor pressure. Ability to wet the electrolyte surface would be desirable but perhaps not essential.

in the porous the electrodethe boundary (7) then takes

R7 E = - In [P&Xi + AP)] - iR0. F

(10)

If AP as a function of flow rate (current) is known, the appropriate substitution can be made. In general, either because of complex electrode structure or because transport may occur by one or more poorly defined mechanisms over a wide pressure range, AP may be expressed as a polynominal in i. AP = aoi + ali . . . .

So that E=A-Blog(i)-iRo---Blog

l+;+y... (

. .

1 (11)

Charge transfer overvoltage r] at the liquid sodiumelectrolyte interface will be small because of the high exchange current io, and proportional to current as expressed by the low field approximation of the Butler-Volmer equation 77

=

R_T 1= F io

Rli.

(12)

This interfacial resistance, RI, will add another resistive term (- iR1) to Equation (8). The RO term will also increase if the area for charge transfer is less than the total interfacial area. Charge transfer overvoltage at the porous electrodeelectrolyte interface is expected to obey the ButlerVolmer equation where now the exchange current io is a function of the activity of sodium at the interface. This activity, a, is related to current and pressure drop across the electrode so that i0 = iiaa

(13)

where p is the symmetry coefficient and ig the standard exchange current. Since the relation between pressure drop across the electrode and current is not known we take afl 2 Kib,

and io 2 Ki,Oifl,

where K is a constant. For small overvoltages 7,

(14)

4

NEILL WEBER

TSF$l

i(l-8)

(15)

0

and for high overvoltages T

<

!xd3 F

B

In (i) - $1,

(Ki$.

(16)

The electronic sheet resistance of the porous electrode must be considered. When significant voltage drops occur across the electrode surface, the mathematical form of the current-voltage response of the cell is complicated. A numerical solution of the non-linear differential equation involved was not attempted. For a given cell geometry there will be an optimum thickness determined by sheet resistance and neutral atom flow resistance. For an electrode to be considered promising, the sheet resistance at optimum thickness should be equal to or smaller than the surface resistance of the solid electrolyte-membrane under the electrode. By distributing current to the electrode through one or a succession of grids of heavier cross-section, better performance can be expected until the area masked by the grids becomes significant. Electrical loss is also incurred as a consequence of the fact that a finite temperature difference is required to sustain heat flow across the electrolyte membrane. Heat is absorbed at the porous electrode principally from sodium evaporation during current flow and thermal radiation to the condenser. This type of loss can also be expressed as a current and temperature dependent voltage drop 7 which in turn can be equated to the product olAT where AT is the temperature drop across the electrolyte. For the evaluation of 01and AT it is convenient to use the equation for the ionic Seebeck coefficient. From the theory of thermocells (Reference [8] has a recent discussion) the Seebeck coefficient 0 of a cell consisting of a cationic conductor fitted with electrodes of the conducting cation metal m and leads of metal ml can be written:

e=

!!&= (s,

_

g,+

_

,q-)lF.

(17)

The quantities S,, s,+ and s,- are respectively the entropy of the conducting cation metal, the transported entropy of m+ ions in the electrolyte and the transported entropy of electrons in the metal lead. The calculation of AT for a TEG cell which obeys Equation (8) proceeds as follows: Using the Kelvin equations, the rate of heat absorbed at the porous electrode

dq

x = rri =

(18)

where 7ris the Peltier heat per unit charge at that interface and 81 is the Seebeck coefficient calculated using S,,, the entropy of sodium at the low pressure pl. If this heat is supplied only from the hot reservoir and if half of the i2Ro heat flows to the porous electrode AT = y (TO1 + jr/i - iRo/2)

(19)

where m and h are the thickness and effective thermal conductivity of the electrolyte, jr is the net radiation flux to the condenser and 01 = 0 + L/TF + R In P~/PI.

(20

The coefficient (Ymay be equated with 81 or if a higher order term is included with 0 + (aE/aT)i so that in terms of the coefficients A and B in Equation (8)

(e+dA

dT-logii+

rl=

1

x Measurements of 0 for polycrystalline 8”-alumina give values near 2.1 x lo-4 V/K in the range 443%800°C. An estimated value for h in this range is 0.02 W/cm K based on data for fused cast /3-alumina refractory brick [9]. E. EfJiency

under load

From experimental current voltage data the thermal efficiency of the electrode-electrolyte system for the cell

30 c

0 400

TBli

I

I

I

500

600

700

TEMPERATURE

800

=‘C

Fig. 3. Calculated efficiency at maximum power for ideal porous electrode.

A Thermoelectric Device Base-d on Beta-Alumina Solid Electrolyte

under load can be calculated. 5 = JWZP

+ E + qs/F).

(22)

Since E is a measured quantity Equation (22) requires no assumptions about the pressure drop over the porous electrode. The results of applying Equation (22) to the case of the ideal porous electrode (Equation 8) at maximum power are shown in Fig. 3. Efficiency as well as power increases with temperature; whereas maximum power decreases rapidly with increasing Ro, efficiency increases slightly. The curves in Fig. 3 were calculated using a cold reservoir temperature of 200°C. This temperature is in the middle of a small range where the vapor pressure of sodium is 1 per cent of the pressure at the porous electrode.

Heater And Thermocouple Wells 7

r

-+

B-Alumina Tube

(

_CVD Plating Injector

(23)

The free energies of formation of beta-alumina [lo] in the range IOOO-1600°C were extrapolated to calculate AF for this reaction. Below 915°C AF is negative by a few kcal, but no evidence has been found by us that this reaction (or the reverse one) takes place [Ill. In fact, samples of single phase ,f?“-alumina in contact with sodium at 400°C for several weeks were not darkened and suffered no change in strength, composition or conductivity [12]. 3. Experimental A. Model TEG The apparatus used to test electrode behavior is shown in Fig. 4. The first objective was to study materials and electrodes so no attempt was made to minimize heat losses or circulate sodium. The ,W-alumina membrane was in the form of a thin walled tube, 6 mm OD, 14 cm long with an 0.88 mm wall thickness. The tube was sealed with glass to an alumina reservoir. The reason for choosing a long tube was to avoid the problem of making a high temperature sodium resistant seal. Three stainless steel wells were sealed into the top of the reservoir for thermocouples and a heater. The cell was filled with sodium through a copper tube which was pinched off to seal the cell. The porous electrode covered a 2 cm length of the ceramic tube remote from the seal. The heater, a platinum coil in a small alumina tube, was designed to produce high uniform temperatures along the section near the porous electrode and temperatures below about 300” at the glass seal. Temperatures along the axis of the tube were measured by sliding a close fitting thermocouple along the steel well. The profiles so obtained are shown in Fig. 5. The current collector for the porous electrode consisted of a molybdenum ‘hose clamp’, two strips of 5 mm molybdenum sheet spot welded to the clamp and a

Current And 7 Voltage Leads Current -Collector

A1203

l/2 NaAlOs + 7/50 Al.

II II!_

Alumina Reservoir -

Beta-alumina might be expected to react with sodium in the following way: 21/50 Na + l/25 Nas 0.8

Tube

?

Stainless Steel Masks

F. Stability of the solid electrolyte

1 /l+---Filling

Fig. 4. Model TEG for testing porous electrodes on 8” alumina solid electrolyte.

coil of 6 mm molybdenum wire wound around the ceramic tube over the strips. The walls of the vacuum chamber served as the sodium condenser. Vacuum was maintained below 5 x 10-s torr. Current was withdrawn from the cell from the copper filling tube and a molybdenum wire on the current collector clamp. Cell potential was measured between an insulated molybdenum wire making contact to the bottom of one of the steel wells and a second molybdenum wire on the clamp. B. Electrode preparation The following are some of the materials and methods that were used to prepare porous electrodes: Graphite from an aerosol spray; gold, silver and platinum from resinate solutions fired in air; molybdenum from an oxide paste reduced in hydrogen; sintered nickel powder; molybdenum from decomposition of the hexacarbonyl. In every case the electrode was put on a freshly gritblasted surface of the ceramic to improve contact area and adherance and to remove any passive layer which may form on exposure to moisture. The molybdenum electrode prepared from the hexacarbonyl could be conveniently applied incrementally without removing the cell from the vacuum system. Molybdenum carbonyl vapor from a plating generator was lead in through a tube terminating in a six element nozzle facing the ceramic tube. By heating the tube above 300°C while pumping, bright metal films were deposited. Masks of stainless steel foil prevented deposition on the tube except where desired. The optimum electrode thicknesses were achieved empirically by measuring electrical output after each small increment

NEILL WEBER

ELECTRODE

100

I 0

I 2

I 4

*

I

I 8

6 LENGTH

I

1

IO

12

I 14

I 16

IS

(cm).

temperature variation in model TEG for several electrode temperature settings.

of deposited metal. Because of a small component of electronic conductivity in the ceramic (discussed more fully in a subsequent section) it was necessary to put a potential of I.5 V (sodium negative) on the cell during the plating operation to suppress any leakage current of sodium which tends to spoil the molybdenum plate. Electrode 1 was prepared with a substrate temperature of 500°C and a CO + CO2 pressure between 1O-2 and 10m3 torr. For electrode 2 the pressure range was the same but the temperature was 300°C. C. Results and discussion Detailed results are given for only the carbonyl molybdenum electrode, since this was the best in terms of stability and electrical performance. The gold, silver and platinum electrodes were all initially promising, but after passing current for several minutes originally adherent films of these metals became flaky and easily detached. The cause of the deterioration was not identified, but compound formation with sodium may have played a role. The graphite electrode was quite good but appeared to undergo small changes on thermal cycling making characterization difficult. All of the rest of the electrodes tested gave extremely poor performance probably because of small effective contact area. The carbonyl molybdenum electrodes were very stable. As judged from current-voltage data and visual inspection, exposure of the electrode to sodium vapor at temperature up to 8OO”C, thermal cycling between 25 and 8OO”C,and exposure to air between runs caused no deterioration. The performance of the molybdenum electrodes number 1 and number 2 were assessed from E vs log i curves plotted from data obtained by discharging the TEG through a decade resistor box. At low currents where most of the polarization ought to vanish, these curves were expected to approach the lines E=A-Blogi. In order to observe this effect it was necessary to take

into account the electronic conductivity of the ceramic so as to compute the actual ion current in the membrane. The electronic conductivity was deduced from E vs i curves following the method of Wagner as applied, for example, by Whittingham and Huggins to the measurement of the electronic conductivity of silver betaalumina [13]. The conductivity ae was calculated from the current plateau using the expression ue = imf/RT

(24)

where i and m are plateau current density and sample thickness. A typical experimental E vs i curve is shown in Fig. 6 together with the calculated evaporation current. The variation of me with temperature is shown in Fig. 7. At 550” equilibrium of the ceramic with sodium takes several hours and the departure of the -4, T =700°C

-3 t

ELECTRONIC CURRENT

CALC. AND

.6

.6

1.0

1.2

1.4

POTENTIAL

1.6

FROM

E=A- Bkq i

AREA

295

cm2

1.6

2.0

2.2

2.4

(VOLTS)

Fig. 6. Measured current and calculated evaporation current vs potential.

A Thermoelectric Device Based on Beta-Alumina Solid Electrolyte -2

-?

of the load current and the electronic current. The curves generally approach the lines E = A - B log i at low current densities which suggests that at least the linear coefficient in the relation for the pressure drop over the electrode (Equation 11) and the voltage drop from radiation cooling (Equation 21) were not large. The same data were used to calculate the polarization 7 defined by the relation

,-

I-

7 = A - B log i - iR, - E

-E i

I

-7 ,L 0.S1

(25)

where Re is the surface resistivity of the ceramic obtained with a similar specimen in a separate experiment [14]. Curves of T,-vs i are shown in Fig. 9. An analysis of the current and temperature dependence of 7 clearly is not possible from these data alone. Of possible significance is the fact that the curves are concave to the current axis which is at least the

I’ 5

7

\

SILVER ~-ALu~~INA SINGLE CRYSTAL Whittingham Et Huggins

\,

I

I

I

I

I

I

1.0

I.1

1.2 m

1.3

1.4

I.5

4,

1.6

TOK

Fig. 7. Variation of electronic conductivity with temperature.

curve from linearity below 450°C may reflect failure to reach equilibrium. Coincident with the appearance of electronic conductivity and presumably associated with it is a gray coloration of the ceramic. As indicated in Fig. 5, a sharp boundary was found axially between white and dark exterior portions of the tube after the porous electrode was exercised 18 hr at 600°C 14 hr at 7OO”C,and l-3 hr at 805°C. In spite of the darkening of the ceramic there was no visual sign of mechanical deterioration. Curves of E vs log i at several temperatures are shown in Fig. 8 where i was computed as the sum

0

.I

.2

.3

I

I

I

I

I

I

.4

.5

.6

.7

.6

.9

CURRENT

DENSITY

amp

1.0

cni’

Fig. 9. Polarization voltage 7 vs corrected current density for electrode number 1. 2.c

805 oc 805°C

1.8 I.6 c; 3B

1.4

w

1.2

602OC

: 2

I.0

V j

MOLYBDENUM ELECTRODE

0.8

# 2

E

0.6 MOLYBDENUM ELECTRODE

01 0

I -I

I

I -2

-3

log CURRENT

I -4

I -5

DENSITY

iy

I

I -6

I -7

-8

amp cni2

Fig. 8. TEG voltage vs log corrected current density for electrode number 1.

o!.

U

I

-1

.

I

I

-2

_

109 CURRENT

-3

-

I -4

DENSITY

I -5 amp

I -6

-7

cm2

Fig. 10. TEG voltage vs log corrected current density for electrode number 2.

NJZLL WJSBER

8

over a wide spectral range. A practical design might therefore simply permit the porous electrode with an emissivity of perhaps O-1 to look directly at the condenser wetted with a layer of liquid sodium. The calculated radiation losses to the condenser at 200°C for 805°C E the limiting cases of infinite parallel planes or long F concentric cylinders with one specularly reflecting 2 .MOLYBDENUM n ELECTRODE # 2 surface are: 7OO”C-0*080 W/cm2, 800”C--0~123 W/cm2, 4 0.1 9OO”C-0.178 W/cm2. The electrical output leads give :: rise to both heat and electrical power losses which can be minimized by increasing output voltage at a 7) COOLING 805 oc ______------given power level. Connecting three or four cells in ___ _--I I I I 0 I series at the high temperature to give an output of .6 1.0 .7 ,S .4 .6 .3 .5 .2 0 .I CURRENT DENSITY amp cni2 2.0 V, for example, results in a calculated thermal efficiency of 23.9 per cent when the efficiency with no Fig. 11. Polarization voltage 7 vs correctedcurrent density for electrode number 2. lead loss is assumed to be 25 per cent. Thermal loss along the sodium return tube can be small because of the heat pumping action of the moving liquid. The form required by Equation (16), and the observation actual magnitude depends on whether this element that the temperature dependence of r) becomes small also functions as a mechanical support for the ceramic in the same temperature range where the ceramic membrane structure. resistivity is nearly independent of temperature. In On the basis of these considerations and the enFigs. 10 and 11 are shown results with electrode number couraging results obtained with the porous electrode, 2 prepared under conditions which are reported to further effort on the construction of a working device favor smaller grain size of the deposited metal 1151. appears to be justified. The utility of such a device, Shown as a dashed line in Fig. 11 is an estimate of the however, depends largely on the very long term durability contribution to the polarization from current and of the solid electrolyte in sodium or sodium vapor at radiation cooling at 805°C using Equation (21). For high temperature about which little is known. this calculation Ro was chosen equal to Re, the ceramic resistance, and the emissivity of the electrode was Acknowledgements-The author wishesto thank Joseph Kummer, taken to be 0.1. At 805°C this electrode delivered O-50 who conceived the idea for this device, for his valuable counsel, W/cm2 maximum power at 0.50 V with an overall He is indebted to Roger Saillant for suggesting the chemical vapor decomposition method for preparing electrodes; to Terry Cole, thermal efficiency for the electrode-electrolyte processes Max Bettman. and Robert Minck for manv helnful discussions of 28 per cent, Further study relating plating conditions and to Gerald’ Tennenhouse and Frank Ruikle for supplying the and electrode morphology to electrical performance may ceramic tubes. lead to slightly better performance. References 4. Other Aspects of Device Design Sources of inefficiency other than the electrode and solid electrolyte are considered for the design of a practical device. Since the cell used for electrode testing was not suitable for measurement of thermal losses, some of these were estimated using available data and tentative design parameters. Heat conduction loss through the vapor on the condenser side of the membrane, assuming residual gas pressure can be kept low, is negligible. This is so because the mean free path in saturated sodium vapor at 200°C is already 19 mm. A substantial leakage of heat from the high temperature occurs by radiation from the porous electrode to the condenser. Since the radiant flux and the sodium atom flux are in parallel, radiation shielding will be almost equally effective in reducing electrical current as thermal loss. The atom flux is analogous to blackbody radiation since the reflectivity of all surfaces is zero. Fortunately, the optical reflectivity of liquid sodium calculated from the Drude equation is greater than 98 per cent at 200°C

[l] J. T. Kummer and Neil1 Weber, Trans. S.A.E. 76, 1003-1007 (1968). [2] J. L. Sudworth and M. D. Hames, Power Sources 3, p. 227, edited by D. H. Collins. Oriel Press, Newcastle upon Tyne _ _ (1970). [3] L. J. Miles and I. Wynn Jones, Op. Cit. ref. 2, p. 245. 141 J. T. Kummer and N. Weber. U.S. Patent 3.458.356 11968). I I ~ II - Assigned to Ford Motor Company. [S] E. L. Dunning, Argonne National Laboratory Report 6246, Office of Technical Services, U.S. Department of Commerce, Washington (1960). [6] I. Langmuir, Phys. Rev. 2, 329 (1913). [7] D. 0. Raleigh, Preprint SC-PP-70-120, Science Center, North American Rockwell Corporation, Thousand Oaks, California. [8] R. J. Ruka, J. E. Bauerle and L. Dykstra, J. Electrochem. Sot. 115,497 (1968). [9] Karl H. Sandmeyer and William A. Miller, Am. Ceram. Sot. Bull. 44, 5414 (1965). [IO] J. T. Kummer, Progress in Solid State Chemistry, Vol. 7, p. 146, edited by J. 0. McCaldin. Pergamon Press, New York (1972). 11l] M. Bettman, Scientific Research Staff, Ford Motor Company, Dearborn, Michigan, unpublished results. 1121 G. Tennenhouse. ibid. Reference 11, umublished results. i13j M. Stanley Whiftingham and Robe& A. Huggins, J. Electrothem. Sot. 118, 1 (1971). [14] J. T. Kummer, op. cit. p. 172. [15] J. J. Lander and L. H. Germer, Metals Technology 14, pp. 42 (No. 6). Tech. Pub]. 2259 (1947).