Electrochemical thermometry: A new approach to the determination of elevated temperatures on the thermodynamic scale

Elechochimica

Acta. 1968, Vol. 13, pp. 1867 to 1874.

Peroamon Press. Printed in Northern Ireland

ELECTROCHEMICAL THERMOMETRY: A NEW APPROACH TO THE DETERMINATION OF ELEVATED TEMPERATURES ON THE THERMODYNAMIC SCALE* W. T. LINDSAY,Jr. and R. J. RUKA Westinghouse

Research Laboratories,

Pittsburgh,

Pennsylvania

15235, U.S.A.

Abstract-A high temperature, solid-electrolyte, oxygen-concentration cell is proposed as a means for determination of high fixed-point temperatures, such as the melting points of silver, gold and palladium, on the thermodynamic scale. An analysis of possible sources of errors in gold-point determinations indicates that the method is potentially comparable in accuracy to high temperature gas thermometry. Preliminary experiments gave results within a few degrees of the accepted values for the silver and gold points. It is believed that more refined measurements can be of considerable value as independent checks on important elevated fixed-point temperatures. R&sun&-Proposition, en vue de la determination de points fixes a haute temperature, dans l%chelle thermodynamique (tels que les points de fusion de l’argent, I’or ou le palladium) dune cellule de temperature &levee solide-electrolyte a concentration d’oxygene. Une analyse des sources d’erreurs possibles dam les determinations du point d’or indiqueque la m&hodeestpotentiellementcomparable, du point de vue de la precision, a la thermometric gazeuse a temperature elevee. Des experiences preliminaires ont don& des resultats en accord, a quelques degres pres, avec les valeurs admises pour les points argent et or. L’on conclut done que des mesures plus raffinees foumiraient ainsi des controles independants pour certains points fixes, particulibrement importants a haute temperature. Zusannnenfassung-Man schlagt eine Hochtemperatur-Sauerstoffkonzentrationszelle mit festem Elektrolyt vor, welche dazu dienen ~011,hohe Fixpunkttemperaturen, wie Schmelzpunkte von Silber, Gold und Palladium, in der thermodynamischen Temperaturskala zu bestimmen. Eine Untersuchung der miiglichen Fehlerquellen in der Schmelzpunktsbestimmung von Gold zeigt, dass die Genauigkeit dieser Methode mit derjenigen von Hochtemperatur-Gasthermometem vergleichbar ist. Vorversuche ergaben Resultate, welche wenige Grade von den ftir Silber und Gold angenommenen Werten abwichen. Wir glauben, dass dieses Messverfahren in verfeinerter Form betrachtliche Bedeutung als unabhiingige Priifmethode fiir hohere Fixpunkttemperaturen erlangen konnte. INTRODUCTION

temperature gas thermometry has so far been the only satisfactory means for determination of elevated fixed-point temperatures on the thermodynamic scale.14 The experimental difficulties of this method are great, and it is important to consider alternative methods that may possibly give results of comparable accuracy. It is the purpose of this paper to present and discuss an alternative method, electrochemical thermometry, that appears to have considerable potential feasibility. We first give an analysis of various sources of error that may be encountered in electrochemical thermometry under idealized conditions. Preliminary experiments, employing a less ideal arrangement of apparatus, are then described. HIGH

THEORETICAL

CONSIDERATIONS

Consider a high temperature galvanic cell of the type M, OZ(pl atm)/Solid Oxide/O&,

atm), M

where M may be platinum or some other suitable metal, and the solid oxide lattice * Manuscript received 23 October 1967. 1867

1868

W. T. LINDSAYand R. J. RUKA

contains oxide-ion vacancies, as, for example, ZrO, with small additions of a stable, lower valency oxide, such as Y,Oa or CaO. Assuming that the electronic conductivity can be neglected, the isothermal emf of the cell will be given by E = (RT/@? ln (filfi>,

(1)

where T is temperature on the thermodynamic scale, R is the gas constant, F is the Faraday and fi and fiare oxygen fugacities at pressures pi and p2. Weissbart and Electrode r connexions I

?

Pressure connexion tube i/4” i.d. Oxygen pressure p, 4

I-----

1’l-I

FIG. 1. Ideal electrochemical

cell for thermometry.

Rukas have investigated the use of this cell as an oxygen gauge. Conversely, if the oxygen fugacity ratio can be fixed or measured satisfactorily, the cell emf will be directly proportional to the temperature T on the thermodynamic scale. Mobius6 reported that temperatures up to at least 1400°C can be measured using a cell with an analogous zirconia-based electrolyte, but with CO-CO, or Hz-H,0 gas mixtures at the electrodes. We believe it is preferable to make use of pure oxygen gas at different partial pressures for precision measurements. A suitable cell for fixed-point temperature determinations would be similar to the idealized cell illustrated by Fig. 1. The electrolyte would consist of a small oxide disk or wafer sealed as a vacuum-tight plug in a short tube of a material that is an electrical insulator. Porous noble metal electrodes, with annealed high-purity lead wires of the same metal, would be applied to a central area on each circular face of the electrolyte. Connexion tubes for gas-pressure measurement would be joined to the cell in as symmetrical a manner as possible, giving the over-all configuration of a U-tube suitable for immersion in a crucible of molten metal. The vertical arms would be long enough to pass entirely out of the furnace for connexion to an external vacuum system and an accurate manometer. Although there are technical problems in construction of a cell exactly matching this description, it is certainly possible to devise a number of practical cell configurations that will approximate the several requirements. In the idealized cell, a principal limitation will arise from measurement of the oxygen-pressure ratio. Non-canceling

1869

Electrochemical thermometry

thermal emf contributions to the cell emf should be small in a well-designed experiment. Errors caused by electronic conduction in the electrolyte can be minimized by measuring the electronic transference number and applying a correction to the cell emf. Relatively negligible errors will arise from thermal transpiration, gas imperfection, gaseous impurities and electrical measurements. Considering all sources of error, it appears to us that careful work with a welldesigned cell should lead to determination of the thermodynamic temperature of the gold point to an accuracy of &0*15”K or better, comparable to accuracies now claimed for gold-point determinations by gas thermometry.2 The following paragraphs discuss the sources of error in more detail. Pressure-ratio measurement

It is desired to determine the value of the pressure ratio that will minimize the maximum fractional error in In (p&d for a given absolute error Ap in the measurement of both p1 and pz. This calculation is simply carried out and gives an optimum 7

I

I

I

I

,o 6-A

*iI

I

I

I

I

I

For ~2, 760 torr Optimum Pl 212 torr Em:, 27.6 pV/OK

1I

2I

3III ’ 4 Pressure

5I 6I ratio p2/4

7I

3I

FIG. 2. Relation of maximum fractional error in In @&) measurement of both ps and pl.

9I

10

to absolute error Ap in

pressure ratio pe/pl = 3.59. Figure 2 shows how the ratio of the maximum fractional error in In (pJp3 to Ap/p2 varies with the pressure ratio. At the optimum ratio, the maximum fractional error in In (pJpJ is 3.59 Ap/p%. Taking pa to be the higher pressure and equal to 760 torr, p1 would be 212 torr. With these pressures, the maximuin temperature error AT, caused by an error Ap torr in the pressure measurement is given by AT, = 4.72 x WTAp, (2) where T is the absolute temperature. Although ordinary manometric measurements are seldom better than f0.1 torr in this pressure range, several manometers capable of precisions on the order of fO-003 torr have been described.‘-” With care in the pressure measurements, and taking into account also the benefits to be derived from statistical treatment of replicate measurements (values of AT, are maximum errors),

1870

W. T. LINDSAYand R. J. RUKA

it seems reasonable to expect that this contribution to error can be held to well below O*l”K at the gold point. Thermal transpiration

The pressures are measured by a manometer at room temperature, but the pressures determining the cell emf are those at the electrodes. The correction for thermal transpiration is small, however, with $/in i.d. gas connexion-tubes and a gas pressure of at least 212 torr. In this case the ratio of mean-free-path to tube diameter is about 6-5 x 10m5 at the gold point. The correction can be estimated from the LosFergussonlO modification of the WebeP equation. It is about 0$X)3 torr at the gold point. Even if the calculated correction is uncertain by 50%, the contribution to error in temperature will be only about O*Ol”K. Gas imperfection

The fugacity ratio is related to the pressure ratio by

In CfiltJ = In (p2/p1) + BpCp2 - pl) + %

(pz2 - p?) + . . . ,

where BP and Cr, are the second and third virial coefficients. (l), it can be shown that

-4np -1 T

By combination

B ~Pz-PP1)+C,(P2-PlYt ’ In (P~PJ

2

In (p2M

” ”

(3) with

(4)

where AT&, is the correction that must be applied to the temperatures calculated if f2/f1 were equal to p2/p1. For the pressures selected above, this becomes

wm,= -T

057Bp + 0*36C,.

Since BP for oxygen is of the order of +3 x IO4 at 103“K, and C, is lo-‘, the correction is about -0.17” at the gold point. The second virial coefficients are fairly well known, however, and the error in this correction should be less than 0.02”C. Gas composition

The method depends on total pressure measurement; it is therefore important that the gas on each side of the cell be high purity oxygen. No difficulty should be experienced with total pressures on the order of several hundred torr, if modern high vacuum techniques and bakeable components are employed. Ultra-high purity oxygen can be added to the vacuum system by an electrolytic technique employing an auxiliary oxide solid electrolyte cell and furnace. With these precautions, it should be possible to maintain total gaseous impurities at or below the 1 ppm level, with negligible resultant effect on the measurements. Electrical measurements

The optimum pressure ratio of 3.59 will give an emf of 27.6 pVI”K, or about 36.9 mV at the gold point. There are commercially available a number of precision potentiometers accurate to O-1pV or better. An error of O-1,DVcorresponds to about

Electrochemicalthermometry

1871

OW4”K; consequently the limitations of the electrical measurements equipment should not impose serious limitations on the method. The effect of thermal and stray emfs cannot be neglected when attempting potentiometric measurements to 0.1 ,uV. An important advantage of the electrochemical thermometry method is that the sign of the cell emf can be reversed by interchanging pressures p1 and pz. This exchange will not affect strays and most thermal emfs (see below, however), and their contributions will be cancelled by averaging successive potential measurements with inverted pressure ratios. Thermogalvanic

emf

A thermogalvanic emf will arise if the cell, including both electrodes, is not completely isothermal. Bauerle and Ruka12 have measured thermogalvanic emfs in oxygen-containing atmospheres for Zr,,.85C~.160185. Their measurements indicate that a temperature difference between electrodes of O.Ol”C will produce an emf in 1 atm oxygen of 4-3-4.5 ,LJVin the neighbourhood of lOOO”C,with a small temperature dependence. This would correspond to an error of about 0.17”C in the measurement of temperature, if the pressure ratio is 3.59. This effect must therefore be considered carefully. It may be noted first that any thermal gradients in the cell that are due to lack of structural or spatial symmetry will not be affected by interchange of gas pressures p1 andp,. The reversal stratagem suggested above for elimination of stray and thermal emfs will also be applicable to these contributions to the temperature gradient and thermogalvanic emf. However, any contributions to the temperature gradient that are due to difirences in heat flow via the gas in the connecting tubes will reverse in sign along with the cell emf and will not be cancelled. Fortunately, radiative and conductive heat flow through the gas are not pressure-sensitive in the range of pressures we are considering; only convection will be affected. The U-tube cell configuration minimizes heat loss from the electrodes by convective processes. However, the possible presence of a non-canceling thermal emf should be investigated in any cell design. Electronic conductivity

in the electrolyte

The net emf E of a galvanic cell with mixed ionic and electronic conductivity

in

the electrolyte is given by E = E,(l -

t3,

(6)

where E,, is the theoretical emf in the absence of electronic conductivity, and t, is the electronic transference number.13 Values of t, equal to or less than 5 x 1O-3 have been reported for Zros5Cao1.&.s5’ 14*15 It is possible to devise methods for open-circuit oxygen transference measurement, with electrode pressures similar to those used in temperature measurement, that will yield values oft, accurate to 10e5. If such a measurement were made with the same cell used for thermometry, the uncertainty in measurement of temperature would be on the order of @Ol”K at the gold point. EXPERIMENTAL

TECHNIQUE

Apparatus

Exploratory experiments made use of the arrangement depicted in Fig. 3. A commercial, nuclear-grade Zr,.,5Ca,.,,0,.,5 tube,* 24 in long x 2 in o.d. x &in * Zirconium Corporation of America. 8

1872

W. T. LINDSAYand R. J. RUIU -Platinum

sheet

umlna thermocouple

Electrode and thermocouple

FIG.3. Apparatus for preliminary electrochemical thermometry experiments.

wall, was suspended concentrically within a 1-a in o.d. Vycor tube. A central region about 1 in long was delineated by two stabilized zirconia bushings acting as internal radiation shields. A l-cm2 porous platinum electrode was fned on the inside of the zirconia tube in this central region, using Hanovia platinum paste,* and a similar second electrode was placed at the same location but on the outside of the tube. Thermocouples (Pt-Pt-10 % Rh) were attached to each of the electrodes. The thermocouples were calibrated against the laboratory standard thermocouple at 96O@C and 1063~0°Cbefore use and again on completion of the experiments, with negligible change of calibration. The central part of the Vycor tube was wrapped externally with platinum sheet to provide shielding and contribute to temperature uniformity, and the entire assembly was centred in a tubular electric furnace with additional radiation shields at each of the projecting tube ends. Cell emfs and thermocouple emfs were measured with a Rubicon Type B-High Precision potentiometer and Eppley standard cell, both of which had recently been calibrated. A selector switch was wired so that an emf of either sign could be measured between any pair of wires, whether platinum or platinum-rhodium. Furnace temperatures were regulated to a constancy of about fO*OYC over periods of time up to 1 h or more by using an auxiliary thermocouple and Leeds $ Northrup Type K-2 potentiometer, with a sensitive galvanometer and photocell controlling a magnetic amplifier and saturable core reactor. However, as expected, temperature uniformity was somewhat less satisfactory than temperature constancy; the thermocouples at the electrodes generally indicated temperatures on opposite sides of the zirconia tube wall differing by 0%l*O”C. Procedure

Arrangements were made for slowly drawing pure oxygen gas or air, dried and CO,-free, through either the inside of the zirconia tube or the annular space between the zirconia tube and the Vycor tube. Measurements were made with the following combinations of gases : air-air, air-oxygen, oxygen-oxygen, and oxygen-air. With slow, steady flow of gases, the temperature was first established so that the average of the two thermocouple readings was as close as possible to either the gold point or silver point. The cell emf was measured several times. Then the gas flows were interrupted, and the final cell emfs were recorded a few seconds later to allow decay * Englehard Industries

Ekctrochemical thermotnetry

1873

of pressure and temperature gradients. The values of emf so obtained were in general slightly different from the steady-state values with flowing gas. A slow decline of cell emf was observed at longer times after interruption of flow, probably as a result of back diffusion and intermixing of the gases. The simple averages of emfs obtained from a number of runs with air-oxygen and oxygen-air were used to calculate the

T('K)= 3&w9 where E,,is the emf averaged as described above, and the relation holds for a cell with CO,-free air on one side and pure oxygen gas at the same total pressure on the other side. RESULTS The results are given in Table 1. It is seen that the temperatures indicated by the cell were about two degrees lower than the International Practical Temperature TABLE

1. RESULTSOF PRELIMINARY EXPERIMENTS

A. Average cell emf, PV B. Temperature indicated by cell, “K

Silver point (960*8”C*)

Gold point (1063~c*)

41,485 (4 ~11s) 1232.2

44,913 (5 runs) 1334.0 (1060*8”C)

C. Average thermocouple temperature, “C D. Deviation, “C * International Practical Temperature Scale values

Scale values. Note, however, that the fixed-point temperatures adopted for the International Practical Temperature Scale are not necessarily correct. Recent gas thermometry results summarized by Mose? indicate temperatures of about 961.9”C for the silver point and 1064.5”C for the gold point, which would increase the deviations to -2*95”C and - 3~8°C respectively. Nevertheless, the deviations are surprisingly small in view of the non-optimum experimental configuration. The neglect of corrections for electronic conductivity and any effects of gas intermixing should both cause the cell result to be too low. CONCLUSIONS The analysis of possible sources of error indicates that solid-oxide electrochemical thermometry is potentially comparable to high temperature gas thermometry for accurate determination of elevated fixed-point temperatures on the thermodynamic scale. Our preliminary experiments do not disclose any unexpected sources of error

1874

W. T. LINDSAY

R. J.

that would be applicable to a cell with static pressures of pure oxygen. These experiments are also of value in demonstrating the advantages of sign-reversal averaging procedures in cancellation of thermogalvanic contributions to the cell emf. With careful experimentation, it is possible that electrochemical thermometry may be a relatively simple method for determination of the higher tied-point temperatures, up to the palladium melting point. Serious consideration should be given to development of electrochemical thermometry to its full potential. Particular attention should be given to the solution of the technological problems of cell construction, to the evaluation of non-canceling contributions to the thermogalvanic emf, and to the determination of electronic conductivities of ultra-high-purity mixed-oxide electrolytes. Acknowledgement-The work.

authors are indebted to T. S. Bulischeck for assistance with the experimental REFERENCES

1. H. T. WENSEL,in Temperature. Its Measurement and Control in Science and Industry, p. 3. Reinhold, New York (1941). 2. H. MOSER, in Temperature. Its Measurement and Control in Science and Industry, Vol. III, Part 1, p. 167. Reinhold, New York (1962). 3. I. I. KMNKOV, A. N. GORDOV, K. S. ISRAILOV and U. V. DNKOV, in Temperature. Zts Measurement and Control in Science and Industry, Vol. III, Part 1, p. 147. Reinhold, New York (1962). 4. J. OISHI, M. AWANO and T. MOCHIZUKI, J.phys. Sot. Japan 11, 311 (1956). 5. J. WEJSSBART and R. J. RUKA, Rev. scient. Znstrum. 32, 593 (1961). 6. H. H. MOB~JS,2. Chemie Lpz. 2,63 (1961). 7. H. MOSER,J. OTTOand W. THOMAS, Z. Phys. 147, 59,76 (1957). 8. L. A. GUILDNER,in Temperature. Its Measurement and Control in Science and Industry, Vol. III, Part 1, p. 151. Reinhold, New York (1962). 9. H. F. STIMSON, in Precision Measurement and Calibration, Vol. II, p. 40. U.S. National Bureau of Standards, Handbook 77 (1961). 10. J. M. Los and R. R. FERGUS~~N,Trans. Faraday Sot. 48,730 (1952). 11. S. WEBERand G. SCHMIDT,Communs. Kammerlingh Onnes Lab., Univ. Leiden Suppl. 22, No. 246C (1936). 12. J. E. BA~JERLE and R. J. RUKA, J. electrochem. Sot. 115,497 (1968). 13. C. WAGNER,Proc. 7th Meeting of CZTCE, p. 361, 376. Buttenvorths, London (1957). 14. D. T. BRAYand U. MERTEN,J. electrochem. Sot. 111,447 (1964). 15. J. WEISSBART and R. J. RUKA, Paper presented at the Electrochemical Society Fall Meeting, Detroit, Mich., 1961. Extended Abstract No. 44, Battery Division (1961). 16. E. GLUEKAUF,in Compendium of Meteorology, ed. T. F. MALONE,p. 3. American Meteorological Society, Boston (1951).