The thermal conductivity of alkaline earth oxides

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BRIT. J. APPL. PHYS., 1963, VOL. 14

The thermal conductivity of alkaline earth oxides

N. A. SURPLICE and R. P. JONES Department of Physics, University of Keele, Staffs. MS. received 25rh June 1963

The comparative thermal conductivities of sintered powders of alkaline earth oxides have been measured in vacuum over the range of temperatures 450-72O"c. The thermal con- ductivities of MgO, CaO, SrO and (BaSr)O were between 0.3 x and 2 .5 x IO-s cal sec-' cm-' degc-', but the thermal conductivity of BaO was at least four times as great, i.e. 8 x 10-s-ll .5 x I O p 5 cal sec-' cm-' degc-'. Possible reasons for this anomaly are discussed; the most likely reason seems to be some difference in the physical structure of the sintered barium oxide.

1. Introduction

There have been many determinations of the thermal conduc- tivity of magnesia (Goldsmith, Watermann and Wirshhorn, 1961, p. 160) but only a few of the thermal conductivities of the other alkaline earth oxides. Kingery and Franc1 (1954) used a comparative method to measure the thermal conduc- tivity of compressed rods of calcium oxide. Weston (1950) and Pengelly (1955) both modified Lee's disk apparatus for use with mixed barium and strontium oxides (BaSr)O, and Pengelly also made measurements on two samples of barium oxide and one of strontium oxide between nicke! disks. Zingermann (1956) used cylindrical cathodes of mixed oxides, (BaSr)O, and measured their thermal conductivity between two helical probes which were embedded in the oxide. The results of Weston for (BaSr)O were almost a factor of ten lower than those of Pengelly and Zingermann. Pengelly found that at 700" c the thermal conductivities of the oxides BaO and SrO were in the ratio 5 :4.

The need for further measurements became apparent during a series of observations of the thermoelectric power of alkaline earth oxides. When one side of a rectangular sample of barium oxide was heated to 725' c then the other side attained a temperature of 625'c, but when a sample of strontium oxide of the same shape and size was similarly heated on one side to 725" c then its other side only reached a temperature of 475' c. This indicated a much greater difference between the thermal conductivity of these two oxides than had been reported previously.

2. Apparatus

The experimental valves had been designed for a study of the thermoelectric power of alkaline earth oxides, but they were also quite easy to use for comparative measurements of their thermal conductivities because all the tubes were iden- tical in their geometrical construction. Each sample of oxide was made from two rectangular cathodes pressed tightly together by light tungsten springs to form a sandwich of carbonate between the metal cores. The cores had previously been cleaned by heating them in vacuum to 1250' C for 15 minutes. The oxide was formed from the carbonate by heating in a vacuum, and the experimental tube was baked and sealed off in the usual way. The final dimensions of the oxide sandwich were 10 mm x 3 mm x 0.15 mm. A detailed account of its preparation has been given in a previous paper (Surplice and Jones 1963). A Pt-Pt/Rh thermocouple was spot-welded to the bare metal where the tip of each core had

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been held in the jig of the spraying machine. In some tubes both cores were made of platinum, in others they were both made of 0-nickel.

3. Method In the first stage of the measurements the equilibrium

temperatures of the cores T , and T, (T,>T,) were measured when only one heater was used and the other heater was switched off. In the second stage of the measurements both heaters were switched on and the power W supplied to each one was varied until both cores reached T2 as their equilibrium temperature. The effective thermal conductance of the sandwich was therefore given by k = W/(Tl - T,) at a mean temperature T. These measurements were repeated for a series of values of T I and T2 down to a mean temperature of about 450" c. Below about 450" c the results became unreliable because of the technical difficulty of measuring the quantities T , - T2 and W with sufficient accuracy with the apparatus available.

Table 1,

T r c ) 700 629 559 492 402

Typical results: barium oxide between platinum cores.

TI - I2 (degc) 113 93 71 60 45 W (mw) 1125 875 682 522 357 k(mwdegc-1) 10.0 9 . 4 9 . 6 8 . 7 7.9 K x 10s (cal sec-1 cm-ldegc-1) 11.9 11.2 11.3 10.3 9.4

Table 2.

TVC) 664 602 553 500 440

Typical results: strontium oxide between platinum cores.

Ti - T2 (degc) 270 252 227 200 172 780 630 570 490 420

k(mwdegc-1) 2.9 2 .5 2.5 2.45 2.4 W (mw)

K x 10s (cal sec-1 cm-ldegc- 1) 3.45 3 . 0 3.0 2.9 2.85

4. Results The thermal conductivity was determined for five sand-

wiches of barium oxide, four of strontium oxide, two of mixed barium and strontium oxides, two of calcium oxide and one of magnesium oxide. Typical results for barium oxide and strontium oxide are given in tables 1 and 2.

The results for all the tubes are shown graphically in figures 1 and 2. The conductivity K has been calculated from the conductance k on the assumption that the effective area and thickness of the conducting path through the oxide was the same as that of the cores. This is justifiable for purposes of

THE T H E R M A L C O N D U C T I V I T Y OF A L K A L I N E E A R T H OXIDES

comparison between the oxides, as also is the neglect of heat radiation between the bare ends of the metal cores. These graphs show clearly that the thermal conductivity of barium oxide was at least four times as great as that of any other of the oxide samples.

BaO

-o---o---o---o--o

Temperature ('Cl Figure 1. Thermal conductivities of sandwiches of oxide between platinum cores. 0, BaO, tube 3, with cold junctions of thermocouples at room temperature; z, BaO, tube 3, with tube cooled by air-blast, and cold junctions of thermocouples at 0"~; 0, BaO, tube 9; 7 , (BaSr)O, tube 2; x, SrO, tube 5 lower line, tube 11 upper line; A, CaO, tube 16; V, MgO,

tube 18.

w I 500 600 700

Temperoture ("0

c t-

Figure 2. Thermal conductivities of sandwiches of oxide between nickel cores. 0. BaO, tube 10; Z, BaO, tube 14 after ageing; 0, BaO, tube 14 before ageing; +, (BaSr)O, tube 8: X , SrO, tube I2lower line, tube 15 upper line; A, CaO, tube 17.

The results for any one sandwich were reproduced to within 3% when heat was conducted through it in the opposite direction, i.e. from anode to cathode. Similarly, they did not alter more than 3 % when the cold junctions of the thermo- couples were kept at ice temperature instead of air temperature and the glass envelope of the tube was cooled by a draught of forced air. These differences of 3 % were much less than the differences of thermal conductivity between samples of the Same oxide, which were about 10 % for barium oxide, and as high as a factor of three for strontium oxide. The thermal conductivity also changed when the oxides were aged for some months: typical changes were about 5 % for barium oxide and 20% for strontium oxide. Such large variations from sample to sample also occur with other properties of oxide cathodes because they are sintered porous powders and not single

crystals; they occur the more readily with strontium oxide because of its thermal decomposition at the normal working temperatures of about 700" c.

The combined effect of heat conduction along paths other than the crystals of oxide can conveniently be classed as a conductance k , in parallel with the conductance ko of the oxide. This gives a resultant k = ko k l which was measured in the experiments. The magnitude of the unwanted heat conductance through the mechanical supports for the cores was estimated from experiments with a special tube in which the cores were left bare and had an evacuated gap of 2 mm between them instead of the usual oxide. The results ob- tained with this tube showed that k , was only about 2 % of k for barium oxide and about 10% of k for strontium oxide.

There was no detectable difference in the amount of power radiated by sandwiches of different types of oxide. The power needed to keep both cores at a given temperature when both heaters were used did not vary any more between the different oxides than between different samples of the same oxide.

There was no long term change in the thermal conductivities of either barium oxide or strontium oxide between platinum cores at 700" c when a potential difference of 2 . 5 v was maintained across them for twelve hours. There was, how- ever, a rapid change of 5 % for barium oxide and 10% for mixed oxides in the sense of increasing the thermal conduc- tivity when the cooler core was positive with respect to the hotter one.

The 'thermoelectric figure of merit' a2cr/K was estimated for 1000c K using these results for K and values of a and G published previously (Surplice and Jones 1963) where a is the thermoelectric power, G the electrical conductivity and K the thermal conductivity. The mean results were 1 X degc-' for (BaSr)O, 0 .6 x degc-' for BaO.

5. Discussion The results given in tables 1 and 2 and in figures 1 and 2 are

of the same order of magnitude as those of Pengelly (1955) and Zingermann (1956), i.e. cal sec-' cm-' degc-'. Although they are not absolute measurements they are valid comparisons for the different oxides since all the sandwiches and their mechanical supports had the same dimensions.

In a series of chemically similar compounds the thermal conductivity usually decreases with increasing molecular weight. A review by Joffk (1956) implies that this is so for all compounds between elements of groups I1 and VI of the Periodic table, including alkaline earth oxides. However, there was the opposite trend among these alkaline earth oxides, and the sandwiches containing the heaviest oxide had by far the greatest thermal conductivity. This is an interest- ing anomaly, and some possible explanations of it are dis- cussed below. It does not appear to be due to any marked differences between the oxides in their absorption and scatter- ing of thermal radiation, nor to different amounts ofelectrcnic or ionic conductivity. It may be due to differences between the sizes and shapes of the tiny crystals that were sintered together in these oxide sandwiches.

Pengelly (1955) found that although the effective conduc- tivity of his barium oxide was 30% greater than that of his strontium oxide at 700" c nearly all of this increase was due to its having a much lower absorption and scattering coefficient for thermal radiation. In his experiments he used a thickness of 0.45 mm of oxide between nickel disks, and he estimated the thermal emissivity to be 0.8 for the interface layer between the oxide and the disk. He quoted the following equation

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degc-I for SrO and 0.1 X

T H E T H E R M A L C O N D U C T I V I T Y O F A L K A L I N E EARTH O X I D E S

from Saunders (1 928-9) for the heat H transferred by radiation between two plane parallel surfaces of area A and emissivity e, which are at temperatures T , and T2 respectively.

H = Au(Tl4 - T24) e2/(2e - e')

where U is Stefan's constant. By substituting in this equation the figures appropriate to his apparatus we find that when the hot disk was at 1000" K then the cool disk received only 1.9 w of heat by transport through the barium oxide, whereas it could have received 4.2 w by radiation if the gap between the disks had been evacuated.

However, in over half of our experiments the cores were of pure platinum and had been cleaned by heating in a vacuum prior to spraying with oxide. Their emissivity would be between 0.10 and 0.18 (Gray 1957, pp. 6-70) and the alkaline earth oxide was only 0.15 mm thick. Using these figures and table 1, we find that with the hot core at 1000" K when 1.125 w was transported through the barium oxide, only 0.1 w could have been radiated across the gap even if the oxide had been perfectly transparent to radiation; and using the appropriate figures for strontium oxide (table 2) we find that just over 0.15 w could be radiated through a non-absorber compared with 0.78 w which was transported through the oxide. All these figures inclxde the heat radiated between the bare ends of the platinum cores. Further evidence for the small proportion of radiation to conduction is provided by the shape of the curves in figures 1 and 2 which show that the apparent conductivity rose only slowly with the temperature. Again, all the oxide sandwiches appeared to radiate approximately the same amount of heat from their oxide coated outside surfaces since they all needed the same power, to within lo%, to keep their cores at the same equal temperatures.

The rapid changes in thermal conductivity which occurred in an electric field were approximately proportional to the electrical conductivities of the oxides, and the small size of these changes showed that there was only a moderate elec- tronic contribution to the transport of heat. The absence of slow changes showed that there was negligible ionic contribu- tion to the thermal conductivity.

Since barium oxide is the most readily sublimed of all the alkaline earth oxides some contribution to its thermal con- ductivity might come from molecules which sublimed near the hot core of the sandwich and then recrystallized near the cool core with release of their latent heat of sublimation. The oxide coating was not much depleted after a year's running at

700" c, so the rate of sublimation could not have exceeded 10-3g sec-', and this small quantity could account for only a negligible proportion of the observed rate of heat transport.

The physical structure of the oxide would be important in the process of heat transport from one core to the other, and although the original coatings of barium and strontium car- bonate had the same density (0.7g ~ m - ~ ) there might be marked differences between the sintered oxide powders which were produced by their subsequent pyrolysis in vacuum. Differences in the average size of the particles, in the distribu- tion of sizes about the mean, and particularly in the areas of contact between them are known to have a marked effect on the electrical properties of sintered powders (Hannay 1959, p. 543) and would have a similar effect on their thermal properties. It would be interesting to repeat these measure- ments on single crystals of barium and strontium oxides when they become available.

Acknowledgments The authors wish to thank Dr. G. H. Metson for many

helpful discussions, Mr. H. Batey for practical advice on the preparation of experimental tubes, Professor D. J. E. Ingram for laboratory facilities and the Admiralty (C.V.D.) for a contract which paid for one of their salaries (R.P.J.) and the necessary equipment.

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GRAY, D. E., 1957, American Institute of Physics Handbook (New York: McGraw-Hill).

HANKAY, N. B., 1959, Semiconductors (New York: Reinhold; London: Chapman and Hall).

JOFFE, A. F., 1956, Canad. J . Phys., 34, 1342. KIKGERY, W. D., and FRANCL, J., 1954, J. Amer. Cerani. Soc.,

PEKGELLY, A. E., 1955, Brit. J. Appl. Phys., 6, 18. SAUNDERS, A. O., 1928-9, Proc. Phys. Soc., 41, 569. SL-RPLICE, N. A., and JOUES, R. P., 1963, Brit. J. Appl. Phys.,

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