Positive temperature coefficient of electrical resistivity in some ZnOTiO2NiO ceramics

Solid-State

Electronics

Pergamon Press 1963. Vol. 6, pp. 111-120.

POSITIVE ELECTRICAL

Printed in Great Britain

TEMPERATURE COEFFICIENT OF RESISTIVITY IN SOME ZnO-TiO,-NiO CERAMICS R. H. PRY

General Electric (Received

and S. P. MITOFF

Research Laboratory,

18 October

Schenectady,

New York

1962; in revised form 15 November 1962)

Abstract-The electrical resistance as a function of temperature of a group of ceramics made from ZnO-TiOs-NiO powders are shown to exhibit an anomalously large positive temperature coefficient of resistivity in the temperature range of -50°C to 400°C. X-ray examinations show these materials to be a two-phase mixture of ZnO and ZnsTiO4 structures with NiO probably in solution in both phases in the composition range studied. No crystallographic transformations occurred, and it is unlikely that any ferroelectric or magnetic transitions occur in the temperature range in which the anomalous electrical properties exist. In order to more fully explore these phenomena, measurements have been made and are reported on the temperature dependence of the thermal e.m.f. and on the frequency and hydrostatic pressure dependence of the electrical resistivity. By variation of the temperature and the time of firing and the composition of these ceramics within the range studied, the resistivity at room temperature can be varied from a few R-cm to 10s Q-cm, and the maximum positive temperature coefficient of resistance can be varied from essentially zero to 2 per cent per “C. R&umB-On demontre que la resistance Clectrique en fonction de la temperature d’un groupe de ceramiques faits de poudres ZnO-TiOa-NiO produit un coefficient de resistivite eleve et irregulier dans la gamme de temperature de -50°C a 400°C. Des examens a rayons X demontrent que ces materiaux consistent en un melange biphase de structures de ZnO et Ti04Zns avec NiO, probablement en solution dans les deux phases de la composition Ctudiee. Aucune transformation cristallographique ne s’est produite et il est improbable que des transitions ferroelectriques ou magnetiques ne se soient produites dans la gamme de temperature oh ces propri&& electriques irregulieres existent. Pour pouvoir explorer plus profondement ce phenomene, des mesures ont CtCprises et repartees sur la dependence de la tension thermale et de la frequence en fonction de la temperature et sur la dependance de la resistivite electrique en fonction de la pression hydrostatique. En variant la temperature, le temps de commutation, et la composition de ces ceramiques dans la gamme sous etude, la resistivite a temperature ambiante peut &tre variee de quelques Q-cm a 10s R-cm, et le coefficient de resistance de temperature maximum positif peut Otre varie de pratiquement zero a 2 pour cent par “C. Zusammenfassung-Bei Untersuchung der Temperaturabhangigkeit des elektrischen Widerstandes von Keramiken aus ZnO-TiOs-NiO-Pulvern ergibt sich ein ungewohnlich grosser positiver Temperaturkoeffizient des Widerstandes in dem Bereich zwischen -50°C bis 400°C. Rontgenstrahluntersuchungen zeigen, dass diese Stoffe Zwei-Phasen-Gemische von ZnO- und ZnsTiO&trukturen sind, wobei, innerhalb des untersuchten Bereiches wahrscheinlich NiO in beiden Phasen gel&t ist. Kristallographische Umwandlungen fanden nicht statt, und das Auftreten ferro-elektrischer oder magnetischer Uberglnge innerhalb des Temperaturbereiches, in dem das anomale elektrische Verhalten besteht, ist nicht anzunehmen. Zur weiteren Klarung dieser Phiinomene unternahm man Messungen der Temperaturabhiingigkeit der thermoelektrischen Kraft und der Abhangigkeit des elektrischen Widerstandes von der Frequenz und dem hydrostatischen Druck. Durch Veranderung der Temperatur und Dauer des Brennprozesses und der Zusammensetzung 111

112

R.

H.

PRY

and S.

P. MITOFF

der Keramiken innerhalb des untersuchten Bereiches war es mcglich, den spezifischen Widerstand

zwischen wenigen R cm bis auf 10s !A cm zu variieren, wiihrend der maximale Temperaturkeoffizient des Widerstandes zwischen praktisch Null und zwei prozent pro “C lag. 1. INTRODUCTION

A SIGNIFICANT portion of the recent literature on electronic semiconduction in ionic compounds has been devoted to those materials exhibiting an anomalously large increase in electrical resistivity with increasing temperature. This has been brought about both because the compounds are useful for many electrical and electronic applications and because this increase in resistance is a physical phenomenon we do not yet understand. The purpose of this paper is to present experimental data on a ceramic material which has largely been ignored in seeking explanations for the above resistivity anomaly. No satisfactory explanation for the anomaly is presented. All other compounds reported to exhibit large increases in resistivity have been ferrimagnetic or ferroelectric, and the temperature region of the increase has been near the Neel or Curie temperature. The ceramic investigated here shows neither ferrimagnetism nor a high dielectric constant but does exhibit an anomalous resistivity increase. Therefore, theories based on temperature changes in dielectric constants or ferrimagnetic ordering apparently are not sufficient to explain all cases. SCHUSTERIUS(~) described a large range of ceramics, composed largely of ZnO and TiOs, that exhibit both negative and positive temperature coefficients of electrical resistivity. The positivetemperature-coefficient materials were unusual, but far more attention has recently been given to doped barium titanate ceramics@-7) than to the GO-based material. HEYWANG@~~)has proposed an explanation for the positive behavior in doped BaTiOs based on the postulate that an energy barrier exists at grain boundaries and that the change in dielectric constant with temperature dictates the ability of electrons to penetrate the barrier. The temperature dependence of the conductivity and dielectric constant are shown to be consistent with the theory, although some details of what is meant by “dielectric constant” in HEYWANG’S theory are not clear. PJZRIAet aZ.(5) also postulate a grain-boundary resistivity in BaTiOs, but say that the resistivity is a function of the mechanical pressure developed at the boundaries

due to the differential thermal expansion of individual grains of different crystallographic orientation. GOODMAN@) in recent work has convincingly demonstrated that the positive temperature coefficient of resistivity in doped BaTiOs depends upon grain boundaries. Single crystals of a given composition and thermal history do not have the positive effect but polycrystalline samples made from the single crystals do. Resistivity increases have also been reported in some compounds as they transform from ferrimagnetic to antiferromagnetic. Here it is proposed that in the low-temperature ordered state the overlap of electron orbitals provides a narrow conduction band which is destroyed at temperatures above the NCel temperature where a continuous overlap does not exist. The materials investigated in this work were formed from powder mixtures of ZnO, TiOs and NiO, which were pressed and subsequently sintered. The electrical properties of the ceramic were studied as a function of composition, sintering times and subsequent heat treatment. For correlation with the literature on other compounds showing the increase in resistivity with increasing temperature, studies of the dielectric constant, the thermal e.m.f., the thermal expansion and the effect of pressure and frequency on the electrical resistivity are included. 2. EXPERIMENTAL,

PROCEDURE

Sample preparation and composition The initial powder compositions of the samples investigated are listed in Table 1. The weighed powders were mixed in a Waring Blendor, with alcohol or water as a wetting agent. The mixed powders were then dried and passed through a 20-mesh screen (size of opening: 0.8 mm). Slab samples were then prepared from these powders by pressing at about 4% tons/ins. In order to maintain some control of the atmosphere surrounding the samples during firing, they were then buried in powder of the sample composition, which was held in an alumina boat. The boat was then placed in a furnace and the sample was fired in a surrounding atmosphere of

COEFFICIENT

IN

SOME

ZnO-TiOt-NiO

CERAMICS

113

Resistivity measurements

Table 1 _zzz=

Most of the resistivity measurements reported were made with rod-shaped samples of square Composition prior to Time at Max. firing cross-section cut from larger slabs after firing but Max. temp. firing (Bal ZnO) Temp. (“C) (hr) before aging. The rods were 1.8 cm long and varied in cross-section from 10 to 25 mms. NiO TiOz A d.c. four-probe potentiometer method was 8.8 0 1400 1 used for the resistivity vs. temperature measure8.6 2 1400 1 ments in order to avoid measuring the specimen 4.5 8 1400 1 contact resistance. 6 8 1150 17 Contacts were made to the specimens for both 6 8 1250 1 6 8 1250 5 current and potential leads by a mechanical 6 8 1300 1 pressure contact. The contacts were 0.010 in. 6 8 1350 1 platinum wires laid across the samples. The 6 8 1400 1 current contacts were placed 2 mm from the 6 8 1450 1 6 8 1500 1 sample ends and the potential contacts were 6 8.2 1400 1 spaced 4 mm apart in the center of the specimen. 4.5 10 1400 1 A chromel-alumel thermocouple pressed against 6 10 1400 1 the sample was used to measure the temperature. 10 10 1400 1 The sample holder was enclosed in a quartz tube 12 10 1400 1 14 10 1400 1 to allow measurements to be made from -195” 6 11 1400 1 to 800°C. Measurements were made above room 6 11 1400 5 temperature in air and below room temperature 6 11 1400 16 in a nitrogen atmosphere. Tests were made to 6 12 1300 1 6 12 1400 1 establish the fact that the absence of oxygen did 6 12 1500 1 not affect the low-temperature resistivity of the 15 15 1400 1 material. Resistivity vs. temperature measurements 5.3 20 1400 1 were made on all samples both before and after 20 20 1400 1 the aging treatment. The measurements of electrical resistance vs. air. The heating and cooling rate for most samples frequency and pressure were made on samples was maintained at about lOO”C/hr. After being where the resistance of the samples and the contact cooled to room temperature the samples were resistance is included in the measurement. subjected to an aging treatment. This treatment However, by comparison of these resistance consisted of holding the samples at 400°C in air measurements with the potentiometer measurefor 16 hr. ment mentioned above, the contact resistance of Most of the samples made were about 95 per the samples with these special contacts was detercent dense. The samples containing smaller mined to be less than 5 per cent of the total amounts of TiOs tended to be more porous when resistance at room temperature, and so could be fired in the way described above. Sample shrinkage neglected. during firing was about 20 per cent. All samples A Wayne Kerr radiofrequency bridge was used after firing were dark green in color, the darkness for the high-frequency impedance measurements. of the shade being associated with the amount of The resistance vs. pressure measurements were NiO added. Chemical analysis of representative made by means of a hydrostatic press with samples showed no observable change in the metal n-pentane as the working fluid. A calibrated piece ion ratios during firing. of manganin wire was inserted with the sample into Photomicrographs of several samples were the pressure chamber to measure the pressure. taken. These showed a two-phase mixture of oxides with an average grain size of between 2 Thermoelectric-power measurements and 5 p. Thermoelectric power was measured by the

114

R.

H.

PRY

and

differential method, i.e. by measurement of the voltage produced by a temperature gradient between the ends of a sample as the average temperature was varied. The samples were pressed between two silver blocks around one of which was wrapped a sheet of mica and then a few turns of 0.010 in. Nichrome wire used as a heater to maintain the temperature gradient between the ends of the sample. The silver blocks were recessed $ in. to fit over the ends of the sample so that the temperature of the ends of the sample would be nearly the same as that of the silver blocks. The silver blocks also served as the potential contacts to the sample. The temperature of each end of the sample was measured by a chromelalumel thermocouple, which passed halfway through the Ag block and pressed against the sample end. A White double potentiometer permitted the simultaneous measurement of the temperature of each end of the sample. Measurements were made below room temperature in an atmosphere of dry nitrogen, and above room temperature in an air atmosphere. 3. EXPERIMENTAL

RESULTS

Electrical resistivity vs. temperature Fig. 1 shows the dependence of the electrical resistivity upon temperature for a representative group of the samples listed in Table 1. All samples shown in this figure were fired at 1400°C for 1 hr, and then aged for 16 hr at 400°C. The temperature coefficient of electrical resistivity, a = (l/p)(dp/dT) (where p is the electrical resistivity and T is the temperature), was positive at room temperature for most of the samples studied. Thus, since a is negative at high and low temperatures, most of the curves of electrical resistivity vs. temperature showed both a maximum and minimum. The maximum occurred between 300” and 400°C and the minimum between - 50” and - 100°C. Fig. l(c) shows the very sharp change in the behavior of the resistivity vs. temperature when the amount of NiO in the sample passes 5 per cent by weight. In Fig. 2, the compositions of the samples listed in Table 1 have been plotted on a ternary diagram. The data from these samples were then used to estimate contour lines of constant roomtemperature resistivity and constant temperature

S.

P. MITOFF

+ g

rEmPERnrURE,~ ‘0’ p $: lo’ 9 E S? ,.

01 -200-1000 1002003004w5X

-1000 100 zw300 400500

TEMPERATURE,%

TEMPERU”RE$T

FIG. 1. Resistivity

ceramics

vs. temperature for some ZnO-base with additions of NiO and TiOz.

coefficient of resistance. Fig. 3 shows the maximum and room-temperature values of the resistivity and temperature coefficient of resistance for two cuts across the ternary diagram of Fig. 2. Fig. 3(a) and (b) indicate the effect of variations in the TiOs concentration at 6 per cent NiO, and Figs. 3(c) and (d) indicate the effect of variations in the NiO concentration at 10 per cent TiOs. Again it can be seen that the positive temperature coefficient is a maximum for between 5 and 7 per cent NiO and between 10 and 12 per cent TiOs. This maximum value is about 2 per cent per degree. Effects of quenching and aging The electrical resistivities of all of the samples measured after slow cooling from the firing temperature were reproducible and independent of time at temperature for holding times of the order of one-half hour. In all cases tested it was possible also to raise or lower the temperature 300°C or more within a few minutes and reproduce the resistivities measured by slow heating or cooling, provided that the temperature corresponding to the maximum resistivity was not exceeded.

COEFFICIENT

IN

SOME

ZnO-TiOs-NiO

0 NiO

5oTiOz 5 (bl

per “C at high temperature and 1 s.5 per cent at 100°C. As outlined earlier, the curves of Fig. 1 correspond to the “aged” curve of Fig. 4(b). The effect of quenching a sample from above the temperature corresponding to the resistance maximum is shown in Fig. 4(a). The numbers on the figure indicate the sequence of measurements and the thermal history of the sample. The measurements shown as curve 1 were made after slow cooling from the firing temperature to room temperature. The sample was then heated to 650°C and quenched to room temperature. The drop in resistivity which accompanies this treatment occurs also in ZnO and is probably due to the generation of interstitial Zn ions created by an oxygen deficiency at high temperatures, which is retained during quenching. The sample was then heated and held at 330°C for 15 hr, 410°C for 24 hr, and 365°C for 60 hr. The rate of rise of resistance at 410°C was constant for the first 5 hr. The resistance then gradually rose more slowly with a (time)li2 dependence. Not only did the resistance of the sample increase beyond its original value with these treatments, but also, as in the case of the sample in Fig. 4(b), the temperature coefficient rose, as indicated by curve 5 in the figure. and firing time Several sets of samples with 6 per cent NiO and between 8 and 12 per cent TiOs were fired at different temperatures. The resistivity temperature characteristics of these samples were then measured after aging. There were no qualitative differences in the temperature dependence of the resistivity for the different compositions studied as a result of variation in firing temperature as shown in Fig. 5. Figure 5(a) shows that the absolute value of the resistivity is lowered .by a factor of about 3 for samples fired at 145O”C, as compared to 1300°C for 1 hr, but the temperature coefficient of resistance is not changed appreciably. Fig. 5(b) shows the effect of extending the firing time within this temperature range. As the firing time is increased, for example at 14OO”C, both the resistivity and the temperature coefficient of resistance decreased markedly. The resistivity results for the sample fired for 5 hr at 1400°C coincide with the results for a sample of identical composition fired for 1 hr at 1500°C. In contrast to this behavior, Fig. 5(c)

Effect of jiring temperature

zno

95

90

85

80

75

70

115

cent

5o TiOe

45 A

CERAMICS

65

60

55

50 50 NIO

FIG. 2. Constant resistivity and temperature coefficient of resistance lines as a function of ZnO, NiO and TiOs content.

If the samples were maintained for a period of several hours at the temperature corresponding to the maximum resistivity, the resistivity gradually increased, as shown in Fig. 4(b). After the temperature of this sample was raised from -195” to 400°C and the resistivity curve measured, the sample was held for 16 hr at 400°C. The resultant curve obtained upon cooling is marked “aged” in the figure. The rate of resistance’ rise at lower aging temperatures has not yet been measured. This sample after holding at 400°C had the highest temperature coefficients of resistance of the group of samples reported, with a maximum Q of 2 per

116

R.

H.

PRY

and

S.

P.

MITOFF

(b)

TiOZS lOWT%

l”i+jr--____rTT

f

0

2

4

6

8

IO

I2

14

it$ii?i

16

0

2

4

6

WT %NiO

8

IO

I2

14

WT 0/oNiO

FIG. 3. Resistivity

and temperature coefficient of resistance as a function of composition for two cuts across the ternary diagram of Fig. 2.

(b)

6WT"/oNi0 IIWT%TiOr BAL.ZnO

I I

4

30-

QUENCHED %I

I -100

I 0

FROM 65Oq----

I I 100 ZOO

I 300

I 400

of low-temperature

-100

0

100

200

300

TEMPEAATUREfC

TEMPERATURE,'%

FIG. 4. Effect

IO/

-200

heat treatment,

after firing, on the electrical

resistivity.

400

COEFFICIENT

‘01

-200

-100

0

IN

100

200

SOME

300

400

ZnO-TiOs-NiO

500

101 0

100

150

200

250

300

TEMPERATURE,OC

TEMPERATURE,%

-200

50

117

CERAMICS

-100

0 TEMPERATURE,%

FIG. 5. Effect of firing temperature

shows the effect on the resistivity of firing the samples below 1300°C. The lower curve of this figure demonstrates that 17 hr at 1150°C was not sufficient time at this temperature for developing the high positive temperature coefficient of resistance behavior. The middle curve demonstrates that a firing time of 1 hr at 1250°C is also not sufficient. A firing time of 5 hr at 125O”C, however, produces a resistance temperature characteristic as shown in the top curve. The behavior of this sample is almost identical with that of a sample of the same composition fired at 1300°C for 1 hr. Thermoelectric power vs. temperature Fig.

6 shows

the thermoelectric

power

as a

and time on the electrical resistivity.

function of temperature for two samples fired at 1400°C for 1 hr and aged. There was no difference in the thermoelectric power of the aged and unaged samples within experimental error. The sign of the thermoelectric power indicates that the excess carriers are electrons. Samples with low electrical resistivity and low temperature coefficient of resistance such as the (4.5 per cent Ni0:8 per cent TiOs) samples show also a lower thermoelectric power than samples with a high resistance and temperature coefficient of resistance, such as the (6 per cent NiO: 8.2 per cent TiOa) sample. The rise in thermoelectric power at low temperatures for these samples coincides with the lowtemperature resistance increase which probably

R.

H.

PRY

and

S.

P.

MITOFF

coefficient of resistance of the sample decreased somewhat with increasing frequency. Inclusion of the parallel capacitance in the real part of the measured impedance makes the frequency dependence somewhat more pronounced but leaves it qualitatively unaltered, since the parallel capacitance is only of the order of 10 pF. Electrical resistivity vs. pressure

FIG.

6. Thermoelectric power vs. temperature ceramic compositions.

for

Fig. 8 shows the effect of hydrostatic pressure on the electrical resistivity of a sample resistor similar to that used for the frequency dependence of Fig. 7. The resistance of the sample increased smoothly with pressure, and no hysteresis was observed when the pressure was reduced. Measurements of the pressure dependence of the resistivity were made only at room temperature.

two

accompanies the reduction in the number of thermally excited conduction electrons from impurities. Electrical resistivity vs. frequency

Fig. 7(a) shows the parallel resistance and capacitance of a sample resistor as a function of frequency. The assumed circuit for the sample and the sample dimensions are shown as insets in this figure. The conducting leads completely covered the sample ends. The temperature dependence of the parallel resistance at zero and 107 c/s is shown in Fig. 7(b). Both the resistivity and temperature

6%

NiO-II%

Crystal structure vs. temperature

X-ray diffraction patterns were made of a sample exhibiting the positive temperature coefficient of resistance while the sample was held at lOO”C, 300°C and 500°C. All diffraction patterns could be analyzed as resulting from two phases, ZnO and ZnaTiOh. No attempt was made to locate the position of the nickel ions. It was presumed that they were in solution in both the ZnO and ZnzTi04 phases. DULIN and BASEtg) have shown that TiO2 does not dissolve to any appreciable extent in ZnO but at equilibrium forms a twophase mixture of ZnO and ZnaTiOe contrary to

TiOz

+

RESISTANCE 25°C

-

(a I IO2

IO4

I

I

IO5

IO6

FREQUENCY,

Frc. 7.

Resistance

I

IO'

0

100

and capacitance of a ZnO-base frequency.

200

300

TEMPERATURE,'%

C/S

resistor

as a function

of

COEFFICIENT

IN

SOME

ZnO-TiOz-NiO

L 30

FIG. 8. Resistance as function of pressure base resistor at 25°C.

for a ZnO-

earlier phase diagrams.(lO) There was no detected difference between patterns taken at different temperatures, except for a uniform change in lattice spacing resulting from the thermal expansion of both phases. 4. DISCUSSION

AND

of the positive resistance Origin

CONCLUSIONS

temperature

coeficient

of

The exponential increase in resistivity with increasing temperature over a broad temperature range cannot be accounted for on the basis of any known temperature-dependent electron-scattering phenomenon in single-crystal semiconductors. In addition, the increase in resistivity with pressure and the differential thermal expansion of the two phases are not sufficient to explain the resistivity temperature behavior on the basis of either straining or separating the conducting phase as the temperature is changed. The fact that there is an optimum timetemperature relationship for the emergence of this anomalous resistivity behavior suggests strongly that it is not an equilibrium property of this multiple-phase ceramic. Further, the fact that this behavior emerges only in those ceramics that contain a large amount of second phase ZnsTiOa suggests that it is not a property of the predominant ZnO phase alone. In fact, since the maximum temperature coefficient of resistance

CERAMICS

119

occurs for this sample when approximately onethird by volume of the sample is this second phase and since the resistivity of the ZnzTiOd-rich ceramic is very high, it may be inferred that the effect is not due to either phase by itself. In the searching for an explanation for the behavior, a grain-boundary effect is quite likely to dominate, as has been proposed by others investigating doped BaTiOs. On BaTiOs the point in favor of grain boundary resistance seems well established by GOODMAN.@) However, in the case of ZnO-based ceramics, it is not clear whether grain-boundary resistance or grainboundary conductance is the important anomaly. Fig. l(a) shows that above 400°C the resistivity of this series of ceramics is behaving like a normal two-phase semiconducting system with a lowresistivity phase, ZnO, and a high-resistivity phase, ZnsTiOd. From this point of view one might conclude that the grain boundaries are very conductive around room temperature. That is to say, the positive temperature coefficient of resistance may be due to an anomalous drop in resistance as room temperature is approached rather than an anomalous rise at higher temperatures. If this is the case, then the minimum resistivity of the grain boundaries for the sample in Fig. l(a) containing 6 per cent NiO and 8 per cent TiOz, which has an average grain size of about 3 CL,is of the order of 105R.

The major conclusion is that no obvious explanation for the resistivity anomaly is at hand, and that the theories proposed for the BaTiOs anomaly do not seem to be applicable. Acknowledgements-The

authors wish to acknowledge the assistance of J. INCOLD and L. VICTOR during the course of this experimental work.

REFERENCES 1. C. A. SCHUSTERIUS,U.S. Pat. 2,982,988 (1939). 2. P. W. HAAIJMAN, R. W. DAM and H. A. KLASENS,

Ned. Put. 84015 (1957). 3. (a) 0. SABURI, J. Phys. Sot. Japan 14, 1159 (1959); (b) 0. SABURI, J. Amer. Ceram. Sot. 44, 54

(1961); (c) 0. SABURI, Experimental Researches in Se&conducting Barium Titanates. Report of Murata Manufacturing Co., Kyoto, Japan (1961); (d) H. A. SAUERand S. S. FLASCHEN, Proceedings of 7th Electronic Components Symposium, Washington, D.C., pp. 4146 (1956); (e) V. J. TENNERY

120

4. 5. 6. 7.

R.

H.

PRY

and

and R. L. COOK, J. Amer. Ceram. Sot. 44, 187 (1961). Y. ICHIKAWA, U.S. Pat. 2, 2,981,699 (1961). W. T. PERIA, W. R. BRATSCHUNand R. D. FENITY. J. Amer. Ceram. Sot. 44, 249 (1961). W. HEYWANG, Solid-State Electron. 3, 51 (1961). W. HEYWANG and R. SCHAFER, Zum Einfluss innerer OberJliichen beim Barium-Titanat-Kaltleiter. Paper presented at Physical Society Meeting, Vienna, Austria (1961).

S.

P.

MITOFF

GOODMAN, 64th Annual Meeting, American Ceramic Society P. IS-Is-61 (1962). 9. F. H. DULIN and D. E. RASE, J. Amer. Ceram. Sot. 43, 125 (1960). 10. S. S. COLE and W. K. NELSON, J. Phys. Chem. 42, 248 (1938). See also, E. M. LEVIN, H. M. MCMURDIE, and F. P. HALL, Phase Diagrams for Ceramists, The Amer. Ceram. Sot., Columbus, Ohio (1956). 8. G.