High dielectric constant ceramics A. von Hippel, R . G. Breckenridge, F. G . Chesley, and Laszlo Tisza LABORQTORY FOR ISSULATION RESEARCH, MASSACHUSETTS INSTll'IiTE OF TSCHNOLOGY, CAMBRIDGE. MASS.
'
Kemlts of an investigation are presented in this payer on titanium dioxide and the alkaline earth titanates, including some mixtures and solid solutions of the barium and -trontium compounds. Dielectric measurements over a wide range of frequencies, temperatures, and voltages, and thermal expansion and x-ray studies have yielded a rather complete picture of the properties and usefulness of these titania ceramics. Barium titanate and the
barium-strontium titanate solid solutions prove to be a new' class of ferroelectric materials. Their peculiar dieledtric behavior was first noted by- the Titanium Alloy Flanufacturing Company, and this behavior proves to be connected with a lattice transition from pseudocubic to cubic. Additional maxima have been found in the dielectric characteristics which correspond to transitions of the second order. These maxima are being studied further.
!I
pounds per square inch from completely dry powder. For larger samples 15 t o 18% of water was added t o improve the bonding. Some other samples were formed by slip casting in plaster of Paris molds; the slip was made of 100 grams of solid dispersed with 30 cc. of 1 % ethylene diamine. Other suitable dispersing agents are 3 cc. of 1% tannic acid with 3 cc. of 10% ammonium hydroxide and 20 cc. of water; or 30 cc. of 1% Daxad No. 23 (Dewey and A m y Chemical Company) per 100 grams of solid. The disks prepared by slip casting were somewhat superior in homogeneity but identical with the pressed samples in electrical properties. Several authors ( I , 14, 2Oj have already pointed out that oxidizing atmospheres and slow firing are a prerequisite for producing low losses in the titania ceramics. In our experiments the neutral atmosphere of an electric furnace was found to be satisfactory, so that' in most cases the firing was done in a Globar furnace. Its temperature was controlled by a Wheelco Capacitrol operating from a platinum, 13y0 rhodium-87% platinum thermocouple; indicated temperature and sample temperature probably agree within 30' C. The disks were set on 100-mesh zirconium dioxide in alundum daggers. S o fluxing was observed a t the firing temperatures used. In all cases the specimens were protected from direct, radiation of the Globars to prevent uneven heating and consequent warping of the disks. A series of preliminary runs had established a satisfactory firing chedule which was used for all subsequent work. The cycle ollows: a steady increase of the temperature with a speed of 100" per hour up to a peak temperature of 13.50" C., holding at this peak for 6 hours, then disconnecting the furnace and cooling in about 8 hours. Samples prepared in this fashion were dense, vitreous bodies without excessive crystal growth. The peak temperature chosen represents a compromise between optimum density and favorable furnace conditions. For calcium tit,anate a peak temperature of 1400" C. was found necessary to produce satisfactory vitrification. After a density determination, the di-ks were prepared for the electrical measwenlent. by applying silver paste (Hanovia Burnish silver paste S o . 28 or Du Pont silver paste S o . 4351) to the two opposite faces and burning on the silver electrodes in a ykcond firing cycle. When cooled t o about 60" C., the edges of the disks were painted with polystyrene dope or ceresin wax to minimize the absorption of moisture. X o electrodes were required for the measurements in the microwave range; instead, plane parallel surfaces and very accurate dimensions are needed. These were obtained hy dry grinding
ATERIALS of high dielectric constant and low loss suitable for use over a wide frequency and temperature range are deL sired for electrical purposes. They are needed in the lower frequency range for condenser construction and in the microwave field as optical media for wave propagation. Several mechanisms of polarization in solid materials may lead to high values of the dielectric constant. By embedding conducting particles in an insulating matrix, "interfacial" polarization and a field distortion can be produced which, for the outside uhserver, give the effect of a large dielectric constant ( 9 ) . This type of polarization is usually connected with high dielectric loss and a long relaxation time, and is thus useless for our purpose. Equally unsatisfactory from our standpoint is the polarization created by the orientation of dipoles. In solids arid liquids such dipoles lag behind the driving field at higher frequencies; thus again appreciable loss and a decrease in polarization result ( 5 ) . A third mechanism of polarization is possible, however. 111 ionic crystal lattices dipole moments are created by the displacing st' ions from their equilibrium positions. Because these ions are atrongly bound, they have resonance frequencies of vibration in the far infrared and may thus follow even microwave fields with$)utdelay if no disturbing coupling exists between them; thus a ;ow loss factor throughout the radio spectrum may be expected. Cnfortunately, this last mechanism is normally accompanied :jy rather low values of the dielectric constant, but a few favorable cases exist-for example, titanium dioxide-which rombine high dielectric constant and low loss. -1 number of investigations have dealt with the remarkable dielectric behavior of titanium dioxide ( I , 6),and recently it was reported that even higher values of polarization than that of titanium dioxide are found in some titanate compounds (20). Because the information so far available does not allow a clear judgment about the properties and usefulness of titania bodies, it was decided t o undertake an investigation of these substances.
.Materials and preparation The titanium dioxide and titanates used in the major portion oi this investigation were obtained from the Titanium Alloy Manufacturing, Company. The properties are summarized in Table I. Compounds from other companies were studied as well, with results in essential agreement with the Tamco materials. The major part of the test samples were preformed by dry pressing Disks, 1 inch in diameter and inrh thick, were pressed at 1000
1097
1098
INDUSTRIAL AND ENGINEERING CHEMISTRY
with a diamond wheel. After grinding, the specimens were again dried in an oven and stored in a desiccator until measured.
Electrical measurements The electrical measurements were made from direct current to 3 X lo9cycles per second on the instruments listed in Table 11.
Vol. 38, No. 11
TABLE I. PROPERTTES OF TXTANIUM COMPOUNDS Composition Ti02
Trade Name Tamco Ticon T
MgTiOa CaTiOs SrTiOs BaTiOa 71% BaTiOa-29% SrTiOa 75% BaTiOa-25% SrTiOs
Tamco Ticon M B Tamco Ticon C Tamco Ticon S Tamco Ticon B
Powder Density Main Impuritiee 4.19" SiOz. AIzOa. CaO (2% 2.2 3.175 4.58" 5.52"
Tamco Ticon B-S 245
5.0
SiOz, AlzOs, NazO
Tamco Ticon B-S 249
5.0
SiOz, Altos, NazO
" Density determined as described b y Schumb and Rittner
(18).
Electrical properties of titania ceramics'
FREQUENCY IN CYCLES PER SECOND
Figure 1.
Dielectric properties of Ticon T (titanium dioxide) at 29' and 78" C.
In our standard holders a temperature range from -40" to +100" C. can be,covered by circulating thermostated liquids through double walls. A special holder was designed for use with the General Radio bridge over a much wider temperature range. Here the sample was kept in vacuo, clamped into a copper block, which could be heated by a small resistance coil or cooled over a slotted brass tube by a vessel filled with a cooling liquid. One side of the disk was separated from the copper block by a quartz plate cut perpendicular to its optic axis; this quartz sheet provided excellent electrical insulation and simultaneously conducted heat almost aa effectively as iron. The temperature was measured by a thermocouple inserted in the copper block next to the sample. Coaxial leads connected the holder with the bridge.
The alternating current measurements on titanium dioxide at two temperatures for a wide range of frequencies are given in Figure 1. They indicate that the dielectric constant does not depend on the frequency but that the material does show a rather large negative coefficient. When measured as a function of temperature, it is found that d ( ~ ' / q , ) / d T = -0.094 (Figure 2), in reasonable agreement with previous measurements ( 1 , 6) ; but a t a critical temperature a rapid increase of C'/EO takes place, the onset of which moves to higher temperatures with higher frequencies. The minimum in the E'/€, curves occurs for eacb frequency a t about the same value of the loss tangent, tan 6 = 0.012. These facts can be understood as a consequence of "interfacial" polarization produced by the piling up of charge carrier@ on crystal boundaries, as the following discussion shows. If, instead of the loss tangents in Figure 1, the dielectric conductivity
where X. = vacuum wave length of measuring frequency, expressed in meters
is plotted as a function of absolute temperature T , an exponential characteristic results: E
u =
Ae-m
(2)
or in a plot of log u against 1/T straight lines are obtained. This temperature dependence shows that the conductivity is produced by charge carriers which can be mobilized by a thermal activation energy of E E 0.51 electron volt or 11.8 kg.-cal. per mole. The deviations from the straight lines observed a t lower temperatures can be ascribed to additional types of carriers liberated a t lattice imperfections with greater ease. Moving in field direction, the carriers are stopped a t crystal boundaries, and a space charge p piles up whicb is proportional to P
-3
. A
Fc
(3)
where j = current density
_A -2c
Figure 2.
Dielectric properties of Ticon T (titanium dioxide) at 60, 1000, and 100,000 cycles per second
charging time per half cycle
1 The equations in this paper are expressed in the rationalized meter-kilogram-second system, because the factor 4n is thus eliminated from the formulas.most frequently encountered in dielectric problems. eo, the dielectric cons t a n t of vacuum in this system, has the magnitude 8.854 X 10-11farad/meter. €'/eo, the specific dielectric constant, e"/eo, the specific loss factor, and tan 6 t"/t, the loss tangent, are numbera independent of a n y system chosen (19).
-
November, 1946
INDUSTRIAL AND ENGINEERING CHEMISTRY
1099 A simple relation between temperature coefficient and thermal expansion can be derived by expressing e f / e , in terms of the average molecular dipole moment per unit of applied field, ,tio, and the number of such molecular dipoles per unit volume, N / V :
It follows that the temperature coefficient of the dielectric constant is given by dT Figure 3.
Reflection coefficient for rwtile (ordinary ray)
Current density j is given by j = r -V d
(4)
That is, the change of the polarizability and of the density with temperature enter. Tentatively, if only the latter is considered and expressed by the coefficient of linear expansion, a, it should be expected that
where V = applied voltage d = sample thickness Therefore,' from Equation 3, P
N
UAV
Using Equation 1, which gives UA tan 6
-
(5)
Z
-
(.'/eo)
tan 6,
The experimeptal results show that relation 9 is not satisfied. The measured value of a = 9.1 X 10-6/' C. when substituted in relation 9, gives d ( e f / e o ) / d T = -0.0026 if a value of e'/e, = 95 is used, whereas a much larger negative temperature coef-
de Ve
9
A t the minima of the e'/co characteristics (Figure 2), about the same interfacial polarization-that is, the same space charge ( p = constant)-has been produced in all three cases. In our experiments d / V is constant; thus, according to Equation 6 this condition can be expressed m tan 6 = constant a t the minima (if the small change in e'/eo is neglected) as observed. The influence of the conductivity on the loss tangent falls as l/u, so that a t high frequencies tan 6 should reach the low value predicted from the infrared spectrum, as discussed later. This is practically true, as the full frequency characteristics (Figure 1) confirm.
14
13
.oos .006
.004 .w2
0 FREQUENCY IN CYCLES PER SECOND
Thermal expansion and temperature coefficient The negative temperature coefficient of capacitance could be a consequence of the thermal expansion of the ceramic; a simple dilatometer was therefore constructed to check the relation. It consisted of a pair of telescopes, mounted 6 inches apart; one of them was equipped with a vernier movement, which allowed EL measurement of the change in length of a 15-cm. sample with an accuracy of *0.0024 cm. Above room temperature the sample was contained in a Globar furnace; below room temperature it was confined in a desiccated glass container and was measured while slowly warming up. Extruded tubing of about '/,-inch diameter and l/le-inch wall thickness, sintered in the ~ t a n d a r dfiring cycle, was used for measurement. The small mass of the material and its large surface area ensured uniform heating and cooling.
Figure 4.
Dielectric properties of Ticon
RIB (magnesium titanate)
TABLE 11. ELECTRICAL IKSTRLThiENTS Instrument 718-B oanacitanoe .. bryddge wg&-apeciai transformer Susceptanoe variation equipment Wave guide instrument Ballistic galvanometer No. 2285-d
General Radio Co. Lab. for Insulation Research (IS) Lab. for Insulation Research (16) Leeds & Northrup Co.
60-10s
1
6
106-1IY
2
6
3X1@
5
6
D.C.
2
9 .
1loo
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 38, No. 11
The TiOz groups have two infrared-active vibrations (onl) these are important for the dielectric constant), a valence vibration of frequency vv and a deformation vibration Ud. It seenip reasonable to identify these frequencies with the two absorption frequencies calculated later from reststrahl measurements. A> the deformation vibration is "softer", we have ud = 180 rm.-. and vu = 500 em.-'.
I70
Icn
150 .I
.01
,001
.mol 10'
ioz 10) io4 IO' io6 IO' FREOUENCY IN CYCLES PER SECOND
'01
Figure 5. Dielectric properties of Ticon C (calcium titanate) at 26" and 82 " C .
..
.I
.01
ficient, d ( e ' / e , ) / d T = -0.094, is observed. Thus we may conclude that the first term in Equation 8 is of decisive importance and that d 2 , l d T is less than zero.
-00I .0001
13'
Mechanism of polarization The dielectric constant of ionic crystals was calculated by Born ( 2 ) under the simple'assumptions that the rigid ions carry out harmonic oscillations and that the field locally acting on these oscillators is equal to the field applied. This model fails to account quantitatively for the large value of the dielectric constant of titanium dioxide and for its temperature dependence. The Born formula,
IO*
103
IO'
FREQUENCY IN CYCLES
106
PER
0'
IO'
IO'
SECOND
Figure 7. Dielectric properties of Ticon S (strontium titanate) at 23' and 88" C.
It may be shown that for a rutile-type structure the dielectric constant becomes anisotropic: Parallel to the tetragonal axib only the deformation vibration is active,
Perpendicular to the tetragonal axis both frequencies enter, where (ze) = effective charge of ions p = crystal density ml, m2 = masses of the two ion types Y , = resonance frequency of oscillators n m = optical index of refraction
Substituting the above values for the frequencies, and for z t the effective charge of the oxygen ion 2e, we obtain ( ~ ' / t ; ) 1.8, which agrees fairly well with the experimental ratio 2 . may be modified for the case of rutile. This tetragonal structure is composed of somewhat distorted Ti06 octahedra ( 1 5 ) or, alQuantitatively, however, the theoretical expression falls short of ternatively, one can imagine it built up of linear groups of TiOZ. the experimental values by a factor 4, the value of el',/e, calcuIt should be pointed out, however, that the lattice is not moleculated from Equation 11A being about 40. It would also lead lar; Le., the binding within a "group" is not stronger than beto an even less negative temperature coefficient than formula 9 , tween groups. hecause the decrease in density is counteracted by the shift of YO to lower frequencies ( 3 ) . Eucken and Biichner ( 6 ) 210 pointed out that the weak point of the above derivation is the assumption that the dipole moment is given by p = (ze)z, where ze is the ion charge and .r is the charge separation; this implies a rigid non190 deformable charge distribution of the ions. Generally, p will be some function of 2, and in Equation 10 zc will have t o be replaced by dp(z)/dz. According t,o 180 Eucken and Buchner, p may be expected to shoiv a large deviation from the linear behavior if the solid i i , IM question represents an intermediate case bet\veei. Q heteropolar and homopolar binding. This seems to be 160 the case for titanium dioxide. This explanation alw accounts qualitatively for the large negative temperature coefficient of dielectric constant observed. Since 150 d p ( z ) j d z may be quite sensitive to the z value, the mechanism of polarization in titanium dioxide' doe.. 140 not differ fundamentally from that found in othei ionic crystals, the quantitative difference being due to a certain electronic instability of the binding in -125 -100 -75 -50 -25 0 25 50 75 100 125 150 TEMPERATURE *C. the present case of t,ransition between ionic anti homopolar binding. Figure 6. Dielectric properties of Ticon C at 1 kilocycle per second $=
400
30
350
2
ch.
C,
300
.OZo
250
l5
200
150 -90
-70
-50
-0
-%
.tM
+IO
+50
+70
+90
tllO
+I30
TEMPERATURE 'C.
This R value is plotted in Rubens' measurements. Our problem is to determine the complex index of refraction which has produced the R characteristics. The plot of the reflecting power indicates two strong absorption bands for the ordinary ray, a more complex spectrum for the extraordinary ray, and the persistence of high reflection towards longer waves, where the crystal has again become transparent. From the reflected intensity a t 300 microns the index of refraction can be calculated: rill = 9.1, n l = 12.9. Thus, in the infrared a dielectric conRtant e;i/eo = na = 83 and € ; / e , = n: = 167 has already been reached, equaling the values known from high frequency measurements on single crystals. .A piece of rutile ceramic of crystal density containing the crystallites in random orientation should have an average dielectric constant,
Dielectric properties ofTicon S at 1 kilocycle per second
Figure 8.
1101
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
November, 1946
+ - 2€#:
e' e;
Infrared absorption and dielectric loss From the foregoing discussion it may be concluded that a dielectric loss should originate from the long wave length tail of the infrared absorption. Unfortunately no measurements are available, either of the infrared absorption coefficient or of the dispersion curve of rutile, the only measurements in the infrared being the reflection measurements of Liebisch and Rubens (8). We will show that it is possible to use the measurements of the reflecting power to obtain some information about the infrared absorption coefficient and, consequently, about the loss factor in the microwave region.
111
because the a direction is twice as frequently represented as the c direction. I t is evident from the reflection data that, for the ordinary ray, two main absorption bands exist corresponding to two fundamental vibrations of the Ti+'++ ion in its oxygen surroundings, as previously suggested-a valence vibration of titanium against oxygen and a deformation vibration of lower frequency. Consequently, it should be possible to represent n* by the superposition of two dispersion regions. n*2
= n:
+
Ai
i =
1300
= A =
&o
€0
PF- 9 + j k i v i v
1,2
The optical index of refraction, n -, can be obtained from the horizontal part of the R curve toward the visible. The two resonance frequencies have to be selected so as to give the correct positions for the maxima a t about 250 cm.-1 and 600 cm.-l of the R curve. Furthermore, the oscillator strengths, A I and A?, are determined by the following two conditions: (a) for Y -P 0 the static index of refraction no results:
€;e.
1200 Iloo
1000
( 6 ) The reflected intensity R goes to zero a t a frequency YJ = YO0 cm.-'. This implies that n 3 1 and nK = 0; hence,
FFEWENCY H CYCLES PER SECOND
Figure 9. Dielectric properties of Ticon B (barium titanate) at 26" and 82" C.
If the complex index of refraction of a material is known, 7L*
where n K
= =
=
n(1
-
j K )
(12)
index of refraction index of absorption
then, from Fresnel's equations, its reflection in air for perpendicular incidence is
.------TEMFfRATURE *C.
rt*rlc,ctc,dintensity where K = inciderit Intensity
Figure 10. Dielectric properties of Ticon B at 1 kilocycle per second and 22.9 volts per cm.
1102
INDUSTRIAL AND ENGINEERING CHEMISTRY MEAWRED AT IO KILOCYCLES AND FlELD STRENGTH OF 22.9 WLTSICM.
1
1
1
1
0
40
80
120
IO 160
rc.
Figure 11. Dielectric properties of Ticon B at 10 kilocycles and 22.9 volts per cm. Finally, attenuation factors k , and k, have to be selected properly so as to reproduce the height and slope of the reflection maxima. Figure 3 shows the results of this calculation. By assuming PI = 500 cm.-1 and kl = = 0.1, two trials were made with the values ~1 = 200 cm.-1 and v1 = 170 cm.-1. It is evident that the measured characteristic can be satisfactorily reproduced and that the true value for Y~ lies between the two values selected. A further calculation, assuming kl = 0.2, gave a result still compatible with the empirical curve, but indicating that the true value probably lies between 0.1 and 0.2. For kl = 0.5 the characteristic is flattened out and irreconcilable with the measurements given. The infrared spectrum just discussed produces a loss tangent in the microwave range:
= 5 X 10-'u(kl
where dimension of
Y
+ 0.016k2)
ss
5 X lo-'
k
Lm.
= cm.-l
Vol. 38, No. 1J
negative than for titanium dioxide (Figure 5). A temperature study of €'/eo and tan 6 a t los cycles (Figure 6) shows that the coefficient is about constant [d(e'/e,)/dT = -0.3121 and the IOSP is low, until conductivity and interfacial polarization develop. The trend indicated for calcium titanate is even more pro nounced for strontium titanate (Figure 7); e'/e0 has risen to 205 a t room temperature, and its temperature coefficient has reached the value d(e'/e,)/dT = -1.76 (Figure 8) a t low temperatures The loss observed for this material is somewhat higher than for calcium titanate. For barium titanate an entirely different type of behavior IF found, as was first noted by Wainer and Salomon (90). The dielectric constant and loss have increased considerably over that, observed for strontium titanate, and the temperature coefficient has apparently become less negative (Figure 9). A more detailed temperature study reveals a complex situation. Measured a t 10' cycles and 22.9 volts per cm. (Figure lo), e'/e, rises from a loa temperature value of about 400, then traverses a small hum€. near room temperature and a very steep maximum a t about 116.5" C., where e ' / e ~ N 6500. The loss tangent, on the othei hand, shows a broad maximum a t temperatures between -60' and +20° C. which seems to consist of two superimposed peaks one near -20" and another near +lo", and in addition, a mini. mum a t +120" C. At lo4cycles (Figure 11) the only pronounced change concerns the maximum of tan 6; it seems that, although a t lo3 cycles it consisted of two maxima, now only the smaller one near +lo" C. remains. Measured with direct current, the remarkable maximum in e'/e0 is apparently masked by interfacial polarization (Figure 12), but at these higher field strengths a new peak a t about 110 C. appears and the peak near 0 becoma more pronounced. The dependence on field strength is alsc shown by measurements a t lo3 cycles and 2.29 volts per cm (Figure 13). Outside of the two peak regions the dielectric con. stant is found to rise somewhat with increasing voltage; but be tween the peaks it is slightly lower a t higher fields. The loss ir generally greater a t high field strength. This behavior nil1 be discussed in more detail later in this report. It was also reported ($0) that the solution of strontium titan. ate in barium titanate shifts the large peak in e'/€, to lower tern. peratures. To investigate this behavior, studies were made OD mixtures containing 71% barium titanate-29% strontium titanate and 75% barium titanate-250fo strontium titanate. For the 71 %-29% mixture the maximum in €'/eo lies a t room temperature (Figure 14); in a 75%-25% solution it is found a t about 40" C (Figure 15). This shift of the peak to lower temperature has beeD
-
Thus, with titanium dioxide it should be possible t o realize a dielectric constant of about 100, while simultaneously keeping the at X = 10 cm. loss tangent down t o The loss calculated in this way represents z theoretical minimum and w ill be increased by such effects as ionic conductivity, interfacial polarization, etc. Experimentally, the loss was found to be about 0.0003, which indicates that we came rather close to the theoretical optimum.
Titanate ceramics Investigations of the alkaline earth titanates similar to those carried out on titanium dioxide reveal that several distinct types of behavior are shown by the available compounds. Magnesium titanate acts like a typical ionic crystal (Figure 4); its dielectric constant is relatively low (€'/eo = 13.4 at 28" C.), the temperature coefficient positive [ d ( e ' / e , ) / d T = +0.0099], and the dielectric loss small. The loss increase towards lower frequencies and higher temperatures is explained by conductivity. Calcium titanate and strontium titanate, on the other hand, resemble titanium dioxide in that they have high dielectric conatants and large negative temperature coefficients. For calcium titanate the dielectric constant has reached a wtlue of 167 a t room $emperatwe, and its temperature coefficient has become more
EWERltTURE*C.
Figure 12.
Static dielectric constant of Ticon B
INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1946
TABLE 111. hfEASUREMEXTS AT
T o C.
- 123
121 119 117 112 107 102 85 70 67 63 50 46 36 31 20 16 8 4 0
+2 4 6 8 10
12 14 16 18 20 22 24 27 29 31 33 36 40 43 46
t'/ce
356 355 367 377 392 410 432 507 609 639 675 691 712 739 773 802 817 841 867 902 930 943 962 995 1040 1114 1237 1323 1342 1352 1343 1303 1302 1294 1287 1277 1268 1259 1248 1245
BaTiOa Tan 6 0.0079 0.0067 0.6071 0.0071 0.0073 0.0074 0.0071 0.0077 0.0191 0.0176 0.0198 0.0261 0.0376 0.0478 0.0588 0.0676 0.0614 0.0570 0.0546 0.0511 0.0524 0.0517 0.0472 0.0493 0.0492 0.0478 0.0403 0.0304 0.0275 0.0222 0.0187 0 0154 0.0167 0.0167 0.0166 0.0167 0.0170 0.0171 0.0176 0.0178
-
5.30), 22.9 Volts/Cm. T o C. c'/e 1244 2.82 -I-52 2.37 1244 56 2.62 1251 60 1227 65 2.68 1237 2.87 68 1250 3.03 72 1261 3.06 74 1281 3.90 78 1310 11.63 81 11.25 84 1342 1363 86 13.37 1381 18.07 88 26.7 1401 90 92 35.3 1430 1484 95 45.6 54.2 1560 98 60.2 1650 100 102 47.9 1702 47.3 104 1832 106 46.1 1963 109 48.7 2210 48.8 3345 111 113 45.4 4540 49.1 5410 114 51.1 6090 115 116 53.4 6475 49.8 116.5 6510 40.3 6475 117 36.9 6390 118 30.1 6225 119 5940 121 25.1 20.0 6475 124 21.7 4890 127 130 21.6 4420 3925 21.4 134 3675 21.3 136 138 21.5 3540 141 21.5 3280 144 21.9 2995 148 22.2 2705
(p
€"/to
Tan 6 0.0183 0.0184 0.0186 0.0180 0.0181 0,0192 0.0182 0.0180 0.0179 0.0179 0.0176 0.0174 0.0174 0.0169 0.0170 0.0171 0.0172 0.0171 0.0169 0.0165 0.0154 0.0150 0.0127 0.0128 0.0133 0.0130 0.0109 0.0120 0.0120 0.0103 0.0102 0.0101 0.0106 0.0113 0.0129 0.0139 0.0150 0.0172 0.0206 0.0263
A
FREQUENCY O F 1 KILOCYCLE PER
c"/ea
investigated in more detail by Jackson and Reddish (Y), who dudied compositions down to 20% barium titanate where the transition temperature is about -190" C . They found a linear relation between the transition temperature and the barium titanate content over this range of composition. Although in the figures just described the over-all situation is clearly evident, their scale is too small for representation of the data within the accuracy of measurement. Table I11 therefore gives some of the measured values of €'/eo and tan 6 for the three cases shown in Figures 10, 14, and 15. In addition, the loss factor E " / E ~ was calculated and plotted in Figure 16, because it is directly proportional to the dielectric conductivity and thus allows a
75% BaTiOs-25% SrTiOa ( p = 5.41), 22.9 Volta/Cm. T o C. t ' / t e Tan 6 d'/ta' 19.1 -82 1274 0.0150 74 1381 0.0162 22.4 62 1498 0.0158 23.7 40.0 45 1748 0.0229 41 1842 0.0254 46.8 36 2005 0.0307 61.6 83.3 24 2420 0.0344 88.9 20 2340 0.0380 94.2 17 2435 0.0387 9 2475 0.0457 113.1 0 2620 0.0523 137.0 $2 2660 0.0532 141.5 6 2839 0.0539 153.0 16 3305 0.0545 180.1 21 3650 0.0525 191.6 29 4130 0.0465 192.1 35 5765 0.0395 227.7 36.5 6060 0.0347 210.3 3 8 . 5 6300 0.0276 173.9 42.5 6140 0.0193 118.5 43.6 5970 0.0163 97.3 68.0 47 5530 0.0123 41.9 50 4850 0.0086 26.3 54 4310 0.0061 13.7 60 3580 0.0038 97 1510 0.0020 2.94
1103
SECOND 71% BaTiOr29W SrTiOa (p 5.231, 18 Volts/Cm. T o C. d/to Tan 6 r"/te .120 1037 0.0099 10.1 1090 0.0114 90 12.4 56 25.5 1420 0.0180 28 79.8 2082 0.0383 2138 0,0557 20 119.0 2225 0.0596 132.5 15 176.5 5 2380 0.0743 2580 0.0900 232.1 4 0 3070 0.0993 305.0 3358 0.1045 351.0 392.0 3760 0.1041 431.0 11 4345 0.0994 6250 0.1191 745.0 13 7770 0.1358 1056 15 9050 0.1199 1086 19 20 11500 0.1008 1102 22 11690 0.0940 1098 22.5 11520 0.0814 938 23 11600 0.0713 826 11530 0.0600 691 24 11220 0.0498 559 25 10810 0.0416 419 26 328 27 10100 0.0327 9400 0.0262 246 28 8098 0.0165 133.2 31 7230 0.0122 88.3 33 6545 0.0098 64.0 35 5180 0.0065 38 33.7 40 26.9 4640 0.0058 42 4530 0.0028 12.7 3955 0.0028 11.09 45 2970 0.0016 63 4.75 3.92 2610 0.0015 57 69 3.95 2470 0.0016 3.46 74 1729 0.0020 1282 0.001Q 94 2.06 4.06 828 0.0049 130 742 0.0088 6.53 142 '611 0.0271 16.6 167 21.0 174 585 0.W59 28.9 550 0.0525 197
-
-
+:
simpler representation of the physical facts than tan 6, if e'/% varies over wide limits. The absolute values of the dielectric constant of the fired CBramics are a function of the density of the material. From the relation between dielectric constant and density 1 4 , which may be rewritten, (18 it follows that: (19
In our case both terms are of importance; for high values of €'/e, a considerable change in e'/eo may result from small density varia. tions. This effect and the dependence on field strength explaic many of the conflicting results reported on t,hese materials.
Thermal expansion and polymorphic transitionm The thermal expansion of the materials, measured in the equip ment previously described, shows nothing unusual in the cme of the magnesium, calcium, and strontium titanates. The ex. pansion proceeds linearly, and this density change would produce only a small negative temperature coefficient of the dielectric conatant, which is contrasted with the coefficient actually observed as follows: d(c'/eo)
dT Material MgTiOi L
-IM
I
-80
I
-40 0 TEMPERATURE .C.
I
40
80
I
no
1
Imo
Figure 13. Dielectric properties of Ticon B at 1 kilocycle per second and 2.29 volts per cm.
CaTiOI SrTiO8
a/" C. 6 . 1 X 10-8 1 . 4 X 10-1 9 . 4 x 10"
Calcd. from density change alone -0.0023 -0.0069 0.0061
-
Obaenred +0.01 -0.31 -1.76
For barium titanate the thermal expansion curves show ont break between -15' and + l o o C., a second between 95' and
INDUSTRIAL AND ENGINEERING CHEMISTRY
1104
Figure 14. Dielectric properties of Ticon R S 245 ( 7 1 7 ~BnTiOs 297' SrTiOa) a t a field strength of 18 Felts per c s m .
+
Vol. 38, No. 11
ture (Figure 17), reveal that in the region of vt>ry high dielectric constant the structure of tht, materials changes from a pseudocubic to a cubic lattice. This transition involves such small structural changes that it can be observed only in reflections 011 the most rlosely spaced planes. This transition has since heen investigated by Rookshy and by Megaw ( I O ) with a high precision camera. and the nature of the pseudocubic form determined It is found that t,he brrium titanate 1:ttire is tetragonal with a - = 3.0960 * 0.0005 A , , c = 4.0263 * 0.0005 A , , c!n = 1.0101 * 0.0002 at 20°C. T o get soriit information a t to the energy involved in the transition, the cooling curve of the 7570 BaTiOa-25y0 SrTiOs material over the transition range was measured. I t was smooth withiii the accuracy of measurement, xyhereas 3 latent heat due t o the polymorphic change of the rubstance should have been detected if it had exceeded about 3 kg.-cal. per mole. Since the energy of transition is probably small, it is likely that the state of strain of the individual crystallite. may affect the transition process t o produce the broad transition wgion obserwd.
Effect of voltage and freqnency
-----
The fact just has been estalilished that the high dielectric W I I stant maxima of barium titanate and the barium-strontium mixtures are connected with the concerted displacement of ions throughout a crystallite, ap evidenced by the lattice chagge; thi. suggests that in the case of these materials we are faced with a cooperative phenomenon in nhich the displacement of the ions is aided by an internal field, so that the whole crystallite falls into a new pattern. The external voltage serves in this case only to orient the polarization as in "ferroelectric" materials. If this conclusion is correct,, the true dielectric constant and loss cannot be determined by bridge measurements, because the sample condenser corresponda t o a nonlinear circuit element. The dielectric properties thus should be investigated by oscillograms allowing an analysis of the whole charging and discharging cycle. Such oscillograms were ohtained by i~ circuit similar t o
TANb
It
Figure 15. Dielectric properties of Ticon BS 249 (75% BaTiOa 25% SrTiOs)at a field strength of 22.9 v o l t s per cm.
+
120" C., and possibly a third above 1200" C. The values uf found in the various temperature regions were as follows:
I,
240
TA 1102 AT :O*
?
I
N
-80" t o -15'C.: a = 1.6 X C. io0 to 900 c.: a = 1.9 x 1 0 - 5 1 0 140" t o 1200" C.: a = 1.4 X C.
c.
In the intervals - 1 5 " to + l o " and 95Oto 120" the sample shows practically no increase in length Tvith temperature. In the 7570 BaTi03-25yo SrTiOa mixture the position of the first break is about maintained, whereas the second one moves t o the range between 40" and 55' C. If the strontium titanate is increased t o 20%, the second break appears near room temperature. Thus, there is no doubt that the second break coincides with the region in xhich the dielectric constant traverses the steep maximum in the temperature characteristics given above. X-ray powder diffraction patterns of the barium titanate and ef the barium-strontium mixtures, taken as a function of tempera-
TEMPERATURE
Figure 16.
'C.
Loss factor of titanate materials
.
November, 1946
INDUSTRIAL AND ENGINEERING CHEMISTRY
1105
-
50"
(
+ 82'
(
+
c
+ loo0 t x + 110" c' + 1150 C' f200"
Tavco Ticox R
0" c.
10" c
I
II
T a w 0 TICOSB-S 245
15" C
20" C
1I
I1
Ta\zco Trcos B-9 249 Figure 17.
X-ray powder diffraction pictures of barium and barium-strontium titanates
c
INDUSTRIAL AND ENGINEERING CHEMISTRY
1106
- 175'
-150" C.
C.
-800
c.
-65'
-200
c.
-50
+30° C.
Figure 18.
c.
-1280
c.
-96' C.
-50'
C.
-350
c.
$ 150
c.
00
c.
c.
$60"
c.
+7500 c.
+lOSo C.
+1200
c.
+125' C.
+450
+W"c.
C.
Vol. 38, No. 11
Oscillographic hysteresis curves for barium titanate
November, 1946
INDUSTRIAL AND ENGINEERING CHEMISTRY
T
"C.
Figure 19. Dielectric constant and dielectric loss of barium titanate from hysteresis curves
that used by Sawyer and Tower (I?'). The voltages in y- and z-direction are proportional to the charge of the sample condenser, Q., and the voltage, V,, applied across it, respectively. Figure 18 shows a typical sequence of pictures taken a t 60 cycles and 4800 volts per cm. for a series of temperatures; the "ferroelectric" ckiaracter of the substance seems obvious. The existence of ferroelectric behavior in barium titanate was denied bv Wul and Goldman (81) but has since been retracted
(ea.
1107
+ l o " , and +120" C. The maximum in all three cases s e e m t o shift with increasing voltage to lower temperatures; the lower maxima, furthermore, are brought out only under high field strengths. .4 plot of the enclosed loop area (which oorresponds t o the energy loss per cycle) as function of temperature again indicatee the three regions of anomalous response (Figure 19, lower graph). In addition, the remanent polarization exhibits peaks near these temperatures, while the coercive force apparently drops steadily and disappears, as do the loop area and remanence, a t about 120" C. where the lattice transforms t o the cubic structure. Consequently, the a.c. measurements such as those in Figure 10 have to be reinterpreted; the maxima of these curves do not show c ' / E , , directly but some kind of integrated value. Its magnitude, in addition, is influenced by the selectivity of the bridge indicator because the current floTTing through the bridge is distorted by the nonlinearity of the ceramic capacitor. The position of the maximum in the temperature scale depends on the voltage applied as Fell, as indicated on Figure 20 which gives the field strength dependence of E ' / E ~ and the loss tangent of Ticon B-S 249 a t 108 cycles and three temperatures up t o the highest voltage obtainable in our bridge equipment. Ballistic measurements of the dielectric constant as a function of the applied field for this material (Figure 21) also proved clearly that e'/e, is strongly dependent on voltage and reaches a maximum which is shifted to lower field strength with high temperature. Simultaneously, the height and shape of the curvee are sensitive to temperature. That the material is far from saturated, even a t 8000 volts per cm., is evident from Figure 22 in which, in analogy to magnetic B-H (induction-field intensity) curves, dielectric flux density D is plotted against field strengtb E from the data of Figure 21. I t is obvious that the effect of t.he applied field on the dielectric constant cannot be explained by assuming that the observed polarization is composed of the independent contributions of the different lattice ions. -4field of about lo7 volts per cm. is required to create an energy comparable to the thermal energy of these ions; that is, our fields of about lo3volts per cm. represent only an extremely small disturbance of the lattice vibrations. Since, in spite of this, these fields have a pronounced effect on the dielectric constant, the existence of a much stronger "internal" field is indicated.
Discussion The facts reported make it evident that the alkaline earth titanates have t o be classified into three groups. The first, represented by magnesium titanate alone, shows the properties of a normal ionic crystal-low dielectric constant, low loss, and a
.
The slope at zero voltage of such hysteresis loops,
= IB
A V" [m] v-l
(20) __
a measure of the initial dielectric
constant of the ceramic under the conditions chosen. The upper graph of Figure 19 gives tan CY values for several voltages and two frequencies as a function of temperature. It is apparent From these measurements, as well as those previously given, t h a t three proaounced regions of anomalous dielectric response exist, centered near -70 ',
0
200
Figure 20.
m
- _.__ + . A -
800 loo0 1200 FIELD STRENGTH VOLTSKM.
603
1400
1600
1800
Field strength dependence of dielectric properties of Ticon B-S 249
1108
Vol. 38, No. 11
INDUSTRIAL AND ENGINEERING CHEMISTRY
jTZ4'"' 1 J -
positive temperature coefficient, d ( e ' / ' e o ) / d T . This separate position of the magnesium titanate is explained by the fact that the !dg++ and the Ti+++- ions are about equal in radius (0.65 and 0.68 8.); consequently, the tpyo ions share three oxygen iunh a:, rqual partners in equivalent positions and a hexagonal lattice .tructure results of predominantly ionic bond character. The fundamental atomic arrangement in the two other groups ,.an be represented by the cubic- "perovskite" structure < 25). Each titanium ion is surrounded b oxygens forming an octaiedral grouping as in TiO,, wlicrea alkaline earth ions placed iit the corners of the cube are surrounded by twelve oxygen i(m-. In accordance with the explanation given previously for the high ;>olarizabilityof rutile, we may expect t,hat all the titanates conFaining TiOs octahedra will exhihit ljigh dielectric constanth ]'ewlting from the transit,ion between heteropolar and hornopolil I bonds as the titanium ion is displaced in its oxygen aurroundinpr. In addition, we can anticipate a trend from calcium to barium, because with increasing size o f thew spacer ions the octahedrii \vi11 he systematically distorted. In the case of cnlcium titarlate or perovskite itself, S h y dzah6 ( 1 2 ) recently showed that it is not truly cubic but n i o i t o 4inic; the neighboring Ti06 ortahedra are slightly tilted again-t
