Effect of Certain Group IV Oxides on Dielectric Constant and Dissipation Factor of Barium Titanate . GFUH-4M W. MARKS AND LESTER A. MONSON U . S . Navy Electronics Laboratory, Sun Diego, Calif.
T
MEASUREMENT OF DIELECTRIC CONSTANTS
HE high dielectric constant of barium titanate renders it
suitable for certain types of capacitors. Previous investigators have reported the effects of impurities and additives on the dielectric and piezoelectric properties of barium titanate single crystals and ceramics. Chief among these have been studies of the effects of certain alkaline earth titanates, particularly strontium titanate (17, di), on the dielectric constant of barium titanate ceramics. The addition of lead titanate (12)in small percentages appears to render the remanent polarization of barium titanate permanent. A systematic investigation has recently been made of the electrical properties and crystal structure of certain ceramic complexes, in which both the barium(I1) and titanium(1V) ions were partially replaced (19). I n general, barium titanate ceramics containing additives have a Curie temperature different from that of the ceramic prepared from the pure compound. The dielectric constants of the mixed ceramics are usually lower than the corresponding values for the pure ceramic. I n order to determine the effects of certain additives on the piezoelectric,, dielectric, and elastic constants of barium titanate, and thus obtain data for better transducer and capacitor design, a study was made first of the dielectric properties of ceramics prepared from mixtures of barium titanate and the dioxides of the following Group IV elements of the periodic table: silicon, titanium, zirconium, cerium, and thorium. Ceiium is one of the rare earths, but it has a valence of four besides the valence of three which is characteristic of these elements, and at times, it has been included in Group IV. The dieIectric constant of barium titanate below the Curie temperature depends upon the electrical field strength ( 5 , 7 , 2s). However, in this work the reversible dielectric constant ( 7 ) was measured in such a way that the direct current field was zero and the alternating current field was 6 to 10 volts per cm.
Samples were mounted for measurement in a carefully insulated, thermostatically controlled, electric oven having a small circulating fan to avoid temperature gradients. Before a series of measurements was begun, the temperature wasraisedto 175' C., where it was held for a minimum of 2 hours in order to free the samples as much as possible from sorbed moisture. The temperature was then lowered to approximately 170" C., the first set of measurements was made, and thereafter a measurement was made every few degrees, descending the temperature scale, to approximately 30" C. After each temperature lowering, the oven was allowed to stabilize for a t least 30 minutes prior to making measurements. Measurements were made on a t least three samples of any given composition. The capacitances and dissipation factors of the disks were measured with a 1000-cycle General Radio impedance bridge Model 650-A, using a Hewlett-Packard 200-D oscillator as a generator. A Dumont 208-D oscilloscope was used as a detector with a General Radio KO.830, 1000-cycle-per-secondfilter and a Hewlett-Packard 459-A preamplifier between the bridge and the oscilloscope for added sensitivity. The bridge, with associated components, was calibrated Rgainst standard capacitances and standard loss factors; the latter had been obtained by means of precision series resistors. The error of measurement of capacitance was within 1% and that of loss factor within &lo%. CORRECTION FOR POROSITY
To obtain more nearly absolute values of dielectric constant for ceramics of various compositions, it is necessary to correct the measured values for the effects of porosity. It can be assumed that the sintering process resulted in the formation of holes which are more or less spherical and then the method of Rushman and Strivens ( 1 7 ) can be followed. Van Santen ( d o ) showed that ellipsoidal holes had the minimum effect in diminishing the dielectric constant when the ellipsoids degenerated to spheres : a small deviation from the spherical shape had little effect. It is first necessary t o evaluate the porosity. This is done by the expression
PREPARATION OF CERAMICS
For the preparation of ceramics chemically pure barium titanate (99.7y0 BaTiOs) and the chemically pure dioxides of silicon, titanium, zirconium, cerium, and thorium were employed. Cerium and thorium dioxides were prepared by igniting hydrated cerous oxalate nonahydrate and thorium nitrate tetrahydrate, respectively. Mixtures of barium titanate and the oxides were prepared, in general, in 0.5,5, 10, 20, 30,40, and 50 mole percentages of oxide. Samples for mixing were accurately weighed out on an analytical balance, and mixtures were ground to uniformity. Disks were prepared for firing by pressing 6 to 10 grams of dry mixture a t 5000 pounds per square inch in a mold 1 inch in inside diameter. The disks were fired in a furnace having Globar resistance units. They were maintained a t 1350' to 1370" C. for 1 to 2 hours, except those containing 5 to 50 mole % silica and 20 to 50 mole yo titania, which were fired a t 1200' to 1250' C. Slumping of the latter occurred on firing a t higher temperatures. During the firing period the disks were supported on Alundum plates which had. been covered with a layer of chemically pure powdered zirconia. Densities of the fired ceramics were determined a t room temperature. The disks were finally foiled with silver 1 to 2 mils thick.
:
1611
- p z - PQ Pr
For better transducer and capacitor design
o x i d e s of c e r t a i n Group IV e l e ments added t o b a r i u m t i t a n a t e
. . . make possible preparation of ceramics with dielectric constants from 5000 to below 100, as desired
1612
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Vol. 47, No. 8
b
Figure 1.
Phase contrast photomicrographs of ceramic samples (250 X ) a. Barium titanate
b. Silica Titanium dioxide d. Zirconium dioxide C.
e. Cerium dioxide f. Thorium dioxide g. 50 mole % silica h. 50 mole 70titanium dioxide
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1955
where z is the volume fract,ion of pore space, p. is the density calculated from crystal structure. data, and pa is the measured density. I n these calculations the variation of density with temperature was not considered. No serious errors result-for example, the density of barium titanate a t 20' C., calculated from the data of Megaw ( I J ) , is 6.06 grams per cc., whereas a t 170' C. it is 6.04 grams per cc. Densities of the oxides used, in grams per cubic centimeter, were calculated from the crystal structure data tabulated by Wycltoff (2.4): SiOz (a-quartz), 2.65; TiOa (rutile), 4.29; ZrOz (monoclinic baddeleyite), 5.64; CeOz, cubic CaF2 structure, 7.22; Tho*, cubic CaFz structure, 10.04. From the above data, the theoretical maximum densities of mixtures were calculated. This, of course, presupposes that no changes to other polymorphic forms and no chemical reactions whatsoever occur on firing, which is rather unlikely. If ml, m2, and pz are taken as the mass fractions and the densities calculated from the crystal structure data of the two constituents of a mixture, then the volume of the mixture is mllp,
+ mz/~2
and the maximum possible density of the mixture is Pm =
mi mJP1
+ + mz/Pz m2
-
= (m1
+ + mzP1
m1~2
mdp1~2
(2)
In attempts t o obtain true dielectric constants from observed values for various compositions it is necessary to apply a mixture formula, allowing for the effects of porosity. A number of such formulas have been developed for calculating the dielectric constant of mixtures from empirical data, but no one formula is of universal application. The problem of calculating the dielectric constants of mixtures has been discussed by Lichtenecker and Rother ( 1 1 , 1 4 ) . Berberich and Bell ( 1 ) found that a logarithmic mixture formula holds approximately for rutile powder mixed with other ceramic powders. Following somewhat the procedure of Rushman and Strivem
Figure 2.
1613
Table I. Porosity Ranges of Fired Samples of Mixtures of B a r i u m Titanate and Oxides Oxide,% Mole
CeOz 0.25-0.29 0.40-0.45 0.44-0.48 0.44-0.46 0.47-0.50 0.44-0.46 50 0.49-0.60 100 0.25-0.44 c P BaTiOs 0.20-0.27. TeEhnical &ade BaTiOa, 0.5 5 10 20 30 40
Ti02 0.19 0.29-0.33 0.22-0.26 0.29-0.37 0.28-0.30 0.24-0.27 0.13-0.14 0.02-0.08
Tho2 0.15 0.21 0.24-0.25 0.26-0.27 0.26-0.31 0.29-0.33 0.30 0.44
i. 50mole
70 zirconium dioxide %ceriumdioxide
Si02 0.17-0.18 0.17-0.19 0.21-0.27 0.34-0.38 0.38-0.48 0.49-0.51 0.39-0 46
0.11.
( 1 7 ) in their investigation of barium titanatestrontium titanate and barium titanate-lead titanate ceramics, the expression E =
2+x - X ) ea
2(1
(3)
has been applied in which eo is the apparent or measured dielectric constant. ( E = €'/eo is the specific dielectric constant and eo is the dielectric constant of free space.) This equation allows for the fact that the dielectric constant of barium titanate is very much greater than that of air, which is taken t o be unity. The porosity ranges of the ceramic samples investigated are given in Table I. Except for ceramics containing cerium dioxide and silica, the porosity was roughly 0.25. Pressed disks containing 5% or more of cerium dioxide do not shrink much on firing, whereas the volume shrinkage of barium titanate disks may be as much as 40%. PHASE CONTRAST STUDIES
Phase contrast photomicrographs of barium titanate and oxide ceramics, taken with a Bausch and Lomb research metallograph, are shown in Figure 1 ( a tof). Figures 1 and 2 (g to I ) are photo-
P h a s e contrast photomicrographs of ceramic samples (250 X )
j . 50 mole
ZrO2 0.16 0.22-0.24 0.25-0.29 0.31-0.34 0.19-0.28 0.25-0.27 0.20-0.22 0.40
k. 20 mole %thoriumdioxide 1. 50 mole %thoriumdioxide
INDUSTRIAL AND ENGINEERING CHEMISTRY
1614
micrographs of ceramics containing barium titanate and the oxides. The illumination after passing through a hyperplane green filter was normally incident on the sample. The barium titanate particles are somewhat coarser than those of the oxides, because of grain grovhh during the firing period. I n Figures 1 and 2 ( g to I ) the darker patches are largely barium titanate; the smaller crystals of the oxides can be seen in the
Vol. 47, No. 8
CHEMICAL REACTIONS
There is the possibility that, when the pressed disks we fired, chemical reactions between barium titanate and the oxide in the mixture may occur-for example, barium titanate and titanium dioxide might react, a t the firing temperatures to form one or more of three other titanates (18): BaTis05, BaTirOp, and BazTi04. The degree of these and other reactions in the solid state will depend not only on concentrations and free energies of formation of the compounds involved but also on the time of firing. The attack ol barium titanate by silica with the formation of silicates is to be expected. With a view to ascertaining whether or not any extensive reactions occurred during the firing period, x-ray powder diagrams were taken of fired and subsequently powdered samples of barium titanate, oxides, and mixtures containing 30 and 50 mole 7 0 of the oxides. Mo Kcor)radiation was applied, a nickel filter having been used to remove the K(p,radiation. Careful comparison of the barium titanate and oxide diffraction patterns with patterns of the mixtures showed that if chemical reactions occurred during the firing period they were only in small percentages of the whole. Berlincourt and Jaffe ( 9 ) found that the limit of the detection of BaTis07and BazTiOl in barium titanate by their x-ray method was 3 mole yo. DIELECTRIC CONSTANT AND DISSIPATION FACTOR
Mean values of the experimentally determined dielectric constants, ea, for the various ceramics as determined by the procedure described were plotted against temperature, and from smoothed curves were obtained the data presented in Tables I1 and 111. The variation t o be expected from these values, dealing with ceramics, is about &lo%. Curie temperatures estimated from the curves are given in Tables I1 and 111. I n general, when the additive concentration was 20 mole yoor higher only rough values could be determined. For purposes of comparison in plotting and to obtain the more nearly absolute values of dielectric constant E , measured values were corrected for porosity by means of Equation 3. These data are presented in Figures 4, 6, 8, 10, 12, and 16.
TEMPERATURE,
Figure 3.
C.
Variation of barium titanate with temperature
ceramics
1-A.
Dielectric constant a. Chemically pure (99.7 5%) b . Technical grade
Correction made for porosity of samples 1-B. Dissipation factor a. Chemically pure b . Technical grade
lighter regions. Some migration of the cations of the additive into the barium titanate lattice is to be expected, with subsequent replacement in the titanium(1V) ion positions. The ionic radii of zirconium, cerium, and thorium are larger than that of titanium, whereas that of silicon is less (10). However, because the oxygen ions have been pushed apart ( I S ) by the barium ions, so that the available space is larger than that ordinarily required by the titanium ion, more space is available for the substituting ions. This should result in less distortion of the lattice. It would not be correct, then, to assume that only twc phases are present. Measurements have recently been made of rates of self-diffusion and transport number of barium ions in sintered, pressed tablets of barium titanate (8). Very black spots in the photographs are due to the voids, previously discussed. The cross sections of these are roughly those of spheres and ellipsoids, which were assumed t o hold in corrections for porosity-e.g., Figure 1, c and d.
TabIe 11. Variation of Dielectric Constant, E,, and Dissipation Factor, D, with Temperature of Barium Titanate Ceramics
c.
Technical Grade a D 0 0 0 0 0 0 0 0 0 0 0 0 0
25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180
Curie
temp.
0 0 0 0 0.003 0 0 0 0 0 0 0.001 0.002 0.005 0.007 0 0
0 0 117 5' 15900
Chemically Pure ~a
D
1400 1360 1330 1300 1260 1240 1220 1200 1190 1190 1190 1200 1205 1220 1250 1290 1340 1405 1510 1670 2040 7250 5470 4290 3550 3050 2650 2330 2070 1860 1720 1640
0 0 0 0 003 0 004 0 005 0 007 0 008 0 010 0 011 0 011 0 012 0 013 0 014 0 016 0 017 0 020 0 022 0 030 0 035 0 038 0 0 001 0 002 0 003 0 004 0 003 0 0 0 0.001 0 002
o;:*o;{
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
August 1955
Table 111.
c.
Variation of Dielectric Constant, E,, with Temperature Mole Percentage of ThOz
Mole Percentage of TiOz
0.5
5
10
20
30
40
50
Av. value
Av. value
C.
0 5
5
30 40 50
..
2460 2485 2530 2650 2930 3500 4530 5230 4430 3615 2800 2150 1725 1460 1280 1180
BaTiOl plus TiOz Ceramics
30
1280
1517
1471
942
531
Curie temp.
1236 1203 1184 1180 1187 1204 1250 1351
1421 1367 1342 1336 1347 1383 1452 1616 2020 6770 4400 3100 2405 1990
1660
3215 2235 1690 1310 1115
..
..
0.5
30
1077
40 50 60 70 80 90 100 110 120 130 140 150
1529 1476 1443 1435 1460 1503 1573 1693 1942 8250 4950 3460 2595 2100 1170
1040 1010 990 980 983 1003 1045 1130 1310 1850 3710 2700 1915 1450 1170
Curie temp.
=
214
943 942 940 940 947 967 1009 1071 1159 1115 975 838 719 614 536
1592
676
..
.. .. .. .. .. .. ..
408
165
.. .. .. .. ..
20
30
40
50
0.5
1160 1192 1136 ' 1310 1440 1680 2124 2314 1956 1600 1298 1046 876 765 692 655
420 426 434 446 466
455 428
193 180 168 160 154
244 218 194 170
{9294; Mole Percentage of ZrOz
5
10
20
30
50
40
Ba TiOa plus ZrOz Ceramics
Av. value
63.5
2060 2130 2225 2350 2570 3100 4540 4610 3730 2915 2235 1750 1440 1210 1065 980
..
__
50
1131" ,8275
n .r,
..
Curie temp.
=
_
..
70 80 90 100 110 120 130 140 150 160 170 180
394 386 382 381 382 388 398 416 452 511 525 464 405 321 294
fi4 1
..
60
Mole Percentage of Si02 5 10 20 30 40 BaTiOa plus Si02 Ceramics
1595
170 180
190
(132' 132O 1129" 124' 16770 13215 (2605 {lZOO
__
160
1438
10
BaTiOz plus ThOz Ceramics =
40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
1615
1440 1370 1320 1270 1240 1240 1300 1400 1780 2150 7770 4570 3270 2470 2020 1740
30 40 50 60 70 80 90 100
1265 1370 1730 1920 1970 1990 2140 2460 3190 5100 3980 3000 2340 1830 1500 1260
1170 1330 1524 1720 1932 2137 2340 2548 2744 2496 2146 1796 1452 1210 IO60
977
1210 1161 1091 996 885 792 717 665 617 573 533 497 466 440 418 403
500 468 442 415 388 363 340 320 304 290 280 269 260 250 242 233
135 133 131 130 129 128 127 126 125 125 124 124 124 125 127 129
Curie temp.
~
5
_
_ M o l e Percentage of CeOz 10
20
30
40
50
BaTiOa plus CeOz Ceramics
30 40 50 A -"n
70 80 90 100 110 120 130 140 150 160 170 180 Curie temp.
3020 2940 2890 2890 2050 3100 3290 3590 4140 5080 3260 2480 1970 1590 1340 1210
910
919 938 978 1041 1128 1235 1320 1369 1305
787 794 814 8.50 904 979 1062 1139 1164 1117 919 721 608 548 493 464
715 722 743 784 858 970 1050 1086 1070 io00 787
510 513 526 :50 986
633 688 731 749 745 542 514 475 443 414 385
459
;121° 114" & 1 0 9 O '100' 115' ,5085 f1390 (lli0 ',lo86 {753
{;;go
1063
821 696
627 566
510
665
577 518
482 464
9ow
8wo
7wo YI
ta' GZ
8
5wo
v_
The dissipation factor, D, which is the tangent of the dielectric loss angle (0= tan 8) is given as measured experimentally. Barium Titanate. Experimental data are given in Table 11. Data corrected for porosity are plotted in Figure 3 for chemically pure (99.7%) and technical grade barium titanate ceramics (Ticon B, Nat,ional Lead Go., New York). The Curie temperature and the dielectric constant a t this temperature of the technical grade ceramic are markedly lower than for the pure ceramic. The pure grade contained a total of about 0.3% of impurities and this, in part, might account for the higher peak dielectric constant temperature (127.8" f 0.3" C.) which has been observed than for single crystals (120' C.) having a domain structure (3). The Curie temperature and the dielectric conFtant a t this temperature depend primarily on the composition of the barium titanate ceramic, b u t firing temperature, porosity, field strength, and perhaps unknown factors partly determine these parameters. When the axes of dielectric constant us. temperature are transformed by t l = t i- 17 and €1 = e 100 and the curve for the
+
E v W 4 W
4ooo
E XCQ
2wo
20
40
€0
I W
80
TEMPERATURE,
120
140
IM)
180
C.
Figure 4. Variation of dielectric constant with temperature for mramics prepared from mixtures of barium titanate and silica
. . .Correction .Chemicallymade pure barium titanate ceramics porosity samples for
of
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
1616
Figure 5 . Variation of dissipatioii factor with temperature for ceramics prepared from mixtures of barium titanate and silica
impure ceramic thus shifted and that for the pure ceramic maintained fixed, the two curves are found to correspond except in the region of the Curie temperature, as shown by the broken line in Figure 3 . Wherever the curves correspond, the slopes arc de d€ the same. Then __ = --, but the temperatures, tl and t?,
df(t,,
4 t d
are not the same. This shows that the form of the curve is not changed except in the region of the Curie point by the presence of the 3% of impurities found in the technical grade material. Barium Titanate-Silica. The curves for dielectric constant and dissipation factor for different compositions are shown in Figures 4 and 5, respectively. Attempts t o prepare a sintered ceramic of d i c a only, suitable for use in making measurements, were not successful. Except for a slight upward shift (2.7') of the Curie ternperaturc, 0.5 mole yo silica does not change the
Vol. 47, No. 8
shape of the dielectric constant curve for pure barium titanate very much. On the low temperature side of the Curie point the curve is higher; the high temperature side remains much the same. The addition of 10 mole yo silica raises further the low temperature side of the curve and also tends to linearize it. The loss factor rises with temperature and composition above about 10 mole % silica. Barium Titanate-Titanium Dioxide. Curves for dielectric constant and dissipation factor are shown in Figures 6 and 7. These curves are similar to those obtained for barium titanatesilica ceramics. On the low temperature side of the Curie point for 5 to 10 mole percentages the curves are higher than for pure barium titanate. Barium Titanate-Cerium Dioxide. The dielectric con3tant curves for these ceramics are less symmetrical (Figure 8) about the Curie temperature axis than those previously described. This is in part due to the rise of the dielectric constant of ceria with temperature. The dissipation factor is markedly raised by the addition of this oxide (Figure 9), 0.5 mol % ceria raises the dielectric constant of barium titanate about 2.5 times on the lowtemperature side of the Curie point. Dielectric constants for ceria above about 115' C. could not be measured accurately because of the high dissipation factor. Barium Titanate-Zirconium Dioxide. Data are presented in Figures 10 and 11. The Curie temperature is markedly lowered by the addition of zirconia. The 5 mole % curve also shows that the second transition temperature a t which barium titanate changes Erom tetragonal to orthorhombic is raised to 45" to 50" C. It has recently been shown ( 4 ) that the two transition points coalesce a t a composition of about 14 mole % of zirconium dioxide. The curves a t 20 mole % and higher have a negative slope and show no peaks in the temperature range investigated. The addition of zirconia tends, a t higher percentages and temperatures, to raise the loss factor. Barium Titanate-Thorium Dioxide. Dielectric constant and dissipation factor curves are shown in Figures 12 and 13. The dissipation factor for these ceramics is not excessive and rhanges but moderately with temperature at the higher concentrations. DISCUSSION
Curie temperatures are plotted against composition in Figure 14 for the ceramic series investigated. The addition of silica to barium titanate raises the Curie point to a maximum value, which apparently does not change with further increase in conrentration. Titania and zirconia in small percentages raise the Curie point to a peak value; further increase in concentration of these oxides lowers it. On the addition of ceria, the Curie temperature reaches a minimum a t between 20 and 30 mole yo;
TEMPERATURE,
' C.
Figure 6. Variation of dielectric constant with temperature for ceramics prepared from mixtures of barium titanate and titanium dioxide Correction made for porosity of samples
Figure 7 . Variation of dissipation factor with temperature for ceramics prepared from mixtures of barium titanate and titanium dioxide
August 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
TEMPERATURE,
O
1617
C.
Figure 8. Variation of dielectric constant with temperature for ceramics prepared from mixtures of barium titanate and cerium dioxide
Figure 9. Variation of dissipation factor with temperature for ceramics prepared from mixtures of barium titanate and cerium dioxide
Correction made for porosity of aamples
thereafter, i t is raised (Figure 8). The rate of change of the Curie temperature in degrees centigrade per mole per cent of oyide added is given for the linear portion of each curve and is recorded on the graph. I n Figure 15, the Curie temperature of barium titanate ceramics having an oxide concentration of 10 mole yo is plotted against the ionic radius of the metal ion in the oxide. The Curie
TEMPERATURE,
O
points fall in the order in which these ions are found in the fourth column of the periodic table. This is true for other fixed concentrations (perhaps above 2 mole %), as an examination of Figure 14 shows. It should be possible to predict roughly the effect of a given oxide, in which the metal ion has a valence of 4, on the Curie temperature-for example, hafnium oxide (HfOz) would be expected to lower the Curie temperature so that i t would lie between the values obtained after the addition of zirconia and thoria, respectively. Figures 14 and 15 give evidence that substitution occurs in the barium titanate lattice. The dielectric constant of a ceramic mill depend on the dielectric constants of the pure constituents, the effect of substitution in and distortion of the lattices resulting in changes in spontaneous polarization, and the manner in which internal fields of force are modified a t the interfaces between boundaries of crystallites.
C.
Figure 10. Variation of dielectric constant with temperature for ceramics prepared from mixtures of barium titanate and zirconium dioxide Correction made for porosity of samples
Figure 11. Variation of dissipation factor with temperature for ceramics prepared from mixtures of barium titanate and zirconium dioxide
INDUSTRIAL A N D ENGINEERING CHEMXSTRY
1618
Vol. 47, No. 8
.e 06
r"
04 02
TEMPERATURE,
Figure 13. Variation of dissipation factor with temperature for ceramics prepared from mixtures of barium titanate and thorium dioxide
C.
Figure 12. Variation of dielectric constant with temperature for ceramicsprepared from mixtures of barium titanate and thorium dioxide Correction made for porosity of samples
Analysis of Data above Curie Temperature, It has been reported (9, 16, 17, 2 2 ) that the variation of the dielectric constant of barium titanate ceramics with temperature, above the Curie temperature, can be represented satisfactorily by the CurieWeiss law of ferromagrietics E, =
e
against concentration for any given additive shows that, for the most part, the values lie on smooth curves. If the equation is applicable to experimental values of dielectric constant, it is, of course, applicable to those values corrected for porosity by use of Equation 3.
Table IV. Law,
E,
Variation of C and 0 of Curie-Weiss
= __ with Concentration of Oxide Added to t - 8'
Barium Titanate
C
-
(4)
t--8
in which c and e are empirical constants. Near the Curie point deviations from the above equation occurs. Roberts ( 1 6 ) has shown this equation to be applicable up t o 360" C. Devonshire (6) has given a theoretical discussion. To determine the applicability of Equation 4 to the present data (Tables I1 and 111), plots were made of the inverse dielectric constant, versus temperature, t, in degrees centigrade. Whenever straight lines resulted for the portion of the plot above the Curie point, values of C and e were determined (Table IV). I n all instances, the magnitude of 0 is below the Curie temperature. 8 decreases with increase in concentration and a plot of
Mole Conon. of Additive in Ceramic Si02
0.5 5 10 20 30
TiOz
0.5 5 10
20 30 ZrOz 0.5 5 10
20 CeOz P OI
I
I
I
I
I
0.5 5
10
20 30 40 50 ThOn 5 10 20 30 BaTiOs, tech. grade BaTiOa, C.P.
c
e,
0
C.
1.105 X 106 0.765 0.741 0.388 0.313
117.4 119.0 106.5 100.0 78.8
1.075 0.650 0.706 0.489 0.492
115.9 111.1 104.5 89.8 52.0
1.096 0.917 0.837 0.787
115.9 85.3 90.8 18.0
0.885 0.499 0.467
104.9 79.8 76.4 74.5 46.6 14.1 -48.7
0,935 0.803 0.631 0.312 1.159 1.015
96.7 94.7 81.4 06.7 100.4 116.5
A careful examination of the dielectric constant data has shown that the exponential expression
I
I 5 lo
15 20 Mol Percent O f Oxkde
I
25
30
35
Figure 14. Variation of Curie temperature w-ith composition for barium tiTanate-Group TV oxide ceramics Slopes in degrees centigrade per mole per cent of oxide given for linear portions of curve
E = aeblT
(5)
where a and b are constants for any given barium titanate ceramic and T is the absolute temperature in degrees Kelvin, can also be used to represent data obtained above the Curie point. To show the application of Equation 5, data for a few representative ceramics are plotted in Figure 16. Wherever data were such that
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
August 1955
Values of a and b in Empirical Expression E = aebiTApplicable above Curie Temperature to Barium Titanate-Group IV Oxide Ceramics
Table V.
Added Si02 TiOz Oxide, Mole % ' a b a 0.5 3 . 3 1 X 10-8 6 . 0 2 2 . 6 6 X 10-8 5 3 . 0 3 X 10-2 4 . 9 3 5.16 X 10-2 10 0.466 3.67 0.396 20 0.533 3.34 3.12 30 ... 2.28 2.56 40 50 For chemically pure BaTiOs, a = 0.141 and
ZrOz
CeOz
b
a
b
6.07 4.63 3.70 2.56
2.33 x 10-3 7.23 X l o - * 1.89 78.6
5.15 4.56 3.00 1.00
...
...
...
c (-) 1
T - r
e
=
T
-
5.63 4.03 3.53 3.09 1.77 1.34 0,921
0 : 286 0.437 1.84 6.05 9.82
...
...
3.84 3.62 2.83 1.95 1.58
...
For purposep of illustration dielectric constants calculated by means of the empirical hyperbolic and logarithmic expressions are compared with data taken from experimental curves for technical grade barium titanate ceramics and for barium titanatezirconium oxide (20 mole %) ceramics (Table VI). At
Table VI. Test of Application above Curie Temperature of Curie-Weiss Law, E, = C / ( t - e), and Exponential Function E, = ebITto Barium Titanate Ceramics Temp.,
-
4 . 9 2 x 10-8 0.102 0.313 0.845 18.2 48.9 104.7
Dielectric Constant, en
where t
ThOz a b
b
E
b = 4.42.
the equation could be applied, values of a and b were deduced and are given for certain ceramics in Table V. The logarithm of b varies roughly directly nyith concentration. How i t occurs that both a hyperbolic and a logarithmic function are applicable for the variation of dielectric constant with temperature above the Curie point can be shown by expansion of these functions in poarer series. The Curie-Weiss law equation may be written as follons: e, =
1619
273 - 0
=
c.
T -r
From exptl. curve
Curie- Weiss law
Exponential function
Technical Grade BaTiOs
Then E,
=
C (ljT
+ r / T 2 + r2/T3 + . . . . +
' G I )
5473 4146 3182 2475 1942 1644
(7)
Expanding the logarithmic function, e, = = a
[I
+ b/T +
bZ 1 . 2! T2
+
C.P.
aeblT
h3 1 . 7 3! T
+ . . . + (n . b"-l T m - l1
The hyperbolic and logarithmic expressions are the same if t e r m above 1/T2can be neglected. Considering the limitations in accuracy of present experimental data, it is not possible to choose between the two functions.
Ionic Radius, A.
Figure 15. Plot of Curie temperature of barium titanate ceramics having oxide concentration of 10 mole q0 2's. ionic radius of metal ion in oxide O G o l d s c h m i d t radius El Wave-mechanical model radius
70 80 90 100 110 120 130 140 150 160 170
BaTiOs
886 792 717 664
617 373 533 497 466 440 418
+ 20 Mole yo ZrOz 890 800 726 665 614 570 53 1 498 468 442 419
863 787 722 665 615 572 533 499 468 44i 416
1620
INDUSTRIAL AND ENGINEERING CHEMISTRY
least over the temperature range investigated, one expression is as good as the other. The rate of the change of dielectric constant with temperature as determined by the logarithmic expression is equal to -be,/T2. SUNIMARY
The addition of certain Group IV oxides to barium titanate in concentrations from 0 t o 50 mole % markedly reduces the dielectric constant of ceramics prepared therefrom over the temperature range 30” to 170’ C. The dissipation factor is not greatly changed from that of pure barium titanate. Analysis of dielectric constant data above the Curie temperature for these ceramics showed that either the Curie-Weiss law or a given exponential function is applicable. It is not possible to choose between the two functions because of the limited accuracy of the experimental data. ACKNOWLEDGMENT
The authors thank Ray Pepinsky and coworkers at the Pennsylvania State University foi preparation of the x-ray diffraction patterns, Joseph Thompson, for taking the phase contrast photomicrographs, Frieda Herreshoff for aid in preparing graphs, and John Hickman for encouragement during the course of this work. LITERATURE CITED (1) Berberich, L. J., and Bell, M.E., J. A p p l . Phys., 11, 681 (1940).
(2) Berlincourt, D. A., and Jaffy; H., Brush Laboratories, “Research on Barium Titanate, 6th Progress Report, No. 515-6, May 1954.
Vol. 47.No. 8
Blattner, W., Kanzig, W., and Merz, W., Helv. Phys. Acta, 22 35 (1949).
Brajer, E. J., Jaffe, H., and Kulcsar, F.,Chicago Meeting, Acoustical Society, Paper E2, October 1951. DeBretteville, A. P., Jr., Ceram. Age., 54, 363-4, 376-9 (1949). Devonshire,A. F., Phil.Mag., 4 0 , 1040 (1949). Donley, I€. L., R C A Rev., 9 , 218 (1948). Garcia-Verduch, A., and Lindner, R., Arkiv K e m i , 5, 313 (1953), Jonker, G. H., and Van Santen, J. H., Chem. Weekblad, 43, 672 (1947).
Kittel, C., “Introduction to Solid State Physics,” Wiley, Ncw York, 1953. Lichtenecker, K., and Rother, K., Physik. Z.. 32, 255 (1931) Mason, W. P., Bell Labs. Record, 2 7 , 2 8 5 (1949). Megaw, H. D., Trans. Faraday Soc., 4ZA, 224 (1947). Reddish, W., Plessner, W., and Jackson, W., Tbid., 42A, 245 (1947).
Roberts, S.,Phys. Rev., 71, 890 (1947). Ibid., 7 5 , 9 8 9 (1949).
Rushman, D. F., and Strivens, M. A., Trans. Faraday
Soc..
42A, 231 (1947).
Statton, W. O., J. Chem. Pkus., 19, 33 (1951). Taylor, A., Horizons, Inc., Cleveland, Ohio, “Piezoelectric Material for High Power Underwater Sound Transducers,” NObsr-63108, Index No. NE-051248, January 1954. Van Santen, J. H., Trans. Faraday Soc., 42A, 249 (1947). Von Hippel, A., Breckenridge, R. G., Chesley, F. G., and Tisaa. L., IND. ENG.CHEM.,38, 1097 (1946). Wul,B., J . Phys. (U.S.S.R.), 10, 95 (1946). Wul, B. M., and Goldman, I. M.,Compt. rend. acad. scz. (U.R.S.S.),4 9 , 177 (1945). Wyckoff, R. W. G., “Crystal Structures,” Chap. IV, “Compounds RXa,” Interscience, New York, 1948. RECEIVED for review February 2, 1954. NEL Professional Contribution No. 12.
ACCEPTEDFebruary 24, 1956.
Sulfate-Bisulfate Equilibrium on Anion Exchange Resins R. E. ANDERSON, W. C. BAUMAN, AND D. F. HARRINGTON Physical Research Laboratory, The Dow Chemical Co., Midland, Mich.
T”
sulfate salts of the quaternam ammonium anion exchange resins are able t o adsorb strong mineral acids from solution. This ability of the resin sulfates to act as weaklv basic resins was observed both by the authors and by Kraus and others, who have published brief communications ( 3 , 4). This phenomenon offers a new method for the removal of strong arids from certain mixtures of solutes without requiring chemical regeneration of the resins. The equilibrium existing among hydrogen, sulfate, and bisulfate ions in a solution oE sulfuric acid is a function of the total molar concentration of sulfuric acid. Sherrill and Noye8 ( 5 ) determined the ionization of sulfuric acid conductometrically a t a number of concentrations up to 0.05M. If the molar concentrations of the three ions formed are plotted on logarithmic paper against the molarity of sulfuric acid present, essentially linear relationships are found. The data of Sherrill and Noyes may thus be extrapolated easily to 0.1M sulfuric acid and qualitatively to 1M sulfuric acid. When an anion exchange resin is placed in a solution, all of the anion species present compete for sites on the resin. The composition of the resin at equilibrium is determined by the relative selectivities shown for the different anions and their relative equivalent concentrations in solution. The relative equivalent concentrations of sulfate and bisulfate ions in sulfuric acid solu-
tion are shown in Figure 1. The equivalent fractions of total anion equivalents in solution which are sulfate ions, X , and which are bisulfataions, 1 - X , are shown as a function of the sulfuric acid molarity, M . The solid lines of Figure 1 are from the data of Sherrill and Noyes ( 5 ) and the dashed lines are a qualitative extrapolation. If sulfate and bisulfate ions are the only anions present, the equilibrium existing with a quaternary resin may be represented as : 2RHSOi SOa-- S 2HSO4&SO4 (1)
+
+
The selectivity expression for this equilibrium when expressed in terms of X and the equivalent fraction of total anion equivalents held by the resin which are sulfate ions, X r , becomes:
I n Equation 2, K ,
sei-
HSOa
is the selectivity coefficient of the resin
for sulfate ion over bisulfate ion defined in terms of concentrations (6). As activity coefficient ratios are not available for most of the species present, Equation 2 can be used only as a first approximation. Cr is the total capacity of the resin phase expressed as equivalents per liter. C is the concentration of total cation or anion equivalents in the solution phase at equilibrium. If
