1117
DIELECTRIC PROPERTIES OF BaTi80.1AND BaTi409
Dielectric Properties of Polycrystalline Barium Trititanate and Barium Tetratitanate by G. W. Marks and C. E. Antoniak Naval Undersea Warfare Center, San Diego Division, San Diego, California 92162 (Received June 16, 1067)
An investigation was made of the dielectric properties of polycrystalline barium trititanate (BaTiaO?)and tetratitanate (BaTi409)in the frequency range 100 cps-10 Mcps, within the temperature range 0-250". The variation of permittivity with temperature at constant frequency is linear, or nearly so, with the exception that dielectric dispersion occurs in the tetratitanate at lower frequencies above about 130". Permittivity values lie within the range from 40 to 60. Log tan S rises nearly linearly with temperature in the high-temperature range for frequencies from 102 to lo5 cps, indicating that maxima occur at still higher temperatures. In both compounds, the direct current resistivity varies linearly with the reciprocal of the Kelvin temperature, whereas the 1-kcps resistivity has a minimum. This shows that the loss tangent is not determined alone by direct current conductivity, particularly at lower temperatures. No evidence of ferroelectricity was found for either of these dielectrics within the range 0-425'.
From their study of phase equilibria in the system BaO-TiOz, Rase and Roy' concluded that there are five intermediate compounds of these oxides. These are barium orthotitanate (BazTi04), barium metatitanate (BaTiOa), barium dititanate (BaTiz05), barium trititanate (Ba'Ti30T),and barium tetratitanate (BaTi40,). An examination of the phase equilibrium diagram of Rase and Roy shows that BazTi04, BaTiOs, BaTi307, and BaTi40pcan be obtained pure by firing corresponding stoichiometric mixtures of baria and titania.' HOWever, the last two of these oxides melt incongruently and so the maximum firing temperatures for the preparation of these compounds in a pure state are limited to temperatures below the incongruent melting point. Some previous work on the dielectric properties of certain of these oxides was done by Skanavi2 and by LipaevaU3 It is our purpose to discuss briefly results that were obtained from an experimental investigation of polycrystalline BaTi307 and polycrystalline BaTi40g.
Experimental Section Preparation of Specimens. Well-blended mixtures (-200 mesh) of dried (500") reagent grade barium carbonate (BaC03) and titanium dioxide (TiO,) were prepared in stoichiometric proportions for the synthesis of BaTi30.1and BaTi4Og. These mixtures were fired a t 1250-1300" for about 5 hr, powdered in a diamond mortar to -200 mesh after cooling, and again fired. X-Ray diffraction powder diagrams of these products, using Mo K a radiation (Zr filter), showed the respective patterns for BaTi307 and BaTi40p as previously described.' Samples of about 8-10 g of these titanates containing a binder of 5% starch solution were pressed into 1 in. diameter disks at 6000-8000 psi and fired for 2 hr at
1200-1230". Preliminary tests of specimens after firing showed that the loss tangent lay within the range 0.1-0.4, which was much too high if BaTi03 is taken as a criterion. The samples were reground, 0.0270 ferric oxide introduced, and disks were again prepared and fired. Subsequent tests at 1 kcps show theloss tangent to be about 0.001, which is the low order of magnitude to be expecteda4t5 Microscopic examination of polished specimens etched with 6 N HC1 containing 3% H F showed that the crystallite size ranged from about 1 to 15 p . Disks for experimentation were cut to a thickness of about 0.1 in., faces were machined plane parallel to within 1 mil, and the densities were then determined. After electroding with silver, measurements were made on two samples of each compound. Replicate tests were made a t each frequency. Densities and porosities of representative samples are given in Table I. Porosity z, which is defined as the volume fraction of pore space, is found from the relation
x: = (Pz
- Pa)/Pz
(1)
p , is the maximum ideal density, ordinarily as deduced from crystal structure data; pa is the density of the specimen. p e for BaTilOo was calculated from crystal structure data whereas p , for BaTi307 is the measurement of Rase and Roy by the pycnometer method.'js (1) D. E. Rase and R. Roy, J . Amer. Ceram. Soc., 38, 102 (1955). (2) G.I. Skanavi, Dokl. Akad. Nauk S S S R , 59, 41 (1948). (3) G.A. Lipaeva, Soviet Phys.-Solid State, 4, 1183 (1962). (4) J. P.Remeika, J . Amer. Chem. Soc., 76, 940 (1954). (5) G.Shirane, F. Jona, and R. Pepinsky, Proc. Ifinst. Radio Engr., 43, 1238 (1955). (6) D.H.Templeton and C. A. Dauben, J . Chem. Phys., 32, 1515 (1960). Volume 72,Number
4 April 1968
1118
G. W. MARKSAND C. E. ANTONIAK
TEMPERATURE ' C
Figure 1. Variation of permittivity with temperature (BaTisOT, density 4.08 g/cm8): (A) 100 cps and 1, 10, and 100 kcps; (B) lower curve, 500 kcps and 1 Mcps, upper curve, 5 Mcps; (C) 10 Mcps, BaTi409; (D) 100 cps (high curve), 1, 10, and 100 kcps are nearly the same; (E) X, 500 kcps; 0, 3 Mcps; (F) 0, 1 Mcps; 0 , 5 Mcps; (G) 10 Mcps.
Table I: Density and Porosity Data Concerning BaTiaOT and BaTirOs -Density, Dielectrio
PZ
BaTia07
4.7
BaTidOg
4.54
g/omJ-------,
Porosity, %
Pa
2
4.08 4.06 4.10 4.16
13.4 13.6 8.9
8.4
Electrical Measurements. Measurements of capacitance and loss tangent were made within the tempem ture range 0-250" and of direct current resistance within the range 10-450". Specimens were maintained a t constant temperature to within k0.5" in a pot furnace for temperatures above ambient and within hO.1" in a chamber in an oil bath for those below. Corrections for capacitance of leads and supports were made when it was deemed necessary. Measuring instruments employed were the following General Radio bridges: Types 716C, 1608A, 1615A, 916A, and 544B. Frequencies up to 10 Mcps were generated with a Hewlett-Packard Model 650A.
Results and Discussion Permittivity and Loss Tangent. The variation of permittivity, e', with temperature for polycrystalline BaTi307 and BaTi409, within the temperature range 0-210" and 100 cps-10 Mcps, is shown in Figure 1. The Journal of Physical Chemistry
The estimated accuracy of these results is *5%. Upper temperature limits at which capacitance measurements could be made by the methods employed were determined by the rise in loss tangent of the samples. Change of permittivity with temperature for BaTi30, at given frequencies is linear or nearly so (Figure 1). Separation of curves at 100 cps and 1, 10, and 100 kcps lay within the limits of experimental error, except above about 220" where a small displacement of the curve for 100 cps occurred. Curves for the tetratitanate are quite similar to those for the trititanate, except that above about 130" dielectric dispersion was found at the lower frequencies. It is observed that at any chosen temperature in the linear interval the permittivity rises with frequency to a maximum which lies between 5 and 10 Mcps. Representative data showing the variation of tan 6 with temperature and frequency at lower frequencies for BaTi307 are plotted in Figure 2 . Similar results were obtained for BaTi409. Log tan 6 rises nearly linearly in the high-temperature range of the curves for frequencies from lo2 to lo5 cps. I n the megacycle region the loss tangent tends to increase with increase in frequency. The rough constancy of tan S with frequency change in the low-frequency region indicates a wide distribution of relaxation times. The presence of a relaxation of large size is suggested by the gradual rise of the loss tangent curves.
DIELECTRIC PROPERTIES OF BaTi30, AND BaTirOg
1119
Table 11: Change of Loss Factor, e", with Frequency and with Temperature for Polycrystalline BaTis0.i and BaTiaOe Frequency, ope
102
Temp, OC
20 50 100 150 200
10s
20 50
Such a relaxation is probably due to interfacial and space-charge polarization. Since the direct current conductivity was found to be rather low a t ambient temperature, the contribution of the conductance to tan 6 was then necessarily low. It is customary' to represent the simultaneous occurrence of loss current and charging current by the introduction of a complex permittivity E = E' - je", where e" = E' tan 6. The dependence of E" on temperature a t stated frequencies is given in Table 11. e'' tends to rise with temperature. At lower frequencies marked changes occur only above about 150". I n the megacycle region, current conduction losses have increased by a factor of lo2or more. Direct Current Conductivity. To learn what fraction of the loss tangent was due to direct current conductivity, measurements were made of the direct current resistance and of capacitance and tan 6 at 1 kcps from room temperature to about 400". Measurements were also made, by way of comparison, on disks of technical grade ceramic barium titanate (97% BaTiOa) having a density of 5.733 g/cm3. Results are plotted in Figures 3 andl 4. Examination of these figures shows that, a t low temperatures, the direct current conductivity represents only a small fraction of the total conductivity in each compound, whereas at higher temperatures it is the greater part of it. That is, the contribution of the direct current conductance to the
0.089
...
...
... ...
0.0066 0.0086 0.039 0.34
...
20 50 100 150 200 240
0.032 0.039 0.029 0.028 0.046 0.36
0.019 0.020 0.027 0.12 0.66
20
50 100 150 200 240
0.035 0.022 0.024 0.018 0.078 1.5
0.018 0.016 0.012 0.043
20 40
0.59 0.47
0.50 0.45
106
20 50
2.9 2.9
2.00 1.97
107
30 50 100 150 200 250
6.5 3.2 2.7 5.6 3.7 2.9
0.74 0.86
80 100 I20 140 160 180 200 220 240 260 TEMPERATURE * C
Figure 2. Variation of tan 6 with temperature and frequency for BaTia07: (A) 100 cps, (B) 1 kcps; (C) 10 kcps; and (D) 100 kcps.
(6")
150 200 250
106 60
(6")
0.039 0.047 0.12 0.53 4.2
104
20 40
BaTirOo loss index
0.042 0.054 0.048 0.065 0.12 0.58
100
0
BaTiaOi loea index
5
x
106
...
...
... ...
1.3
6.4 8.9 5.5
experimentally determined tan 6 is significant at higher temperatures. For example, in BaTilOg the ratio of the 1-kcps conductivity to the direct current conduca t 60". tivityis 4 X Temperature CoefJicientof Permittivity. Temperature coefficients of permittivity (1/e') (dE'/dt) were evaluated from the plots of permittivity us. temperature at the frequencies shown in Figure 1. Values a t 20" are given in Table 111. These coefficients do not change much in magnitude with rising temperature until the region of temperature dispersion appears ; thereafter they become large and positive. Piercy8 has discussed the factors which contribute to the sign and magnitude of the temperature coefficient: (a) the coefficient of linear expansion, p, and (7) H. Frolich, "Theory of Dielectrics," 2nd ed, Oxford University Press, Fair Lawn, N. J., 1958, Chapter I, p 192. (8) B. Piercy, Trans. Faraday Soc., 55, 39 (1959).
Volume 72, Number 4 April 1968
a. w. M A R K S AND c. E. ANTONIAK
1120 10'
(l/E)(de/dt) =
10'
L.
cs
108
2
9
108
IO'
0
x 105 103
IO4
0.002
0003
0.002
0.003
0.002
0.003
I/T
Figure 3. Variation of 1 kcps resistivity, r n , in ohm centimeters with reciprocal of the Kelvin temperature, T, for ceramic: (a) BaTia07; (b) BaTiaOe; and (c) BaTiOa.
10') 10'2
IO"
2: t 2
10'0
b $ IO9 0
n 108
107
I/T
Figure 4. Variation of dc resistivity, r, in ohm centimeters with reciprocal of the Kelvin temperature, T , for ceramic: (a) BaTirOo; (b) BaTirO7; and (c) BaTi03.
Table I11 : Temperature Coefficient of Permittivity (l/e')(de'/dt) and Numerical Values of A = (l/e')(de'/dt)/ tan 8 at 20" for Ceramic BaTia0.i and BaTiaO, Ceramic
BaTi807
BaTi40~
Frequency
S - So(T) I4
( l/d) dr'/dt
100 cps-100 kcps - 4 . 5 X 10-4 500 kcps and 1 Mcps -3.4 X l o u 4 5 Mcps -2.0 x 10-4
0.02 0.62
10 Mcps
0
100 cps-100 kcps 500 kcps 1 Mcps 3 Mcps 5 Mcps
10 Mcps
0 0 -2.0 -2.0 -2.0 -1.9 4.7
x x x x x
0.009
0
10-4 10-4 10-4 10-4 10-4
0.04 0.04
...
0.01 0.06
the temperature coefficient of electronic and ionic polarizabilities (l/a) (daldt) result in the contribution (l/ew)(dcm/dt)> and (b) a contribution which is the result of dielectric relaxations. The equation derived by Piercy8can be written in the form of eq 2. The Journal of Physical Chemistry
The volume coefficient (l/v) (dvldt) is taken equal to 3P; a is the sum of the electronic and ionic polarizabilities. The derivation of this equation is partly based on the differentiation of the Clausius-Mossotti equation and strictly speaking is applicable only to those dielectrics to which this relationship applies. It is assumed that tan 6 is independent of frequency. Examination of the loss tangent vs. temperature curves a t fixed frequencies up to 105 cps for BaTi307and BaTi40s showed that the loss tangent is essentially constant a t any chosen temperature within the range investigated. It is seen that the temperature coefficient of permittivity will be negative only if the volume coefficient of expansion (30) is the predominating factor when (l/a)(da/dt), j3, and d tan S/dt are positive. Negative values of (l/e) (deldt) for BaTi307 and BaTi409 in the low-frequency and low-temperature regions indicate that the polarizability coefficient (l/a)(da/dt) is smaller than 36 and that tan S is negligible. There is a marked increase in d tan S/dt a t higher temperatures for BaTi408 with the result that the slope of the temperature coefficient of permittivity becomes positive. Any value of d tan 6/dt occurring in the temperature dispersion region at a low frequency shifts to higher temperatures with increase in frequency. The entropy change (in electrostatic cgs units) per cubic centimeter of a dielectric, on the application of a static field E , is given by the relationship =
(d€,/hT)E2/8a
(3)
where Tis the Kelvin temperature, &(T) is the entropy per unit volume in the absence of the field E , and es is the static permittivity which is essentially the same as the low-frequency permittivity.' The slope of the 100-cps curve for BaTi30, (Figure 1) is -0.022 deg-', whereas that for BaTi409 at the same frequency was taken t o be zero. I n the case of BaTi30,, a t a field strength of 30 V/cm ( E = 0.1) the entropy decrease, as found from eq 3 is -8.8 X esu/cm3, indicating a slight ordering in the presence of the field. Activation Energies. A comparison of the activation energy for the large dispersion in the high-temperature region with that for direct current conduction yields further knowledge concerning this particular relaxation process. We follow the procedure in which the approximation is made that there is but a single relaxation time and that eo' - E, ' is not temperature dependents8 If fi and T t , and f j and T,are any two frequencies and Kelvin temperatures, respectively, at which the capac-
1121
DIELECTRIC PROPERTIES OF BaTi307 AND BaTirOs ities of the sample are the same, the activation energy
El of the relaxation is given by
where k is the Boltzmann constant. Examinatiou of the Debye equations, which refer to a dispersion mechanism with but a single relaxation time T, shows that tan 6 also remains constant when U T is constant.7 Equation 4 is then applied by first choosing a value of tan 6 for the region under study and reading temperatures off the tan 6 vs. temperature curves and recording the frequencies. Activation energies obtained by use of the two above given procedures for this large dispersion are given in colunins 2 and 3 of Table IV. Frequencies chosen were in the range 102-1oj cps and temperatures were in the neighborhood of 200". In the case of BaTiaO7, dielectric dispersion had not occurred sufficiently a t the higher ternperatures to permit the evaluation of
El. The activation energy Ez for dc conduction was evaluated from the log (resistivity) vs. l / T plot (Figure 3). For BaTi307 and BaTi40s these resistivity curves lie well across the region of the large dielectric dispersion. Values for Ez are given in Table IV. Table IV : Activation Energies, E, by Different Procedures --Activation Dielectric diapersion, Ceramic
eV
BaTiOs BaTir07 BaTi40s
... . . I
0.80
energy, E, fromTan 8, eV
... 0.88 0.74
Direct current conduction, eV
0.85 1.05 1.03
Tests for Ferroelectricity. An examination of Figure 1 shows that marked changes in permittivity with temperature rise were not observed for either dielectric in the temperature range 0-260". Thus no phase changes are indicated in this region. To determine whether or not these compounds are ferroelectric, respective disks of each were mounted in a 60-cps display circuit. The hysteresis loop, characteristic of ferroelectrics, was not observed in the temperature range 0-425". Also the maximum polarization was low and roughly 0.01 that for ceramic barium titanate under like conditions.9 Examples are shown in Figure 5 . The ratio of the polarizations at 10 kV/cm, P N ( B ~ T ~ ~ O ~ ) / P M ( B was ~ Tabout ~ O ~0.005. ), Structure and Ferroelectricity. The atomic arrangement a t ambient temperatures of the five intermediate compounds in the BaO-TiOz system has been determined with the exception of BaTiaO,. Only the metatitanate, BaTiOir,displays ferroelectricity. The reasons
KVKM
Figure 5 , Evidence of lack of ferroelectricity in BaTir07 and BaTi*09at 25". Upper curves, linear variation of the maximum polarization with peak field strength; lower curve, unpolarized ceramic BaTiOl.
for this will now be pointed out. The orthotitanate, BazTi04, has the monoclinic space group P21/m and thus belongs to the point groups 2/m, which is a nonpolar crystal class, and so at least at room temperature this titanate is not ferroelectric.lo The environment of the titanium site is not the usual octahedral arrangement so characteristic of perovskite-type titanates, but rather a more nearly tetrahedral arrangement of oxygen sites about the titanium ion, thus resembling a sulfate ion. I n barium dititanate, BaTizOs, the titanium atoms lie in a distorted structure of octahedra of oxygen atoms." The space group is A2/m, which is also one of the nonpolar crystal class 2/m. Barium tetratitanate, BaTi409, has the symmetry of the nonpolar orthorhombic class (mmm) at room temperature.6 The titanium sites lie in distorted octahedra which share edges and corners three dimensionally. The titanium atoms are not a t the centers of these octahedra so that polarized octahedra are the result, but the over-all structure is a centric one, so that this titanate is not ferroelectric either. In barium metatitanate the titanium atoms lie within octahedra of oxygen atoms which share their corners with those of neighboring octahedra. At ordinary temperatures this compound belongs to the tetragonal space group P4/mm, which implies that the fourfold symmetry aftis is polar, and hence this material is ferroelectric.12 (9) G. W. Marks, D. L . Waidelich, and L. A. Monson, Commun. Electron., 2 6 , 469 (1956). (10) J. A. Bland, Acta Cryst., 14,875 (1961). (11) F. W.Harrison, {bid., 9, 495 (1956). (12) H . D.Megaw, "Ferroelectricity in Crystals," Methuen and Co., London, 1957,Chapter 4.
Volume 78, Number 4 April 1968
W. J. MACKNIGHT, L. W. MCKENNA,B. E. READ,AND R. S. STEIN
1122
Summary 1. Within the temperature range 0-260" and the frequency range 100 cps-10 Rilcps, the permittivity, E', of ceramic BaTia07and ceramic BaTi40svaries linearly with temperature. 2. The loss tangent of both dielectrics a t any chosen temperature within the range 0-150" remains
essentially constant with increase in frequency up to lo5 CPS. 3. Activation energies from direct current conduction measurements are 1.05 eV for BaTi307and 1.03 eV for BaTi40s. 4. No evidence of ferroelectricity was found for either of these dielectrics within the range 0-425".
Properties of EthyleneMethacrylic Acid Copolymers and Their Sodium Salts: Infrared Studies by W. J. MacKnight,' L. W. McKenna, B. E. Read, and R. S. Stein Department of Chemistry and Polymer Science and Engineering Program, University of Massachusetts, Amherst, Massachusetts 01008 (Received June 20, 1967)
An infrared spectroscopic investigation of ethylene-methacrylic acid copolymers and their sodium salts has been carried out. All the copolymers studied were based on a parent copolymer containing 4.1 mol % of methacrylic acid groups. This was then neutralized to various extents (from 0 to 78%) with sodium hydroxide. The per cent ionization was determined from the integrated absorbance of the 1700 om-' un-ionized carbonyl stretching band. Temperature-dependent infraied studies showed that the behavior of the un-ionized acid groups over the entire range of ionization is quantitatively comparable to that of low molecular weight carboxylic acids in nonpolar solvents. A monomer-dimer equilibrium exists among the acid groups and they are almost completely in the form of hydrogen-bonded dimers at room temperature. The heat of dissociation of the dimers was found to be 11.6 kcal mol-'. Thus each hydrogen-bond has a bond strength of 5.8 kcal mol-'. Infrared dichroism studies established that there is a significant amount of crystallinity even a t the highest degree of ionization, that the hydrogen bonds are intermolecular in nature, and that the ionized carboxylate groups have a preferred orientation out of the plane of the main chain of the copolymer.
Introduction This work represents part of a continuing study of the role of intermolecular forces on the physical and mechanical properties of polymers. The ethylenemethacrylic acid copolymers and their sodium salts provide an interesting system for such investigations. It has been established2that the ionization of these acid copolymers results in a significant eiihancement of their tensile strengths and melt viscosities. These findings were explained on the basis of the introduction of strong interchain ionic links.2 The validity of this interpretation is somewhat doubtful, however, and alternative explanations have recently been proposed. a I n this paper are reported the results of an infrared study on films of ethylene-methacrylic acid copolymers, ionized to various extents with sodium. The per cent ionization was determined by analysis of the infrared spectra. The equilibrium constant for the dissociation of carboxylic acid dimers and their heat of dissociation were obtained from temperature-dependent infrared The Journal of Physical Chemistry
studies. Infrared dichroism indicated that the hydrogen bonds f a m e d between un-ionized carboxyl groups are intermolecular. The implications of these findings concerning the mechanical properties of the materials are discussed elsewhere.3
Experimental Section The starting material was a partially ionized copolymer of ethylene and methacrylic acid kindly supplied by the Du pant co. Its structure may be represented schematically as
CHa -(CH&HJ
.-(CH2-C-),
I
l
COOH COO-Na+ (1) TOwhom correspondence should be addressed.
