Dielectric properties of microwave ceramics investigated by infrared and submillimetre spectroscopy

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Femelectrics, 1996, Vol. 176, pp. 145-165 Reprints available directly from the publisher Photocopying permitted by license only

8 1996 OPA (Overseas Publishers Association) Amsterdam B.V. published in The Netherlands

under license by Gordon and Breach Science Publishers SA

Printed in Malaysia

DIELECTRIC PROPERTIES OF MICROWAVE CERAMICS INVESTIGATED BY INFRARED AND

SUBMILLIMETRE SPECTROSCOPY

J. PETZELT and S. KAMBA Institute of Physics, Czech Acad. Sci., Na Slovance 2, 180 40 Praha 8,

Czech Republic

and

G. V. KOZLOV and A. A. VOLKOV Institute of General Physics, Russian Acad. Sci, 117 942 Moscow, Russia

(Received June 26, 1995)

Results of our 10 years study of more than 80 microwave ceramics varying in composition and processing with the aid of infrared reflectivity and submillimetre transmission spectroscopy are reviewed. These techniques are unavoidable for understanding the origin of microwave permittivity and losses. Extrap- olation from submillimetre to microwave range is discussed as well as the observed steep overall increase in losses on increasing permittivity. The most important structural parameter for dielectric properties is the packing degree. Ideally packed structures show the lowest permittivity and losses. O n lowering the packing degree, permittivity and losses increase and the lattice becomes more anhannonic. Extrinsic part of losses due to defects is discussed on the basis of their temperature and frequency dependences, but no clear quantitative conclusions can be drawn in most cases.

Keywords: Microwave ceramics, infrared rejlectivity, submillimetre transmission, dielectric losses, microwave pennirtivity.

1. GENERAL CONSIDERATIONS

Microwave (MW) ceramics are frequently used as MW dielectric resonators in in- tegrated circuits. The basic requirement is high enough permittivity &' to allow for sufficient reduction in size (proportional to lm), almost temperature independent E' to ensure stability of the resonance frequency and low dielectric losses d to provide sufficiently high quality Q of the resonator (Q = E'M - lb-ld). The choice of suitable materials has been so far largely empirical and especially the problem of minimization of losses by material processing and the separation of intrinsic (unavoidable) and extrinsic MW losses seems to be very difficult and has not yet been studied in a systematic way. Also the relation between the lattice structure and MW dielectric properties (values of E' and &") was not investigated until very recently. The most promising approach to understand the MW dielectric properties is to study the higher frequency dielectric response including the whole submillimetre (SMM) and infrared (IR) range. Namely, recent theoretical analysis has shown' that the intrinsic losses in pure single crystals in the low-frequency range well below the polar phonon eigenfrequencies (v << vi) at not extremely low and high temperatures are dominated by two phonon difference absorption processes. For small frequencies v << yT (yT is the mean damping of thermal phonons) their contribution to loss is

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146 J. PETZELT et al.

proportional to frequency. -yT is typically in the order of 10"- lot2 Hz at room temperature so that in the whole MW range the projwrtionality E" a u is expected to be obeyed for intrinsic losses. If also in SMM range this relation is obeyed, SMM transmission spectroscopy enables to extrapolate the loss spectrum to zero and to estimate the intrinstic MW losses.

This method has a great advantage in that the SMM losses are much higher than MW ones and therefore are more easily measurable in a broad frequency range (typically 5-100 cm-') using an optic arrangement (Fourier transform or backward- wave-oscillator monochromatic spectroscopy). However, one has to take into account that the proportionality E" Q Y itself does not guarantee the intrinsic nature of all the losses. shows that e.g. the charged-defect induced one-phonon absorption of acoustic branches also yields E" Q u if the point charges are uncorrelated (this holds for v 2 G/E, C is the mean acoustic velocity and 5 correlation length of charge compensation, C/E lies in the range of 10'o-lO1l Hz). Therefore the knowledge of the frequency dependence of losses itself is insufficient to estimate their intrinsic and extrinsic parts. To enable this, also measurements of the temperature dependences of loss spectra are necessary. Assuming e.g. frozen-in point defects whose concentration is temperature independent below room temperature, one could expect that finite background losses are still present for T + 0 which gives a measure for extrinsic loss part. Namely, the intrinsic low-frequency losses are expected to vanish for T + 0 quite steeply, E" a T" with a up to 9 depending on the point symmetry of the lattice'" and therefore are negligibly small at low temperatures T - -= 100 K.

Historically the first experimental study of the high-frequency dielectric response in MW ceramics was based on IR reflectivity measurements? The IR reflectivity of Ba(Zn,,Ta,)O, type ceramics was fitted with a model of sum of classical damped oscillators and the calculated complex dielectric function was extrapolated to MW range and compared with the directly measured values. Whereas E' agreed within 5% (which stays within the limits of accuracy of reflectivity measurements and fit), extrapolated losses were 2-3 times smaller than the measured ones.

Since then, the simple classical damped oscillator model which fits the IR reflectivity data was frequently used (with more or less success) for extrapolation of the dielectric data from IR down to the MW range!-'* It generally works quite well for permittivity estimates which are not too sensitive to processing details (under the assumption of negligible porosity) and gives no appreciable dispersion in the MW range. For losses it also fulfills the simple proportionality &" a u in the low frequency limit as expected from the microscopic theory, but there is no need for good quantitative agreement. The reason is that only special two-phonon absorption processes close to the lines of degeneracy of phonon branches are operative in the M W range, whereas two-phonon processes all over Brillouin zone are operative close to the polar phonon eigenfrequencies and determine the damping of polar modes?'3v14 Recently the problem was treated more quantitatively and estimates" show that around room temperature the oscillator model should yield by an order of magnitude higher MW losses than the microscopic theory predicts in the case of small permittivity compounds, but may yield the right order of magnitude for compounds with E' 2 20. Also the temperature dependences of MW losses are different for both approaches.'" Whereas the microscopic theory predicts steep decrease of losses on cooling (see above) and quadratic temperatures dependence on heating (E" Q T'), the oscillator

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PROPERTIES OF MICROWAVE CERAMICS 147

model predicts MW losses proportional to relevant polar phonon damping which remains finite for T + 0 and roughly proportional to T for T 2 T D where TD is the Debye temperature (E" a T). Therefore at sufficiently high temperahues according to the microscopic theory the MW losses may always exceed those extrapolated from the oscillator model.

Summarizing, the IR reflectivity approach gives a good estimate of MW permittivity but may fail in estimates of MW losses. The SMM transmission is much more promising for these estimates. First, it is more accurate for evaluation of losses, and second, if proportionality E" a u is obeyed in the SMM range, this dependence may be assumed to be valid down to MW.

Our task during the 10 years was to determine the whole IR and SMM dielectric response in many commercial as well as laboratory-processed MW ceramics, com- pare it with known MW data and discuss the extrapolation procedure from IR to M W using the ideas mentioned. Also we started the study of the difficult but important problem of the relation among M W permittivity, losses, crystal structure and ionic parameters. Our original data have been published in several papers4*'*g*1'*12'5-19 and here we would like to review them, complement by some new data and discuss in light of the above mentioned theories.

2. EXPERIMENT

Ceramics for our studies were processed in several collaborating laboratories or were provided by companies producing them commercially. Also the MW dielectric char- acteristics was performed by the ceramics producer. Care was taken to achieve high density, at least 95% of the theoretical one. For IR reflectivity measurement (30- 3000 cm-') the ceramic pellets were ground and polished to obtain a flat glancing surface (diam. 6-10 mm). For SMM Fourier transmission measurements (15-100 cm-') the pellets were cut and polished resulting in plane-parallel discs of the thick- ness of 0.3-0.6 mm. For SMM and near-milhnetre (NMM) backward-wave-oscillator (BWO) spectroscopy (5-30 cm-') mostly thicker plane-parallel discs (-1-2 m) were used.

Fourier spectroscopy measurements were carried out using Bruker IFS 113v vacuum interferometer. Normal specular reflectivity (angle of incidence 110) was evaluated by Kramers-Kronig analysis" and more recently only by fitting. Classical 3- parameter oscillator model was mostly preferred rather than the generalized Cparameter one.zo The reason for it was that with the latter model sometimes neg- ative E" values appeared in limited spectral ranges and the low-frequency tail in E"(u) (important for the extrapolation to MW) could not be decomposed into an additive contribution of individual oscillators. Neither of the drawbacks does occur in the classical oscillator model, but the overall quality of the fit might be worse. The relative accuracy of the low-frequency E' and E" values is estimated to 2 5 % and +30%, respectively, due to limited accuracy of the reflectivity (22%) as well as some ambiguity of the fit (especially for high permittivity materials). Fourier transmission measurements were performed using He-cooled Ge bolometer (working in the 15-100 cm-' range) and higher resolution (5 0.5 cm-') to resolve correctly the interference maxima and minima due to the multiple passage of light through the

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sample. The spectra were evaluated in a standard way, determining first the refractive index from the positions of interference maxima and then the absorption from the transmission to these maxima?' The estimated accuracy is 22% and 25% for E' and E" values, respectively.

BWO spectroscop~ uses the same measurements method as Fourier transmission. Due to our rather transparent samples, no phase of the transmitted light needs to be measured. Due to thicker samples the interference patterns are more dense and the evaluated optimal constant more accurate. The estimated accuracy is 20.5% and 23% for E' and E" (down to -0.01), respectively. This accuracy is comparable to most accurate MW measurements techniques with reduced probability of spurious effects and systematic errors in case of the BWO open-air optic technique.

Temperature dependences were studied in some cases with both transmission techniques. Standard Heflow cryostats and furnaces were used to cover the temperature range 10-600 K.

3. RESULTS

In Table I we give directly measured and extrapolated MW E' and Q X v values for the representative compounds. The quality Q = E'/E" so that if E' is dispersionless and E" Q u, the product Q X v is independent of frequency. The comparison of Q X u values from MW and SMM and extrapolating them from IR measurements allows us to assess about the validity of the E" 0: u dependence in the MW and NMM wave range or validity of the oscillator model down to the MW range, respectively.

Let us comment on some of the results in Table I. First of all, there is no serious problem with E' values, where the agreement between SMM and MW range is mostly better than -3% which is fully within the limits of experimental error. The exceptions are the high permittivity B&'r2T4012 and BaL,a2TiOl2 materials (samples No. 30 and 3 1) where a clear relaxational dispersion is observed below the polar phonon region with relaxation frequencies near 5 and 20 cm-', respectively" (see Figure 1). It is interesting to note that according to our IR reflectivity data, there are no remarkable differences in the phonon spectra of samples No. 28-31 even though the permittivity varies between 79 and 106. Figure 1 shows that the differences in E' are mostly caused by this extra relaxation below the lowest phonon frequency near 42 cm-' (most pronounced in BaJ-.a2Ti0,3 and not by variation in polar mode frequencies.1o Second, all the well processed ceramics show a good agreement (within 30%) between Q X u values in MW and SMM range, proving that the E" a v dependence is well obeyed below -10 cm-' (down to at least 5 GHz).

The following exceptions may be noticed: Ba(MglTa,)O, (No. 6) was prepared at EPF Lausanne from the calcined Siemens powder. The sample was compared to that prepared by Murata (No. 5). Chemical analysis has shown good stoichiometry and no differences in either of composition and IR reflectivity spectra. However, microstructural analysis discovered a dense structure of antiphase boundaries (faults in the B-site ordering) within grains of sample No. 6 absent in sample No. 5. More- over, traces of a second phase inclusions with less Ba and lower Mg/Ta ratio were found by optical microscopy and energy dispersive spectroscopy analysis in the sam-

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TABLE I List of representative MW ceramics with MW dielectric characterization and extrapolated data from

SMM and IR range. References: Material No. 1, 24, 26. 27,'' 2: 3, 10. 22, 29." 5, 7, 8. 9. 21,' 11- 19."" 28, 30. 31.= 32-36.= The abbreviation Vt%K belongs to Research Institute of

Electrotechnical Ceramics, Hradec W o v e (no longer exists). -

!!! - 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

32 33 34 35 36 -

Abbr.

MT MCT MCT BMT BMT BMST BZT BZZT BZZT BMW BIT BYT BIN BGT BNT BYN BGN BNN ZT ZTS ZTS ZTS ZTS ZTS

- - MW 9.9 17 21 20 25 23 24 28 30 29 19 25 30 33 34 36 37 41 41 38 38 38 37 36 37 42 75 79 92 97 106

76 68 64 46 31

- -

-

SMM - - lo 17 21

? 26 23 24 28 30 29 19 25 30 34 33 35 36 41 43 37 38 38 36 35 37 42 73 77 90 87 102

? 68 64

? 34 -

- I

MW 300 180 69 50 330 50 270 150 150 87 110 130 46 56 9 44 26 7 19 23 59 50 52 40 35 32 8.5 4.5 5.9. 3.6 0.6

16 30 25 31 82

- -

-

- Y (TI IMM 400 170 63

? 450 220 260 170 130 110 178 138 93 31 55 42 69 30 23 28 47 44 54 54 26 30 12 12 14 5.9 2.8

? 34 33

? 62

- -

-

m - - !

44c 65

? 22c 22c

? 13C

? 2c 360 330 230 40 160 60 150 60 50 15

? 19 1 ? 26

? ? 16 21 9.9 2.4

16 19 19 20 33 -

Compang

Siemens Epsilon Murata Siemens Murata Murata Mnrata Siemens

Murata 3iemens Epsilon

Siemens

Producer Laboratory VUEK Univ. Aveiro

+ EPF Lausanne

EPF Lausanne EPF Lausanne EPF Lausanne EPF Lausanne EPF Lausanne EPF Lausanne EPF Lausanne EPF Lausanne EPF Lausanne Univ. Manchester

VUEK

VUEK VUEK

Univ. Manchester

Univ. Manchester

Univ. Manchester Univ. Manchester Inst. J. Stefan, Ljubljana

ple No. 6. The SMM absorption of sample No. 6 is about two times higher than that of sample No. 5 and shows a weak broad absorption peak near 50 cm-' overlapping with the monotonously increasing absorption background. Its ongin may be either the second phase or the antiphase-boundary induced one-phonon absorption of acoustic phonons. In any case, sample No. 6 cannot be treated as optimally processed which causes an increase in the M W and SMM losses.

In the case of some of the Ba(B:nB;rr)O, perovskites additional complications arise: proximity of structural phase transitions for BYT (No. 13, T, = 253 K) and BYN (No. 17, T, = 260 K) and presence of additional paramagnetic losses for BGT (No. 15) and BGN (No. 18)." The structural transition is connected with the a p pearance of IR inactive soft phonon modezs which provides an additional temperature

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I 1 I I I 1 I 1

0 10 20 30 v (cm')

FIGURE 1 SMM dielectric spectra of BaN&TiiO,. (BNT. No. 28). BaPr2TbO12 @€T, No. 30) and BaLa,TbO,z (BLT, No. 31). Note. that the results were obtained on samples with 6 different thicknesses and agree perfectly with each other.

and frequency dependent channel for the two-phonon absorption not considered in the gened The magnetic losses have not yet been analyzed quantitatively, but their temperature dependence in the MW range correlates with that of the paramagnetic susceptibility" and they are negligible in the SMM range. All these facts explain the disagreement between Q X u values in M W and SMM range for samples No. 13, 15, 17 and 18.

Finally, the disagreement between Q X v values in MW and S M M range for BaLn2"'ii0,2 compounds (No. 27-3 1) is caused by additional Mw or SMM dielectric relaxation, as already mentioned (see Figure 1).

Let us now comment on the Q X v values obtained from the IR reflectivity fit. In many cases the agreement with SMM and MW values is surprizingly good taking into account that such agreement seems not to be theoretically j~stified."'~ Always it gives a right order of magnitude, at least. In most cases the extrapolated Q X Y

values are higher than those measured directly. Exceptions are Ba(MglnTam)03 (No. S), Ba(Zn,Zr,Ta)O, (No. 10) and (Zr,SN)TiO, (No. 22) where the losses extrapolated from IR reflectivity are too high. In addition to microscopic arguments also IR an- isotropy may cause effective increase in extrapolated losses in a polycrystalline sample. Namely, averaging over all crystal orientations may cause broadening of reflec-

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Wavenurnber(cm-'l FIGURE 2 Temperature dependence of the SMM loss spectra in MgTi03: 1% La ceramics. The peaks belong to L+Ti207 second-phase phonons. From Reference 19.

tivity bands which then influences the fit parameters including an effective increase in phonon damping and consequently in extrapolated losses.

Table I does not include al l samples we have investigated. In the case of Mg'I"103 we studied 14 samples' which differed in the way of sintering and by dopants Nb" La3+, C?, Coz+, Ni2+, MgO, Ca"i03. All the samples exhibited practically the same IR reflectivity, but differed in both SMM and MW losses by up to a factor of 4. Good correlation between losses in both regions remained valid for all the samples. This means that for the additional extrinsic losses the proportionality E" a Y' is also roughly fulfilled. On the other hand, IR reflectivity is not to sensitive to the details of processing and to s m a l l concentration (of the order of 1 wt%) of dopants.

The origin of extrinsic losses was investigated in the case of MgTiO,: l%h3'.'' In this case three additional absorption peaks were observed in our SMM spectra (at 45, 52 and 82 cm-') not present in the pure MgTi03 (see Figure 2). Microstructural analysis has shown that La forms a second phase of &IT207. Direct IR reflectivity measurements on pure La2Ti2O, ceramics confirmed that the extra peaks belong to the three lowest polar phonon modes in this compound. Also the weak temperature dependence of the ~ " ( u ) spectra of MgTi03:La (Figure 2) supported this ~icture. '~ Therefore the reason for increased MW losses in the doped sample is mainly the more lossy second phase.

Extrinsic losses in the pure MgTi03 sample were also studied by temperature dependence of the SMM transmission in the 5-300 K range" (see Figure 3). It can be seen that below 200 K the losses below 30 cm-' are practically temperature

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0 5 0 ~

a 0

A O .

300K a 2 0 0 K 0 5 K *

A 0

a 0 . a 0 .*

20 40 60 80 Wavenumber 1 cm-’ 1

FIGURE 3 Temperature dependence of the SMM loss spectra in pure MgTiO, (No. 2). From Reference 19.

independent and amount to about half of the room-temperature value. Assuming that the concentration of defects is temperature independent below 300 K as well as the extrinsic losses caused by them, it follows that about half of the room-temperature losses is of extrinsic origin even in a best processed MgTiO, sample. The extrinsic losses also satisfy the E” 0: u proportionality at least between 10 and 30 cm-’.

Another series of samples not included in Table I concerns the (CaTi03),-x(I-a (MglnTiln)03)x system.’’ Sample No. 26 is for x = 0.49, other investigated samples have x = 0.333, 0.169, 0.097 and 0. In this series the MW permittivity increases from 42 up to 180 which was shown to be caused mainly by the lowest polar-mode frequency which shifts from 170 down to 106 cm-’ in the same series. However, the samples were not optimized for the MW losses and not measured with transmission techniques.

Also in the (Zr,Sn)Ti04 (ZTS) system we have studied more samples, particularly from the University of Manchester. We studied pure W104 under various cooling conditions after sintering, Zr,Ti,O,: Y3+, and Zr0.8Sn,,2Ti04: x wt% F&03 (x = 0, 0.5, 2.4). The reflectivity spectra are rather complex in that they do not show a distinct peak structure and are similar to each other and to those already published.8*” Only the ZrsTi,O, sample shows more structure in reflectivity (-15 peaks) than W i O , (-10 peaks) and (ZrSn) TiO, (-7 peaks). Comparison with the results by Kudesia et aL8 shows that our best samples give higher overall reflectivity than their samples which show moreover a high scatter of the overall reflectivity magnitude. This is obviously due to the surface mechanical quality and cannot indicate anything relevant on the extrapolated losses. In this respect the results of Reference 8 are not conclusive. Our SMM transmission as well as MW data correlate well with the reflectivities, but show also some scatter in permittivity (between 31 and 40) as well as in losses (Q X u between 10 and 26 THz) indicating that even our sample quality is not sufficient for drawing quantitative conclusions. In Table I (No. 25) we pre-

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0 200 400 600 800 1000 Wavenumber (crii')

FIGURE 4 Reflectivity spectra of some (Ba,Sr)(Zr,Ti)Q ceramics. The increase. in low-frequency reflectivity for y-decrease from 0.973 to 0.25 corresponds to increase in permittivity from 30 to -200.

sented the results for our best sample (Zro.8S&.2Ti0,) but the SMM data are taken for the 0.5% FqO, doped sample which showed better Q X v value.

Not included into Table I is also a group of perovskite ceramics with the general formula (B~r,~x)(ZryTi ,~y)O, which for x = 0.29 and y = 0.95 gives E' = 30 and Q X v = 23 THz at 10 cm-I. On increasing x and decreasing y both E' and E" increase up to a ferroelectric composition for x 2 0.6 and y = 0. In this way a series of materials can be prepared with a quasicontinuous change from the MW transparency up to high opacity and permittivity at the ferroelectric composition end.% Our reflectivity data (Figure 4) and evaluated d'(~) spectra (Figure 5 ) show that these changes are caused by softening of the strongest polar mode near 220 cm-' at the low permittivity end. This mode, which corresponds predominantly to the ferroelectric Zr(Ti) f) 0 valence vibrations,'* couples to at least two lower-frequency modes and on softening (approaching the ferroelectric end) transfers its oscillator strength to them. This corresponds to anticrossing of this mode with both lower modes on approaching the ferroelectric composition so that at this end the lowest-frequency mode represents the ferroelectric soft mode, in agreement with the common experience.

Finally, we would like to mention a new perspective group of MW materials, also not included into Table I, with a very high permittivity, AgTa,-xNbxO, perovskite system?' It displays a complex phase diagram with several phase transitions of an-

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154 J. PEIZELT ef al.

Wavenumber (crn-') FIGURE 5 Permittivity (a) and loss spectra (b) from the fit to reffectivifies in Figure 4.

tiferroelectric nature and complex dielectric behaviour, but the appreciable dispersion of permittivity sets in only above 10'' Hz so that at hiw frequencies low losses are expected. ~'(300 K, 5 cm-') varies nonmonotonously between -170 for x = 0, reach- ing maximum -400 at x - 0.5 and dropping again, to -200 for x = 1. In the range of maximum E', &'/dT is close to zero near room temperature and the estimated Q X v is 1.4 THz yielding Q (1 GHz) = 5000 with reasonably small size of the resonator? Our recent IR reflectivity and SMM transmission measurements for x = 0, 0.3, 0.4, 0.5, 0.6, 0.7 and lma have revealed a strong low frequency mode (see Figure 6), well underdamped for x = 0 (at 300 K vo = 80 cm-', y = 7 cm-', AE = 90) which slightly softens on increasing x. Simultaneously, an extra overdamped mode develops in the SMM spectra (analogy to the central mode in Raman spectra?. For x = 0.6,300 K, its relaxational frequency spectra is v, = 1.5 cm-I and dielectric strength A&, = 250; for x = 1, 300 K, v, = 27 cm-', A&, = 130; for x = 1, 650 K, v, = 15 cm-', A&, = 900. The relaxation dies out on cooling and disappears from the spectra at low temperatures (see Figures 5,7 and 8). This brings evidence of the anharmonic origin of this excitation and of partly order-disorder nature of the first- order transition near 630 K.

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- x=0.27 y=0.973

x=0.27

-

- -

y=o.9

0 200 400 600 800 1000 Wavenumber (cm-'1

FIG- 5 (Contintced)

4. DISCUSSION

4.1. Loss Dependence on Permittivity

From Table I one striking but well known property follows: the losses increase quite steeply with increasing permittivity, irrespectively of the crystal structure. This is demonstrated in Figure 9 where the Q X v values in SMM range are plotted against E' values at 10 cm-'. Using a primitive single effective oscillator model with eigen- frequency vo, damping y and strength S, one can qualitatively understand this tendency from the well known formula

S vi - v 2 + i q

E(V) =

neglecting the high-frequency permittivity E, << E,,. For v cc vo we get E' = E,, = S/ vi, E" = vSyIvd = v&y/S and Q X v = vi/y = Sly&. If one could assume the oscillator strength s = e2/(tm,.V)/(e = effective charge of the oscillator, m = its reduced mass, E,. = permittivity of vacuum, V = volume of the unit cell) and damping y to be independent of the material permittivity, one would expect Q X v a (&)-I(&" a <). As seen from Figure 9, the actual mean dependence is steeper, at least as Q x

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156 J. PE'IZELT et al.

400

200

0

50 0

50 0

50 0

2 00

100

0

T= 523K AgTa,-, Nb,O,

x = l

x = 03

X = 0.6

x =o

Wavenumber I cm') FIGURE 6 IR and SMM loss spectra of the Ag(Ta,Nb)O, system at 523 K. The results are calculated from the simultaneous fit to reflectivity and S M M transmission.

u a (6)-2(E" a d). This means that average damping andor mass are increasing or the effective charge is decreasing with increasing 6. The first possibility seems to be most probable and it indicates increase in anharmonicity (at least for the lowest- frequency modes) on increasing 4. This correlates also with the fact that high permittivity materials show the central-mode-type relaxational dispersion below optic phonon frequencies characteristic of highly anharmonic materials like ferroelectrics close to T, (see BaLnzT4012 compounds No. 29-31 or Ag(Nb,Ta)O, materials).

The problem of how the MW losses depend on permittivity can be solved in more detail and in a more reasonable way only for a group of isostructural compounds. This was studied in the complex perovskite family Ba(B',nB';n)O, (No. 11 - 19). Var- ying the B ions, variation of permittivity between 19 and 43 was achieved and the losses increase approximately with the 4th power of E', &" a (E')~ as demonstrated in Figure 10 for u = 10 cm-'.

This steep dependence, steeper than the overall dependence in Figure 9, may be understood from the theoretical analysis of two-phonon difference processes between low lying polar optic bran~hes.'~ It was shown that if this is the dominant mechanism and the variation in E,, is caused by frequency variation of the lowest polar branch,

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PROPERTIES OF MICROWAVE CERAMlCS 157

600

1 400 w

200

I w

600

400

200

n - 1 10 100 1000

v (cm’1 FIGURE 7 Temperature dependence of the IR and SMM loss spectra of AgNbo, (a) above the phase transition near 630 K, (b) below it. Notice the dominant appearance of the soft relaxation in the whole Spectra.

one can expect a power dependence E’ a with a lying between 5 (if the branch is dispersionless) and 2.5 (if the branch is strongly dispersive like in displacive ferroelectrics). If the dominant two-phonon process concerns a non-polar branch, a = 2 like for the classical oscillator model.

All these estimates are made under the assumption of constant anharmonicity (independent of E,,), which may not always be valid even within one structural type. Actually, in our case e.g. niobates (No. 14, 17-19) show higher mode damping and therefore higher anharmonicity than the corresponding tantalates (No. 12, 13, 15, 16).” Also the contribution to two-phonon processes from nonpolar low-lying branches seems not to be negligible.” Therefore the increase in anharmonicity seems certainly to play an important role in the steep loss vs. permittivity dependence even for our Ba(B;,B‘;,)03 system. Due to several polar and nonpolar branche~’~’’~ with

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158 J. PElZELT et al.

/. AEr I , ,:/ , , , , ]I0 0 ' 0 0 200 400 600 8001ooo

T ( K ) FIGURE 8 Temperature dependence of the soft relaxation parameters in AgNbO, (v, relaxation frequency, A&, dielecrric strength). Notice that A&, decreases to 0 for T + 0 faster than l/v, so that the product AGV, (relaxation strength) also vanishes for T + 0.

1000 t I I I I I I I I I I

FIGURE 9 Product of quality and frequency Q X v as a function of permittivity, both at 10 cm-'. The numeration of materials is from Table I. The overall tendency is close to Q X Y a (E)-* (full line) and certainly not a (&)-I (broken line) which follows from the oscillator model as discussed in the text.

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I oo

'E 0

10''

10-8 10 100

€'(lo cm-') FIGURE 10 Losses vs. permittivity (at 10 cm-') dependence for the Ba(B;An)O3 (BB'B") family (No. 11 - 19 plus BaFe,,Nb,,O, (BFN)). Full circles for BIN and BFN indicate disorder in the B'-B" sublattice and therefore higher losses. From Reference 14.

unknown dispersion which are populated at room temperature and therefore may take part in two-phonon difference processes, it is difficult to estimate quantitatively which origin for the steep loss vs. permittivity dependence dominates.

4.2. Loss Dependence on Structure

In our set of complex perovskite compounds we have established an interesting simple dependence of dielectric properties on structural packing fraction." Varying the B' and B" ions it turns out that neither valence nor ionic mass play an important role in dielectric properties. The only relevant parameter is the ionic size which determines the packing fraction, i.e. the degree of filling the space. As both Ta5+ and Nb" ions have the same ionic size, the size of the B' ion directly determines the packing fraction. In perovskites this is characterized by so called tolerance factor t" which approaches unity for ideal packing. In Figure 11 we show the E' vs t and E" vs t dependence for v = 10 cm-I. A clear tendency to minimize E' and E" for t + 1 is seen. The exception of Ba (InmnNbln)O3 (BIN) can be understood from the B-ion disorder observed only in this compound which causes increase in both the losses and permittivity. In the cases when t < 1, the Ba" ions have too much room which leads to a decrease of the force constant for BaZ+ oscillations. As it is known that Baz+ motion is mostly involved in the lowest polar mode (Ba t) BO, vibrations), increase in the ionic size in the In3+ - Y3+ - Gd3+ - Nd3+ sequence causes decrease

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160 J. PETZELT er af.

45

40

35

30

25

20

15

0

BYT

0 BIN

BIT 1 c 4

0.95 0.97 0.99 1.01 1.03 1.05 Tolerance factor

BIN 0

1 o - ~

1 o - ~ 0.95 0.97 0.99 1.01 1.03 1.05

Tolerance factor FIGURE 11 Permittivity and loss dependence on the tolerance factor r in the Ba(Ba;,)Q family. t is determined according to

t = (RBa) + ~(o))n/Z

where R(A) is the radius of the A ion. From Reference 17.

in the lowest polar mode frequency from 130 to 104 cm-' and themfore increase in E' and E".

Another system where a pronounced variation of G, is found within almost the same structural type is the (LamTiO,)l-, (LaAIO,), ceramic system (No. 32-36). Our IR reflectiviv shows that the large value of &, for small x is caused mainly by an additional IR mode near 125 c m - I which weakens with increasing n and disappears for x - 0.3. The second lowest mode hardens from 157 + to 184 cm-' on changing x from 0.04 (the lowest possible x with single phase samples) to 1." Both modes

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are heavily damped for small x,= but for x = 1 the 184 cm-' mode is by an order of magnitude less damped.m The extra mode at 125 cm-' can be a Brillouin zone boundary mode folded to the Brillouin zone centre by doubling of the c-axis lattice constant for x < 0.2.3' So it seems that the cubic-orthorhombic transition near x = 0.2 with doubling the c lattice constant?' might be at origin of the E,, increase with decreasing x. The role of the A-site vacancies in dielectric properties and lattice dynamics remains, however, to be clarified.

The last system of isostructural compounds with relatively large variation of E,, is the BaLn,Ti,O,, family (No. 27-31). As already mentioned, our results (Figure lU) show that the main cause of the E,, variation is an additional dielectric relaxation below polar phonon frequencies. This relaxation, which weakens and finally disappears in the sequence La-Ce-Pr-Nd-Sm-Eu) was at lower temperatures and frequencies observed also by Poplavko et ul.32*33 For La compound the relaxation frequency shifts from -5 X 10" Hz at 300 K23 over -10" Hz near 120 K down to I d Hz near 15 K." Its nature seems to be open for discussion, even if in Reference 33 an electronic origin was suggested. Also Raju et ul." suggested an electronic origin, so called nephelauxetic effect (reduction in interelectronic repulsion in a rare-earth ion due to formation of a complex), to be partly responsible (together with the packing fraction) for the variation in permittivity. However, th is effect is expected to influence the electronic polarizability of the Ln3+ ion only, and through it the effective charge of IR modes where Ln vibration is taking part. Our IR data demonstrate that this effect is of no great importance. Our point of view is that the relaxation concerns some sort of dynamical disorder in the ionic motion which is inherent to high degree of anharmonicity in the lattice. The temperature dependence of the dielectric behav- i0&2.33 reminds rather that of dipolar or quadrupolar glasses. Concerning the relation between permittivity and structure, let us mention that, like in the Ba(B;nB:n)03 system, there exists a clear simple correlation between the permittivity and Ln3+ ion size. As in this case the correlation to packing fraction is not so evident (the unit cell volume varies with the compound only slightly), it looks as if larger Ln3+ ions would show up tendency to larger lattice anharmonicity.

4.3. Intrinsic and Extrinsic Losses

As discussed in Section 1, the known frequency dependence of the loss factor C(v) is not always sufficient to estimate the extrinsic loss contribution. Extrinsic and intrinsic losses often show a similar frequency dependence so that a temperature (T) dependence of losses should be determined, as well. In the higher frequency range vi >> v 2 yT the theory' predicts linear &" a T dependence for the intrinsic (two-phonon) processes at intermediate and higher T. All estimates of the extrinsic contributions are based on the assumption that the concentration of defects acting as a source of extrinsic losses (through IR activation of acoustic branches) is independent of T at normal and low T. Therefore also the extrinsic losses should be roughly independent of T. Extrapolating the observed &"(T) = AT + &: dependences to T = 0, one can assume that the background losses E: represent the extrinsic ones. This procedure was used to estimate the intrinsic and extrinsic losses for the Ba(B:, Byn)03 compounds in the SMM range?" The results show that the extrinsic part amounts to from -20% up to -70% of the total room-temperature losses in the

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162 J. PETZUT er al.

IS

'w 03

OD1

I

Zr0.04Zn0.32Ta0.64 '3 --- I

300K / 100 K

I 1 DO loo0 3000 10000

vIGHz)

FIGURE 12 Temperature dependence of SMM losses for sample No. 5 (full line) and 9 (broken line) from Table I.

studied tantalates. However, the results are somewhat frequency dependent for a particular material. Moreover, the pure linear &"(T) dependence is theoretically expected only at sufficiently high frequencies where &"@) = Y*. This regime is practically realized (if at all) only near the upper frequency limit of our transmission measurements. At lower frequencies some crossover to &" = T2 dependence is expected. Nevertheless, we always have observed purely linear T dependence between 300 and 600 K. Three factors may complicate the theoretical considerations concerning T depen-

dences. First, in our substances by far not all optical phonon branches are populated at room temperature. On increasing T, two-phonon processes from newly excited branches may become important and may influence the T dependences of overall losses. Second, the presence of phase transitions introduces T anomalies into phonon frequencies (soft branch) and changes the symmetry (new splitting of phonon branches). This may intraduce anomalies in T dependences near phase transition temperatures T,. Actually, a change of the slope on &" vs T plots at T, is always observed." Third, low T measurements of Ba(YInTalR) (BYT)" indicate that &"(T) + 0 for T + 0 at 10 cm-' even if extrapolation from high T behaviour gives high background loss (Gk" (300 K) - 0.7). It is clear that either practically all the losses are intrinsic, but in this case their T dependence (&" a C T below 200 K) completely contradicts the theory which for the C4 group predicts &" a T".' or the present extrinsic losses are T dependent satisfying &Lt + 0 for T + 0. In this case the origin of extrinsic losses remains unclear.

Therefore, the estimates of extrinsic losses from the high T behaviour based on

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OD1 L I I I 300 1000 3000 10000

v IGHz) FIGURE 13 Temperature dependence of SMM losses for sample No. 7 and 21 from Table I.

the assumption E",, = E: are not reliable. Even low T behaviour does not allow us to make quantitative conclusion on extrinsic losses, as seen in the case of BYT. In Figures 12 and 13 we present the T dependence of SMM losses for 4 Murata cerarnics (No. 5, 7, 9, 21). Only ZTS ceramics (No. 21) show monotonous behaviour in the whole T and u range. Relatively reasonable looks also the behaviour of pure MgTi03 (No. 2, see Figure 3 and discussion in Section 3). The other three samples show some anomalous increase in low T low u losses. Similar behaviour was found for sample No. 5 and 9 at 10 G H z . ~ It brings evidence of some weak relaxational processes caused e.g. by fast hopping of some defects of unknown origin in these

It becomes clear that elucidating the nature of low T losses and separation of extrinsic and intrinsic losses even at room temperature requires a thorough techno- logical work on a selected type of materials combined with extremely broad frequency and temperature spectral investigations, not yet carried out for any material.

samples.

5. CONCLUSIONS

-Permittivity E' is practically dispersionless below Hz and determined by one-phonon absorption processes (oscillator model valid) for all materials with not too high permittivities.

-For very high E' > 100 additional relaxational dispersion occurs in the SMM or

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164 J. PETZELT er af.

lower frequency range ( B ~ T i i O l z , Ag(TaNb)O,, ferroelectrics). Its origin may be strong lattice anharmonicity.

-In well processed ceramics the room-temperature losses are always proportional to frequency, ~ " ( v ) a v for v < 10 cm-' (300 GHz). For higher u a steeper dependence sets in, but the predicted E" of u2 dependence is mostly obscured by steeper dependences due to proximity of phonon eigenfrequencies (as seen from the fits with damped oscillator model).

-The temperature dependence of losses is mostly linear or sublinear, especially at lower temperatures, contrary to theoretical expectation for intrinsic losses. The expected E" a T' dependence at lower frequencies v < 10 cm-' and higher temperatures T > To was never observed. It seems that extrinsic losses of unknown origin are comparable to intrinsic ones at room temperature even in well processed commercial ceramics in the broad range of 10'o-lO1' Hz.

-Extrapolation of losses from oscillator model which fits the IR reflectivity spectra gives the correct order of magnitude of intrinsic M W losses and in many cases works better than expected from theory.

-IR reflectivity is not as sensitive to processing as MW and SMM losses, providing sufficiently dense ceramics ( ~ 9 5 % of theoretical density) are available. It may be used for a first estimate of intrinsic MW properties of a new material. SMM transmission may be used for closer and more accurate estimate of MW properties.

-Systematic study of dielectric properties in the Ba(BinBTn)03 complex perovskite system has shown that the decisive parameter is the structural packing density (B'-ion size). High density (ideal packing) causes low E" and E' and vice versa. Ionic valence and mass are of no appreciable importance.

-Losses steeply increase with permittivity at a fixed frequency (E" a (E')~ for the Ba(B;,B:,)03 system, and approximately E" a (E')~ for al l structural types). This dependence may be understood microscopically for one structural type even with- out changing the degree of anharmoncity. However, existing spectroscopic data indicate increase in admmonicity with increasing permittivity.

ACKNOWJXDGEMENTS

The authors would l i e to thank all the numerous collaborators: B. Gorshunov, V. Voitsekhovskii. G. Komandin and A. Pnmii (Institute of General physics) for the BWO and some Fourier spectroscopy measurements, V. Koukal for initiation of the whole research area and providing samples of the Czech origin, N. Setter and R. Zunnuhlen (EF'F Lausanne) for collaboration on Ba(BinB"d3 materials, H. Tamm (Murata) for providing the Murata samples. R. Freer (University Manchester) for collaboration on ZTS and BaLnJiiO,l materials. V. Ferreira and J. Baptista (University Aveiro) for collaboration on MgliO, materials, M. Valant and D. Kolar (Institut J. Stefan, Ljubljana) for collaboration on Lay;rro,- LaAIO, compounds, A. Kania (University Katovice) for collaboration on Ag(Nb,Ta)O, system. V. R. K. Murthy (Indian Institute of Technology. Madras) for collaboration on @a, Sr)Zr,'ll)O, materials and Siemens Co. for providing their commercial samples. The work was supported by the Grant Agency of the Czech Rep. (project No. 202193/0691) and Russian Foundation of Fundamental Research (project NO. 93-02-15910).

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Dielectric properties of microwave ceramics investigated by infrared and submillimetre spectroscopy

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Transcript of Dielectric properties of microwave ceramics investigated by infrared and submillimetre spectroscopy