Indi an Journal of Pure & Applied Phys ics Vol. 39, November 2001, pp. 7 18-725

Impedance spectroscopic studies in SrBi4 Ti40 15

N Venkat Ramulu , M Aparna , G Prasad, G S Kumar & T Bhima Sankaram

Materials Research Laboratory. Department of Phys ics. Osmania University, Hyderabad 500 007

Received 20 March 200 I : revised I 5 June 200 I: accepted 22 August 200 I

The impedance measurements have been performed in the temperature range of 30 to 600 oc and the frequency range I kHz to I 0 MHz on four-layered SrBi4 Ti40 15 . The imagi nary components of impedance Z ", the electri cal mod ul us M" and ac conduct ivity have been computed. both as a function of frequency and temperature. The peaks appear in Z" ve rsus frequency plots and they shift towards lower frequencies at the temperature up to 500 oc and above 525 oc th ey shift towards higher frequenci es. Similar behaviour is observed in M" versus frequency plots. IZ "I values decrease with increase of temperature. while IM"I va lues decrease up to 500 °C and above 525 oc these va lues are found to inc rease wi th temperature. Complex impedance diagrams are nearly semic ircles at hi gher temperatures . Results are interpreted in terms of possible cond uct ivity mechani sms present in the sample.

1 Introduction

Bi smuth-layer structured ferroelectrics are an important class of lead free ferroelectric compounds with general formula (Bi 20 2)2+ (Am-IB"'O' "'+Ir-, e.g. Bi4Ti,0 12, BaBi4Ti40 15 , SrB i4Ti40 15 , etc. As in other types of ferroelectrics these compounds also have the presence of ions of small size and large charge (e.g. Ti4+, Nb'+, Ta5+, etc .,) in oxygen octahedra, which are linked through corners forming continuous chains of oxygen-metal-oxygen . Such a structural arrangement is favorable for the occurrence of ferroelectricity in ox ides 1·' .

Ito et al.4 synthesized several compound s in thi s fami ly and examined their crystal structure. The structure comprises a stacking of m-perovskite like units of normal composition AB03 between Bi20 2 layers along the pseudo-tet ragonal c-axis. It is noteworthy that the continuous extension of the 0-M-0 chains along the c-axis is interrupted not only by the presence of Bi20 2 layers but also by the tran slati on of the perovskite units in the plane perpendicular to the c-ax is. Bi smuth layer structure ferroelectrics (BLSF) in general have relatively hi gh Curie temperatures, high coercivity, low dielectric dissipation factor, high ani sotropy and dielectric strength5·7 . These compounds find app licati ons in fe rroelectri c random access memory (FRAM) with high fatigue endurancex and in high temperature piezoelectric sensors9

. Fatigue 111 ferroelectric devices has been studied for several years and

several mechani sms have been proposed to explain thi s degradation phenomenon.

There has been considerable interest in the potential of bi smuth titanate (Bi4Ti,0 12) as high temperature piezoelectric sensor, which has sma ll diel ectric constant and low dielectric loss tangent. The addition of SrTiO, to the Bi4Ti 30 12 results into a material , which can be electrically poled easily and ex hibits very stabl e die lectri c and piezoelectric properties6

·9

. It also results in the formation of compounds with a large number of perovskite units , with increas in g Sr concentration, such as SrBixTi 70 27 , Sr2Bi4Ti,0 1x and SrBi4Ti40 15 within two consecutive bismuth oxide layers. In this paper a study of impedance spectroscopy of the conventionally sintered polycrystalline sampl es of SrBi4Ti401_1 has been presented. The molecular formula of the compound studied is Bi20 , 4(Bi 21 .. Sr114 11-1 Ti03). Here is un-occupancy in A position of the perovskite (ABO,) structure of the layer compound.

2 Experimental Details

The Polycrysta lline sample SrBi4Ti40 15 was prepared by employing solid state react ive sintering. The initi al compounds SrC03, Bi20 , and Ti02 of AR-grade with 99.99% purity were mixed in appropriate rat ios. The mixture was thoroughly grounded and the particle size of the starting materi als was of the order of one micron. The mixture was stacked in a crucible and sintered isothermally in air at 850 oc for two and half hou rs

VENKAT RAMULU et al: IMPEDANCE SPECTROSCOPIC STUDIES 719

20 35 40 45 50 55 60 e ,deg

65 70

Fig. I - X-ray diffractogram of SBT

c .. ;;; c 0 0 0

·;::: u CD a; c

3000

SBT

2500

2000

1500

1000

500

Dielectric loss at

2.0 10kHz

1.5

"" c 1.0-.l!

0.5

0 .0

50kHz

100kHz

(a)

10 kHz

50 kHz

,---, 0 0 0

., 0

0

0 0

0 0

0

0 " 0

v 0

0 0 0

00

00

1,'

100 200 300 400 500 600

Temperature ("C)

Fig. 2 - Variation of (a) dielectric permitivity and (b) dielectric loss with temperature at frequencies mentioned for SBT

and then furnace cooled. The material so formed was crushed and powdered by repeated grinding in the ethanol medium. Pellets were made by pressing the powder into cylinders (dia 1.2 em and height 1-2 mm) at a pressure of 10 Mpa. Sample was finally sintered at I I 00 °C for 2 hrs . The ent ire sintering protocol was carried out in a temperature-controlled furnace .

2 1 X-ray diffraction

X-ray diffractogram of the powder samples were taken using Cu-Ka radiation at a scanning speed of one degree per min (Fig. I). Formation of a single­phase material was confirmed by unambiguously indexing of a ll the recorded peaks on the basi s of a distorted tetragonal celF. The lattice constants a, h and c were evaluated. Using this data X-ray densities were computed and compared with those experimentally determined . The experimental density of the sample was found to be above 95 % of the X-ray density.

2.2 Poling procedure

Sample was poled e lectrically prior to the dielectric measurements . The poling was done at 150 oc under a de field of 20 KV /em and cooled to room temperature rapid ly in the presence of the field. Poling above 150 oc was not possible due to

increased conductivity of the sample.

2.3 Electrical measurements

The dielectric and impedance measurements were made in the frequency range of I kHz- I 0 MHz and in the temperature range of 30 to 600 oc. The

720 INDIAN 1 PURE & APPL PHYS, VOL 39, NOVEMBER 2001

large faces of the pellets were initially coated with silver paint and dried at II 0 °C. Data were collected in steps by using a HP-4192A impedance analyzer interfaced to a computer. The acquisition of data at sti II higher temperatures was restricted by the enhanced conductivity of the samples. The dielectric constant was determined by measuring the capacitance of the electrically poled sample, at fixed frequencies of I 0, 50 and I 00 kHz, with increasing temperature up to 600 oc. 3 Results and Discussion

Fig. 2 shows the temperature dependence of the dielectric constant (Fig. (2a)) and loss tangent (Fig. 2(b)) studied at three different frequencies. The

00000 (a)

1\ 50000 / ". \ . \

40000 . \.I '\ ,.

c30000 \ -~ N. \l

2llOOO \ . \ \ \ ·

10000 ... . \·~ . . ..... ·, {:.

'· ·.~ 0

""0 ... ::::::~.

18000

(c) HltllO ;/\

1<1000 \ \

12000

10000 ~~~\ c:

/~ 8000

N oooO

/ <1000

.---·~ 2000 .~

.--'

0.1 to 100 1000 10000 -Frequency(kHz)

dielectric constant versus frequency plots show a peak at 530 °C, which corresponds to the Curie temperature and the transition temperature is in close agreement with reported results '·' . The value of dielectric constant at the peak decreases with the increasing frequency. The magnitude of decrease is large at lower frequencies and smal l at higher frequencies and appears to tend to a saturation value. Dielectric loss tangent (Fig. (2b)) shows a peak at lower temperatures and the peak temperature corresponds to the shoulder of the peak observed in dielectric constant versus temperature graph. Dielectric loss also decreases with the increase in frequency and the magnitude of decrease is larger at lower frequencies . Die lectric constant

(b) -6

12x10

- 7 8..1)1(10 !h'\ ~

................. \ lj --~-. \~

-7 ~\ 4J)Jrt0 . ~\. ........--., ~--

~~ ---.....,..______,. ______ .:;:/ 0.0

(d)--<>-- at 525°C -6 'o

2.0J.10 -~P-at 550 C

j, -v- at 575 °C - 6 -+ at600'°C Ui<10 !

~ - 6 ~ .2x10 , . ~.

-7 8.0x10

~ / ,, -7 ~ '~I 4.1k10

~ ~--- ~ ~:-;,. --~ .. _ ?---

0.0

0.1 10 too 1000 10000

Frequency(kHz)

Fig. 3- Variation of imagi nary part of impedance (Z") and modulus (M ") as a function of frequency

for SBT at the temperatures indicated

VENKAT RAMULU eta/: IMPEDANCE SPECTROSCOPIC STUDIES 721

and loss tangent show little temperature up to about 400 °C.

10

~FromZ'

---FromM'"

variation

I /

425 <450 475 500 525 550 575 600

Temperalure ('C)

with

Fig. 4-Peak frequencies as a function of temperature

The impedance data is analyzed in terms of four parameters, the impedance Z* = Z-jZ'; the electric modulus M* = jroC,:Z* where ro is the angular frequency, c(J is the free space capacitance of the sample cell with air gap in place of sample. Variations of the typical impedance parameters (Z" and M") with frequency (in the temperature ranges indicated) are given in Figs 3(a), (b), (c) and (d). It is convenient to divide the measurements into two graphs, one corresponding to the temperature below 500 °C, as shown in Figs 3(a) and (b), and the other corresponding to temperature close to the Curie point (>525 °C) and above, as shown in Figs 3 (c) and (d). From the position of peaks the relaxation times are calculated using the relation (l)'t = I. The modulus plots Jay emphasis on elements of the ceramics with smallest capacitances, while impedance plots highlight the elements with largest resistance. Hence the modulus plots show an increase in values of M' and M" with the increase in frequency which is consistent with decreasing Z ' and Z' values with increasing frequency.

The experimental data was obtained at different set temperatures of the sample. The Z' and M" plots show peaks in the frequency range and temperature range studied. The peak position in the frequency plot (Fig. 4) shifts to higher frequencies as the temperature of the sample is raised . The frequency

variation curves become broader at higher temperatures. From the peak maxima, the values of 't, and 'tm have been calculated and are found to be dependent on temperature.

10-1!..., -----------y----;---:1 (a)

~ -3 g 10 L_r-~~-~.-~-r-~~-r---~ "' .s (b)

~ 10"'"1

-2 10

1.14

0

1.17

0

1.26 1.29

Fig. 5- Variation of relaxation time as a function

of inverse of temperature

Inverse of this maxtma frequency 't, ts calculated and plotted as a function of inverse of temperature (Fig. 5(a)) and this parameter appears to follow the Arrhenius relation 't, = 't0eEikT with £=

0.62 ± 0.05 eV and 'to= 7.96 x JO·x s. A similar plot (Fig. 5(b)) from impedance versus frequency graphs for 'tm (inverse of the peak frequencies of M" versus frequency graphs) have activation energy E = 0. 17 ± 0.05 eV and 'to= 1.46 x I o-~ s. It should be remembered that the ac conductivity process is

722 INDIAN 1 PURE & APPL PHYS, VOL 39, NOVEMBER 2001

1.00..1o5c,-- - - - --- - - - ---- --,

c • . 4 N s.oo.1o

4 2.50><10

(a)

.I

-6 2.5x10

-6 2.0x10

- 6 1.5x10

-6 1.0x10

-7 5.0x10

(c)

--------~___:::---.. ..... , ~~- ---~ ~ • ~.~'- "'-.... 425"c

...-----·~ •• _"' -..., 450·e·-.. 500"C -........_ 475"C '-., '-o...., ·---..'II . ...

0.00+----,.--;-4~----,--;-4~----,--:-4--.----i 5 0.0+-~--=,-....,_7..--.-::-6 ---,,---;-6~-.-::-6 ----1 :-6 0.00 2.50><10 . 5.00..10 750x10 1.00..10 o.o 5.0x10 1.0x11i 1.5x10 2.0x10- 2.5x10

3.0x1o4 2.0x1o6T------ - - - - - - - - - --,

4 2.5x10

4 2.0x10

(b)

-6 1.5x10

(d)

O.OO-f.0-~5.~0x1r-O-:-J-.-1,-.0xT1-:04~-1.5x,.-104~-2.-0x1r-0-;4-.-2.-5x1T-:04~-3.-10x104 0.0+----,.-_7:;--....---r--:-6--.----,--:c6~--l -6 0.0 5.0x10 1.0x10- 1.5x10- 2.0x10

z· n M'

Fig. 6-Cole-Cole plots of SBT at different temperatures

dependent on the capacitance of the sample. The relaxation times obtained from the peak W

111't= I of

the frequency explicit plots of Z' , M" and tan8 are respectively given as 't,='t, -r; ,= 't I r, 'tTano = -rl ..Jr, where r is the relaxation ratio and is given by (E/f..c). The relaxation ratio r plays a vital role in determining the value of the relaxation time and therefore determines at what frequency the imaginary part of a particular dielectric function will have a peak. The present results indicate that 't, > 'tm

and the values of relaxation ratio (r) is given by 't,j't, = I I r and is found to be within 2.5 to 14 for SBT samples in the temperature range of present

measurements. It is seen that Z' and M" peaks shift to lower frequencies as the temperature is increased in the temperature range below 500 °C. In the temperature range 525 °C and above, it is observed that both Z' peaks as well as M" peaks shift to higher frequencies . Z' and M" peaks are broad indicating multiple relaxations and de viation from Debye behaviour. Both the peaks represent the same physical relaxation phenomenon.

The data when plotted in complex plane z " versus Z (Figs 6(a) and (b)) and M" versus M' ((Figs 6(c) and (d)] give an idea about the resistive, capacitive and relaxation behaviour of the charne

b

VENKAT RAMULU et al: IMPEDANCE SPECTROSCOPIC STUDIES

entities in the sample":", The resistance of thesample (ac and de) is given by the intercept of theimpedance plots (2" versus Z) and capacitance ofthe sample is represented by the intercept of theplots on the M-axis at high frequency side in M "versus M plots. The plots are more or less semi-circles. The values of EclCz are calculated from theplots of Fig. 6(b) and the values are plotted as afunction of temperature (Fig. 7). This plot showsminima around 510°C, which is close to thetransition temperature. The data appear to be usefulfor finding the transition temperatures as well as theconductivity behaviour. Thus the ac impedance datahelps us to find the dielectric behaviour of thesample before and after the transition temperature.

I05~ ~ __ ~

Fig. 7 - Plot of capacitance (£.,/C2) versus IOJ/T

The ac conductivity data is extremely usefulwhen the conduction is related to localized hoppingof charge species. The real part of conductivity as afunction of frequency at different temperatures isplotted in Fig. 8. The conductivity plots show thatthe conduction in these samples is thermallyactivated. The ac conductivity is sum of two terms,o ac = cr de + c' (ro) and c' (co) = A ron,where o de isthe conductivity under direct current, A is a constantwhich is a function of temperature and ro is theangular frequency. From these plots on the lowfrequency side, n comes out to be 0.8 to 0.9. Asalready stated the conduction in the present sampleis a thermally activated process. The variable A is afunction of temperature and it depends on number of

723

sites available for the charge carriers for hopping.The o' (0) is computed from the intercepts of theplots at m ~ 0 (points at lower frequencies). TheFig. 9 shows the Arrhenius plot of cr'<k(0) versustemperature, in the temperature range 30-600 "C,The linear graph is split into two regions. Theactivation energies in these two regions (250-5000c) and above 500 °C are 0.80 and 1.04 eVrespecti vel y.

;~-400°C.----6-425"c

-310 '---9-45(tC

~7ftC~·C·

-71_~~~~~~~~~~~~~~10 "'0 1 2 10:'\lE_31:.;0 10_- 10--'" ~_,

lE-6

100

G kHz100010

Fig. 8 - Plot of log (O'ac) versus frequency at differenttemperatures mentioned

As we have evidence for localized relaxations,the conduction can be due to barrier hopping. Insuch a case the charge displacement within thesample is by discrete hops of length R betweenrandomly distributed localized sites. Analysis of

724 INDIAN J PURE & APPL PHYS, VOL 39, NOVEMBER 2001

polarization moments is associated with theformula":

N2 R_ ro2'l'a'(ro) =- J a(R)p(R) 2 2 dR

2 Ro l+ro'l'

where N is the number of sites per unit volume,a(R) is the polarizability and peR) is the probabilityof the another site being located at a distancebetween Rand R + dR. The relaxation time t is thetime associated with a hop distance of R.

-7

-8 \v" 1.0geV\"\

0\°0o

-9

'eIiC.- -10~.o -:1:1;\:)go••• -11

ooe-

°0 ~.8OeV0",

00oo·00

0",ooסס

00000-12

-13 -I------..--..----.-'""""T-:---r-,--..-----j1.0 1.5 2.0 2.5 3.0

1031T(I<"')

Fig. 9 - Plot of log (Ode) versus I03/T

The charge mobility is caused by thermallyactivated process and involves crossing of thepotential barrier W separating two sides. Thismechanism is associated with a relaxation timegiven in the form:

't = 'to exp (Elk1)

The relaxation times are calculated from the peaksof Z' or M' plots and log 't thus obtained is plottedas a function of lo-11T as shown in Fig. 5. Theactivation energy comes out as 0.62 eV. Therelaxation time is associated with the CBH(correlated barrier hopping) model. The height ofthe barrier Wm is related to the distance R as:

[)~

-IC 2kT r

R=-- 1--IOg(~E,Wm Wm 0

where C is a constant and E. is related to thedistance between the oxygen sites in the octahedrain perovskite structure. Wm is the energy required fortransporting a charge from infinity to the site underconsideration and is the activation energy obtainedfrom de Arrhenius plot. The conduction species(charge carriers) have to cross a potential barrier Wseparating two sites. At lower temperatures, the bulksamples can have two mechanisms of conduction.One due to long-range ac conduction and the otherdue to localized transport of the charges, which arebound. Bindings of the charges arise due to dipolarinteraction (Coulomb interaction) between thecharge carrier and the ion in the lattice.

The polarization and conductivity variation of asample is associated with the displacement of thecharge carriers, which move within the sample bydiscrete jumps between two localized sites separatedby a distance.

The de conductivity plot (Fig. 9) indicates thatthere are two slopes above 250°C. At lowertemperatures the data tends to deviate from thestraight line. Grain boundary effects and defect ioncomplexes, or charge carrier-ion complexes in theceramics influence the conduction at lowertemperature. This is evident from MOO frequencyexplicit curves. At lower frequencies there is a peakand the peak represents capacitance inverse. Themagnitude does not change much with temperature.Therefore it is natural to infer that this capacitanceindicated at lower frequencies should be associatedwith grain boundaries, other than the bulk of thegrains 10. The low values of MOO at these frequenciesalso indicate large capacitance values. The grainboundary effects and dipole complexes control theactivation process at lower temperatures. At highertemperatures the dipoles may disassociate andcontribute to long-range conductivity. The peakvalues in MOO curve at higher frequencies appear tochange with temperature and hence the capacitancewould increase with temperature appreciably. Therelaxation time also changes with temperature. Asthe peaks appear to have shifted beyond the range offrequency of the ac field applied it is not possible topredict variation of r, associated with these peaks.

VENKAT RAMULU et at: IMPEDANCE SPECTROSCOPIC STUDIES 725

In conclusion, the study of dielectric andimpedance properties of SBT sample showsmultiple relaxation behaviour. Relaxation timesobtained from impedance and modulus plots appearto follow Arrhenius relation. A double well potentialbarrier model is used to understand the results.

Acknowledgements

The authors thank UGC, Govt of India forsanction of a research project under which this workwas performed and also Dr Ravi Kumar, nCT forextending XRD facilities.

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