list of publications -...

LIST OF PUBLICATIONS

1 . Synthesis, characterization and ion dynamic studies of NASICON type glasses G. Govindaraj, C.R. Mariappan, Solid State Ionics 147 (2002) 49.

2. Ac conductivity, dielectric studies and conductivity scaling of NASICON materials C.R. Mariappan, G. Govindaraj, Mater. Sci. Eng. B 94 (2002) 82.

3. Scaling behavior in the frequency dependent conductivity of NASICON glasses C.R. Mariappan, G. Govindaraj, J. ivater. Sci. Lett. 2 1 (2002) 1401.

4. Frequency dependent electrical properties of the Na3Fe2P3011 and NaFeCdP3OI2 NASICON material C.R. Mariappan, G. Govindaraj, (Eds.) B.V.R. Chowdari, et al., in: Solid State Ionics: Trends in New Mellennium, World Scientific, Singapore (2002) pp. 629.

5. Conductivity and ion dynamic studies in the N ~ , ; i + ~ T i l 3.x(P04)3.3-x (0 5 x 5 0.5) NASICON materials.

C.R. Mariappan, G. Govindaraj, Solid State Ionics (2003) communicated.

6. Conductivity dispersion and scaling studies in AsByP;O12 orthophosphate: (A=Na; B=Fe, TiCd, TiZn) C.R. Mariappan,G. Govindaraj, Physica B (2003) communicated.

7. Vitrification of K3M2P3OI2 (M = B, Al, Bi) NASICON type materials and electrical relaxation studies C.R. Mariappan, G. Govindaraj, S. Vinoth Rathan. G. Vijaya Prakash, Muter. Lett. (2003) communicated.

8. Preparation, characterization, ac conductivity and permittivity studies on vitreous M4A1CdP30l2 (M=Li, Na, K) system C.R. Mariappan, G. Govindaraj, S. Vinoth Rathan, G. Vijaya Prakash, Mateu. Sci. Eng. B (2003) communicated.

9. Synthesis, characterization and electrical conductivity studies on A;Bi2P3012 (A=Na, K) materials C.R. Mariappan, G. Govindaraj, L. Rarnya, S. Hariharan, Mater. Res. Bull. (2003) communicated.

10. Ionic conductivity and relaxation dynamics in A;TiBrP3012 (A = Li, IS; B' = Zn, Cd) NASICON type glasses C.R. Mariappan, G. Govindaraj, J Non-Cryst. Solids (2004) to be communicated.

Papers acceptedlpresented in conferences/symposia

1. Poster Title: Preparation and ac conductivity studies of NASICON glasses, C.R. Mariappan, G. Govindaraj, Presented in 44"' DAE - Solid State Physics Symposium, held at Bhabha Atomic Research Centre, Mumbai, (26-30, December, 2001), India.

2. Poster Title: Scaling behavior in the frequency dependent conductivity of NASICON glasses, C.R. Mariappan, G. Govindaraj, Presented in 44lh DAE - Solid State Physics Symposium, held at Bhabha Atomic Research Centre, Mumbai (26-30, December, 2001), India.

3. Paper accepted for oral presentation: Preparation and electrical conductivity studies of NASICON type materials, C.R. Mariappan, G. Govindaraj, 5'" National Conference Solid State Ionics, held at Nagpur University, Nagpur, (15-17 February, 2002), India.

4. Poster Title: Frequency dependent electrical properties of the Na;Fe2P301z and NaFeCdP301z NASICON material, C.R. Mariappan, G. Govindaraj, Presented in 8'h Asian Conference on Solid State Ionics: Trends in A ~ M ] Millennium, held at Langkawi, (15-19, December 2002), Malaysia.

5. Poster Title: Electrical conductivity studies of the Nq.~+xTil,3.,(P04)3.3-x (0 5 x I 0.6) NASICON materials, G. Govindaraj, C.R. Mariappan, Presented in 8'" Asian Conference on Solid State Ionics: Trends in New Millennium, held at Langkawi, (15- 19, December 2002), Malaysia.

SOLID STATE IONICS

Solid State Ionics 147 (2002) 49-59

Synthesis, characterization and ion dynamic studies of NASICON type glasses

G. Govindaraj *, C.R. Mariappan Ru~inun School of Physics. Po~idichery U ~ ~ i v e r s i ~ : R. V iVagar; Kalupet, Potidichery 605 014, lndiu

Received 6 July 2001; received in revised fonii I? December 2001; accepted 24 Decenibsr 2001

Abstract

Different NASICON type ionic conducting systems with general formula An,B,,P301Z were prepared by quenching method, where A=Na, and B = Al, Ti, AICd, TiCd and TiZn. The prepared compounds were characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and differential scanning calorimetry (DSC). The electrical conductivity measurements were made on the different systems as a function of frequency at different temperatures. Jonscher's universal power law is applied to discuss the ac and dc conductivity and the scaling of conductivity spectrum. The conductivity spectra of the compounds show the power law feature and scaling behavior when the conductivity spectra are scaled vertically by dc conductivity and horizontally by hopping rate. The dc conductivity of the compounds is found to be in the range 10 - 9 - 1 ~ - S cm - ' at 423 K. The dc conductivity and hopping rate activation energies are found to be in the range 0.47-1.13 eV. 0 2002 Elsevier Science B.V. All rights reserved.

PACS. 66.30 Hs; 77.22 Ch Ke.wvords: NASICOK type glasses; Ac conducttvity; Activarion energy; Ion dynamics; Scaling analysis

In the last few decades, there has been much interest in finding new solids with high ionic conductivity for applications of solid state batteries, fuel cells, sensor, etc. Several glasses have been shown to have high ionic conductivity and are referred to as superionic conducting glasses [1,2]. Among the glass formers, the phosphates are the best glass former and

Corresponding author. Tel.: +91-4 13-655 177x382; fax: +91- 413-655265.

E-mail addresses: [email protected] (G. Govindaraj), cnnarilQredithnail.com (C.R. Mariappan).

have been widely investigated [3-61. The general formula of phosphate network systems is ArnBnP3Ol2, where A is an alkali metal ion and B is one or more ions in tri-, tetra- or pentavalent state [7,8]. The monovalent A ions can easily migrate in the lattice with low activation energy. This family of phosphate network systems is often referred to as 'NASICONs' (acronym for 'Na' super ionic conductors) [S]. There are new structural families found in the NASICONs systems 191. The NASICON @ai ,.xZrtSixP3 - x012, 0 <x < 3) systems have three-dimensional framework structures and have high ionic conductivity (x = 2, - 0.2 mhos at 573 K) comparable to that of two- dimensional networks, such as 0-aluminas [lo-121. A number of phosphate network-based NASICON

0167-273810215 - see front matter O 2002 Elsevier Science B.V. All rights resenred. PII: $ 0 1 6 7 - 2 7 3 8 ( 0 2 ) 0 0 0 0 5 - X

50 G. Govinduir~, C.R. Muriuppupan /Solid Stu/e lorlies 147 (1002) 49-59

typc compounds have been studicd in the rcccnt ycars [8,12].

In the present work, NASICON type materials A,B,P30i2 are studied, where A is an alkali metal ion (Na'), B is one or more ions in tri-, tetra- or pentavalent state (Al, Ti, AICd, TiCd, TiZn). The NASICON type materials (1) Na3TiZnP3OI2, (2) Na3 TiCdP30,?, (3) Na4AlCdZnP3Ol~. (4) NajAlrP301z, ( 5 ) NasTiP30,1 and (6) Na&IP3OI2 were prepared and characterized by X-ray diffractiori (XRD), Four- ier transfonn infrared spectroscopy (FTIR) and differential scanning calorimetry (DSC). The electrical conductit8ity measurements were carried out on the preparcd materials using ac impedance analyzer at different temperatures. The frequency-dependent conductivity and the pemiittivity wcre used for the characterization of the ion dynamics in thcsc matc- rials.

Thc mcasurcd ac conductivity, o,,(cj), is generally cxpresscd as [I;]:

where (7dc is dc conduct~vity and ( r r is an angular frequency. The frequency-dependent conductivity, d ((01. results from the contribution of localized ionic ]lops, i c , qu%l-buunded cliargcs thai can be undcr- stood as dipolar rturicntatlon processes Thc essential pllqsiccrl background for tkc ac conductivti) (Eq. ( I ) ) ftas bccn discussed by selicrttl authars [!A-161. I t is vabd far wide range of cystall~ne as ivell as for amorphous materials [ 17,181.

The ac conductivity of the prepared samples a a s anafyzed using the modifid form of Eq. ( I ) in Secl~on 3. The scaling behavior in ac conductlvrty IS studied for the prepared samples and observed the time- ternpentun: suprposition principle.

2. Experimental

The NASICON compounds i V ~ i ~ T i Z n P ~ 0 ~ ~ , Ha, TiCdP,Otz. NaaAlC@,Ol2, Na,A12P30,2, NaSTiP, 011 and Na&lP,OI, were synthesized using the re- agents NazCO~(SU), Ti02(SDF), CdO(SDF), ZnO (Rambaxy), A1203(SDF) and NH4H2W4(SDF). The calculated amounts of the starting materials of I0 g in single batch were ground to give B homogeneous

mixrurc. Thc finely ground mixture was then placed in silica crucibie and lieatcd siowiy in an electrical furnace until the temperature reachcd to 573 K. The slow heating up to 573 K decomposes the ammo- nium dihydrogen orthophosphate mixture. The mixture was again ground and heated in a silica crucible for - 14 h at temperature range 800- 1000 K with- out melting the mixtures. The batch was hcated fur- ther to temperatures of 1273 - 1373 K and stirred for 5-10 min to ensure homogeneity. The ~nelts were poured into a stainless steel plate and quenched ra- pidly by pressing with another stainless stccl plate at room temperature.

XRD spectra were rccordcd for all the compounds using thc Rigaku miniflcx X-ray diffracror~lctcr with monochromatic Cu K,, radiation of wavelength of i.= 1.541 A at various glancing angles between 5' and 65". FTIR spectra were recorded in ~ h c wave nuinbcr rangc 3000-500 cm "' ' using ABB BOMEM MB 104 FTIR spectrophotometcr by KBr pellet mclhod at room telnpcrature and 40 scans at 4 cm - ' resolution wcre averaged. Thc DSC mcasure- ments wcre carricd out using a Pcrkin-Elmer DSC-IV unit with a heating rate of 30 Kln~in.

The dcnsity of the glass bits free of air bubbles and crack on visual examination was detcrmincd by the Archimedes' principle. The density of the glass samples was obtained using a 25-cm' spccific gravity mcasurt~nent and iolucne as thc incrt immersion liquid. The dcnsity is obtaincd fioi~?: thc relation:

where is thc density of the sample, Pya is thc we~ght of the sample in air, 4 is the weight of h e sample fully immersed in liquid and pi is the density of the liquid used. Thc enor in the density of measurement is within F 0.04 g/crn3. The molar volumes were calculated as V , = M / p , where M is the corresponding molecular weight of the samples.

Tbe finely ground samples were made into cylin- dncal pellet of dimension 10 mm diameter and - 2.5 mm thickness pressed at a pressure of 5000 kg/cm2. Then, the pellets were sintered 373 K at 2 h. The sintered pellets were used for electrical conductivity measurements. Tbe electrical conductivity studies were canied out by sandwiching these pellets between

G. Govir~darqj. C.R. Mariappuil /Solid State lonics 147 (2002) 49-59 51

two silver electrodes. Parallel conductance and capa- c~tance were measured at different temperature in the frequency range fiom 20 Hz to 100 kHz using Zen- tech Automatic compound Analyzer Model 3305.

3. Results and discussion

The amorphous nature of the samples was con- firmed by XRD studies. All the prepared compounds were found to be ill amorphous nature except Na,.41P3012 system. The results are shown in Fig. 1. The compound Na6AIP3012 was found to be in polycrystalline nature. Crystalline nature of the compounds Na4AICdPjOl2 and Na3TiCdP3012 was studied by sintering. The XRD spectra of these

Fig. 1. Powder XRD patterns of different NASICON tyx compounds (Cu K, radiation).

20 (degrccs)

Fig. 2 . X-ray diffraction of NajAICdPiOlz and NaiTiCdP3012 glasses after heated at 873 K for h h (Cu K,, radiation).

compounds are shown In Fig. 2. The co~npounds Na4AI CdP3012 and NajTiCdP30 fonn crystalline phases when heated to 873 K at 6 h, which 'd~ssolves' into the amorphous matrlx at higher temperature.

Fig. 3 shows the FTIR absorption spectra observed for the different compounds The bands observed in

3000 2500 2000 1500 1000 500

wavenumber [cm-'1

Fig. 3. FTIR absorption spectra of different NASICON type compounds.

52 G. Govir~daruj, C.R. Mariappar~ /Solid Slare Ionics 147 (2002) 49-59

the region - 560 cm - ' in all samples are attributed to the asymmetric bending vibration modes of O-P- 0 units [19-211. The bands seen in the region 705- 730 cm - ' are ascribed to the P-0-P stretching vibration [21]. The bands in the region 1052-940 crn - ' indicate in the presence of the poq3 - ionic groups vibration [21-231. The bands viewed in the region 920-880 cm - ' in Na3TiCdP3012, Na3TiZnP3012 and NaSTiPjOlz samples are assigned to the P-0-P bending vibration [21]. The observed bands In the region - 1 130 cm - ', h'a6A1Pj012, Na3AlzP3OI2 and Na5TiP3012 samples may be exhibited to the PO'- ) ionic vibration 121,241. The bands seen in the region 1660-1600 cm - ' in all sainples arc traced to the free H20 n~olecules bending vibration Inode [ 2 1 I.

The DSC was used to find the glass transition temperature. Thc DSC scan was run only for the Na4AlCdP30,2 sample up to 773 K and a typical result is shown in Fig. 4. For the other glass samplcs, DSC scan was run up to 573 K and, in this tcmpcr- aturc region, no phase transitions was observed. The glass transition temperature (T,) is above 573 K for ail the prepared glassy materials.

Fig. 4. Typical DSC curvc far h 1Vt~tICdPt0~~ glass.

3.1. Electrical conductivip shicfics

'rhe measured parallel co~lductancc and capacitance data were converted with appropriate geometric factor to find thc ac conductivity (~(oJ) iil co~ivuntional units (S cm - ') and dielectric permittivity c' (w), rcs- pectively. Ac conductivity curves for diffcrcnt NASI- CON type compounds arc shown in Figs. 5 and 6. It is clear from Figs. 5 and 6 that the conductisiry spcctra have power law features. The powcr law behavior is analyzed using Jonscher's u~iivcrsal power lni cqua- tion, and then Eq. (1 ) may bc re~vrii!cn as 1751:

where n is the frequency esponunt in rhc range 0<11< 1. Both n,~, and :f arc thcr~naliy activated quantities. The n,,, = Kc:),, is thc frequency-inlicpcnd- cnt dc conductivity and A' is rllc ci?nstniit of propor- tionality defined as 1261:

where is thc gcometricai factor u l i ~ c l ~ lnciude correlated factor, 1. is the conccnintiun of mobiic ions on N equlvalcnt latrice sitcs per unit \-uiurnc. (1 ts the hopplng d~stancc, e 1s ~ l t c cicctmnic chargc. 1'1s the absolute tempcrdtare and k IS thc Moitr,ln;inn's constant. Tlte diagranis of ci(ii)) versus angular frelluciiey In log-log scaic are s ! ~ u u ~ i In F~gs 5 :ind h dl

different tc~npenlurca Thc sc cwducti\irq spc.c:ra In F~gs. 5 and h h a v ~ the fu l lc~rny f;.&itures: The conductivrty 1s al~nost found to be ticqucnc)-lnds pendent in law frcqitcnc~cs region and 11 is equal to bulk conductlsity (in !hi. pl~tcau rcylim) In t t ~ c h ~ g h frequency r c g m , thc porker law katutc a(cti) att)"is

observed. The power law rcglnle of the ac sonduc!iv- ity is much Irss tcmpcraturu-dopundent illan ihc dc conduciivity, At low tcmpcratures, thc cunducriu~ty data art. found t be scattcrcd at law frcqucncics awing to ihc high resistance of the siinplcs At high temperatures, thc conduct~v~ty dao arc showing dispersion at low fregucnc~es due to elccmdc polar- ration. The universal power law brhavier obeys m both the glasses and plycrysulline NASICON materials. The parameters ah, A and n have bccn extracted by fitting the measured data using Eq. (3) hven- kg-FAarquatdt method of nonlinear least square fifiing was used to extract the panunem o&, A and

i;, ~~l~ i ' l l l i~ i i l ' r i / , C ' N !*fnr~il iy~i,c~n . Sol~ti Sicl!c 101iic:s 1.17 (2002j 49-59

Ywl

$2 l o 3 loS l o 5 lo6 I(O\ [radlsec]

c: 474 K 463 K 453 K

c 443 K 433 K

+ 423 K 4: 408 K x 393 K

-----power law

(wi [radlsec]

fit

law fit

law fit

o f ~ a r ~ & P I O t r , fiia;fCBP,OI: and N&AIC~P,(II? gla\hc% The dl!Ercnl s ~ m b i s ro chc k~r nonitnear fits in the I:q 131

G. GovLldaruj, C.R. Muriuppun /Solid Stole lonics 147 (2002) 49-59

C . . .,..,.*I . ...-...I . . -*.....I . . .d

l o 2 l o 3 lo4 l o 5 106

(a) [radlsec]

(a) f radlsec]

473 K 463 K 453 K 443 K 433 K 423 K 408 K 393 K

-power law fit

c 453 K G 423 K A 393 K v 363 K

- power law fit

473 K 463 K 453 K 443 K 433 K 423 K

-power law fit

Rg. 6. Freqwqaepnrdcnt ionic condu&ty speclra of N a f l ~ P ~ 0 1 2 and N%TiP$& glasges. and Na&Pf012 polyaybl(illine matcaial. The different symbols qmt the aperimend data at diffarnt tmpmtms Pud ~atinwus line rqmmcr the bast nonlimar fits to the Eq. (3).

G. Govindaruj C,R. iliuriappat~ l Solid State lonics 147 (2002) 49-59 55

Tablc i Parameters obtained from the fits of ac conductivity ineasurelnents by Eqs. (3) and (6) for Na3TiZnPsO12 glass

Te~nperature (K) bdc (S cin - I) A (S c ~ n - ' rad - ") 11 ( ? 0.031 tu, (rad s - ')

393 4.25 x 10 - ' 1 . 4 4 ~ lo-" ' 0.55 2.76 x 10' 408 7.3i x 1 0 ' ~ 8.59 x 1 0 - " 0.6 1 5.49 x lo4 423 1.8 x 3.63 x l o - ' ' 0.70 ! . O x 10' 433 1 . 9 9 ~ l o - ' 3.38 x 10- " 0.7 i 1.78 x 10' 443 2.95 x 10- ' 1 . 0 0 ~ l o - " 0.81 3.03 x I 0' 453 4.43 :; 1 0 - 7 1.1s x 10 - 1 1 0.80 4.45 x ioS 463 6.09 x 10 1.82 x 1 0 " 0.78 5.73 lo5 473 9.10 Y 10 ' 1 . 0 2 ~ 10." 0.82 9.23 x lo5

11. The fitted paraIneters are tabulated for different samples and are given in Tables I and 2. In Figs. 5 and 6, the points represent the experimental ac conductivity data and the continuous line represents the fitted values by using Eq. (3). Thc dc conductivity was temperature-dependent and was found to obey the Arrhcnius fonn:

where n(0) is the pre-exponential factor of the dc conduct~v~ty and E, IS the actnation energy for the mob~le Ions The hopping ratc, ( r ~ ~ , is the frequency at which r i1 t r ) ) " ;2~ ,~ , and is also obtalned from the un~rcrs:tI law

where (I), and n arc material-dependent. (rip is temperature-dependent [I71 and is fitted to the Arrlienius equation:

where CJ,, is rhc pre-exponent factor of the hopping ratc and E, is the activation energy for hopping rate. The inverse of the hopping rate is equal to the

relaxation time. Fig. 7(a) and (b) shows logloadcT versus IOOOiT and logl oo), versus 1000/T, respectively; the continuous line is fitted linc to Arrhenius equation.

Activation energies E, and Ed were dctcnnined using Arrhenius equation by linear regression. The activation energies E, and E_ of the various NASI- CON samples wcre tabulated in Table 3. The activation energy E, for dc conductivity is found to close to activation energy E, for hopping. This indicates that the charge carrier has to ~ \ ~ e r come the same energy barrier while conducting as well as while relaxing 1271. The different samples' molcc- ular weight, density, molar volume and dc conductivity at 423 K wcre obtained and arc shown in ~ a b f e 4.

The real par: of dielectric permlltivlty for thc different NASICON type glasses is measured as a function of frequency at different temperatures. The results are shown in Fig. 8 by plotting I as a function of frequency, (!), for the glasses Na3T~ZnP3OI2, Na3TiCdP3012 and Na4AICdP3Ol2 at d~fferent temperatures. The real part of dielectric penniltivity d (10)

substantially rises at Iow Frequency as shoun in Fig. 8. This is due to an additional consequcncc of free charge carrier, which is the artifact of electrode polar-

Tablc ! Paraincrcn obialned from the fits of ac conduct~vity mmurements by Eqs, (3) and (61 for Na5TiP10i2 glass

Tetnnerarun (K) cr*(Scm ') A (S c:n ' rad "1 n ( r 0 0 3 ) CY, (rad s ' I

56 G. Govirzdaruj, C.R. Marinppan i Solid Siaie lorlrcs I47 (2002) 49-59

Fig. 7. (a) and (b) Arrhenius plots of iog,o(uT) versus IOOOITand loglo(w,) versus 1000/73 respectively, for different NASICON type compounds. The solid lines represent the Arrhenius fits.

~zation. This occurs when ions are unable to exchange with typical silver metal electrodes and pile up near the interface. At high frequencies, due to high periodic reversal of the field at the interface, the contribution of charge carriers (ions) towards the dielectric constant decreases with increasing frequency. Hence, E' (a) decreases with increasing Eiequency. Similar features are observed for other samples.

3.2. Ac conductivity scaling

In the last few years, researchers struggle to understand the dynamics of the mobile ions in solid

Table 3 Activation energy E,, for dc conductiviiy, nd,, and activation energy E,, for hopping rate, to,, of different NASICON iype samples obtained from Arrhenius Eqs. ( 5 ) and (7), respectiveiy

Colnposition E, ieV) Ed ((el')

( t o.or) ( + 0.03)

ion conductors by interpret~ng the frcqucncy-dcpcnd- ent features in their clcctric and diciectric response. The conductivity representarion is a suitabio tool for comparing the ion dynamics of the different maieri- als [28].

Scal~ng 1s an important feature in ally data c t d l -

uation program The study of conduct~t~ty spectra o f several materials at different ternperarurcs lcads to a scahng law, a(w)hdc = F(~ l ( i l , ) , wllere (IJ, 1.s arbl- trary detem~ined character~st~c frequency This 1s called time-ten~perature superposition pr~nclplc (TTSP) [28-341. The ability to scale dlffercnr data sets so as to collapse a11 to one common curve indicates that thc proccss can bc ~cparatcd into a common physlcal rncchan~sm modlficd only b) tiler- modynamics scaics [28] Differcni authors ilacc studied the scaling in several rnaterlals i2c1.331 by scaling the frequency av:s w~th various pararnctcrs [28-341. Were, we have applied a scallng approach uslng the hopping frequency, (I),, as charactcnstic frequency to scale the frcqucncy axls and the dc conductivity as the scaling parameter for the con-

Table 4 Name of the syaem with their molecuhr weigh!, density. molar volume and dc conductivitv at 423 K

Name of the Molecular Densiy Molar a& (S cm " '1 sample we~ght M p (@ern1} volume at 423 K

(g) rm (cm') Na3TiZnP3012 467.13 2.91 160.53 1.58 x !Ow' Na3XCdP30i2 514.17 2.88 178.53 3 38 x 16 ' NaS\lCdP,O,, 516.26 3.12 165.47 9.44 x 10- " Na&12P~0~2 407.83 2.53 161.20 7.16 x 10 ' NaSTiPJO)z 447.73 2.64 169.59 1.59 x 10 " Na6AIP30~Z 449.82 2.71 165.99 9.24 x 10

LO); [radlsec]

lo2 lo3 10' lo5 lo6 ((d) [radlsec]

Frg 8. tag-bg pbl of E( (a) v m w tiK diffwnr NASICON r y p ~ g l w a nr drffermt icmpcratura.

58 G. Govi~ldaraj, C.R. ,Uuriuppun /Solid State 1011ics 147 (2002) 49-.i9

ductivity axis [29-311. This type of conductivity scaling is expressed as:

Such a scaling of the conductivity spectra at various temperatures (above 423 K) for the different NASICON type samples is presented in Figs. 9 and 10. The scaled ac conductivity data collapse into a single master curve, and it implies that the relaxation mechanism is independent of the temperature. The

Fig 10. Master plot of the conductivity data for Nnl~l2PIO1: glasi and Na&IP,0j2 poiycrystall~ne maieriais,

P \

5' w 0

Na3TiZnP30il sample shows temperature-dependent frequency exponent n in Table 1, when fitted lo Eq. (3). Even though the Na3TiZnP30i2 sample shows temperaturedependent n, the master curve has bcen

1: observed. Similar results are shown for the ionically ., , . ,.- conducting oxide glasses [29,30]. These observations

0-4 "'10-3 10.2 101 are explained by using the effective-medium theory (30). In Fig. 10, the Na6A1P3012 sample in tow

(9 frequency region conductivity deviates from the master curve due to electrode effect. Figs. 9 and 10 ciearIy

~ l g . 9. Conductivity master curves for Na,TtCdP,O,, and show that the conductivity master curve does not N ~ A l C d p ~ 0 , ~ glasses. depend on temperature ad lhese indicate the TTSP.

J O L I R N A I . O F ~ I A T E R I I \ I . S S C I E N C E I.ETTERS 2 1 . 2 0 0 2 , l 4 0 l - 1103

Scaling behavior in the frequency dependent conductivity of NASICON glasses

C. R. MARIAPPAN, G. GOVINDARAJC Rarnan School of Physics, Pondicherry University, R. V: Nagar, Kalaper, Pondicherry 605 0 14, India E-mail: [email protected]; [email protected]

Ion dynamic processes in ionically conducting rriate- rials have been subject of deep scientiiic interest for past Sew years and also i t is a ctiailenging problcrn j 1-61, The studies oi' electrical relasation process iii

ioaic coriducting sc4ids arc very ilnportorit. The rclatiorl beriveen clectr-icul re!:1s3ti01i ;LI IL~ g1;iss corrlposiiion has heen studied c~tcnsrvely. Thus, the typical i'e:!:iire of ion dyiiarnical procchses tias hceri !lie i.ernarhable success iri developing theories that expliiili relnx:itiori pheiiorn- eila iri glasses [7-171. The ion iiyri;!rnic processes have beer1 studied by electrical coilduiti\.ity dispersion. 111 thr ion coiiductirig malerials rhc ac condilcriviiy is gcri- era11y \veil approxirnarcd by [ I 31

\shere n;i, is the dc conductivity, w , is the hopping Src- quency of charge carriers and tr is the dimensioiiless frequency exponent. The study of the ao conduciivity spectra of se\i.r;ll glasses at diCfere~it teriiper;iturcs leads to a sc;ilirig la- and i t is c:iIIed ;! tir1~e-le11>pera1~1r SU-

~xrposixiun principle [ 1-51, This illtails t i i ; ~ ~ fix a given rr~aterial ;he conductivity isorhenns car1 he collapsed io a ii~;ister curve up011 appropriate scaling of the conductivity ~ ~ n d frcyuency axis. Xlrious workers have consid- ered ;kc ~oildiictivity di1f;r scaled by dc cor~dtictivity nd,. ;ind thc fi'erjc~e~icy axis scaicd hy different parameters 11-51.

Kahr~t 151 arid Ghosh cr ill. [I41 tins iaken, :u,,, the

NaAICdPiO12 (NACP). These three NASICON glasses preparation, characterization, and the electrical coiiduciivity (the parallel conductance and capaci~nnce) measurements, in the frequency range 1 0 Hz lo 1 0 ' Hz :'or difkreilt terxpenitures were described i i i our car- licr work ) 161. The conductivity and permittivity ivere obtained hy riiulriplying appropriate geometric factors ~vitli measured conductance and capacitance.

Thc 3c co~iductivity spectra ;li difi'ese~it teriiper:l:urcs i'or NTXP glasses are stio\'.ri as in Fig. I . The ac cori- tIuct;l\.ity, cr(cu), is I'rcqucnc) i~idependsili bclo\v a ch;ir- iicteristic crobscner fsecluenq. II! this i':-tqucncy range. ~ ( ( o ) , is identical to [he dc coriducti.riry, D,:~. Above the crossover tiequciicy. ~ ( c o ) , i~icrcascs with fiequericy. The conductiviry spectra are analyzed in the !'r:~r~-iework of a coiiductivity formalism briefly outlined below.

The dc conducri~ity in Equation I call be obtained i'ro111 the Nemst-Einstein rel;~:ion in terms of the hopping l'requency up, ;iiiil charge-carriel. C ~ I I C C I I I ~ ~ I ~ ~ O : ~ 11,

a5

where / I is lhc mobiliry; L, is the cli;il.ge of ri~i>bile ions: (I;, is hopping disrarice which is take11 as npproxiriiation oi'a diameter of NaT catiorl (3.C-l -1 110" h: ~111) : k is the E3oItzliianli constaiir: and 1% is a dirni.~~siurilesl; georrlet- rical factor equal to If6 ii)r isotropri 1nedi;i such as

hopprrip I ~ C L ~ U ~ I I L ) a'r a r~dlrng tditor tor the ireqclerii? ax15 Kolrng PI t r i 6 I ] fla\e consrciezed (11 nd, I' ~ n d (11)

ndL ah d \cdllilg f , i i l ~ ) ~ \ 10 \c,tlc !he ireqtresic!, &XIS

ftlr %&rxc)tz\ rC"rIIper;itcIre\ 'ind cor11pusrItrfil, uliere 1 I \

the tnoie fractrc~n uf rllohrle jiiIjial~) io11\ d r ~ l T I \ lhc dbsolute rcrilperdture The canrcr cunceiitmtlon 11, 1%

prupurt~o~ldi tu .% Sid~botloi~i [?I ha\ used ( u ~ , / E o ~ & i for the scal~ng frequency, where rtp,, IS the pcrnirtllill) of free \Face and Ac = ( r , - F - , ) 15 the penntttr\rll change from the unrelaed baseline c, to tu11j relaxed level F , Ttus scaling frequency IS equal r~~t ru sonle numrncal factor trines the crossover or hopptng frequency accordkng to the Bartan-NaLd~~ma-Namrk.iu~ relaxation [ 15).

In the pnsenl work, we have examtned the two i) pr.i bsnk-1 ofcond'Jc'~vig~ waling a ~ ~ m a c h for thredl f fcren~ NA- f i i r u r r 1 1 rcyenry kpcdn, cln,j&l,ubr> rw.lr.l ,, lrr \ rygt SlCON E"Na"-super ionic conductors) g l a~ws , n ~ - dlttsrcnt ieinyrarurrs T ~ C the &\r I ~~~~t ,,,, I

m ~ l y , NniTrZnP101~ (NTZP). N ~ . I T I C ~ P I O , : (hTCP1. The inur plc~ ir icrgtn, i a\ futrllun of I I R K L O I. t s r r dlftilcrrt gia1ur.

glasses. Using Equations 1 and 2 can be written as

Both the carrier concentration n, and the hopping frequency up may be thermally activated. The conductivity spectra are fitted to Equation 3 for different temperatures for all the glasses and the parameters n,. wp andn extracted. In Fig. 1, the ac conductivity spectra are shown for different temperatures for NTZP glass with the values of n (n ?C 0.01 ). The results are found to be in agreement with the Equation 3 for all the temperatures.

The temperature dependence of the carrier concentration n, is shown as an inset in Fig. 1 for the NTZP, NTCP, and NACP glasses. It is clear from the inset in Fig. 1 , that, the carrier concentration n, is almost independent of temperature, i.e., the activation energy for creation of charge carriers is negligible. However, the NACP glass carrier concentration is slight greater than NTZP, NTCP glasses.

The general form of the ac conductivity scaling law is [2]

where wo is characteristic frequency. Two types of seal- ing approaches are studied for ac conductiviry spectra. In the first scaling approach, each frequency dependent conductivity data are scaled by the dc conductivily, ad,,

and each frequency is scaled by considering the characteristic frequency oo as a hopping frequency up. The scaled conductivity spectra (conductivity master curve) for the NTZP glass at different temperatures using the first scaling approach is shown in Fig. 2. The ac conductivity data are superimposed into a single curve. In the second scaling approach, each ac conductivity data are scaled by CJ~, and each frequency is scaled by considering the characteristic frequency wo = ad,T/n,, where n, the carrier concentration is proponional to x (the mole fraction of mobile (alkali) ions). The results are shown as an inset in Fig. 2. The conductivity spectra for different temperatures cotlapse into a single curve

Figure 2 Conductivity master curves of b T P glass using 9 and rIdcT/n, (inset) is scaling frequency at different temperatures.

log ((L, qicdcT) [(radlsec)(crn~)l(~/cm)~]

Figure 3 The plot showing log(w/w,,) versus iop(wn,,'nd,?'j oi N R P glasses at d~fferent temperatures. The inset plot is lopicu/re,,,) vursus logiwn,/nd,T) for diifere~lt glabsr.; at 7 =A53 K.

(conductivity master curve). The two type of scaling indicate that the relaxation mechanism is independent of temperature. From Equation 2, the characteristic frequency coo is proportional to the hopping frequency

and the factor (2nk/ve'tr;) is the proportiunrtlity constant. In the case of the first scaling approach, thr frequency is scaled by wp. Ir is clear from Equation 5. that wp is proportional to 0d~Tl r7~ . Therefore, when we scaled the frequency axis in the second approach by 0dcT/n,, we get a similar scaling feature as obser~~ed in the first case. In order 10 reconfirm the silnilarity of the scaling feature in both the scaling :ippro~ches, we have presented in Fig. 3, the log(co/op) versus log(un,/ad,T) for NTZPglasses and for the other three glasses, NTZP, NTCP, and NACP at T = 453 K (inset).

We have shown in Fig. 4, the conductivity Inas- ter curves for three different NASICON glasses ar T =453 K for both types of scaling approach. Wt. observe that the conductivity specrra at a parricular

Figuw 4 T ~ c scakd condwtv~ty spenra ss ~n Frg. 2 AU r = 153 K fa different g h .

te~nperature are superin~posed into a single cul-ve. The results in Fig. 1, indicate that the ionic relrixntion mechanism is independent of various NASICON glasses. We have obtained the conductivity master curve Frequency exponent 11 = 0.69 using Equation 4 for both types of scaling approach. The same value of the conductivity master curve frequency exponent 17 indicates that both scaling approaches have similar features.

The scaling behavior in the ac conductivity spectra of NASICON glasses (i) Na3TiZrtPiOlz, (ii) Na3TiCdP;Olz, (iii) N+A1CdP3OI2 were studied in the frriniework of conductivity formalism. The two different ac conductivity scaling approaches are used ro study the ac conductivity spectra and the both scaling approaches have the same features. From the scaling studies i t found that the ionic relaxation mcch;inism in the I';ASICON glasses is indepeildent of te~iiperature anci [he different NASICOK glasses.

Acknowledgments The financial support by the LTGC-research award schcrt~c No. 30-64/98/SA-I1 and UGC research project No. E 10-71/Y?(SK-I) is grateftlll~ acknoivlcdged for this \s80rk.

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10 P . bl,ZAS. J . i ' h 1 ~ I i K S O N . A . U L ' N D I I , $ 5 ' . DII:'II:IIIC'II

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,3243 IS. J . C. 1) > R k , J .Vo;~.C??~.ri. S<;I:<!.T 88 I l9Sbi 271 If> C; . G O V 13 1) A K ,\ J .111dC, i< . %:;\I< I ,\ PI',? S , . S ~ ~ l , ~ i . S i ~ ~ ! t ~ l o , t : ~ ~ ~ ,

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