electiucal properties of nano crystalline aip04

8/2/2019 Electiucal Properties of Nano Crystalline Aip04

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Chapter 5ELECTIUCAL PROPERTIES OF NANOCRYSTALLINE AIP04

5.1. IntroductionThe enhanced electrical properties of nanocrystalline materials exhibiting

unusual properties play a vital role in the development of new ma ter ia~s . '~heelectronic, optical, catalytic and electrical properties of nanostrucmred materials aremany times superior to their bulk form and depend strongly on size, shape,composition and preparation conditions? The large surface to volume ratio and thevariations in electronic structure. have dramatic effects on transport and catalyticproperties. The major po:rtion of atoms located at surfaces or interfaces greatlyinfluence the transport of ions and electrons through solids. In addition short-rangerearrangement or redistribution of ions and electrons may cause electrical orchemical polarization. This effect is more dominant in nanophase dielectricmaterials. Each interface will polarize in its unique way when the system issubjected to an applied electric field.6 Studies on the effect of temperature andfrequency on the dielectric behavior and a.c. electrical conductivity offer valuableinformation about the conduction phenomenon in nanostructured materials.'Dielectric behavior can effectively be used to study the electrical properties of grainboundaries, since majority of atoms of nanomaterials reside at grain bo~ndar ies .~ ,~Impedance spectroscopic studies give valuable information about the grain andgrain boundary characteristics of nanophase materials. The origin of resistance orcapacitance, its dispersion with small signal frequencies and the role of defects beobtained from these s t ~ d i e s . ' ~

In determining the electrical properties of nanocrystalline materials, thegrain boundaries and grain interfaces play important roles.""3 Grain boundaries 'ofnanophase materials are in a disordered state with large defect densities, which canact as traps for charge caniers jiom adjoining The dielectric propertiesof materials are mainly due to contributions from electronic, ionic, dipolar andspace charge .Among these, the most important contribution for


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Chapter 5 118

polycrystalline materials in bulk form is the electronic polarization, present in theoptical range of frequencies. The next contribution is from ionic polarization, whicharises due to the relative displacement of positive and negative ions. Dipolar ororientation polarization arises from molecules having a permanent electric dipolemoment that can change its orientation when an electric field is applied. Spacecharge polarization or interfacial polarization arises from accumulation of chargecarriers at structural interfaces.I9 These mobile charges are impeded by interfaces,since they are trapped in the material and are not supplied or discharged at anelectrode. Space charges resulting from these phenomena appear as an increase incapacitance as far as the exterior circuit is concerned.

For the electrical characterization of materials including solid electrolytes,ceramics and nanocrystals, impedance spectroscopy is accepted as an importanttoo1.1~2~5~2a24mpedance spectra usually include features that are directly related to

25-27the grain boundary structure of particles. The impedance spectroscopic analysisof nanophase ZnO has been reported1 and the spectrum was interpreted on the basisof resistive grain boundaries and conductive grain cores. Win and ~ei tjans ' tudiedthe frequency dependent ionic conductivity of nanocrystalline CaF2 throughimpedance spectroscopy. I!lectric:al properties of nano-CeOz have also beenreported through impedance spectroscopy."

In this chapter, the variation of dielectric constant, dielectric loss and a.c.electrical conductivity of n- AlPOj samples of different grain sizes are studied as afunction of sample temperature and frequency of the applied electric field. Theenhancement of the dielectric properties due to nanocrystallization and withreduction in grain size of the sample are analyzed in terms of existing theories andreferences of previous works in this field. The impedance spectroscopic analysis ofthe sample is canied out and the grain boundary parameters of the sample arededuced.5.2. Experimental

Nano-sized aluminium phosphate (A lp03 in three different grain sizes wasprepared from the thennolysis of new polymer matrix based precursor solutions.


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Electrical Properties of N~mocrystal l ine lp06 119-The resulting powders are nano-sized, and are of high purity. Details of thepreparation28are given in the synthesis part of section 2.2. In the present study,stoichiometric amounts of the reactants were taken such that the concentration ofthe reactants were 1.0 rnol L", 0.5 mol L-' and 0.1 mol L" to produce nanosizedA1P04 samples of average grain sizes16.34 nm, 13.59 nm and 12.04 nmrespectively, (samples A l , A2 & A3). In order to determine the crystal structure ofnanocrystalline A1P04, the calculated 'd'values are compared with the standardICDD-PDF data of cubic AIP04. All the samples are found to be of cubic structure.The nanoparticles were consolidated into pellets of diameter 13mm and thickness1-2 mm by applying a pressure of about 0.4 GPa. Both faces of the pellets werecoated with colloidal silver. Conducting leads were attached to both faces of thepellets and the samples were then encapsulated using nonconducting epoxy powder.For electrical conductivity measurements, the encapsulated pellets were immersedin an oil bath, the temperature of which could be regulated with an accuracy of&.IoC. The capacitance (C,), the modulus of complex impedance (JZI) and phaseangle (8) f the samples were measured using a Hewlett-Packard 4192A impedanceanalyzer over the frequency range 100 Hz -3 MHz and over the temperature range300K to 373K.5.3. Results andDiscussion5.3(i)Dielectric constant

The real and imaginary parts of the dielectric constant E' and E" of the givensamples were calculatecl from the measured values of capacitance Cpand dielectricloss using the formulae

E" = E' tan 6 (5.2)where d is the thickness, A is the cross sectional area of the given sample, eo is thepermittivity of free space and lan 6 is dielectric loss factor.

The variation of dielectric constant for nano Alp04 samples of differentgrain sizes with frequency of the applied field is presented in Fig.5.1 - Fig.5.3. The


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Chapter 5 120

dielectric constants of all the samples are high at low frequencies that decreaserapidly with the applied frequency at all temperatures. The dielectric constant ofsample A3 at 323 K decreases from a value of 273 at 100 Hz to 8 at 3 MHz. Forsamples A2 and Al, the corresponding variations are from 192 to 8 and from 110 to5 respectively. The variation of dielectric constant with grain size of nano-A1P04 isshown in Fig.5.4. It can be seen that the dielectric constant (E ' ) at 323 K and at 100Hz decreases from 273 to 108 when the particle size increases from 12 nm to 16nm. Similar variations are observed for higher frequencies, but at very highfrequencies no variation of E' with grain size is observed.

The variations of dielectric constant with temperature for nano-Alp04 ofdifferent grain sizes are shown in Fig.5.5 to Fig.5.7. It is seen that the dielectricconstant at 300 K is very small which suddenly increases and attains the maximum-.

log fFig. 5.1. Variation of dielectric constant of n-AIPO, sample A3 with frequency


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Electrica[ Properties of Nanocrystalline A1P04 12 1

log fFig. 5.2. Variation of dielectric consta?t of n- AIPO, sample A2 with frequency

log f/Fig. 5.3. ariation of dielectric constant of n-AIPO, sample A1 with frequency


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122Chapter 5 -_ - ----_p-.- __ - - .--80

- 0 - 1 KH z-r- 100 K H ~

-m-, 160 ~C 100 \\. ---.120 ' I.-L-.0'U 80 'L.

ial-u -.0 \----A !A !I i

I I I12 33 14 15 16 17Grain size (nm )

Fig. 5.4. Variation of dielectric constant(E') with grain size of nano-AIPO, at 323K

- - --=- 1KHz-0- IOKHZ--A- 100KHz-r- 1MHz

c 4 MHz0

v -

nI . 1 ' I . I 1 . 1 '290 300 310 320 330 340 350 360 370 380

T(K)Fig.5.5.Vanation of dielectric constant (e') with temperature of sample A3


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Electrical Properties of Na,tocrystallineALP04 123

T(K)Fig .5.6 . Variation of dielectric constant (E') with temperature of sample A2

0.-L

m-(I)a

T(K)Fig.5.7 . Variation of dielectric constant (E') with temperature of sample A1


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Chapter 5 124

value at 323 K and then decreases as temperature increases. This effect is moreprominent at low frequencies as shown in the figures. For high frequencies thedielectric constants of all the samples are much lower and does not vary appreciablywith temperature. The maximum value of the d~electric onstant of AlP04 sampleA3 decreased from 120 at 1 KHz to 8 at 3 MHz. In the case of sample A2, thecorresponding variation is from 65 to 8 and for sample Al, it is from 47 to 5respectively

Valuable information about various aspects has been brought out from themeasurement of dielectric properties: of nanostructured materials. Large dielectricconstant at low frequencies were reported for different materials by manyauthors. .29-37 Biju and ~ h a d ' d ~tudied the dielectric relaxation mechanism byconsidering nanostructured NiQ as a carrier dominated dielectric with high densityof hopping charge carriers. Cochrane and 13etchersostudied the ionic conductivityin silver iodide and reported a very high dielectric constant at the low frequencyregion. Ponpandian and ~ara~anasam~~~studiedhe electrical conductivity anddielectric properties of nanocrystall~neZnFezO, of various grain sizes throughimpedance analysis. Their results clearly indxcate the presence of dielectricrelaxation in these materials. Joshy and Abdul IChadarS investigated the grainboundary properties of nano-2;nO and Zn0-AlzQ3nanocomposites. They reportedthe conductivity due to grain boundaries is higher than that due to grains. This isattributed to the trapping of electrons by traps present in grain boundaries. Abdullaand ~ u s u f ~ ~tudied the frequency dependence of dielectric constants of some Mg-Zn fenites and they observeti very large value of E' at low frequencies. Thedielectric properties of nanophase AgzHgb and Ag2Hgb-Al203 nanocompositeswere investigated by Sankara Narayanan Potty and Abdul ~ h a d a r ~ ~nd theobserved changes in the dielectric properties were attributed to the grain boundaryproperties of nanophase materials. The enhanced electrical conductivity ofnanophaseA ~ I ~ ~nd changes in the dielectric properties of nanophase ZnS, BaTiO3and c ~ s ~ ~ - ~ ~n comparison with their bulk have also been reported.

A large volume percentage of nanocrystalline materials consist of grain orinterface boundaries. These boundaries contain defects such as dangling bonds,


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Electrical Pr ope rties o f Nanocrystal'line AlP O, 125

vacancies, vacancy clusters etc:" These defects can cause a positive or negativespace charge distribution at interfaces. The space charges can move on theapplication of an external electric field and when they are trapped by the defects, lotof dipole moments are formed. This is space charge polarization. Hence the spacecharge effect will be a pnsminent factor, which decides the dielectric properties inmaterials with small particle sizes.39 In addition ion jump polarization may also begreater in nanocrystalline materials since there will be a number of positions in thegrain boundaries for the ions to occupy. When an electric field is applied, the ionand vacancy can exchange positions by a simple jump of the cation to a neighboringposition. The charge displacement occurs by an atom jump rather than movementabout an equilibrium position. Space charges resulting from these phenomenaappear as an increase in capacitance, which leads to an increase in the dielectricconstant, as far as the exterior circuit is concerned. Thus the high values of thedielectric constant in the present study may be attributed to the increased ion jumporientation effect and the increased space charge effect exhibited by nanoparticles.Along with these, the d.c.conductivity effects can also enhance the value of thedielectric con~tant.~he large d.c.conductivity observed in fast ion conductors isinterpreted as due to random hopping of mobile ions from site to site.40 Innanocrystalline materials,, increased d.c. conductivity can be expected due tohopping by the presence of high density of trap sites. Also, at low frequencies thedielectric loss is inversely proportional to frequency, which indicates larged .c . condu~ t iv i t~ ~ ~s frequenc:~ ncreases beyond a particular limit, the spacecharges cannot sustain with the field and hence the polarization decreases, leadingto a decrease in the value of E' .

Most of the atoms in nanocrystalline materials reside in grainboundaries,'4A2which become electrically active as a result of charge trapping. Thedipole moment can easily follow the changes in electric f i e ~ d , " . ~ ~ . ~ ~specially atlow frequencies. Hence the contributions to dielectric constant increases throughspace charge polarization and rotation direction polarization, which occur mainly ininterfaces?' Thus the dielectric constant of nanostructured materials, should belarger than that of conver~tionalmaterials. An assembly of space charge caniers in adielectric requires enough time to line up their axes parallel to an alternating


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Chapter 5 126

electric field. At low frequencies, the dielectric will get the time for this. But if thefrequency of the field reversal increases beyond a certain limit, the space chargecarriers cannot keep up with the field and their directions lag behind the field,resulting a lowering of dielectric constant of the materiaLd5As the frequency of thealternating field continuously increases, at some stage the space charge carriers willhave started to move before the field reversal, leading to a rather frequencyindependent dielectric constant. The observation that &' decreases sharply withfrequency and remains almost a constant at very high frequencies, should beattributed to the increased inertiad6of the dipoles, as described above.

The dielectric constant of nano-Alp04 initially increases sharply withtemperature to a sufficiently high value and thereafter decreases with temperature.At sufficiently high temperatures, d.c.conductivity increases exponentially as,

tr = IS 0 exp (-EAT) (5.3)The d.c.conductivity effects enhance the value of the dielectric co n~t an t. ~lso, atsufficiently high temperature; the dielectric loss is dominated by the conductivity ofthe sample resulting an increase in dielectric con~tant.~'he increased space chargepolarization and conductivity effects at the beginning of the rise in temperature isthe reason for the sharp increase of the dielectric constant at low frequencies. Astemperature increases, the :;pace charge and ion jump polarization are laggingbehind the applied field, resulting a decrease in dielectric constant.5.3(ii)Dielectric Loss

In dielectric materials, usually dielectric losses occur due to absorptioncurrent. The orientation of molecules along the direction of the applied electric fieldin polar dielectrics, requires a part of electric energy to overcome the forces ofinternal friction. Another part of electric energy is utilized for rotations of dipolarmolecules and other kinds of'molecular transfer from one position to another, whichalso involve energy losses.The dielectric loss of a material is given as4'

where a is the conductivity and o s the frequency.


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Electrical Properties of Nan:ocrystullineAlp04 127

The variations of dielectric loss factor ( t a n 6) of nano-Alp04 samples ofdifferent grain size with frequency are shown in Fig.5.8 - Fig.S.lO. It can be seenthat ta n 6 decreases with increase of frequency and at higher frequencies the lossangle has almost the same value at all temperatures. For nano-A1P04 sample A3,the dielectric loss at 323 K is 16 at 100 Hz, which decreases to 0.6 at 3 MHz. Thecorresponding variations for samples A2 is from 13 to 0.4 and for Al, from 10 to0.1 respectively. The same behaviour is observed with lower values for all othertemperatures except room temperature, where ta n 6 do not change with frequency.

The variations of tan ii for different temperatures are shown in Fig.S.ll -Fig.5.13. For all samples in the present study, ta n 6 initially increases withtemperature, attains a maximum value and thereafter decreases at a slower rate. Forsample A3, the value of dielectric loss at 1KHz increases from 0.3 at 300 K o 12 at323 K and then decreases to 0.8 at 373 K. The corresponding variations for sampleA2 is from 0.3 to 10,which decreases to 0.1. For sample A l , it is from 0.1 to 8 and

log fFig.5.8. Variation of dielectric loss (tan 6) of n-AIPO, sample A3 with frequency


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Chapter 5 128

log fFig .5.9. Variation of dielectric loss (tan 6) of n- AIPO, sample A 2 with frequency

-2 3 4 5 6 7

log fFig.5.10. Variation of dielectric loss (tan 6) of n- AIPO, sample A1 with frequency


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Electrical Properties of Nunocrystalline ALP04 129--

12

-A- 100KHz1 0-r- 1 MHz/-0.-

A/-A-~

0 4

02 *---0 0 -7

(K)Fig.5 .11. Variation of dielectric loss (tan6)of AIPO, sample A3 with temperature

T(K)~ i ~ 5 . 1 2 .ariation of dielectric loss (tan8)of AIPO, sample A 2 with temperature


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Chapter 5 130-~ ~ -.

-*- 1OKHz- - A 1OOKHz-r- 1MHz/-

&/-A -\.--7-

*--*-- l*---- *--t - - T - - - - r . I . I ~ I ~ I ~ I ~ I ~ i290 300 310 320 330 340 350 360 370 380

T(K)Fig.5.13. Variat~on f dielectric loss (tan6)ofAIPO, sampleA1 with temperature

then to 0.1 respectively. The nature of variations are similar, but with reducedvalues for all other higher frequencies as shown in the figures.

Absorption current4' in nonpolar dielectrics can be attributed to theinhomogeneity in the elecbical properties of dielectrics. The formation of spacecharges under the action of an external electric field will initiate the redistributionof charges within the volume of the dielectric. Inhomogeneity is inevitable in atechnical ceramic material. Dielectrics always have, to some extent, impurities,pores filled with air, inclusions of hygroscopic water, etc." As a result, propertiesof the material may vary in different parts of the volume.

In nanophase materials, the grain boundaries have an amorphous or glassy48-51structure. All the inhomogenities, defects, space charge formation etc. together

produces an absorption current, which results in dielectric losses. Due to thepresence of dangling bonds at the surface, the surface layers of nanoparticles will behighly reactive and there is a chance of adsorption of gases like oxygen or nitrogen.These adsorbed gases cart also cause an increase in dielectric loss. Thus ananophase ceramic acts as a lossy dielectric" with high dielectric loss at low


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Electrical Prope rties of Nanocrystalline ALP04 131

frequencies, which decreases at higher frequencies. In nanophase materials,inhomogeneities like defects and space charge formation in the interface layersproduce an absorption c:urrent resulting in a dielectric loss. Also, enhancement ind.c. conductivity will give rise to dielectric 10sses.'~ he absences of peaks in thefrequency versus dielectric loss curves of the present samples show the widedistribution of relaxation times65.3(iii)A.C. conductivity

The a.c. electrical conductivity of the samples can be calculated using theequation

oat = 22xfc0 .sf tan 6 (5.5)where f is the frequency, eo is the permittivity of free space, E' is the real part ofthe measured complex dielectric constant and tan 6 s the dielectric loss factor.

The frequency dependence of a.c. electrical conductivities (no,) of nano-AIR34 samples with different grain sizes are shown in Fig.5.14- Fig.5.16. It can beseen that ow increases .with frequency for all samples. For nano-AIR34 sample A3,omat 323 K and at 1 0 Hz is 0.2 x 10.' ohm-' cm", which increases to 37 x 10.'ohm-'cm-' at 3 MHz. For sample A2, at 323 K, the value varies from 0.1 x 10.~ohm.' cm-I to 23 x 10.'' ohm-lcm-' when the frequency increases from 100 Hz to 3MHz. For sample Al, the corresponding variation is from 0.2 x 10.' ohm-' cm-' to18 x 10.~ hm-' cm" a:; the frequency varies from 100 Hz to 3 MHz.The nature offrequency dependence of on, is the same for all samples at all temperatures. Thevalues of a,,, at higher frequencies reduce as temperature increases.

The variation of 0, with temperature for different fixed frequencies of allthe three nano samples of AIP04 are shown in Fig.5.17-Fig.5.19. The value of oocatroom temperature (300 K) rises to a peak value at about 323 K and then decreasesslowly for all samples. For sample A3, a,, at 3 MHz increases from 12 x 10.' ohm-'cm-I at 300 K to 37 x. 10" ohm-' cm-' at 323 K, which decreases as temperature


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Chapter 5 132

Fig.5.14. Variation of a.c. conductivity (0,) with frequency of sample A3

log fFig.5.15. Variation of a .c. conductivity (0,) with frequency of sample A 2


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Electrical Properties of Nanocrystalline AIPOd 133I,I2 3 4 5 6 7log f

Fig.5.16. Variation of a.c. conductivity (aac)with frequency of sample A1

increases and falls to 2 x 10-5ohm-' cm-I at 373 K. The corresponding variation forsample A2 is from 8 ~ 1 0 ' " hm-' cm-I at 300 K to 23 xlo-' ohm-' cm" at 323 K,which decreases to 9 x 10." ohm-' cm-I at 373 K. For sample Al, it is from 7 x 10.~ohm-' cm" at 300 K to 18 :u 10" ohm" cm'l at 323 K and then to 8 x 10" ohm-' cm-' at 373 K. The nature remains similar, but no much appreciable variations asfrequencies are decreased.

Improved electrical conductivity has been reported for many nanophasematerials. 10.20.21,34-37 Enhanced electrical conductivity observed in nano AgI hasbeen attributed to defect structure of n a n ~ ~ a r t i c l e s . ~ ~n nano ~ e 0 2 "he enhancedelectrical properties are explained on the basis of interfacial defect formation. Puinand ~ ei t jans ' eported frequency dependent conductivity of nano CaFz and theyobserved an increase of the conductivity compared to single crystalline CaFz bymore than four orders of magnitude.2 An increased ionic conductivity was alsoobserved for nanostructured yttria stabilized ~ i r c o n i a . ~ ~


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Chapter 5 134

Fig.5.17. Variation of a.c.conductivity (o,Jwith tem perature of sample A 3

-.-K Hz--0- lOKHz-A- 100KHz-v- 1M H z& M H z

-----* /--vA-A/-+===-n-L-- I b- 4

290 300 310 320 330 340 350 360 370 380

T ( K )Fig.5.18. Variation of a.c.conductivity (oac)with emperature of sample A 2


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Electrical Properties ofNanocrvstalline A lp0 4 135

Fig.5.19. Variation of a.c.conductivity (o,,)with temperature of sample A1

The a.c. conductivity has been attributed to losses due to bound charges.However, every material! will have some free charges, and under the applied lowfrequency, these charges can follow the field and cause conduction current givingrise to energy losses. Hence measured a.c. conductivity am s given by52

where a& is the d.c. conductivity and aocs the true value of the a.c. conductivity.The enhancement of a.c. conductivity was explained by many

authors5'"' on the basis of excess ion vacancies due to the high conduction of thespace charge layer. The a.c. conductivities strongly depend on the particle size, theconcentration and heat treatment of the sample and the premelting of theelectrolytes. Also, the frequency dependent data indicated that the enhancement wasdue to grains rather than grain boundary or surface conduction. Many authorspresented different arguments on the frequency dependence of a.c. conductivityexhibited by nanocrystalline materials in the high frequency region. They are thequantum mechanical tunneling mode^^'.^^.^' and hopping barrier model.5s"~ o l l a k ~ ~as shown that the temperature dependence of conductivity is due tomultiple hopes.


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The nature of frequenc.y and temperature dependence of a.c. conductivity ofthe present samples, suggests an electronic hopping mechanism, exhibited by alarge number of nanocrystalline materials. This hopping mechanism is compatiblewith the highly disordered or amorphous structure of the grain boundary layers ofnanophase materials, having high densities of localized levels. The physicalsignificance of this type of frequency dependence comes from the fact that analternating current can affect an electron confined to two traps.6'.62The time itspends in each trap will depend on the energy difference of the two trap states. Anapplied a.c. field will alter this energy difference and produces a net polarization,which lags behind the field.61362his polarization, which is out of phase with theapplied electric field, is measured as a.c. conductivity.5.3(iv) Impedance spectroscopic analysis

The complex plane impedance analysis of a number of polycrystalline aswell as nanocrystalline materials have been reported.1-5.20-24 Lee et.all reported theimpedance spectra of nanophase ZnO (grain size 60 nm) and found only onesemicircle in the impedance spectrum, which was explained as the grain boundaryarc. The impedance analysis of nanophase ZnO (grain size 13 nm)' exhibited twopartially overlapping semicircles corresponding to grain and grain boundarycontributions. But the impedance specua of ZnO- Alz03nanocomposite5was foundto consist of only one arc, which was explained due to the fact that the conductionprocess through the grain cores and grain boundaries have identical time constants.Also the arcs were found to be highly depressed, which indicates a distribution ofrelaxation times. Chiang et.all' reported the impedance spectroscopic analysis ofnanocrystalline CeOz and observed a low frequency arc corresponding to grains.The complex impedance spectrum of nano Ca& was reported to contain a smallsegment of the electmje polarization arc at low frequency and a large anddepressed arc due to grain boundary at high frequency. Complex plane impedanceanalysis of polycrystalline BaTi03, showed a smaller arc due to grain and a largegrain boundary arc2' The high value of impedance at grain boundary was explained


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Electrical Properties of Nanocrystalline AlP04 137

on the basis of the presence of air gaps and high electrical inhomogenities in theregion of the neck between grains. Aoki et. aL2'studied the impedance of highpurity ZrOz, stabilized with CaO, having different grain sizes. The two well-separated semicircles found at higher frequencies were attributed to contributionsfrom the grain interiors and grain boundaries, and the trace of a third semicircle atlow frequencies due to the electrode interface impedance. The arc due to grains wasfound to be higher than that due to grain boundaries. The impedance spectra ofpolycrystalline ceria showed1 a small arc corresponding to grain contribution and alarge semicircle due to grain boundary contribution.

The impedance spectra of the present sample, nanocrystalline Alp04 ofdifferent grain sizes at thn:e different temperatures are shown in Fig. 5.20 -Fig.5.22. All the plots contain depressed or distorted semicircle due to the fact thatthey are made up of two partially overlapping semicircular arcs. Depressed arcsmay arise due to several relaxation times or due to a continuous distribution ofrelaxation times.26The two semicircles at high and low frequencies are identified asdue to grain and grain boundary phenomena respectively.26Resistances due to grainand grain boundary are given by the intercepts of the high and low frequency arcswith the x-axis. In the present study, only the high frequency arc is prominent. Thecontribution to impedance due to grain is very small compared to the grainboundary contribution. The single arc reported in the impedance spectrum of ZnOby Lee et al' has been interpreted as due to grain boundary contribution. The singlearc for all the samples in the present study is in agreement with this observation.The results also reveal that the impedance of nanostructured materials depends onboth grain size and temperature of measurement. Sample A3, having grain size 12nm (Fig.5.20), has the highest impedance. The nature of variation remains the same,but the diameters of the semic:ircles gradually increase as temperature rises. Similarvariations are observed for samples A2 and Al, with higher grain sizes (13.6 nmand 16.3 nm). In these cases, the impedance values are diminished, as shown in Fig.5.21 and Fig.5.22.


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____---.___300

A

Fl20:f A, I 3 : A 353KA AEr 0 10 0Y loo 1

01

A 0 00 I

I I 8 1

0 50 100 150Z'(k ohm)Fig.5 .20. Impedance spectra of n-AIPO, sample A3 for different temperatures

- 150s A00 0

00 00

50 A 0 aA 0 0

0lOl?--50 100 Z'(k ohm)50 v 200 s 250Fig .5.2 1. lmpedance spectra of n-AIPO, sample A2 for different temperatures


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Electrical Pro perties of Nailocrystalline A lP 04 139

Z'(k ohm)Fig.5.22. Impedance spectra n- AIPO, sample A1 for different temperatures

Fig.5.23. A typical impedance spectrum showing all fitting parameters


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Chapter 5 140

A typical impedance spectrum showing all fitting parameters is given inFig.5.23. The resistance R due to grain boundary is given by the intercept of the arcwith the x-axis. The diameter of the arc increases as temperature increases. Thecontribution to the total resistance of the sample Rgb by the grain boundary is givenby the diameter of the arc,69as:shown in the figure. pgb is the angle of depression ofthe semicircle center due to the tilting of the semicircle. The mean relaxation timefor the grain boundary processes, t g b = Rgb Cgb. which is the inverse of the peakfrequency and thus the grain boundary capacitance C8b can be calculated. TheCole-Cole expression69 or the resulting complex impedance can be written as

R - R,z*( gb)= Ro+ - I-agb (5.7)I + ( i mgb rgbjwhere R and R, are respectively the intercepts with the real impedance axis at thehigh frequency end and low frequency end. The parameter a,b measures thedeviation of the shape of the impedance plot from the ideal semicircular shape ofthe grain boundary. a g b is given by

The computed parameters of the various grain boundary contributions aretabulated in table.5.1.The results show that the conductivities of each sample, due to

Table 5.1: Grain boundary parameters of nano Alp04 samples

Sample

A1

A2

A3

C g b(pF)2.242.873.412.793.363.972.883.544.12

Ogb(X10-6ncm ')

3.253.673.983.544.21-.87

4.4 1 -5.025.54 -

Tg b(deg )

81014282415373934

Temperature313 K323 K353K313 K323 K353 K313 K323 K353K

Rgb(kn)73130175170220240180200220

(rad/sec)611

26801675210813531050192914121103


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Electrical Properties of NartocrystallineAlP04 141

grain boundaries (ugh), increase with temperature. Thus, it is confirmed that, thepresence of grain boundaries in nanocrystalline materials is responsible for theobserved variations in the conductivities nanocrystalline AIP04.

The impedance of nanocrystalline A1P04 in the present investigation wasfound to arise from both grain and grain boundary contributions of which the majorcomponent is the latter. The presence of grains and grain boundaries in nanophasematerials are very important in determining their electrical properties.63." Asignificant fraction of atoms in nanophase materials reside in grain boundaryenvironments where they occupy positions relaxed65 from normal sites. The grainboundary resistivity may be attributed to partial or complete blocking of charge

66, 67carriers due to the presence of defects at the grain boundaries . Thus the overallimpedance behavior of the three samples arises mainly from contributions due tograin boundaries. The intergranular porosity largely alters the diameter of the grainboundary arc in the impedance spectrum, which is a measure of the grain boundaryresistance. Since the grain boundary resistance is very large compared with grainresistance, conductivity in the present study is attributed mainly through grains,which is characteristic of ionic conductors. The lesser conductivity in the grainboundaries, observed in the present study may be due to impurity phases, porosityand the large area of grain boundary region.68 It can be seen from the figures thatthe grain conductivity (diameter of the grain boundary arc) increases as particle sizedecreases.5.4. Conclusion

The dielectric propexties of nanocrystalline Alp04 having three differentgrain sizes were investigated over a wide range of frequencies 100 Hz -3 MHz andover the temperature from 300 K to 373 K. The dielectric constants (E ' ) of all thesamples are high at low frequencies that decrease with frequency at alltemperatures. The dielectric constant initially increases with temperature to asufficiently high value and thereafter decreases as temperature is further increased.Dielectric loss (tan 6) decreases with frequency and at higher frequencies the lossangle has the same low value at all temperatures. Also, tan 6 was found to increasewith temperature, attains a peak value and then decreases at a slower rate. The a.c.


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electrical conductivity ( u~ , )ncreases with frequency for all samples. uachas a lowvalue at room temperature (300 K), which suddenly rises to a peak value at 323 Kand then decreases slowly for all samples. E', tan 6 and ua,were found to depend ongrain size, frequency and temperature. Grain boundary parameters of all the nanoAlp04 samples are obtained through impedance spectroscopic analysis. Theimpedance spectra of nanocrystalline Alp04 in the present investigation show thatthe imped ance arises from both grain and grain boundary com pon ents of which themajor compo nent is from grain boundary.References

I . J Lee, J H Hwang, J J Mashek, 'I'0 Mason, A E Miller and R W Siegel, J.Marer. Res. 10,2295 (1995)

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electiucal properties of nano crystalline aip04

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