Nuclear Instruments and Methods in Physics Research B 316 (2013) 232–238

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Nuclear Instruments and Methods in Physics Research B

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Gamma-radiation-induced dielectric relaxation characteristicsof layered crystals of phlogopite mica

0168-583X/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.nimb.2013.09.018

⇑ Corresponding author. Mobile: +91 99144 90280.E-mail address: mohansinghphysics@gmail.com (M. Singh).

Navjeet Kaur a, Mohan Singh a,⇑, Lakhwant Singh a, A.M. Awasthi b, Jitender Kumar b

a Department of Physics, Guru Nanak Dev University, Amritsar, Punjab 143005, Indiab Thermodynamics Laboratory, UGC-DAE Consortium for Scientific Research, Indore 452001, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 May 2013Received in revised form 18 September 2013Available online 12 October 2013

Keywords:MicaDielectric relaxationElectrical engineering

In the present investigation, the influence of gamma irradiation on the dielectric relaxation characteris-tics of phlogopite mica was studied over the frequency range of 0.1 Hz–10 MHz and in the temperaturerange of 593–813 K by measuring the dielectric permittivity, electric modulus and conductivity. Bycomparing the dielectric spectra obtained for pristine and irradiated samples, it was observed thatgamma irradiation significantly enhances the dielectric constants (e0 and e00) of phlogopite mica becauseof the production of defects and lattice disorder by the gamma irradiation. The values of the activationenergy for pristine and irradiated mica (determined from the electric modulus and the conductivity) werefound to be substantially similar, suggesting that the same types of charge carriers are involved in therelaxation mechanism. The experimentally measured electric modulus and conductivity data could bewell interpreted by the Havriliak–Negami dielectric relaxation function. The scaling of the electric-modulus spectra of both pristine and irradiated mica results in a master curve, which indicates thatthe relaxation mechanism is independent of temperature. Cole–Cole plots were also employed to analyzethe non-Debye relaxation mechanism. This research will boost the reader’s interest concerning theemerging contributions of irradiation and materials such as mica in electrical engineering.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Modern technology has focused our interest in enhancing theperformance of various devices in electrical engineering. Consider-able resources have been invested in both experimental andtheoretical research, but the possibility of employing materialsavailable in nature and exploring their potential for cutting-edgeapplications in technology has been largely neglected. Amongseveral natural materials that could be considered for this purpose,micaceous minerals are very stable, sensitive and abundantmaterials in their most advantageous forms, and they stand outover others because of their tremendous prospects for fruitfulapplications [1–7]. Dielectric measurements have proven to be acrucial tool in the study of relaxation behavior. A completeunderstanding of the dielectric relaxation of micaceous mineralsis important from the standpoint of applications. Dielectricrelaxation spectroscopy of annealed phlogopite mica at varioustemperatures has also been studied by the present authors [2].We are currently focusing on the different routes through whichthe material can provide more beneficial and high-quality results.In the present research article, a study of the gamma-radiation-

induced dielectric relaxation characteristics of the phlogopite micais presented. The interaction of ionizing radiation, especially cradiation, with matter is very significant [1,3–5,8]. Ionizing radia-tion leads to the production of defects as a result of various pro-cesses involved during the interaction, e.g., atomic displacementscan be caused by momentum and energy transfer to electrons orby the rearrangement of atoms. These irradiation-induced effectsand defects can stimulate significant improvement in the dielectricproperties of the material. The present investigation was con-ducted to understand the effects of ionizing radiation (c radiation)on the dielectric relaxation spectroscopy of phlogopite mica over arange of temperature (593–813 K) and frequency (0.1 Hz–10 MHz).To the best of our knowledge, this is the first attempt that has beenmade to study the influence of gamma irradiation on the dielectricproperties of phlogopite mica over a wide range of frequency andtemperature.

2. Experimental details

In the present research, sheets of phlogopite mica (�200 lmthick) supplied by Shree GR Exports Private Limited, Kolkata, India,were used. These phlogopite-mica sheets were irradiated withgamma rays (doses ranged from 5 kGy to 100 kGy) using a 60Cogamma source at room temperature that was acquired from the

1 2 3 4 5 6 70.0

0.1

0.2

0.3

0.4

ε''

log ω (rads-1)

Pristine5 kGy10 kGy20 kGy25 kGy50 kGy100 kGy

Fig. 2. Frequency dependence of the dielectric loss (e00) of phlogopite micasubjected to various gamma-ray doses.

N. Kaur et al. / Nuclear Instruments and Methods in Physics Research B 316 (2013) 232–238 233

Inter University Accelerator Centre (IUAC), New Delhi, India. Thedose rate in the gamma chamber at the time of irradiation was�7.88 kGy/h. The dielectric constant (e0) and dielectric loss (e00)for the gamma-irradiated samples were measured in the frequencyrange of 0.1 Hz–10 MHz at room temperature. The variation ofthese two parameters (e0 and e00) as a function of frequency for sam-ples subjected to various gamma doses is depicted in Figs. 1 and 2,respectively. It was observed that the dielectric constant (e0) andthe dielectric loss (e00) increase with increasing gamma dose andexhibit maxima for the phlogopite mica that was irradiated witha 25 kGy gamma dose. The 25 kGy gamma-irradiated sample wastherefore identified as the one that should prove to be most infor-mative for a deeper understanding of the gamma-irradiation-in-duced dielectric relaxation characteristics of phlogopite mica. Thedielectric relaxation characterization of pristine and 25 kGy gam-ma-dose-irradiated phlogopite mica was executed in the frequencyrange off 0.1 Hz–10 MHz and over the temperature range of 593–813 K. All the dielectric measurements were performed using aNOVO-CONTROL (Alpha-A) high-performance frequency analyzerinstalled at the UGC-DAE Consortium for Scientific Research, In-dore, India. The phlogopite sample was mounted in a sampleholder between two parallel electrodes, forming a mica capacitor.To minimize noise disturbance, proper shielding of the sampleholder was implemented. The theoretical curve fitting of themeasured conductivity and electric-modulus data was performedusing the Havriliak–Negami dielectric relaxation formulationsuperimposed with a conductivity term, as given below [9]:

e� xð Þ ¼ e0 � ie00 ¼ �irdc

e0x

� �n

þ De1þ ixsð Þa� �b þ e1

( )ð1Þ

where e0 is the vacuum permittivity, s is the characteristic relaxa-tion time, and e1 represents the value of e0 at infinite frequency.De, which is known as the relaxation strength, gives the differencebetween e0 at zero and infinite frequency (e1). De is proportional tothe area under the maximum value or the relaxation peak of e00. aand b are the symmetry- and asymmetry-dependent broadeningparameters, respectively. The parameter a is related to depicts thebroadness of the spectrum and determines the slope of the low-fre-quency side of the relaxation in the dielectric loss e00. The parameterb is related to the asymmetry of the spectra, and the value of �abdetermines the slope of the high-frequency side of the e00 relaxation

1 2 3 4 5 6 71.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0Pristine5 kGy10 kGy20 kGy25 kGy50 kGy100 kGy

ε'

log ω(rads-1)

Fig. 1. Frequency dependence of the dielectric constant (e0) of phlogopite micasubjected to various gamma-ray doses.

curve. The value of both parameters a and b are constrained to liebetween 0 and 1.

3. Results and discussion

Dielectric relaxation spectroscopy was used to study theinfluence of an applied electric field on pristine and gamma-irradi-ated phlogopite mica. The frequency- and temperature-dependentbehavior of the dielectric permittivity (e⁄ = e0 � ie00) demonstratesthe response of the phlogopite to the applied field by providinginformation regarding the properties of the material. The dielectricpermittivity (e⁄) develops from the space-charge polarizationoriginating within the dielectric material. The real part (e0)represents the polarizability, and the imaginary part (e00) repre-sents the energy losses attributable to the polarization and ionicconduction. Each polarization mechanism dominates at a certaincharacteristic relaxation frequency.

The frequency response (0.1 Hz–10 MHz) of the dielectric con-stant (e0) and dielectric loss (e00) of phlogopite mica before and aftergamma irradiation (5–100 kGy) at room temperature is presentedin Figs. 1 and 2, respectively. These results demonstrate that thedielectric constant (e0) and dielectric loss (e00) increase with increas-ing gamma dose up to 25 kGy and then decrease for higher gammadoses. The increase in the dielectric constant (e0) and dielectric loss(e00) with the increase in the accumulated gamma dose up to25 kGy may be attributable to the disturbance in the materialstructure caused by the production of atomic displacements andvarious lattice defects. As the gamma dose increases up to25 kGy, more ions are activated with lattice disorders, and theirinteractions and migration through the material increase thespace-charge polarization and thereby increase the dielectric con-stant (e0) and dielectric loss (e00). Above 25 kGy, as the gamma doseincreases, the dielectric constant and dielectric loss decrease be-cause of the rearrangement of atoms and primary defects in thematerial. This means that at higher gamma doses, redistributionof the incident energy occurs, and stable defects are formed thatsuppress the migration of carriers and the polarization effect,which in turn decreases the dielectric constant and dielectric loss.It is also observed that e0 decreases as the frequency increasesbecause the dipoles can no longer comply with the field at high fre-quencies. A similar trend is observed for the dielectric loss (e00) forvarying frequencies and gamma doses (Fig. 2). The increase in thedielectric constant of mica near 25 kGy is a characteristic feature of

234 N. Kaur et al. / Nuclear Instruments and Methods in Physics Research B 316 (2013) 232–238

the enhancement of its dielectric properties. Therefore, thephlogopite sample that was irradiated with 25 kGy was chosenas the subject of further study of its dielectric characteristics as afunction of frequency and temperature.

Fig. 3 presents the frequency dependence of the real part (e0) ofthe complex dielectric permittivity (e⁄) for pristine and 25 kGygamma-irradiated phlogopite mica at various temperatures (593–813 K). The imaginary part (e00) of the complex dielectric permittiv-ity (e⁄) for pristine and 25 kGy gamma-irradiated phlogopite micain the temperature range 593–813 K is shown in Fig. 4. Figs. 3 and4 illustrate that the dielectric constant (e0) and the dielectric loss(e00) decrease with increasing frequency at all temperatures andmerge in the high-frequency regime. The trend of the variation inthe dielectric constants e0 and e00 with frequency is the same forboth the pristine and gamma-irradiated samples, but the gammairradiation enhanced the values of e0 and e00. This enhancementmay be attributable to the increase in lattice disorder anddistortion in the material upon irradiation, which results in the in-crease of the space-charge polarization. The frequency dependenceof e0 and e00 elucidates the relaxation phenomena of the material re-lated to the frequency-dependent orientation polarization. Whenthe field frequency is very small i.e., (x� 1/s), the permanentelectric dipoles align themselves in the direction of the field, there-by contributing to the large space-charge polarization and leading

1 2 3 4 5 6 7

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Pristine

793 K773 K753 K

593 K613 K633 K653 K673 K693 K713 K733 K

813 Kε'

log ω (rads-1)

0 1 2 3 4 5 6 7 80

5

10

15

20

25

30

35

40

45

Irradiated

693 K713 K733 K

673 K

ε '

log ω (rads-1)

593 K613 K633 K653 K

753 K773 K793 K813 K

Fig. 3. Frequency dependence of e0 of pristine and 25 kGy gamma-dose-irradiatedphlogopite mica at various temperatures.

to the manifestation of large values of e0 and e00. This fast-growingtendency of e0 and e00 serves as evidence of the presence of DC con-ductivity. As the frequency increases, the electric dipoles start tolag behind the field, and the dielectric constant e0 and dielectricloss e00 slowly decrease. At the characteristic frequency (x = 1/s),the dielectric constant e0 and dielectric loss e00 drop abruptly, indi-cating that the material has entered the relaxation regime. In thehigher-frequency realm (x� 1/s), the variation in the field is sorapid that the electric dipoles do not have enough time to alignthemselves along the direction of the field. Their contribution tothe space-charge polarization becomes negligible, and the valuesof the dielectric constant e0 and dielectric loss e00 decrease withincreasing frequency. At higher frequency, we can make theapproximation e0 � e1 where e1 is the high-frequency dielectricconstant e0. Figs. 3 and 4 also show distinctly that in the low-fre-quency region, e0 and e00 increase with increasing temperature. Thismay be because of the thermally triggered dielectric relaxation ofthe mica. The high values of e0 and e00 at low frequencies and hightemperatures may also be attributable to electrode polarizationarising from free-charge buildup at interfaces within the bulk ofthe material and at the interface between the sample and theelectrode.

The electric modulus was also been measured to investigate thedielectric relaxation behavior of pristine and gamma-irradiated

0 1 2 3 4 5 6 7 8

0

1

2

3

4

5

6

7

8

9

10

11

12

13 Pristine

773 K753 K

793 K

ε''

log ω (rads-1)

593 K613 K633 K653 K673 K693 K713 K733 K

813 K

0 1 2 3 4 5 6 7 8

0

200

400

600

800

1000

1200

1400

1600

1800Irradiated

753 K733 K713 K693 K

ε''

log ω (rads-1)

593 K613 K633 K653 K673 K

773 K793 K813 K

Fig. 4. Frequency dependence of e00 of pristine and 25 kGy gamma-dose-irradiatedphlogopite mica at various temperatures.

N. Kaur et al. / Nuclear Instruments and Methods in Physics Research B 316 (2013) 232–238 235

phlogopite mica. This quantity reflects the bulk dielectric responseof the sample. The complex electric modulus (M⁄) is defined as theinverse of the complex dielectric permittivity (e⁄) using the follow-ing relation:

M� ¼ 1e�¼ M0 þ iM00 ¼ e0

e0ð Þ2 þ e0ð Þ2

!þ i

e00

e0ð Þ2 þ e00ð Þ2

!ð2Þ

where e0 and e00 are the real and imaginary parts of the complexdielectric permittivity, respectively. M0 and M00 are the real andimaginary parts of the complex electric modulus, respectively.

The frequency dependence of (M⁄) is given as [10]:

M� xð Þ ¼ 1e1

1�Z 1

0e�ixt �du

dt

� �dt

� �ð3Þ

where e1 represents the dielectric constant at high frequency, andM1 is its reciprocal. /(t) is the relaxation function, which describesthe decay of the electric field in the material. M0 is related to theelectrical stiffness of the material, and any change in it is accompa-nied by a loss peak in M00.

Fig. 5 represents the variation of the real part (M0) of the electricmodulus (M⁄) as a function of frequency over the temperaturerange of 593–813 K for pristine and 25 kGy gamma-irradiatedphlogopite mica. The imaginary part (M00) of the electric modulus

1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Pristine

M'

log ω (rads-1)

593 K613 K633 K653 K673 K693 K713 K733 K 753 K773 K793 K 813 K

1 2 3 4 5 6 7-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Irradiated

593 K613 K633 K653 K673 K693 K713 K733 K 753 K773 K793 K 813 K

M'

log ω (rads-1)

Fig. 5. Frequency dependence of the real part (M0) of the electric modulus ofpristine and 25 kGy gamma-dose-irradiated phlogopite mica at varioustemperatures.

(M⁄) for pristine and 25 kGy gamma-irradiated phlogopite micain the temperature range of 593–813 K is shown in Fig. 6. In thedielectric-loss (e00) plot, a relaxation peak is observed in the mea-sured frequency range. In the electric-modulus plots, peaks appearthat indicate the presence of a relaxation phenomenon in thematerial. From Fig. 5, it can be seen that at lower frequencies,the value of M0 is very low and approaches zero at all temperaturesfor both the pristine and 25 kGy gamma-irradiated samples, indi-cating that the contribution of the electrode polarization to theelectric modulus is negligible. As the frequency increases, M0

increases continuously, and dispersion behavior is observed thatcorresponds to the high-frequency limiting value of M0 (M0

1). It isalso observed that the value of M0 decreases with increasing intemperature in the low-frequency region but is less sensitive totemperature in the high-frequency range.

The imaginary part of the electric modulus M00 (Fig. 6) for pris-tine and 25 kGy gamma irradiated phlogopite mica is indicative ofthe energy loss under the applied electric field. The experimentaldata of M00 were fitted with the Havriliak–Negami function (Eq.(1)), and these fits are also presented in Fig. 6. It is clear that theexperimental data are in close agreement with the theoretical ap-proach throughout the entire frequency and temperature rangeunder investigation. Fig. 6 shows that the M00 curves display asym-metric maxima (M00

max) at characteristic frequencies centered at the

0 1 2 3 4 5 6 7

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

Pristine593 K613 K633 K653 K673 K693 K713 K733 K 753 K773 K793 K 813 K

M''

log ω (rads-1)

0 1 2 3 4 5 6 7

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35Irradiated 593 K

613 K633 K653 K673 K693 K713 K733 K 753 K773 K793 K 813 K

M''

log ω (rads-1)

Fig. 6. Frequency dependence of the imaginary part (M00) of the electric modulus ofpristine and 25 kGy gamma-dose-irradiated phlogopite mica at various tempera-tures. The solid lines are the theoretical fitted curves.

-2 -1 0 1 2 3 4 5 60.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1Pristine

M''/

M'' m

ax

773 K753 K733 K713 K

M'/M

' max

log (ω /ωm

)

593 K613 K633 K653 K673 K693 K

793 K813 K

-3 -2 -1 0 1 2 3 4 5 60.0

0.2

0.4

0.6

0.8

1.0

-3 -2 -1 0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

log (ω /ωm)

M'/M

' max

Irradiated

M''/

M'' m

ax

773 K

733 K753 K

713 K

593 K613 K633 K653 K673 K693 K

793 K813 K

Fig. 8. Normalized behavior of M0 and M00 of pristine and 25 kGy gamma-dose-irradiated phlogopite mica at various temperatures.

236 N. Kaur et al. / Nuclear Instruments and Methods in Physics Research B 316 (2013) 232–238

corresponding dispersion regions of M0, which indicates maximalconduction losses. The variation of M00 with temperature can be ex-plained on the basis that as the temperature increases, the chargecarriers become thermally activated, i.e., the movement of thecharge carriers becomes faster, which decreases the relaxationtime and increases the relaxation frequency. Thus, there is a shiftin the position of the peak maximum M00

max toward the higher-frequency side as the temperature increases [11]. The influenceof the gamma radiation is clearly indicated in the graph. Fig. 6demonstrates that irradiation leads to greater scatter in the M00

curves and causes the M00 peaks of the irradiated sample to shifttoward higher frequencies compared to the pristine sample.

The frequency-dependent spectra of M00 exhibit two distinct fre-quency regions below and above M00

max. The frequency region belowM00

max corresponds to long-range motion of the charge carriers, andthe frequency region above M00

max corresponds to short-range orlocalized motion of the charge carriers (the carriers are constrainedin a particular well). The characteristic frequency xm is indicativeof the transition from long-range to short-range mobility of chargecarriers. The characteristic frequency xm that corresponds to M00

max

yields the most probable relaxation time sm via the conditionxmsm = 1. The most probable relaxation time according to theArrhenius law is given by:

xm ¼ x0e �Ea=kBT½ � ð4Þ

where x0 is a pre-exponential factor, Ea is the activation energy forthe relaxation process and kB is the Boltzmann constant. Fig. 7shows the plot of logxm versus the inverse of the absolute temper-ature (103/T) for pristine and 25 kGy gamma-irradiated phlogopitemica. From the numerical fitting analysis, the values of the activa-tion energy for pristine and 25 kGy gamma-irradiated phlogopitewere found to be 0.68 eV and 1.24 eV, respectively. The value ofthe activation energy for the 25 kGy gamma-irradiated sample isgreater than that for the pristine sample, which indicates that thegamma-irradiated sample requires more energy to initiate electricconduction.

To achieve a deeper understanding of the relaxation mechanismthroughout the entire frequency and temperature range, (theelectric-modulus spectra were normalized). Fig. 8 shows the scaledspectra for the real (M0) and imaginary (M00) parts of the electricmodulus at various temperatures for pristine and 25 kGy

1.2 1.3 1.4 1.5 1.6 1.70.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

4.4

Pristine

Irradiated

Log

ωm

103/T (K-1)

Fig. 7. Temperature dependence of the most probable relaxation frequencyobtained from the frequency-dependent M00 of pristine and 25 kGy gamma-dose-irradiated phlogopite mica. The symbols represent the experimental data, and thesolid lines are the least-squares fits.

gamma-irradiated phlogopite mica, where the frequency axis isscaled by the characteristic frequency xm, the M0 axis is scaledby M0

max, and M00 is scaled by M00max. Fig. 8 clearly illustrates the near

perfect overlapping of the all the modulus curves into a commonmaster curve. This overlap may be attributed to the distributionof relaxation times in the conduction process. These resultsconfirm that the relaxation mechanism exhibits temperature-independent dynamical processes.

The Cole–Cole graph for the electric modulus of pristine and25 kGy gamma-irradiated phlogopite mica at various temperatures(593–813 K) is shown in Fig. 9. The solid lines in the figurerepresent the fits (using the Havriliak–Negami function) to thedata, and the symbols represent the experimental electric-modu-lus data. As the temperature increases, the curves become morecomplete. This behavior is indicative of a temperature-dependentelectrical conduction mechanism. As the temperature increases,the mobility of the charge carriers increases, which enhances theconductivity. The depressed semicircles imply a certain deviationfrom the ideal Debye behavior.

To investigate the microscopic movement of the charge carriersand the conduction behavior of the material, the frequency-depen-dent electrical conductivity at various temperatures (593–813 K)was studied. The frequency dependence of the electrical conductiv-ity for the pristine and 25 kGy gamma-irradiated samples is shownin Fig. 10. In Fig. 10, the conductivity exhibits a universalcharacteristic, i.e., in low the frequency-region, it exhibits nearly

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Pristine

593K613K633K653K673K693K713K733K753K773K793K813K

M''

M'

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0Irradiated 593K

613K633K653K673K693K713K733K753K773K793K813K M

''

M'

Fig. 9. Cole–Cole plots of the electric modulus of pristine and 25 kGy gamma-dose-irradiated phlogopite mica at various temperatures. The symbols represent theexperimental data points, and the solid lines are the fits to the data.

0 1 2 3 4 5 6 7

-12.5

-12.0

-11.5

-11.0

-10.5

-10.0

-9.5

-9.0

-8.5Pristine

593 K613 K633 K653 K673 K693 K713 K733 K 753 K773 K793 K 813 K

logσ

ac(Ω

m)-1

log ω (rads-1)

0 1 2 3 4 5 6 7-12.5

-12.0

-11.5

-11.0

-10.5

-10.0

-9.5

-9.0

-8.5

-8.0

-7.5Irradiated

593 K613 K633 K653 K673 K693 K713 K733 K 753 K773 K793 K 813 K

logσ

ac(Ω

m)-1

log ω (rads-1)

Fig. 10. Frequency dependence of the AC conductivity of pristine and 25 kGygamma-dose-irradiated phlogopite mica at various temperatures. The solid linesare the theoretical fits.

Table 1The values of DC conductivity of pristine and 25 kGy gamma dose irradiatedphlogopite mica.

Temp. (K) rdc [S/cm] pristine rdc [S/cm] irradiated

593 4.02 10�13 7.441 10�13

613 6.22 10�13 1.916 10�12

633 9.212 10�13 4.75 10�12

653 1.269 10�12 9.865 10�12

673 1.784 10�12 1.93 10�11

693 2.503 10�12 3.47 10�11

713 3.337 10�12 6.79 10�11

733 4.262 10�12 1.124 10�10

753 5.431 10�12 1.693 10�10

773 6.552 10�12 4.585 10�10

793 7.569 10�12 6.178 10�10

813 8.901 10�12 6.364 10�10

N. Kaur et al. / Nuclear Instruments and Methods in Physics Research B 316 (2013) 232–238 237

invariant behavior, which corresponds to DC conductivity (rdc)[12]. As the temperature increases, the DC conductivity increases.A transition from DC to dispersive behavior occurs at highfrequency. It can also be seen from Fig. 10 that the high-frequencydispersion region of the conductivity begins to decrease or shifttoward the higher-frequency side as the temperature increase. Thisfeature signifies the presence of a thermally activated processcaused by the increase in the charge-carrier energy.

The AC conductivity spectra exhibit the universal Jonscher’slaw:

rac ¼ rdc þ Axs ð5Þ

where rdc represents the temperature-dependent DC conductivityand is linked to the drift mobility of the charge carriers. A (atemperature-dependent parameter) gives the intensity of thepolarizability, and s is the power-law exponent, whose value liesbetween 0 and 1. The second term in the right-hand side of theabove equation incorporates AC dependence and describe the entiredispersion process.

The experimental conductivity spectra for the pristine and25 kGy gamma-irradiated-phlogopite mica were fitted with theHavriliak–Negami function, and the fits are also presented inFig. 10. The DC conductivity values (rdc) of pristine andgamma-irradiated phlogopite mica at various temperatures were

calculated and are given in Table 1. The DC conductivity (rdc) tendsto increase with increasing temperature because as the tempera-ture increases, the number of charge carriers that have sufficientenergy to overcome the potential barriers related to the conduc-tion mechanism increases [13].

Fig. 11 shows the plot of logrdc vs. 103/T for pristine and 25 kGygamma-irradiated phlogopite mica. The behavior of rdc follows theArrhenius law, which can be written as:

1.2 1.3 1.4 1.5 1.6 1.7

-12.4

-12.0

-11.6

-11.2

-10.8

-10.4

-10.0

-9.6

-9.2

-8.8

Log

σdc

103/T (K-1)

Irradiated

Pristine

Fig. 11. Temperature dependence of the DC conductivity of pristine and 25 kGygamma-dose-irradiated phlogopite mica. The symbols represent the experimentaldata, and the solid lines are the least-squares fits.

238 N. Kaur et al. / Nuclear Instruments and Methods in Physics Research B 316 (2013) 232–238

rdc ¼ r0e �Er=kBT½ � ð6Þ

where r0 is a pre-exponential factor, and Er is the activation energyof the conduction process. The values of the activation energy (Er)calculated from the least-squares fits of Fig. 11 were found to be0.59 eV and 1.31 eV for pristine and gamma-irradiated phlogopite,respectively, which are nearly the same as the values that werecalculated from the electric-modulus data. This quantitative agree-ment indicates that the charge carriers that are responsible for theconduction mechanism are the same charge carriers that participatein the relaxation process in phlogopite mica.

4. Conclusions

The present work reports the results of our investigation of thedielectric relaxation mechanism of pristine and gamma-irradiatedphlogopite mica using the dielectric and conductivity relaxationspectroscopy techniques over a wide range of frequency (0.1 Hz–10 MHz) and temperature (593–813 K). The frequency-dependentmaxima in the imaginary part of the electric modulus and the DCconductivity were found to obey the Arrhenius law. The values of

the activation energy for pristine and irradiated phlogopite micathat were obtained from the electric-modulus data and the con-ductivity data are very similar to each other, suggesting that therelaxation and conductivity processes may be attributed to thesame type of charge carriers. Spectral curve fitting of the electric-modulus and conductivity data was performed using a Havriliak–Negami relaxation function and the derived values of the DCconductivity proved to be well suited to explaining the conductionmechanism in the material. The scaling of the electric-modulusspectra that were obtained at all temperatures to normalized plotsrevealed a perfect overlap of all curves into a common mastercurve, which indicates that the relaxation mechanism involved inthe dynamical processes is temperature independent. The Cole–Cole plots (using modulus data) exhibit depressed semicircles,which reflect the non-Debye behavior of the material. From allthese results, it can be concluded that gamma irradiation playsan important role in enhancing the dielectric characteristics ofphlogopite mica, and more research efforts should directed towardthe utilization of efficient natural micaceous materials and theirradiation thereof in various branches of science and technology,particularly in electrical engineering.

Acknowledgments

One of the authors (N. Kaur) thankfully acknowledges theUniversity Grants Commission (UGC, India) for providing a SeniorResearch Fellowship (SRF).

References

[1] N. Kaur, L. Singh, M. Singh, S.P. Lochab, Radiat. Phys. Chem. 87 (2013) 26–30.[2] N. Kaur, M. Singh, A. Singh, A.M. Awasthi, L. Singh, Physica B: Condens. Matter.

407 (2012) 4489–4494.[3] L. Singh, N. Kaur, M. Singh, Indian J. Pure Appl. Phys. 50 (2012) 14–18.[4] N. Kaur, L. Singh, M. Singh, S.P. Lochab, Nucl. Instr. Meth. Phys. Res. B 290

(2012) 1–5.[5] M. Singh, N. Kaur, L. Singh, Nucl. Instr. Meth. Phys. Res. B 276 (2012) 19–24.[6] M. Singh, N. Kaur, L. Singh, Radiat. Phys. Chem. 79 (2010) 1180–1188.[7] M. Singh, N. Kaur, L. Singh, Nucl. Instr. Meth. Phys. Res. B 268 (2010) 2617–

2625.[8] E. Suljovrujic, Radiat. Phys. Chem. 79 (2010) 751–757.[9] S. Havriliak, S. Negami, J. Polym. Sci. C 14 (1966) 99–117.

[10] P.B. Macedo, C.T. Moynihan, R. Bose, Phys. Chem. Glasses 13 (1972) 171–179.[11] A. Karmakar, A. Ghosh, J. Appl. Phys. 110 (2011) 034101–034106.[12] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics Press, London,

1983.[13] M.M. Costa, G.F.M. Pires, A.J. Terezo, M.P.F. Graça, A.S.B. Sombra, J. Appl. Phys.

110 (2011) 034107.