Dielectric Behavior Of β- Lead Fluoride

Dielectric Behavior Of – Lead Fluoride

Y. Ranga Reddy

Vidya Bharathi Institute of Technology, Pembarthy, Warangal Dist. A.P. India

Abstract– A detailed study of effect of temperature and frequency on dielectric constant ( ) and loss (tan ) of -PbF2 was performed. The measurements were taken from the frequency range of 102Hz to 5x107Hz and in the temperature range of -1800C to 2400C. The value of static dielectric constant at room temperature is 28.00. The value of ac conductivity is calculated from the relation, 0 tan where

Schoonman et al [9] reported the ionic and electronic conductivity in very limited temperature region (325K- 410K). The measurement of dielectric constant ( ) and loss (tan ) of -PbF2 in a wide

range of frequency and at higher temperatures is not reported so far.

In the present investigation, dielectric properties of

– PbF2 have been measured in the temperature

0 is the permittivity of the free space and is the

angular frequency. The activation energy for conduction in the intrinsic region of the plot versus

reciprocal of temperature is calculated to be 0.92 eV.

Keywords- Dielectric constant, dielectric loss, electrical conductivity, activation energy.

1. INTRODUCTION

   Lead fluoride can found either is cubic structure with four molecules per unit cell ( -PbF2) or in orthorhombic phase ( PbF2) at high temperatures [1]. Cubic phase becomes a super ionic conductor at high temperatures .The conductivity of – PbF2 is

   one of the highest values for any known solid ionic conductors [2]. As it exhibits a variety of interesting physical properties like radiation resistance [3], high ionic conductivity at a relatively low temperature, associated specific heat anomaly, behaving as an extrinsic semiconductor [4] attracted considerable recent attention.

   Denham et al [5] has derived the dielectric properties of lead fluoride from experimental studies on infra- red and Raman spectra. Direct measurement of dielectric properties has been reported by Axe et al [6]. Samara [7] studied the effect of temperature and pressure on dielectric properties of cubic and orthorhombic modifications of lead fluoride over the range of 4K to 350K. Complex admittance study on

   -PbF2 was done by Bonn and Schoonman [8].

   range of -1800C to 2400C and in the frequency range of 102Hz to 5x107Hz.

2. EXPERIMENTAL

   A pure colorless single crystal of -PbF2, supplied by M/S Optovac Inc., was used for the present investigation. A plate of 5mm diameter and 2mm thick was cut from the crystal with a diamond cutter. Silver paint was applied on either side of the sample, after grinding and polishing with carborundum powder and emery paper, to ensure good contact and to remove air gaps between the sample and electrodes. The sample was dried before taking the measurements.

   Measurements of dielectric constant ( ) and loss (tan ) were made with GR 716C capacitance bridge in the frequency range 102Hz to 5x105Hz and with Marconi circuit Magnification Meter TF 329G in conjunction with laboratory built sample holder in the range of the frequency 105Hz to107Hz .Temperature measurements were carried out in the range of -1800C to 2400C. The fallowing procedure was used for the low temperature measurements:

   The sample holder with sample was inserted in to liquid nitrogen bath and allowed to remain until a steady temperature was reached, which was checked by constant reading of the millivolt meter. For taking

   measurements at different temperatures the sample holder was slowly lifted out of the bath allowing the

   Table.1.Values of and tan of – PbF2 at room temperature and at a frequency of 106.Hz

   temperature to rise steadily. Readings were recorded

   at intervals of 10K.

   The temperature measurement was accurate to +10C. ( ) and (tan ) are measured with accuracies of 3%

   and 5% respectively.

3. RESULTS AND DISCUSSION

The variation of dielectric constant ( ) with frequency for -PbF2 is shown in Fig.1.

tan source

29.30 – Samara [7]

27.40(cal.) – Axe at al [6]

26.30 – Axe at al [6]

28.00 10-3 present work

The variation of dielectric loss (tan ) with frequency at room temperature is measured for the first time and is shown in Fig.2.

Fig.1.Variation of dielectric constant with frequency

The value of is at 102 Hz is 125. A fast decrease in

the dielectric constant is observed up to a frequency of 105 Hz beyond which it is constant. The frequency

tan

101

100

10-1

10-2

10-3

10-4

102 103 104 105 106 107

Frequency

independent value is 28.00 and is taken as static dielectric constant. The value of static dielectric constant of the present work and the earlier reported values are shown in Table 1.

The value of dielectric constant of -lead fluoride is nearly four times the value for other fluorite structures. For alkaline earth fluorides [10-12] and EuF2 [13], the values of dielectric constant range

from 6.00 to8.00.The high value in -PbF2 is

2

2

0

0

attributed by samara [7] as being due to several causes like i) a large value of electronic enhancement factor, [( 0 2) / 3] where is the optical dielectric constant, ii) abnormally small value of resonance frequency and iii) large value of polarizability of lead.

Fig.2.variation of tan with frequency

The value of tan is very high at 102 Hz and decreases to a value of 10-4 at 107 Hz.

The dielectric constant at low frequencies depends on electronic, ionic, dipolar orientation and space charge polarization. Contributions due to electronic and ionic polarization are frequency- independent where

are dipolar orientation and space-charge contributions are frequency dependent. Fig.1 & 2 shows that and tan are frequency dependent in the low frequency

region. This behavior can be attributed to the presence of space charge polarization due to unknown impurities and other imperfections, which would be negligible at higher frequencies [14]. The low loss value of tan of the order of 10-4 indicated high grade purity of the sample used for the present investigation.

The variation of with temperature from300C to 2400C at various frequencies is shown Figure 3.

The dielectric constant slowly increases from 300C to certain temperature and the variation above that temperature is rapid. This behavior is similar to the

Fig.3. variation of with temperature

variation of other crystals of fluorite structure [15, 13]. The temperature variation of the dielectric constant is frequency dependent. The value of dielectric constant is high at low frequencies for the same temperature. At 106Hz, the increase in dielectric constant is linear from 300C to 1400C and above 1400C the rise in is rapid. The dependence of the high temperature dielectric constant on frequency may be attributed to the creation and destruction of the dipoles at such temperatures [10].

The variation of with temperature from -1800C to 300C is shown in Figure 4.

There is a departure from the usual trend in the low temperature region. A slow decrease of dielectric constant was observed from-1800C to room temperature. Lead fluoride behaves as an

extrinsic semiconductor [16] in the low temperature region; predominantly it contains n-type electronic conductivity. The electronic conductivity behavior of

lead fluoride would show a gradua change from

n-type to p-type conductivity; whereas the magnitude of the electronic component of the electrical conductivity would decrease with increasing

temperature [17], may be attributed for this behavior of in the low temperatures.

Fig.4. variation of with temperature from -1800C to 300C

An attempt was made to fit the experimental values of the static dielectric constant with temperature at a frequency of 106 Hz to an empirical equation .Several forms of equations were tried but it was found that no single equation can represent the data over the entire region of temperature satisfactorily. However the data in different temperature ranges could be represented by the fallowing equations:

i) =28.08-1.05×10-3t .(1)

in the temperature region -1800C to 300C ii) = 26.93+ 3.16 x 10-2 t (2)

in the temperature region -1800C to 300C.

iii) = 66.22 54.41 x 10-2 t + 2.139 x 10-3 t2

(3)

In the temperature region 1470C to 2400C In all the above equations t is the temperature in 0C.

The variation of tan with temperature at different frequencies is shown in the Figure.5.

The values of tan are higher at low frequencies and high temperatures. This behavior is due to defects arising out of thermally generated charge carriers.

Fig.5. variation of tan with temperature at various frequencies

At 104 Hz, tan increases with temperature up to 950C and then decreases slightly, showing a Debye- type relaxation peak at 950C. Similar peaks are observed at 1200C and 2200C for frequencies 105 Hz and 106 Hz respectively. The peaks shift towards higher temperature for higher frequencies. Such peaks have been observed by Agrawal [18] in the same range of temperature and frequencies in the case of CaF2 when doped with either Mn or Na as impurity. Presence of such impurities which is not uncommon might be responsible for the occurrence of relaxation peaks. In the present work the peaks may be due to dipoles formed by unidentified impurities.

The activation energy for the rotation of the dipoles in the crystal have been calculated using the fallowing relation

f = f0e-E/KT . (4)

where f is the frequency of the relaxation peak at a temperature T. f0 is constant, K is the Boltzmann constant and E is the activation energy. The input data for the calculation of activation energy for the rotation of the dipoles is given in table 2.

Table.2: Temperature at which the relaxation peaks are observed for -Lead fluoride.

The calculated value of activation energy for the rotation of dipoles is 0.06eV.

The experimental data on variation of and tan with temperature have been used to obtain the values of dielectric conductivity by the equation

= 0 tan (5)

where 0 is the vacuum dielectric constant and is the angular frequency. The plot of against reciprocal temperature at various frequencies is shown in figure 6.

Fig.6. Plot of log against (103/T) K -1

At higher temperature the variation is linear and frequency independent. The variation of conductivity with temperature is given by the equation

=A e E/KT ..(6)

where E is the activation energy. The activation energy has two different values Ee and Ei at moderate temperatures (extrinsic region) and at high temperatures (intrinsic region), respectively. These values can be calculated from the slope of the curves at their respective regions.

Further Ee = Wm . (7)

And Ei = Wm + Wf/2 (8)

where Wm and Wf are the energy of mobility of defects and formation energy of defects, respectively. The calculated values of energies are listed in Table.3.

Table 3: Values of Wm , Ei, and Wf of -Lead fluoride Crystal Wm (eV) Ei (eV) Wf (eV)

-PbF2 0.32 0.78 0.92

It is not possible, in this temperature region, to understand the nature of the charge carriers responsible for conduction from the present measurements.

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