DETERMINATION OF DIELECTRIC CONSTANT VARIATION DUE TO THE EXPOSURE TO GAMMA-RAY L.C. TUGULAN Horia Hulubei National Institute for Nuclear Physics and Engineering, P.O. Box MG-6, RO-077125 Bucharest-Magurele, Romania E-mails:
[email protected] Received June 23, 2017
Abstract. In this paper, the variation of the dielectric constant (relative electrical permittivity) as a result of the exposure to gamma-ray was studied. The material used in this study was BK-7 type glass. Several samples were exposed to gamma-ray in order to obtain different absorbed dose values. Different dielectric constant values, as a function of the absorbed dose, were determined, by using photo-spectrometric techniques. The results showed that the dependence of the dielectric constant to the absorbed dose presents linear regions, which make the dielectric constant a quantity that can be used in gamma-ray dosimetry. Key words: dielectric constant, gamma-ray, absorbed dose.
1. INTRODUCTION
Light is an electromagnetic wave, propagating with a speed of 3 108 m s-1. In the UV-VIS-IR wavelengths region, the electromagnetic radiation is produced by atomic and molecular transitions, leading to different specific frequency values. It is supposed that this kind of light source is represented by a concentration of constituents which emit waves (quanta) having random initial phases. This incoherent and unpolarized type of oscillation of the electromagnetic field represents the natural light. The mathematical representation of a monochromatic light wave [1–3] can be expressed either by electric field or magnetic field:
A( x, t ) A0 exp i(k x t ) , where: A: E( x ,t ) – electric field in V m-1; H ( x ,t ) – magnetic field in A m-1; A0: (E0; H0) – peak value; x – position vector in Cartesian coordinates; Romanian Journal of Physics 63, 202 (2018)
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k – the wave vector in x direction in m-1 k ; ω – the period of oscillation in radians (ω = 2 × π × ν); t – time in s-1; φ – starting phase angle in radians. The direct measurable quantity from the equation (1) is the optical intensity, which can be related to the electric field by a proportional factor, I ~ E2. The main optical phenomena producing when light reaches a material are transmission, reflection and absorption [4]. By measuring these three parameters using photo-spectrometric techniques, a quantification of other important optical parameters can be obtained [5]. It was demonstrated that the propagation speed and the other characteristics of the electric field carried by an electromagnetic field depend to the properties of the passing thru materials [6–9]. In this paper, the variation of the dielectric constant as a result of the exposure to gamma-ray was studied, starting from high quality photo-spectrometric measurements [10–16]. The material used in this study was BK-7 type glass, several samples being exposed to gamma-ray in order to obtain different absorbed dose values. Different dielectric constant values, as a function of the absorbed dose, were determined. The results showed that the dependence of the dielectric constant to the absorbed dose presents linear regions, which make the dielectric constant a quantity that can be used in gamma-ray dosimetry [17, 18].
2. THE EXPERIMENT
Several BK-7 type glass samples (10 mm thickness) were exposed to a Co60 gamma-ray source (1.25 MeV), inside an irradiation chamber, in order to obtain different absorbed dose values (Table 1). The dose debit was constant, 6.2 kGy/h. The obtained doses values were placed between 0.04 kGy and 21 kGy. For the measurements of absorbed doses, an ECB dosimeter system with an average measurement uncertainty of 2.5 % (k = 2) was used. Using three monochromatic sources of light (475 nm, 490 nm and 530 nm) [19], high quality photo-spectrometric measurements were performed. Table 1 Absorbed doses values and their associated uncertainties D (kGy) σD (kGy) (k = 2)
0.04 0.001
0.08 0.002
Absorbed dose values 0.17 0.33 0.66 0.003 0.006 0.01
1.3 0.1
2.7 0.1
5.3 0.1
10.6 0.2
21.0 0.4
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3. RESULTS AND DISCUSSIONS
The variation of transmitted light intensity thru the irradiated glass samples as a function of the absorbed dose is shown in Fig. 1a, and the one of the reflected light intensity is shown in Fig. 1b.
Fig. 1a – Transmitted light intensity vs. absorbed dose.
Fig. 1b – Reflected light intensity vs. absorbed dose.
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The dielectric constant [20–22] is a fundamental intrinsic property of a material, and consists of both real and imaginary parts, as follows (2): 1 i 2 , (2) where: ε1 – real dielectric constant; ε2 – imaginary dielectric constant. The real part indicates how the speed of light can be slowed down in a material, following Equation (3):
1 n2 k 2 , where:
I 1 r . I0 – n – refractive index ( n I 1 r . I0
– k – extinction coefficient ( k
0.5
0.5
);
I ln 0 ); 4 x I tr .
– λ – wavelength; – Itr. – transmitted light intensity; – I0 – initial intensity; – Ir. – reflected light intensity; – x – sample thickness (10 mm); – ε1 – real part of dielectric constant.
Fig. 2 – The real dielectric constant of BK-7 glass vs. absorbed dose.
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The real part of the dielectric constant characterizes a dielectric from the point of view of its polarizing capability. It represents elastic electric permittivity and shows the variation of electric capacity of a material. The variation of real dielectric constant of the irradiated samples as a function of the absorbed dose is shown in Fig. 2. As it can be seen from Fig. 2, the real part of the dielectric constant decreases linearly with the increase of the absorbed dose, and, therefore, it can be used as an estimator for absorbed dose value. The liner region of the dependence between the real dielectric constant and the absorbed dose is placed between 0.17 kGy and 21 kGy for 475 nm wavelength, between 0 kGy and 2.7 kGy for 490 nm wavelength, respectively between 0.33 kGy and 2.7 kGy for 530 nm wavelength. The real dielectric constant showed a decreased polarizing capability of the irradiated glass, as the absorbed dose increased (Fig. 2). The imaginary part of the dielectric constant deals with the absorption of the energy by a dielectric from electric field due to dipole motion. The imaginary dielectric constant is expressed in Equation (4):
2 2 n k where: – ε2 represents the imaginary part of dielectric constant.
Fig. 3 – The imaginary dielectric constant of BK-7 glass vs. absorbed dose.
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The imaginary part of the dielectric constant characterizes a dielectric from the point of view of the energy deposition in its volume. It represents inelastic electric permittivity and shows the thermal effect occurred into the material, due to slow polarization mechanisms. The variation of imaginary dielectric constant of the irradiated samples as a function of the absorbed dose is shown in Fig. 3. As it can be seen from Fig. 3, the imaginary part of the dielectric constant increases linearly with the increase of the absorbed dose, and, therefore, it can also be used as an estimator for absorbed dose value. The liner region of the dependence between the imaginary dielectric constant and the absorbed dose is placed between 0.33 kGy and 21 kGy, for all three wavelengths used. The increase of the imaginary dielectric constant as a function of increasing of the absorbed dose value indicates an increased energy loss in the irradiated samples. As it was shown, the real and the imaginary parts of the dielectric constant showed a linear dependence with the increase of the absorbed dose, on certain dose intervals, making them suitable to be used as parameters in gamma-ray dosimetry. The analytical expression of the variation of dielectric constant as a function of the absorbed dose has the following form (5):
1,2 i
(a 1,2 )i (b 1,2 )i log( Dd ) ,
(5)
where: ε1,2 – real and imaginary dielectric constants; Dd – absorbed dose; aɛ1,2; bɛ1,2 – fitting parameters. By applying the uncertainties propagation law (6) [23–26] to Equation (5), the uncertainty associated to the method can be determined (7):
2 1, 2
2
( x) i (a ) i 1, 2
( x) i 2 ( a1, 2 )i (b ) i 1, 2
2 (2a
log( Di ) d (2b
1, 2
2
( x) i 2 ( b1, 2 ) Di
2
) 1, 2 i
1, 2
)
(b1, 2 ) i 2.3 Di d
2
D2 i
D2 i
d
.
d
(6)
(7)
All the quantities from Equation (7) are known, Table 2. By fitting the dielectric constant as a function of the absorbed dose value, the calibration curves were obtained, as it can be seen in Table 3. By using them, an unknown absorbed dose value can be determined.
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Table 2 The fitting parameters and their associated uncertainties Dielectric constant
The absorbed dose range [kGy]
Real dielectric constant Imaginary dielectric constant
Fitting parameters
a
b
σa
σb
0.17 – 21 0 – 2.7 0.33 – 2.7
ε1 (475 nm) ε1 (490 nm) ε1 (530 nm) 2 107 (475 nm)
2.23 2.17 2.25 93
0.04 0.08 0.07 140
0.003 0.005 0.005 5.4
0.005 0.007 0.016 7.4
0.33 – 21
2 107 (490 nm)
82
140
8.1
11
2 10 (530 nm)
75
110
4.4
5.9
7
Table 3 Dielectric constant linear variation curves Wavelength
Real dielectric constant – ε1
Imaginary dielectric constant – ε2
475 nm
2 9.25 106 14 106 log( D)
490 nm
1 2.23 0.04 log( D) 1 2.17 0.08 log( D)
530 nm
1 2.25 0.07 log( D)
2 8.2 106 14 106 log( D) 2 7.5 106 11106 log( D)
4. CONCLUSIONS
As it was shown in this paper, the exposure of optical glass to gamma-ray leads to modifications of its parameters, such is its dielectric constant. The real and the imaginary parts of the dielectric constant were determined for several BK-7 glasses exposed to gamma-ray, by using photo-spectrometric measurements. From the point of view of the dielectric constant of oxidic glasses, it was experimentally demonstrated that their exposure to gamma-rays leads to their decreased polarizing capacity and to an increased energy loss in their volume, highlighted by the decreased real part of the dielectric constant, respectively by its increased imaginary part. As it was shown, the dielectric constant can be used as a dosimetric parameter, since its dependence to the increase of the absorbed dose is linear, for both its real and imaginary parts, on certain intervals. The analytical expression of the variation of dielectric constant as a function of the absorbed dose was obtained. The expressions obtained for the real and imaginary parts of the dielectric constant are practically calibration curves. By using them, an unknown absorbed dose value can be determined. Using the uncertainties propagation law, the uncertainty associated to the method was determined.
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