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Calculation of Protective Shields Made of Lead Glass for X-Rays N.D.T. Industrial Equipment J. Reyes-Romero , Universidad Central de Venezuela, Facultad de Ingenieria, Departamento de Física Aplicada, Los Chaguaramos, Caracas 1041, Venezuela. Email : reyesj@camelot.rect.ucv.ve. A-M Ghiordanescu, Universitatea din Bucuresti., Facultatea de Fizica, Platforma Magurele, Bucuresti, Romania. B. Hurtado, Universidad Experimental Politecnica " Luis Caballero Mejias", Departamento de Ciencias Basicas, La Yaguara, Caracas, Venezuela. Contact

ABSTRACT

This paper presents the calculation of the radiation dose in an X-Ray N.D.T Industrial Equipment on Shields of Lead Glass, with known composition and thickness. Using a suitable algorithm a program of calculus was written in Basic and can be used in any personal computer. The experimental verification of this calculation was done through an equipment of detection with a detector of Na I (TI) and a window of Be for the x-radiation. The Protective Shields was made of lead glass with thickness of millimeters for dose rate lower than 0,75 mR/h necessary for the personnel's suitable protection for personnel working in N.D.T. Industrial Radiography.

INTRODUCTION.

The personnel working in N.D.T. Industrial radiography can be subjected to irradiation by x- ray or gamma-quanta. The ionization produced in living tissues by the radiations evoke a biological effect in the human organism. The degree of irradiation of any material can be characterized by the absorbed radiation dose D ( or briefly, radiation dose or simply dose). This is defined as the energy of the radiation absorbed by a kilogram of the material. The unit of the radiation dose is the rad. It equals a radiation dose such that 1 Kg absorbs an energy of 0.01 J. In the SI system the unit of radiation dose is the gray: 1 Gr=100 rads. The radiation dose referred to a unit time is called the dose rate. The biological effect of radiation on organisms also depends on the dose rate. The exposure dose from a x-rays or gamma rays source can be reduced to the maximum permissible dose by various ways: by increasing the distance between the source and working site, by protective shields, by reducing the working time , etc, [1,2].

CALCULATION OF THE RADIATION DOSE.

In an x-ray installation with electric current I, and a potential difference DV₀ in the anode a potential P_X is obtained for the radiation given by,

(1)


R being the efficiency of the braking given by the expression [3],

(2)


W is the energy of the accelerated electrons in the x-ray tube,

(3)


and Wc is the critical energy; the energy of the electrons for which in an anode with a given Z, the lost of the braking radiation is equal to the lost of radiation by ionization. If Wc is measured in MeV then it has a value of about [3],

(4)

In the other hand, the spectrum of x-radiation emitted is considered continuous and therefore the maximum frequency or the minimum wavelength of the radiation emitted is given by the following equations [6],

(5)

(6)

The passage of a type of spectrum in function with the frequency of a spectrum in function with the wavelength is given thought the equation [7],

(7)

(8)

For the calculation we selected the type of empirical spectrum [2],

(9)

in which a = 2,5.10¹⁵ for n < n₀ y a = 0 for n > n₀ , for v measured in Hz and C_t is a constant. Substituting in (9) and doing obtained,

(10)

in which the spectrum is taken by E_min < E < E₀ ; the energies are measured in KeV and therefore the value of E₀ in KeV is equal to the value of V₀ in KV. The area below the curve (10) in the interval, [E_min,E₀] , is given by the expression,

(11)

in which V₀ is measured in KV and E_min in KeV.

The expression for the absorbed dose rate "d" to the distance r from the focus for the installation of x-rays, supposing valid the spectrum (10) and also taking into consideration that there is no absorbent in the trajectory of the radiation, we obtain by the definition of the absorbed dose D, as the energy transferred by the radiation, in mass units, the irradiated substance

(12)

being J the total energy of radiation per time unit and per area unit, m(E) the absorbance coefficient of the x-radiation when E is the energy of the quanta and r the density of the absorbent substance. Taking into consideration the focus of a punctual source that emits uniformly in all directions, for the quanta that have the energy included between E and E+dE , we have the energy where

(13)

(14)

P_x is the x-radiation potential given by the equation (1), is the spectrum given by the equation (10) and A is the area below the curve given by the equation (11) . Substituting (13) and (14) in (12) we obtain

(15)

If we measured then [d] = W/Kg. To measured [d] = R/h we multiply the equation (15) by 4, 1.10⁵,

(16)

Taking into consideration the trajectory of the x-radiation, present as absorbents. A film of air or oil that cools down the anode of a thickness , a window of Be of the x-ray tube of a thickness X_Be, the air between the Be window and the point located at a distance r from the focus to the point where we calculate the dose supposed to have a determined thickness(r is the radius of the tube) Xair,, a glass window with lead Pb of a thickness X_ST. In this case, the expression below the integral is multiplied by S₂S₃S₄S₅ which represent the probabilities that the x-radiation would not be absorbed, respectively by the Berilium window , the film of water (oil), the layer of air , the lead window. This is presented under the form of

Under these circumstances we have the following expression for the dose rate "d" in (R/h)

(17)

For the calculation of the absorbance coefficients that are part of the equation 17, we will use for an element with Z < 50 the empirical expression proposed in [4]

(18)

(19)

Where Z is the number of the order of the element, A the mass number, l the wavelength in is measured in . The equation (18) is valid for the wavelength where E_K is the binding energy of the electron of the K level of the element with a number of order Z. For l_k < l < l_L1,

(20)

And for l_L1 < l < l_M1,

(21)

Where E_L1 and E_M1 are the binding energies in the levels L₁ and M₁ respectively. For the light elements that are part of the composition of the window, the equations (18)-(21) are not enough for energies greater than 40 KeV. Therefore using the values for the absorbance coefficients given in [6], fitting m/r as a function of the type

(22)

Being

(23)

In the case where the material is made of K elements, the absorbance coefficient is given by

(24)

being , the number of atoms of the lot "i" of the molecule, A_i the atomic mass of the element and M the molecular mass. The lead glass (st), having in its composition S_iO₂, PbO, Na₂O, K₂O,CeO₂ and with concentrations C₁, C₂, C₃, C₄, C₅, respectively, the absorbance coefficient was calculated using the following expression.

The calculus program was written in Basic, and can be used in any personal computer. The entry data asked by the program are, zetac= z of the anode, ima= current in mA, ukv= voltage in KV, radio= distance for which we calculate the dose in meters, eneri= minimum energy of the x-radiation in KeV, denerg= integration step, fagua= the thickness of the layer of water on the anode in cm, fBe= thickness of the Be window in cm, abpb= thickness of the window of lead glass in cm, C1= concentration of the S_iO₂ e in %,..., C5= concentration of CeO₂ in %, rost= density of the lead glass in . Then we calculate the rand= efficiency of the installation of x-rays, pot x= the potential x and the area below the curve , obtained by (11).
The integration is done by the rectangle method. We calculate for each quantum of energy "energ", the height "intger" of a rectangle of width "denerg", Sumat= value of the obtained integral , dosis= dose in R/h calculated according to (17). The program is running introducing the concentration of the elements that constitute the glass, Ci, its density rost and thickness abpb. We determine the value of the thickness of the glass at a distance "radio", demanded by the norms; an allowed dose of 0.75 m R/h.

EXPERIMENTAL.

In order to verify the accuracy of the calculation for the coefficient obtained by the equations 18-25 we used glass samples with a density r = 3,56. of several thicknesses in the order of the mm for which we determined the coefficient m for several energies. In the TABLE 1 we present the experimental values and the calculated values of m.

Energía x [KeV]	59	80	122
	2,05±0,03	1,22±0,03	1,46±0,03
	1,98±10%	0,88±10%	1,42±10%
TABLE 1 :

For the experimental verification of the calculation of the dose, was used an installation of detection with a detector of Na I (TI) and a window of Be connected to a personal computer. In front of the detector , we put a source of ⁵⁷Co of a known activity. The source emits an x-radiation of 6.4 Kev and y of 14 KeV, 122 KeV and 136 KeV . We fixed the window in such a manner that the equipment could detect the quanta of 122 KeV and 136 KeV ( average of energy is about 128KeV) . Between the source and the detector we put lead glass absorbents of known thicknesses X_st.
The dose "d " calculated then has a value, according to the equations (12)...(17).

(26)

The dose D found experimentally is

(27)

Where R is the velocity of counting of the installation in pulse/h, "a" is the radius of the detector in m, fab is the probability that the Quantum is not absorbed in the window of the detector and e_f is the probability that the quantum g would be register in the photopeak. The values of fab and e_f where calculated according to the procedure indicated in[3]. In the equation (27) L is measured in counts/s and E is measured in J. If we measure L in mCi and E in KeV, the other measurements keep in the SI units, then

(28)

where is the coefficient of mass absorbance of the glass, , X_st is the thickness of the lead glass, is the coefficient of mass absorbance of the window, X_f is the thickness of the window of the source, is the absorbance coefficient of the air masses , X_aire is the thickness between the source and the place where the dose is measured.

EXPERIMENTAL RESULTS AND CONCLUSIONS

The experimental data used for the dose calculation were the following:
Concentrations in the lead glass of S_iO₂, C1 = 46,25 %; PbO , C2 = 43,38 % ; Na₂O, C3 = 4,38 %; K₂O, C4 = 5,58 %; CeO₂, C5 = 0,31 % ; Z = 74 for tungsten. Thickness of water film is cero cm (0 cm), ), thickness of the Berilium film is 0,01 cm; distances from the focus to the screen were r1 = 0,2 m , r2 = 0,5 m, r3 = 1 m; the electrical current was between 20 mA and 30 mA and the electrical potential, between 25 KV and 160 KV.
We present in the TABLE 2 the values of the dose rate calculate and in the TABLE 3 the thicknessess of lead glass values obtained for a dose rate lower than 0.75 mR/h.

V(KeV)	I(mA)	Dose calculate (R/min)
25	20	4800
50	30	16700
100	30	36600
160	19	40000
TABLE 2 :

V (KeV)	I (mA)	r(m)	d(cm)
50	20	0.20	1.40
50	20	0.50	1.20
50	20	1.00	1.12
100	30	0.20	7.00
100	30	0.50	6.50
100	30	1.00	6.00
160	19	0.20	8.00
160	19	0.50	6.00
160	19	1.00	6.00
TABLE 3 :

Bibliography.

1. Levin, V. E; " Nuclear Physics and Nuclear Reactor", Edit. Mir , Moscou, 1981
2. Ursu, I; " Fizica si Technologia materialelo nucleare", Edt. Academiei, Bucuresti 1982.
3. Dumitru,S; "Dozimetrie si Radioprotectie",ICEFIZ, Bucuresti,1987
4. M.A. Blohin, Fizica Radiatiilor, Atomizdat,1957
5. ** ,"Lucrari Practice de Fizica Nucleara", Univ. de Bucarest, 1987
6. In. J. Appl. Rad. Vol.33,1269,1982.

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