·Table of Contents
·Methods and Instrumentation
Calculation of Protective Shields Made of Lead Glass for X-Rays N.D.T. Industrial EquipmentJ. Reyes-Romero ,
Universidad Central de Venezuela, Facultad de Ingenieria, Departamento de Física Aplicada, Los Chaguaramos, Caracas 1041, Venezuela.
Email : email@example.com.
Universitatea din Bucuresti., Facultatea de Fizica, Platforma Magurele, Bucuresti, Romania.
Universidad Experimental Politecnica " Luis Caballero Mejias", Departamento de Ciencias Basicas, La Yaguara, Caracas, Venezuela.
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 ,
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 ,
For the calculation we selected the type of empirical spectrum ,
in which a = 2,5.1015 for n < n0 y a = 0 for n > n0 , for v measured in Hz and Ct is a constant. Substituting in (9) and doing obtained,
in which the spectrum is taken by Emin < 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, [Emin,E0] , is given by the expression,
in which V0 is measured in KV and Emin 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
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
Px 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
If we measured then [d] = W/Kg. To measured [d] = R/h we multiply the equation (15) by 4, 1.105,
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 XBe, 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 XST. 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)
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 
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 EK is the binding energy of the electron of the K level of the element with a number of order Z. For lk < l < lL1,
And for lL1 < l < lM1,
Where EL1 and EM1 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 , fitting m/r as a function of the type
In the case where the material is made of K elements, the absorbance coefficient is given by
being , the number of atoms of the lot "i" of the molecule, Ai the atomic mass of the element and M the molecular mass. The lead glass (st), having in its composition SiO2, 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 SiO2 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.
|Energía x [KeV]||59||80||122|
|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 Xst.
The dose "d " calculated then has a value, according to the equations (12)...(17).
The dose D found experimentally is
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 ef is the probability that the quantum g would be register in the photopeak. The values of fab and ef where calculated according to the procedure indicated in. 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
where is the coefficient of mass absorbance of the glass, , Xst is the thickness of the lead glass, is the coefficient of mass absorbance of the window, Xf is the thickness of the window of the source, is the absorbance coefficient of the air masses , Xaire is the thickness between the source and the place where the dose is measured.
|V(KeV)||I(mA)||Dose calculate (R/min)|
|TABLE 2 :|
|V (KeV)||I (mA)||r(m)||d(cm)|
|TABLE 3 :|
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