Industrial Application of Hard X-Rays for Radiography and Selection of the Energy Range of These Rays

A. A. Vorob'ev, E. K. Zaradovskaya

By radiographing products with the aid of X-rays, it is possible to observe on a fluorescent screen and photographic plate their internal structure and hidden defects in the material. Such determination of defects in a product and in the material is of great value, since it is not accompanied by destruction or by any other disturbance of the object being tested.

At the present time it is generally accepted that, among all methods of nondestructive testing of materials—electromagnetic methods, acoustic methods, and others—radiography with the aid of X-rays is the most important and the method that yields the greatest amount of information.

At first the development of the technique for obtaining X-rays proceeded very slowly. Until 1913, an ion tube with a cold cathode served for obtaining X-rays. Of great importance was the development in 1913 of an industrial model of an X-ray tube with a heated cathode (Coolidge, Lilienfeld). This tube made it possible to control easily the quantity and quality of the X-radiation emitted by it. In 1920 a mobile X-ray unit was constructed (G.E.). In 1923 a protected X-ray tube was built (Philips). In 1928 a shielded tube was created, which has been preserved in its basic features up to the present time.

As the source of high voltage in X-ray installations up to 1911, an inductor was used. Later it began to be displaced by the transformer with a closed core. In 1938 there appeared installations with cascade generators for 600 kV and higher, a resonant transformer, electrostatic generators with moving belts, and, after 1941, accelerator installations (betatron, synchrotron, linear accelerator, microtron).

In 1937 A. A. Vorob'ev developed the basic circuits of pulsed radiography. At the present time pulsed radiography is being successfully applied to the study of short-duration processes proceeding at high speed. The economic and technical advantages of pulsed radiography make it possible to apply this method to the solution of ordinary problems.

In connection with the broad application of X-rays for flaw detection, the correct choice of the magnitude of their energy is of substantial importance.

At present, one of the principal fields of application of X-rays is the aircraft industry, which uses materials that weakly absorb X-rays (nonferrous metals and alloys, plastics, etc.). In this field, installations with an operating voltage of 100–500 kV will suffice. Improvement of the installations will proceed along the lines of increasing their mobility and compactness, increasing the intensity of radiation, improving operating characteristics and finish, and so forth.

In heavy machine building, for radiographing products made of materials that strongly absorb X-rays, installations of ever higher operating voltage and increased intensity must be used.

It is known that with an increase in the kinetic energy of the electrons whose deceleration produces X-rays, the radiation output rises sharply. For example, at an electron velocity of 100 kV only 1.11% of their kinetic energy is converted into radiation energy, while at an electron velocity of 150 kV already 2.2% is converted.

When X-rays are excited in a betatron with electron energies of 20 MeV, the radiation output is 65%. Only 35% of their kinetic energy is spent on heating the target bombarded by the electrons. As the hardness of the radiation increases, the accessible thickness of the metal layer that can be radiographed with the given radiation also increases considerably, and the time required for this is reduced. For example, increasing the voltage on an X-ray tube from 400 to 1000 kV reduces the exposure from 5 hours to 2 minutes. Increasing the voltage from 1000 to 2000 kV leads to a further 78-fold reduction of the exposure. To obtain an X-ray photograph of a steel casting 203 mm thick, with a tube voltage of 1 million volts, a time of 4.5 hours was required, whereas at a voltage of 2000 kV only 3.5 minutes were required.

A steel plate 350 mm thick can be radiographed with an X-ray installation operating at 2000 kV in 4 hours, whereas for this operation an apparatus with an operating voltage of 1000 kV would require 12 weeks. At a voltage of 4000 kV the same steel plate could be radiographed in 1 minute.

With the aid of an X-ray installation of 2 million volts it is possible to carry out radiography of steel castings with a layer thickness of 30 cm. In practice, with an installation of 1 million volts, radiography of castings 30 cm thick is already impossible; whereas at a voltage of 2 million volts, at a distance of 1 m from the output end of the tube, satisfactory images are obtained with an exposure of 2 hours.

Radiographs taken with the aid of a 2-million-volt apparatus make it possible to evaluate defects with an accuracy of 1–2% in steel castings from 2 to 25 cm thick.

Radiography with rays of a hardness of 2 million volts also has the advantage over radiography with less hard rays that, in one exposure, by placing the object at a greater distance, a large surface of the part can be irradiated at once. The power and greater hardness of the radiation make it possible to take pictures at a large distance from the tube and with comparatively small exposure, which gives a clearer image and reduces distortions. Usually, when radiographing articles of different thicknesses, it is necessary to change the exposure accordingly. If one and the same object contains sections of different thicknesses, then in radiography they have to be brought to a “uniform thickness” by build-up. When radiographing with rays of a hardness of 1 million volts, and especially 2 million volts, the necessity for such build-up almost disappears. Excellent radiographs of heavy [[unclear: continuation cut off at bottom of page]]

are also obtained from specimens having parts made of materials with different absorbing power.

X-ray flaw detection has advantages over flaw detection using the γ-rays of radium. For example, radiography of a 12-centimeter armor-steel plate for ship plating with the γ-rays of radium requires four hours. X-rays of 1 million volts hardness give a satisfactory solution of this problem in 10 minutes.

The absorption of hard X-rays depends strongly on the energy of the radiation quantum and on the nature of the absorber. The linear attenuation coefficient \(\mu\) is determined experimentally by the exponential law

\[ I = I_0 e^{-\mu d}, \tag{1} \]

where

\[ \begin{aligned} d &\text{— thickness of the absorber layer,}\\ I_0 &\text{— intensity of the radiation before absorption,}\\ I &\text{— intensity of the radiation after absorption.} \end{aligned} \]

The linear attenuation coefficient consists of four parts:

\[ \mu = \tau + \sigma + \pi + \eta. \tag{2} \]

The magnitude of the coefficient of true photoelectric absorption, calculated per atom \((\tau_a)\), depends approximately on the third power of the wavelength \(\lambda\) and the fourth power of the nuclear charge \(Z\), i.e.,

\[ \tau_a = K Z^4 \lambda^3, \tag{3} \]

where \(K\) is constant over a certain interval of wavelengths. It undergoes an abrupt change at different critical voltages corresponding to different energy levels of the electron shells within the atom. The scattering coefficient \(\sigma\) also consists of two essentially different parts. At low voltages there is the so-called classical scattering without change of wavelength, which is determined by the formula

\[ \frac{\sigma_0}{\rho} = 0.4 \frac{Z}{A}, \tag{4} \]

where \(\dfrac{\sigma_0}{\rho}\) is the mass scattering coefficient,

\(Z\) is the atomic number,

\(A\) is the atomic weight.

With an increase in the energy of the incident radiation, Compton scattering will occur, as a result of which the wavelength of the scattered radiation increases. A quantum of radiation with frequency \(\nu\), colliding with an electron, thereby loses part of its energy, transferring it to the electron. The electron, having received a certain additional energy, moves with a definite velocity determined by the law of conservation of energy.

The next fundamental condition in Compton scattering is the condition of conservation of the total momentum before and after the collision. With the aid of these basic propositions it can be shown that the increase in wavelength upon scattering does not depend on the wavelength of the incident radiation and is approximately expressed by the equation

\[ \Delta \lambda = 0.024 (1 - \cos \varphi), \tag{5} \]

where \(\varphi\) is the scattering angle.

Theory and experiment show that the value of the scattering coefficient \(\sigma\) for hard rays deviates considerably from the classical value given by formula (4). The magnitude of this deviation can approximately be obtained from the formula

\[ \frac{\sigma}{\rho}=P\,\frac{\sigma_0}{\rho}. \tag{6} \]

Here \(P\) is a multiplier less than unity and dependent on the wavelength.

If the magnitude of the energy quantum is greater than \(2m_0C^2\), where \(m_0\) is the rest mass of the electron and \(C\) is the velocity of light, i.e., the quantum magnitude is greater than \(1.02\) MeV, then a third absorption factor appears, whose role increases with increasing atomic number of the element and with the magnitude of the radiation quantum \(h\nu\). This increase in the absorption coefficient is caused by pair production. A radiation quantum in the vicinity of the atomic nucleus gives rise to a positive and a negative electron, expending all its energy on this. This additional absorption is characterized by the coefficient \(\pi\) and is possible only under the condition that \(h\nu > 2 \cdot 0.51\) MeV. According to theory, the absorption coefficient due to pair production, under the condition that

\[ \frac{h\nu}{m_0C^2} \gg 1 \]

and calculated per atom, is approximately given by the formula

\[ \pi_a=\frac{r_0}{137}Z\left(3.1\ln\frac{2h\nu}{mc^2}-8.1\right), \tag{7} \]

where \(r_0\) is the electron radius.

Figure 1 shows, for lead, the dependence of the coefficient of linear attenuation \(\mu\), as well as of its three components \(\tau\), \(\sigma\), and \(\pi\), on the energy of the radiation quantum. The values of the coefficients \(\tau\), \(\sigma\), and \(\pi\) are calculated theoretically—

Fig. 1. Dependence of the coefficient of linear attenuation on quantum energy for aluminum, copper, and lead. For lead the coefficients \(\mu\), \(\tau\), \(\sigma\), and \(\pi\) are shown.

—for the coefficient \(\tau\), the theoretical and experimental values agree well. From the presented data it is evident that photoelectric absorption plays a large role for the long-wavelength part of the spectrum at low energies and that pair production is observed in the region of higher energy values. In the energy range from \(0.5\) to \(5\) MeV, attenuation of the radiation intensity is mainly due to scattering \(\sigma\). In Fig. 1 the corresponding values of the attenuation coefficient are also plotted—

tables for copper and aluminum. From the data presented it is evident that the attenuation of radiation in passing through copper and aluminum is less than the attenuation in lead.

At high values of the radiation energy, nuclear processes set in, determining the fourth component of the absorption coefficient $\tau$.

Figure 2 shows the most important types of interaction of high-energy photons (X-ray and gamma radiation) with matter, which determine the attenuation of radiation.

In Fig. 3 are shown curves of the dependence of the attenuation coefficient of monochromatic $\gamma$-radiation on the quantum energy when passing through steel for a 25 MeV betatron. The dependence of the absorption coefficient for other materials has the same form as the curve presented for steel.

From the course of these curves it is evident that the most intense part of the radiation falls in the region of low absorption. Consequently, X-rays in the range from 3 to 25 MeV are the most penetrating, and their absorption coefficient in this same region is almost constant.

In Fig. 4 the curve $D$ represents the total coefficient of linear attenuation in $\mathrm{cm}^{-1}$ for iron as a function of the radiation quantum energy, expressed in MeV.

Fig. 2. The most important types of interaction of high-energy photons.

The curve $A$ shows the variation of photoelectric absorption as a function of the quantum energy. As can be seen, this process of liberation

Fig. 3. Dependence of the attenuation coefficient of hard monochromatic radiation in iron on the quantum energy.

of orbital electrons loses its significance at quantum energies above 0.5 MeV. Curve B represents the variation of the Compton-scattering coefficient as a function of quantum energy. This process is predominant in the energy region from several hundred kiloelectron-volts to eight MeV. It is known that in Compton scattering the radiation quanta, having reduced their energy in collisions with electrons, continue to move in the same direction.

Fig. 4. Attenuation in iron of monochromatic radiation as a function of quantum energy
D—linear attenuation coefficient;
A—photoelectric absorption coefficient;
B—Compton-scattering coefficient;
C—pair-production coefficient.

Such scattered radiation will produce a fogging effect on the photographic plate. These secondary phenomena are undesirable when thick layers are being radiographed.

Curve C represents the formation of electron–positron pairs, which begins at a quantum energy of 1.02 MeV and takes place near the atomic nucleus. Radiation quanta having an energy greater than 1.02 MeV and causing the formation of a positron–electron pair transfer their excess energy to the particles formed in the form of kinetic energy.

From consideration of the total absorption curve D it follows that, for iron, the minimum absorption is observed at a radiation energy of about 8 MeV. It is evident that this radiation will be the most penetrating. For materials having a high atomic number, the minimum of the absorption coefficient occurs at lower values of quantum energy; for example, for lead it should be expected at 3 MeV.

If it were possible to create a powerful homogeneous beam of quanta with an energy of the order of 8 MeV, for example by means of an electrostatic generator (statitron), this would be a satisfactory solution to the problem of creating an X-ray source for radiographing iron. However, the radiation obtained as a result of the braking of accelerated electrons in a tungsten target is the usual “white” spectrum. Figure 5 shows the energy distribution in the radiation spectrum of a 25 MeV betatron. It is evident that, in order to increase the number of quanta with an energy of 8 MeV

it is necessary to increase the maximum energy in the spectrum. It is also desirable that the radiation spectrum contain a large number of quanta that undergo complete absorption, producing positron–electron pairs. Compton absorption, which gives secondary radiation, is undesirable for the reasons indicated above. Also undesirable is a large number of quanta that will give pairs with high kinetic energy. These pairs, being slowed down in iron, in turn produce soft radiation, which fogs the photographic plate. Such a phenomenon occurs, for example, when radiographing with radiation from a 40 MeV betatron, when many pairs are formed.

Fig. 5. Energy distribution in relative units in the radiation spectrum of a 25 MeV betatron

Fig. 6. Radiation intensity in relative units as a function of the maximum betatron energy after passing through a layer of steel.

Figure 6 shows the radiation intensity as a function of the upper energy limit after the radiation has passed through a steel layer 250 mm thick. In these experiments radiation from a 100 MeV betatron was used.

From consideration of the curve presented in Fig. 7, it is evident that rays with an energy of about 25 MeV have the greatest penetrating power.

Fig. 7. Change in the linear attenuation coefficient of hard radiation as a function of radiation energy

The exposure of the photographic plate by secondary rays at a primary-ray energy of 10 MeV proved to be three times greater than at a primary-ray energy of 22 MeV. The fogging of the photographic film caused by secondary rays when primary radiation of 22 MeV is used is, in general, small.

The action of secondary radiation can be weakened further if the photographic film is moved away from the object. The intensity of the secondary radiation will then decrease inversely proportional to the square of the distance from the specimen, whereas the primary radiation will decrease inversely proportional to the square of the distance from the target.

It is possible to arrange that only 20% of the fogging of the photographic film will be associated with secondary radiation.

Another indication of the small role of secondary radiation is the fact that, in steel, one can observe a crack approximately 0.8 mm thick, independently of the thickness of the steel layer.

In the practice of radiography with rays of low hardness, cracks that are clearly visible in a thin specimen are not visible in thick ones. The reason for this is that, in radiography with X-rays having energies of several hundred kiloelectronvolts, as the thickness of the specimen increases, ever more significant secondary radiation is produced. The density of the fogging of the photographic film caused by secondary rays may be many times greater than the density of the fogging caused by primary rays.

In the case of primary radiation that produces little secondary radiation, an increase in the thickness of the layer of material in front of the photographic film is accompanied by attenuation of the intensity of the rays incident on the film. In practice the image is not distorted, and only a different—longer—exposure is required. In radiography of iron 50 and 300 mm thick, a crack was revealed with equal sharpness.

In radiography of products with X-rays of ordinary energy, measures must be taken to prevent scattered radiation.

in the chamber and on the photographic plate. For this purpose, in order to obtain a denser shadow image on the X-ray film, a thin lead screen, for example 1.02 mm thick, is sometimes placed directly in front of it. This screen absorbs the soft rays and reduces the fogging of the X-ray film. The direct beam of rays, only slightly weakened when passing through thin layers of material in an article of complex shape, must be blocked by increasing the thickness of the layer of material. The absence of scattering of rays at an energy of 20 MeV eliminates the need for such blocking for specimens, even though they may be more than 30 cm thick.

In a betatron a narrow beam of rays is obtained. The accelerated electrons are focused into a band with transverse dimensions of \(1 \times 1\) mm.

The electron beam, upon striking the target, creates a radiation source 1 mm high. The width of this source can be very small, in accordance with the pitch of the spiral expansion of the electron beam. By choosing a target of small dimensions, one can obtain a “point” source of radiation. In a 22 MeV betatron the height of the target is 0.25 mm. To obtain a high recording speed of the phenomenon on photographic film, it was placed between two fluorescent screens.

For radiography of iron, the most suitable is a betatron with a radiation energy of 25 MeV.

With the aid of X-rays under industrial conditions, radiography is carried out of articles in thick layers, measured in hundreds of millimeters. The time required for radiography is measured in tens of minutes, i.e., it is practically acceptable.

The opinions, expressed quite recently by a number of investigators, that X-rays cannot be used for investigating materials in thick layers should be considered obsolete.

The principles for selecting the radiation energy range for purposes of radiography by means of X-rays, set forth in the present article, proceed from definite technical methods of carrying out this operation. New technical methods should be sought in order to use harder rays with energies of 50 MeV and higher. Further work is needed on increasing the intensity of X-ray sources. In this respect, especially promising in the energy range of the order of 8–10 MeV, which is of interest for radiographic technique, are the electrostatic generator with a moving belt (statitron), the betatron, and the linear accelerator.

Researchers have always been attracted by the prospect of constructing a microscope for viewing an object in X-rays. The short wavelength of X-radiation would make it possible to obtain a greater magnification than is possible with visible light or with electron waves in an electron microscope.

An advantage of the X-ray microscope over the electron microscope is also that the object need not be placed in a vacuum. With the aid of X-rays, the internal details of the structure of materials and objects will be visible. At the present time a laboratory model of an X-ray microscope has been created.

In the design of the microscope the principle is used of reflection of X-rays from a polished surface, provided that the rays fall at a very small angle to the surface, almost parallel to it. The microscope consists of an X-ray tube and two concave mirrors, upon which the rays fall at an angle of less than \(0.5^\circ\) after they have passed through the specimen. The mirrors change the direction of the rays in such a way as to obtain on the photographic film an enlarged image of the object.

With the aid of mirrors an image magnification of 10 times was obtained; in addition, this image was further magnified 10 times by photographic enlargement. Such a

Thus, the total magnification obtained with the aid of the X-ray microscope was 100 times.

The mirror consists of plates of fused quartz whose surfaces had the finest polish and were coated with platinum. To improve focusing, the curvature of the surface along which the plates were bent was adjusted by hand. The optical system and the specimen holder are mounted in a compact unit placed close to the X-ray tube. The cassette with the photographic film is positioned at a distance of 30–50 cm from the optical unit. The tube, the optical unit, and the cassette are all mounted on a single guiding device. Experiments with the laboratory model showed the high resolving power of the X-ray microscope.

The industrial prospects for the X-ray microscope are exceptionally great. This method will complement and broaden the use of X-rays in industry.