ABSORPTION OF X-RAYS IN CRYSTALS OF ALKALI-HALIDE SALTS

A. D. SHCHELOKOV

(Presented by Professor, Doctor A. A. Vorob'ev)

A beam of X-rays 7 (Fig. 1) with a divergence angle of 5–6° from the X-ray tube 1, after passing through filters 3 and 4 (0.3 mm Cu + 0.6 mm Al) and aperture 5 of 3 mm diameter in a lead plate 6 of 12 mm thickness, fell on an ionization chamber 8 of the AG type, whose current was measured with a U_sDD-5 direct-current amplifier. The characteristics of the rays were: voltage on the tube 102 kV, effective wavelength \(\lambda_{\mathrm{eff}} = 0.22 \, \text{\AA}\), heterogeneity \(h = 1.38\) [6], minimum limiting wavelength \(\lambda_0 = 0.12 \, \text{\AA}\).

Samples 9, placed in the path of beam 7, were plates \(\sim 0.5 \times 0.5\) cm, cleaved from single crystals of alkali-halide salts, with thicknesses \(d\) from 0.3 to 12 mm.

The initial beam intensity \(J_0\) (without a sample) and the intensity after passage were measured in relative units—

Fig. 1. Diagram of the apparatus for determining the absorption of X-rays in solid bodies

Fig. 2. Absorption curves of X-rays in crystals of alkali-halide salts, \(\lambda_{\mathrm{eff}} = 0.22 \, \text{\AA}\), \(h = 1.38\)

of the sample, \(J\), from which the curves of the dependence of \(\lg J/J_0\) on \(d\), presented in Fig. 2, were constructed. From the slope of the curves, the linear absorption coefficients \(\mu\), effective in the thickness interval \(0 \div 1\) mm, were determined, and from \(\mu\) the mass absorption coefficients \(\mu/\rho\) (\(\rho\) is the density) were found; these are placed in Table 1 in increasing order. For comparison, the table gives \(\mu/\rho\) for copper, measured under the same conditions.

Table 1

Mass absorption coefficient at \(\lambda_{\mathrm{eff}} = 0.22\ \text{\AA}\)

For comparison of the change in \(\mu/\rho\) with the change in other characteristics, Table 1 gives the density, molecular weight, lattice energy, and absorption constant \(C\) (see below).

As is seen from the table, \(\mu/\rho\) of alkali-halide crystals has no linear dependence on density; with increasing crystal-lattice energy, \(\mu/\rho\) generally decreases—rapidly for heavy salts, slowly for light ones (Fig. 3).

According to Fig. 2, the tested crystals, with respect to absorption, are divided into 3 groups (3 families of curves).

The obtained values of \(\mu/\rho\) for alkali-halide salts are satisfactorily described by the approximate formula:

\[ \mu/\rho = 1.95 \cdot 10^{-2} \cdot \lambda^{2.8} \cdot C, \qquad (\lambda \ll \lambda_k) \tag{1} \]

where

\[ C=\frac{A_1 Z_1^{2.58}+A_2 Z_2^{2.58}}{A_1+A_2}, \tag{2} \]

\[ \lambda \text{ is the wavelength of the absorbed rays in \AA;} \]

\(A_1\) and \(A_2\) are the atomic weights of the atoms composing the salt;
\(Z_1\) and \(Z_2\) are the atomic numbers in Mendeleev’s table.

Formula (1) was obtained on the basis of Glocker’s formula [2] for the mass coefficient of photoelectric absorption and the additivity law [1–5] under the following assumptions and conditions: 1) for X-rays with quantum energies less than 350–400 keV, the total absorption coefficient \(\mu\) may be taken equal to the coefficient of photoelectric absorption \(\tau\) (\(\mu \simeq \tau\)); 2) the wavelengths of X-rays from 0.34 to 0.03 Å are smaller than all wavelengths of the K-band edge

absorption edges \((\lambda_k)\) of the atoms constituting the alkali-halide salts \((\lambda < \lambda_k)\).

The quantity \(C\) (2), being a dimensionless constant for a given substance, characterizes the absorbing ability of the substance with respect to X-rays and, unlike \(\mu/\rho\), does not depend on \(\lambda\) for alkali-halide salts in the interval from about 0.3 to 0.03 Å.

Fig. 3. Relation of \(\mu/\rho\) and of the absorption constant \(C\) of alkali-halide crystals to the lattice energy. \((-\cdot-\circ-\cdot-\circ-\cdot-)\)—theoretical, \((\circ,\Delta,\square,\times)\)—experimental, \(\lambda_{\mathrm{eff}}=0.22\) Å.

The mass absorption coefficient \(\mu/\rho\) at \(\lambda=\mathrm{const}\) depends linearly on \(C\).

The absorption constant \(C\) (2) may be represented as follows:

\[ C = p_1 Z_1^{2.58} + p_2 Z_2^{2.58} = Z_{\mathrm{eff}}^{2.58}, \tag{3} \]

where \(p_1\) and \(p_2\) are the weight fractions of the atoms constituting the molecule of the alkali-halide salt.

The number \(Z_{\mathrm{eff}}\), according to (3), may be interpreted as the effective number of electrons in the molecule (with respect to absorption), since the atomic numbers \(Z_1\) and \(Z_2\) of the atoms physically denote the numbers of electrons in the constituent atoms.

\(Z_{\mathrm{eff}}\) is practically equal to the additively obtained number of electrons

\[ Z_{\mathrm{ad}} = p_1 Z_1 + p_2 Z_2. \]

The constant \(C\), therefore, is determined, according to (3), by the effective number of electrons in the molecule of the substance.

Table 2 gives, for all alkali-halide salts, the absorption constants \(C\) and the numbers \(Z_{\mathrm{eff}}\).

In order of increasing absorption, alkali-halide salts, according to

Table 2

Key to the table

● — salt beginning a group.
■ — salt ending a group.
] — symbol separating groups.

In the graph: vertical axis — absorption constant $C \times 10^{-3}$; horizontal axis — ordinal number in the absorption series. Groups I, II, III, and IV are marked.

Fig. 4. Magnitude of the absorption constant $C$ of alkali-halide salts as a function of the number in the absorption series. The latter is divided, according to the value of $\mu/\rho$, into 4 groups: ($\mu/\rho$ is proportional to $C$).

(1) or (2), are arranged in a series that breaks up into 4 groups, as shown in Fig. 4.

The satisfactory agreement of formula (1) with the experimental data is shown in Figs. 5 and 6.

The deviation of experimental curve 2 (Fig. 5) from straight line 3, calculated from (1), in the region of large \(C\) is explained by the insufficient mono-

Fig. 5. Dependence of \(\mu/\rho\) of alkali-halide crystals on the absorption constant \(C\). For rays far from monochromatic rays, with \(\lambda_{\mathrm{eff}} = 0.34\ \text{\AA}\), curves 4 are calculated and 1 is experimental. For rays closer to monochromatic, with \(\lambda_{\mathrm{eff}} = 0.22\ \text{\AA}\), curves 3 are calculated and 2 is experimental.

In the graph: ordinate \(\mu/\rho\), \(\mathrm{cm}^2/\mathrm{g}\); abscissa \(C \cdot 10^{-3}\). The indicated salts include LiF, LiCl, LiBr, LiI, NaCl, NaBr, KBr, RbCl, and RbBr; the slopes marked are \(n=1.59\) and \(n=1.385\).

Fig. 6. Dependence of \(\mu/\rho\) of alkali-halide salts on composition. At the iodide level—the IV group of crystals; at the bromide level—the III group, etc.

In the graph: ordinate \(\mathrm{cm}^2/\mathrm{g}\); abscissa “Composition.” Along the abscissa are Li, Na, K, Rb, Cs, with halides F, Cl, Br, I. The plotted points are marked: “○○○—calculated \(\mu/\rho\),” “×××—experimental \(\mu/\rho\),” for \(\lambda_{\mathrm{eff}} = 0.215\ \text{\AA}\). The curve labels are: 1—iodides, 2—bromides, 3—fluorides, 4—chlorides. The regions are marked I group, II group, III group, IV group.

chromaticity of the rays used. For rays far from monochromaticity, the discrepancy is still greater (curve 1—experi-

experimental, 4—calculated from (1). The value of \(\mu/\rho\) for KJ, found from Fig. 1 for a thickness \(d\) close to zero (in this case the filtration of the rays in KJ is almost absent), gives an experimental point that shifts from curve 2 to calculated curve 3. The shift of the experimental value of \(\mu/\rho\) for NaBr toward smaller values than is required according to the absorption series from (1) (Fig. 4) is explained by the strong hygroscopicity of NaBr, which at the time of measurement in a room atmosphere partially deliquesced and reduced its thickness.

In Table 2, attention is drawn to a definite regularity in the increase of the values \(Z_{\mathrm{eff}}\) or \(C\) (and consequently also \(\mu/\rho\)) with change in composition.

LITERATURE

1. Korsunskii M. I. Physics of X-rays, ONTI, Moscow–Leningrad, 1936.

2. Gloker R. X-rays and the Testing of Materials, GITTL, Moscow–Leningrad, 1932.

3. Aglintsev K. K. Dosimetry of Ionizing Radiations, GITTL, Moscow–Leningrad, 1950.

4. Poroikov I. V. Physical Foundations of X-ray Dosimetry, GIS and R, Moscow–Leningrad, 1934.

5. Kharadzha F. N. General Course of X-ray Engineering, GEI, 1956.

6. Grechishkin S. V. Fundamentals of X-ray-Therapeutic Practice, Medgiz, 1952.

ERRATA

Izv. TPI, vol. 95.