MEASUREMENT OF X-RAY SCATTERING BY A SINGLE CRYSTAL USING A GEIGER COUNTER*)

In the work under discussion, the general merits and shortcomings were investigated of the method of measuring, with a Geiger counter, X-rays both reflected from the nodal planes of a crystal and diffusely scattered.

At the same time, the author investigated the variation of the ratio of diffuse scattering to Bragg scattering as a function of various factors, and also investigated the dependence of diffuse scattering on the mosaic structure of the crystal.

Single crystals of urea and of oxalic-acid dihydrate were used as objects. The choice of objects was dictated by the availability of several careful structural studies devoted to these crystals. Comparative experiments were carried out with copper and molybdenum radiation ($K_{\alpha}$ and $K_{\beta}$ lines). Two counter fillings were tested: a mixture of methyl bromide with argon and with krypton.

Commercial Geiger counters gave, in the author’s laboratory, a background of 16–24 counts per minute. On the same scale, the reflection from the 110 plane of urea for copper radiation should have given more than a million counts per minute. Taking into account the magnitude and fluctuation of the background, the author believes that, with a counting time of 10 minutes, the minimum detectable intensity should be taken as 10 counts per minute (above background). Thus, the measurement interval of the Geiger counter is entirely sufficient for solving any structural problems, since intensities 100 thousand times weaker than the strongest reflection can be measured.

It should be emphasized that the use of automatic recording, offered by many firms, sharply reduces this ratio. In this case, even at maximum sensitivity, reflections can be measured which are only 300 times weaker than the strongest. This is insufficient, and therefore the author quite rightly concludes that the use of Geiger counters for the purposes of precise structural analysis is possible only without automatic recording, with separate counts being made for each given setting of the spectrograph.

Even within the indicated limits, automatic recording is greatly hindered when it is necessary to determine the areas of the curves (integral reflections). The measurement of the areas of crooked curves loses all meaning because of the nonlinearity of the scale, the absence of indications during slow counting, and other defects.

The author draws attention to the need for exceptional care in installing the counter in the X-ray spectrograph, dictated by the nonuniform sensitivity of the counter over its cross section.

A very essential circumstance is that the instrument operates linearly only within a very narrow region. A calibration curve is necessary and must be checked repeatedly. The instrument at the author’s disposal possessed linearity up to 100–150 pulses per second. At frequencies above 2000 pulses per second the counter ceases to resolve pulses. Thus, stronger reflections have to be attenuated. For this purpose the author uses filters, namely placing in the path of the beam $n$ foils of equal thickness. If one foil attenuates by a factor of $e^{-x}$, then $n$ sheets—

*) K. Lonsdale, Acta Crystallographica 1, 12 (1948).

MEASUREMENTS OF X-RAY SCATTERING BY A SINGLE CRYSTAL

… foils attenuate the beam by \(e^{-nx}\) times. The linearity of the calibration curve can be checked by plotting, on a logarithmic graph, the number of pulses as a function of the number of foils and by comparing the resulting curve with the straight line \(e^{-nx}\) as a function of \(n\). The results are the same whether the foils are placed in the path of the primary or of the scattered beam. Naturally, the counting of intensities is statistical in character. An accuracy of 1% at 1000 pulses, 7% at 20 pulses, and 15–20% at one pulse per second may be achieved. This accuracy is obtained with a counting time of half a minute. The background is 0.33 pulse per second.

The author carried out a careful investigation of the influence, on the deviation of the calibration curve from a linear course, that may arise from the presence in the spectrum of harmonics of the fundamental wavelength. The results of this investigation are as follows:

1. The influence of the wavelengths \(\dfrac{\lambda}{2}\) and \(\dfrac{\lambda}{3}\) should have consisted in the acquisition by the curve of a concave form at the origin of coordinates (at large numbers of pulses). Experiment shows that the calibration curve is, on the contrary, convex at large numbers of pulses and straight or concave at small numbers of pulses.

2. The effect of harmonics and of the white spectrum when nickel foils are used is negligibly small.

3. The deviation of calibration curves from linearity, which usually occurs at more than 100 pulses per second, is a property of the instrument and is not determined by the properties of the primary beam or by the features of the construction of the calibration curve.

4. The influence of harmonics when working with molybdenum radiation is considerably greater, but nevertheless it does not have a substantial effect on the measurements.

All these data allow the author to assert that the Geiger counter is suitable for solving such structural problems. However, the existing automatic devices that make it possible to record reflection curves are not suitable for this purpose. Unfortunately, the author did not dwell on a comparison of the operation of the Geiger counter and the ionization chamber. It is thought that the exceptional slowness of work with a counter without automatic recording makes its use inexpedient for measurements of very weak reflections. The lower limit, of course, lies lower for counters.

It seems to us that the most expedient would be an X-ray spectrograph with an interchangeable ionization chamber and Geiger counter.

The author further gives detailed data on the method and on the results of measuring thermal scattering. The measurements may be carried out in two ways—at a stationary crystal and at a stationary counter.

The change in the mosaic structure of the crystal and the influence of this change on the intensity were studied by comparing the scattering of the crystal before and after quenching in liquid air. Crystals of urea showed no significant change either in Bragg or in diffuse scattering. Crystals of oxalic acid dihydrate changed only the Bragg scattering. This result is quite natural, since in thermal scattering there are no strict phase relations of the kind that occur in reflection from lattice planes. Therefore, in order to make any judgment about the relation of the intensities of diffracted and diffuse-scattered radiations, one must deal with ideally mosaic crystals. For urea the author obtained the following…

data for the 110, 220, 330 reflections: thermal waves of length 200 Å along the \([110]\) direction—the ratios of diffuse scattering to Bragg scattering are \(0.557 \cdot 10^{-3}\), \(3.30 \cdot 10^{-3}\), and \(9.12 \cdot 10^{-3}\); waves of 40 Å in the same direction—the ratios are \(0.095 \cdot 10^{-3}\), \(0.65 \cdot 10^{-3}\), and \(2.00 \cdot 10^{-3}\). These data are given for copper radiation. The corresponding figures for molybdenum radiation are: \(0.114 \cdot 10^{-3}\), \(1.40 \cdot 10^{-3}\), and \(6.48 \cdot 10^{-3}\) for the longer wavelength, and \(0.056 \cdot 10^{-3}\), \(0.55 \cdot 10^{-3}\), and \(3.0 \cdot 10^{-3}\) for the shorter. All the waves are transverse.

The intensities of thermal scattering also reach one hundredth in the case of tartaric acid dihydrate.

A. Kitaigorodskii