Translation of Remarks on the Apparent Selective Reflection of X-rays in Crystals, ca. 1920s (sci3.001.30); and The Canonical Distribution, May 10, 1925 (sci3.001.7)

Translation of Remarks on the Apparent Selective Reflection of X-rays in Crystals.

Wilkossel Z.f.P. 23,278 (1924)

In recent years observations which appear to indicate a selective reflection of the x-ray lines of crystal atoms have produced great interest. While Mie was able to explain his observations almost quite entirely by already known methods ¹ the complete significance is still lacking of the { ¹ G. Mie Z.f.P. 18, 105(1923) } observations carried out in a somewhat different manner by Clark and Duane ². { ² Proe, Nat, Ac, Sc. 1922 Mai, 1923 April } The possibility of selective reflection especially deserves interest, for the present conceptions, according to which characteristic radiation proceeds from independent events in which different atoms, into which randomly distributed verweilzeiten are distributed, do not predict a coherence such as is necessary for such phenomena. The authors themselves recognise that a change in theory is necessary to produce the definite time-relation between the fluorescent emission, and Duane³ developed { ³ W Duane, ibid, May 1923 } a conception which would also require the abnormal intensity relations of the lines (K beta, stronger than K alpha) which this curves show. As will be shown in the following, however, considerations can be drawn from the Duane curves themselves, with the help of some simple calculations, which also explain at least the most important part of the phenomena by known methods. The author as far hasn't the impression that something positive has been shown to require changing previous ideas.

We next give the essentials of Clark and Duane's observations by describing an especially pregnant case. If one produces the white spectrum from a W anticathode with the 100-planes of a CsI₃ crystal in the Braggonian method (using atom chamber with double the angular velocity of the crystal) there occurs already far below the antical potential of W (69300 v.), namely in the region of that of I, sharp lines on the ordinary white spectrum, which are repeated in various orders as multiples of the same. If one goes from a small angle through the first order, there is first a weak white spectrum. At an angle which is equal to corresponds to the reflection of CsK obs, the intensity rises 5-fold in less than 10', falls again to 3/4 of this value, shows a second weak rise-- which the author attributes to the K-lines of Cs,-- and slowly drops, so as perhaps to form a picture of the white radiation, much stronger than before the first jump, until in the second order there is again a sharp rise. This is observed in 3 orders; at still greater angles this relatively complicated kind of crystal gives still further peaks which correspond to the reflection of the iodine lines from

the more closely spaces I- planes. The authors callattribute the first jump to the IK obs. edge, the peak K beta, the bump on the down side K alpha (all of Cs), which are excited in the crystal atoms with exact time relations, so that there is a definite phase relation for interference in the emission of different atoms of the same kind on the lattice. This interpretation, if one couldn't get around it, would necessitate a fundamental change in our ideas of fluorescence-mechanism.

The authors themselves note that K beta always appears astoundingly stronger than K alpha. It moreover appears from the curves that these making do not correspond to a sharp line formation, such as would be expected from the sharpness of the first edge. The base on which it sits is not closed as quickly as the edge of the coresponding rise, but with a considerable intensity slowly decreasing to longer wave-lengths, so that as stated already one has the impression that, just like white radiation from the angle corresponding to the edge on, that it appears to belong to the maximum of the curve of white radiation already present, which suddenly jumps at a point to five-fold greater intensity. In this way a corespondingly weak alpha line is put on the down slope, which for beta the authors' pictures are not to be said to be convincing, as to whether a further line is superimposed on the maximum due to the sudden rise. A sudden multiplication of the intensity is apparently an important part of the whole curve-course, which appears next so often after a corresponding "formation of characteristic radiation."

Such an effect follows directly from the observed characteristics of those curves for CsI₃, that the waves to be represented penetrate the crystal suddenly much stronger and deeper with the upon passing the quite close absorption edges Cs & I and then, as Bragg had already noted qualitatively in 1914, are scattered with greater intensity. The crystal itself must have the effect of an absorption leaf of Cs and I-- it is analagous to the well-known influence of the anticathode edge on the white spectrum only here the jump is stronger, since X-rays penetrate farther than cathode rays, a greater absorption thickness is affective, and it can be easily calculated.

If we take for illustration a scattering coefficent sigma, in a path delta x of the beam at the distance x from the entrance the contribution of the primary intensity I to scattered radiation will be

delta S_i = sigma I delta x = sigma I _o e^{-delta x}delta x.

On account of the equality of angles of incidence and reflection it must again pass through the thickness x. As the wave-length is unchanged, there is the same absorption coefficient, so that

delta S_a = delta S_i e^{-delta x}= sigma I_o e^{-2delta x}delta x

For a practically infinitely thick crystal altogether

S_a= sigma I _o/2 [delta]

The white spectrum runs steadily for the wave-lengths corresponding to the K edge of the crystal-substance, and so does the scattering coefficient is the representation the intensity jump corresponding to this edge is, if the absorption coefficients on the two sides of the K-edge are alpha and alpha₊, equal to the reciprocal ratio of these; i.e.

S₊/S_- = alpha_-/alpha₊

This relation has is for the group of elements around Cu 7.4¹, for Ag about 6; for C₃ and I, with which we {¹v. d. D. Ph. qes. 1b, 898 (1914)} have to deal, Glocker² gives 5.22 (for Z=54). The intensity ratio for the first jump on the Duane curve for C₅I₃co 12.0/2.4 = 5.0 {² Glocker P.2. 19,66 (1918) } The jump the absorption coefficients of the crystal-substances accordingly gives here almost quantitatively the "curve of the absorption edge of the characteristic frequency of crystal atoms."

One obtains an entirely similar curve by reflection from the 100planes of K I. The job is still simpler, since the renewed occurence of higher maxima in the higher orders is missing. The ratio of the absorption coefficients of the I K edge must be less here, since there is indifferent K mixed in. One obtains by applying the usual relations

calculated absorption jumps 4.05, 4.06

and reads from the figure the intensity jumps 4.09, 4.2 for the two pictures of the first order. The agreement again occurs within the limit of accuracy for the steep maximum of the steep remainder of the curves.

While the chief point of the phenomenon here is satisfactorily explained, a measurement of Clark and Duane ( [wie der pepebene] von Kerr Walter) 110- planes of K I shows a jump of 12 or 13 fold, while the absorption phenomenon here permits one of only 4.06 fold. Since it appears very remarkable that in two cases only the theoretical jump is to be expected, and in the third a 3-times too high jump occurs, it would be very desirable, in case there isnt an error in the ordinate-figures, to repeat the measurements.

In regard for order to determine that the peaks coming in in the higher orders of CsI₃ belong to more closely spaced I-planes, while the special

conceptions of the author exclude the idea that here also an interfering wave-train proceeds from the iodine alone as its characteristic radiation. It appears difficult to obtain an active definite insight into the actual structure from data ling before the author.

There remains still to be explained how there may occur a weak picture of a K (K alpha) line of the crystal element, which seems indeed is our conception of Duane's curves to be an important one of the previously not understood phenomena. An idea which likes in this region is based on the published observations of Walters¹ {1 Z.f.P. 20,257 (1923)} who wouldn't find this line by photography with a rotating crystal. One easily explains that radiation produced in the crystal would be reflected by the rest of the crystal at the corresponding angle, just as though it came from outside. If as seems here, only a small region of the crystal is excited, then a sheaf of small rays will be sent out For this phenomenon no coherence of the radiation of different atoms is necessary-- a crystal anticathode, in which excitation occurs through cathode rays, would show the same action. The question now is how strong would it be, since it would, going in all directions, be superimposed in the direct beams. In this it would be expected, since the chracteristic radiation in general occurs at a given depth, that and so has to penetrate a number of net planes, that a weak minimum would occur through inward reflection. With a crystal anticathode, for which the mean effective depth is only a few Mu on account of the high absorption of cathode rays, the minimum would be still weaker that an excitation with X-rays. In any case over compensation would be expected by the maximum produced by reflection of the backward beam on layers of planes limited only by the absorption of the radiation. The necessary directions are fixed by the crystal and rotate with it. Their angle with the net planes is accordingly that at which reflection would occur if the radiation came from outside. If, as do Clark and Duane, one uses an ionization chamber, one would fine that this beam will hit the chamber at the same angle as though it came from outside: There now occurs the idea as to whether the wave-lenths of the white spectrum which coincide with the characteristic rays would be reflected especially strongly. If one uses photographically, as did Walter, the effect of different crystal positions, then the reflection position of characteristic rays cannot be observed, since the beam considered rotates with the crystal and accordingly darkens equally a large portion of the photographic plate. To be sure

Kerr Walter obtained the first effect, the absorption edge, but not the lines. In order to prove whether this effect accounts quantitatively for the results of Duane's experiments different ways can be used. Experimentally the directions of the observation that the beam moves with the crystal beyond the position at which reflection of the same ray occurs from outside can be established. Since such reflections should appear for all planes for all possible order it seems improbable that they exist, since they havent been found previously. Of course for the usual crystals NaCl, CaCO₃ or sugar the heaviest atoms have such long characteristic rays that they wouldn't be reflected [(Lambda is greater than 2 delta)] or would permit only a narrow bundle. For Zn in ZnS or I in KI an extensive array of such reflection would be possible, and could be shown for these substances if the intensity were sufficient to stand out on top of the white radiation and produce the [alpha- wast] of ClarkDuane's curve. Since it deviates from the ordinary reflection law the question rises as to whether we haven't a trace of these reflections in the "X peaks" of these authors, since indeed these vanish at the excitation limit of characteristic radiation. The author doesn't believe this, for the direction relations of this peak cant according to the description be brought into agreement with the expected properties of the reflections considered. It is to be desired next that these phenomena be further substantiated.

So if now out ofthe whole observation appears to give nothing definite leading beyond the sphere of previously known phenomena, still it cant be said that no interest accompanies an exact as possible quantitative verification of the effect of an absorption edge in the crystal, which is the chief part of these experiments. Our calculations assume that the absorption edge comes completely into play, not bearing in mind considering accordingly that at this angle an especial "absorp extinction-coefficient" comes into play, according to Darwins' in an ideal crystal this far exceeds the normal absorption coefficient; {Darwin Phil Mag 27, 315 & 675, (1914) Bragg, Jams & Bozanquist, Phil Mag March & July 1921} the ray should be entirely absorbed at the correct angle at a depth at which only a slight weakening would occur from the normal absorption. Since this "extinction" goes back to interference, and accordingly to radiation, there is no reason