CI. The Absorption of X-Rays and Fluorescent X-Ray Spectra, By Professor C. G. Barkla, M. A., D.Sc, and V. Collier, B.Sc, University of London, Kings College [Communicated by the Authors. The expenses of this research have been partially covered by a Government Grant through the Royal Society.]. General Absorption Curves. IN a paper on " The Absorption of Röntgen Rays " [citation redacted] Barkla and Sadler showed how the absorption by a given element of beams of homogeneous X-radiation varies with the general absorbability of the radiation employed. [The general absorbability may be measured in any substance whose spectral lines in X-rays are not within the range of absorbability and not near it on its more absorbable side. Aluminium is a convenient substance for all ranges usually dealt with, or even the much wider range covered by these experiments.] Curves showing the relation between the absorption in an element R say and in Al were given, and 988 [header] the characteristics o£ the relation were seen to be the same whatever the element R employed. At that time, however, the series of spectral lines [citation redacted] had not been observed, nor had sufficient experiments been made to accurately test the generality of the curves over a large range of penetrating power, especially in the region of the spectral lines. In further experiments [t In this paper, as in the paper by Barkla and Sadler, the absorption coefficient X is defined by the equation [formula redacted] in the usual notation. It should be noticed, however, that I represents the intensity of radiation of the same penetrating power as the incident radiation transmitted in the same direction as that of the incident radiation. It does not include the scattered or transformed radiations.] we have therefore examined the absorption of X-rays by Br and Ag, the latter of whose spectral lines of series K is about 35'5 times as penetrating as that characteristic of Fe. If we plot, as previously, absorption in Br or in Ag as ordinates, and absorption in Al of the corresponding homogeneous radiations as abscissae, we get a curve possessing similar characteristics to those previously published for the absorbing elements Fe, Ni, Cu, and Zn. This was, of course, expected. If, however, we arrange the scales of ordinates and abscissae for each [figure reacted] Showing relation between absorption in element R and in standard substance (Aluminium) in region of spectral line of R. One curve K is common to all elements R if spectral line is of series K. Curve L shows similar relation when spectral line is of series L. absorbing substance such that the absorption of Fe radiation [citation redacted] in Fe, Ni radiation in Ni, Cu radiation in Cu, &c, are all indicated by the one point A (fig. 1), it appears that there is [header] 989 not only a similarity in general features, but that one absorption curve is common to all absorbing substances. The exactness of this in the case of absorption by Fe, Ni, Gu, Zn, and Br is remarkable, and is illustrated in fig. 1 by a few points obtained from experiments on absorption by each of these elements. Thus in fig. 1, curve K is seen to pass through points indicating absorption by Fe, Ni, Gu, Zn, and Br. In explanation of the notation it should be pointed out that the letters GuFe, for instance, denote absorption of Gu radiation by Fe. The points obtained from experiments on absorption by Ag do not fall exactly on the curve and have been omitted. There appears in this case to be a small displacement to the left. This might be caused by the one value AgAg being slightly too large. But quite apart from small possible errors of experiment, slight displacements to left or right are to be expected, as absorption in Al does not provide a perfect standard of reference — that is a perfect scale of abscissæ. We thus see that for all these substances there is little or no variation in the shape of their absorption curves in the region of their spectral lines of series K. The connexion between the curve for a particular absorbing substance and the spectral line of that substance is shown in fig. 1, A being placed vertically above the spectral line shown in the lower portion of the figure. In order to investigate the shape of the absorption curve in the region of the spectral line of series L, experiments were made on the absorption of homogeneous beams of X-rays by Au and Pt. The spectral lines of series L for these elements is within the range of absorbability most easily experimented upon. The results are given in Table I. (p. 990). If now we compare the shape of the curves by arranging that the absorption of Au radiation (series L) in Au and of Pt radiation (series L) in Pt is coincident on the figure with the point A corresponding to Zn radiation (series K) in Zn, &c, we at once see a marked difference. Curve L (fig. 1) passes through points obtained by these experiments on Pt and Au. It possesses similar characteristics to curve K, but the ordinates are of very different magnitude. Thus the shape of the absorption curves in the region of a spectral line depends on the series to which the spectral line belongs and not to any appreciable extent upon the particular element in which the absorptions are made. By a combination of the two curves K and L we get one absorption curve which is characteristic of every element 990 [header] Table I. Mass absorption coefficients [formula redacted]. Radiator. Absorber. [table redacted] General absorption curve showing relation between absorption in element R and in standard substance (Aluminium). The connexion with the fluorescent X-ray spectrum is shown by the position of the spectral lines of It in the lower portion of figure. hitherto experimented upon. Thus fig. 2 shows in the lower portion the fluorescent line spectrum of any element, horizontal distances from left to right representing instead of wave-lengths, absorbability in aluminium. Tw t o definite absorbabilities have been found in the fluorescent X-radiation from a number of elements, the line of series L being roughly 300 times as absorbable as that of series K. As the [header] 991 distance between the two lines on the spectrum is so great compared with the distance of one from the end, the scale of abscissae has been made different in the two halves of the diagram separated by the broken line. The scale on the right-hand side has been reduced to about [formula redacted] that on the left. From many substances only the spectral line of series K has been observed, from others only that of series L, and from many light elements neither line, but there is strong evidence of the existence of both lines and indeed lines of other series not yet observed in the fluorescent spectra of many elements. There is no evidence that these lines do not exist in the fluorescent spectra of all elements. The curve shown above the characteristic spectrum of an element R, say, represents by its ordinates the relative absorptions in that particular element of the radiations whose absorbability in Al is represented by abscissa). The ordinates to the right of the vertical broken line have been reduced in something like the same ratio as the abscissa), though not accurately so, as from no single element has the complete absorption curve been obtained ; consequently the true relative values of the ordinates in the two halves of the diagram have not been determined. In the case of some substances, the curve has been obtained in the region of the spectral line K only, in others in the region of line L, and in still others in regions far removed from the two. We thus have, as far as is at present known, cue fluorescent spectrum characteristic of all elements, the only difference between the various elements being that the scale of absorbability varies from element to element. Corresponding to this spectrum there is one absorption curve characteristic of all elements, the scale of absorptions (ordinates) varying with the element. The character of this absorption curve for an element R, say, may be expressed as follows : — Commencing with rays of more absorbable type than the L line in the spectrum of R, the absorption in R is proportional to the absorption in the standard substance S. This is represented by the straight line AB, which being produced passes through the origin. As the radiation becomes more penetrating in type than the L line the absorption in R ceases to diminish at the same rate as in S, and then increases rapidly along CD. It then slowly approximates to proportionality with absorption in S, as shown by the line EF. Before the penetrating power of the K line is reached, the absorption in R becomes proportional to the absorption in S, as shown by the line GH. Again, when more penetrating rays than those of the K line 992 [header] are used, the absorption in R rises above that of proportionality with S, and then rises rapidly as shown by IJ, the character of the rest of the curve being similar to that obtained on the more penetrating side of the L line, the features, however, being more strongly marked. The similarity of the absorption curves may be mathematically expressed thus : — [formula redacted] That is, the coefficient of absorption of any X- radiation in any element R divided by the coefficient of absorption of the radiation characteristic of R in R itself is a function of the coefficient of absorption of that X-radiation in S divided by the coefficient of absorption of the radiation characteristic of R in S, — the characteristic radiations being of the series K. This function is independent — or, at any rate, approximately independent — of the absorbing substance R for all substances hitherto experimented upon. The relation between the absorption of a definite homogeneous X-radiation by various elements and the atomic weight of those absorbing elements has been indicated by one of us in a paper on " The Phenomena of X-ray Trans- mission '[citation redacted]. Observation of the similarity of the behaviour of all substances shows that it is possible to construct more accurately the curves showing the relation between these quantities. Thus if we plot absorption [formula redacted] of a certain homogeneous X-radiation — say. Ni radiation of series K — by various elements, and the atomic weight of those elements, we have insufficient data to determine the shape of the curve in many regions. But by alteration of the scales of ordinates and abscissæ in similar curves got from experiments on homogeneous X-radiations of neighbouring penetrating power, we can build up a more accurate curve showing the relation. There is a slight variation in form between the curves obtained from experiments on radiations widely different in penetrating power, for the ratio of the atomic weights of the elements giving radiations of the same penetrating power (one in series K, the other in series L) is not a constant for all penetrating powers. The curve shown in fig. 3 gives the relation between the absorption of Ni radiation (series K) by equal, masses of [header] 993 elements, and the atomic weight of these elements. The points obtained by experiments with the actual Ni-radiation are shown by crosses ( x ) and those by experiments on radiations of neighbouring penetrating power by circles (O). [figure redacted] Showing absorption of a homogeneous X-radiation by equal masses of various elements. The particular radiation used is characteristic of elements of atomic weight 61*3 and 160 approximately (series K and L respectively). For more penetrating radiations the maxima and minima are further to the right : for more absorbable radiations they are to the left. It may be observed that the absorption increases with the atomic weight of the absorbing substance, as long as the fluorescent X-radiations of the same series are intensely excited in the absorbing substance. When, however, the atomic weight of the absorbing element becomes so high and its fluorescent radiation of either series K or series L so penetrating that it is not excited (or is only slightly excited) by the radiation used, then the absorption suddenly drops. We thus get a general rise of absorption with atomic weight of the absorbing substance, with sudden drops within a much narrower region of atomic weights. The letters L, M, N, &c. indicate the spectral lines emitted under exposure to the particular radiation dealt with. These explain the rise and fall in the curve. Thus, the particular radiation used (Ni radiation of series K) is capable of exciting in elements of lower atomic weight than 61*3 the radiations of series K, L, M, &c. In elements of atomic weight from 61'3 to about 160, it excites radiations of series L, M, &c, but not of series K. Less energy of the particular primary radiation is thus absorbed than would have been the case if K radiation had been excited. Again, in elements of higher atomic [footer] 994 [header] weight than 160, neither the K nor the L radiation is excited, and again the absorption is less than what it would have been if these radiations had been excited. Similar curves may be obtained by using any homogeneous X-radiation, but if the radiation is of more penetrating type, all the maxima and minima are displaced to the right, and if more absorbable to the left. Absorption in Elements of Low Atomic Weight. The absorption by light elements is interesting, because when penetrating rays are transmitted through them by far the greater proportion of the radiation is merely scattered, and if surrounded by light elements rescattered. It has been shown by one of us that the energy of Röntgen radiation lost by scattering during transmission through a thickness dx of a light element is given by the expression [formula redacted] where s is a constant for rays of all penetrating powers, and is proportional simply to the density of the light scattering substance. Thus, if [formula redacted] is the mass-absorption coefficient, we may by analogy call the mass-scattering coefficient. This is constant for all matter made up of light atoms. The lightest elements absorb much less than heavier ones, mass for mass, so that [formula redacted] diminishes with the atomic weight of the absorbing element. It also diminishes as the penetrating power of the radiation increases. As [formula redacted] remains constant, [formula redacted] [formula redacted] (which is the fraction of the absorption coefficient [formula redacted] due to scattering) becomes great when penetrating rays are passed through light elements. Now, as the penetrating power of a radiation varies, the absorptions in any two substances remain approximately proportional, provided the range of penetrating power experimented upon does not include or approach on the more penetrating side the penetrating power of a fluorescent radiation characteristic of either A or B. If we may be allowed, for the sake of simplicity, to express this in the terms applied to light, it may be stated thus : — The absorptions of X-rays in two substances A and B bear an approximately constant ratio, one to the other over a range of wave-lengths not including a spectral line of either and not near to a spectral line of either on the side of shorter wave-lengths. As the scattering is independent of the wave-length, we should expect this law to cease to hold when the loss by scattering is an appreciable [header] 995 fraction of the total less. By experimenting on the absorption of radiations of high penetrating power by elements of low atomic weight, this may be tested. In Table II., column 2, are given the ratios of absorption in carbon to absorption in aluminium of various homogeneous X-radiations. The value rises from '1 to "4. If, however, the scattering coefficient - be subtracted from each absorption coefficient, as given in Table I., we find that the ratio of absorptions is again constant, as shown in column 3. [[formula redacted] has been previously shown to be *2.] Thus to obtain perfect generality in the absorption laws it is necessary to neglect (or subtract from the total absorption as defined above) the absorption due to scattering. This becomes the most important term in the absorption of penetrating radiations by light elements, something like 80 per cent, of Ba radiation (series K), for instance, being scattered by carbon. A larger proportion is, of course, scattered by elements of still lower atomic weight. Table II. Radiation : the fluorescent X-radiation, series K, from elements below'i Ratio of absorption in carbon to absorption in aluminium [absorption includes radiation scattered]. Ratio of absorption in carbon to absorption in aluminium [absorption does not include radiation scattered]. [table redacted] Absorption in Gases and Vapours. No systematic experiments have previously been made on the absorption of homogeneous beams of X-rays by gases. There appears, however, to be no doubt as to the generality of the absorption laws, whether applied to solids, liquids, or [footer] 996 [header] gases. The work of Benoist with heterogeneous beams showed that, and since his time hundreds of experiments have only shown that X-ray phenomena are independent of the physical state of the substance concerned. It is, however, necessary in many investigations to know the magnitude of the absorption of homogeneous X-radiations by substances which are usually in the gaseous state, and which were not dealt with by Barkla and Sadler. Experiments were made on the absorption by air at various pressures. The absorption was found to be proportional to the pressure within small errors of experiment. The absorption of the more penetrating rays was too small to be determined experimentally by the method used, but the absorption of the fluorescent radiations (series K) from copper and zinc were found as below. Knowing the absorption of the homogeneous radiations in aluminium and the absorption of these two particular radiations in air, by the law of proportionality of absorption (after elimination of that portion due to scattering) the absorption in air of many radiations was calculated [Sadler has experimentally determined X in air for As radiation. The agreement with the value given is very close.]. Thus, using the notation [formula redacted] as before, [formula redacted] is constant. In determining the absorption coefficients for any other gas, the ionization in an electroscope was observed first with air in the absorbing chamber in the path of the beam and subsequently with the particular gas in that absorbing chamber. Then [formula redacted] where [lambda] a and [lambda]g are the coefficients of absorption in air and in the gas, x the length of the path through the absorbing- gas, 1^ and I a the intensities as measured by the ionization after traversing the gas and air respectively. The only unknown was [lambda] g . In the experiments on vapours, the absorption by a mixture of air and vapour at known partial pressures was determined and a correction was subsequently made for the absorption by the air present. The results are given below (Table III.). The values given in italics were obtained by interpolation. From these results it may be observed that the laws of absorption are the same for gases as for solids : — The absorptions in two gases A and B bear an approximately constant ratio one to the other through a range of absorbability not including a spectral line of either A or B, and not approaching one of these spectral lines on the more penetrating side. [header] 997 Table III. — Absorption Coefficients (X) a Radiation : the homogeneous fluorescent radiation (series K) from elements below. [table redacted] As the rays absorbed become more penetrating (as measured by any substance whose spectral lines are far removed) than a spectral line of A or B, the absorption in that particular substance rises in the manner shown in fig. 1, and ultimately approximates to proportionality again for radiations far removed from the spectral line. It may be remarked, too, that the absorption in S0 2 is as much greater than in SH 2 as may be expected from the law that the total absorption is the sum of the atomic absorptions. From the most accurate experiments on the absorption by S0 2 and SH 2 it is evident that the absorption in oxygen is about 1*3 times that in air (neglecting the absorption due to scattering). The absorption by hydrogen is neglected. This result is interesting from the fact that the ionizations in the gases S0 2 and SH 2 are in the reverse order of magnitude [citation redacted]. Summary. Continuing the work of Barkla and Sadler, the absorption of radiations whose penetrating power is close to that of the spectral lines of the absorbing substances has been investigated in detail. The relation between the absorption in an element R and the absorption measured in a substance whose spectral lines are far removed is found to be practically identical for all substances experimented upon. One curve is drawn showing the relation for all substances. The relations in the neighbourhood of spectral lines of series K and series L are, however, widely different. The absorptions in various gases and vapours have been determined and the generality of the laws further verified.