“g‘fl'Q—w’fi-fla. —- . -—_ " ‘ __‘_—'_~_‘ I l l TIT IN I T 1 TM! l’l’l‘lll ‘ l’ 'u ., T U £393 THIN EMISSION OF THE OONTINOOOS X-RAY ENEROY TRON THIN ALONINON FOllS m THESIS FOR OERREE OF MASTER OF SCIENCE MICHTGAN STATE COLLEGE HOWARD RICHARD KELLY 1940 TlllIIHIIJIHIITIllUlillllllHllilllHlillHllllllllllTIHO 31293 01774 9601 r LIBRARY Michigan State Unlversity PLACE IN RETURN Box to remove this checkout from your record. to AVOID FINE return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE we compels-p14 EMISSION OF THE COHTIBUOUS X-RAX ENERGY FROM THIE ALUMINUM.FOILS by Howard Richard Kelly A Thesis Submitted to the Graduate School of Michigan State College of Agriculture and Applied Science in partial fulfilment of the requirements for the degree of MASTE R OF SC flilé CL‘ Department of Physics 1940 I wish to thank my associates in the Dapartment of Physics whose suggestions and assistance were freely extended when needed, and sepecially Dr. J.C. Clark, who suggested this problem and under whose guidance the re- search was carried out. 'MK/«wg _‘2_,3?4i4 0 CCNTLEIS l?tzg;£5 I. Introduction 1 A. History of problem II. Experimental Apparatus 4 A. The x-ray tube 1. Conditions to be satisfied 2. Description.cf tube B. High voltage power supply 1. Source of High voltage 2. Measurement of voltage and current 0. Measurement of intensity 1. Standard ionization chamber 2. Balanced foil method 3. Timing of eXposures D. arrangement of Apparatus III. Balancing of Ross Filters 11 IV. Use of Standard Ionization Chamber 14 A. Capacitance of elctrometer circuit B. Saturation current correction C . Flue re scence conne ct ion 7. Absorption Corrections 17 P £1.88 VI. Characteristics of Targets Used 19 A. Scattering and retardation B. Fooussing of cathode rays C. Effect of target backing VII. Results 22 A. Azimuthal curves B. Absolute values of emission intensity - C. Comparison with theory VIII. Bibliography 82 IETRODUCIICN One of the more difficult problems in x-rays that has interested physicists concerns the nature of the emission process which gives rise to the continuous x- ray Spectrum. An attempt was made to explain it on a classical basis in 1909 by Sommerfeld (1). He used Stokes' hypothesis, which assumes a rectilinear decele- ration of a cathode ray by the atoms of the target, and his predictions were unquestioned as to validity for a number of years. However, in 1928, experimental data published by Kulenkampff (2) showed Sommerfeld's theory to be incorrect, and the same paper pointed out why the rectilinear deceleration hypothesis was false. Immediately following the published eXperimental data by Kulenkampff, Sommerfeld worked out a new theory, based on the new wave mechanics (5). This still re- quired that the radiation arise from the deceleration of an electron, but allowed transverse components of acceleration, under which the electron could follow a hyperbolic path. Sommerfeld's theory has been extended by Scherzer (4) to allow for relativistic corrections, and Sauter (5) has deveIOped a wave mechanical rela- tivistic theory. Meanwhile, Kramers (6) worked out a theory using the Bohr correspondence principle. The development of these theories is still far from completion, and depends on having more eXperimental data to show which parts of the theory are correct and which parts need revision. This dependence on experi- ment was shown in the immediate reaction to Kulenkampff's work by Sommerfeld. The most important experimental data so far has been taken by Kulenkampff (2) and his asso- ciate thm (7) using thin foils of magnesium and aluminum as targets. In addition, Duane (8) made some measurements using a jet of mercury vapor as his target, Nicholas (9) used thin gold foils, and more recently, Thordarson (10), Corrigan and Cassen (11) and Van Atta (12) used thicker targets with considerably higher cathode ray accelerat- ing voltage. In all the work done by these men, the curves obtained from their data have been relative, so that comparison with theory has been carried out by ad- justment with one point on the curve and finding how the others compare with respect to it. No attempts have been made to obtain absolute intensities, so that the theories could be checked directly. It is therefore the purpose of the research described in this paper, to ob- tain some absolute measurements of intensity of x-rays in the continuous spectrum from thin targets, and to compare the measured data with theoretical values. Since the experimental results of Nicholas and Duane have been superceded by much better data, taken by Kulenkampff and thm (loc. cit.), only the later two will be considered here. The general procedure in all these experiments has been to obtain azimuthal intensity distribution curves as functions of x-ray tube voltage and wave length. Kulenkampff's method of obtaining iso- ohromats was to measure intensities with various thick- nesses of absorbing filters, and from the variation obtain the intensity due to a given wave length interval, and to estimate the mean wave length for this interval. thm used practically the same method for rays near the low wave length limit, but for a measurement at longer wave lengths, applied a method due to Ross.03)A cepper filter of appropriate thickness is transparent to rays near the low wave length limit for cOpper. An aluminum filter can be made to have the same tranSparency for the region of the short wave limit, but will absorb strongly in the neighborhood of the copper K-limit. The difference in the transmitted intensities for the two filters gave thm a measure of the intensity in a range just above the copper K-limit. Neither of the methods used by thm gives a well defined narrow wavelength band, the difficulty being that the intensity distribution of the measured x-ray, as a function of wave length is not uniform. A means of obtaining a narrower and more uniform interval, due to Ross (15), and more completely discussed by Kirk- patrick (14), was used for the measurements herewith reported. This method will be described later in this report. II. EXPERIMENTA APPARATUS A. The X-Ray Tube In order to find experimentally the intensity of x-rays as a function of cathode ray energy, direction of emission, and wave length, certain eXperimental con- ditions must be satisfied. In the first place, the cathode rays must be incident on the target with a de~ finite direction and energy. Second, the change of direction and retardation of the cathode rays in the target before the emission process takes place must be minimized. Third, provision must be made for measure- ment of intensity at various angles with respect to the direction of the cathode ray beam. These were satisfied by Kulenkampff I2) and thm (7) by collimation of cath- ode rays with circular apertures, the use of very thin aluminum or magnesium targets, and an ionization cham- ber (or geiger counter) that could be rotated about an axis through the x-ray target. The tube used in the research herein reported satisfies the same conditions in a somewhat different manner. The target is kept thin, like those of thm, but the collimation of cathode rays is accomplished by surrounding the hot cathode with a small steel disk to provide a uniform field between the cathode and target. The variation of azimuthal angle is made by rotating the entire x-ray tube support on a solidly mounted base. The tube is shown in horizontal cross section in Fig. I. Electrons are given off by the cathode C, and those which are not stOpped by the thin target T are collected by the anode A. The target and anode are the only parts of the entire x-ray tube at positive poten- tial, while the cathode and chamber wall are negative. Thus the cathode filament itself need only be insulated from the metal chamber wall for 12 volts, while the en- tire tube must be insulated from ground for the full tube voltage. The tube itself is a steel cylinder of which the entire top plate can be removed. The inside dimen- sions are a depth of 2.5 inches and a diameter of 8 inches. The target is not placed in the center of the cylinder, but removed one inch in the direction of the cathode fila- ment. On the center of the bottom plate is attached a 2 inch pyrex tube, leading to an oil diffusion pump for evacuation. The leads for the target and anode, which are 5/8 inch and 1/4 inch brass rods, enter through holes in the removable top plate through pyrex tubes of small- er dimensions. These leads are shown in a vertical cross section of the tube in.Fig. 2. The anode consists of an aluminum cup 1 1/2 inches long and one inch wide, out- side dimensions. The target and its brass rod support are attached to a brass plate at the top of the pyrex tube insulator, so they can be easily removed. The tar- gets are mounted on rectangular steel wire frames, one inch by 1 1/4 inches, an end of the wire being inserted 0 - 160° F13. 1 x-rqr Ezporimntul Tube «1 r» // \ \ ’ l i 1 .n "i \ / \ t ‘ \ ’ I ' ‘ // ‘ / l‘ / ‘ | I c | ’ \ ‘ // t \ / I I D / I . t / ‘ [\ \\ \\ \ \ 'I/ / T \ \ \ \ \ f \ \ \ .‘ \ \ I Fig. 2 x-m Experimental Tube in a hole in the end of the brass rod support and clamp— ed with a small set screw. The plane or the target can thus be turned at any angle with reapect to the cathode ray direction. The x-rays leave the tube through the window V. This is a horizontal slot in the tube wall, 3/4 inch wide, covered with an aluminum window .0056 cm. thick. Since the absorption coefficient of aluminum is low, this thickness does not seriously diminish the inten- sity of the beam for the wave lengths used. The x-ray tube is mounted firmly by means of 8 inch porcelain insulators on a steel frame which can be easily rotated about an axis through the aluminum foil target. This steel frame also supports the dif- fusion pump used to evacuate the chamber. Outside views of the x-ray tube, showing its general appear- ance and mounting or lfSllatOTS are shown in the photo- graphs in Fig. 38 and Fig. 3b. 5. The High Voltage Power Supply One important requirement for obtaining reliable data in this work is that there must be a supply of constant high voltage, which can be accurately measur- ed, and a means of controlling and measuring accu'ate- ly the space current in the x-ray tube. The high volt- age was obtained from a voltate doubler circuit, which uses two 120 kilovolt Kenotron rectifiers supplied by a 500 cycle 250 volt transformer. as. 30. km Experimental rubs 113. 31) km Experimental Tube The 500 cycle generator is driven by a 3.0. motor from a 115 volt storage battery, supplemented by a D.C. gen- erator. The capacity of the condensers used in the voltage doubler circuit are of such value that the sim- ple voltage amounts to only 20 volts per milliampere. The high voltage is regulated by a rheostat in series with the field coils of the 500 cycle generator. The voltage measurement was made with an electros- tatic voltmeter shown in.Fig. 4. This uses a bi-filar suSpension to eliminate inconstancy due to changing torsion constants, and the scale is about 540 cm. from the mirror on the suSpension. This allows a sensitiv- ity of about 20 volts /mm. in the neighborhood of 31 kilovolts. The voltmeter is calibrated with a Bragg Spectrometer and Coolidge x-ray tube by finding the low wave length limit correSponding to be given volt- meter scale reading. It would be impossible to measure accurately the small currents used here by merely inserting a meter in either lead of the circuit, since this meter would also record corona currents, which are usually much greater than the tube currents being used. To eliminate this trouble, the entire cathode filament system, including the leads, the 12 volt source, and the current controls are enclosed in an electrostatic shield at negative po- tential, the cathode system being insulated from the shield for at least 12 volts. Fig. 4 Electrostatic voltmeter The microammeter is inserted between the cathode current source and the shield, and thus measures only the actual epace current leaving the cathode in the tube. This cur- rent cannot go to the tube walls, since they are at nega- tive potential, so must be collected at the target and anode. The microammeter used is made by the Sensitive Research Instrument Corporation, model 3, number 12489, '7 amperes / scale and was used with a sensitivity of 10 division, so that the current of 10"6 amperes used in this work could be measured quite accurately. C. Measurement of Intensity Since the purpose of this research is to measure the absolute value of emission intensity, a known frac- tion of the x-ray beam had to be measured. For this purpose, a standard ionization chamber was designed and built, and is shown in two cross sectional diagrams in Fig. 5 as well as in a photograph in Fig. 6. The cham- ber consists of a brass cylinder with mica windows at the ends and collector plates of thin aluminum sheet, the chamber being filled with C Hg Br gas at about 68 cm. pressure. Since the x-ray tube could be rotated, the ionization chamber was permanently mounted. The x- ray beam entered through the mica window and produced ions inside the chamber. In order to eliminate the and effects of irregularity of field, the ion collector was divided into three parts. The central part was connect- ed to the electrometer and the two end portions were Fig. 5 Standard lamination Chamber Fig. 5 Ionization Chamber attached directly to the grounded (negative) chamber. The positive plate is much larger and nearly surrounds the collector electrode, to shield the x-ray beam path from the negatively charged chamber wall. The positive and negative collector supports are inserted through glass and amber insulation, respectively. It is also desirable to measure only the intensity in a narrow wave length band, so that the distribution curves obtained will be isochromats, or curves of con- stant wave length. It has already been pointed out that the absorption methods used by Kulenkampff and thm do not give a narrow wave length band of uniform intensity. A better method, described by Kirkpatrick (14), uses two absorbing filters of adjacent elements in the atomic table, whose thicknesses can be chosen such that the ab- sorption will be the same for both, except in the narrow interval between their respective K-absorption limits. By the proper choice of filter elements, one can obtain either a narrow or a wide wave length interval, over which the difference in transmitted intensities is quite uniform. The actual measurement of intensity is made by ob- serving the deflection of a Compton electrometer, which deflection is a function of the total charge collected from a known region in the ionization chamber during a given time interval. In order to have comparable read- ings, this eXposure time interval must be known. - lO - The exposure was controlled by a magnetic shutter, show- en in the photograph in Fig. 6, Operated through a relay system by a photoelectric cell in a pendulum clock. D. Arrangement of Apparatus The general arrangement of apparatus is shown in Fig. 7. The x-ray beam passes from the target through the aluminum window N of the tube and an aperture in the lead house in which the x-ray tube is located. The aperture in the lead house is Opened and closed by the magnetic shutter S. The balanced Hose filters F and a defining aperture A are between the shutter andv the ionization chamber. This defining aperture has an area of .86 square centineters, and is of such size and shape that the balanced filters and other apertures and windows are large enough to pass all possible rays from the focal Spot on the target through the defining aper- ture. The aperture A is immediately in front of the ionization chamber window and 54 cm. from the target of the x-ray tube. H lHJ Hr Fig. 7 General Arrangement of Apparatus III. BALANCIfiG F ROSS FILTERS In his discussion of noes filters, Kirkpatrick (14) shows not only that two such filters should have the same total absorption at all points outside the interval between their k-limits, but also that there is a pre- ferred thickness, with which the maximum intensity dif- ference will be obtained. This intensity difference is given by I 3 I. (ea/"Lt, c ‘fl‘tjnd I,AAbeing the total unfiltered intensity in the wave length band of A) width,/& the absorption coefficient of either element just above its Kelimityug the absorp- tion coefficient of the same element just below its K-limit, and t the thickness of the filter. The value of t that makes I a maximum is found by setting . ~fflnt —¢"sz aJ/I't' : IoA/‘EMLC “f/“JC J30 For this to be true, the quantity in brackets must be zero, so that .yfl‘t -yu{? /“1.e : /“:‘e setting €;?. 3 y' and taking logarithms, z ’flgt 1‘ /03 3" 'flst Then 1' 2 1%,}: and, factoring [‘4 from the denominator and again substituting r for fly/‘L one I obtains Kirkpatrick‘s eXpression: 1-111;— Mot ’ ”11”") [‘0 In order to have strictly monochromatic measure- ments, the K-absorption limits defining the wave length interval used should be very close together, but the intensity differences become quite small at the same time. It was decided that the wave length interval of about .021 Angstroms between the silver and cadmium K-limits would be most suitable, and these two elements were used as filters. Using values of/‘(:. and/4, for silver, as given in the appendix of Compton and Allison,(l1) the Optimum thickness for silver is found to be _ [-35' .n. 2‘3"” I fife/0.41.533? cm. = .0033 cm. = .0013 inches, the density/g of silver being taken as 10.6 gm./cm.3. The thickness of cadmium used must be such that just outside the wave length interval used the absorption is the same for both filters. This means that eiflA, 2‘" “/“CJ ZCJ :6 0" From this equation, E ’t 7.27/01» x.ool3 . ‘7- ‘, A3 . :1 w :: ,00/9’7 up. tq' We; ' /o.l.£ 2! K67 Films of the above thicknesses were obtained from Baker An] & 00., New JerseyAmounted‘in a brass holder, shown in the photograph in.Fig. 6. This was made to hold one filter perpendicular to the x-ray beam, while the other filter could be rotated about a vertical axis. Then any small inaccuracy in rolling the metal for the thin films could be compensated by changing the effective thickness of one film. When each film was tested rough- ly with the Bragg Spectrometer, it was found that the cadmium was not quite thick enough to balance the silver. By turning the cadmium through a small angle, a balance was obtained for which the absorption of the two films was the same for all wave lengths outside the band of wave lengths under consideration here from the low wave length limit up to about 0.75 Angstroms. For longer wave lengths, the transmitted intensities are quite small andzgs not important to have a perfect balance. It can therefore be safely assumed that the difference in trans- mitted intensities for silver and cadmium is due only to rays in the wave length interval between the K-limits of the two elements. :x.RAY5 V. I fl GE -L. :l :I c1___ "N mL. P 1—411 Fig. 8 Blootromtor calibration Circuit Iv. us}; or STMEDJLRD IOI-lIZATIOlE camera A. Capacitance of Electrometer circuit The application of a standard ionization chamber to absolute intensity measurements requires that one know the total charge 1 produced in the chamber during the time x-rays are allowed to enter. Assuming that all the ions produced are collected by the elctrometer circuit, the electrometer quadrants are raised to a potential V such that d 3 CB V, CB being the capacitance of the electrometer system and Q the total charge. To find the charge correSponding to a Specific electrometer deflection 81 it is then necessary to measure CE and the potential v1 necessary to produce a deflection $1. This accomplished by the circuit shown in diagram in Fig. 8. Since ballistic electrometer deflections were used for taking data, known voltages V1 were applied by means of the potentiometer P directly to the electrometer system to produce ballistic deflections in the range in which the instrument was used. Then a standard condenser 01, Specifically a Precision condenser of the General Radio 00., type 222, serial #660, was placed in series with the electrometer system and new voltages V1 applied to produce the same deflection 81. In Fig. 9, S is plot- ted as a function of VI and again as a function of V1. Using a well known relation for condensers in series, then for v1 and V1 corresponding to a particular deflec- r13. 9 Electrometor Calibration o tion ( or particular charge ), QE v1 = 01(V1 - v1). The value of 01 as used was 102 micro-microfarads, and for any deflection in the range utilized, the value of V1 - v1 was calculated from points on the graph to be v1 .415. This gives a value of 42.3 micro-microf- arads for the capacitance of the electrometer system, which capacitance is constant for the small deflections used here. The total charge collected can then be found by multiplying this by the prOper vlaue of VI from the graph. B. Saturation Current Corrections. so far it has been assumed that all the ions formed reached the collecting plates. Webster and Yeatman (15) have shown that the field intensity between the collect- or plates of the ionization chamber must be strong enough to sweep out all the ions before recombination occurs. For taking data, eight "B” bateries, supplying 373 volts, were used. As a test for the condition of saturation described by Nebster and Yeatman the curves in.Fig. 10 were made by chnging the voltage on the ionization chamber, with a constant source of x-rays at least three times as intense as any abtainel for the actual data, and constant exposure time. The trend of the curve in- dicates that the design of the ionization chamber is sufficiently good that practically complete saturation occurs at 373 volts, and that no correction is necessary. «mi ‘ t 913 Volts 150.... no; ' qo___ l J l 200 400 volts Fig. 10 Voltage Saturation Curve: C. Fluorscence Correction in the Standard Ionization Chamber When a beam of x-rays passes through the relatively heavy gas (CH5 Br) used as the absorber in the ionization chamber utilized in these experiments, two principal kinds of absorption occur. The first of these, and in our case negligible, is that due to scattering of the x-rays by the gas molecules. The second kind of absorption process is that due to the so-called photoelectric absorption. In this case x-rays interact with the highly bound elec- trons close to the nucleus of the gas atom, which elec- trons are ejected with energies equal to the difference between the energy of the incident quantum of of x-rays and their atomic binding energy. This difference in energy amounts to 13,100 electron volts for the bromine Keelectrons. Photoelectrons of this energy have a range less than 3 millimeters in CH5 Br at the pressure used here. However, the ejection of the Br. K-electron leaves the atom in an excited state, following which there may be an emission of a quantum of Br K radiation. The minimum amount of gas that this radiation must pass through before it reaches the collecting electrode is 3 centimeters, and in passing through this distance the intensity of this fluorescent radiation is reduced 82%. The actual computations required to arrive at this value are involved, and have already been made for a similar ionization chamber by J.C. Clarifies}- V. ABSORPTION CORRECTIONS It is necessary to know the fraction of the ori- . ginal intensity of x-rays at the target which is ab- sorbed in the useful part of the ionization chamber. Considering the general arrangement of apparatus shown in Fig. 7, and defining ID to be the original intensity at the target, 11 the intensity penetrating the x-ray tube window, I2 the intensity emerging from the Ross filter, 15 the intensity penetrating the mica window of the ionization chamber, I4 the intensity reaching the front end of the ion collecting electrode, and 15 the intensity leaving the other end of the same elec- trode. Then the fraction of the original intensity being absorbed in the useful region of the ionization chamber is given by 19 - 15 . This must be calculated for the silver filter and the cadmium filter for the mean wave length being used, and the difference will be the fraction of the original intensity in the wave length band being considered. This fraction pr0portion- al to the electrometer deflection obtained. If t1 is the thickness of the aluminum window of the x-ray tube, t2 the thickness of the silver or cad- mium filter, t3 the thickness of the mica window of the ionization chamber, 11 the distance from the mica window to the front end of the collecting electrode, 12 the length of the collecting electrode, one may write: -13- I _1_ e'FntTo j: . 6",“ T‘ ‘ 'flmiq t :1: = I, e ’ ’ 44,. 1. $7.13.: I Ir’l—‘Ie’flar a Where/u, is the linear absorption coefficient for the Ross filter being used. Combining these equations, the fraction of the original intensity reaching the front end of the collecting electrode is given by I .. e - (,«m t, +Mm. t. qua 1, «44,. r.) F... . The fraction of original intensity that passes the far —- I end of the collecting electrode 13 1": e Wu 2 "1 1 afl I ihe difference between these two fractions, I", (I- C 5" 7 will be the fraction of the original intensity absorbed in the section of ionization chamber containing the col- lecting electrode. - l9 - VI. CHARACTER OF TARGETS USED A. Scattering and Retardation. It is already been explained why it is necessary to use thin targets for these measurements. Kulen- kampff (2) used targets of commercial aluminum foil about 0.6 microns thick, and calculated the retardation of electrons in foils of this thickness from the Thom- son-Whiddington law. He also made measurements of the amount of scattering of the electrons in the same foils, and drew the conclusion that neither retardation nof' scattering was enough to influence his data appreciably. thm (7) made some measurements with several thicknesses at 31 kilovolts, and found that his experimental results were influenced considerably by changes in thickness from 0.15 microns to 0.6 microns, so he chose to use thicknesses of 0.1 micron or less, made by evaporating magnesium on thin celluloid films. The foils used in the research reported here were made by evaporating al- uminum on cellophane, and are approximately the same thickness as those used by thm. It is also interesting to note how the energy loss (retardation) compares at 0.1 micron and 0.6 microns. Using the Thomson~flhidding- ton law sz "f v: .. bat and using values of 9.7 x lOHfor b and 6 x 10"5 cm. for x, Kulenkampff obtained an energy loss of 3.2% at - go - an energy of El kilovolts. If one substitues l x 10‘5 for x, the energy loss becomes 0.45%, which is a very substantial reduction. B. Focussing of Cathode Rays It has been pointed out that the direction of the cathode rays between the filament and target of the x- ray tube should be well defined. For the design of tube used here, this means that the electric field bet- ween the target and cathode should be uniform so that no divergence of the cathode rays will occur. The hot filament used was a flat circular coil of tungsten, 5 millimeters in diameter, and upon examination of used targets, the focal Spot has plainly distinguishable, being oval, about 5 millimeters high and 8 millimeters long. On some targets which had been used only a short time, the outer portion of the focal spot showed a rough image of the corresponding part of the filament. From these observations, it has been concluded that the tar- gets used, aided by the disk about the cathode filament, produced a very uniform field, so that all the electrons were incident on the target in the same direction. A trial run with a target set at an angle of 45° to the cathode ray beam showed a distorted focal Spot being formed, so all actual measurements were made with the cathode rays incident perpendicularly on the target surface. 0. Effect of target backing One would not eXpect the cellophane, which was used as a base on which to evaporate aluminum, to con- tribute an appreciable amount to the x-ray intensity produced by the target. A trial measurement was made to test this assumption, by using a cellOphahe target without aduminum. A focal Spot was formed that coincid- ed almost eaactly with those on the aluminum targets, but the intensity of radiation emitted was about 2% of that obtained with aluminum. The difference in inten- sity when silver and cadmium filters were interchanged was too small to measure. (‘0 I3 VII. RESULTS A. Azimuthal Curves The data for azimuthal intensity distribution were taken as follows: The x-ray tube was run with a constant voltage of 51,700 volts and a constant cur- rent of one microampere, and for an orientation of the tube such that a line from the center of the focal spot through the ionizszt ion chamber made an angle 6 with the direction of the incident cathode rays, electrometer deflections were recorded for exposure times of 15 scoonds, first through the cadmium filter, then through the silver filter. This procedure was repeated at antular intervals of 10° frame = 30° to 9- 150°. The data for a typical run are given in table I, and these points plotted in polar coordinates in.Pig. 11. An azimuthal distribution curve is drawn through these points, which compares fav- VI orably with curves given by Bohmfl) Points from this and subsequent data show Some variation from this curve due to the error in measurement of such small differences. The curve as it is drawn is determined by weighted aver- ges of all the data recorded here, the weighting being determined by the steadiness of tube voltage and cur- rent at the time the observation in question was made. The value of 9 for the maximum intensity appears at 570 on the curve, while hghm's maximum value apnears at 550 o ble I b cadmium S silver difference 9 (mm) (mm) (mm) 50° 110.2 101.8 8.4 40° 118.0 108.0 10.0 50° 120.1 108.9 11.2 600 119.6 108.1 11.5 70° 115.0 102.7 10.5 80° 101.0 92.1 8.9 100° 76.1 70.1 6.0 110° 70.8 65.7 5.5 *1200 57.1 55.1 2.0 1500 50.9 47.1 5.8 140° 45.2 41.5 1.7 *150° 57.9 54.9 5.0 *Current not very steady Table II. 8 cadmium 8 silver difference 9 (mm) (mm) (mm) 145° 40.1 58.8 1.5 1550 46.1 42.2 5.9 125° 55.2 50.4 2.8 115° 65.9 58.0 5.9 105° 72.1 65.8 6.5 75° 105.8 95.0 8.8 F 65° 111.1 102.0 9.1 a 55° 114.1 106.0 8.1 45° 115.8 105.9 7.9 “‘ voltage not steady Table 2 lists some deflections observed at angles half way between those used for Table I. It will be noticed that no fifiues of 9 are used nearer than 10° to the 90° direction. Observations made edgewise along the target are found to be quite inconsistent, probably partly due to absorption in the wire frame holding the target and to the very much increased apparent thick- ness of aluminum in this direction. The observations recorded in table 3 were repeated at each angle used to average out errors in measurement. Table III 8 Cadmium S silVer diffs rence average 9 (mm) (mm) (mm) for 0 50° 106.2 97.5 8.7 106.9 98.1 8.8 8.75 40° 111.9 102.6 9.5 112.2 102.0 10.4 111.9 102.4 9.5 9.66 50° 115.9 104.0 9.9 115.0 104.5 10.5 10.2 60° 112.0 101.5 10.5 112.1 101.0 12.0 115.5 101.1 12.2 1. 11.45 70° 104.9 98.0 6.9 104.9 96.8 8.1 7.5 80° 95.4 86.9 8.5 98.1 88.1 10.0 95.1 88.6 7.5 8.6 100° 75.0 69.0 6.0 75.0 68.7 6.5 6.15 110° 65.8 60.5 5.5 65.5 61.0 4.5 4.8 120° 56.0 55.0 5.0 56.0 52.0 4.0 5.5 150° 50.2 46.5 5.9 11 50.1 45.0 4.1 4.0 B. Absolute values of emission intensity It has been shown in section V that the fraction of the original intensity in the wave length interval being studied which leaves the target in the solid angle subtended by the lead defining aperture, and which is absorbed in the region of the collecting electrode, is given by (I c’f‘u L.) (e “‘44! ‘1 */‘P 1'- ‘j‘mat; 4 fly... 3.} The I‘lpand t2 apply to the particular Boss filter being used, If one calculates the fraction for each filter and take the difference, one obtains the ratio of the radiation absorbed to produce the difference in de- flections observed on the electrometer to the original intensity mentioned above. Calling this ratio R, we have ,fl.‘ j, [6'01” t, *f‘I-«a, 3: 47‘5“! “37?) R = o 90(l ”e ..(Vfl.lth‘i/Kuuiathlivptflnl' f/hcdftcé) E . In this equation the constant .90 is that due to the unabsorbed fluorescent radiation produced within the standard ionization chamber a detailed discussion of this absorption correction is given by J.C. Clark?” Since our objective is to find the number of x- ray quanta of mean wave length .474 A0 produced, the electrometer deflection differences must be interpret- ed. A calculation has been carried out for 0 = 60° - 5‘47 - using an average value of 11.45 millimeters for the deflection difference. in section (IV a), the capa- citance of the electrometer system was shown to be 42.5 micro-microfarads. The curve of deflection as a function of applied voltage is a straight line, so a given difference in deflections will represent the same difference in potential at any deflection in the range used. The deflection difference of 11.45 milli- meters is found to correspond to a potential difference of .0108 volts. Solving ior the charge from the re- lation ‘ AQ" C AV and dividing by the eXposure time of 15 seconds, the charge collected per second is 3.05 x 10-14 coulombs /sec.: one uses the relations: Charge associated with one ion pair (one electron): 1.8 x 10.19 coulombs. Energy of one quantum (.474 Angstroms)= 26,150 electron volts. Energy required to produce ion pair = 25.4 electron volts. The value of 25.4 electron volts of energy for each ion pair formed is the same as was used recently by J.C Clark (18). Using these relations, one obtains the result that 3.05 x 10‘14 coulombs/sec. = 188.5 quanta /sec. equ. (2). The solid angle subtended by the defining aperture 2 of .86 cm . at a distance of 34 cm. from the target is .86 O = .00074 Spherical radians or .000059 of a 34 “ sphere. The number of electrons per second incident on the target with the current of one microampere is 1 X 10"6 COUlODbS/SGCO 2 6.25 x 1012 electrons/sec. 1.6 x lO'lgooulombs/electron To determine the number of atoms present in a square centimeter of target foil, it is necessary to know the thickness of the target or the mass/0mg. A section of foil was weighed by Prof. E. Leininger with the aid of a micro-balance, and 51.1 cm2. of foil contained 1.96 milligrams of aluminum. This correSponds to a thick- ness of 1.4 x 10"5 cm. The number of atoms/cmgis given by 8': .39 0 as where H is avogadgo's number, m the mass of an area A, and u the atomic weight. Then n = 6.06 x 1033 x 1.96 x 10’3 = 8.65 x 1017 atom 51.1 x 28.97 6557' To evaluate equation (1), it is necessary to know the absorption coefficient of CH5 Br, designated as in equation (1), was measured with a Bragg Spectrometer at the pressure of 88.3 cm. Hg. used and found to be .0782. The other absorption coefficients were obtained from Compton and Allison (17) and are as follows at .474 angstroms. .. 29.. 1.70 X 2.7 2 4.6 cm'1 81 ‘/(é:ea #98 [Aficd The thicknesses of absorbers are 4.658 cm'1 58.7 x 10.6: 623 cm'1 9.34 x 8.67: 81.0 cm‘1 t1 : .0056 cm. tag = .0055 cm. ted = .0057 cm. 11: 7.8 cm. 12 = 10.0 cm. t3 3 .0045 cm. Then lflLal t1 2 .0256 lumica t3 = .020 /ucd tcd 3 .300 flBr 11 = .610 /MBr l2 3 .782 Equation.(1) then becomes (e “0956 - e -20713) .9 (1 -€.457) (£.38.3 - .066) .156 .9 (1-e -0783) R Then since R is the measured fraction of the total number of quanta emitted in the solid angle used, the number of quanta per sec. in this solid angle is 188.5 - 1208 quanta per seconds 050 This value, 1208, represents the number of quanta in the wave length bandA A =.O215 A0 of mean wave length 474. 0A° emitted per-second by an aluminum foil target of thickness 1.4 x 10"5 cm, in a solid angle of .000744 Spherical radians at an angle of 60° with reSpect to the direction of the incident cathode ray beam. With the azimuthal distribution curve plotted in Fig. 11, a dotted curve is added which represents Scherzer's theoretical results as plotted by thm (7). The azimuthal distribution curve obtained here agrees quite well with the theoretical curve when the two are normalized to be identical at 6 2 90°. The agreement is not as good at small and large angles, where the in- tensity differences measured are small, and the error correspondingly larger. Owing to the laborious numerical calculations in- volved in evaluating Scherzer's theory, a direct quan- tities comparison with this theory has not as yet been carried out for the absolute value 0f continuous x-ray energy. l. 2. 3. 4. 6. 7. 8. 9. 10. ll. 12. - 31- BIBLIOGRAEHY Sommerfeld, 2., Phys.2tschr 10, 969 (1909) 1‘ r! n Kulenkampfr, H., Untersuchungen uber Roentgenbrem- " strahlung von dunnen Aluminum.Polien. Annalen der Physik 87, 597 (1928) v! Sommerfeld, A., Uber die Beugung und Bremsung der Electronen. Annalen der Physik 11, 257 (1931) Scherzer, 0., fiber die Ausstrahlung bei der Bremsung von Protonen und schneller Electronen. Annalen der Physik (5) 13, 157 (1932) Sauter, F. Uber die Bremstrahlung schneller Electronen Annalen der Physik 20, 407 (1954) Kramers, H. A., 2511. nag. 46, 856 (1923) thm, K. Untersuchungen uber die Azimutale Intensi: tatsverteilung der Beetgenbremstrahlung: Annalen der Physik (5) 55, 315 (1958) Duane, W. Proo. Nat. Acad. Amer. 15, 662 (1927) and 14, 450 (1928) Nicholas, W.W. Bur. of Std. Jour. of Res. 2, 857 (1929) Thordarson, S. Annalen der Physik (5) 55, 135 (1939) Corrigan, K45. and Benedict Cassen. Spatial Dis- tribution of Radiation from a Supervoltage Roentge§ tube and its Significance in Therapy. Amer. Jour. of Roentgenology and Radium Therapy. 55, 811 (1957) Van Atta, L.C. and D.L. Horthrup Measurements of Roentgen-Bay Production in the Range 0.8 to 2.0 15. 14. 17. CG Million Volts. Amer. Jour. of Roent. and Radium Ther- apy 41, 655 (1959) Rose, P.A. JOSA 16, 453 (1928) Kirkpatrick, P. One the Theory and Use of Ross Filters Review of Scientific Instruments 10, 186 (1959) Webster, P.L. and R.H.'Yeatman J.0.S.n. 17, 254 (1928) Clark, J.C. A measurement of the Absolute Probabilitx of KAElectron Ionization of Silver by Cathode Bays. Physical Review 48, 50 (1955) Compton, A.H. and S.K. Allison. X-rays in Theory and Experiment 2nd ed. (1956) MICHIGAN STQTE UNIV. LIBRQRIES \Illlllllll111111111111Illl||||||111111111111 31293017749601