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CONTINUOUS X-RAY INTENSITY
FROM ALUMINUM TARGETS AS A
FUNCTION OF ELECTRON ENERGY

Thesis for the Degree of M. S.
MICHIGAN STATE COLLEGE

Andre Francois Reno

194!

 

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To AVOID FINES return on or before date due.
MAY BE W with earner due date If requested.

DATE DUE m DATE DUE I

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CONTINUOUS X—ERY INTELSITY FROM
ALUMINUM TARGETS £8 A FUECTION

OF ELECTTON EKELGY

by

Andre Francois Reno

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

MASTER OF SCIENCE

Department of Physics

1941

ACKNOVLEDGKENT

Tn: writer wishes to express his sincere
thanks to Lr. J. C. Clerk for suggesting the
problem and for his aid; and also to Professor
C. V. Chapmen for extending the facilities of

the Physics Department.

I.
II.

III.

IV

CONTENTS

Introduction

Historical Discussion of Theories and
Experiments Concerning the Continuous X-hay
Spectrum.

Theoretical Equations due to Sauter, and
Their Svaluation for Conditions of this
EXperiment.

A. Theoretical Equations.

B. Quantities Used in Computation.

C. Computations for Bombarding Electron
Energies of 50, 40, 5U, 60, and 80 KEV.

EXperimental Apparatus.

a. General Discussion of Baperimental
Conditions to be Satisfied.

B. Production of the x-Rays.
1. High Voltage Source
2. The X-Ray Tube
3. The Thin Film Targets
4. Ross' Balanced Filters
5. Standard Ionization Chamber

C. Electrostatic Capacity of Electrometer
Circuit.

The Working Equation Used to Reduce the
EXperimental Data.

A. Fraction of X-Rays Measured to Those
Produced.

B. Absolute Intensity Formula.

N)

12

14

14
l6
17
18
18

19'

24

24

VI.

VII.

IX.

MDLEURTMSNTS
A. Target Thicknesses
B. Absolute X-Ray Intensities Tabulated.

Comparison with Theory.
A. Intensity — Electron energy curves.

B. Discussion of Results.

Bibliography.

I. INTRODUCTION

The study of radiation resulting when fast moving
electrons strike matter has provided the physicist with
invaluable data from which basic laws governing atomic
collision phenomena have been deduced. Moreover, from
a theoretical standpoint, the underlying phenomena of
nature have often been most easily predicted from a
consideration of energy relations between impinging
electrons and resultant radiation. As measurements
became more refined, theories based upon classical
macroscopic mechanics were seen to be rough approximations
only. The advent of the new mechanics enabled the
theorist to give a more exact picture of the workings of
nature. Hewever, due to the difficulties of the mathe-
matics involved, approximations had to be employed,the
validity of which could be determined only by comparison
with experimental results.

The intensity of the continuous x-ray radiation
produced by an electron colliding with a nucleus is a
function of several factors. These may briefLw}:1ated as
that due to azimuthal angle of observation with respect to
the direction of the cathode ray beam, the energy of the
bombarding cathode rays, the atomic number of the bombarded
atom, and the wave length of the emitted radiation. The
investigation was undertaken to experimentally determine
the absolute intensity of the continuous radiation of

wave length 474 XU as a function of bombarding electron

energy, and to compare this data with the results

predicted by the most recent theory of this problem.

II.
Historical Discussion of Theories and Experiments Concerning

the Continuous X-ray Spectrum

As early as 1898, Stokes and Thompson (1) proposed
an explanation of the continuous radiation process as
irregular electromagnetic pulses due to acceleration of
the bombarding cathode rays by the atoms of the target.
Sommerfeld.(2) in 1909, using classical electromagnetic
theory, presented a more complete explanation of this
phenomena. It w as not until 1928 that reliable experi-
mental data on the intensity of emission of the continuous
x—rays were made available by Kulenkampff (3). In these
results the earlier theories were shown to be in error,
principally as regards the spatial distribution of the
emitted x-ray energy. In the meantime Kramers, utilizing
early quantum mechanics principles, presented a theory
which compared favorably with data of Nicholas (5),
particularly as regards the short wave length limit. The
theory failed to predict Kulenkampff's results of azimuthal
distribution however.

With the development of the wave mechanics, Sommer-
feld,(6) in 1931 developed a theory in which he represented

'an electron by its rigorous eigenfunction. The treatment

was nonrelativistic. Because of this and other necessary

-3-

restrictions imposed in order to obtain a solution of
the problem, results were obtained wnich differed con~
siderably with.Kulenkampff's experiments.

Scherzer (7) in 195%.using a relativistic treatment
of the wave mechanics and employing Dirac wave functions,
calculated the intensity distribution at the short wave
length limit. Since the short wave length limit
restriction reduces the usefulness of the theory and
because a more recent work by Sauter (8) is more
inclusive, no attempt has been made in this thesis to
make a comparison of experimental results with Scherzer's
theory. .

Sauter's first paper (8), dealing with this subject,
employed a wave mechanical treatment, simplified by repre-
senting the retarded electron as a modified plane wave.
That is, he employed Born approximations which are valid
only when the initial kinetic energy of the incident
electron is much greater than the energy required for K
shell ionization. The wave function is considered in
such a manner that the wave is plane at infinity; when
actually, the wave front is affected by the nucleus at
infinity.

Sauter's second paper (9) is a relativistic treatment
of the problem. In this deveIOpment, he obtains a
formula for the resultant continuous x-ray energy, which,
to date, furnishes the most complete results of theory

with.which to make exp rimental comparisons. The

-4-

resultant expression for the energy, Jhdv, of a particular
frequency in the frequency range d9, stated as equation
11 in his paper (9), is reproduced in this thesis as
equation 1 below. If p0 and p represent the initial
and final momentum of the bombarding electron and mc2
the rest mass energy of the electron, then the non-
relativistic approximation is valid when p0, p<¢<.m02.
Upon making this approximation, equation 1 simplifies
to the earlier expression he obtained in the non-
relativistic treatment (8) of this problem.

Sauter's nonrelativistic approximation differs from
Sommerfeld's equation by only a frequency dependent, not
a direction dependent, factor. This factor is approxi-
mately unity except at the short wave length limit where
Born's approximation is no longer valid. Now, by multi-
plying the nonrelativistic approximation by this frequency
dependent factor, Sommerfeld's corresponding rigorously
valid equation is obtained. Sauter's results also agree
with those of Scherzer to within the same frequency
dependent factor. In view of these considerations,
Sauter assumes that the relativistic equation 1, multi-
plied by the correction factor, given as formula 15 of
his paper.(9x and as formula 2 below, results in a valid
approximation for the entire spectral range. It is this

resulting equation 1, multiplied by the correction factor,_

formula 2, which is used for theoretical computations in

-5-

this thesis.

Due to the mathematical difficulties, all of the
theories have been develOped on the basis of the retarda-
tion of one electron by an isolated nucleus, without
taking account of the screening action of the external
electrons.

Recent experimental data have been obtained by H.

R. Kelly (10) for absolute intensities of the continuous
x-ray radiation from thin aluminum targets as a function
of azimuthal angle, using a bombarding electron energy
of 51.7 kev. This data was normalized at the azimuthal
angle of 900 to coincide with the relative intensities
as plotted by thm (ll) from Scherzer's equation. The
agreement is quite good, the maximum intensity from
Kelly's data falling at 9 3 57°, while the maximum as
calculated by thm occurs at O = 55°. The agreement is
not as good at large and small values of 9 where the
intensity of radiation is much smaller and the consequent
errors of observation greater.

Clark and Kelly (12) report absolute intensity
measurements of wave length 474 XU from thin aluminum
targets, using the bombarding electron energy of 51.7 kev.
Their results are greater than those predicted by Sauter's
theory.

Smick and Kirkpatrick (15) report measurements of

absolute intensities from Nickel targets, bombarded with

-6-

electrons of 15 kev energy, of a wave length 1.451 g

and an azimuthal angle of 88°. Their results are in
agreement with Sauter's theory after it has been slightly
modified to more fully approximate the conditions of the
eXperiment.

Harworth.and Kirkpatrick (l4) announce relative
intensity measurements of the continuous spectrum from
Nickel targets bombarded with electrons of energy 10 to
180 kev. The authors state only partial agreement with
theory. The results are given in abStract form; and at
this time no discussion can be made of the nature of the

discrepancies between data and theory.

III.
Theoretical Equations due to Sauter and their Evaluation

for Conditions of this Experiment

A. Theoretical Equations:

The follOWing three equations given by Sauter (9)
as formulas ll, 15, and 14 respectively,are those which
are evaluated for the conditions of this experiment.
Henceforth in this report they will be referred to as

formulas 1, 2, and 5.

04d»

-7-

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The following formula 2 is what Sauter designates as the
"Correction Factor" which.must be applied to equation 1
to obtain the "Corrected" formula 5, valid in the whole

Spectral range.

 

(ZflaZf
leaf
Cea%¥1- .-_£%;%7 z
/ e

The f inal equation used for computations of Sauter's

theory is given in the final equation 5, which is
znwz

corn 7- 31 v 7'7—
JJ ”/11 JJv(c‘z‘3.1z-z)(/-e~$‘z) 3

The quantity'(J;dv) corrected gives the energy per

 

unit area, per electron, per second, per atom, per unit
area of target, where observations are made at a distance
R f rom the target and at an azimuthal angle of 9.

The quantities entering these equations are as follows:

Planck's constant

Charge on electron

rest mass of electron

velocity of light

distance of defining aperture from the x-ray
target.

woamp‘
Illlutl

-8—

Atomic number of bombarded nucleus.

Initial Total Energy of bombarding electron.
Total energy of electron after collision.
Initial momentum of bombarding electron.
Momentum of electron after collision.
Momentum of quantum.

Angle at which quantum is emitted with respect
to incident electron direction.

Ratio of velocity of incident electron to the
velocity of light.

Ratio of velocity of electron after collision
to that of light. .

“0|:lele
O
NH

0

an (DQ’U
u

‘m
H

U : 30(1 —flocos 9)
(Y : 21ze2 = the fine structure constant.
hc ’

‘Beferring to the following vector diagram representing
the momenta and energies of the type of collision con-

sidered here,

Jr: 9
RI

 

it is seen that the momentum §>of the incident electron is
p0 :54’54'?

Transposing:

B-fi-P: Bo-q

Sauter defines the quantity Po as

2 __ __
Po : (p + P)2 5 (p0 - q)2

-9-

which by the vector diagram is

2 q a - 2Qgcos 9 ‘

'13
ll
*(3
O
4.

Sauter neglects the energy aecuired by the nucleus during
the collision process, so that

E 2 E0 - hi).
The initial energy is obtained from the relation:
so - (KE)O 4 mc2 .
Using the relativistic kinetic energy, total energy is
given by

E s mcz [(l-ffi‘gfé - l] + mc2.
Thus fl and A may be solved for, using the initial
and final total energies.

/g 2 : l _ m2 4

E
The momenta of the electron before and after collision
may be evaluated from the expressions involving their
total energies.

p : mv (l -/92)-% where v g/gc.
Utilizing the value of ,3 2 above,
p2 : EZ/cz - m2c2
Likewise
p02: Bog/cz- mzcg
B. Quantities Used in the Computations

To evaluate the expressions 1 and 2, the values of the

physical constants e, m, and h used were those given by

DuMond (15), and are:

-10..

-28

m = 9.1l780 x 10 gm
—10

e = 4.80650 x 10 esu
-27

h = 6.65428 x 10 erg—sec.

c 2 2.99776 cm/sec.

Other quantities entering into the calculations are as

follows:
Z : 15 for Aluminum
R a 54.0 cm = distance of defining aperture from
* target.
9 ; 6OO : Azimuthal angle of observation.

The wave lengths of the K absorption limits of Cd and of
Ag which were used were taken from the tables given by
Compton and Allison (16). These are

Ace“ limit) = 465.15 XU

AAg(K limit) _ 484.48 XU ,‘

From these we get
18 -l
6.4728 x 10 sec

#Cd (K limit)

18 -l
‘6.1876 x 10 sec

V Ag (K limit) .
The constant factors which enter equations 1 and 2 have been
calculated on the basis of the above constants. They are

as follow 5:

Mean frequency between absorption limits of the Ross

balanced foils.

-11-

18 -1
1’ = 'flbd _ pkg = 6.5502 x 10 sec
2
17 .-1
AV: UCd __ IJAg = 2.85244 x 10 sec
-8
h U = 4.19965 x 10 ergs
—l2
14y = 1.60556 x 10 ergs
-18
q = th 31.40092x10 gmgg
c sec

and the expression which.we arbitrarily place equal to A,
6 2 -71
A = 2e Z = 5.81752 x.10
2 5
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-14-
IV. Experimental Apparatus

A. General Discussion _£_Experimental Conditions to be
Satisfied:

 

The theory with.which the experimental results of
this work are to be compared concerns the collision
process between a bombarding electron of known total energy
and an isolated atom; which process may result in the
emission of a quantum of continuous x-ray energy of
Specified frequency at a definite azimuthal angle. The
energy of the bombarding electron must be controlled, and
the number of these electrons colliding with a nucleus
per unit target area should be kept as small as possible
and yet be accurately determined. These two requirements
are fulfilled by controlling the x—ray tube voltage and
current closely. The next important item is to have as
few atoms per unit area of the target as feasible and still
determine their number. This involves using a very thin
target (of Aluminum in this case) and knowing its thickness.
As implied above, it is also necessary to make measure-
ments on a known frequency range of quanta emitted at a
known azimuthal angle; both of which are fulfilled in
this experiment. Finally, the number of quanta produced
per unit of time under the given conditions must be
measured. The procedure involved in determining all of
these factors is treated below.
B. Production g£_§73§1_.

l. The High Voltage Source:

The power supply used in this work has been described

-15-
by Pettitt (17). It consists of a voltage doubler
circuit employing two “Kenotron” rectifier tubes, an
electrostatic voltmeten and a special circuit and
equipment used for controlling and measuring the emission
of electrons in the x-ray tube. The voltage doubler
circuit uses a 500 cycle source of power, and the
electrical constants of the circuit are such that the
ripple voltage is approximately 20 volts per milli—
ampere. The calibration of the electrostatic voltmeter
is accomplished by short wave length limit measurements
made with the Bragg spectrometer. A schematic overall
diagram of the apparatus is shown in figure 1.

In order to read the very small current used in the
x-ray tube (of the order of 0.1 microampere), it is
necessary that the entire cathode system,from the point
where the current is measured,be electrostatically
shielded so that no corona currents interfere with the
measurement. The microammeter is connected between the
shield and cathode current source and must read the actual
Space current in the tube. The instrument used for
measuring the current is a General Electric reflecting
type galvanometer, number 52C, 25661. It has a current
sensitivity of .008f1a. per division, and is critically
damped with an external resistance of 46,000 ohms. The
instrument was shunted so as to have a sensitivity of

0.01 microampere per division.

  

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-16—
2. The X-Raerube

 

"‘"s

The tube shown diagramatically in figure a is made
of a steel cylinder 2% inches deep, 8 inch diameter. The
top plate is removable. A two inch diameter pyrex glass
tube leads from the center of the bottom plate to the
oil diffusion pump. A spiral tungsten cathode is mounted
by the wall of the tube. At the opposite end of the
diameter passing through the cathode is mounted the
aluminum anode cup of 1% inch diameter. Focusing of the
electron beam is accomplished by a small steel disk placed
behind the cathode. The aluminum anode is mounted on a
brass rod which extends upward in a pyrex tube of 2}
inch diameter and is fastened to a brass cap at the tube's
top. The targets are placed one inch off center in the
direction of the cathode. The thin film targets are
mounted on a rectangular steel wire frame, 1 inch by 1}
inches. This frame fastens in a brass rod which extends
upward in a pyrex tube of 1% inch diameter and fastens to
a removable brass plate at the top of the pyrex tube.

The anode and target are thus well insulated from the
metal tank of the tube which is at the same potential as
the cathode. The only positive potentials in the tube
are on the target and anode, assuring that all space
current is actually collected at these points. The tube
must then be insulated from ground for one-half the tube
voltage. A horizontal slot three-fourths inch.wide is
cut in the tube wall and covered with an aluminum window

of .0195 cm. thickness. The entire tube may be rotated

 

A noJe

A

rec-’0’
Cc Ifiole

K

 

{Acfucl 51'}.

f7, 3

-17-

about an axis through the target, thus enabling
azimuthal determinations of intensity to be made.

5. Thin Film Targets

 

The theory deals with radiation resulting from the
retardation of a single electron by an isolated nucleus.
This, of course, is not possible to obtain experimentally;
nor would the intensity be perceptible were the condition
obtainable. In order to fulfill this condition as well
as to eliminate the possibility of the electron losing
energy by minor collisions before the major retardation
occurs, it is requisite that the target be as thin as
possible concomitant with a reasonable intensity. A
typical target is given in figure 3, showing the well
defined focal spot. Not only does the small cathode
current of 0.15 microampere increase the life of a
target; but also, the theoretical conditions are, thereby,
more closely approximated.

‘The target backing is commercial cellOphane, cleaned
with alcohol. Measurements with cellophane targets alone
in the tube showed no measurable intensity from them.
Thus no correction has been applied to the backing
material. The aluminum is evaporated on the targets in
a specially constructed evaporation chamber. Four
targets, along with a Michelson interferometer mirror,
were mounted in the evaporation chamber and coated
simultaneously. The mirror was then used to measure the

target thickness, a subject treated separately below.

Fx, 3

 

A /um inu m nryef

-18-
4. Ross' Balanced Filters

 

To isolate a narrow region dIIOf the continuous
x—ray spectrum, a method devised by Ross and discuss-d
by Kirkpatrick (18) is employed. This method uses two
adjacent elements in the atomic table. The filter
thicknesses are such.tlet their absorptions are the same-
for the x-ray radiation, except in the narrow band
between their K absorption limits. By interposing first
one filter and then the other in the path of the X-ray
beam, the intensity of radiation within this band that
is measured, .iS _ proportional to the difference in
magnitudes of the galvanometer deflections for the
respective filters. The narrower the band between the
K absorption limits, the more strictly monochromatic
will be the measurements. However, the band width must
be sufficient to produce measurable differences in
intensity. '

The discussion of Ross filters by Kirkpatrick (18)
shows that there is a preferred thickness for which
the maximum intensity difference will be obtained from
the filters. The filters used are of Cd and Ag and the
values of thickness are worked out by H. R. Kelly (10).
This allows a band 21.55 XU wide at the mean wave length
of 475.80 XU.

5. Standard Ionization Chamber

The x-rays pass through a defining lead aperture of
0.9fiicm2 cross section into the standard ionization
chamber. The cylindrical chamber is of brass with.mica

windows at either end. The collector plates are of

-19-
aluminum. Guard rings assure a uniform electric field
over the collector plate wnere ions are collected for
measurement. The chamber is filled with CH3Br gas at
68 cm pressure. The absorption of x—rays within the chamber
takes place principally by photoelectric absorption.

In the photoelectric absorption process, the
quanta interact with the bromine atom, ejecting an electron
from one of its shells. The energy used in ejecting an
electron from a carbon atom is negligibly small compared
with the energy required for the bromine atom. The ions
formed in the electric field are then drawn over to the
collector electrodes, which charge is transmitted to the
electrometer.

C. Electrostatic Capacity g§_Electrometer Circuit

 

In order to convert electrometer deflections to the
correSponding voltage on the collector plates of the
ionization chamber and thence to units of charge, it is
necessary to know the capacitance of the electrometer
system. The circuit for determining this capacitance
is given in figure 4 below.

2272‘!
'. l

r

 

 

 

 

l
| C

 

 

 

 

 

 

 

 

r 11)“—
| LL ‘

370v #—

TJ'H‘ F -+—

 

-20-
C 2 Capacity of Electrometer System.
K = Capacity of Standard Condenser.

v - Volts applied directly on quadrants
of electrometer.

V Volts applied to standard condenser.

When the charge collected in the ionization chamber
is Q, the potential v, transmitted to the electrometer
quadrants is given by
Q 2 CV

This potential gives the electrometer a definite deflection
8 . By applying known voltages direct to the electrometer
circuit, and noting the corresponding readings of the
instrument, curves relating electrometer deflections to
applied voltage may be drawn. Then all that is required

to determine the charge collected, causing a given
electrometer deflection, is the capacity C of.the
electrometer circuit. For the particular instrument used,
the relationship of voltage to electrometer deflection was
a straight line. In determining the capacitance of the
system, known voltages were applied to a standard condenser
(General Radio Co. type 222, serial 660) placed in series
with the electrometer circuit, and the deflection of the
instrument recorded. This data gave a straight line
relating electrometer deflection to applied voltage with

a known capacitance in series with the electrometer
Circuit's unknown capacitance. If now a voltage, v,
applied directly to the electrometer circuit gives a

deflection¢5, then, as we noted, the charge on the

electrometer is given by

Q 2 CV 4

And if a voltage, V, applied to the standard condenser
of capacitance K, gives the same dsflection of the
electrometer, then the charge on the electrometer is again
Q. This time Q is given by
Q = l V 5
4

l l
K C

Equating 4 and 5 and solving for C gives

c=y_-1)1<. a
V

Now, let "a" be the slope of the straight line obtained
from a plot of v against;3, and "b" the lepe of the

straight line obtained from a plot of V against«5.

a a 5 b = é

v V

Equation 6 becomes

C 3 a - l K , 7
b

which is the expression used for determining the
capacitance of the system. Hewever, there exists the
difficulty that the slope b, and consequently the experi-
mentally determined value of C, changes materially with a
change in K. The proper value of K to use for determining
C must be chosen.

For any given experimental value of C, consider the

error dC as determined from equation 7. This is

"Ck-

2 2 a ' a 2 2 s a
(dC) = (a/b - 1) (dK) + (K/b) (da) + (aK/b ) (db)

The values of da and db are calculated from their
respective equations.

5: av and 5: bV

1

Thus:

da 2 d6 — {2 dv .

l _
v V
Sinc e the voltage applied with and without K in the
circuit is the same, and since the error dv and dV in
determining the applied voltage is the same in both
instances.
da 2 db

Knowing from many determinations of electrometer deflections
that the calibration curve was linear, the mean of
many deflections for an applied voltage of 0.09 was used
to obtain the curve of figure 5. From this data

a = 98.7/.O9 = 1096.7 mm per volt.
The data below was used for the determination of
capacitance, using a value of K I 581fqlf.

volts time during which 8 mm
voltage is applied

0.90 15 sec. 88.8
98.3
92.4
91.9
88.l
94.2
92.4

mean 91.4

n
-113-

The mean deflection was 91.4nnn. The number, n,
of readings was 7; and the sum of the squares of the
mean deviations from the mean equals 28.55. The expression

for probable error is

 

2
0.6745 QEImean deviations from the mean)_
nIn-l)

 

 

d8 = 0.5745 ./%8.55/7.6 : 0.55 mm

The voltage could be determined to within .0001 volt.

Then
2 2 2 2 2 2
(da) : (db) : (1/.09) (0.55) + (91.4/(.09) c0001)
: 58.57
da = db = 6.2 mm per volt.

Now, the error, dC, from expression 8 may be calculated.
The probable error dK in the capacitance of the standard
condenser was taken as 1pr. Data taken using a value of
K = 58.0(gf.,yielded a mean electrometer deflection of
56.8 mm. Then

b = 8-/V = 56.8/.09 = 651.1 mm per volt
Voltage applied direct to electrometer gave a g 1097
mm per volt. Using the value found before for da and db,

we get 2 2 2
(d0) (98.7/56.8 - l) +(58/651) 58.67
2

. (1097.58/(651)2) 58.67

do a 1.55 f.
Several values of dC for correSponding values of the
standard capacity K were found in this manner and plotted

in figure 6. This curve shows that a minimum error will

-24-

be made in determining the unknown capacitance by using
a value of K between 55ffif and lUOyyf. The mean
capacity found using several values of K within this

range gave C = 39.64ny.

V.
The Vorking Equation Used to Reduce the Experimental Data
A. Fraction 9£_x—rays measured in the ionization chamber
to those produced at target.
For this analysis, reference will be made to the
f ollowing figure 7 which shows the arrangement of

apparatus in the path of the measured x-ray beam.

 

 

 

 

 

 

 

[00

K W!

 

F136

Here,

‘

d

(‘1
(.4

Pr

(‘5
84

II

II

Original intensity of x-rays produced at
target.

Intensity of x-rays passing the x-ray tube
window.

Intensity of x-rays passing the Ross filter.

Intensity of x-rays passing the mica window
of ionization chamber.

Intensity of rays reaching front end of
collecting electrooe of ionization chamber.

Intensity of rays leaving rear end of
collecting-electrode.

Thickness of Al window of x—ray tube.
Thickness of Ag or Cd filter.
Thickness of mica window.

Distance from mica window to front end of
collector electrooe.

Length of collecting electrode.
Linear absorption coefficient of Al window.

Linear absorption coefficient for Ag or Cd.
(depending on which is being considered)

Linear absorption coefficient of mice.

Linear absorption coefficient of methyl
bromide in chamber.

The fraction of the original intensity of radiation

produced that is absorbed in the useful part of the

chamber is then given by

fal4-IS

Io

With the Cd filter in the path, a deflection of the

electrometer is obtained which is proportional to f.

-26-

Likewise, for the Ag filter, and we may represent this
as:

50d: 14*15 ,5lg: 14-15

0 o

The various intensities are related to each other as
follows:

11 : Io eXP(‘Plt1)

Ia = 11 exp(-92t2) 3 IO exp(—yltl-yztg)
and similarly; so that finally

5
15 - Io exp(72;64iti)
l:

4
and I - I .w _ I ‘Z: . .

Then , ‘ 4

4
-eXP (123.19 itl)Ag] , 9

The constant 0.90 which appears above is now
discussed. The assumption has been made in this discussion
that all the ions formed were collected before recombining.
To test whether this were actually true or not, a
continuous source of x-rays were produced at least three
times as intense as those to be measured. Electrometer
deflections were then plotted against voltage applied
to the collector electrodes from "B" batteries. The
curve indicated that at 570 volts applied voltage, the
ions were sw ept out of the chamber to within one percent.
This correction has been applied to the equation relating

electrometer deflection to IO.

-27-

The quanta absorbed photoelectrically in the
ionization chamber produce photoelectrons and positive
bromine ions. When a photoelectron is produced by
ejecting an electron from an inner level of the bromine
atom, this particular electronic level is left incomplete.
Another electron may fall into this level with a conse-
quent radiation of a bromineAvuantum, if the K shell
happens to be the particular level in question. Not all
of the relatively short fluorescent bromine K rays will
be absorbed before they reach the walls or ends of the
chamber. Practically all of the L and M quanta so
produced will be absorbed however. Furthermore, by the
Same pro ess, there will be produced in the front and
back guard plate regions, quanta which are not pzrt of

”fight-d i vflcns'i“ .
the ehamberkand there proouce ions. This correction
was made by J. C. Clark (19) for the particular ionization
chamber used. The solution of this problem involves a
mathematical formulation of the above considerations,
having regard of the geometry of the ionization chamber,
and necessitates graphical integration.

In order to evaluate the exponentials in equation
9, the thicknesses and absorption coefficients of the
aluminum, balanced filters, mica window, and methyl

bromide must be known. These are given below.

-l
t1 : 0.1?3mm H1 : 4.6 CH]
-1
tde= O. UU 7 cm (IQCdZBl.O cm
“ -l
tgAgZ 0.0U55 cm 612Ag=625 cm
-l
t5 : 0.0o45 cm (‘5 = 4.658 cm
t4 : 7.d cm f4. 3 0.070: at 68.5
cm Hg
t5 : 10.0 cm

The linear absorption values are from Compton and
Allison (20) and are for a wave length of 0.474 3.
Substituting the above values in equation 9, we get

S I 0.146 10
This equation represents the ratio of the radiation of

mean frecuency'fl= VCd - fihg_ measured to that
2

 

produced at the target.

B. Absolute Intensity Formula.

 

As was pointed out, the electrometer was calibrated
so that a given deflection corresponds to a known voltage;
and this in turn to an amount of charge given by Q 2 Cv.
Dividing by the chrrge on the electron gives the number
of ions collected. Or, number of ions collected per
second 3 CAV/et, where

C

capacitance of electrometer system.

AV = vogtageéA difference correSponding to
Cd -
AV - l/a( g6Cd — 5kg) -_- l/1097(5Cd-5Ag);
and is then the produced voltage on
the electrometer due to the quanta
defined by the frequency limits of
the cadmium and silver filters.

e - Charge on the electron.

t = Time the radiation is allowed to enter
chamber.

-29-

Various measurements have been made to determine the
energy required to produce a pair of ions in gases by
the absorption of x-rays. Stockmeyer (kl) has sumaerized
the results concerning this constant, and, together with
determinations of his own, gives, for methyl bromide,

6,: 25.4 electron volts per ion pair.
—.L‘¢
Tt's is E X l.6 x lU ergs per ion pair.
Thus, the energy measured per second oassing through an
aperture of unit area at a distance R from the target :
-12

cAwel.6 x lU . 11
a e t

 

There "a" is the area of the defining aperture used in
the experiment.

In this equation, theAN term is directly proportional
to the difference between the electrometer deflections
with Cd and Ag filters in the path; that is,

3Cd - (Sag N AV.
The energy thus produced at the target per second of
mean frequency is equal to that measured (given by
formula ll) divided by the ratio of that measured to
that produced (given by formulas 9 and 10). We may

express this as:

 

Energy produced per second at . _12
the target per unit area distant : CAZ€}-: i 10
K.) O

"R" from the target

-20-

The number of electrons produced in the time
interval "t" is given by

it , where is is the Space current

(D

in the x—ray tube.

The number of atoms per unit area of the target is

Mal 9 uher e
A

N : Avogadro's number,f): density, X0 = target

thickness and A = Atomic weight of target material.
We thus see that the energy produced at the target per
second, per electron, per atom, per unit area of the

target, per unit area at the distance R from the target, is

 

-12
CeAV'lJZX U) /it
s a e t e

 

N fxO/A

This is more compactly written in equation 12. used for

evaluating the emporimentally determined data.

 

 

42
J1, d1): CeAvAlexlO 12
2
S a t N x0 1
_-, 1.60 x 10-16 06A . A1112
Eelein t

The units associated with each of the terms used in
expression 12 may well be stated here. These are given

on the following page.

N =
X =

i =

-51-
electrometer system capacity (Farads)
energy per ion pair (electron volts)

potential difference corresponding to
electrometer deflections 50d —§ag (volts)

atomic weight of target (gms/gm atom)
ratio defined by equation 10

area of defining aperture (cme)
exposure time (sec)

ongadro's number (atoms/gm atom)
Target thickness (cm)

x-ray tube current (coulombs/sec.)

Then, the units of lady are

1)

A. Target

J d0 : ergs per cm2 at a specified distance from

the target per sec per electron per atom
per cm“ of target.

VI.

Measurements

Thickness Measurements.

 

 

An interferometer plate, whicn has previously had a

reflecting

center of a

portion of
a 1/8 inch

surface evaporated on it, is placed in the
square, the four targets at the corners. A
the plate through the center is blocked off by

strip of mica. In this manner, a film of

the thickness of the targets is evaporated on the two

exposed portions each side of the center strip. 1"hen

the plate is placed in a Michelson interferometer, the

interference fringes of the center portion will be

diaplaced with respect to those at the edges by an

~32
amount proportional to the Optical path difference
introduced by the deposited film. The distance between
2 adjacent fringes of the same set corresponds to an
Optical path difference of X/B. The fraction of a
fringe shift, then, correSponds to the actual thickness
of the deposited film; and this thickness is the same

fraction of A/B. The photograph, figure 8, is of a

fringe system produced as described above.

 

F793

Calling the fringe displacement d' and the distance
between fringes of the same set d, the equation for
calculating the thickness of the deposited film is

x0: d'/d A/2 , is
We see that the smaller A is, the greater will be the
relative displacement. All photographs were made with
the interferometer adjusted for white light fringes, in
order that any components adjacent to the principle line
used for photographing should give an interference fringe
in practically the same position as that produced by the

principal component; and that'there should be a maximum

-55-
contrast between light and dark portions of the field.
Lines used were those of mercury ath: 5461 g and

.A:.5654 X. Comparator readings were taken of the
fringe shift for the calculation of thickness. The
following Table II shows a typical set of measuremen s
to determine target thickness.

Table II
A1 2365, Photographic Plate B, A: 5654 K

Distances between Fringes Fringe Diaplacement
mm mm

0
\J

mommemooemomesmpmemoqmm

NOPHNWHMNCNNZ‘OODHCN

DD N) {Y} (‘3) 2‘.” (‘0 NJ 750 3‘7‘: 1‘0 (\9 PC 1‘3 1‘

mean = 22.2 mm. mean = 5.1 mm

Mean fractional displacement = 5.1/22.2

Target thickness : Xo= 5.1/22.2 X éfiéfi X = 4ll E.

Z

. -24
DJ-
Table III summarizes the measurements made on

target thickness for all the targets used.

Table III
Veight Number Thickness

Interferometer Lambda Thickness of Fringes x
Plate Number Used Weight of
Observa—
tion.
0
Al 26E 5461 A 344 n 18 6192
0
A1 26E 6654 A 380 A 15 5700
0
a1 26E aasa 3 411 a 25 9455
o

Weighted mean thickness = 581 A

B. Absolute X-ng_lntensities
Placing the appropriate values of the constants in
equation 12 results in an equation for intensity of
radiation in terms of v alone. This is herewith shown:
-l2 -l2

JV dv : 1.6 x 10 x 39.64 x 10 ¥a25'4 X 26.96 . AV

0.146 x 0 912 X 6.0268x 1050 x 2.70 x

581 X 10 X 15 x 10 x 900 (all as denominator)

,

where for the conditions of the experiment

A

26.96 gm/gram atom
2
0.912 cm

Q,‘
n

25
2 6.028 x 10 . atoms per gram atom

2.70 gm/cmr6

“b 21
H

I 681 x 10’8 cm.

N

H.
H

-8
15 X 10 amperes

t Z 50 sec.

-55-
The remaining constants have already been given. This
equation reduces to 15, the one used in calculating
the data of this experiment.
J1) d1) = 5.896 x 10-5 Av 15

where J,,d17will be expressed in ergs per sec per cm“,

at distance R from target, per electron per atom per

" \

cm” of target, WhEHWAV'iS eXpressed in volts.

The eXperimental data to be presented in this
thesis was obtained from observations using four thin
aluminum targets on cellophane backing films. These
four targets were evaporated at the same time as the
interferomete slate A1 #26 E was made. The measurements
covering the thickness of the targets, and made on this
interferometer plate, are those presented above under
section A of Part VI of this thesis. These four targets
have been designated Al 26 A, B, C, D. A complete set
of data for target Al 26 C is given in the following
Table IV. The data shown in table V are the mean values
cfi'6Cd — 5Ag for each x-ray tube voltage used on targets
a1 26 A, E, and D. Curves showing the variation of
JV d9 as a function of bombarding electron energy are
shown in figure 9. Also shown in figure 9 is a curve
labled "mean" which is the mean values of JVdQ of all
data collected throughout the voltage range 31.7 to

44.0 kev.

Q:

60 , exposure

Tube current 0.15 microamperes.

Tube

Voltage

KV

44.00
44.00
44 0Q

-‘.

44.00

41.40
41.40
41.40
41.40

58.45
58.45
58.45
58.45

89.5
88.2
88.5
88.9

74.0
74.0
74.9

59.5
60.8
61.0
60.0

thrbrblb
putsonb

CDDi—‘Cfi

51.4
51.2
51.4
50.8

82.2
81.0
80.0
85.6

Mean

69.0
68.2
68.5
71.0

Mean

55.0
55.7
55.5
55.6

Mean

40.8
40.5
40.6
40.8

M6811

29.5
29.0
29.2
28.9

Mean

 

 

 

01 2‘3 (‘5 DC
0 O O O
(‘3 03 O3 01

 

IL"
LO
(1)

HNZ‘“Z\"
LONMH

 

In
H
C:

5Cd(mr:;) 6Ag(mm) 6Cd ~6Ag Av(volts)
x 100

6.75

4.75

2.86

2.02

time 50

sec.

1.12

0.79

-57-

Table V

9 = 60°, eXposure time 50 sec., tube current 0.15 micro-
amperes.

Al #26 Tube Mean
Targets Voltage «5C3 ‘6A9 -Av'volts JV d9(ergs56et c.)
KV mm 1 100 x 10

A 51.75 2.60 2.50 0.97

B 51.75 1.46 1.40 0.55

D 51.75 2.00 1.92 .75

B 54.77 2.68 2.58 1.00

A 55.75 4.46 4.29 1.67

D 55.75 2.98 2.87 1.12

A 58.45 5.54 5.55 2.08

B 58.45 4.25 4.09 1.59

D 58.45 4.50 4.15 1.61

B 41.40 5.12 4.92 1.92

A 2.50 7.87 7.57 2.95

D 42.50 6.55 6.09 2.57

B 44.00 6.55 6.50 2.45

a ac

m f 5'..ch 2&3.” neigoaiom
O? . m n

  

3

s
4...: t .3
3.64 5.3.... _< z
s

2
:9 33.

 

VII.
Comparison of Experiments with Theory
A. Intensity versus electron energy curves.

In figure 10 the results of the computations of
JvdV(corrected) and the mean values of JVdVdetermined
experimentally are shown plotted as a function of the
energy of the bombarding electron. As is seen, the com-
putation for the theoretical values have been carried out
for a voltage range from 50 to 80 KV, while the
experimental results extend over a range from 51.75 to
44.0 KV. In these curves, the absolute values of x-ray

intensity are expressed in the units used throughout this
2
work; namely ergs per sec per cm at a distance of 54 cm
2
from the target per electron per atom per cm of the

target.

B. Discussion of Results.

 

As is seen in figure 10, the results of these
experiments are in agreement with the theory only in the
order of magnitude of the absolute values of x-ray
intensities. Many errors exist in the various measure-
ments, as well as in such quantities not measured, but
used from the literature, such as energy required to
produce a pair of ions and the density of the very thin
aluminum targets produced by the evaporation process.
These errors are all involved in the final values of
Jvdfl, so a discrepancy between theory and experiment of
the absolute value of defl would not be surprising,

ssuming the theory correct. The aLove mentioned errors

9‘

remain practically the same for all bombarding electron

3281:.

00......

3 3: pals“ 9.0.33.0 flcigmaen. m
0.. on

x

“COEofiilu

3.

u.—

toflabiw.

 

energies, and the discrepancy between the experiments
and theory in this reSpect is more disturbing. No other
similar eXperiments fave as yet been reported. Indeed
only one other experiment (15) is reported which allows
a comparison with this to be made is reported. These
authors show an agreement between theory and experiment
for absolute values of intensity for Nickel targets at
electron energies of 15 Kev. More experimental results
than those reported here are obviously required before

definite conclusions can be drawn.

10.

11.

L).

15.

l4.

15.

-40-

Bibliography

 
 

Compton, A. H., and S. K. Allison, X-i:
and Experiment,_2no ed. (1956), page 97.

 

Sommerfeld, A., Uber die beugung und Bremsung der
Electroneg, Annaleh oer Physik, 10, 969, 1909.

 

Kulenkampff, H., Untersuchungen uber Rbntgenbremstrahr
lung von dunnen Aluminum Folien, annalen der Physik,
87, 597, 192

Kramers, H. A., Phil. Meg., 46, 856, 1925.

Nicholas, W. W., Bur. of Std. Jour. of Res., 2, 857,
1929.

Sommerfeld, A., 0 ber diebeugung und Bremsung der
Electronen, Annalen der Physik, 5, 11, 257, 1951.

 

Scherzer, 0., fiber die Ausstrahlung bei der Bremsung,
von Protonen und schneller Electronen, Annalen der
Physik, 5, 15, 157, 1952.

 

Sauter, F., Zur unrelativistischen Theorie des
kontinuerlichen antgenspectrumg, Annalen der
Physik, 5, 18, 486, 1955.

Sauter, F., Uber die Bremstrahlung schneller Electronen,
Annelen der Physik, 5, 20, 407, 1954.

Kelly, H. R., Emission 9§_the C ontinuous X—Lay Energy
from Thin Aluminum Foils, Michigan State College,
Master of Science Thesis.

 

u

Bohm, K., Untersuchnngen fiber die Asimtale Intensitats-
verteilung der Roentgenbremstrahlung, Annalcn der
Physik, 5, 55, 515, 1958.

Clark, J. C. and H. R. Kelly, Phys. kev., 59, 220, 1941.

Smick, E., and P. Kirkpatrick, Bulletin of the American
Physical Society, 16, June 1941.

Harworth, K, and P. Kirkpatrick, Bulletin of the
American Physicrl Society, 16, June 1941.

DuMond, J. W. M., A Complete Isometric Consistency
Chart for the natural Constants g, m, and h.
Phys. Rev. 58, 457, 1940.

 

 

l6.

17.

18.

19.

Compton, A. H., and S. K. Allison, X—Rays in Theory

and Experiment, 2nd ed. 1956, page 795.

 

Pettitt, N., The Determiration of 1-I1 y Mass
Abs orption Coefficients for Columbium from

0. 200 to 0. 500 Angstrom Units. SMichigan State
College Master of Ecicmlce Tnes

 

 

Kirkpatrick, P., 0Q the Theory cnd Us e_§_Ross
Filters, Reviev of Scientific Instruments, 1
186,1909.

 

O

)

 

5 Measurement of the Absolute
SK— Electron Ionization g§_Silver
s, 48, 50, 1955. Ph’s. Rev.

Clark, J . C.
Probability 0
Bi Cathode RE

 

 

H3».

 

5|

Compton, A. H., and S. K. Allison, X— —Rays in
Theory and Experiment, 2nd ed (1956), page 802.

 

W. S. Stockmeyer, U ntersuchung_2ur Anwendung der
Ionisstionsmessmethode bei Pdntgenstrahlen,
Annalen der Physik, 12, 105, 71, 1952.

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