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ENTENSITY OF THE CONTINUOUS
X-RAY SPECTRUM FROM ANTIMONY
TARGETS AS A FUNCTION
OF WAVELENGTH

Thesis for the Degree of M. 5.
MICHIGAN STATE COLLEGE

Robert Harold Esling
1942

 

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII III III

I _ 1293017014774 ;

 

 

LIBRARY
Michigan State
, University

 

 

 

 

 

PLACE IN RETURN Box to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

DATE DUE DATE DUE DATE DUE

 

INTEISITY OF THE COITIKUOUS X-RAY
SPECTRUK'FROX AIT SEXY TARGnTS AS

A FUNCTION OF KAVJLEKGTE

by
Robert Harold Esling

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

1942

ACKNOWLEDGEXEL

Many thanks are due to the members of the
physics department for their aid and
suggestions and especially to Dr. J. C. Clark,

at whose suggestion and under whose guidance

.X/

this study was made.

   

142801

Table of Contents

Introduction

Theory

Experimental Requirenents
Experinental Apparatus

Theoretical Calculations
Experimental Results

Comparison of Experiment with Theory
Appendix

Notes and References

Page

17
21
32
34

4O

Introduction

The difficulties inherent in any experimental technique
known to date for determining the absolute values of the
intensities of continuous x-ray emission (Bremsstrahlung)
have influenced most early investigators in this field to
make only theoretical studies of the probleml, and of the
later experimental studies made, most of the measurements of
intensity have been measurements only of relative intensityg.
It is the purpose of this paper to present an experimental
study of the Bremsstrahlung by the measurement of the abso-
lute intensities under specific conditions and to compare
the results obtained with the theoretical intensities calcu-

lated for the same conditions according to one of the later

theoretical studies of the subject.

H. R. Kelly3 and A. F. Reno4 have each given a rather
complete review of the work done, in this field. It is
sufficient therefore to remark here that of the later
theories preposed some agreement of experimental data and
theoretical calculations has been obtained for a relativis—
tic equation develOped by F. Sauterso The eXperimental data
mentioned was obtained from studies of the energy Jydll as a
function of the azimuthal angle of emission6 or as a function
of the energy of the incident electron7.

In this report a comparison between experimental and

theoretical values of dev as a function of wavelength will be

presented.

-1...

Theory

In the quantum theory of the radiation processes the
probability function.q;, of the transition probability for a
process in which n quanta are emitted or absorbed, will be
proportional to egn where e is the electronic chargee. It
may also be shown that if we consider the Coulomb interaction
between two free particles as a small perturbation causing a
deflection of the particles, this deflection is equivalent in
the power of e involved to the emission or absorption of two
light quanta. Then if we classify the radiation processes

It

. 2
according to the values of e we have:

lst order-mwaaeg; one light quantum is involved in the
interaction.

2nd order-~unve4; two light quanta are involved.

5rd order--avve6; three light quanta, or one quantum and a
Coulomb deflection are involved.

The Bremsstrahlung is a particular example of third order

processes. It is the case of the interaction between a

free electron and a free nucleus. In this case the Coulomb

interaction is proportional to e22 so that the expansion

mentioned above is really an expansion in terms of 622. The

first term of this approximation represents Born's approxi-

mation.

Most of the theories written for the nremsstrahlung have

been based on Born's approximation and are, in that respect,

_ z -

only valid for the lighter elements and high primary veloc-
ities of the bombarding electron since it may be shown that

Born's approximation gives correct results only if

 

 

2.. 2 2 2
4-1r 4e << 1 and 417' Ze (<1
th hv
where v0 and v represent the velocities of the electron

before and after collision. From these conditions we
would expect the theory to break down for high atomic
numbers even though the primary energy were high. For example,

2 2 9
for lead, 2. - 82, the value of 4&2 Be .- 3.76 .

 

Sauter's (loc. cit) early work resulted in a non-relativ-
istic expression for Jydl’, the intensity in a frequency range
dV , per electron, per atom, per unit area of target for
observations made at a distance R from the target and at an
azimuthal angle of e. {is later work resulted in a relativis-
tic expression for Jgdzl. Both of these expressions were
developed using Born's approximation and consequently were
limited in their range of validity. He pointed out, however,
that Sommerfeld's (loc. cit.) rigorously valid formula could
be obtained by multiplication of the earlier non relativistic

expression by

 

 

(2110(8)2
BOB
‘ 27MB '1 beams )
(IE3 30 ) ( 3 (l)
where ot=.—%g31_ - the fine structure constant,
B = the atomic number of the nucleus,
v

I3 = '73"

the velocity of the electron after collision,

4
It

Vb - the velocity of the electron before collision,

0
II

the velocity of light,

6 = the Naperian base
and concluded it would seem reasonable that multiplication of
the later relativistic expression by this same factor would
yeild an expression for lvdzlwhich would be valid over the
entire spectral range. This assumption he judged to be
correct on the basis of some calculation made by Haue, which
though then unpublished, were confided to Sauter.

For high values of,po, (i.e., for high primary velocities),
the correction factor (equation 1) deviates from unity
chiefly at the short wavelength limit. For small values of
po the value of equation 1 becomes smaller than unity except
in the immediate neighborhood of the short wavelength limit.
In this study we are interested in the latter situation as
may be seen by the theoretical calculations on page 20.
There, the value of the correction factor approaches unity
only near the short wavelength limit.

Some mention should be made of the screening of the pure
Coulomb field by the charge distribution surrounding the
nucleus. Sauter's work does not take into account this
screening effect -- not because the effect is negligible but
probably because the mathematics which account for the
screening are too unwieldly to handle. Heitler10 gives a
brief discussion of the effect for high energy quanta but we

have no information regarding the magnitude of the effect for

the eXperimental energies which we shall use. for lack of
information, therefore, the effect of screening shall of
necessity be neglected in this study.

The relativistic expression develOped by Sauter is

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where e - the electronic charge,
Z - the atomic number of the nucleus,
R - the distance to the defining aperature from the
target,
0 = the velocity of light,

p = the momentum of the electron after collision,

Po . the momentum of the electron before collision,
1’ = the frequency of the emitted quantum,

E = the initial total energy of the bombarding electron,
E ' the total energy of the electron after collision,

m = the rest mass of the electron,

59 8 the angle, with respect to the v direction, at

O

which the quantum is emitted,

...5 -

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ll

Plank's constant,

° the momentum of a quantum,
1
[Dog 1 <12 -Zpgcos9]/3.

Upon multiplication of eq. 2 by eq. 1 we have

q
PO
(fire! 2) 2

.flnp #_fi_
nay-rag
(€2ni25/)//_€ flj

which is assumed to be valid in the whole spectral range.

 

 

 

 

(5)

 

J24."- d7/ 5'- JV 6/7}

 

This equation (eq. 3) is the one in which we are most interest—
ed since the experimental results obtained shall be compared
with theoretical values of Iv calculated by eq. 3 for the

wavelengths used in the experimental study.

Experimental Requirements

The ideal method of experimentally checking any theory of
the Bremsstrahlung would be to make studies of the quanta
produced simultaneously with the Coulomb deflection of a
single electron in the field of a single nucleus. To exper-
imentally isolate a single electron and a single nucleus as
free particles is of course difficult. Possibly the required
conditions could be obtained with a cloud chamber but it is
doubtful whether the quantum associated with a given Coulomb
deflection could be studied with any such apparatus. To
approximate these ideal experimental conditions we must have
a constant electron source supplying electrons at a constant
rate, all of these electrons having equal initial energies.
These electrons must then be made to pass through a screen
of atoms and the quanta emitted in a known time are the
quanta studied. This screen of atoms should be thin enough
that all the electron—nucleus interactions approximate the
ideal conditions. The thickness of the screen of atoms
should therefore be only sufficient to produce an accurately
measureable number of quanta.

When the foregoing conditions are satisfied as nearly as
possible it is necessary to have the quanta-measuring
apparatus as sensitive as possible in order that the quanta

from the very thin atomic screens may be accurately measured.

 

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Pig. 1

Experimental Apparatus

The Constant Electron Scource:

The actual electron source was a spiral tungsten filament
made of 8 mil wire, and was electrostatically shielded so
that the electrons given off were collimated into a beam
which had an elliptical cross section of about 1.2 square
cm. at the target of the experimental x—ray tube (the atomic
screen). As may be seen from the complete wiring diagram of
the apparatus (figure!) the constant high voltage was
supplied by a voltage-doubler circuit and high-voltage 500M
transforheIu This voltage supply was controlled by adjust-
ing the current through the field coils of a 500“! alternator
which was connected to the primary of the high-voltage
transformer. This particular voltage supply has been des-

cribed by Pettittll.

To supply electrons at a o3nstant rate the space current
through the experimental tube must be accurately controlled.
This was done by means of a rheostat, manually operated, in
series with the filament, while the entire current-control
unit was electrostatically shielded to eliminate corona
loses from the measured current. This arrangement has been
described by kelly and Reno (loo. cit.) except that the
meter which they used has been replaced with a General
Electric galvanometer # 32C236Gl shunted to read 9.3 x 10-9

amperes per division.

Whenever'neasurements were made to obtain data for this
study two Operators were required, one to control the vol-
tage and current, to keep them constant, and one to make

measurements on the x-radiation studied.

The Screen of Atoms:

The targets used in the experimental x-ray tube were
formed by evaporating antimony onto a cellophane backing in
the manner described by kelly and Reno. The thicknesses of

12 and

the targets were measured by the interferometer method
were of the order of magnitude of 150A to 250 A. It will be
observed from the sample target shown below that the thin
targets used were transparent. Little is known about the
atomic arrangement in these very thin films, so, in order to
reduce the eXperimental data we shall have to assume a
uniform distribution of the atoms throughout the thin film.
kelly and Reno made intensity measurements on targets of
plain cellOphane, with no metallic film evaporated onto them,
and decided that the intensity of K-
radiation from the cellophane back-

ing was negligible. Consequently,

no correction in their reports was

 

made for the backing material.

Fritzl3 later made measurements on the

effect of the backing material by using different thicknesses
of backing material and determining the corresponding inten-

sities of x-radiation from the targets. his work indicates

 

 

 

 

 

 

 

 

 

 

 

I

  

Y""""

 

 

 

 

-Po-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A ANODE

T TARGET

- K CATHOD E

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hg. 2

that for the cellophane backing used in this work (thick-
ness .002 cm.) the backing effectively increases the true
intensity of radiation by about 32fi. The fact that the
cellophane alone gives a negligible amount of radiation
whereas the cellOphane in conjunction with a metallic film
contributes appreciably to the number of quanta radiated is
possibly explained by a rediffusion of the electrons through
the metaflic foil thus causing extra collisions and yielding
extra quanta. As the thickness of the backing is increased
the number of electrons slowed down and rediffused through
the metallic film.would be increased.

In this report the figure developed by Fritz will be used

as a correction factor to take account of the target backing.
... Q

The Experimental X-Ray Tube:

The filament and thin target were used in the experimental
x-ray tube described by kelly and were arranged as shown in
figure 2. The tube is essentially a short steel cylinder
which has an inside diameter of 8 inches and an inside height
of 2.5 inches. The target support and anode are insulated
from the steel tank by means of heavy pyrex tubes so that the
tank may be kept at a negative potential. This arrangement
eliminates the production of x-ray by electrons bombarding
the walls of the tank and thus all the radiation studied
comes from the target. (The series of defining aperatures
prevent radiation from the anode from entering the ionization

chamber.) The window through which the x-rays leave the tube

is made of aluminum, .04 mm. thiCk, and is large enough to

permit the study of radiattenergy at all angles between 120

and 1600 with respect to the direction of the incident elec-
tron. The tube was evacuated by means of a Jenco-Hyvac fore

pump in conjunction with an oil diffusion pump.

The guanta—measuring Apparatus:

The variables in Sauter's theory are JV, d1), 1’, E0, Z,
and 9 . In this report J, was studied as a function of
1! alone. It was necessary, therefore, to have some experi-
mental means of effectively monochromatizing the radiation
to be studied and it was decided that Ross filters14a would
serve the purpose well. These filters give effectively
monochromatic results without absorbing so much of the
energy that they make the accurate readings difficult.

Ross filters are a combination of two filters made of
elements near each other, preferably adjacent, in the period-
ic table. The thickness of these filters are adjusted so that
both filters have the same absorption in all parts of the
spectrum except between the K absorption limits of the two
elements. A monochromatizing effect is produced by allowing
the filters to alternately intercept a beam of non-monochrom-
atic radiation while measurements are made of the intensity
of unabsorbed radiation. Any difference in the effect of
the two filters must then be due to the unbalanced region
between the two K absorption limits. For elements adjacent

in the periodic table this "pass band" is quite narrow (JHBA,

_.// -

.021A, and .054A for the filters used in this work). The
mean wavelength Of each pass band is considered to be the
wavelength of the monochromatic radiation studied.

There is an Optimum thickness for the foils used in Ross

filters. The expression for transmitted band intensity has

 

a maximum value when the filter thickness is 14b
t log r
o‘ f4,_(r-l)
where t0 = the Optimum filter thickness,
)h.= the linear absorption coefficient on the long
wavelength side of the pass band,
_ s
1‘ " fl/f‘t.
f“,= the linear absorption coefficient on the short

wavelength side of the pass band.
This expression is obtained in the following manner:
Using the well known expression for the absorption of x-

radiation,

. I - I e-Ft
C

where IO 8 the inten-
sity of the radiation

incident on the filter,

 

 

I 3 the intensity of

 

the radiation passed

Fig. 3

by the filter, [1- = the
linear absorption coefficient for wavelength 1 , and t = the

thickness of the absorbing foil we may write:

_/2._

= - t _ -,u t
IL 103 PI. and IS Ice 8

Now the pass band intensity is prOportional to the area Of
the pass band (see figure 3) which in turn is proportional
to

AIAA= I. (e”““— e”“‘t )A)

Then to find the optimum thickness,

gang):L42(fl‘e-flst_FLe-flit)=0

whence
- - it.

[(36 F‘i. =/’(Le F

We define
-Lt.
r=e(/’s/‘) = [if
#1.

Then

l0] 1‘ = (fl; ’FL) t;
= [(1. ‘7'}?‘0 {'-
=,u;(r-I)t.

OI' . 1“: /o r
flblr—I)

It is preferable, though not necessary, that the filters
used be of Optimum thickness. In practice the two filters
are mounted in a carrier frame and a condition Of "balance"
obtained by natating one of the filters slightly with res-
pect to the other in order to adjust the effective thickness

of the rotated filter.

.. l3 .-

Kirkpatrick (loc. cit.) had discussed Ross filters in
detail and points out that it is sometimes advisable to use
a third element in conjunction with one of the two basic
filters as a means of obtaining a better balance than would
otherwise be possible. This was done with one of the filters
used in this work.

The filters used were:

Filter Mean A.of pass Calculated tO
oniid
Antimony
0415 A ------- :5)"
Tin 6.27 x 10 cm.

. -5 15
Cadium 5.57 x 10 cm.
Silver 3.55 x 10 cm.
Molybdenum ‘ 2.53 x 10-0 cm.
Columhium 2.90 x 10 cm.

' A thin aluminum foil (.001 cm. thick) was used in conjunc-
tion with the molybdenum filter.

The wavelengths available through the use of Ross filters
are limited in number. The condition that the two filters
in a given filter system must be near each other, prefer-
ably adjacent in the periodic table makes only a few
elements readily usuable as filters since only a few elements
available in foil form meet this condition. In an effort to
Overcome this limiting characteristic of the filters ex-
perimenters have made filters of metallic salts evenly
distributed in a beeswax or other binder, but this technique

has the disadvantage of introducing other elements into the

no ’4 .—

absorbing foil.

For the experimental study reported in this paper it
was decided that at least three filter systems should be used,
that is, that the theory should be checked at at least three
points. Only two Ross filters, however, were readily avail-
able for a study in the region where our equipmentlnade it
convenient to work. Cadium, silver, molybdenum, and colume
bium were readily available in foil form, rolled to the
desired thickness, from Baker and Company, Incorporated. Tin
was also available so it was Observed that if an antimony
filter were prepared and balanced with the tin foil a third
wavelength would be available. Antimony, however, was
brittle and could not be rolled into a foil by any known
method. A new method was therefore developed of evaporating
the antimony onto cellophane backing so as to form a foil of
the desired thickness. This method, discussed in the appen-
dix,produced a filter of pure antimony and was therefore con-
sidered to be better than a filter formed by distributing an
antimony salt in a binder.

The absolute intensity of the quanta passed by the Ross
filters was measured by determining the number of ion pairs
formed in an ionization chamber. The charge produced, due
to the formation of these ion pairs, was recorded by a
Compton electrometer. The ionization chamber used was the one
used and described by Kelly and Reno. It was made of brass
with mica windows at the ends and was filled with CH5Br at a

pressure of about 68 cm. The collector plates were Of thin

aluminum sheet and were equiped mith electrostatic guard
rings to eliminate end effects due to irregularities of the
field at the ends of the collector plates. Sufficient volt-
age (450 volts) was applied across the collector plates to
obtain practically saturation current. It is estimated from
previous work ( see Kelly, 100. cit., fig. 10) that 96% of
the ions formed were collected before recombination. A
small correction was also made for the fluorescent effect
(see pp. 24).

The electromcter used was a new one made at the Stanford
University instrument shOp by Mr. B. G. Stuart and had a
sensitivity of about 5700 mm. per volt. In using the elec-
trometer the "strictly ballistic" method discussed by

17

Webster and Yeatman was employed.

-l6—

Theoretical Calculations

The theoretical values of J}, with Which the experi-
mental results of this work are compared were calculated from
equation 3 after dividing equation 5 by dzl. The values of
the various terms in the formula as well as the final correct—
ed values of JV are listed on the following pages and the
theoretical values of J» are plotted as a function of J in

figure 0 where they are compared with the experimental re-

sults.

_ ,7 -

Values of constants used in calculating JV

by Sauter's equation:

~28
n1: 9.11780 x 10 gm.

fl-,,,_ ~10
e = 4.00050 x 10 esu
‘ AN -”
n_= 6.65aao x 10 erg-sec
m ,
c : 2.99776 x 10 cm./sec.

Z
R = 3400 cm
C)

= 60'

F -7
E0: 8.8301 X 10 BIgS
,e.,= .57405

7.1827 x 10,7 erge

F
u

po 1.1024 x 10mngm-cm/seo.

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’90-

Experimental Results

The working equation:
The quantities neasured experirentally are not the values
of JD,dL/ but are related to Jv d2! by a relationship which

shall be termed as the'Working equation".

To begin with, only a fraction of flied!”
fon/oh of
the intensity of the x— l/w/nJow ch’m""7

 

9!

radiation saving the

l
- .o “‘ "“ '“‘fi ----- 1-#
target ls measured. Be- fargeff rung-15W ,

”1'2. Win Jaw

t

 

 

 

tween the target and the

effective portion of the F; . 4

ionization chamber are several absorbing materials which dim-
inish the measured intensity. The fact that the absorption
coefficients vary with wavelength does not complicate the
problem as it would seem at first, because, since we are
interested only in the radiation of wavelength equal to the
mean wavelength of the pass sand we may consider the absorp-
tion to be that of monochromatic radiation whose wavelength
is the mean wavelength of the pass band. Kore strictly, we
shall consider wnat happens to the intensity of radiation
having initial intensity 102/ dZ/at the tarcet where L) is
the mean frequency of the pass band and d2/ is the frequency
range of the pass band. The snail variation of the linear
absorption coefficients shall be neglected over the range of
t

he pass band. fiaure 4 shows the positions of the absorb—

Q

in; materials which d‘minish the intensity of the measured

__)

radiation.

-2]...

The aluminum window of the X-ray tube was .004 cm. thick

and the fraction of the intensity transmitted by the window

at the wavelengths used in this problem was:

A _
I"

- .415
I
0v

The absorption of

.9874

.474 .635 A

.9818 .9582

the silver and cadmium filters were

calculated according to Reno's work with these filters.

Since, however, the values of the linear absorption coef-

ficients were not readily available for antimony and colum-

bium the fraction of initial intensity transmitted by each

of the antimony, tin,
was measured directly
a bragg spectrometer.

different filters are

Filter

18
Compton and Allison

able to calculate the

molybdenum, and columbium filters
by placing each filter in the path of
The fractions transmitted by the

listed below:

I,” /I.v at wavelength}

.415 A .7010
.415 A .1807
.474 A .7410
.474 A .1280
.635 A .6800
.635 A .1431

give an expression whereby one is

absorption of the .0043 cm. mica

‘Window. Using this expression we find that the fractions

transmitted by the mica window are:

_. 21....

= .415 .474 .635 A

A
: hp” 9: . r
IByI/Ezv oJQUg . 804 9061

Next, between the mica window and the effective portion of
the ionization chamber, the radiation studied passes through
7.8 cm. of CH5Br at a pressure of 68.3 cm. of Hg. IA chamber
of known length containing UHSBr having the same density as
the CHBBr in the ionization chamber was placed in the path
of a Bragg spectrometer and the absorption measured. From

data thus obtained it was found that the fractions of radia-

tion transmitted by the first part of the ionization chamber

we re 2
R = .415 .474 .655 A
I!” ,/3,v = .666 .545 .279

Now combining the effects of all the absorbers in the path
the fraction of the initial intensity arriving at the front
of the collector plates with different filters in the path

was calculated to be:

Filter 141’ / IO”
Sb .415 A .4546
Sn .415 l .1172
66 .474 A .5887
A3 .474 A .0671
10 .655 A .1758
Cb .655 A .0566

Finally, the radiation actually studied was that absorbed

-,23 _

in the effective portion of the chamber. This portion was
10 cm. long so from the data previously taken on the ab-
sorption of CH3Br we calculated the fraction absorbed in

this part of the chamber to be:

 

 

 

A = .415 .474 .655 A
I -I
i” 5” .406 .545 .806

41/

. 1 I4 -I I4:
and upon taking the proauct v 5V . ‘V we get the
I I
4y 41/

fraction of the initial intensity absorbed in the effective
part of the ionization chamber.

The deflection of the electrometer when any given filter
is in place is proportional to the amount of radiation
absorbed in the effective portion or the ionization chamber.
So, if 6. and 6, represent the respective deflections of the
electrometer when the two foils of a Boss filter system are
placed in the path then (6L - 6. ) is preportional to the

measured intensity Im vdw’.

(5- Marl... 0/” (flamed? 1:) -(——:)](£______4v ”ivy a.

or 65" 07901, Jr!

Sons
8“ =./004 Lyn/1!

8m ~S: = 06351“. J.

vvhere the fi gure .96 is the correction for the saturation
(Burrent (see page 16), the figure .68 is the correction for
‘the target backing (see page 10) and K - .851 represents
the correction for the fraction of the incident radiation

ILost in fluorescent radiation from excited Br ions in the

-24-

ionization chamber. Thus:

K ' 1 - kfg
kf is the ratio of the average intensity of incident radia-
tion. Clarklg, working with an identical ionization chamber
found the value of kf to be .119 whence K - .881.

We must next consider the relationship between the de-
flection of the electrometer and the number of ions formed
in the ionization chamber. The electrometer is calibrated
to give a deflection that is linear with respect to the
quantity of charge collected in the chamber. The deflection
is then

5- kq= k-GV
where 5 = the deflection of the electrometer in mm.
k - the charge sensitivity of the electrometer in
mm.

coulomb
Q ‘ the charge in coulombs

the capacity of the electrometer system in farads
V = the potential difference in volts applied to the
electrometer system.

The difference in deflection for a given Ross filter is

8,, - 5, .-= kc(V.-4)=kCAv
6a-55

whence k

= CLA\/

 

Iwa, if the right hand side of the last equation is divided
'by the product of the charge on an electron and the time
during which radiation is absorbed in the chamber we obtain

the number, n, of ion pairs produced in the ionization

_ 215..

chamber per second:

CAv_ _ Sa- Sb
n = 85 ‘ ket

 

where e - the electronic charge in coulombs,
t = the exposure time in seconds.

Then the energy measured by the ionization chamber per unit
of time is equal to the number of ion pairs multiplied by
the energy per ion pair which is given by Jtockmeyerg to
be 25.4 electron volts or 4.06 x 10- eras.

1f the radiation entering the ionization chamber enters
through an aperature of cross section a the energy measured
in the chamber per second per unit area at a distance R
from the target for the mean wavelength of a given pass band
is

4.06 x 10-11
(6.

Imv db" keta

ergs ‘_
‘61)) sec — cm.“

 

But the measured intensity Im d1): BI dz!
.v

where

B - (.96)(.68)(o881) [(554278 —(“1'§:,L) b M)
‘V

I 41’

so that

 

 

fl

sec-cm.“

 

4.06 x 10'"11 .(Sa " 81d ergs
B

IOvdvr- keta

We wish, however, to obtain the intensity of radiation
f‘vom the interaction of a single electron and a single
flucleus per unit area of target. 80 we must take account
Of the number of electrons striking the target during the

exposure time and of the number of atoms per unit area of

-26-

target. During the exposure timetthe number of electrons

incident upon the target is

 

where i = the current through the x-ray tube in amperes,
e - the electronic charge in coulombs.

The number of atoms per square cm. of target is

pr atoms
M = A

cm“

. A 23
where N . Avogadro's number = 6.00 x 10

p - the density of the target in g/cm3
x - the thickness of the target in cm.
A = the atomic weight of the target element in g/mole.

Applying these corrections to the expression for IO dzzwe

 

 

7/
get
4.06 x 10'11 . (5a -Sb) . e . A
J. <17 = keta ' B ' ""i't‘ "'Nfi—x
4.06A x 10"11 .(Sa-Sb)
.3 kitgahpx B

37

4.165 (8a- 5b) /B x 10-

The units of I” d1! are ergs per second flowing through a
square cm. at a distance R and azimuthal angle 9 from the
target, generated by a single electron incident upon a

ssingle atom per square cm. of target.
IDetermination of the charge sensitivity, k:

In order h) evaluate the expression for J” dz! it is

Iiecessary to know the charge sensitivity of the electrometer

-27-

system. This was determined by measuring the capacitance of

the system. We know

8;: k0,, . kCEV;
and if a known capacitance is placed in series with the

electrometer system (see figure 5)

5': k(_E§E§__) v-

J
CE+CS
Suppose v;' 2V} Then if 61 ' SJ ,

C C

_ ES o2v
CEV ' 0E70S

 

 

or CE = CS :-u_

)l
l

 

 

 

 

 

 

 

 

E = electrometer
C - std. condenser
p - potentiometer

Fig. 5

Applying a potential difference directly to the electro—
Ineter system a certain deflection was obtained. Then the
standard, variable condenser was put in series with the
elfiactrometer system.and the standard capacitance varied
uIl'til the same deflection was obtained with the potential

difference across the series system equal to twice the origin-

-493.-

al potential difference across the electrometer system alone.
This method of measuring the capacitance is considered to
be as accurate as the method used by helly and Reno and has

the advantage of reasuring C directly. The value of C

E E

obtained by this method was 94.0/9uié

Experimental data:

The technical difficulties encountered in obtaining the
experimental data made the task a difficult one. The
greatest difficulty arose from the fragility of the targets
since sudden, large surges of current due to gas bursts in
the experimental x—ray tube or to sudden discharging of the
condensers often destroyed targets before any data could be
obtained. The results here presented are calculated using
the data from antimony targets 11-3 and III-l, which data

is considered to be the most reliable obtained in this

study.
Target Sb II-3
Voltage: 40 kv. Current: 9.6 x 10-7 amp.
Exposure: 5 sec. Thickness: 2.35 x 10-5 cm.
Average égb-é;h - 13.8 mm.
80, - 8A5 - 22.5 min-
(5”. ’Scb - 20.0 mm.
The values of B and dz) are:
.415 .474 .635 A
B : .0970 .1004 .0635
dV': 5.1082 2.8524 2.4622 x 1017

so dividing the working equation for ery by dy 'we get

JV = 1.907 x 10'53 at .415 A
JV - 5.245 x 10‘52 at .474 A
JV . 5.528 x 10’52 at .655 A

-30..

The data from target III-1 was obtained at 33 Kv. and
only for wavelengths of .415 A and .635 A.

Target III-1

Voltage: 33 kv. Current: 9.6 x 10-7 amp.
Exposure: 5 sec. Thickness: 1.71 x 10"6 cm.
Average 55‘-55~ = 4u5 mm.
" 8M0 -ng =12.7 mm.
The values of B and dz! are as previously listed so that
T - .854 x 10'52 at .415 A

°v
-52
J7 - 4.649 x 10 at .635 A
The constant factors used in evaluating the working
equation were:

121.71 g/mole.

k = 6.122 x 1013 mm./coulomb
a = .912 cm.2
N = 6.06 x 10”"3 atoms/mole

6.22 g/cm.3

‘\6

- 3/ -

 

 

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«hoH N mmsaa> Hapmosfihmmxm .AH
OH M modaa> Haowpmpomne .

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wavc16n~

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theory.

. 6: Conparison of experimental results with

Fig

_Comparison of experiment with theory:

The experimental results are plotted with the theoret-
ical curve in fig. 6.

Previous experimentors in this field have not obtained
exact agreement with theory. Comparitively good agreement
of experimental results with theory has been obtained for
the spatial distribution6 but Reno4, studying JVdV as a
function of voltage, agreed only roughly with the theory.
It will be observed from the results here presented that
(a) the experimental order of magnitude is greater, (b) the
experimental curves do not appear to have a non-zero in-
tensity at the short wavelength limit. Indeed, the exper-
imental curves look very much like intensity curves from
thick targets. Possibly, to approximate the ideal eXperi-
mental conditions it will be necessary to use even thinner
atomic screens than those used in this work. If, however,
that is necessary, a new method of determing target thick~
ness must be devised since the method used in this study
was limited to 150 Alzot

0n the other hand, it is possible that, while the theory
accounts for the spatial distribution fairly well, the
theory is not entirely accurate in other respects and con-
sequently correlation between all theoretical calculations
51nd experimental results are not to be eXpected. In view
(of the failure of other experimental data to check the

theory except for the spatial distribution it would seem

_,32:_

that this is the case. Before any definite statement can
be made, however, with respect to this particular study

some revision of apparatus is in order so that data can be
taken under the most nearly ideal experimental conditions

possible.

-_33 -

Appendix

Preparation 9: the Antimony Filter

 

The Dimensions of the Foil

An antimony foil of the prOper thickness was prepared by
evaporating the metal onto a backing sheet which had a
negligible absorption in the wavelength region where the tin-
antimony filter was to be used. Since it was difficult to
obtain aluminum foil which was not only sufficiently thin to
have an absorption comparable with that of commercial
cellophane but also free from small holes, cellophane was
used as a backing material. The cellophane used (approxi-
mately .002 cm. thick) was tested and found to have a
negligible absorption in the wavelength region where the
filter was to be used.

The Optimum thickness of the tin foil to be used with the
prepared antimony foil was calculated ”45 to be .006 cm.
(see pp. 14). Although no information was available re-
garding the density of thin films of antimony deposited by
evaporation, the tabulated density of crystalline antimony
was close to that of tin so the desired thickness of the
antimony foil was therefore expected to be approximately
.006 cm. Considerable latitude in the thickness of one of
the foils is allowed since the final condition of equal
absorption by both foils is accomplished by rotating one of

them to adjust its effective thickness.

-34..

ouh<x0a<>w
>ZOZ:z< “.0 2.3m»)
.5 ed cs 0.6 0w ed QM 0d 0..

b b _

 

     
 

pd md «0 m.0 ad ..0

0

414.141

m

 

:4me

11114

 

 

 

0.0
O ,

r

u l _
H 1

I J _
VA n

1 N
3

T. M. I.

I V 4

OJ

,. W n
S

I I.
m

OO_W

.l S

.I v.

T ox.

Toe

 

In order to obtain the desired thickness of antimony
deposited by evaporation it was convenient to know the
relationship between the amount of metal evaporated and the
corresponding thiCKness of deposit. To determine this re—
lationship various amounts of pure antimony were evaporated
and the thickness of the corresponding films obtained were
determined. for relatively thin films (2000A to 3500A) the
metal was powdered in a mortar and then evaporated from a
V-shaped trough formed from a .003 x .8 x 3.0 cm. piece of
molybdenum. This trough technique is in contrast to the
common practice of evaporating from a filament to which the
molten metal will adhere. It is desireable to use a trough
to which molten metal will not adhere. CaldwellZJ ,
evaporating different elements from filaments of various
metals, furnishes data on the wetting prOperties of metals.
The thickness of the antimony foil formed in each case was
determined from interferometer measurements ”2 , using the
mercury green line isolated from a low pressure mercury arc
spectrum by suitable filters as the interferometer source
rather than the ultra violet lines mentioned in reference
/Z.. Figure A—l (detail), shows the results of the four
foils prepared in this region.

To prepare thicker foils it was necessary to evaporate
more antimony than could he held in a single trough. The
use of a large trough was prohibited by the current capacity
of the electrical system so an arrangement of three parallel

troughs was used (figure A-2). Each trough was controlled

.3;..

 

 

Fig. A " 2

 

r», A-3

g...

by a separate switch. This arrangement could be made to
handle about one gram of metal but was somewhat awkward

to use. Good control was partially dependent upon the
ability of the operator to see the metal in the troughs.

This was rather difficult, however, since the coating of
antimony on the inside of the evaporator jar became opaque
before all the metal was evaporated. Nevertheless, two foils
were prepared by this method and the data obtained showed
that the curve definitely was not linear in the region 2000 A
to 10,000 A. It appeared, however, hiat the curve was
approaching linearity between 4,000 A and 10,000 A.

By this method sixty foils, each 10,000 A thick, would
have to be prepared in order to make the finished filter. A
new technique was therefore introduced with which it was
possible by four successive evaporations on the same cello-
phane backing to simultaneously prepare four foils, each
150,000 A thick. The finely ground antimony was placed in
a .75 m1. micro-analysis crucible which was nested in a
spiral filament made of 15 mil tungsten wire (figure A-3).
This method would easily handle 2.0 grams of antimony for
each evaporation. The crucible containing the antimony was
accurately weighted before and after each evaporation to
determine the amount of metal evaporated. The sleight error
introduced by the deposit of tungsten on the outside of the
crucible was considered negligible.

In order to prepare four foils simultaneously a piece of

'cellophane large enough to be cut into four foils was mounted

-34..

in a cylindrical frame of 13.5 cm. radius. This distance was
sufficiently large to give a uniform deposit over the surface
to be coated but was still within the range of high speed
antimony atoms leaving the heated crucible. The crucible was
placed at the center of the cylinder.

Films prepared by this technique were too thick to be con-
veniently measured by interferometer methods since the fringe

shift would have been about 55 fringes for l.“ 5461 A, but
the deposit was heavy enough to make possible the determina-
tion of thickness by weight-area measurements. The density
of the antimony was taken to be 6.618 grams per ems.

It will be observed that for the relatively thick foils
the curve (figure A-l) is linear, though for the thin foils
this was not true. If this effect is in any way due to a
potential barrier set up about the cellophane, either by ion
bombardment when a high voltage is applied to the evaporator
chamber during the outgassing process or by some charge
carried by the evaporated particles, then this effect should
be eliminated by using aluminum foil or some other conductor
as a backing material for the evaporated foil. The final
single foil prepared was measured to be 154,000 A thick,

2.5 cm. wide, and 20.5 cm. long.

The Uniformity of the Foil
It was necessary that the final four-fold foil prepared be
uniform over an area at least as great as that of the de-

fining aperature of the x—ray beam with which the filter

-37-

 

£13. 14‘4-

0254mm 330m «uh—ZOxuz
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o o o 0 00000000000.

0000000

«an:

ooooooooooooooooooo

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a .3: o

d
NOIlDTHJG BIBNOUDJH

 

 

 

 

 

 

system was to be later used. To test for uniformity the
single foil was wound around two vertical pins in such a
manner that four thicknesses of absorbing foil might be pre-
sented to a narrow beam (less than 1.0 mm.) of x-rays. The
pins were firmly fixed on the travelling base of a micro-
meter screw which was placed between the defining slits of a
Bragg spectrometer (figure A-4) so that the four thicknesses
were perpendicular to the beam. Absorption readings were
taken at points one millimeter apart across the four-fold
foil, the absorption being measured as a function of the
ionization produced in an ionization chamber. The x-ray
source was kept constant by manual control of x-ray tube
current and constant potential high voltage. It will be
observed (figure A-5) that the variations in electrometer
deflections are less than one millimeter over a section of
foil 1.4 cm. in length. The variation is within the accuracy
of the apparatus.

In its final form the filter had to be at least .4 x 2.20Hh
This was easily prepared from the uniform portion of the four-
fold foil. Actually, the final foil was made 1.0 cm. wide so
that it might be rotated appreciably with out becoming effect-
ively narrower than the defining aperature with which it was
to be used. The pieces of foil were cut to size and cemented
to an aluminum frame which was then mounted with the tin foil
in the balanced filter holder.

If the four-fold had not been uniform over a sufficiently

large area the four foils could have been mounted separately

-33-

 

 

 

0:4
WAVELENGTH

0:3

 

0:2

 

[50.1

0

 

and a condition of uniform absorption accomplished by dis-
placing one of them with respect to the others. That is,

if the non-uniformity of each foil had been wedge—like the
thickness would be changed by sliding the wedges with respect

to each other.

The Balanced Tin-Antimony Filter

Once the tin and antimony foils had been mounted together
in a balanced filter holder they were adjusted so that they
absorbed equally at all wavelengths except between their K
limits. This was accomplished by placing the foils alter-
nately in the x—ray path of a Bragg spectrometer and rotating
one of the foils until its effective absorbing thickness
matched that of the other foil. In this particular case the
antimony foil was perpendicular to the x—ray beam and the tin
foil was rotated about 4° from the perpendicular. The absorp-

tion curves are shown in figure A-6.

.39~

3.

4.

BIBLIOC TRAPHY and NOTES

The references made in the course of this
paper are grouped according to the phase of the

subject. .

Sommerfeld, A., Uber die Beugung und Bremsung der
dlectronen. Ann. d. Phys. 11:257. 1931.

Scherzer, 0., Uber die Ausstrahlung bei der Bremsung
von Protonen und schneller Electronen. Ann. d. Phys.

 

13:137. 1932.

Sauter, F., Uber die Bremstrahlung schneller Electronen.
Ann. d. Phys. 20:404. 1934.

Kramers, H.A., Phil. Mag. 46:836. 1923.

Kulenkampff, H., Untersuchungen uber Roentgenbremstrah-
lugg von dunnen Aluminum Folien. Ann. d. Phys. 87:597.

 

1928.

Bohm, K., Untersuchungen uber die Azimutale Intensitat-
sverteilung der Roentgenbremstrahlung. Ann. d. Phys.
33:315. 1938.

Duane, W., Proc. Nat. Acad. Amer. 13:315. 1927 and
14:450. 1928.

Nichols, W.W., Bur. Std. J. Res. 2:837. 1929.
Thordarson, 8., Ann. d. Phys. 35:135. 1939.

Corrigan, K.E. and Cassen, B., Spatial Distribution g;
Radiation from a Supervoltage Roentgen Tube and Its
Significance in Therapy. Am. J. of Roentgenology and
Radium Therapy. 33:811. 1937.

Van Atta, L. and Northrup, D., Leasurements of Roentgen-
Ray Production in the Range 0.8 to 2. 0 Lillion Volts.
Am. J. of Roentenology and Radium Therapy 41: 633. 1939.

Kelly, H., Emission g; the Qontinugu us X- Bay Energy from
Thin Aluminum Leila. Thusi m: h aster L: Lience 511
Michigan State College. 1940

Reno, A., Continuous X-Ray Intensity From Aluminum
Targets as a Function of Electron Energy. Thesis for
Laster of Science at Michigan State College. 1941.

 

-,4o -

5.

9.
10.
11.

12.

13.

14a.

15.

16.

17.

18.

Sauter, F., loc. cit.

Kelly, H., 100. cit.
Honerjager, B., Ann. d. Phys. 38:33. 1940

Clark, J.C., and Kelly, B., An Absolute Determination 93
the Continuous X—Rav Energv From Thin Aluminum Targets.
Phys. Rev. 59:220. 1941.

Reno, A., 100. cit.

Harworth, K. and Kirkpatrick, P., Relative intensities
in the Nickel Cintinuous X—Ray Spectrum. Bul. Am. Phys.
Soc. 16: June, 1941.

Heitler, N., Quantum Theory 9: Radiation. Clarenden
Press, Oxford. 1936. p. 97.

Ibid. p. 162.
Ibid. p. 167.

Pettitt, N., Determination g: X-Ray Mass Absorption
Coefficients for Columbium from .200 tg .500 Angstrom
Units. Thesis for Master of Science at Lichigan State
College. 1938.

Clark, J.C. and Fritz, N., Egg Q: Ultraviolet C‘ource for
Interferomete; Eeasprements a: Thickness of Thin
Metallic Films. Rev. Sci. Inst. 12:438. 1941.

 

 

 

 

Fritz, N., The Effect 2£_Thickness 2; Supporting Films

for Thin Targets Used lg X-Ray Intensity Measurements.

Thesis for Master of Science at Michigan State College.
1942.

Ross, P., Phys. Rev. 28:425. 1926.
Kirkpatrick, P., 9g the Theory and Use 9: Ross Filters.
Rev. Sci. Inst. 10:186. 1939.

According to Kelly, 100. cit.

The value of the absorption coefficient used in this
calculation was obtained from J. 0. Clark in a private
conversation.

Webster, D. and Yeatman, R., J. 0p. Soc. Am. and Rev.
Sci. Inst. 17:248. 1938.

Compton, A.H., and Allison, S.K., X-Rays in Theory and
EXperiment. D. Van Nostrand. 1936. p. 520.

 

19.

20.

21.

Clark, J. 0., A leasurore t of the Absolute Probability
of K-Electron Ionization.g§* Silver _y Cathode Rays.
Phys. Rev. 48:30. 1935.

 

 

 

 

 

Stockmeyer, N., Ann. d. Phys. 12:71. 1932.

Caldwell, W., The Lvaporation of Lolten Letals from IZot
Filaments. J. App. Phys. 12% 779. 1941.

 

 

 

-,42,-

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