-
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--~I
THE USE OF MEtIYL IODIDE AS A HIGH Z MLATERIAL
IN BLUELE CLil)ILRS
by
RICHARD KUThEO YAIHALOTO
SUEiiTTED IN PARTIAL FULFILI ,E NT OF TUE
REQUIRLiENTS FOR T-E DEGREE OF
EAC-ELOR OF SCIENCE
at the
iA-SSACIEU'SETTS INSTITUTE OF TECH1OLOGY
(1957)
Signature of Author4r.
Certified by..
..--
--
-r .
..
*
......
*
*
* *
.......
Thesis Supervisor
'J7ll-
The possibility of operating a bubble chmnber using
a high Z liquid composed of 30] (by volume) methyl iodide
(Ci3 I) and 70
propane (Ehg)
is discussed in this paper.
A theoretical method of obtaining the operating temperature of a bubble chamber is
also discussed, with appli-
cation to the above mentioned mixture.
The mixture was
found to operate successfully at a temperature of 850C
in
contrast to the theoretical value of 67'C.
i-f
- W'-Psa;
Table of Contents
I.
II.
III.
IV.
V.
VII.
VIII.
. . .
. . . .
.
. . .
.
. .
General Theory of Operation of Bubble Chamber ..
Theoretical Calculation of Operating Temperature.
III. 1
Equation for Bubble of Equilibrium Radius
III. 2
Energy Needed to Create a Bubble of Radius
III. 3
Approximations for Mixtures . " .
Radiation Length for Pure Propane and
70% Propane Mixture . 0 0 . 0 0 0 . .0
Description of Appara tus.
*
.
.
*
.
.
.3
Iiethyl Iodide-
30
.
0
.
.
.
.
0
.
.
.
Description of Cycli c Operation of the Chamber.
V. 1
VI.
.
Introduction.
Experimental Procedur e.
. .
. .
.6
.9
. . 10
Experimental Results.
..
.0
. . . . . . 11
Conclusion.
.
.
. .
. . . . 12
Figures .
.
.
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.
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(3)
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Photos.
. .
(1) . .
. .
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IF
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I
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I
,
TNTF'RODUCTION
The observation of electron-pairs converted from gamma-
rays produced in a hydrogen event is of importance in certain
experiments.
Thus, a bubble chamber utilizing a high d(ensity
and high Z (atomic nunber) liquid is of value.
In this experiment, we were interested in investigating
the possibilities of using a "sensitive" liquid comnosed of
propane (C3 H)
(hydrogenic comnonent)
and iodomethane (high Z
component).
II
GERTERAL TH-EORY OF OPEIATION OF
TLEULE ChAMi-IER
It is well known that a super-heated liquid will boil
spontaneously if the liquid is somehow excited while in this
state.
The bubble chamber utilizes excitation energy from
high energy particles passing thru the super-heated liquid-thus leaving a track of bubbles tracing the path of the
i
particle.
In
order to attain a super-heated condition of the
liquid in the chamber, a hydrostatic pressure greater than
the vapor-pressure of the liquid is applied on the liquid,
thus allowing only a liquid phase.
If the hydrostatic
pressure is suddenly decreased to a value lower than the
vapor pressure at the specific temperature of the liquid at
that time, the liquid will be in a state of super-heat.
this time, a particle passing through the chamber will
cause the liquid to boil along its path.
III
Ti'HEORETICAL CALCULATION OF OPERATING TETERATURE
III 1.
Eouation for Eubble of Equilibrium Radius r,
Given a bubble of radius r, composed of vapor
At
-2in a liquid of the same component (see figure 1),
the out-
ward force tending to tear the bubble apart, due to the
iS
pressure in the bubblgiven by:
(1)
F= Trr'P
where PV is equal to the vapor pressure of the liquid.
The
inward force tending to collapse the bubble due to the hydrostatic pressure on the liquid is given by:
where Pe is equal to the applied hydrostatic pressure.
A
third force acting on the bubble is due to the surface tension
and tends to collapse the bubble--this is given by:
(3)
F = 2T rTwhere q-is the coefficient of surface tension.
Hence,
the equation for equilibrium is:
or
r r. P,
Tr.7- +
'TrP
r,
)
where r. now represents the critical radius of a bubble in
equilibrium.
Solving for
trI
~4
, we have:
r.
(5)
Bubbles of radii smaller than rP will collapse comrpletely,
where as bubtles of radii larger than r. will grow indefinitely.
III 2.
Energy Needed to Create a Bubble of Radius
The energy needed to create a bubble of radius
r.
may be found at once by considering the heat needed to evaporate
an amount of liquid equivalent to the amount of vapor contained
in the bubble--the PdV work done arainst the hydrostatic
pressure and the work done in forming the liquid-vapor surface
of the bubble, all during the process of growth fromrO to r'=
-3The heat needed to evaporate an amount of liquid equivalent to the vapor contained by a spherical bubble of radius
r, is given by:
E
NH-
(Io)
H= 4rr
Pv
where (N) is the number of gas molecules contained in the
bubble, (V) the volume of the bubble, (H) the heat of vaporization per molecule, (T) the temperature in *K, and (k) the
Boltzmann's Constant.
We have assumed the vapor in the
bubble to be an ideal gas.
The PdV work done by the bubble in growing from zero
volume to V is given by:
"3
r
Sr
where Pe is the constant applied hydrostatic pressure.
(I))
Finally, the energy needed to form the liquid-vapor
surface of the bubble is given by"
ES
-Wr'r
(L)
Therefore, the total energy needed to form a bubble of
radius
r, is given by:
E,= Es+Eev=
trr.ar +
Substituting eq. (5) for r,
-T.3"
- r
)
P, +
r H
we are left withl )
rrt
+ szrrP
(3
We see that this equation is an implicit function of temperature only, since all variable parameters involved are functions
of temperature.
Hence, it is possible to plot E. as a function
of temperature, and knowing the amount of energy lost by a
particle in a region of the order of the critical bubble
volume, we may determine the temperature of the operating point.
III 3.
Approximations for Mixtures
For cases where the t"sensitive" liquid is pure, the
parameters involved in the energy equation (eq. 13) may be
-I+found in almost any physical-chemistry handbook
of tables,
where as, for mixtures of liquids, they generally cannot be
found.
We may, however, make certain approximations to
determine these parameters for mixtures.
Raoult's Lawu of partial pressures for solutions may be
used to determine the vapor pressure of a mixture where the
vapor pressure of one component is much greater than the
vapor pressure of the other.
Thus for a mixture consisting
of components with largely differing vapor pressures, the
total vapor pressure may be approximated by:
P..=
P X.
where Pv is the total vapor pressure of the mixture; Po, the
vapor pressure of the component with greater vapor pressure;
Xo, the mole fraction of this component; ie., -) where No is
N+N.
the number of moles of the component with greater vapor
pressure, and N is the number of moles of the component
.with lower vapor pressure.
If the mixture obeys Raoult's Law7 and we assume no
interaction between components to occur, the total heat of
vaporization will then be equal to that of the component
with higher vapor pressure.
This is evident from the fact
that nearly all the vapor is composed of the component with
higher vapor pressure.
In the limit, as the vapor pressure
of one component approaches zero, this is exactly true.
This can be shown analytically by use of the ClausiusClapeyron equation as follows:
solution; then P=PoXo is exact.
Let us assume a perfect
Now,
the Clausius-Clapeyron
-5equation states that:
dP = L_ 4H
dr
-rT
A Vs)
but, from Raoult's Law:
x. d
g
dT
-H
.- --
4V
7
Assuming the vapor to be a perfect gas, and the specific
molar volume of the liquid to be negligible compared to that
of the gas, we have: AV= V -,4
C1-
A7,T
R
=
T
-
If the liquid were composed entirely of the liquid
with vapor pressure Po, we would have:
,//Yo
dP,4
dT
Ta
Po
.=/.
O...
06)
R
Unfortunately, there is no simple way of determining
the coefficient of surface tension of a mixture of liquids,
unless a direct measurement is made.
There is a possibility
of using the Parachor for homologous mixtures, which we
will, however, not use because of the possibility that our
mixtures are not homologous.
Instead, we will make reason-
able assumptions as to the values of the surface tensions
for mixtures, by considering the values of the surface
tensions for the pure components, and their concentrations
in the mixture.
For pure propane, this is all quite unnecessary as all
parameters are readily available in handbooks.
The plot
for energy versus temperature for pure propane has been made
and is shown in figure 2 on the following page.
The experi-
mental operating temperature is found to fall within the
calculated range.
To find the operating temperature range,
we assume the energy needed to form a bubble of critical
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60
.
70
80
-6-
radius to be between 10 and 30 electron volts, which is
approximately- equal to the energy needed to ionize one
molecule contained in the critical radius(,/otIm).
The
hydrostatic-pressure (Pe) has been set equal to one
atmosphere.
An Energy-temperature plot has also been
30% (by volume) methyl iodide--70,
lmade for a
propane
where
witure,
the surface tension has been assumed equal to th1at of pure
propane.
The total vapor pressure was found by the use of
Raoult's Law--this approximation is fairly good since the
vapor-pressure of propane is
much higher than that for
methyl iodide at any given temperature,
viz.,
15 atm. for
propane as conpared with latm. for methyl iodide,
at 46'C
The resulting plot is shown in figure 3.
IV
RADIATION LENGTH FOR PUR
URE PROPNE
E
AND 30
ETh,-YL IODIDE-
70. PROPANL IIXTURE
In this section, we are interested in calculating the
decrease in radition length obtained by adding 30, (by
volume) methyl iodide to pure propane,
and by adding 50,.
(by volume) methyl iodide to pure propane.*
The expression for the radiation length for high energy
electrons is
Where:
given by:
( -fine
X=
a
l
3
structure constant (4~)
Z = atomic number of material
No-
AvoCadro's number (6.023 x 10
molecules per mole)
re= classical radius of electron
A = atomic weight of material
*This :.mixture has not been tried in the bubble chamber
as to date, but will be tried in the 6" chamber in the near future.
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II
.
:
-7and that for a substance composed of several elementst'
whereA,4,---Xf'are the radiation lengths for each component
and~~,---P* the fractional weights for the corresponding
elements.
For carbon, we have
iodine XgaB.Ifl5
.
=z2
, for hydrogen±E4u
Hence, for pure propane we have:
may be neglected in comparison to
of order l0'ewhile
- is of order 1 l
of the carbon in propane(Pe)
$3. ~
is3CI,
and for
since it is
The fractional weight
is equal to
-
.
Therefore, M.
or, since the density of propane at room temperature
X.o
127s.
By the same method,
we find the
radiation length for a mixture of 30% (by volume) of methyl
iodide in propane to be 12.15 cm. and for a mixture of 50%
methyl iod.e in propane, 7.62 cm.
Thus we find the radia-
tion length of the liquid to be decreased by a factor of
.105 by adding 30% (by volume) methyl iodide, and by a
factor of .167 by adding 50% methyl iodide.
Hence, it is possible to have several radiation lengths
(2-3) in a bubble chamber of dimensions o 10 inches.
This
is of importance where one desires to observe electron pairs
converted from gama-rays produced in a hydrogen event.
V
DESCRIPTION OF APPARATUS
The bubble chamber used in this experiment has a
sensitive volume, 4.5 inch by 1 inch (I.D.).
The sensitive
body is made of a pyrex glass tube (.25 inch wall thickness)
sealed at one end by an aluminum plug fitted with a butyl
~ _~
-
-8rubber "O-ring."
The base of the chamber is made of stain-
less steel and mounted on an all-aluminum stand for rigidity.
(See figure 4).
Expansion and compression of the "sensitive" liquid is
accomplished by the use of a relatively light stainless-steel
piston fitted with a dynamic "O-eing" seal.
The piston is
driven on the compression stroke by compressed nitrogen.
On the expansion stroke, the piston may be driven back by
the rapid vaporization of the compressed liquid in the
chamber (method used in this experiment) or by compressed
nitrogen.
The complete cycle is controlled by an electro.
mechanical solenoid valve.
The sensitive body of the chamber is enclosed in a
glass casing, and is heated by a hot-air flow passing through
the enclosed region.
This method of heating is sufficient
because of the relatively small thermal-inertia of the
system.
The air flow is heated by passage through a
thermally-insulated nichrome electric heater.
A temperature
control and two temperature measurement thermistors are
placed near the sensitive body.
The temperature-measuring
thermistors are placed at opposite ends of the chamber to
determine any temperature gradients that may arise.
The
electric current for the heater is controlled by a thyratron
control circuit in conjunction with the temperature control
thermistor.
The temperature is measured by a D.C. Wheat-
stone bridge employing the temperature measurement thermistor
as one of its balance arms.
The temperature may be read
from a temperature-galvanometer current plot, or by the
W-~
10
Bubble Chamber Ready for Operation
Fig. 4
~___ _~__
-9conventional null :rcthod (used
'or hihieur accuracy).
The electronic co-Iiponnts oi' the sy tem coisist of a
variaLle pulsc-gencrator,
valve power-supply,
trigger circuit, delay circuits,
electronic camera-flash plower supply,
signal mixer, and a cathode ray oscilloscope.
diagram of the electronic circuitry is
A block
sh;own in figure 5.
A 35 mii. Lell and Howell "Eyemo" miovie camera,
adapted for single frame advance or a Land Polaroid camera
may be used for photography.
The latter is generally used
for izmlecliate examination of results.
V
1. Description of Cyclic Operation of the Chamber
(See block diagram in figure 5)
The pulse generator is set to produce pulses at
a constant desired rate, only one of -which is allowed to
pass the trigger circuit when the trigger switch is depressed.
The resulting single pulse then enters three of
the four delay dircuits simultaneously.
Delay (1) is used
to fend a gate of desired width to valve driver (1), which
alloiws the valve to open and thus cause expansion.
Delay (2)
is used to send a delayed pulse into delay (3) which then
sends a gate of desired width to valve driver (2) closing
the valve, causing compression.
Delay (4) is used to send
a delayed pulse to the camera-flash power supply, thus
causing the camera-flash to fire at the appropriate time.
The signal mixer is merely used to superiipose all
signals on the time axis of the CRO0
to time all signals.
thus
aking it
possible
- 9. r-L tiec 1i-romp /;
t
Ayoo
A: 0 d- -- 4ep
,510t P",afy.*a.*
igE~-
_1 ~___XI_1__~
_:~ ~_rr~_~_
_ _~~~~_ _~_~_~~~~ _
__ _~_I~
-10VI
EXPiRIIENT.L PROCEDURE
The general procedure used in this experiment is simple
and straight forward.
A one milli-Curie radium source is
used to insure that a constant flux of gamma-rays pass
through the chamber.
Thus, expansion of the chamber at
random times will yield tracks of Compton-electrons.
By
this method, we are able to measure the number of tracks
(if desired) knowing the
flux of gamma-rays to be constant,
and comparison of track numbers may be made for different
sensitive liquids, and for different operating conditions.
Also, the rate of bubble growth may be measured by measuring
the bubble sizes from tracks photographed with different
flash delays.
A graph of bubble size versus time delay of
the flash may then be plotted.
The slope of this curve
will determine the rate of bubble growth.
The excitation
particles (gamma-rays) may be assumed to enter the chamberat exactly the same time (after expansion has taken place)
in each track photograph.
This is a good assumption since
the radium source has a high constant flux.
Of course, the
largest bubble in each photo will have to be measured in
order to give consistent results; the largest bubble is
formed by the first
gamma-ray entering the chamber daring
the sensitive time.
However, in this experiment, we were interested in
merely observing tracks--that is, to see if the liquid
mixture tested was a possible track-yielding liquid.
(Note:
theoretically any liquid will yield tracks if the
operating conditions are suitable.
However, our chamber was
_
=I- *
C-
..
limited to a temperature range of 25*C to 120*C and a
pressure range of 0 psi to 600 psi).
To carry out this
test we took photographs with a Land Polaroid ca'- :era,
VII
E'RIM INTAL RESULTS
23
(by volume) of methyl iodide was added to 77
propane and was found to be readily miscible.
of
The tenpera-
ture was then raised to 65C and traces of tracks were
evident, as shown in photo (2).
It can be seen from the
photo that the number of tracks were low, due to insufficient
heating.
When the temperature was raised to 750C, distinct
tracks were seen, as shown in photo (3).
Thus, this mixture
was found to be a track-yielding liquid.
Comparin g
(3)
oto
to photo (1), it is immediately noticible that the
tracks in photo (3) are shorter.
knomwn
This confirms the well-
depenence of radiation length since photo (1) was
taken using pure propane.
However,
it
is
reasonable to
believe that the number of tracks in photo (3)
much greater than that of photo (1),
should be
because of the higher
Z, but this is not evident from the photo, due to poor
contrast and poor resolution of the Polaroid film.
After finding it
possible to obtain tracks from a 23%
methyl iodide mixture, the concentration of methyl iodide
was increased to 30..
Tracks were observed at a slightly
higher temperature of 850C, compared with the 75OC temperature required for the 231 mixture (see photo (4)).
It can
be seen from Photo (4) that the average track lengtihs are
shorter than those in both photo (1) and photo (3).
The vapor-pressure versus temperature plot for the 30%
-r
Photo 1. Electron tracks
in pure propane
(C 3 H 8 ) at 600C.
Photo 2. Electron tracks
in 23% methyl iodide
(CH3I) and 77% propane
(C 3 H8) mixture at 65*C.
Photo 3. Electron tracks
in 23% methyl iodide
(CH 3 I) and 77% propane
0
(C H 8 ) mixture at 75 C.
Photo 4. Electron tracks
in 30% methyl iodide
(CH 3 I) and 70% propane
(C 3 H 8 ) mixture at 85*C.
3
M#"
.. ,laO#
-----
,+-i~~~~~~~~---
--- ----
---
, -,41.4
- - . ....................
.'
:
; ........
.... 0
9
... .... .
1
:............
'---070
-
-------
YO
- ---
6
---------
161
- ----- --------O
-
---
8.
2
/
--
7-r
-
70
---
-- --- ---------------
.---
-12-
mixture is shown in figure (6).
We note that the theoret-
ical curve (using Raoult's Law) is somewhat lower than the
experimental curve.
However, the experimental curve lies
eurve
lower than the pure propaneK-thus Raoult's Law is a first
approximation to the true vapor-pressure curve.
The theoretical operating point. for the 30
mixture
is shown in figure 3--comparison of the experimental operating temperature with the theoretical operating temperature
shows the theoretical value to be somewhat low.
This is
probably due to the error in the value used for the coefficient of surface tension.
VIII
CONCLUSION
It is possible to operate a bubble chamber using a
liquid composed of a high Z material (CHSI) dissolved in
propane (CHS).
The advantages of using this uniform high Z-
hydrogen mixture are:
a)
Interaction of high-energy particles with protons
may be carried out.
b)
The possibility of studying the gamma-rays emitted
from such interactions, by observing the electronpairs produced in the high Z material.
c)
The operating temperature and pressure are relatively
low(in the region where pure propane operates).
't
_
ACKNOWLEDGEMENT
The author is especially indebted to Dr. Irwin A. Pless,
for the use of his bubble chamber and electronic equipment,
but more so for his constant guidance and advice, both
theoretical and technical, throughout the entire experiment.
The author would also like to express his appreciation and
gratitude to Prof. Robert W. Williams and Mr. Alfred E. Brenner
for their suggestions.
--~--T~------
References
D. A.
and Rahm,
D. C., Phys.
Rev. 2,
p.
1.
Glaser,
1955.
2.
Pless, I. A.
935-7, 1956.
3.
Rossi, B., High-Enerqy Particles, Prentice-Hall,
p. 50-5, 1956.
4.
Glaser, D. A., Phys.
5.
Glaser, D. A., Phys. Rev. 87,
474-9,
and Plano, R. J., Rev. Sci. Instrum., 22,
Rev.
,91p.
762-3, 1953.
p. 665, 1952.
N. Y.,