THE SOVIET JOURNAL OF ATOMIC ENERGY VOL. 4 NO. 2

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• Document Creation Date: January 4, 2017
• Document Release Date: September 13, 2013
• Sequence Number: 2
• Publication Date: February 1, 1958
• Content Type: REPORT

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THE SOVIET JOURNAL OF
vol. 4, no. 2
February, 1958'
OMIC ENERGY
ATOMHa5I
HFHM
TRANSLATED. FROM RUSSIAN
CONSULTANTS BUREAU, INC.
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vol. 4, no. 2
February, 1958
THE SOVIET JOURNAL OF
ATOMIC ENERGY
ATOMNAIA ENERGIIA
A publication of the Academy of Sciences of the USSR
Annual Subscription
Single Issue
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volume I, number 1 january 1956
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Copyright 1958
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EDITORIAL BOARD
OF
A TOMNAIA ENERGIIA
A. I. Alikhanov, A. A. Bochvar, V. S. Emerianov, V. S. Fursov,
V. F. Kalinin, G. V. Kurdiumov, A. V. Lebedinskii, 1.1. Novikov
(Editor-in-Chief),V.V.Semenov (Executive Secretary),V.I.Veksler,
A. P. Vinogradov, N. A. Vlasov ( Assistant Editor-in-Chief).
Printed in the United States
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HISTORICAL DEVELOPMENT OF THE CYCLOTRON
(SURVEY OF THE LITERATURE)
L. M. Nemenov
A short survey, based on the published literature, is given of the historical develop-
ment of cyclotron devices. The basic parameters and main features of cyclotrons are given.
The paper is illustrated by photographs taken from the literature.
Almost thirty years have passed since the first enunciation of the principle of the magnetic resonance
accelerator ? the cyclotron, a machine which has played an extremely important role in nuclear research.
Because of its universal application, the cyclotron is, at present, one of the most widely used types of accelerators.
Using the published literature, we shall trace the evolution of the cyclotron during this time, a period in
which the rapid development of nuclear physics imposed ever-increasing requirements on the cyclotron.
Using the cyclotron it is possible to accelerate ions of virtually all elements from hydrogen to neon and
to study a large number of nuclear reactions which occur when charged particles interact with matter. The
cyclotron is a source of fast, monochromatic neutrons and, with a sufficiently intense beam of charged particles,
allows us to obtain a flux of partially polarized neutrons. By exploiting the discontinuous nature of the ion beam
from a cyclotron it is possible to investigate neutron spectra, determining the fast-neutron energy by time-of-
flight methods; using a so-called "pulsed beam" we can investigate the interaction of slow neutrons with matter.
In certain cases the cyclotron is used as a source of hard y -rays. Finally, it can be used to obtain a number of
nuclides of high specific radioactivity.
The first paper on the principle of a cyclical resonance accelerator in which a high voltage is not used
was that of Lawrence and Edlefsen [1] in 1930. In 1931, using a cyclotron with a pole diameter of 100 mm,
Lawrence and M. Livingston were able to accelerate ions of molecular hydrogen to an energy of 80 key. This
primitive, laboratory-built device became the prototype of modern cyclical accelerators.
In that same year, Lawrence and M. Livingston, using an improved machine (Fig. 1), were successful in
accelerating protons to an energy of 1,22 Mev. In this work it was noted that a change in the magnetic field
of several tenths of a percent was sufficient to disturb the resonance condition. In their basic description the
authors indicated the method used for correcting inhomogeneities (the introduction of pieces of iron between
the pole pieces of the magnet and the roof of the accelerator chamber). The electric field of a condenser was
used to deflect the beam of charged particles. The beam current at the terminal radius was 10-9 amp,but
the authors discussed the possibility of obtaining currents of the order of 10-7 amp.
In 1932, using an improved machine, these same authors accelerated deuterons to 3.6 Mev. A current
of 10-9 amp was detected with a measuring electrode (Faraday cylinder) which was set up beyond the de-
flection system. In 1933 ions of molecular hydrogen were accelerated to 4.8 Mev in this same accelerator.
In this work an oscillator system consisting of two dees was used.
Using a chamber with a roof diameter of 690 mm, in 1934 the same workers accelerated ions of molecular
hydrogen to 5 Mev (Fig. 2) while in 1935 a current of molecular hydrogen ions of 10 -5 amp was obtained be-
yond the deflection system in this same apparatus,
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In 1936 great progress was made. Lawrence and Cooksey [2] built a new chamber with a roof diameter of
700 mm and accelerated deuterons to 5 Mev; moreover, using a deflection system, for the first time it was
possible to extract a beam of charged particles with a current strength of 5 ? amp from the chamber through a
Fig. 1. Cyclotron with which protons were accelerated
to an energy of 1.22 Mev. Upper photograph ? general
view; lower photograph ? acceleration chamber with
one dee.
thin platinum window. The radio-frequency
generator, using a self-excited push-pull circuit,
delivered radio-frequency power of the order of
25 kw. The potential difference between the dees
was 50-100 kv. The magnetic field correction was realized by introducing iron discs between the pole pieces
of the magnet and the ends of the accelerator chamber. For the first time attention was paid to the fact that
the geometric center of the accelerator chamber does not coincide with the center of the particle orbit and it
was shown that this effect can be avoided by additional corrections of the magnetic field. An electrode for
measuring the beam current was located in the chamber beyond the deflection system. Provision was made for
Fig. 2. Accelerator chamber with two dees with
which ions of molecular hydrogen were accelerated
to 5 Mev.
Fig. 3. Accelerator chamber in which deuterons
were accelerated to an energy of 8 Mev and
extracted.
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mounting a target for exposure on this same device; the target was cooled by circulating water. In this cyclo-
tron the first experiments with fast neutrons obtained by bombarding beryllium with deuterons were carried out.
The authors also proposed that it was feasible to extract the beam in a tube under vacuum to a considerable
distance from the cyclotron in order to reduce the background of radiation from the machine itself. In this
same year Du Bridge and Barnes constructed a similar machine and accelerated protons to 6 Mev at a beam
current of several microamperes.
Fig. 4. General view of the cyclotron in which
vacuum coaxial resonance lines were first used.
In 1937 Lawrence and Cooksey (3) built
a highly improved accelerator (Fig. 3). The
dee circuit was water cooled. The chamber
was provided with reliable vacuum valves.
Means were provided for measuring the dee
potentials. For the first time the deflection
system was provided with a thin element of
refractory metal in order to reduce the losses
of charged particles from the beam which
entered the condenser. Also, for the first time,
use was made of a probe with a sliding seal
developed by R. Wilson for measuring the current
of accelerated particles at any radius (based on
heating of water). It was also possible to fasten
a target to this same probe. Vacuum ports
placed beyond the deflection system made it
'possible to operate the apparatus and remove
irradiated targets without disturbing the vacuum
in the accelerator chamber. The beam was ex-
tracted to the outside through a thin metal foil
fastened.to a plate through which a large number
of holes were drilled.
The authors obtained 8 Mev deuterons,
Tlie'current at the terminal radius was 100 amp.
The current in the extracted beam was several
microamperes. The construction of this cyclo-
tron represented an important achievement since
it was the first machine to employ sophisticated
engineering techniques.
In this same year, in Leningrad the first
cyclotron in the USSR and Europe was built
(magnet diameter of 1000 mm (4)); Alvarez
and his co-workers made the first attempt to remove an exposed target from the cyclotron; Veksler and M.
Leontovich, on the basis of work by Tuve and Lamar, constructed and tested the first capillary ion source for
a cyclotron; Bethe published the first paper on the theory of the cyclotron,
1938 was an especially fruitful year in the development of accelerators.
Dunning and Anderson [5], using an idea proposed by Sloan, for the first time applied a quarter-wave
coaxial resonant vacuum line for applying the radio-frequency voltage to the dees (Fig. 4), This improvement
made it possible to eliminate the glass insulators which limited the magnitude of the voltage which could be
applied to the dees.
Alvarez obtained an intermittent beam of thermal neutrons by modulating the beam of deuterons in-
cident on a beryllium target. Wilson and Kamen carried out interesting experiments for verifying the theory
of the cyclotron. Allen et al. accelerated deuterons to 9.7 Mev, obtaining a current of 1 ji amp in the ex-
tracted beam.
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This year was also extremely fruitful in theoretical work. Here,we must mention the fundamental re-
search carried out by Rose on the theory of the cyclotron [6], the work by Khurgin on the limiting particle
energy in a cyclotron [7] and Wilson's work on electrostatic and magnetic beam focussing [8]. However, one
of the most significant events of that year in the field of acceleration techniques was the appearance of a
paper by Thomas who showed that charged particles can be accelerated to significantly higher energies in a
cyclotron if an azimuthal asymmetry is introduced in the magnetic field. Actually, in this work Thomas
touched upon the "strong focussing" principle. However, his proposal was not exploited since the creation of
a magnetic field with the required configuration represented a problem of extreme difficulty. At that time
even the problem of correcting the magnetic field in an ordinary cyclotron was one of no mean difficulty.
Fig. 5. General view of the Berkeley cyclotron with which deuterons were first accelerated to an energy
of 22 Mev.
The design of a giant cyclotron with a pole-piece diameter of 4.7 m for accelerating deuterons to an
energy of 100 Mev, proposed by Lawrence in the pre-war period, and the important discovery [10] made in-
dependently by Veksler (1944), and McMillan (1945) diverted the attention of physicists from the proposal
made by Thomas for more than ten years.
In 1939 Lawrence, Alvarez and their colleagues put into operation the largest cyclotron in the world;
this machine had a pole diameter of 1500 mm (Fig. 5) [11]. The weight of the magnet was 200 tons. The
construction of the accelerator chamber was considerably different from that which had been used up to that
time. Its basic advantage was the fact that the dees and the resonant lines could be removed from the chamber
while the chamber remained between the poles of the magnet. Thus, this operation did not disturb the magnetic
field corrections.
The resonant line of the cyclotron was rather complicated in construction. Special devices were used to
permit adjustment of the position of the dees without disturbing the vacuum. At first the deflection system was
set up inside the dees. In the early design a radiofrequency voltage was "induced' in the deflection system;
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this had an effect on the intensity distribution in the extracted beam. The modified system was found to be
free from this shortcoming.
In this apparatus McMillan, and Salisbury improved a capillary ion source developed by M. Livingston,
Holloway and Becker. To improve the efficiency of ion extraction from the source a rib was added to the dees,
thereby increasing the gradient of the radiofrequency field. This modification resulted in a seven-fold in-
crease in the current of accelerated particle. The beam was extracted through a window cooled by a hydrogen
jet which Was developed by F. Curie.
The machine was evacuated by oil diffusion
pumps with a capacity of 3000 liters/sec. The
accelerator chamber was so large that it had to
be mounted on a special flatcar. With this
machine protons at 9 Mev were obtained on an
internal target with a current of 25 i amp.
Deuterons were accelerated to an energy of
16 Mev (the current on the internal target was
10 ?amp, the current in the extracted beam
was 1 ?amp ). Before the start of the war a
deuteron energy of 22 Mev was obtained with
this cyclotron; this was a record for the time.
In 1940, Alvarez accelerated C 1:26 ions
to an energy of 50 Mev, carrying out experi-
ments to investigate the interaction of multiply-
ed ions with matter. The beam intensity
erminal radius of the cyclotron was
s same year Curtis was able to con-
source in which it was possible to
incandescent filament without dis-
t '4, vacuum in the ac-celerator chamber.
ilSq1i42) published a paper in which con-
sideratsin was given to problems of electric and
magnetic focussing, ion production in the
central part of the cyclotron and displacement
of particle trajectories.
In 1942, Condit, using the 11/2 meter
cyclotron at Berkeley, accelerated C +126 ions
to 85 Mev and 0+1: ions to 113 Mev. The
interaction of multiply' charged ions with
matter was studied in a Wilson chamber.
Fig. 6. Accelerator chamber with resonance lines
and dees of the cyclotron at the Massachusetts
Institute of Technology (the upper chamber cover
is removed). Using this chamber deuterons with
an energy of 15 Mev were obtained. Deuteron
currents of up to 1 ma were achieved at the ter-
minal radius.
net diameter of 1050 mm (magnet weight about 90 tons).
all the earlier theoretical results and experience acquired
In 1944 M. Livingston [13] published
data on a new machine which was one of the
most advanced of its kind. He obtained out-
standing results with a cyclotron having a mag-
In designing this machine Livingston made use of
in operation of all existing machines. Livingston
took particular pains in the correction of the magnetic field. The decrease in magnetic field at the extraction
radius was 1.8%. The magnetic field corrections were applied by means of piles of discs which were placed in
the gaps between the chamber covers and the pole pieces. A remotely controlled variable condenser was used
to adjust the frequency of the resonant circuit. Movable shorting elements for the resonance lines were pro-
vided in the form of spring contacts. The intense beams of charged particles were detected by a rotating target
which was constructed; with this rotating target it was possible to increase the thermal stability by distributing
the heat load over a large surface.
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Fig. 7. General view of the 11 meter cyclotron at the Institute for Atomic Energy, Academy of Sciences, USSR. [The color
plate has been graciously provided by the Soviet publishers of Atomnaia Energiia.]
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Fig. 8. Diagram of the Oak Ridge cyclotron with vertical acceleration chamber. 1) Dee system;
2) motor generator; 3) vacuum chamber; 4) magnet winding; 5) radiofrequency generator;
6) magnet yoke.
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In addition, the Livingston design provided a number of features to facilitate all operations associated
with adjustment, assembly, and disassembly of the various units of the cyclotron (Fig. 6), Most of the operations
were carried out remotely from a central control panel. Livingston was one of the first to consider the problem
of personnel protection against radiation and to take effective measures for radiation safety.
After adjustment of the cyclotron Livingston was able to obtain a record result: deuterons were accelerated
to 15 Mev. The current at the terminal radius was about 1 ma and the current in the extracted beam was
approximately 100 JI amp. The potential difference between the dees under these conditions was 140 kv.
In this same year Kruger and his colleagues published a report on an interesting version of the cyclotron
[14]. The deflection system made it possible to extract the beam of charged particles in a direction parallel
to the slit between the dees. Under these conditions the magnet yoke does not hinder the extraction of the
beam and the installation of an analyzing magnet.
Setting up a potential difference of 150 kv between the
dees, the authors accelerated deuterons to 10 Mev and obtained an extracted beam current of 100 !lamp. In
this apparatus the first attempt was made to obtain a monochromatic extracted beam of charged particles from
a cyclotron. For this purpose use was made of an analyzing magnet which deflected the beam through an angle
of 51*; collimating slits were set up in front of and in back of the magnet. The authors obtained a deuteron
beam with an energy spread of 0.1%.
In 1946 Tobias and Segre accelerated C+4 ions to an energy of 96 Mev at the Berkeley cyclotron. After
several months York et al., using this same apparatus, accelerated ions of both carbon isotopes (C ll to 135 Mev
with a current of 103 ions/sec and C +4 to 146 Mev with a current of 103 ions/sec).
In 1947 the one-and-a-half meter cyclotron of the Institute for Atomic Energy, Academy of Sciences,
USSR was started up [15] (Fig. 7). To reduce ion bunching, in 1950 a long ridge was added to the dees, there-
by reducing the geometric dimensions of the electric-field region close to the source.
In this same cyclotron use was made, for the first time, of a deflection system with an inhomogeneous
electric field which, in addition to deflecting the beam of charged particles, provided focussing in the horizontal
direction. Later, calculations were carried out on deflection systems with electrodes of hyperbolic cross section.
These calculations are used as a basis for the design of deflection systems for cyclotrons being built in the USSR.
Use was also made of additional windings, connected in opposition, on the pole pieces of the magnet which,
without disturbing the resonance conditions, made it possible to shift the median plane of the magnetic field
upward or downward depending on the current in the windings. This system facilitates considerably the adjust-
ment of the median plane of the magnetic field of the cyclotron.
In 1952, R. Livingston [16) published a description of the largest cyclotron in the world, built at Oak Ridge,
With this machine a record proton energy was achieved ? 24 Mev (the particle current at the terminal radius
was 1 ma). The machine was built specially for work with internal targets.
Since this cyclotron was intended only for proton acceleration (low field intensity),in spite of the large
pole-piece diameter (2100 mm) the magnet weighs only 250 tons, The magnet is C-shaped. In order to avoid
collapse of the posts to which the dees are fastened, instead of using the usual (horizontal) configuration the
accelerator chamber is placed between the poles of the magnet in a vertical position (Fig. 8),
The potential difference between the dees is 440 kv. In order to avoid electrical breakdown in the
accelerator chamber at these high voltages, the dees are also connected to a fixed negative potential of
1000 volts, This is possible through the use of support rods insulated from the tank of the resonance line. To
solve this problem Livingston departed from the use of two coaxial resonant lines, placing the supports for both
dees in a common tank. To reduce the level of induced activity in this apparatus, for the first time use was
made of graphite shielding on the inner surfaces of the dees which are suceptible to bombardment by the
accelerated particles.
This cyclotron may well be considered the prototype of semi-industrial cyclotrons used for manufacture
of radioisotopes.
In this same year a paper was published on the Birmingham cyclotron [17], the construction of which was
started before the war under the leadership of Oliphant. In this cyclotron ions of molecular hydrogen and
deuterons were accelerated to an energy of 25 Mev? The current at the terminal radius was 16 ;lamp. The
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energy which was achieved represented a record for the one-and-a-half meter cyclotron. However, because
of the difficulty of deflecting the beam, it was necessary to reduce the deuteron energy to 20 Mev. Under
these conditions the particle current at the terminal radius was 350 bi amp and in the deflected beam 70 1' amp.
To eliminate the background of radiation from the cyclotron itself the beam of charged particles is
extracted, by means of a supplementary magnet, through the main shielding into a special installation (at a
distance of about three meters from the cyclotron). The current density at the target reached 1 j amp/ cm2
with an energy spread of approximately 1% in the beam.
In 1952 Atterling and Lindstrom [18] reported on a cyclotron with a pole diameter of 2250 mm (Fig. 9).
The construction of this cyclotron had been started in 1945. This machine was essentially the same as the
machine at Oak Ridge but the accelerator chamber was in the horizontal position while the magnet (weight
430 tons) made it possible to obtain a larger induction in the space between the pole pieces. Deuterons have
been accelerated to 25 Mev in this machine. The current at the terminal radius is 100 bi amp. The cyclotron
was designed for work with internal targets and was later used to accelerate multiply-charged ions.
Fig. 9. Stockholm cyclotron with a pole piece diameter of 2250 mm.
In that same year, Bender et al. [19] published an original solution to the problem of extracting a beam
of charged particles to a large distance from the cyclotron. The authors used two rotatable magnets. The first
magnet was used to focus the particles and to analyze them by energy. This system made it possible to obtain
an intermediate focus point at which it was possible to set up a movable diaphragm to collimate the beam.
The energy spread in the proton beam (energy 8 Mev) was 0.1% while the particle current was 1 ?amp. In
the experimental chamber, in which the target was located, there was an additional magnet for energy analysis
of products resulting from the reactions between protons and the target.
In 1953 Walker and Fremlin [20] reported on a new method for accelerating multiply charged ions based
on the fact that in a cyclotron it is possible to accelerate simultaneously ions whose rotational frequencies are
odd multiples. Thus, for example, it is possible to accelerate simultaneously sextuply charged and doubly charged
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ions. In the course of acceleration, the doubly charged ions lose electrons as a result of "peeling' on the
residual gas. The sextuply charged ions thus formed are then accelerated to the terminal radius. This method
was used at the Birmingham cyclotron to accelerate C ions to energies of the order of 120 Mev. A short-
coming of the method is the small current of accelerated particles which can be obtained and the large energy
spread in the ions of the beam because of the large dimensions of the region in which the sextuply charged ions
are formed.
In research on a number of problems in physics one requires a considerable reduction in the radiation back-
ground produced by the cyclotron itself at the location of the detection apparatus. This is achieved by locating
the target and the detection apparatus in a special installation (experimental chamber) which is protected by
shielding walls. Under these conditions the diverging beam extracted from the cyclotron chamber must be
focussed on the target. At first this focussing was accomplished by means of a double focussing magnet, located
in the neighborhood of the main magnet of the cyclotron. With the appearance of quadrupole magnetic lenses
the problem of small aperture beam focussing for non-monochromatic beams was simplified considerably be-
cause of the flexibility of this type of system. At the same time, in working with quadrupole lenses, in neutron
experiments it has become customary to use magnets which are set up in the cyclotron chamber; with these it
is possible to bend the beam so that the irradiated target becomes"invisible," thereby removing a basic source
of background radiation.
In 1954 R. Livingston reported data on a cyclotron (pole face diameter of 1580-/Mm) designed for obtaining
intense beams of multiply-charged ions [21]. A slit ion source, developed by the author in 1949-1952, was em-
ployed. The resonance circuit was similar to that of the Oak Ridge cyclotron (Fig. 10). The capacity of the
vacuum pumps was 12,000 liters/sec. This machine was designed as a model for a cyclotron with a pole dia -
meter of 2500 mm in which it is proposed to accelerate multiply charged ions.
In the same year Schmidt et al. reported on a one-and-a-half meter cyclotron at the University of
Washington [22]. The design of the machine was started in 1948 and in 1952 ions of molecular hydrogen were
accelerated to 21 Mev at a current of 125 izamp
at the terminal radius. The potential difference
between the dees is 220-250 kv. Especially
noteworthy are the planning of the cyclotron
laboratory, the spacious experimental chamber
for work with remote targets, and the excellent
shielding against radiation.
In 1955 Karo, Martin and Rose published
information on the Melbourne variable-energy
cyclotron with which protons can be accelerated
to 2-12.5 Mev and deuterons to 4-6.3 Mev. To
cover this wide frequency range the variable
condenser is located at the point at which the
dee is connected to the support rod of the re-
sonance line. Reliable high frequency contact
is provided by a hydraulic system. To improve
the distribution of radio-frequency voltage
along the accelerating slit, a scheme with one
dee was chosen; the rod for the resonance line
is at the center of this dee. Because the edges
of the chamber cover are rounded it is possible
to work without noticeable saturation effects at
high fields. The radiofrequency potential with
respect to ground is 100 kv. The weight of the magnet is 45 tons. As yet no data on the operation of the
apparatus as a whole is available.
Thornton et al. [23] (University of California) have designed a cyclotron with a pole diameter of 2250 mm.
The machine is designed to provide monoenergetic neutrons in the energy region from 2 to 30 Mev. With
appropriate values of the magnetic field and adjustment of the frequency of the rf generator (which can be
Fig. 10. Resonance circuit of the Oak Ridge cyclo-
tron (diameter 1580 mm) built as a model of a
larger cyclotron to be used for accelerating multiply-
charged ions.
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carried out without disturbing the vacuum) the cyclotron can accelerate protons to energies ranging from 2.6 to
14 Mev, deuterons from 5.2 to 12.5 Mev, and tritons from 3.7 to 8,3 Mev. Another feature of this cyclotron is
the special shape of the magnet pole pieces which reduces considerably the divergence of the deflected beam.
The correction of the magnetic field in this cyclotron is accomplished by means of special coils. The
accelerator chamber has one dee (potential 170 kv). At the location of the second dee there is a system which
deflects the beam of charged particles to a considerable distance from the terminal radius. The beam extracted
from the cyclotron has an intermediate focal point which makes it possible (with some loss of intensity) to obtain
a monochromatic beam of particles on a remote target which is located behind the shield, in a special experi-
mental chamber.
Another interesting cyclotron is that at Los Alamos (pole diameter 105 cm) [23]. This machine was
moved from Harvard University and reconstructed as a variable-energy cyclotron (proton energy 3.5-9 Mev,
deuterons 7-17,5 Mev, and tritons 10.5-12 Mev).
This cyclotron makes use of a modification of an azimuthal variation in magnetic field as proposed by
Thomas. 350* ircin sectors are located inside the vacuum chamber (at the top and bottom). This apparatus
provides "strong focussing" starting at the small acceleration radii and provides additional axial stability and
tends to center the beam. In this way a certain reduction of the dee threshold voltage is obtained. One of the
three sectors is located in front of the deflection system; this arrangement tends to increase the radial deflection
of the ion beam. As reported by the authors, the weakening of the magnetic field in the azimuthal direction
facilitates extraction of the beam and reduces considerably the voltage required for the deflection system. Iron
wedges of appropriate shape reduce divergence of the extracted beam as it passes through the fringing field of the
magnet. The final focussing of the beam is accomplished by means of quadrupole magnetic lenses. An addi-
tional analyzing magnet is used to steer the beam to the right or to the left. Two magnets, placed in front of
the quadrupole lenses are used to obtain small displacements of the beam as a whole in the horizontal and ver-
tical directions. Energy analysis is carried out by means of a system of slits located on both sides of the
analyzing magnet. The magnetic field corrections for the cyclotron are realized by means of special coils
which are located both in the vacuum chamber as well as in the space between the pole pieces of the magnet
and the chamber covers. The focussed beam passes through the main field into the experimental chamber in
which the target being investigated is installed. At the terminal radius of this cyclotron currents of the order of
2 ma are obtained for protons, deuterons, and tritons. The maximum current in the external beam is 100 ji amp.
A number of improvements have been incorporated into the one-and-one-half meter cyclotron at the
Institute for Atomic Energy, Academy of Sciences, USSR between 1951 and 1956 [15].
To carry out experiments in which fast-neutron energies are determined by time-of-flight methods, stabi-
lization systems have been installed for the dee potentials, frequency of the resonance system, and the voltage
applied to the deflection system.
Azimuthal correction of the magnetic field is carried out by movable iron elements in the gap between
the pole pieces and the cover by means of remote control from the control panel. In addition to accelerating
protons, deuterons and a-particles, this cyclotron has been used to accelerate multiply charged ions of carbon,
nitrogen and oxygen. An extremely effective source of multiply-charged ions [24] has been developed for use
with this cyclotron.
To control the cyclotron during operation a number of special pickup units and probes, which are re-
motely controlled, have been developed. All the basic control operations for the machine are carried out at
a central control console. The physics studies are carried out behind the main shielding wall in an experimental
chamber; the beam of charged particles extracted from the cyclotron chamber comes to a focus at this point.
A new type of cyclotron machine (pole diameter 1200 mm) designed for university laboratories was de-
veloped in 1956 in the USSR. The deflection system used in this cyclotron which employs electrodes of hyper-
bolic cross section, makes it possible to extract virtually the entire deflected beam of charged particles to a
distance of several meters, using small-aperture magnetic quadrupole lenses.
At the Geneva Conference in 1955, Lawrence reported on experiments carried out with electron
models of a cyclotron with ?a magnetic field varying in the azimuthal direction.* The design of this
* This work was published in 1956 [25].
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accelerator is based on the work by Thomas mentioned above.
Experiments carried out with a model using wclover-leaf" pole pieces offer convincing evidence of the
possibility of constructing a fixed frequency cyclotron which will make it possible to accelerate charged particles
to energies such as are obtained in presently available proton-synchrotron g but with much higher particle currents
(the order of several milliamperes). The problem of deflection and extraction of the charged particle beam in
a cyclotron of this type will be considerably easier,thus making it possible to achieve a particle extraction co-
efficient of 90% as compared with 5=7% in the proton-synchrotron.
In conclusion, we may expect that the cyclotron, used as an accelerator, will serve as one of the work
horses of nuclear physics for a long time to come.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
LITERATURE CITED
E. 0. Lawrence and N. E. Edlefsen, Science 72, 376 (1930),
E. 0. Lawrence and D. Cooksey, Phys. Rev, 50, 1131 (1936).
E. 0, Lawrence and D. Cooksey, Phys. Rev. 86, 411 (1937).
V. N. Rukavishnikov, Phys. Rev, 52, 1077 (1937).
L R. Dunning and H. L. Anderson, Phys. Rev. 53, 334 (1938).
M. E. Rose, Phys. Rev. 53, 675 (1938); 53, 715 (1938),
Ia. L. Khurgin, D9klady Akad. Nauk SSSR 19, 5, 237 (1938).
R. R. Wilson, Phys. Rev. 53, 213 (1938); 53, 408 (1938); 54, 240 (1938).
L. N. Thomas, Phys. Rev. 54, 580 (1938); 54, 588 (1938),
[10] V. I. Veksler, Doklady Akad. Nauk SSSR 43, 363 (1944); 44, 393 (1944);
Phys. Rev. 68, 143 (1945).
E. M. Mc Millan,
[11] E. 0, Lawrence et al., Phys. Rev. 56, 124 (1939).
[12] R. R. Wilson, J. Appl. Phys. 11, 12, 781 (1940).
[13] M. S. Livingston, J. Appl, Phys. 15, 2, 128 (1949).
[14] P. G. Kruger et al., Rev. Sci. Instr. 15, 333 k1944).
[15] L. M. Nemenov, S. P. Kalinin, L. F. Kondrashev, E. S. Mironov, A. A. Naumov, V. S. Panasiuk,
N. D. Fedorov, N. N. Khaldin, and A. A. Chubakov, J. Atomic Energy (USSR) 2, 36 (1957)."
[16] R. S. Livingston, Nature 170, 4319, 221 (1952).
[17] Nature 169, 4299, 476 (1952).
[18] H. Atterling, and G. Lindstrom , Nature 169, 4298, 432 (1952),
[19] R. S. Bender et al., Rev, Sci. Instr. 23, 542 (1952).
[20] D. Walker and J. H. Fremlin, Nature 171, 189 (1953).
[21] R. S. Livingston, Nature 173, 54 (1954),
[22] F. H. Schmidt et al., Rev. Sci. Instr. 25, 499 (1954).
[23] R. L. Thornton et al., "Cyclotrons designed for precision fast neutron cross section measurements,"
(Report No. 584 presented by the U. S. Delegation to the International Conference on the Peaceful Uses
of Atomic Energy, Geneva, 1955),
*See C. B. Translation.
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[24] P. M. Morozov, B. N. Makov, and M. S. Ioffe, J. Atomic Energy (USSR) 2, 272 (1957)."
[25] B. H. Smith, and K. R. MacKenzie, Rev. M.. Instr. 27, 485 (1956); L. Ruby, M. Heusinkveld
et al., Rev. Sc!. Instr. 27, 490 (1956); E. L. Kelly, R. V. Pyle et al., Rev. Sci. Instr. 27, 493 (1956).
Received May 21, 1957.
* See C. B. Translation.
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ALLOWABLE FREQUENCY MULTIPLICATION RATIOS IN SYNCHROTRONS
E. M. Moroz and M. S. Rabinovich
The energy dependence of the amplitude of .synchrotron oscillations due to radiation
fluctuations is investigated. A simple stationary solution for the phase equation is obtained;
this 'equation can. be applied, with accuracy sufficient for practical purposes, to all large
synchrotrons. It is shown that in accelerating electrons to energiesto several millions of
election volts the value of the maximum allowable frequency multiplication is sharply
limited and is determined by the limiting amplitude of the accelerating voltage. *
In the design of electron accelerators intended for high energies, the choice of the radiofrequency
multiplication ratio is very important. In the present paper this problem is considered with regard to the de-
leterious effects of synchrotron oscillations produced by fluctuations in the electron radiation at high energies.
The linearized equation for the radial synchrotron oscillations is of the form
122y = g (g) (1)
The frequency of the synchrotron oscillations n and the damping factor p are determined by the expressions
0 1/q1(eV sin tps
3-4n P
P = 1?n
(2)
(3)
where os and Es are the equilibrium phase and energy, co is the electron rotation frequency, 2. is the radio-
frequency multiplication ratio, n -.is the magnetic field index, P is the power associated with the electron
radiation as averaged Over 1 revolution (it is assumed that there is no radiation in the straight sections of the
race track), i.e.,
p 2ce2 74
3R: 1+k'
(4)
* Certain results of the present work are similar to the conclusions reached in [5] which appeared recently
(note added in proof).
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where
E
Ym.c2Vj2
X
Ni
= 2nR 9
(5)
(6)
(i is the length of a straight section, N is the number of sections, Rs is the equilibrium radius). Finally
K ?
? n) (1 +
In all cases of practical interest the following inequality is satisfied:
p2 .g2.
(7)
(9)
The problem is essentially that of finding a solution for Equation (1) in the case in which the external
force g (t) is the effect of the radiation fluctuations. After finding the amplitude of the radial synchrotron
oscillations Ay it is an easy matter to compute the amplitude of the phase oscillations A, using the formula
or, taking account of (2) and (7) ,
Ay A
_
:Rs ? ?n)qK
(1+0 eV sin
(9)
(10)
The expression for the mean square fluctuation amplitude (211,) given in [1] is rather complicated. However,
it can be shown that in accelerators designed for high electron energies this solution is not significantly different
from the simpler stationary solution
where
55 nhcqyal '
17+0A3
(33)
(34)
(1 + X)a (3-4n) E
Bev
It is difficult to satisfy the condition given in (34) in accelerators with high radiofrequency multiplication
ratios and weak focussing; if this condition is not fulfilled it is possible that a rather large fraction of the particles
will not be trapped in the acceleration cycle.
LITERATURE CITED
DA A. A. Kolomenskii and A. N. Lebedev, Supplement No. 4, J. Atomic Energy (USSR) 1957, p. 31.*
[2] A. A. Sokolov and I. M. Ternov, Doklady Akad. Nauk SSSR 97, 823 (1954).
[3] M. Sands, Phys. Rev. 97, 470 (1955).
RJ N. M. Blechman and D. Courant, Phys. Rev. 74, 140 (1948).
(5) A. N. Dedenko, J. Tech, Phys. 27, 1624 (1957).
Received July 17, 1957.
* Original Russian pagination. See. C. B. Translation.
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y -RAY SPECTRA EXCITED IN INELASTIC SCATTERING OF FAST NEUTRONS
ON MANGANESE, ALUMINUM, IRON, COPPER, TIN, AND ANTIMONY*
I. F. Barchuk, M. V. Pasechnik, and Iu. A. Tsybul'ko
The study of inelastic scattering of fast neutrons is an important problem of both
theoretical and practical interest. From the theoretical point of view the importance
of this work lies in the possibility of obtaining data concerning levels in stable nuclei.
The practical value arises in connection with the important role played by inelastic
scattering of neutrons in fast-neutron reactors as well as the fact that the extension of
reactor theory to fast-neutron reactors requires data on the spectra of inelastically
scattered neutrons [1, 2]. In this connection the necessity for developing a neutron
spectrometer for fast neutrons and y -spectroscopy for inelastic neutron scattering is
obvious. In the last 5-'? years a great deal of work has been devoted to this problem.
The present work reports on measurements of y -ray spectra excited in inelastic
scattering of 2.8 Mev neutrons by manganese, aluminum, iron, copper, tin and antimony.
The measurements were carried out with a scintillation spectrometer consisting of an
Na! (TI) crystal, a FEU-1B photomultiplier and a 50-channel pulse-height analyzer with
a magnetic-drum memory. The spectrometer resolution was 6.5-7% for y-rays from
Co63. y -Rays of the following energies (Mev) were found: in manganese 0.97, 1,41,
1.92, 2.3; in aluminum 0,84, 1.00, 1.80, 2.16; in iron 0.84, 1.25, 1,46, 1.70; in
copper 0,63, 0,78, 0.96, 1.12, 1.38, 1.46, 1,72, 2.03; in tin 0.84, 1.16, 1.50, 1.80,
2,16; in antimony 1.04, 1.50, 1.84, 2.16.
The present paper is devoted to a description of experiments in which studies were made of the y-spectra
excited in inelastic scattering of 2.8 Mev neutrons on manganese, aluminum, iron, copper, tin and antimony.
The measurements of the y -spectra excited in inelastic neutron scattering were performed with the
apparatus shown in Fig. 1. The neutrons were obtained by means of the D(d, n)He3 reaction using a low-voltage
accelerator operating at voltages of 140-150 kv. The deuteron beam, with a current strength of 100-110? amp,
bombarded an aluminum hemisphere 40 mm in diameter with walls 0.3 mm in thickness. The hemisphere was
the end of the target part of the accelerator vacuum system. As a result of deuteron occlusion in the aluminum
a deuterium target was obtained. The intensity of the neutron source was 200-300 ? curies radon beryllium
equivalent. The target part of the apparatus was fabricated from a thin-walled duraluminum tube 50 mm in
diameter and 190 cm long. Thus the target was at a distance of 2-3 meters from all massive elements of the
accelerator and walls ,ceiling, and floor of the installation. With this arrangement in the target part of the
apparatus the neutron source emitted a negligibly small amount of y-radiation as compared with the other
targets.
* Abbreviated version of a paper appearing in the "Ukrainian Journal of Physics."
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The scintillation spectrometer consisted of an Nal (Ti) crystal 60 mm in diameter and 50 mm high and
a FE U-18 photomultiplier. The photomultiplier and crystal were located inside a thin-walled cylindrical
container of sheet iron as protection against light.
3 4 5 at 6 7
Il? .447r
pat
Deuteron
beam
89
Fig. 1. Diagram of the experiment. 1) Target; 2) paraffin plus boron;
3) lead; 4) manganese oxide; 5) NaI(T1) crystal; 6) FEU-13 photomulti-
plier; 7) case; 8) toroidal scatterer; 9) glass.
Fig. 2. y -Ray pulse spectrum emitted by a Co?
sample. Upper photograph ? pulse spectrum in
a binary system.; lower photograph ? pulse spectrum
in a linear system.
176
menu
Fig. 3. y -Ray pulse spectrum emitted by a Sbmi
sample. Upper photograph ? pulse spectrum in a
binary system; lower photograph ? pulse spectrum
in a linear system.
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The pulses from the photomultiplier were fed to a preamplifier, amplifier and the multi-channel pulse
height analyzer. The pulse analyzer, with a magnetic-drum memory [3], made it possible to use 50 or 80
channels with a capacity of 2" or 2" pulses per channel,respectively. The pulse spectrum was observed in
binary and linear systems by means of two cathode-ray tubes. The time resolution of the analyzer was 1.511 sec;
the departure from linearity of the amplitude characteristic was less than 1% for a pulse height of 50 volts. The
amplifier of the spectrometer was linear to better than 0.25% for a pulse height of 80 volts, To obtain the best
resolution and linearity for 7-ray energies up to 3 Mev, the optimum operating conditions for the FEU-1B were
determined experimentally [4]. All units of the spectrometer were fed by electronically stabilized power
supplies. A detailed description of the circuit and adjustment of the spectrometer will be given in a separate
paper.
In Figs. 2 and 3 are shown photographs of the pulse spectra obtained with the spectrometer crystal irradiated
by 7-rays from Coe? (7-ray energy of 1,17 and 1.33 Mev) and Sb 124 (7-ray energy of 0,60 and 1.68 Mev [5])
with 80 channels in operation and a discriminator threshold applied to fifteen channels. In the upper parts of
these figures are shown photographs of the pulse spectra in the binary system; the bottom part shows the spectra
In the linear system. As is apparent from Fig. 2 the energy resolution of the spectrometer is approximately
6.5-7% for 7-rays from Co60. To shield the spectrometer crystal from the direct neutron beam and 7-rays
from the target use was made of a truncated cone, the upper part of which was made from paraffin (95 %)
with a mixture of amorphous boron (5%); the lower part was made from lead. The paraffin cone was 25 cm
high and 12 to 80 mm in cross section diameter while the lead was 5 cm high and 80 to 90 mm in cross-
section diameter. The addition of boron to the paraffin reduced considerably the background of 7-rays pro-
duced by radiative capture of neutrons in the paraffin.
2000
-s
1000
0
1
I.1'
14g (n, n'y) Mg
?
...,.
...,
tzs
1
...,
0,
a.i
I
0 0.5 40 1.5 2.0
7-ray energy, Mev
Fig. 4. 7-Ray pulse spectrum produced in
inelastic scattering of 2.8 Mev neutrons on
manganese.
2.5
3000
a)
,(1 2000
9000
Lo
RI (t7, n'
1 ) RI
e:,
ac. cz,
cs. ...._-
i
41
0,5 9,0 1.5
7-ray energy, Mev
2,0
Fig. 5. 7-Ray pulse spectrum produced in inelastic
scattering of 2.8 Mev neutrons on aluminum.
The scatterer was a toroid made from the element being investigated, 130 mm in diameter and with a
cross-section diameter of 20-30 mm (the thicker scatterers were those of the light element).
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The spectrometer, shield cone and scatterer were attached to the ceiling and walls of the installation by
steel rods which were coaxial with the deuteron beam so that the distance from the target to the center of the
crystal was 40 cm. Using this experimental geometry the neutrons and y -rays which reached the center of
the crystal from the scatterer were scattered at an angle of 1000.
The neutron flux was monitored by means of an aluminum AS-1 8 -counter to which was attached a
silver cylinder 10 mm in diameter, 50 mm high and with a wall thickness of 0,3 min. The counter and this
cylinder were placed inside a cylinder of paraffin 30 cm in diameter and 30 cm high along its axis. Readings
were made for electrons with short half lives (24.2 seconds and 2.3 minutes) produced in the silver upon neutron
absorption. The operation of the monitor was checked by comparison with readings of an "all-wave" boron
counter. The comparison indicated that the ratio of counts for these two counters was within the limits of the
statistical errors. The monitor was placed at a distance of 1.5 meters from the accelerator target at an angle
of 150? with respect to the deuteron beam.
Two measurements were made to obtain the y -ray spectrum ? with the scatterer and without the
scatterer, using the same total number of counts in the monitor. The pulse spectrum produced by y -rays in-
cident on the spectrometer crystal from the scatterer was obtained by subtracting the number of pulses in each
channel of the analyzer obtained in these measurements. It should be noted, however, that a definite contribution
to the results is due to pulses produced by 7.-rays arising as a result of inelastic scattering and radiative capture
of neutrons in the Nal (Ti) crystal. These neutrons reach the crystal from the scatterer.
3000
"S 2000
12
1000
r-
,.?
.43
cs,
c;
cs
Fe (n,n'i' ) Fe
yr
,
_I
4)
cv
tra
?
Cz,
^.
05 1.0 1.
y -ray energy, Mev
'Co
.0
.Q2000
12
000
ts.
oc.
t....
Cu (c7
n') Cu
? ,..
.:,
cs
...:-.
0,
.z.
2.0 2.5 0 0.5 1.0 1.5
y -ray energy, Mev
2.0
Fig. 6. y -Ray pulse spectrum produced in in- Fig. 7. y -Ray pulse spectrum produced in in-
elastic scattering of 2.8 Mev neutrons on iron, elastic scattering of 2.8 Mev neutrons on copper.
An investigation was made of the pulse-height distribution for the background of y -rays and neutrons
produced when the apparatus was operated without the scatterer. The necessity for such a study arises as a
result of the fact that this distribution is not smooth; it has a complicated structure with peaks. Drift in the
spectrometer amplifier and the appearance of new background peaks during the experiment can introduce
considerable errors in the spectra when the background is subtracted. In the present experiments a control
on amplifier drift in the spectrometer was realized by taking pulse spectra for 7-rays from Sb124 and Co60
after each exposure. In the calculations only those data were taken in which no drift effects were noted, It
was shown that the shape of the pulse spectrum due to the background when the apparatus was operated without
a scatterer was constant within the limits of the statistical errors,
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The increase during the experiment of the long period of the component background of y-rays produced
as a result of neutron absorption by the surrounding elements and the crystal had no noticeable effect on the
pulse spectrum. This was verified by subtracting two background pulse spectra measured before and after
operation of the neutron generator.
3000
1000
0,5 1.0 1,5 2,0
y -rays energy,Mev
Fig. 8. y -Ray pulse spectrum produced in inelastic
scattering of 2.8 Mev neutrons on tin.
2.5
4000
3000
0
8 200
100
17-
1
\
v.
c.:)...
Sb Nn't
)Sb
I
(z)
..f
CO
.......
1
to
,S4
,
?
0 0.5 IC 1,5 2.0
y-rays energy, Mev
2.5
Fig. 9. y -Ray pulse spectrum produced in inelastic
scattering of 2,8 Mev neutrons on antimony.
TABLE 1
Gamma Rays Excited in Inelastic Scattering of
2.8 Mev Neutrons.
Element
y -Ray
energy, Mev
Relative in-
tensitiny of
y -le
Manganese
0.97?0.05
0.3
1.41?0.02
1.0
1.92?0.04
0.2
2.3
Aluminum
0.84+0.02
0.6
1.00+0.02
1.0
1.80?0.05
0.8
2.16+0.03
0.7
Iron
0,84+0.02
1.0
1,25+0.04
0.1
1,46+0.04
0.1
1.70+0.04
0.1
Copper
0,63+0.04
0,3
0.78+0.08
0.6
0.96+0.02
1,0
1.12+0.04
0.9
1.38+0.04
0,6
1.46+0.04
0.5
1.72+0.04
0.4
2.03+0.04
0.4
Tin
0.84+0,02
0.6
1.16+0.02
1.0
1.50+0.04
0.3
1.80+0.04
0.4
2.16+0.04
0.3
Antimony.
1,04+0.02
1.0
1.50+0.04
0.4
1.84+0.04
0.4
2.16+0.04
0.2
In Figs. 4-9 are shown spectra of y -rays pro-
duced in the exposure of the scatterer to 2.8 Mev
neutrons measured with fifty channels of the analyzer
in operation. In all cases in which the spectrometer
covers the low energies a clearly defined peak is noted
at a y -ray energy of 0.5 Mev. This is due to y -rays
excited by scattered neutrons in the NaI(TI) crystal.
It follows from W-8] that in inelastic scattering of
neutrons by sodium and iodine an intense y-line with
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an energy of approximately 0.5 Mev is excited. Gamma lines at other energies, excited by neutrons in the
crystal, have small intensities and had no noticeable effect on the spectra being studied.
The y -ray energies for all elements measured in the present work are shown in the second column of
the table. In the third column are given the relative intensities of the y -lines with respect to the most in-
tense line for each element individually. The intensities of the lines are determined in very approximate
fashion because of the difficulties encountered in resolving the complicated spectrum into the elementary
spectra. In carrying out this resolution use was made of the line shapes obtained by exposing the crystal of
the spectrometer to y -rays of known energy from radioactive isotopes. In determining the intensities of the
y -lines using the data of [9] corrections were introduced to take account of the dependence of the photo-effect
in the Na! (Ti) crystal on y -ray energy. In view of the fact that the crystal was of rather large dimensions the
peak intensities show contributions due to the Compton effect and the effects of pair-production in the crystal.
However no corrections were introduced to take account of the energy dependence of these effects. From a
qualitative evaluation of these effects it may be concluded that the relative y -line intensities shown in the
table are somewhat low for y -rays with energies below 2 Mev and somewhat high for higher energy y-rays.
The authors wish to take this opportunity to thank L. M. Beliaev and G. F. Dobrzhanskii of the Institute
of Crystallography, Academy of Sciences, USSR for making the Na! (T1) crystal and for kindly allowing us to
use it in carrying out the present work.
LITERATURE CITED
[1] G. Gurvits et al., Proceedings of the International Conference on the Peaceful Uses of Atomic
Energy, Geneva, 1955 (Academy of Sciences Press, USSR Moscow, 1957) Vol. IV, p. 387.
[2] D. Okrent, R. Avery, and H. Hummel, Proceedings of the International Conference on the Peaceful
Uses of Atomic Energy, Geneva, 1955,(U. N., 1956,) Vol. 5, p. 347.
[3] R. G. Ofengenden, Dissertation, Institute of Physics, Academy of Sciences, Ukrainian SSR,
Kiev (1956).
[4] I. F. Barchuk, E. A. Galkin, M. V. Pasechnik, and N. N. Pucherov, Izv. Akad. Nauk SSSR, Ser.
Fiz. 19, 352 (1955).
[5] B. S. Dzhelepov and L. K. Peker, Decay Schemes for Radioactive Isotopes, Academy of Sciences
Press, USSR (1957).
[6] U. E. Scherrer, B. A. Allison, and X. R aust, Phys. Rev. 96, 386 (1954).
[7] J. L. Morgan, Phys. Rev. 103, 1031 (1956).
[8] E. A. Wolf, Phil. Mag. 1, 102 (1956).
[9] G. Birks, Scintillation Counters, IL (1955).
Received August 22, 1957.
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TRANSMISSION OF SCATTERED y -RADIATION IN WATER
V. I. Kukhtevich, Iu. A. Kazanskii,
Sh. S. Nikolaishvili, and S. G. Tsypin
Measurements have been made of the attenuation of doses of scattered y -photons
from Au "8, Cow, and Na 24 sources as a function of the distance between the source and
the detector for various collimation angles, thereby eliminating the possibility of primary
y -radiation from entering the detector. The measurements were carried out at distances
ranging from 3 to 4 and 8 to 12 mean-free-paths for the y -photons. The collimation
angles were varied from 30 to 80?. The experimental data which were obtained are com-
pared with the results of calculations based on an assumption which allows the problem
to be reduced to the calculation of a triple integral rather than the direct solution of the
kinetic equation. Satisfactory agreement is found between the experimental and theoretical
results.
In analyzing the transmission of scattered radiation in low-Z materials (air, water, concrete, earth, etc.)
the distance between the source and the detector may conveniently be divided into three regions. In the first
region, which is less than one mean-free-path in length, the y -photons experience a single scattering. The
second region is a transition region in which multiple scattering of y-photons becomes more important than
single scattering; this region extends from 1 to 3-4 mean-free-paths for the y -photons. Finally, the third region,
which is greater than 3-4 mean-free-paths for the y -photons, is characterized by an overwhelming predomi-
nance of multiple scattering of y -photons as compared with single scattering.
The transmission of scattered y-radiation in media of low-Z has been considered in the first and second
regions in [1-3]. In [1] a study was made of the transmission of y -radiation from Au188, Cow, and Na 2I sources.
The measurements were carried out in water with source-detector distances of one mean-free-path of the
y -photon (first region). In [2] an investigation was made of the attenuation of scattered radiation from a
Cow source in air. The detector was covered by lead cones with various opening angles (from 10 to 180?).
The distance between the source and the detector was varied from 0.7 to 2.5 mean-free-paths of the y-photons
(first and second regions). In [3] a determination was made of the attenuation of scattered y -photons from a
unidirectional Cow source in water at distances of 1 to 3-4 mean-free-paths of the y-photons (second region).
In the present paper we present the results of an investigation of the transmission of y -photons in water
In the "asymptotic" region (third region). The measurements were made in Water using doses of scattered
y -radiation from sources with energies of 0.4-2.8 Mev using collimated y -sources.
EXPERIMENTAL METHODS
The measurements of y-radiation scattering in water were carried out in an iron tank 6 m in diameter
and 4 m high (Fig. 1). The y-radiation sources were placed in an opening in a lead container fastened to the
I-beams by means of 'a suspension arrangement. The container was located at a distance of 2 m from the
bottom of the tank and the side wall. The upper aperture of the container was covered with a lead plug. The
y-photon collimation angle was changed by varying the vertical position of the y-source along the axis of the
hole,
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The water level in the tank was maintained at the height sufficient to guarantee "infinite" geometry
under the experimental conditions. The thickness of the container walls was 40 cm, corresponding to an
attenuation of more than 107 for the primary
flux of y -photons for the most penetrating
y -rays from a Nall source (E = 2.76 Mev) and
in the worst case the background due to the
primary radiation wag less than 101? of the
? X - ? scattered radiation.
source ?
-- detector ?
The detector was a counter with a sen-
sitive volume of approximately 4 cm3. The
use of the y -counter was conditioned by the
fact that the intensity of the scattered y -photons
in water is not very large while the slopes of
the attenuation curves in water, measured by
a y -counter and a small ionization chamber,
agree in'the energy region 0.4-2.8 Mev (from
the data of preliminary experiments).
Fig. 1. Diagram of the experimental arrangement. The detector was placed in a water-tight
a:collimation angle. container of plexiglas in the same horizontal
plane as the lower base of the source container.
The distance from the detector to the axis of the collimator was measured with an accuracy of 0.1 cm.
The Auiss source (basic energy E0 = 0.411 Mev) was a slab of dimensions 1 x 1 x 0.05 cm3, enclosed in an
aluminum jacket of wall thickness 0.01 cm. The initial activity of the source was 15 curies.
182
PI%
10-
10.
10
JO
10-
f0-4
-
10-5
-
fo'k
.
10-'
-
10-.8
c'S
Ns.
(2)
10-4
10.5
10-6
le
.
"i
\
0
\
\
\
.
?
\
\
\
.
.
c(,
?
? ?
'
.
2
3
.
.
?
60
70
80
90
100
110
120
130 It0
CITI
Fig. 2. The dose percent P as a function of the distance x
from an Au198 source (a1 = 79?, a2 = 52.5?, as = 32?).
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The Co" source (energy ED = 1.17 Mev and E0 = 1.33 Mev) was in the form of a cylinder 1 cm high
and 1 cm in diameter which was also enclosed in an aluminum shell of wall thickness 0.02 cm. The activity
of this source during the time of the measurements was 3.5 curies. The Na24 source (energies E0 = 1.38 Mev
and E0 = 2,76 Mev) was a sphere of nickel of wall thickness 0.01 cm and radius 1.35 cm filled with NaF. At
the beginning of the measurements the activity of this source was 2 curies.
P, %
10
10
10
10
,
e
\
\
\
\
\
\ \
\
1
\
No
\ '
\
60 80 100 120 MO 160 . 180 700
X, CM
Fig. 3. The dose percent P as a function of the. distance x,
from a:? Co" source (a; = 82?, a2 = 59?, as = 470),
-
Results of the Measurements
The results of the measurements are shown in Figs. 2-4, giving the dose percentage P (radiation scattered
and transmitted through the water) as a function of the distance x between the detector and the axis of the con-
tainer at various collimation angles a, The dose percentage P is defined as the percent ratio of the radiation
dose recorded by the detector to the radiation dose which leaves the collimator aperture, in accordance with
the expression
I (X, Eg, a) 100,
P (x, E0, a) (E0)0K (Es, Es)
(1)
where I (x, Es, a) is the intensity of the scattered y -photons with mean energy Es, as measured by a detector
located in the water at a distance x for a collimation angle a; F (E0) =47r Rz I0 (E0, R) is the intensity of
the y -radiation of the source; here 10(E0, R) is the intensity of the y -radiation of the primary energy E0
measured by a detector in air at a distance R from the source (to eliminate effects due to scattered radiation
the measurements of the quantity I0 (E0, R) was carried out at a height of 4 m above the earth); K (E0, Es)
Is a factor for converting the number of counts in the y -counter into dose units [4].
The mean energy of the scattered y -photons Es was computed from the slope of the attenuation curve
for the y -radiation, taking multiple scattering into account [5]; 0 is the solid angle at which the y -radiation
emerges from the lead collimator; the calculation of 0 was carried out taking into account the transmission
of the y -photons through the edge of the lead collimator.
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It should be noted that in the dose percent measured with the Na24 source (Fig. 4) the main contribution
is due to 2.76 Mev y -photons. A calculation indicates that in this case the contribution in dose percent, due
to 1.38 Mev photons, even at the closest distance (x pe 70 cm) is less than 5-10% (see also 13]).
f0-5
ro-
10
-...
s...
-....
''..
N.
',..
-..
,..o.?
-...
.t...cx.
.....
-...
-...
-...
.....
-..
-..
......
....
,...
,...
......
,..?
-;
-..
s...
.
?,..
s..
60
70
.90 100 110 120 130 140
x, cm
Fig. 4. The dose percent P as a function of the distance x from an Na24 source (c = 80?,
a2 = 62?, as = 46?).
The contribution in the dose percent for y -photons from Au198 with energies of 0.68 and 1.09 Mev is
less than 5-8% of the 0.411 Mev y -photons at the greatest distance between the source and detector.
The mean-square error in the measurements for all y -sources was less than 5%.
Calculation*
The calculation of the dose of y-radiation scattered in the water using the above-described arrangement
of source and detector was carried out under the following assumptions:
1. It is assumed that the y -radiation source is an isotropic, monochromatic point source.
2. The y -radiation source is inside a cylinder made of a material which absorbs completely all radiation
incident upon it. The source of scattered radiation is the "radiating* cone (Pig. 5), the opening angle of which
Is determined by the position of the source along the axis of the cylinder.
* The numerical calculations were carried out by T. I. Stavinskii and V. A. Mosolov.
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3. The medium is assumed to be infinite and the cylinder does not disturb the homogeneity of the medium.
Denoting by No (x, E) the spectral distribution of the scattered )-photons at the point D, we define the
dose 1(x) at the point D by the following integral:
E0
I (x)=-- N (x, E) a (E)EdE,
b
(2)
where E0 is the energy of the incident y -photon and pa (E) is the absorption coefficient for the y -photon
energy in air.
Thus the calculation of 1(x) means essentially finding the spectral distribution No (x, E) of the scattered
radiation at the point D.
Finding the function No (x, E) is a mathematical
problem of great difficulty. In order to solve this prob-
lem an assumption was made which allowed us to use
the results of the solution of a simpler problem: it is
assumed that the element of volume of the "radiating"
cone at point Q is an isotropic point source of mono-
chromatic radiation. The total number of y -photons
// emitted by the source is equal to the total number of
primary y-photons scattered at the elementary volume
being considered, where the energy of the scattered
y -photons is
Fig, 5. Geometry for calculating the dose
of scattered y -radiation in water.
a) Radius of the aperture in a container;
s) source; a) collimation angle;
D) detector; 0) scattering angle; Q)
point volume element of the "radiating"
cone.
0
E ?
? - (1?cos 8)'
(K0=
/ (3)
--o
where 0 is the angle between SQ ^ and QD (Fig. 5).
Granting this assumption the function 1(x) can
be given by the integral
0 2
I(x) ? F E 0118 (Bo) C J de 1-ta (E)
X
32n2x 1 + Ko (1?cos 0)
81
-HP? x2
dxB E, p. x
x exp [ sixn 010 sine) ?2 x p. sin 8 +2 mi ,
(4)
where F is the total number of y -photons emitted by the source S with energy E0; B (E, {ix) is the dose
accumulation factor for an isotropic point source of y -photons with energy E at the distance x from the
source; ps(E0) is the scattering coefficient for y -photons with energies E0; II= (E), p0 = p (E0) are
the attenuation factors for y -photons with energies E and E0, respectively.
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The limits of integration in Equation (4) for values of x large as compared with the dimensions of the
collimator are obtained from the following relations: 4.
xt 1, = r4-0 2ai, a, arc, tg 17.c?521'
cos2 a
X2 0,
tg 4p* = 1/tg2 a ? ctg2 0,
e1 =--a, 2 ? 2 .1?a 0 ?a
2 .1-1- '
where a is the opening angle of the *radiating" cone.
The relations given in (5) are correct to an accuracy up to quantities of order
the collimator).
We now assume that x varies over some limited energy region. Then the function B (E, px) can be
given by the approximate expression
a
(5)
(a is the radius of
B (E, p.x) B0 (E)(6)
where K is a parameter which depends on the energy E and the values of x being considered.
Further, we take
ileff (1? K ) Pi
after a suitable transformation, in place of Equation (4), we obtain
2a
/ (x), FEON (E0) C d' Ra (E)/30 (E) \.,
872x 3 ' 1+Ko (1? cos ?0) '
0
aro tg rtg2 a?otg2 8
X
S dp X
0
X
exp [ x(p.0? p..eff cos0
sin 0
X sin z [Leff cos z )] dz,
Tr
where E = 6 + 2
? , while E is determined in accordance with Equation (3).
(7)
(8)
A direct computation of the integral in (8) is difficult. In order to obtain an approximate value for this
integral, at the outset, we may note that the inner double integral, multiplied by pa (E)B a (E)
' is a
function of x which reaches a maximum at a certain value g = g 0. The larger x the smaller is go and
the sharper the maximum. Hence, in computing the inner double integral we may limit ourselves to values
of E in the region of zero.
? 'tg' :+3 'tan,' 'ctg' 'cot' ? Publisher.
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On the basis of these remarks we may replace the quantities sin z and cos z respectively by z and 1
under the integral sign. Then, neglecting the difference between at and a and carrying out the double in-
tegration over z sand co, we obtain
where
FE01-ts (Eo)
1(X) X
87.0x
f (t) e?eff (a)x
(t) -1--111:1E7:())1. cB:s(E?9) x
?exp VO?P?of COS
sin 0
110-F?ieneff?cos 9
s 0 .\
) X
X arc tg 1,f1g2 a - ctg2
and by peff we are to understand ueff [E (g )]. We rewrite Equation (9):
where
2a
/ (x)?
FEolLs (Eo)ita e -AM g dt,
8Tor
X = Peff (t) - (t).
Now, to find an approximate value for the integral in (10) we make use of the method of "steepest
descent" [6];
I (x)=--
F E0?.81E o) I () e--P.eff(-)
4rc ji-gr V. X" () x
(9)
(10)
where the values of the functions f(g ), X" (g ) and ? eff (g ) are to be taken at the point g = , where
is the root of the equation
(e) = O.
(11')
? Finally, relating the dose 1(x) to the dose of. primary radiation which emerges from the collimator,we
obtain the following expression for the dose percent.:
P (x, Eo, ct).= 100. P.' (E.?)
2::ligr X
(&)/1(X" OA I e-v?effa)?x
[ra-vcos a Ect(M.)] x VT
sin a
(12)
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where
CK)
E, (y) e?us
SUMMARY
In Figs. 2-4, in addition to the experimental curves for the dose percent of scattered radiation,we show
calculated curves computed from Equation (12). The values of the functions p (E), Iia (E), and B (E, fix)
were taken from [5].
The computed values are normalized to the experimental values at the point x = 98.5 cm. The absolute
values of the computed curves differ from the experimentally obtained values by less than a factor of 2.
It should be noted that since the effective attenuation coefficients of the dose percent obtained from the
experimental data are in agreement with the calculated data the discrepancy indicated remains essentially
constant regardless of the source-detector distance.
These discrepancies are explained by error in the Measurement of the distance at which the computed
dose is determined. This error is about 5-10 centimeters.
It is interesting to note that in the source-detector distance region being investigated (third region) the
change of dose percent with distance may be given by the relation [e Pen. x, x ], whereas the intensity
of singly scattered y -photons falls off with distance in accordance with relation [e Peff x /x].
In conclusion the authors wish to express their gratitude to Dr. Phys.-Math. Sciences A. K. Krasin for
setting up the problem and for illuminating discussions on the results of the measurements, to Dr. Phys.-Math.
Sciences G. I. Marchuk for a number of remarks concerned with the calculation and also to V. A. Tolstikov
for participating in the present series of experiments.
LITERATURE CITED
[1] M. A. VanDilla, and G. J. Hine, Nucleonics 10, 1, 54 (1952).
[2] B. W. Soole, Proc. Roy. Soc. 230, 343 (1955).
[3] T. Rockwell, Shielding of Nuclear Reactors, IL (1958).
[4] W. K. Sinclair, Nucleonics 7, 6, 21 (1950),
[5] U. Fano, Nucleonics 11, 8, 8 (1953); 9, 55 (1953).
[6] M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable,
(State Tech. Press, Moscow-Leningrad, 1951).
Received March 16, 1957.
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ESTIMATE OF DOSE IN THE INHALATION OF RADON
L.S. Ruzer
The inhalation of radon takes place both in industry and in natural conditions (by
far the major part of the natural radiation dose is due to radon). The question of com-
puting the dose due to inhalation of radon is therefore of practical interest.
This paper gives an analytical expression for A y(t) - the y-ray activity of RaC
in the inhalation of radon - and demonstrates a method of computing the mean coeffi-
cient of retention of short-lived products of radon decay. The link between A (t) and
the value of the integral absorbed dose due to Rn, RaA, RaC' is established; formulas
are given for computing the dose due to long-lived products of radon decay.
INTRODUCTION
The biological action of radon and its short-lived decay products on the respiratory organs is due mainly
to the a-emitters Rn, RaA and RaC', since the total a-particle energy of these elements is considerably greater
than the 8- and y -ray energies of RaB and RaC, and also because of the greater biological effectiveness of a-
rays as compared with 8- and 7-rays.
The quantity of short-lived products of radon decay deposited in the respiratory system may be estimated
from the y -emission of RaB and, mainly, RaC. In the present article the link is found between the integral ab-
sorbed dose-due to the a-emitters mentioned and the y -activity of products deposited in the respiratory system,
mainly RaC.
Basic Premises
1. The short-lived daughter products of radon decay are always present in the air. The ratio of their quan-
tity to the "equilibrium" we will call the degree of equilibrium ?IA (for RaA), ?TB (for RaB) and 7ic (for RaC).
2. If the biological object is in a space of sufficiently large volume, the radon concentration in the respir-
atory system will be equal to the concentration in an "emanatorium" (a curies/liter) and the respiration volume
per minute will be
vi v ? n liter/min,
where v is the volume of one inhalation, and n is the number of inhalations per minute.
3. After each inhalation a definite part of RaA (6A), RaB (68) and RaC (6c) is retainedi)the rate of entry of
each of the elements will be 3.7. 1010? 60? cr-iti-g- atoms/min, and the rate of accumulation in the respiratory
system will be
cl
a atoms/min
*The term "emanatorium" is used arbitrarily and denotes merely a space containing radon.
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(1)
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where X is the decay constant (in min-1) for RaA, RaB, RaCjespectively; a = 222.10" dis/min per 1 curie of
active matter.
4. According to the existing data [1] for the half-periods of elimination of short-lived radon products from
the lungs, complete decay takes place before excretion in appreciable quantities begins.
Analytical Expression for the y -Ray Activity of RaC
To find an analytical expression for the y-ray activity of RaC as a function of time A y(t) we will assume
that this activity is due to RAG retained in the respiratory system and also to RaC formed from RaA, RaB and Rn.
An expression for the number of RAG atoms present at a given moment, allowing for decay (Ni), and for
I
the number of RAG atoms obtained from RaB (NE), from RaA (N1) and from Rn (NcV ) can be obtained by using
the solution of the equation for a chain of radioactive transformations of i links, where only the primary radio-
active substance is present initially:
dis/rnin
36
32
28
24
20
18
12
8
4
4,(t)
0 TO 40 60 eo 100 1201401601RO TM
t, mirr-
Fig 1. Functions gA (0, EB (t) and gC(t) (min), repre-
senting the contributions of RaA, RaB and RaC to Ay(t).
In this case the solution has the form [2];
N = cicX1t+ea.eX2t c? ? e-xtt, (2)
X2'ka? ? ?kt-i
Ni'XI (A2?ki) (X3?Ki)?(Xi?X1)
(3)
c, =N2 ? X1 (k1?Ai.)(A2-41/41).??(ki-i?ki) ?
X2Xa ? ? ? X
Formulas (2) and (3) are applicable also when the
element with index 2 accumulates at some con-
stant rate Q, as happens in the case considered.
Then
[ I Xa Xd Xi e-X2t
A,= X. ? , 0
X2 i?A 4 ? . Xie?X81 X2?Xe ? ? ?
?
(4)
(5)
(6)
(7)
(8)
(X2?X8) ? ? ? (ki?W ? ? ? ? ? ? (A2?X6)
Substituting in turn in Expression (4) the values QA. QB and Qc from
(I_
? ? ? (Xt?i?
(1),we obtain
aqvg-fle'c e?xct\
,
Ay_ //Pi 4t? 11B ke ? e?X ? ? e? Xct
( ?
XD?Xc
4311.,... a got AT1A Xc? e?X At
L (X13?XA) (XC? XA
XA ? XC ? e?XBt
XA X13 e?Xci
(X A?Xn) (X ?X) (XA?Xc) (X8?Ac) J
? Xc
--= aqV [i
(143-4) (xc?xA)
4?kc?6-xue xnxB?e?xci 1
(XA-43) (Ac-A8) (An?Xc)(143?xc) J
*Ng, Ng
ment.
are the number of atoms-of elements with indices 2, 3, . . . , iirespectively, at the initial mo-
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where V is the mean volume of respiratory paths. Assuming in the future that 6A = B= ac = 6 and neglect-
ing the contribution of radon itself we obtain an expression for the total activity Ay by summation:
AT = aqvi6 kA A (t) -4- -71A3 (1)+71cc (1)].
(9)
Functions gA(t), gB(t) and gc (t), the graphs of which are given on Figure 1, characterize the contributions
to Ay of RaA, RaB and RaC aespectively. Here we also give the summed curve
ay (t) = A (t) (t) (t)
Ay may be obtained experimentally by comparison with sources of radon or by using a dummy; nA,
TIB and Tic are determined by the usual methods [3,4].* Expression (9) makes it possible to determine the mean
retention coefficient 6. In particular, with t > 200 min,
AT
8
apt.(11'-{-??+r)
(10)
The rising branch of curve ay(t) is in good agreement with experimental results obtained on white rats [5], the
descending portion corresponds to the natural decay of the accumulated daughter products of radon and also agrees
well with the experimental results of the same work. The form of this curve characterizes the change in the y -
ray activity in time for any object breathing radon when ?IA = riB = tic.*?
Formula for Computing the Integral Absorbed Dose
The integral absorbed dose for the respiratory paths is
= Di +D1 = DA + Dce
where D'1 and DA are fractions of dose during stay in the emanatorium and after removal from it;
Di= D'id- ERn ARn (t) + EA S AA (0 dt Ec, Ac, (t) dt,
(12)
(13)
where E is the a-particle energy of Rn, FtaA and RaC'. Applying to this case the Solution (4) and assuming that
Xc, ? XA, XB, Xc,neglecting Rn decay, we obtain
D ;= am PlApA (t) + 1Bpi (t) lcpc (01
(14)
?In the USSR we have now produced an electrofilter EF-2 (see J. Atomic Energy (USSR) 3, 10, 356 (1957)
[C. B, translation page 1217] which may be used for this purpose. (Note added in proof.)
**For a tentative estimate of the mean degree of equilibrium n a comparatively simple method, proposed by
G.E. Gur'e and the author, may be employed.
Usually, for determining radon concentration in an emanatorium a sample is taken into a previously evacu-
ated ionization chamber (for instance, the "emanation" chamber of the SG-1M electrometer assembly) and the
value of the ionization current is measured. The nature of the current increase and its value at t = 0 are con-
nected with the mean degree of equilibrium.
We denote; Jo ionization current due to radon at t 0; J1 ? current due to decay products at t = 0;
J2 = Jo + ? sum of currents at t = 0 and J ?maximum value of ionization current. Taking Jo = 0.460J [6] we
obtain
JI -- 0 . 460J
1_J ?Jo_ Jr?Jo = 0.540J
--=1.85 (2?.2.? 0.460).
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Figure 2 shows functions cpA(t), cpB(t) and ioc (t) which indicate the contributions of RaA, RaB and RaC to
D'1, and also d'1(t) = QA (t) + cpB(t) + (pc(t).
For t > 200 min
Comparing (14) with (9) we have
di (t) = (0.93t ? 45.0) ? 10-3 erg. mm2 (15)
Di A1 VA TA (t)-E-71n Pu0; + 41+,
(1)
as it is known that the OH radical is a strong oxidant in an acidic medium. Its normal potential for reduction
to 1120 equals 2.8 v [3]. It is also possible that oxidation also occurs with the participation of unstable higher'
nitrogen oxides.
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The radiation-chemical oxidation yield of plutonium was very low. The highest yield, obtained in
0.3 N HNO3, was equal to approximately 0,05 ion /100 ev. ?The decrease in the initial yield with an increase
in the NO; ion concentration was, apparently, due to the capacity of reduced plutonium to form complexes
with the nitrate ion [10 -12]. The low reactivity of such a complex was confirmed with nonradiation experi-
ments. It is known, for example, that the thermal oxidation of plutonium with nitric acid was considerably
slowed down at high nitric acid or uranyl nitrate concentrations [13]. We observed a similar phenomenon in
the nonradiation oxidation of plutonium with potassium dichromate. In this reaction the oxidation was retarded
much more strongly by nitric acid than by nitrate salts at equal NO3- ion concentrations. The results of the
radiation-chemical oxidation of plutonium are also related to this phenomenon. It was suppressed more
effectively by nitric acid than by sodium nitrate.
The absence of reduction in these solutions could be explained by a possible reaction with atomic
hydrogen
Pu0; 11+ 3I-I Pu" + 211,0
being fully suppressed by the reaction
NO; H NO2 + OH-
(2)
(3)
with the existing ratio of plutonium ion and NO3- concentrations, As the experimental data given show,
plutonium reduction in nitric acid solutions becomes possible if the solution contains UO2(NO3 )2,
Miller et al. [14] established that under the effect of ionizing radiation, pentavalent uranium formed in
solutions of uranyl salts. The normal oxidation-reduction potential of the UO2"-/UO2+ pair is equal to 0.05 v
[15], i.e., close to that of hydrogen. On this basis the following scheme for plutonium reduction under the
effect of UO 2+ ions may be proposed:
Pup; UO: -4- 4H+ ---> Pu" 1,10; + 211.20. (4)
Due to the commensurable concentration of uranyl and nitrate ions the H radicals were distributed between
them. With this, the reduction rate of the NO3- ion by the UO2+ ion was considerably less than its reduction by
atomic hydrogen and as a result UO2+ accumulated to a concentration that was sufficient for plutonium re-
duction.
The changes observed in the valence state of plutonium in solutions containing UO2(NO3 )2 may be
explained by the simultaneous occurrence, from the very beginning of irradiation, of two opposed processes ?
oxidation and reduction?with oxidation predominating up to 0,3 M UO2(NO3)2 and reduction predominating
after 0.6 M. At the start of irradiation the oxidation and reduction rates were equal in the range of UO2(NO3)2
concentrations from 0.3 to 0.6 M. The start of plutonium reduction only after the absorption of a definite
energy dose showed that it was possible only after certain radiation-chemical reactions in the system. Direct
experiments, whose results are given graphically in Figs. 6 and 7, showed that-plutonium reduction in suitable
solutions was due to the presence of sufficient nitrous acid in them, formed due to radiation or introduced into
the starting solution. However, its role in this process remains unclear. It is possible that it slows down plutonium
oxidation ,as it is an acceptor of OH radicals.
Turning to solutions containing K2Cr207, we may note that plutonium oxidation was observed in them at
any UO2(NO3)2 concentrations at the start of irradiation. The increase in yield due to K2Cr207 may be caused
by the oxidation of pentavalent uranium that was formed by Cr207-- ions. After the reduction of all the potassium
dichromate in solutions of 0.3 M HNO3 and 0,1 N K2Cr207 with varying u02(NO3)2 concentrations, the character
of the changes in the valence state of plutonium was, in general, the same as in solutions not containing K2Cr207?
Plutonium reduction in the presence of K2Cr207, observed in solutions with 1.5 N HNO3, apparently should
be attributed to increased complex formation by the reduced plutonium at this acidity. This hypothesis requires
additional experimental data for substantiation,
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LITERATURE CITED
[1] M. Kasha and G. E. Sheline, The Transuranium Elements, (McGraw-Hill Co., New York, 1949)
1, P. 180.
[2] M. Kasha, ibid., p. 295.
[3] V. I. Medvedovskii, N. A. Bakh, and E. V. Zhuravskaia, Collection of Works on Radiational
Chemistry (Acad. Sc!. USSR Press, 1955) p. '71.
[4] J. Weiss, W. Bernstein, and B. Kuper, J. Chem. Phys. 22, 1593 (1954).
[5] B. V. Kurchatov, V. I. Grebenshchikova, N. B. Cherniavskaya, andV. N. lakoxlev, Investigations
in the Fields of Geology, Chemistry, and Metallurgy (Reports of the Soviet Delegation to the International
Conference on the Peaceful Uses of Atomic Energy) (Acad. Sci. USSR Press, 1955):p. 219.
[6] R. E. Connick and W. H. McVey, The Transuranium Elements (McGraw-Hill Co., New York, 1949)
1, p. 142.
[7] R., E. Connick, ibid., p. 280.
[8] G. Seaborg and J. Katz, Actinides, (Foreign Lit. Press, 1955) p. 231 (Russian translation).
[9] V. Latimer, The Oxidation States of Elements and Their Potentials in Aqueous Solutions (Foreign
Lit. Press, 1954) p. 51 (Russian translation).
[10] J. C. Hindman and D. P. Ames, The Transuranium Elements, (McGraw-Hill Co., New York, 1949)
1, p. 348.
[1.1] J. C. Hindman, ibid., p. 348.
[12] C. E. McLane, J. S. Dixon, and J. C. Hindman, ibid., p. 388.
[13] K. A. Kraus, ibid., p. 264.
[14] N. B. Miller, Ts. I. Zalkind, and V. I..Veselovskii, The Effect of Ionizing Radiation on Inorganic
and Organic Systems, Coll. of Articles (Acad. Sc!. USSR Press, 1958) p. 93.
[15] H. G. Heal and G. N. Thomas, Trans. Farad. Soc. 45, 11 (1949).
210
Received April 23, 1957.
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STUDY OF THE ZIRCONIUM APEX OF THE Zr ? Ta ? Nb PHASE DIAGRAM
V. S. Emel'ianov, lu. G. Godin, and A. I, Evstiukhin
Metallographical examination, thermal analysis and electrical resistance measure-
ments have been applied to a study of the zirconium apex, up to 82% zirconium and a
temperature of 1200?C, of the ternary system Zr?Ta?Nb, with limited solubility of
tantalum and niobium in a- zirconium.( y phase), limited solubility and complete solu-
bility of niobium in 8-zirconium, with eutectoid decomposition of the B solid solution
and three-phase eutectoid equilibrium B a + y between a- and 8-zirconium.
In the investigated portion of the Zr?Ta?Nb phase diagram, the following phase regions
were found: a) two one-phase regions a and a; b) three two-phase regions a + 8,
B + y and a + y ; c) one three-phase region a + B + y ; the 8 region contracts
as the temperature falls below 1200?C.
The solubility of tantalum and niobium in a-zirconium in the system Zr?Ta?Nb
is about 0.5%. On passing from Zr?Ta to Zr?Nb, the a + B and 8 +y regions are
displaced toward lower temperature and high niobium concentrations; the boundaries of
the a + y and a + B + y regions are lowered from 790? for Zr?Ta to 612?C for
Zr?Nb. Passing between the a + 8 and 8 + y regions is a binary eutectoid line which,
from Zr? Ta to Zr?Nb is displaced toward lower temperatures and higher niobium con-
centrations. The solubility of niobium in a zirconium in the Zr?Nb system is about
0.5% by weight. Eutectoid decomposition in the Zr?Ta system shifts the maximum of
the martensitic -like transformation to the left and results in an increase in the stability
of the B phase at room temperature in quenched alloys.
The literature contains no information on the ternary system Zr?Ta?Nb. The constitutional diagrams
for the Zr?Ta and Zr?Nb phases comprised in this system have already been studied [1-3]. In the investi-
gations [2] and [3] of the Zr?Nb system, however, there are discrepancies in the temperature of the eutectoid
decomposition (615-560?C), the position of the eutectoid point (17.5-12 %niobium) and the temperature of
the minimum on the solidus curve. It is also known [4] that the eutectoid temperature in this system is 800?C,
and that the solubility of niobium in a zirconium at 750? C is less than 5%. As regards the binary system
Ta?Nb, this system is represented by a continuous series of solid solutions [5],
We have studied the zirconium apex of the ternary diagram bounded by the curves corresponding to 82%
zirconium and the temperature 1200? C and have also investigated the solid state transformation in the Zr?Nb
system, The metallographical and thermal and x-ray analysis methods described in the previous paper [1]
were used in the investigation.
In constructing the zirconium apex of the phase diagram of the system Zr?Ta?Nb, five polythermal
? Nb
cross sections were taken through the point of the apex with the ratio ? - 0.2, 0,5, 1,0, 2.0, and 5.0.
0/0 Ta
The serial numbers of these cross sections are 1, 2, etc. Alloys containing 0,5, 1.0, 2,0, 3,0, 4,0, 7.0, 10.0,
12.0, 14.0, 16.0, and 18.0% by weight of tantalum and niobium were prepared for each polythermal cross section,
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In preparing the alloys, rods of zirconium iodide of the following composition (% by weight) were used:
hafnium 1.1, nitrogen 2 ? 10 -s, iron 3 ? 10_3, silicon 1.5 ? 10-2, calcium 5 ? 10 , carbon 9 .10-3, chlorine
2.6 ? 10 -s, tungsten 3 ? 10-3, molybdenum 1.4 ? 10 -3, manganese 1.5 ? 10 -4, oxygen 5 ? 10 -s, hydrogen 3 ? 10g.
Tantalum and niobium were used in the form of thin ribbon. The tantalum dontained the following im-
purities (% by weight): niobium 0.5, titanium 0.06, tungsten 0.02, iron < 0.05, molybdenum 0.03, silicon
< 0.1; the niobium contained: tantalum 0.5, titanium 0.2, iron 0.08, silicon 0.08.
No chemical analysis was made of the specimens, due to the difficulty in separating tantalum and niobium.
As a check on the composition, the alloys as cast were weighed on an industrial balance. Usually, the difference
in weight before and after melting amounted to hundredths of a gram. The heat-treatment conditions of the
alloys are shown in the following table:
Heat-Treatment Conditions of the Alloys
Annealing
temp.,
?C
Annealing
period,
hours
Annealing
temp.,
?C
Annealing
period,
hours
1200
60
730
450
1000
80
700
560
900
190
670
600
820
260
645
600
790
360
625
600
765
370
600
600
The temperature records were made at heating and cooling rates of 6-8 degree! mm. The results of the
thermal analysis of the polythermal cross sections Nos. 1, 3, and 5 are represented in Figs. 1, 3, and 5 by thin
dot-and-dash lines. They show that the temperature of the a-8 transformation decreases with increase in
tantalum and niobium content of each polythermal cross section. The boundaries of the three-phase region
(a + 8 + y ), as well as the boundaries of the two-phase region (a + 8 ) fall from the first to the fifth poly-
thermal cross section.
According to the data of the thermal analysis, the solubility of tantalum and niobium is: for the first
cross section 4%, for the third 5%, for the fifth 6%. The temperatures at which maximum solubility of tantalum
and niobium in zirconium is observed decrease from 750?C in the first cross section to 675?C in the fifth.
Metallographical Examination
A study of the structure of the cast alloys showed that solid solutions of tantalum and niobium were
present in the system investigated. Alloys containing small amounts of tantalum and niobium had a martensitic-
like structure of the transformed 8 phase. X-ray phase analysis established that in alloys of high tantalum and
niobium content, the 8 phase is stabilized by quenching, and is partly transformed into a needle-like phase. In
the structure of all these alloys, needle-like precipitations of a phase were observed against the light background
of 8 - phase.
Figures 1 to 5 show the polythermal cross sections based on the results of metallographical examination of
the quenched alloys. Study of the microstructure of the alloys quenched after annealing at 1200 and 1000? C
showed that at these temperatures, throughout the entire region examined, there is a continuous range of solid
solutions based on 8-zirconium and having different structures. Alloys containing slight additions of tantalum
and niobium have a characteristic martensitic-like structure (Fig. 6). As the content of tantalum and niobium
is increased, the martensitic-like structure of the transformed B phase passes into the needle structure of the
a phase on a background of fixed 8 phase (Fig. 7). It is observed that the higher the ratio of niobium content
to that of tantalum in a given polythermal cross section, the lower is the content of tantalum and niobium at
which fixing of the 8 phase by quenching commences, i.e., the addition of niobium to alloys of the Zr? Ta
system increases the stability of the 8 phase at room temperature.
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P,
_____
y
13
C/ ?
-?-----
/
I ?
I
I'
I
nn
N.
- -----L=_____
?N/3./
_ '__,I,z...........--n..
?._.
? .1
no
I. -..
__ _____,.__.
a , 1
____
_ .
nC
no
nfl
or
DC
0/
01
Zr, weight 010
900
810
790
765.
730
700
645
600
Fig. 1. Polythermal cross section No. 1 of the
system Zr? Ta?Nb, with constant ratio of per-
centage content of niobium to tantalum equal
to 0.2. ? -- results of thermal analy-
sis; 0 8 phase; ? 8 +y phases; x a + 8
phases; ? a + 8 + y phases; ? a + y phases.
810
790
765
730
700
670
645
88 86 84 82
Zr, weight 0/0
Fig. 2, Polythermal cross section No. 2 of the
system Zr? Ta?Nb with constant ratio of the
percentage content of niobium to tantalum
equal to 0.5. 0 phase; ? a y phases;
x + 8 phases; A a + 8 +y phases;
? a + y phases.
--,
\
P' i
\
----?7
?.?\
'
?
\.
.
. or +/3-
?-
?
71
-t--
I
..._
?
?
-----,..,
-- Y ---- -2-'3
I
t,---
1
i
1
li
I_
.
a -,
.
99 98 97 96
93 90 88 86 84 81
Zr weight To
Fig. 3. Polythermal cross section No. 3 of the system
Zr?Ta?Nb with constant ratio of the percentage
content of niobium to tantalum equal to 0.1.
---- results of thermal analysis; 0 8
phase; ? 8 + y phases; x a + 8 phases; ?
+B + y phases; ? a + y phases.
900
810
790
765
730
700
670
645
600
Jul..Milli
I
.
1111111
13
1111.111.1.1645111111.1111/
I iii
111111bEIIII:111/i
nil
iiiilaimme.:1
c(.11
MINI
on esiosiivp+7
RiCEM
iz
MOM
OM=
tionsilmin11111111
1111111ms
99 98 97 96
93 .90 88 86 84
Zr, weight %
Fig. 4. Polythermal cross section No. 4. of the
system Zr? Ta?Nb with constant ratio of the per-
centage content of niobium to tantalum equal to
2.0. 0 8 phase; 1111 a +7 phases; x
a+8 phases; A a + 8 + y phases; ? a + y
phases.
900
862
820
790
765
730
700
670
645
525
600
89
213
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,\.
N
?e---1
\1
I\
\
a
b....
- ? p
.\\1
1.
WI
0( ? 13-r
4.--.--
'
?
'
I
,
7 it,
I
??
?4
41.1
CX + y
1
.1_
99 98 97 96
900
870
790
765
730
700
93 90 88 85 64 82
Zr, weight %,
Fig. 5. Polythermal cross section No. 5 of the
system Zr? Ta?Nb with constant ratio of the
percentage content of niobium to tantalum equal
to 5.0.
? ? ? -- results of thermal analysis'
670
645
625
600
0 8 phase; III 8 + y phases; x
phases; ? a + 8 + y phases; ?
phases.
a? a
a + y
On quenching from 900?C in alloys of the
first and second polythermal cross sections, there
is precipitation of the y -phase, a solid solution
of a- zirconium in a solid solution of tantalum
and niobium. The existence of the y -phase was
confirmed by x-ray phase analysis; lines of this
phase appeared on the diffraction pattern of the
alloy of the first polythermal cross section, con-
taining 18% tantalum and niobium, quenched
from 900? C? On lowering the quenching tem-
perature, the precipitation of y phase was also
revealed in alloys of the third (Fig. 8) and fourth
polythermal cross sections. In alloys of the fifth
polythermal cross section, separations of the
y -phase were not observed on quenching from a
temperature above the a + 8 + y region. The
results of the metallographical examination of
the quenched alloys showed that the boundary
between the 8 phase and 8 + y phase, with
%Nb
increase in the ratio in the alloys, is
Ta
shifted toward a lower zirconium content (see
Figs. 2-6) and the temperature of the commence-
ment of the separation of the y -phase from the
B solid solution is lowered.
The two-phase region a + B was found in
all polythermal cross sections at temperatures
below 862 C. The typical structure of the two-
phase a + 8 region is shown in Fig. 9. The upper
boundary of this region is shifted, from the first
cross section to the fifth, toward a lower concentration of zirconium and an increase in the %Nb / To Ta ratio
in the alloys, and in the fifth cross section passes beyond the limit of the investigated region.
Fig. 6. Microstructure of the alloy from the first
polythermal cross section containing 7% tantalum
and niobium. Martensitic -like structure of the
transformed B phase. Quenched from 1000?C.
(x 200).
214
Fig. 7. Microstracture of the alloy from the fifth
polythermal cross section containing 16% tantalum
and niobium. Needle structure of the a phase on
a background of fixed 8 phase. Quenched from
1200?C, (x 200).
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By extrapolating the upper boundaries of the a + B and a y regions to intersection, we obtained points
on the four polythermal cross sections which, when connected, form a line of eutectoid transformation. With
0/0 Nb
increase in the Ta ratio of the alloys, this line is shifted toward higher niobium concentrations and lower
temperatures, In the fifth polythermal cross section, the point situated on the binary eutectoid line is outside
the region of concentrations investigated.
According to the data of this metallographical examination, the maximum solubility of tantalum and
niobium in a.- zirconium is about 0.5% by weight.
Fig. 8. Microstructure of the alloy from the third
polythermal cross section containing 18% tantalum
and niobium. Separations of the y phase visible
on a background of fixed 8 phase and needle
a- phase. Quenched from 800?C. ( x 500).
Fig, 9. Microstructure of the alloy from the
fourth polythermal cross section containing 10%
tantalum and niobium. Two-phase a + B
structure. Quenched from 730?C. ( X 500).
An x-ray study of the solubility of tantalum and niobium in zirconium using an IKROS back-reflection
camera failed to reveal any appreciable variation in the lattice constants of a-zirconium for alloys of all five
polythermal cross sections containing 0,5 and 1,0 % by weight of niobium and tantalum; This is also evidence
of the insignificant solubility of tantalum and niobium in a-zirconium.
The temperature of the commencement of the eutectoid decomposition of the 8 solid solution was de-
termined from the appearance of dark, finely dispersed precipitates of eutectoid in the structure of the alloys.
The x-ray diffraction patterns of such alloys, even for low tantalum and niobium contents, showed lines of the
y phase, the intensity of which increases with decrease in the quenching temperature.
The temperature of complete decomposition of the a solid solution was determined from the disappearance
of elongated separations of a or B phase from the structure of the quenched alloys. Figure 10 shows the structure
of the alloy of the second polythermal cross section containing 7% tantalum and niobium, quenched from 700?C,
the coagulated precipitations of y phase being visible on the background of a phase.
Since the data obtained in our study of the ternary system Zr?Ta?Nb, with regard to solubility in the
a phase and the position of the binary eutectoid line, were not in agreement with the data of [2] and [3] con-
cerning the Zr?Nb system, we made an additional study of the latter.
Alloys were prepared containing 0.3, 0.7, 1.0, 1.5, 2.5, 4.0, 10.0, 12,5, 14.0, 16.0, 18.0, and 20%by
weight of niobium. After homogenizing at 1200?C for 40 hours, the alloys were annealed at 600 and 625?C,
followed by quenching in water.
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All the alloys quenched from 625?C had a two-phase structure a + 8 , except the alloy containing
0.3% niobium. Extrapolation of the binary eutectoid line in the ternary system to intersection with the binary
system Zr?Nb showed that the eutectoid point of the Zr?Nb system is at about 24% niobium,
Fig. 10, Microstructure of alloy from the second
polythermal cross section containing 7% tantalum
and niobium, a + 8 Quenched from 700?C,
( x 1000).
Fig. 12. Microstructure of alloy containing 0.3%
niobium. One-phase a solid solution. Quenched
from 625?C, ( x 500).
216
Fig. 11. Microstructure of alloy containing 20%
niobium. Two-phase a + y structure.
Quenched from 600?C. ( X 500).
Fig. 13. Microstructure of alloy containing 0.7%
niobium. Precipitations of 8 phase visible on
background of a phase. Quenched from 625?C,
( x 500).
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All the alloys quenched from 600?C, with the exception of the alloy containing 0.3 % niobium, had a
two-phase a + y structure. Figure 11 shows the structure of the alloy containing 20% niobium quenched
from 600?C. The a + y eutectoid is visible on the background of a phase. The temperature of eutectoid
decomposition accordingly lies between 600 and 625?C. We assumed it to be equal to 612 f 13?C, which
is in good agreement with the values of [2].
Examination of the microstructure of alloys with 0.3 and 0.7% niobium, quenched from 625?C, showed
that the alloy with 0.3 To niobium consists of one-phase a solid solution (Fig. 12), and the alloy with 0.7%
niobium consists of a solid solution and transformed 8-phase (Fig. 13). It was therefore assumed that the
solubility of niobium in a-zirconium is about 0.5%, which is in good agreement with the solubility of tantalum
and niobium in a zirconium as determined for the ternary system.
Fig. 14., Projection of parts of the ternary phase diagram Zr?Ta?Nb on the concentration
plane of the triangle.
It will be seen from Figs. 1, 3, and 5, that the data of the metallographical analysis of the ternary
system Zr? Ta?Nb differ considerably from the results of the thermal analysis. There are also considerable
discrepancies between published results of thermal and dilatometer analyses and on the measurement of the
electrical resistance on heating of alloys of the Zr?Nb system, and the results of our metallographical studies
of this system (Fig. 14). These discrepancies are evidently due to the different degrees of approximation of
the alloys to the equilibrium condition according to the methods of investigation employed. It is evident
that metallographical examination of the alloys quenched after deformation and lengthy annealing (which
assists in bringing them to the equilibrium condition) produces more reliable information regarding the phase
diagrams. The methods of thermal and dilatometer analyses and the method of measuring the electrical re-
sistance, where heating and cooling of the alloys proceed at a relatively high rate, in the present case evidently
fix the nonequilibrium phase transitions.
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The results of the metallographical analysis were used in constructing a number of isothermal cross
sections of the investigated region (Fig. 15) of the phase diagram of the system Zr?Ta?Nb.
The isothermal cross section at 900?C has two regions: a one-phase region of 8-solid solution and a
two-phase region V.
The isothermal section at 820'C, in addition to the foregoing regions, has two new regions: the two-phase
+ 8 and the one-phase a region. In this section, the B region has become narrower and the 8 + y
region has widened.
In the isothermal section at 720? C, the three-phase region a+ + y appears; the 8 and 8 +
regions are narrower and the a and a + B regions are wider.
The isothermal section at 730?C has six phase regions; the dimensions of the a region are practically
unchanged; the a + 8 + y region has widened considerably; the a + ,B and B + y regions
have become narrower and the a + y region has appeared.
In the isothermal sections for the temperatures 700 and 645?C, two regions are absent: the two-phase
+ y region and the one-phase B region.
(t>
Zr
820? 's
Zr
Zr
a
MR\
/MAU
/AA 111
AfammEma
if
-Ar7411MC
?
Zr
90e
AD:
manum
ks Air-11\
191111WeAl....
z,\?
a fp
Zr
IA?
Fig. 15. Isothermal sections of the system Zr?Ta?Nb.
The region constructed for the zirconium apex of the ternary system Zr? Ta?Nb has limited solubility
of tantalum and niobium in a?zirconium, limited solubility of these elements in 8-zirconium with eutectoid
decomposition of the B solid solution and three-phase eutectoid equilibrium 8 a + y between a and
zirconium. Figure 14 shows the projections of these regions on the concentration plane of the triangle.
The three-phase eutectoid equilibrium B a + y corresponds to the monovariant lines BC and EF
descending from the nonvariant points B' and E' of the Zr?Ta system to the corresponding nonvariant points
C' and F' of the Zr?Nb system below them.
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The two-phase equilibrium B a corresponds to the surfaces DBCH and DEF of the transformation of
a- zirconium to a-zirconium; the two-phase equilibrium g y to the solubility surface ABC. The three-
phase solid of the eutectoid equilibrium B a + y is formed by the three ruled surfaces BCHFE, ABC,
and AEFH, In projection, the latter surface merges with the higher surfaces.
Measurement of the Hardness and Electrical Resistance
of Cast and Quenched Alloys
With the object of obtaining additional information on the system Zr?Ta?Nb , the hardness and electrical
resistance of cast and quenched alloys were measured. The hardness was measured on a Rockwell instrument
according to the Rc60 scale. The results obtained were converted into standard Brinell hardness values HB.
Figure 16 shows curves of hardness values plotted against composition for alloys cast and quenched from the
temperatures 1200, 820, 765, 700, and 600?C for all five polythermal cross sections. Examination of these
curves shows that the addition of tantalum and niobium to zirconium considerably increases its hardness. In
the third, fourth and fifth cross sections, the hardness curves show a well-pronounced maximum, due to the
martensitic-like transformation of the cubic 8 phase into the hexagonal a phase on quenching. This maximum
Is observed for these cross sections in alloys, quenched from a temperature above the boundary of the a + y
region. In the second section, the maximum is just beginning to show and in the first section it is absent al-
together. The existence of a maximum on the hardness curves of binary alloys (quenched from 1200?C) of the
system Zr?Ta [1], corresponding to the alloy containing about 28% by weight of tantalum, shows, however,
that such a maximum ought also to be present on the hardness curves of the first polythermal cross section, but
beyond the limits of the concentration region investigated.
"19
400
300
200
100
cast
400
300
200
100
min
MIMI!

" gra...a..tram
99989796 93 90 .88 8
765?
84
mummirifoniusuggina
IMMIIMIIWANNLVAWM?11
MINIMIMNIM11111.1MM
VAIN
111?111PffilIMMIERri.
MErlSow!...,1111MMIII/11
OrM.E'IME111111.111111Mfiii
pird.1=11
Vaill111111=1 MMINIIIMM=
111111INIMENNIMM==
11111111111111111111=111111111MMEIIIIIMI
111111=MINERIM9
99989796 93 90
88
86 84 82
400
300
200
100
400
300
200
100
1200?
3
5
99989796 93 90 88 86 84 82
700?
I WM
111111111111?11~/4=1?11:411OMIN
111111111M111W/INWIMMEM
immommimmImpems
ounnumarAmemmiowram
NiForkirmirma..Ism
borarisiummonmemm
miummummemommom
Imummiumminsom
mosmonsinommisounum
monsolimomminumil
inumemaimmum=mism
99399796 93 90 88 86 84
Zr. weight %
400
100
200
9.9989796
93 90 88 86 84
600?
82
82 99989796 93 90 88 86 84 82
Fig, 16, Hardness curves of alloys of the system Zr?Ta?Nb cast and quenched from different
temperatures for five polythermal cross sections (1-5) with constant ratio of the percentage con-
tent of niobium to tantalum.
The position of the maxima on the hardness curves of alloys, quenched from temperatures above the
boundaries of the two-phase region a + y, makes it impossible to determine by the hardness method the
phase boundaries situated in the investigated concentration region.
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The position of the maxima on the hardness curves of the alloys corresponds to the different total contents
of tantalum and niobium in all five polythermal cross sections and shifts toward alloys of high zirconium con-
tent when the ratio of the content of niobium to tantalum for the given cross section is increased. This in-
dicates that an increase in the addition of niobium to binary alloys of the system Zr?Ta results in a narrowing
of the range of martensitic-like transformation and, consequently, in an increase in the stabilization of the
8 phase, by quenching, at room temperature. There are no maxima on the hardness curves of alloys quenched
from the two-phase region a + y.
The dependence of hardness upon the composition of alloys quenched from the two-phase region a + y
(600?C) shows that the solubility of tantalum and niobium in a..zirconium is not high, which is in agreement
with the results of the metallographical examination.
The dependence of hardness upon composition of alloys of the system Zr?Nb quenched from 600?C
Is similar to the curve of Fig. 16. It shows that the solubility of niobium in a-zirconium is low, being about
0.5 % niobium, which is in good agreement with the results of metallographical examination.
The curves of electrical resistance versus composition for alloys of the first, third and fifth polythermal
cross sections, quenched from the a + y region, are similar in character to the corresponding hardness curves.
LITERATURE CITED
[1] V. S. Emel'ianov, Iu. G. Godin, and A. N. Evstiukhin, J. Atomic Energy (USSR) 2, 1, 42 (1957).*
[2] B. A. Rodgers and D. F. Atkins, J. Metals 9, 1034 (1955).
[3] Iu. F. Bychkov, A. N. Rozanov, and D. M. Skorov,,J. Atomic Energy (USSR) 2, 2, 146 (1957).*
[4] R. F. Domogala and D. J. M. McPherson, J. Metals, 5, 619 (1956).
[5] S. A. Pogodin, K. P. Belova, N. F. Blagov, L. M. Venediktov, E., A. Kamenskaia, and M. B. Reifman,
Jubilee Collection of the Work of the State Rare Metals Scientific Research Institute (In Press).
Received April 10, 1957.
* See C. B. Translation.
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PROBLEM OF THE IODINE METHOD OF PURIFICATION OF ZIRCONIUM
K.D. Sinel'nikov, F.I. Busol and G.I. Stepanova
A method is proposed for the determination of the equilibrium constants k and k'
for the reactions Zr + 212? ZrI4 = 0 and 21 ?12 = 0, which is based on the measure-
ment of the amount of iodine or zirconium liberated in the decomposition of zirconium
tetraiodide on a heated surface in the process of establishing equilibrium. The decom-
position of the tetraiodide was carried out at 900-1600?C on a tungsten filament. The
temperature distribution between filament and vessel walls was neglected.
The dependence of the sum of atomic and molecular iodine pressures PI + ph on
zirconium tetraiodide pressure pzri4 was determined at 1430?C, and on temperature for
PZrI4 pi 50 mm Hg. The values of kka Pi 35 (mm Hg)3 at 1430?C and k 0.07 mmHg
at 400?C, found from the results, differ substantially from known thermodynamic data,
but give good agreement between the authors' formula [1] and experimental results on
the iodide process of zirconium purification.
INTRODUCTION
Reference [1] proposed a theory for the iodide process of zirconium purification, which was based on the
supposition that in the region of a filament on which pure zirconium is being deposited and in the region of the
original metal, there is equilibrium between the reactions
Zr + 212? ZrI4 = 0, (1)
21 ?12 -= O. (2)
This supposition is valid for the pressure range in which the mean free path length of the molecules is much less
than the dimensions of the reaction vessel. Since the temperature of the filament is higher than the temperature
of the original metal, the equilibrium concentration of ZrI4 close to the filament is less than its equilibrium con-
centration close to the unpurified zirconium. The resulting diffusion flow ensures the transport of zirconium to
the filament. The dependence of the flow of zirconium upon the equilibrium constants of Reactions (1) and (2)
and upon the Zr4pressure in the region of the original metal, this pressure being usually known, is determined in
[1]. The relationships obtained in particular provide an explanation for the existence of maximum flow with vari-
ation in pressure of zirconium tetraiodide and the displacement of the maximum towards higher pressures when
the filament temperature is increased. When, however, the constants k and k' calculated from thermodynamic
data [2] are used, the results obtained in [1] do not agree quantitatively with experiment.
Since the satisfactory qualitative explanation of many aspects of the process described cannot be accidental,
we assumed that the thermodynamic data [2], obtained for zirconium chlorides by an indirect method, were er-
roneous, and we carried out direct measurements of the constants in which we were interested.*
It should be pointed out that very little is known about the equilibrium constant of Reaction (1), although
attempts have been made to measure this magnitude at high temperatures [3-5]. The constant le has been deter-
mined in a Wide temperature range.
*Doubt as to the accuracy of the thermodynamic data [2] has also been expressed previously [3].
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Measurement of the Constants
Principle of the method. For determining the equilibrium constants of Reaction (1)
k = 142/13ZrI4 (3)
and Reaction (2)
k' = pi/ph (4)
it is necessary to measure the partial pressures of zirconium tetraiodide pzr14, atomic iodine pi and molecular
iodine ph at the given temperature. We measured the pressure of the tetraiodide pzrh and the sum of the pres-
sures of atomic and molecular iodine pi + p12 connected by the relationship
+ if 2= (kle2)1/4pyifi1 /c1/2p1/21? (5)
zri
Knowing the relationship between pi + p12 and pzrh, the values of the constants can be found.
The following method was used for making the measurements. A fairly large amount of zirconium tetra-
iodide is introduced into the usual zirconium purification apparatus. The pressure of the ZrI4 vapor in the appa-
ratus is determined by the temperature of the coldest part. Some of the tetraiodide introduced is dissociated
with the separation of zirconium and iodine. The dissociation of the tetraiodide will obviously continue until the
pressure of the liberated iodine attains equilibrium value, determined by the highest temperature in the apparatus.
(The iodine vapor should not of course be saturated.) In the present case, the electrically heated tungsten fila-
ment had the highest temperature.
In the dissociation of ZrI4 close to the filament, both molecular and atomic iodine are liberated, the rela-
tion between their partial pressures being determined by the value of the constant k' at the temperature of the
equilibrium region, which extends for at least several mean free path lengths.* The concentration of atomic io-
dine rapidly falls as the distance from the filament increases. Since the region of effective dissociation of io-
dine is small compared with the volume of the vessel, the number of iodine atoms Ni in the vessel is small com-
pared with the number of iodine molecules N12. With this approximation N12 is determined from the amount m
of zirconium separated on the filament or the amount of liberated iodine m' by means of the relationships
2m
NI2IT ' ,
= A 0; NI
2 m' [A.
(6)
where A and ? are,respectively,the atomic weight of zirconium and the molecular weight of iodine; No is Avo-
gadro's constant. The pressure of molecular iodine in the vessel and consequently the sum of the pressures of at-
omic and molecular iodine close to the filament is then determined by the approximate equation
2RT
P1-1-- 2 N0V '
(7)
where R is the gas constant, T the mean temperature in the vessel and V the total volume of the vessel.
Experimental method and results. The apparatus is shown diagrammatically in Figure 1. The glass vessel
12 was evacuated and outgassed for two hours at ?500?C and a vacuum of ?10-5.mm Hg, after which the apparatus
was sealed off at 2 and the ampoule containing 1 g of tetraiodide was broken. The entire apparatus, with the ex-
ception of the lower half of bulb 6, was heated to 400?C. The temperature of the lower half of bulb 6, determin-
ing the pressure of zirconium tetraiodide in the apparatus, was regulated by means of a bath filled with molten
tin. After the given pressure pzrh had been established in the apparatus, the heating current for the filament 13
*It should be pointed out that the temperature is much less than the filament temperature, due to the fact that
when thin filaments are heated in rarefied gases, there is a temperature drop between filament and gas. Thus, ac-
cording to Langmuir [6], for nitrogen and hydrogen at pressures of 1-10 mm Hg and a filament temperature
?1500?C, the temperature drop amounts to several hundred degrees over a mean free path length.
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fl
6
12 13
14
15
Fig. 1. Diagram of apparatus; 1) connecting piece; 2,3,5,7,11) pin-
ches; 4,6) bulbs; 8) striker; 9) ampoule containing Zr14; 10) tube;
12) vessel; 13) tungsten filament; 14) molybdenum electrodes; 15)
end of apparatus.
was switched on. In the first series of experiments, the filament was a tungsten wire 0.08 mm in diameter, in
the second series the diameter of the wire was 1.2 mm. The filament temperature was measured by means of
an optical pyrometer.
The course of the dissociation of ZrI4 could be observed by the variation of current in the filament, which
was appreciable when thin filaments were used. At first, the current increased somewhat (by 0.2-0.5 amp) de-
pending upon pzrh, but the increase in current soon ceased (after three to five minutes). This meant that the
deposition of zirconium on the filament had ceased and consequently the partial pressure of the iodide had
reached equilibrium value.
Some time after switching on the filament heating current (-20 min) the tin bath was quickly removed
and bulb 6 was immersed in liquid nitrogen. The result was that the vapors of iodine and tetraiodide froze prac-
tically instantaneously.'
In the first series of experiments, the equilibrium pressure of iodine was determined from the amount m
of zirconium deposited on tie filament and found by weighing the filament before and after the experiment.
The filament temperature was maintained at 1430?C. The pressure pzrh was varied within the limits 0.2-50
mm Hg. The results of the measurements are given in Table 1.
TABLE 1
Temperature
of bulb 6, ?C
Pressure of
tetraiodide
vapor pzrh,
mm Hg
Weight of zir-
conium m ,
mg
Volume V,
cm3
Sum of pressures
PI + PI2.
mm Hg
235
0.2
1
555
1.7
263
1.0
1.8
528
3.1
310
10
3.6
525
6.3
340
34
8.3
577
13.2
350
50
3.9
528
6.8
In the second series of experiments, the equilibrium pressure of the iodine was determined by weighing the
liberated iodine. For this purpose, after freezing the iodine and tetraiodide vapors in bulb 6, the latter was
sealed off at 3, the iodine was sublimed from 6 to 4 and the latter sealed off at 5. The amount of liberated io-
dine was found by weighing 4 with and without iodine and introducing a correction for the weight of air con-
tained in bulb 4.
The first group of the second series of experiments repeated the experiments of the first series and was car-
ried out for the purpose of comparing the two sets of experiments and also for obtaining more exact information
of the dependence of p/ + ph upon pzat. (The first series of experiments showed considerable scatter, evidently
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due to insufficiently accurate temperature measurement in this case.) The filament temperature was 1430?C.
The pressure of zirconium tetraiodide was measured within the limits 1-50 mm Hg. Table 2 shows the results of
this group of measurements.
TABLE 2
Temperature
of bulb 6,?C
Pressure of
tetraiodide
vapor,mm Hg
Weight of to-
dine m, mg
Volume V,
cm8
Sum of pres-
sures pi + Ph ,
mm lig
263
1
12.1
640
3.1
281
2.5
13.7
656
3.5
295
5
16.3
660
4.1
311
10
17.2
655
4.3
328
20
18.7
655
4.7
339
35
17.4
647
4.4
350
50
18.9
640
4.9
In the second group of the second series of measurements, the pressure of the tetraiodide vapor was kept
constant (-50 mm Hg) and the temperature of the filament was varied from 1570 to 960?C. The results of these
measurements are given in Table 3.
TABLE 3*
Filament tern-
perature, ?C
Weight of io-
dine m', mg
Volume V,
cm3
Sum of pres-
sures PI + ph .
mm Hg
1570
48
545
14.5
1510
30
565
8.8
1510
35
565
10.2
1450
24
562
7.1
1390
29
590
8.1
1330
19
530
5.0
1330
21
600
5.8
1270
21
540
6.4
1270
23
620
6.2
1210
15
560
4.4
1150
15
560
4.4
1150
12.5
565
3.7
1080
13
560
3.8
1030
16
567
4.7
960
9
565
2.6
400
7
560
2.1
400
6.8
555
1.7
*The last two measurements were made without switching on
the filament heating current.
Comparison of the data of Tables 1 and 2 shows that for corresponding vapor pressures of ZrI4, the values
of the iodine pressure agree sufficiently well. This means that the liberation of iodine is in fact due to dissocia-
tion of the tetraiodide on the filament and not to any other reactions.
The slow variation in the value of PI + pi2 with variation in the vapor pressure of ZrI4 suggests that the
principal term in the measured sum for a filament temperature of 1430?C is the pressure of atomic iodine, which
,is proportional to the fourth root of pzat (pi = (kke2)1/4P114ZrI4). This is confirmed by the graph (Figure 2) where
the values of p/ + p12 (from Tables 1 and 2) have been plotted on the ordinate axis and p on the abscissa axis.
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8
1
I
?
o
t
o
?
0.5
7.0
1,5
20
25
n3/4
'Zr
Fig. 2, Dependence of the total iodine pressure PI+ P12 on
(PZrI4)1/4. Tfilament = 1430? C.
The experimental points lie satisfactorily on a straight line, the tangent of the angle of slope of which gives
kk.2 PI 35 (mm Hg)s. According to the thermodynamic data [2] at 1400?C, kk's F:d 0.4 (mm Hg)3. If we consider,
however, that in our experiments k' corresponds to a much lower temperature, the discrepancy between the value
of kk'2 found and that calculated is still greater.
Examination of the data of Table 3 draws attention to the fact that the equilibrium pressure of iodine varies
appreciably only in the range of 1570-1200?C. On further reduction in the temperature, the rate of change of
pi + p12 diminishes and becomes particularly small in the range 1000-400?C. At the same time, it is important
that even at 400?C, the pressure of the liberated iodine is quite considerable. Since the dissociation of iodine is
negligible at this temperature the predominant term in the sum PI + p/2 is the pressure of molecular iodine,
equal to
kil2p1/
Z14
From this we obtain the value of interest to us for the equilibrium constant of Reaction (1) at 400?C, i.e., k
F:10.07 mm Hg, differing by many orders from the value determined in accordance with the formula
ln k = ?
RT '
(8)
where PF is the change in free energy in the dissociation of tetraiodide calculated from the data of [2].
The causes of such a large discrepancy are obscure. It may be thought, however, that the value of 6,F used
is high, due to the high value for the heat of formation of zirconium cited in [2] (AH298 = ?160 kcal/mole and
= ?73T ? AH298 = 111 kcal/mole at 400?C). This is supported, for example, by the data of [4] and [7], in
which the dependence of the degree of dissociation of the molecules of ZrI4 on the temperature of the support
was obtained in the range 1100-1500?C. Evaluation of the results of [4] and [7] gives a value of E PS 20 kcal/mole
for the bond energy of a mole of tetraiodide, approximately equal to ttie heat of formation of the tetraiodide.
We shall now show that the values obtained by us for the constants ensure fairly good agreement of the for-
mulas in [1] with experimental data on the iodide process of zirconium purification. We shall use for this pur-
pose the experimental dependence of the rate of deposit of zirconium upon the pressure of the tetraiodide vapor*
"The curve shown in Figure 3 was obtained in an investigation of the factors affecting the rate of deposition of
zirconium. The experiments were made in glass vessels of ?1 liter capacity, having a special branch, the tem-
perature of which was regulated by the vapor pressure of ZrI4. The starting material was 20 g of zirconium chips.
The temperature of filament and starting material was kept constant at 1450 and 400?C. 0.5-1 g of iodine was
Introduced into the vessel. The zirconium was deposited on a tungsten filament 800 mm long and 0.08 mm in
diameter. ?
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4.0
0
150 200 250
Ternperkture
300
350
of branch, ?C
Fig. 3. Dependence of rate of deposition of
zirconium upon temperature of branch-piece
(pressure of zirconium tetraiodide vapor).
Tfilament = 1450?C.
o
bO
0
0
?
0
04
4,0
3.0
2.5
2.0
IS
1.0
0.5
.fir
1:1
0
1100
1200 1300 1400 1500
Filament temperature, ?C
Fig. 4. Dependence of rate of zirconium de-
position upon filament temperature: I)
PZrI4 = 0.9 mm Hg; II) PZrI4 = 0.2 mm Hg.
of the purification process. Furthermore, the
mentioned deficiency.
(Figure 3) and Formula (20) from [1], which is correct for in-
termediate pressures*:
w = B 1_ Ic:/2
Pzi1r214 ?k2lc2. '
where k1 and k2 are the values of the constant k at 400 and
1450?C, respectively; k'2 is the value of the constant k' at
1450?C. After substituting in (9) the values W1 = 3.24,
W2 = 3.63 and W3 = 3.20 g/hour ? dm for pressures of tetra-
iodide vapor of 0.5, 1.12 and 2.14 mm Hg, respectively, we
obtain a system of three equations with three unknowns.
Solution of this system gives kJ. 0.072 mm Hg, k2k'22 54
(mm Hg)3, B Ps 5 g/hour ? dm. It is not difficult to see that
the values of k1 and k2k'i agree with the measured values.
The limit values of the rate of deposition at high fil-
ament temperatures, expressed by the formula
(9)
1412
1+
Pzrli
(10)
are likewise in good agreement with the measured value of
the constant kl. Figure 4 shows the experimental curves for
the dependence of rate of zirconium deposition upon fila-
ment temperature at pressures pzti4 0.9 and 0.2 mm Hg.**
It will be seen from the curves that above 1450?C, the rate
of deposition reaches a limit value, Wlimtt being 3.60 and
3.30 g/hour? dm, respectively. By substituting B = 5 g/hour ?
? dm in Formula (10) we get Wumit = 3.95 and Wlimit =
= 3.14 g/hour ? dm.
It should be pointed out that such an important factor
as the true temperature distribution between filament and
vessel wall was not taken into account in this investigation.
At the same time, a knowledge of this distribution is abso-
lutely necessary, since die value of constant k' depends ma-
terially upon the temperature distribution in the vicinity of
the filament. Furthermore, the value of constant kis deter-
mined, in all probability, by the surface temperature of the
filament. Nevertheless, the values obtained for the constants
are of definite interest, since the temperature distribution in
the vicinity of the filament is practically the same as in the
iodide method of zirconium purification. Thus, the meas-
ured values of the constants do actually define the behavior
determination of the constant k at 400?C is free from the above-
LITERATURE CITED
[1] G.I. Stepanova and F.I. Busol, J. Atomic Energy (USSR) 3, 10, 344 (1957).***
?Transition from the value of flow to rate of deposition merely involves introduction of the
stead of A.
*The curves of Figure 4 were obtained in the same conditions as the curve of Figure 3.
???Original Russian pagination. See C.B. translation.
226
constant B in-
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1950).
[2] L.L. Quill, The Chemistry and Metallurgy of Miscellaneous Materials (McGraw Hill Book Co., Inc.,
[3] Lustmann and Kerze, The Metallurgy of Zirconium (McGraw Hill Book Co., Inc., 1955), p. 135.
[4] LH. Doring and K. Moliere, Z. Elektrochem. 56, 403 (1956).
[5] V.S. Emel'ianov, P.D. Bystrov and A.I. Evtiukhin, J. Atomic Energy (USSR) 1, 1, 43 (1956).*
[6] I. Langmuir, J. Amer. Chem. Soc. 37, 417 (1915).
[7] R.B. Holden and B. Kopelman, J. Electrochem, Soc. 100, 120 (1953).
Received April 11, 1957
*Original Russian pagination. See C.B. translation.
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LETTERS TO THE EDITOR
HIGH-VOLTAGE SOURCES FOR ONE-SHOT HIGH-CURRENT ACCELERATORS
B. S. Novikovskii
The particle currents available from electrostatic generators are limited, in the best cases,to the order
of several tens of microamperes; on the other hand, at the present time there are problems whose solution re-
quires particle currents of the order of several milliamperes and even tens of milliamperes at energies of
2-3 Mev. The construction of an electrostatic generator with currents of this type is not feasible. For this
reason attention is once again merited by one-shot accelerators which use voltage-multipliers.
The usual voltage multiplier (Fig. 1) is not convenient since the output voltage has a high ripple component
and the internal resistance is high; these factors limit the application of the circuit as a high-voltage source for
high-current, one-shot accelerators.
There are three basic formulas for making circuit calculations: these give the output-voltage ripple
6U , the voltage drop AU, and the optimum number of voltage-multiplying stages nopt;
8 u = i n(n+1)
IC 2 '
A ?
/UmaxiC
nopf=
where i is the load current, f is the frequency of the supply voltage. C is the capacity for one stage,
Lima, is the maximum voltage at the input to the circuit and n is the number of stages.
These formulas indicate that the construction of a high-voltage accelerator to obtain protons with energies
of the order of 2 Mev and currents of 5-10 ma is an extremely difficult technical problem when ordinary voltage
multiplying circuits are used. In a great deal of experimental research, especially for work with thin targets,
the energy of the accelerated particles from the accelerator must be extremely precise, generally to within an
accuracy of 0.1-0.05 %. Attempts have been made to construct a high-current accelerator which satisfies the
requirements given above.
At the end of 1955 a paper by Heilpern appeared* in which a proposal was made for a symmetric
voltage-multiplying circuit (Fig. 2) having better characteristics than the usual circuit (Fig. 1). As compared
with the ordinary circuit, the symmetric circuit requires twice the number of rectifiers, plus an additional
condenser column. Unfortunately, in this paper, as in other papers on the cascade generator, no analysis is
given of the operation of the circuit nor are basic calculation formulas presented (except the formula for 6U),
thus making the analysis of the feasibility of this proposed method very difficult.
The author has made an analysis of the operation of the symmetric circuit, deriving the basic formulas
and checking them in practice. From this work it has been found that the symmetric circuit has an unquestioned
advantage as compared with the ordinary voltage-multiplying circuit. It was found that in the symmetric circuit
the basic formulas for 6U, AU, and nopt are the following:
W. Heilpern, Hely. phys. acta 28, 485 (1955),
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i n
SU= .7 ,
i = (In3+1n2+1;\
6 4 12 )
Umax./C
'opt-2 i ?
Thus, the ripple voltage in a circuit of this kind is (n + 1) times smaller, the voltage drop is four times smaller
and the optimum number of cascades is twice as large as in the usual multiplying circuit.
,eO,e,,I,,0
00
Fig. 1. Ordinary voltage-multiplying circuit. Fig. 2. Symmetric voltage-multiplying circuit.
To clarify this point we consider a cascade generator made up of an ordinary circuit and a symmetric
circuit. We assume that i = 5 ma, f = 10 kc, C = 0,1 pf, , Umax = 50 kv, and n = 25. Under unloaded
conditions both generators produce the same voltage (without taking account of the voltage drop due to para-
sitic capacities) Uxx = 2 Umax ? n = 2500 kv ? Under load, however, the behavior of these two generators is
completely different.
The results of a comparison are shown in the table; it is apparent that as far as voltage excursions are
concerned the symmetric circuit is as good as an electrostatic generator at load currents which can not be
achieved in the latter.
In the future it may be feasible to use three-phase (Fig. 3) and multi-phase voltage multiplying circuits,
especially in those cases in which still higher currents are required. A three-phase circuit requires four con-
denser columns but an ordinary voltage multiplier made from these condensers (actually two ordinary circuits
in parallel) is considerably worse than the three-phase circuit both with regard to voltage drop and ripple.
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To verify these considerations a voltage multiplier circuit was constructed which could be easily con-
verted from ordinary operation to symmetric operation and three-phase operation. The capacity of a stage
was 1 pf ; the rectifiers were Type AVS-7-3p selenium banks; the number of stages was varied from 2 to
10; the frequency of the supply voltage was 50 cps.
Fig. 3. Three-phase voltage-multiplying circuit.
9
.61/
Enup
eu,v
300
200
100
1
3
2
3
5
6 it
Fig. 4. The ripple in the output voltage 6U has
a function of the number of stages n for a load
current i = 1 ma. 1) Ordinary circuit; 2)
symmetric circuit; 3) three-phase circuit.
dU, kv
5
4
3
6 U
Fig. 5. The quantity ? as a function of the
0
2
1
3
11
number of stages n for a load current i = 1 ma. 2 3 4 5 6 7 8 9
1) Ordinary circuit; 2) symmetric circuit; 3)
three-phase circuit.
Fig. 6. The output voltage drop AU as a function
of the number of stages n for a load current i =
= 2 ma. 1) Ordinary circuit; 2) symmetric
circuit; 3) three-phase circuit.
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TABLE 1
Comparison of the Ordinary and Symmetric Circuits.
Ordinary
circuit
Symmetric
circuit
6U, kv
16.25
0.625
AU, kv
-.130
Uxx -AU,
Ugen kv
1980
2370
6 U,
0.82
0.03
The experiments indicated that the ripple voltage in the symmetric circuit was reduced by more than a
factor of (n + 1) as compared with the ordinary voltage multiplying circuit. The three-phase circuit was
characterized by a ripple voltage higher than that of the symmetric circuit but considerably smaller than the
ordinary circuit (Fig. 4). It is of interest to
note that in the symmetric circuit the ratio
opt U
? is a fixed quantity for any number of
stages (Fig. 5). The voltage drop in the sym-
10
metric circuit is down by a factor somewhat
less than 4 as compared with the ordinary cir-
cuit (Fig. 6). This is probably explained by
the fact that the selenium column operates at
a reduced voltage. The three-phase circuit is
characterized by the smallest voltage drop.
The advantage of this circuit is particularly
pronounced when the number of stages is in-
creased. The optimum number of stages is
found to be in agreement with the formula
which was obtained; in the symmetric circuit
the number is larger than the ordinary circuit
by a factor of 2 while in the three-phase circuit
it is approximately a factor of 2.5 larger (Fig. 7).
Thus, the ordinary voltage multiplier
circuit cannot compete with the symmetric or
three-phase circuits in any respect. In machines
in which the basic requirement is voltage stability, the symmetric circuit appears to be most advantageous. In
machines in which the highest possible current and voltage are required, the three-phase voltage multiplier
circuit is to be preferred.
0,5 1,5 1 i, ma
Fig. 7. The optimum number of stages nopt as
a function of load current 1. 1) Ordinary circuit;
2) symmetric circuit; 3) three-phase circuit
(in the form shown).
Received June 27, 1957.
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ELECTRON TEMPERATURE AND DEGREE OF IONIZATION IN THE
INITIAL STAGES OF AN INTENSE PULSED DISCHARGE1
V.I. Kogan
In the present paper we present certain approximation formulas for the electron temperature and the de-
gree of ionization in the initial stages of an intense pulsed discharge in hydrogen [1], based on the assumption
that the electronic ionization mechanism is the predominant one.
1. In the case being considered,in which the discharge occurs in the course of several microseconds at low
pressure (approximately 0.05-2 mm Hg), the hydrogen cannot achieve thermal dynamic equilibrium nor, in gen-
eral, any stationary state. Hence, the relation between the electron temperature and the degree of ionization
cannot be written in terms of the Saha thermodynamic formula alone, but also requires formulas based on an
equilibrium of independent inverse processes (for example, ionization by electron impact and pair recombination).
We proceed directly from the simplified equations for balance between ionized and excited atoms,2 assuming
the chief mechanism for excitation and ionization to be electron impact;
(v.ai) nno
n* = (me) nno? ?1 n*.
(1)
(2)
Here no, n? and n are the number of unexcited atoms, the number of excited atoms, and the number of electrons
(ions) in 1 ems, respectively; vis the velocity of the electron; a i and oe are the cross sections for atomic ion-
ization and excitation by the electron; T is the mean radiation lifetime for the excited atom; the angular
brackets indicate averages taken over the electron velocity distribution. In these equations we neglect recom-
bination and removal of electrons from the volume as well as slow processes. Estimates show that these assump-
tions are justified for the densities and times being considered.
It has been shown experimentally [2] that the intensity of the radiation(proportional to the number of pho-
tons Oh) increases up to a time ti equal to ?10-8 sec. Consequently, ns/ti. Since r is approximately
10-8 sec and is much smaller than t1, n*/r ? n*. Simplifying Equation (2) and using Equation (1) we have
(vai)
(n*Pc) (vac)
(3)
Thus, the rate of ionization (n) is approximately proportional to the number of photons (n*/T) emitted per second.
This result is used as a basis for the remainder of the analysis.
2. Since the atom has many levels and a corresponding number of transitions from excited and emissive
levels, whereas in the experiments [2] the lines of the Balmer series were observed, Equations (1-3) should be
written for each transition is --> n/ --> n'/', where n' = 2; n = 3, 4, 5, .. The literature contains data on
cross sections for ionization and excitation of hydrogen atoms by electrons [3,4], computed in Born approxima-
tion, as well as the intensities of the Balmer lines [5]. Using these data we can compute the number of ioniza-
1 This work was completed in 1954.
2 The hydrogen may be assumed to be almost completely dissociated since no molecular bands are observed
in the luminous radiation from the discharge.
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tion events C, which occur for one "average" (cf. below) Balmer quantum as a function of electron energy ?. The
results of the calculations are given in Table 1.
TABLE 1
The Number of Ionization Events c for One "Aver-
age" Balmer Photon as a Function of Electron Energy
e. ev
13.5
20
30
50,
100
200
300
co
? 0
3.0
5.5
8.2
10.0
10.8
10.4
5.55
The computed ratio between the number of Balmer photons Ha, HB, HT, (HT denotes the summation over
the line H in all higher lines of the Balmer series) which are found for the same number of ionization events,
depends weakly on energy and may be represented roughly by the ratio va : v : u1 3: 1:1. This proportion-
ality justifies the introduction of an "average" energy for the Balmer photon used in computing C:
+ so vo + Z.17vi) (v. + vo +
From the last relations it follows that under the conditions of excitation and emission being considered (absence
of thermodynamic equilibrium) the intensity of the Ha line amounts to about half the total intensity of the
Balmer series.
3. Using a method similar to that employed in Section 2 we can compute the following quantities, aver-
aged over a Maxwellian distribution of electron velocities at a temperature Te: 1) the ionization intensity 11; =
=030; 2) the total intensity of the Balmer lines JB(erg ? cm3' sec -1); 3) the number of ionization events C
which occur for a Balmer photon. The results are shown in Table 2.
TABLE 2
The Intensity of Ionization if, the Total Intensity of the Balmer Lines JB/nno and the Number of Ionization
Events C Associated with One Balmer Photon as a Function of Electron Temperature Te
Te pv)
0
3
5
10
15
20
30
50
100
200
300
IF 10-8
)
0
0.05
0.25
1.3
2.4
3.1
4.2
5.1
5.5
5.0
4.3
-
--csem:
(
JB inno (10-20e4ic-cma)
0
0.06
0.25
0.84
1.26
1.47
1.70
1.85
1.88
1,73
1.68
C
0
2.2
3.7
5.7
6.9
7.7
8.8
10.0
10.5
10.4
9.4
5.55
The asymptotic expression for lir (Te) as Te co can be written analytically:
(t)Jt) 0.92.10-7 T12 ln (3.5v) cm3/sec
(4)
Using the functional dependence of ai (?) close to threshold [4], we can find an approximate formula for the other
limiting case Te ? Wi (Wi =-- 13.5 ev is the ionization energy):
wo V2Teg(1+ 2Te)
m exp cm3/sec,
\ T e
234
(5)
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where 00 sz3 4'10-17 cm2 and m is the mass of the electron.
We may note that our use of the theoretical values for al and ae, computed in Born approximation, does
not reduce significantly the reliability of the calculations even with Te equal to several electron volts; this re-
sult does not necessarily apply to the higher temperatures.
4. The calculations carried out in Sections 2 and 3, based on the introduction of the function C(Ta), re-
present an average of Equation (3) over excitation and emission processes relating to the Balmer series. The
"average" equation corresponding to Equation (3) is of the form
= nph C (Te), (6)
where nph is the number of Balmer photons emitted in one second per 1 cm3 of volume. Assuming that Te and
no are fixed over the cross section of the discharge and that no also remains constant in time,* integrating Equa-
tions (1, 6) over this cross section we have
Nno*(Te), (7)
= Nph C (Te), (8)
where N(t) and Nph(t) are the number of electrons and photons emitted in one second per centimeter of discharge
length. Nph is measured experimentally while the functions * and C are found above,so that (7) and (8) are es-
sentially a system of two equations for the functions N(t) and Te (t).
We solve this system under the assumption that Te