6
Bull. Soc. Photogr. Imag. Japan. (2019) Vol. 29 No. 1: 6–12

Original Paper

Dispersion of Latent Image Specks in Silver-salt Photographic Materials Formed
by Exposure to an Electron Beam with Constant Energy
Ken'ichi Kuge1, Kenzo Kawata2, Takaharu Kobayashi2, Mitsuhiro Kimura3, Nakahiro Yasuda4, Satoshi Kodaira5

Abstract: e system used to analyze the process of the formation of latent image specks (LISs) in silver-salt photographic materials due to radiationTh
exposure to obtain the dispersion index, which is the number of LISs in a silver halide grain formed by one impact of high-energy particle,
was improved. By using the electron beam from a transmission electron microscope, electrons of uniform energy could be produced for irradiation purposes. The number of electrons impacting a single silver halide grain along with the energy of each electron was controlled byvarying the current density and the applied voltage. A new analysis method which included the probability that LIS may not be formed despite an impact of high-energy particle was proposed. The number of LISs was counted by the arrested development method. The probability
and the dispersion index were estimated at approximately 0.5 and 1, respectively, for an unsensitized emulsion with cubic grains. This method
will be useful in the design of new nuclear emulsion plates.

Key words:

Silver-salt photography, Nuclear emulsion, Dispersion of latent image specks, Electron-beam exposure, Poisson distribution

1. Introduction
Nuclear emulsion plates incorporating silver-salt photographic
materials have been used for the detection of radiation tracks in the
search for elementary particles from the dawn of this form of research1)~4) up to the present day.5)~11) These plates possess several specific characteristics, such as high resolution and three-dimensional
detector.
An understanding of the photosensitive process in silver-salt photographic materials, which corresponds to the formation process oflatent image speck (LIS), is also important for radiation detection byusing nuclear emulsion plates.12)~14) In the case of light exposure,
LISs are formed by excited electrons generated by incident photons
on a silver halide grain.14)~16) The excited electron is captured at aparticular type of electron trap termed a sensitivity center and neutralized by an interstitial silver ion to form a silver atom. Repetitionof this process produces an LIS consisting of silver atoms. These
LISs act as a catalyst to reduce the silver halide grain to silver grainthrough the development process and an image consisting of silver
grains appears.
This includes many stochastic processes, such as the time-interval
distribution of excitation and the number distribution of excitedelectrons in each grain. Therefore, the analysis of the LIS formation
process, including these distributions, becomes very complicated.
An analysis of the sensitivity of these materials was carried out by
measuring the number of incident photons and statistically analyzReceived 2nd April, 2019; Accepted 23rd May, 20191:

ing the processes. Simulations were conducted by Hamilton17) andcontinued by Hailstone18) to analyze this stochastic process using
Monte Carlo methods. Typically, because the first LIS acts as astrong electron trap and effectively gathers other excited electrons,
only one LIS is formed in a grain. This is termed the concentration
theory.14), 19), 20)
There are many other unknown factors associated with the formation process of LISs through radiation exposures, which have inspired attempts at analyzing the process.21)~28) A large number ofelectrons are excited by one impact of high-energy charged particle,
and a plurality of LISs is often formed in one grain simultaneously
in spite of the concentration theory. This phenomenon is called thedispersion of LISs14), 20). Usually this brings about a decrease in sensitivity. Quantitative estimation of the degree of dispersion for each
emulsion is very important because this characteristic is strongly
affected by the properties of the emulsion.
As the former problem associated with the time interval distribution of excitation by photons is avoidable, radiation exposure would
make the analysis of the formation process simple. In previous reports on the study of the LIS formation process due to radiation
exposure21)~24), the distribution of the number of LISs formed on one
silver halide grain was experimentally analyzed, and the mean number of high-energy charged-particles impacting one grain w was
estimated using statistical analysis. The mean number of LISs v in
one grain was obtained experimentally and the mean number of
LISs z formed in one grain by one impact of charged particle was

Isotope Research Center, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
Faculty of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
3:
Nagoya Proton Therapy Center, 1-1-1 Hirate-cho, Kita-ku, Nagoya 462-8508, Japan
4:
Research Institute of Nuclear Engineering, Fukui University, 1-3-33 Kanawa-cho, Tsuruga 914-0055, Japan
5:
National Institute of Radiological Sciences/QST, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555, Japan2:

Ken'ichi Kuge, Kenzo Kawata, Takaharu Kobayashi, Mitsuhiro Kimura, Nakahiro Yasuda, Satoshi Kodaira

Dispersion of latent image specks in silver-salt photographic materials formed by exposure to an electron beam with constant energy

then calculated. This value z could be regarded as a dispersion index
that indicates the degree of the dispersion of LISs.
The latter problem associated with the distribution of the numberof excited electrons still remains because charged particles possess a
distribution of energy and the number of electrons excited in eachsilver halide grain is different. This deteriorates the accuracy of thedispersion-index measurement. However, when electron-beam irradiation is used, the energy of each irradiated electron can be madeuniform by adjusting the applied voltage. The energy transferred toeach silver halide grain by one impact becomes nearly uniform, andthe formation of LISs proceeds with an equivalent number of excited electrons in each grain. Consequently, the formation process becomes nearly identical, making the analysis simpler. A transmission
electron microscope was used as a convenient apparatus for electron-beam irradiation and a new method was developed to analyze
the LIS formation process. We analyzed the dispersion of LISs
formed by the electron-beam irradiation and will report the resultshere.

2. Theory
The calculation process for z was based on the following two hypotheses.21)~24)
Hypothesis 1:
The process involving charged particles impacting each silver halide grain is a random process.
Hypothesis 2:
Because the energy lost by an impacting charged particle is verylarge, many electrons are excited at the instant of the impact. Consequently, LISs are always formed in each silver halide grain absorbing
the energy of the impacting charged particles. Some reports haveshowed that a silver halide grain became developable after one impact of high-energy electron.29),30)
The distribution q (m) of impact times m at each grain will obey the
Poisson distribution following from Hypothesis 1, and can be given
as follows:q ( m)

e w wmm! (1)The probability that a charged particle will not impact a grain isgiven by Eq. (2):q (0)e w (2)This can be regarded as the ratio of grains which do not have any
LISs following from Hypothesis 2.
When the distribution f (n) is set for the number of LISs n in one
silver halide grain obtained experimentally, the ratio of grains f (0),which do not have any LISs, is equal to q (0). A method that can beused to count the number of LISs in one grain, termed as the arrested development technique, has already been proposed by many researchers21)~24),31)~36).

f (0)q ( 0)

e w (3)Consequently, the value w can be estimated experimentally from thevalue f (0).

w

7ln f (0) (4)The mean number v of LISs in a grain formed by w charged particles, which impacts on a grain, can be determined experimentallyand be used to yield v/w, which can provide the mean number z of
LISs formed by one impact of charged particle. This z value can beobtained experimentally from the slope of the straight line throughthe plotted points of w and v for different radiation exposure values.
Previously, it was noted that LISs were always formed by one impact of charged particle on a silver halide grain, as described in Hypothesis 2. However, the value f (0) often changed for materials withdifferent sensitization levels in spite of being exposed to the sameradiation. This suggests a case in which an LIS is not formed eventhough a charged particle impacts a grain. In this case f (0) does notagree with q (0). This would occur when the energy loss is small,leading to only a small number of electrons being excited, or when
the recombination process between excited electrons and holes proceeds vigorously.
Therefore, the case in which an LIS is not formed, despite an
impact of charged particle, should be taken into consideration. The
probability that an LIS is not formed even when a charged particle
impacts a grain is assumed to be k.
The mean number of events in which LISs are formed on a silver
halide grain when charged particles impact the grain w times is assumed to be w*. This value w* should be significantly correlated withthe experimental results. The distribution r (l) of the number of
events l in which LISs are formed is then considered. When theprobability k is constant, formation events for LISs after electron
impacts proceed randomly, and r (l) can be described by the Poisson
distribution in the same way as Eq. (1).

( )=

×

(0) =



=

ln{ (0)}

!

(5)The ratio of non-formation of an LIS is given as r(0).
(6)

This equals f (0), obtained experimentally.
(7)

The probability that an LIS is not formed even if m charged particles impact in sequence is km. Therefore, f (0) becomes the sum withm of the ratio of non-formation of an LIS despite m charged particles impacting the grain.

f (0)k m q ( m)q(0) kq(1) k 2 q(2)(8)Because q (m) is given by Eq. (1), this can be substituted into Eq. (8)as follows:
m 0

km

f (0)

e w wmm!

e w(k w) mm!
m 0

e (1 k ) w

(9)Taylor expansion can be used for e . As f(0) is equal to r(0), this leads
to the correlation between w and w*.
m 0xw* = (1 – k)w (10)In the case of irradiation from an electron beam with uniform
applied voltage, each electron possesses a uniform energy. The ener-

8Bull. Soc. Photogr. Imag. Japan. Vol. 29 No. 1 (2019)

gy of the electron E is given as E = e × V, where V is applied voltage
and e is the elementary charge. Furthermore, by adjusting the current density of the electron beam and arranging the grains with amono-grain layer on the base, the mean number of electrons g impacting one silver halide grain can be controlled. The value g is given
by Eq.(11), where I is the current density, S is the cross-section of
the grain, and t is the irradiation time of electron beam.

=

× ×


(11)
The value g can be considered as being equal to w and the probability k can be estimated from the ratio of g and w*. Both values can beobtained experimentally.

=1


(12)
This will provide information about the formation efficiency of LISs
under exposure to electron-beam irradiation.
Because the dispersion index is given for the number of formed
LISs, z* is equal to the number of LISs when one event of the formation of some LISs proceeds.

z =

=(

)

(13)
This z* value expresses the real degree of the dispersion of LISs,
even if an LIS is not formed with probability k at an impact ofcharged particle.

3. Experiment
The photographic emulsion used in this experiment was composed of pure silver bromide unsensitized cubic grains of 0.76 μm
edge length. The emulsion was applied to a plastic film-base to forma mono-grain layer. Because there was no overlapping of the emulsion grains, each grain was exposed to the same amount of electron-beam irradiation. An image of this film surface taken using an
atomic force microscope (AFM) is shown in Fig. 1. The grains do
not overlap and the upper half of the grains projects from the gelatin
layer, although the shape of the cube was not clear in this figure dueto the thin, soft gelatin layer covering the grains which disturbed thescanning by AFM probe. Observation with a conventional optical
microscope also indicated that all grains were arranged on the basewith one face of the cube facing directly above. These images indicated that square density of the grains was 96000 grains/mm2, andratio of grains overlapping was only 0.004%. Consequently, the crosssection of a grain was found to be (0.76)2 μm2 and the path length ofan electron travelling through a grain was 0.76 μm.
Films coated the emulsion were set on film holders for a transmission electron microscope ( JEOL, JEM 1200Ex) and the holders
were set in the microscope. The emulsion grains were irradiated byan electron beam uniformly, because any observation sample was not
set in the microscope. The applied voltages were 40, 60, or 80 kV, andone electron possessed an energy of 40, 60 or 80 keV. The variable g
was adjusted by altering the current density of the electron beam.
The irradiation characteristics of the electron beam are shown in
Table 1.
LISs were detected using an arrested development method, performed with the arrested developer as described by Mifune36. Because the development rate was suppressed in this developer, only asmall area around the LIS was developed to produce a developed
silver cluster that was much smaller than the silver halide grain. The
emulsion layer was dissolved after development to extract the silver
halide grains, and carbon replicas of the grain were prepared. These
replicas were observed with the same transmission electron microscope. The small, developed silver clusters in one silver halide grain
were counted to obtain the number of LISs. An electron micrographof the small developed silver clusters on the carbon replicas of thesilver halide grains is shown in Fig. 2, where the black lumps are thedeveloped silver clusters formed at each LIS. The clusters on one
hundred or more grains were counted.
Table 1 C ondition for the irradiation of electron beam
Current
density(pA/cm2)
Exposureperiod(second)
g

3.5

17.7

17.7

17.7

17.7

1

1

2

4

8

0.1

0.5

1

2

4

Cross section of the grain =(0.76)2 μm2

500nm
Fig. 1 A
 FM image of the surface of photographic film with mono-grain
layer.

Fig. 2 E lectron micrograph of small developed silver clusters on carbon
replicas of silver halide grains. The black lumps are the developed
silver clusters.

Ken'ichi Kuge, Kenzo Kawata, Takaharu Kobayashi, Mitsuhiro Kimura, Nakahiro Yasuda, Satoshi Kodaira

Dispersion of latent image specks in silver-salt photographic materials formed by exposure to an electron beam with constant energy

The mean number of LISs v on a grain and the distribution of thenumber f (n) were obtained experimentally. The value w* was thencalculated from f (0). The relationships between each w* value andits corresponding v value were then plotted, and the value z* wasobtained from the slope of the straight line through these plotted
points. The relationships between w* and g obtained from the current density were also plotted, and the probability k was estimatedfrom the slope of straight line through these plotted points.

with a high associated correlation coefficient.
The relationships between g and v are shown in Fig. 4 for eachapplied voltage. Plotting g versus v yielded a straight line, and theslopes of the straight-line graphs were all similar and were approximately 0.5 for all applied voltages, while the straight lines do notpass through the origin.
The relationships between g and w* obtained from each f (0) value
are shown in Fig. 5 for each applied voltage. The plotted points
formed a straight line but did not pass through the origin for any of
the applied voltages. The gradient of the slope was approximately
0.5. These relationships were similar to those of g and v as shown in
Fig. 4.
The relationships between w* and v are shown in Fig. 6 for eachapplied voltage. The plotted points also formed a straight line. The
correlation coefficients were all greater than 0.99, suggesting a goodcorrelation. The line passed through the origin and v values were notsaturated even when w* increased above a value of one, while the vvalue found in previous results showed a tendency to be saturated
with an increase in w*.21)~24) The gradient of the slope, which represents the value z*, was nearly unity for all applied voltages. This
indicated that only one LIS was formed by an impact of single elec-

4. Results
The distributions of the number of LISs in a grain f (n) after exposure to an electron beam with an applied voltage of 40, 60 and 80
kV are shown in Fig. 3 for each g value. Values of v for each g are also
shown in the figure. The distribution form increases in width alongwith an increase in g, thereby suggesting an increase in the numberof LISs in one silver halide grain. In the case of previous radiation
exposures21)~24), large numbers of LISs were formed by each impact
of charged particle, and the distribution often showed two peaks at
n = 0 and at n > 1. There was only one peak in this experiment andthe shape of the distribution obeyed the Poisson distribution law

0.8

(a)

(c)

g=0.1, v=0.28
g=0.5, v=0.42
g=1.0, v=0.39
g=2.0, v=0.98
g=4.0, v=2.1

f(n)

0.6

g=0.1, v=0.24
g=0.5, v=0.46
g=1.0, v=0.72
g=2.0, v=1.2
g=4.0, v=2.3(b)

g=0.1, v=0.36
g=0.5, v=0.52
g=1.0, v=0.83
g=2.0, v=1.1
g=4.0, v=2.3

0.4

0.2

0

0

1

2

3

4

5

6

7

0

1

2

4

3

5

6

7

0

1

2

3

5

4

6

7

n
Fig. 3 Th e distribution of the number of LISs n on a silver halide grain for different g values, where g is the mean number of high-energy electrons
impacting a grain, obtained from the current density of the electron beam, and v is the mean number of LISs on one grain. The applied voltageof electron beam was (a) 40 kV, (b) 60 kV, and (c) 80 kV.

4
3

(b)

(a)

(c)

v

2
1
0

1

2

3

4

0

1

9

2

3

4

0

1

2

3

4

g
Fig. 4 Relationships between g and v for various accelerating voltages. The applied voltage of electron beam was (a) 40 kV,(b) 60 kV, and (c) 80 kV.

10Bull. Soc. Photogr. Imag. Japan. Vol. 29 No. 1 (2019)

4

w*

(b)

(a)

3

(c)

2
1
0

1

2

3

4

0

1

2

3

4

0

1

2

3

4

g
Fig. 5 Relationships between g and w* for various accelerating voltages. The applied voltage of electron beam was (a) 40
kV, (b) 60 kV, and (c) 80 kV.

3
(a)

(c)

(b)

v

2
z*=1.00

1

0

1

2

z*=1.01z*=1.02

3 0

1

2

3 0

1

2

3

w*
Fig. 6 Relationships between w* and v for various accelerating voltages. The applied voltage of electron beam was (a) 40
kV, (b) 60 kV, and (c) 80 kV.
Table 2 Relations of g to v and w*, and z values for each applied voltage
Applied voltage(kV)
Relations ofg to v

Relations ofg to w*
z*

40

60

80

v = 0.49g+0.27

v = 0.52g+0.19

v = 0.45g+0.22

w* = 0.48g+0.28 w* = 0.50g+0.21 w* = 0.47g+0.14
1.0

1.0

1.0

tron. The relationships of g to v and w*, and z values for each applied
voltage are summarized in Table 2.

5. Discussion
The mean number of LIS formation events w* in one silver halide
grain due to impacts of high-energy electron was derived experimentally from f (0) values at the distribution of LISs, which was asimilar process used in previous experiments21)~24) involving radiation
exposure. In this experiment, the mean number of electrons impacting one silver halide grain g was newly derived from the current
density of the irradiating electron beam.
If LISs are always formed by an electron impact, the probability k
becomes 0, and w* agrees with g. However, the gradient of the slopeof the straight line through the plotted points of w* and g was approximately 0.5. The probability k was calculated to be approximately 0.5 from Eq. (12), and this indicated that approximately half ofthe high-energy electrons impacting a grain did not form an LIS.
The number of excited electrons in one silver halide grain was
calculated from the line energy-loss in silver halide, the electron-passin the grain, and the energy required to excite one electron in silver
halide. The energy loss for an electron passing through a silver bromide cubic grain of 0.76 μm edge length as obtained from the Bethe'
Equation37 was 2.2 keV for an electron of energy of 40 keV, 1.7 keV
for that of 60 keV, and 1.4 keV for that of 80 keV.
Ihama used an energy of 5.8 eV as the energy required to produce
one excited electron due to the passage of a high-energy electron
through silver bromide.38 Using this value, the number of electrons
generated by excitation was found to be approximately 380 at 40
keV, 290 at 60 keV, and 240 at 80 keV. Ihama estimated that the
number of electrons excited by an electron of 30 keV was 500 while
an electron of 1 MeV would excite 100 electrons in an octahedralgrain whose circle-equivalent diameter was 0.8 μm. These estimations were similar to the results of this study.
There were some reports which indicated that the minimum offour silver atoms were required to make one developable LIS.14),20),39)
The estimated number of excited electrons was sufficient to form
developable LISs in all grains impacted by the electron beam. Consequently, there must be a large loss process associated with the excited electrons. The same number of holes is always generated at
excitation, and recombination is the most probable loss process inthe absence of any effective process to remove these holes. The emul-

Ken'ichi Kuge, Kenzo Kawata, Takaharu Kobayashi, Mitsuhiro Kimura, Nakahiro Yasuda, Satoshi Kodaira

Dispersion of latent image specks in silver-salt photographic materials formed by exposure to an electron beam with constant energy

sion used in this experiment was an unsensitized one, therefore,
many of the formed holes would not be removed, and vigorous recombination would proceed in each grain, leading to half of thegrains not being able to form any LIS. Prevention of the recombination would drastically increase the sensitivity to radiation exposure.
The value z*, including the probability k, is, however, also useful as
an index for the degree of dispersion of LISs. The result whichshowed that z* was approximately equal to one suggested that only
one latent image speck was formed when one electron impacted thegrain despite a large amount of energy being provided to the grain.
Previous results involving radiation exposure for emulsions with sulfur, sulfur-plus-gold, or reduction sensitization21)~24) showed that z
yielded a value greater than one, depending on the type and level ofsensitization, and a plurality of LISs was formed. On the other hand,z was found to be nearly equal to one for unsensitized emulsions
with cubic grains. Similarly, the dispersion of LISs did not appear
and only one LIS was formed by each impact of high-energy electron in this experiment, because the emulsion used was an unsensitized one composed of cubic grains. When an LIS is first formed, it
attracts all excited electrons in the grain because there is no effective
electron trap which can compete against the capture of excited electrons to form LIS. It is regarded as a characteristic phenomenon of
unsensitized emulsions containing cubic grains that only one LIS isformed in a grain by one impact event. The concentration theory14),19),20) is consistent even for radiation exposure.
On the other hand, the plotted points of w*-v in Fig. 6 were always on a straight line, even when the value w* was larger than one.
This suggested that new LISs were formed even after the second or
third high-energy electron impacted the grain and even though
LISs already existed in the grain. The formation of new LISs by
subsequent impacts of electron proceeded in spite of the existence ofsome LISs. The concentration theory was therefore not effective inthis case, and this leads to the following consideration. The working
area of the concentration theory in a grain has certain limitations.
When the grain size is larger than this area, new LISs can be formedin sites outside of this area, as previously proposed.34 Therefore other
LISs could be formed in other areas of the grains of 0.76 μm size as
used in this experiment, which were larger than the 0.2 μm grain
sizes used in the previous reports.21)~24) The distribution of f (n) in
Fig. 3 would obey the Poisson distribution, because the formation of
LISs within specific areas in the grain was a random process. The
validity of this consideration will be inspected as part of future investigations through the use of an emulsion with a smaller grain size.
Although the applied voltage was altered from 40 to 80 kV, therelationship between w* and g for each voltage showed only a small
variation. It was expected that w* would depend on the applied voltage because the number of excited electrons changed as describedabove. The absence of such a phenomenon was considered as follows.
The same number of holes as electrons is always formed by excitation and the total number of electron-hole pairs varies with varying applied voltage. On the other hand, there will be a limitation interms of hole scavenging capacity to prevent recombination in silver
halide grains. The number of electrons surviving recombination will
become the same as the number of scavenged holes and be kept at

11

the same level, even though the number of electron-hole pairs increases. This also explains similar values for the probability k for eachapplied voltage.
The slopes of the straight-lines in Fig. 4 or Fig. 5 do not passthrough the origin. One possible reason is fog formation, because
fog would increase v and w* values uniformly and the line would
deviate from the origin. However, the fog level of this emulsion was
not so high due to the unsensitized one. Another reason is competition of surface and internal sensitivities. The size of this emulsion
grain is enough large to have internal sensitivity, and the unsensitized emulsions often have high internal sensitivity.40)~42) Competition of excited electrons would occur between surface and internalsites. When the surface sensitivity is slightly dominant, LISs areformed on the surface preferentially at small g values, and the probability k becomes high. However, when internal LISs are formed
following the increase of g value, the probability k decreases because
the development method used this experiment cannot detect theinternal LIS. Then, the slope becomes small and the line seems todeviate from the origin. This internal sensitivity could also affect tomake the probability k smaller.
Due to the use of the electron-beam and the method described inthis paper, handling of radioactive materials is not required, and theexperimentation is more convenient than that using previously reported methods. Moreover, the precision of the LIS-dispersion-index measurement was higher, and the accuracy was improved incomparison with the previous radiation exposures as shown in theplots of w*-v, which were well set on a straight line along with ahigh correlation coefficient.
These considerations suggest that the measurement of z* values
will be useful for the analysis of the LIS formation process. The
characteristic differences in the emulsions can be estimated by comparing z* values, and this will provide useful information for preparing nuclear emulsions with specific properties.

Acknowledgements
This work was performed as a Research Project with Heavy Ionsat the National Institute of Radiation Sciences/QST, Heavy Ion
Medical Accelerator in Chiba (NIRS-HIMAC) of 21P212~18H212.
This work was supported by JSPS KAKENHI Grant Numbers
26287037, 15K13476 and 18H03699.

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