19
Bull. Soc. Photogr. Imag. Japan. (2017) Vol. 27 No. 2: 19–25

Original Paper

Structural Study of the Ionic Conductivity in Double-Structured Grains of Silver
Iodobromide
Seiji Yamashita*, Naoto Oshima**, Shunji Takada***, and Ken’ichi Kuge***

Abstract:

 e prepared silver iodobromide double-structured grains with different iodide content in the core and the shell, and determinedW
their ionic conductivities by measuring their dielectric loss responses. The responses were reproduced quantitatively by the calculations based on Pauly-Schwan/Hanai (PS/H) theory, which is therefore proved to be an effective means for designing the silver iodobromide double-structured grains suitable for latent image formation.

Key words:

Silver iodobromide double-structured grain, Dielectric loss response, Ionic conductivity, Pauly-Schwann/Hanai theory

1. Introduction
Silver-iodobromide double-structured grains have been used forhigh-sensitivity photographic materials such as color negative films. 1)2)3)
With increasing iodide content, absorption of blue light increases
but development rate decreases. Therefore, double-structured grains
with a high silver-iodide-content core and low silver-iodide-content
shell were used to increase both light absorption and developmentrate. Furthermore, it was found that the edge dislocation formed at
the boundary between the core and shell acted as a primary photoelectron trap, causing an increase in sensitivity. 4) Consequently, double-structured grains were used not only for blue-sensitive emulsions, but also for spectrally sensitized green- and red-sensitive
emulsions.5)6)7) The reason of increase in sensitivity in the double-structured grains has been discussed previously from a viewpointof electronic process as mentioned above.
After electrons were trapped in the latent image formation sites,
the recombination process with holes and the neutralization processwith interstitial silver ions compete each other. 8)9) It is known thatthe recombination process becomes predominant when the neutralization is too slow, and the dispersion of latent image specks occurs
when the neutralization is too fast.8)9) The ionic conductivity of silver
iodobromide changes with silver iodide concentration. 7) Therefore,
the increase in sensitivity will be achieved when we can set the ionic
conductivity of shell in the double-structured grains optimally.
However, there is no report on the ionic conductivity of silver iodobromide double-structured grains. Maxwell-Wagner theory (MWReceived 25th, April 2016; Accepted 19th, October 2017

theory) has been used to analyze the dielectric loss response of silver
halide grains, which is a practical theory to evaluate the ionic conductivity of them. However, this theory is only applicable to a dispersion system of uniform grains.10)11)
The authors previously prepared double-structured grains of silver
bromide with different ionic conductivities in core and shell by doping polyvalent cations in each phase and found that their dielectricloss responses can be explained by Pauly-Schwan / Hanai (PS/H)
theory.12)
We prepared silver iodobromide double-structured grains whose
core or shell has high silver- iodide-content, measured their dielectric loss response experimentally, and analyzed the results using
PS/H theory. Here, we report the behavior and analysis of ionic conductivity in the silver iodobromide double-structured grains.

2. Experimental method
We prepared two kinds of emulsions with uniform grains. Sample
1 consisted of pure silver bromide and Sample 2 consisted of silver
iodobromide containing 27 mol% silver iodide. Then, we prepared
two kinds of emulsions with double-structured grains. Sample 3 wasdesigned that the core had silver iodobromide with 27 mol% iodide
and the shell had silver bromide. Sample 4 was designed that thecore and shell was exchanged with respect to Sample 3. They wereprepared using the controlled double-jet method under the grain
growth conditions in which the halide ion concentration exceeded
the silver ion concentration slightly. The halogen composition during*Medical Systems Research & Development Center, Research & Development Management Headquarters, Fuji Film Corporation
798, Miyanodai, Kaisei-machi, Ashigarakami-gun, Kanagawa 258-8538, Japan**Fuji Film Corporation (retired), present address:

1-7-12, Higashi-cho, Oiso-machi, Naka-gun, Kanagawa 255-0002, Japan***Graduate School of Advanced Integration Science, Chiba University
1-33, Yayoi-cho, Inage-ku, Chiba-city, Chiba 263-8522, Japan

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Bull. Soc. Photogr. Imag. Japan. Vol. 27 No. 2 (2017)

Table 1 Crystallographic data for four types of silver halide emulsion grains used in this report.
Sample No.
1

2

3

4

Halide Composition
Core

Shell

Volume Ratio ofCore to Shell

Crystal Habit

AgBrI

－

－

Octahedral

AgBr

AgBrI
AgBr

－

AgBr

AgBrI

Fig. 1 Experimental results of dielectric loss responses for Samples 1, 2, and3 at R.T. The solid line with two peaks shows the dielectric loss curvefor Sample 3. Here, fL is the peak frequency of the dielectric loss peakin the lower-frequency region, and fH is the one in the higher-frequency region of Sample 3. Broken lines show the dielectric loss
curves for Sample 1 in the lower-frequency region and Sample 2 in
the higher-frequency region; f1 is the peak frequency of the low-frequency peak and f2 is that of the high-frequency peak. In this experiment, the measuring range of each dielectric loss peak was set within
the range that can determine the position and shape of the peak corresponding to the ionic conductivity.

the growth of silver iodobromide phase was controlled to be 27
mol% silver iodide. The sphere-equivalent diameter and shell thickness of the double-structured grains were set to 1.00 µm and 0.10µm, respectively. Crystallographic data of the silver halide grains
prepared here are shown in Table 1. The grains of Sample 3 containing silver iodobromide core and silver bromide shell were cubo-octahedral grains with {111} and {100} faces. The grains of Samples 1,
2, and 4 were octahedral grains with {111} faces.
The formation energy of interstitial silver ions from the crystal
surface is smaller than that in the bulk and varies with the crystal
habit of silver halide grains. This causes that the ionic conductivity ofgrains changes with crystal habit and size, even if halogen composition is the same.9)13) To suppress these effects, 1-phenyl-5-mercaptotetrazole ( PMT, 1 × 10-3 mol/molAg) was added to the emulsion justbefore coating.12) Since adsorbed PMT suppresses the formation ofinterstitial silver ions from the crystal surfaces, the grains become tohave the same ionic conductivity as the one of large crystals.13) The
emulsions were coated and dried to produce a dry film of 100 µm
thick for measurements of dielectric loss response.
Two kinds of impedance analyzers were used to measure dielectric loss response.13) An INST Frequency Analyzer 5720B (NF

－

1:1

1:1

Grain Size (μm)

Octahedral

Cubo-Octahedral
Octahedral

0.8

0.8

1.0

1.0

Fig. 2 Experimental results of dielectric loss responses for Samples 1, 2, and4 at R.T. The solid line shows the dielectric loss curve for Sample 4.
Here, f is the peak frequency of the dielectric loss peak for Sample 4.
Broken lines show the dielectric loss curves for Sample 1 in the lower-frequency region and Sample 2 in the higher-frequency region; f1
is the peak frequency of the low-frequency peak and f2 is that of thehigh-frequency peak. In this experiment, the measuring range of eachdielectric loss peak was set within the range that can determine theposition and shape of the peak corresponding to the ionic conductivity.

Electronics) was used to measure low frequency characteristics anda 4192A Impedance Analyzer (Hewlett Packard) was used to measure high frequency characteristics. The temperature dependence ofionic conductivity was measured using a cryostat. The silver iodide
contents in core and shell of the double-structured grains were determined from the lattice constants obtained by powder X-ray diffraction.14)

3. Experimental results
3.1 Measurement of dielectric loss response
The dielectric loss responses of Samples 1, 2, and 3 are shown in
Fig. 1. Sample 3, which consists of double-structured grains withsilver-iodobromide core, indicates two dielectric loss peaks (shownby the solid line). Since the peak frequency of the dielectric loss is
proportional to the ionic conductivity11), the high frequency peak(maximum frequency fH ) reflects the ionic conductivity of the corewith high ionic conductivity, and the low frequency peak (maximum
frequency fL) reflects that of the shell with low ionic conductivity.
Dashed lines represent the dielectric loss responses of Sample 1 andSample 2 which consist of uniform grains of silver-bromide (maximum frequency f1) or silver iodobromide (maximum frequency f2).

Seiji Yamashita, Naoto Oshima, Shunji Takada, and Ken’ichi Kuge

21

Structural Study of the Ionic Conductivity in Double-Structured Grains of Silver Iodobromide

Both show a symmetric single peak.
Fig. 2 shows the dielectric loss responses of Sample 4 (double-structured grains with silver-iodobromide shell), and Sample 1
and Sample 2 (uniform grains). Sample 4 (indicated by a solid line)
shows a single dielectric loss peak (maximum frequency f ). Dashedlines represent the dielectric loss responses of Sample 1 and Sample
2 as same as in Fig.1. The peak of Sample 4 is almost at the same
position as the peak of Sample 2.
3.2 Estimation of halide composition from X-Ray diffraction
patterns
Figure 3 shows the X-ray diffraction patterns for the silver halide
grains of Samples 3 and 4. The lower and upper abscissas indicate
the X-ray diffraction angle (2θ) and the silver iodide content (mol%).
The diffraction patterns of both samples contain two peaks, corresponding to the core and shell compositions. The diffraction peak on
the left side, reflecting the silver-iodobromide phase, indicates thatsilver iodide content is about 27 mol% for both grains in Samples 3
and 4.
The diffraction peak on the right side for the core of Sample 4
indicates a pure silver-bromide phase, as originally designed, but thecorresponding peak for the shell of Sample 3 shifts to the left, indicating that the phase includes small amount of silver iodide at aconcentration of 2–3%.

3.3 Temperature dependence of ionic conductivity
The peak frequency of the dielectric loss fmax is proportional to theionic conductivity σ.11) The temperature dependence of the ionic
conductivity follows the relation shown in equation (1), when the
charge carrier is an interstitial silver ion. The activation energy is
given by the sum of the migration energy Ui and the formation energy ΔGi of interstitial silver ion.15) Here, n is the concentration ofinterstitial silver ion, e is the elementary charge, μ is the mobility ofinterstitial silver ion, C is a constant, T is the absolute temperature,and k is the Boltzmann constant.
σ = neμ = (C /T ) exp [ – (Ui + ΔGi ) / kT ](1)

Fig. 4 shows an Arrhenius plot of ionic conductivity obtained
from the temperature dependence of the dielectric loss responses ofSamples 1–4. We used another measurement system for these experiments13). We obtained the ionic conductivities corresponding to thepeaks of Sample 3 and 4 by approximating each peak as the one of
single structured grain with M/W theory. Therefore, these ionic conductivities for the double-structured grains are different from theactual ionic conductivities of each phase,12) but we consider that
their temperature dependences reflect the dependence of the ionic
conductivity in each phase.
The plot points of Sample 1 (uniform grains of silver bromide)
and Sample 2 (uniform grains of silver iodobromide) were aligned
almost linearly. The activation energies obtained from the slope ofthese lines were 0.52 eV and 0.33 eV, respectively, which were significantly different. The plot points of high frequency peak of Sam--2

Sample 1
Sample 2-1
log log((σT / ΩT)
cm-1K)-3

Sample 3/LF
Sample 3/HF

-4Sample 4

-5

-6

-7

-8

3

3.5

4

4.5

5

1000/T(K)K）
1000/（T/Fig. 3 X-ray diffraction patterns of Samples 3 and 4. The bottom abscissa
indicates iodide concentration of silver iodobromide grains, whichcorresponds to the diffraction angle of the silver iodobromide crystal,and the top abscissa indicates 2θ angle. CuKβ line and {220} diffraction angle are used for this experiment.

Fig. 4 Temperature dependence of the ionic conductivity obtained experimentally in Sample 1 (□), Sample 2 (◇), low-frequency peak (LF) in
Sample 3 (△), high-frequency peak (HF) in Samples 3 (○), andSample 4 (＊). These temperature dependence data in this figure wasobtained from the different experiments from that in Fig.1 and 2.

22

Bull. Soc. Photogr. Imag. Japan. Vol. 27 No. 2 (2017)ume ratio, we calculated the constants α, β, γ, and ξ of equation (2).
In this way, it is possible to calculate the frequency dependences ofcomplex permittivity of Samples 3 and 4 (consisting of double-structured grains). Here, the relative dielectric constants of silver bromide
and silver iodobromide were assumed to be 13.0.18) In addition, therelative permittivity of the gelatin medium was 3.0 (obtained fromexperimental data). The conductivity of it was much smaller thanthat of silver halide and was negligible. The characteristic values used
for calculation are listed in Table 3.
The calculated result of the dielectric loss response of Sample 3(high ionic conductivity in the core) is shown with a solid line in Fig.
5. Sample 3 showed two dielectric loss peaks reflecting the core(high frequency peak: maximum frequency f High) and shell (low frequency peak: maximum frequency f Low). The broken lines show thecalculation results of the dielectric loss response of Sample 1 (maximum frequency fAgBr; composed of uniform grains of silver bromide)
and the dielectric loss response of Sample 2 (maximum frequency
fAgBrI; composed of uniform grains of silver iodobromide). These two
peaks overlapped considerably with the two peaks of Sample 3.
The calculated result of the dielectric loss response of Sample 4(high ionic conductivity in the shell) is shown with the solid line in
Fig. 6. The dielectric loss response of Sample 4 was different fromthat of Sample 3. It shows a single dielectric loss peak (maximum
frequency f *). The broken lines are calculated results of the dielectricloss response of Samples 1 and 2, as in Fig. 5. The peak of Sample 4
appeared at a position close to the peak of Sample 2.

ple 3 and the peak of Sample 4 were in the same region as those of
Sample 2. Their activation energies were 0.24 eV and 0.28 eV, respectively. The ionic conductivity obtained from the low frequency
peak of Sample 3 was between the ionic conductivities of Sample 1
and Sample 2, and its activation energy was 0.46 eV. These results
are listed in Table 2.

4. Calculation using Pauly-Schwan/Hanai theory
The dielectric loss response of double-structured grains was calculated using PS / H theory.16) A detailed description of PS / H theory is given in reference 16. This theory is an extension of MW theory. The dielectric loss response of the system described in MW
theory includes one relaxation time. The complex dielectric constant
ε* of the system described in PS / H theory contains two different
relaxation times τ1 and τ2, as shown in equation (2). It is the maindifference between two theories. The reason for this difference is thatinterfacial polarization exists not only between the medium andshell but also between the shell and core in the case of double-structured grains. α, β, γ, ξ in equation (2) are constants calculated fromthe complex permittivity of the medium, core, and shell and theirvolume ratios. Equations (3) and (4) show the frequency dependence of two maxima included in the dielectric loss response (thecomplex component of dielectric constant). In this theory, we assume that the double-structured grains are composed of sphericalcore and shell, since grains are treated as spheres.
ε*= α +βγξ++1+jωτ1
1+jωτ2jωβωτ β( 1+jωτ) = 1+ω
τ
γ
ωτ γ
=
Im (
1+jωτ ) 1+ω τ
Im

1

2

1
2
2
2

(2)

2

(3)

2

(4)

1

2

5. Discussion

When MW theory is applied to the dielectric loss responses of
uniform grains composed of silver bromide or silver iodobromide,
the ionic conductivity of each phases can be determined. These values can be regarded as the conductivities of the core and shell of the
double-structured grains. Further, we set the complex permittivity ofthe medium, and of the core and shell. Finally, by setting each volTable 2 Ionic conductivities and activation energies of the samples obtained
from the experimental results in Fig.1, 2 and Fig. 4.

Sample 1

Sample 2
Sample 3
Sample 4

Ionic Conductivity(Ω–1·cm–1)
at R.T.

Activation Energy (eV) at
240– 298 K

4.0 × 10–6

0.33

6.3 × 10-8

0.52
0.24
0.46

(High) 2.3 × 10–6
(Low) 1.8 × 10–7

0.28

2.7 × 10–6

5.1 Analysis of dielectric loss response by PS / H theory
The calculated results of dielectric loss responses of Samples 1–4
from PS/H theory shown in Figs. 5 and 6 were consistent qualitatively well with the experimental results shown in Figs. 1 and 2. In
our previous paper, we showed that the dielectric loss responses ofdouble-structured grains whose core and shell had different ionic
conductivities by doping polyvalent cations were explained by PS/H
theory.12) It was confirmed again that the experimental behavior of
dielectric loss response for double-structured grains with different
ionic conductivity on the silver bromide/silver iodobromide system
was also explained by PS/H theory.
There were some differences, however, between the experimental
and calculated results. Then, we analyzed the difference in the case of
Sample 3 in detail. The first difference is in the peak frequencies. The
high frequency peak (fHigh) corresponding to the core of Sample 3
shifts from the peak (fAgBrI) of Sample 2 toward the lower frequency
side by about 0.15 decades in calculation (Fig. 5), and by 0.25 decades in experiment (Fig. 1). On the other hand, the low frequency

Table 3 Parameters used for the calculation of dielectric loss curves for Sample 3 and 4. σcore and σshell
are obtained from the experimental data of Samples 1 and 2.
Sample No.
3

4

Volume Ratio ofCore to Shellεmedium

εcore

εshellσcore(Ω–1·cm–1)

σshell(Ω–1·cm–1)

1:1

3.0

3.0

13.0

13.0

4×10–66.3×10–8

1:1

13.0

13.0

6.3×10–8

4×10–6

Structural Study of the Ionic Conductivity in Double-Structured Grains of Silver Iodobromide

LF Peak Height/HF Peak Height

Seiji Yamashita, Naoto Oshima, Shunji Takada, and Ken’ichi Kuge

1.1
1
0.9

Fig. 6 Calculation results of dielectric loss responses for Samples 1, 2, and 4.
The solid line shows the dielectric loss curve for Sample 4 calculated
by Pauly-Schwan/Hanai theory. Here, f * is the peak frequency of thedielectric loss peak for Sample 4. Broken lines show the dielectric loss
curves for Sample 1 composed of AgBr in the lower-frequency region, and Sample 2 composed of AgBrI in the higher-frequency region calculated by Maxwell-Wagner theory; fAgBr is the peak frequency of the low-frequency peak and fAgBrI is that of the high-frequency
peak.

peak (fLow ) corresponding to the shell shifts from the peak (fAgBr) of
Sample 1 to the higher frequency side by 0.2 decades in calculation
and by 0.5 decades in experiment. The deference of lower frequency
peak between calculation and experiment in Sample 3 is larger thanthat of high frequency peak, and this indicates that the real ionic
conductivity of the shell is about twice as large as the calculated result.

Sample 3 Exp

0.8
0.7
0.6
0.5
0.4

Fig. 5 Calculation results of dielectric loss responses for Samples 1, 2, and 3.
The solid line shows the dielectric loss curve for Sample 3 calculated
by Pauly-Schwan/Hanai theory. Here, fLow is the peak frequency ofthe dielectric loss peak in the lower-frequency region, and fHigh is theone in the higher-frequency region for Sample 3. Broken lines show
the dielectric loss curves for Sample 1 composed of AgBr in the lower-frequency region, and Sample 2 composed of AgBrI in the higher-frequency region calculated by Maxwell-Wagner theory; fAgBr is thepeak frequency of the low-frequency peak and fAgBrI is that of thehigh-frequency peak.

23

0

0.5

1

log( core/ shell)

1.5

2Fig. 7 Relationships between the peak height ratio of the high-frequency(HF) peak to low-frequency (LF) peak and ionic conductivity ratio oflog (σcore / σshell) for the dielectric loss response of double- structured
grains in Sample 3. ○, △ indicate the calculation results and ● indicates the experimental result.

This difference is also appeared in the temperature dependence in
Fig. 4. The temperature dependence of the peak frequencies in thehigh frequency side peak of Sample 3 and that of Sample 4 reflecting the ionic conductivity of silver iodobromide phase is similar tothat of Sample 2. In contrast, the temperature dependence of thepeak frequency in the low frequency side peak of Sample 3 is clearly
different from that of the peak of Sample 1.
The X-ray diffraction patterns in Fig. 3 indicated that the shell of
the double-structured grains of Sample 3 contained 2–3 mol% silver
iodide. It is known that the ionic conductivity increases when silver
iodide is mixed with silver bromide. Takada reported that the ionic
conductivity increased by about two times (0.3 decades) when 2
mol% silver iodide was mixed in silver bromide.7) Therefore, the shiftof the low frequency peak (fL) to higher frequency is consistent with
X-ray diffraction data which predicted that the shell contains about
2 mol% silver iodide. The contamination of silver iodide in the shellis considered to be due to re-dissolution of a part of the core (containing a large amount of silver iodide) at the time of shell formation. Such re-dissolution can be suppressed by setting conditions
that reduce the solubility of silver halide during shell formation.
The second difference is the peak height. Calculation of the peakheight ratio (PHR) of double-structured grain leads to the value 0.6
when σcore and σshell are the same as the conductivities of Sample 2(silver iodobromide) and Sample 1 (silver bromide) obtained experimentally. The logarithmic value for the ratio of conductivities ofSample 1 and Sample 2 is 1.8 decades. Similarly, the PHR values arecalculated to 0.8 and 1.0 when the logarithmic ratio of σcore and σshell
are 0.9 and 0 decades, respectively. Fig. 7 shows the relationship between PHR and the logarithmic ratio of σcore and σshell. This relation
represented that three open circles were on a straight line and thelogarithmic ratio of conductivity is almost proportional to PHR.
Because σshell of Sample 3 is two times larger than the ionic conduc-24

Bull. Soc. Photogr. Imag. Japan. Vol. 27 No. 2 (2017)

tivity of Sample 1, the logarithmic ratio of σcore and σshell changes
from 1.8 to 1.5 decades, and the PHR corresponding to this value is0.67 as shown by the triangle in Fig. 7. On the other hand, the experimental PHR value for Sample 3 is 0.8 as shown by a closed
circle in Fig. 7. This value is larger than the calculated value of 0.67.
This difference is explained by the increase in the volume of theshell with respect to the volume of the core.12) In Sample 3, the volume of the core decreases and the volume of the shell increases whencore re-dissolution occurs during shell formation. The shell will contain 2 mol% silver iodide, when the core containing 27 mol% silver
iodide is re-dissolved by about 7%. Hence, the volume of the shellincreases with the amount of re-dissolution and it is estimated thatthe volume ratio of the core and shell changes from 1:1 to 1:0.87.
Fig. 8 shows the relationship between the volume ratio and the ratioof the peak heights obtained from the calculation. The peak heightratio increased by about 0.15 when the volume ratio changed from
1.0 to 0.87. This value is approximately equal to the difference between the peak height ratio estimated from the calculation (0.67) inFig. 7 and that obtained from the experimental result (0.8). Furthermore, the reduction in core volume due to this re-dissolution explains the slightly large shift of the high frequency peak to the lower
frequency side for the experiment in Fig. 1 compared with the cal-Fig. 8 Relationships between the peak height ratio of the high-frequency(HF) peak to low-frequency (LF) peak in the dielectric loss responseand volume ratio of core to shell for the double structured grains in
Sample 3. ○ and △ indicate calculating points for the volume ratioof core to shell = 1.0 and 0.87 respectively.

culation results in Fig.5.12)
Similar increase in shell volume due to re-dissolution of core in
Sample 4 is probably responsible for the slightly small shift of thehigh frequency peak from the peak frequency of Sample 2 for theexperiment in Fig 2 to the lower frequency side compared with thecalculation in Fig.6. In our previous paper, we calculated the dielectric loss responses of similar grain structure to Sample 4 19), and thedielectric loss peak shifted to the higher frequency side, as the volume ratio of shell to core increases.
It is concluded that the difference in the peak height ratio is dueto the change in the volume ratio by the re-dissolution of the core.
PS/H theory explains these behaviors well. It will be possible to prevent the mixing of silver iodide in the shell, when the solubility
during shell formation is lowered to prevent re-dissolution of thecore.
Estimation of the ionic conductivity for double-structured grainsof different iodide-content and volume ratio in core and shell is possible by the use of PS/H theory. This will assist the design of double-structured grains without the tedious and repetitive measurements of ionic conductivity. By adjusting silver iodide content andvolume ratio in core and shell, we can prepare the suitable grains forlatent image formation.
Finally, we considered about the possibility that the interstitial
silver ions diffused from the core to shell when they existed at highconcentration in the core. In this cases the volume ratio of the core
to shell apparently increases. As shown in Fig. 8, this will reduce theratio of peak height, although the experimental result was opposite.
Therefore, it is concluded that the diffusion of interstitial silver ionsfrom the core to shell rarely occurs.
5.2 Ionic conductivity of silver iodobromide phase
Next, we consider the ionic conductivity of the silver iodobromide
phase. From the results of the temperature dependence in Fig 4
which is summarized in Table 4, the ionic conductivity of silver bromide grains (Sample 1) with adsorbed PMT was 6.3 × 10-8 Ω -1·cm-1
at room temperature, and its activation energy was 0.52 eV. In contrast, the silver iodobromide grains (Sample 2) containing 27 mol%of silver iodide had ionic conductivity of 4.0 × 10-5 Ω-1·cm-1 and activation energy of 0.33 eV. Silver iodobromide grains have high ionic conductivity and low activation energy.
Silver halide micro-crystals exhibit the same ionic conductivity aslarge crystals by adsorbing PMT on their surfaces sufficiently tosuppress the formation of interstitial silver ions.13) Although there is

Table 4 Ionic conductivity and its activation energy of the β-AgI large crystal (Ref. 18) in the intrinsic region, and those of Sample 1 (AgBr) and Sample 2 (AgBr73I27) grains on which PMT was adsorbed. The measurement temperature range was
240–298 K.
β-AgI
Ref. 18

Lattice Constant (Å)
Ionic Conductivity at Room
Temperature (Ω–1·cm–1)
Activation Energy of Ionic
Conductivity (eV)Sample 1
AgBr Microcrystal With PMT

Sample 2
AgBr73I27 Microcrystal With PMT

6.3×10-8

4 × 10–6

0.52

0.33

a = 4.59, c = 7.52
5.77
hexagonal wurtzite type face-centered cubic rock salt type
6 × 10–8 (c||)

1.3 × 10–7 (c⊥)
0.79 (c||),0.59 (c⊥)

5.86
face-centered cubic rock salt type

Seiji Yamashita, Naoto Oshima, Shunji Takada, and Ken’ichi Kuge

Structural Study of the Ionic Conductivity in Double-Structured Grains of Silver Iodobromide

no experimental data on the ionic conductivity of silver iodide grains
on which PMT is adsorbed, we can compare the ionic conductivityof silver iodobromide grains with that of large silver iodide crystals.
Table 4 shows values of ionic conductivity and activation energy including those of β-type silver iodide. The ionic conductivity of silver
iodide depends on the crystal orientation; the ionic conductivity
perpendicular to the c-axis direction is higher than that for the other orientations.9)20)21) Its value is 1.3 × 10-7 Ω-1 ·cm-1 at room temperature and the activation energy is reported to be 0.59 eV.9) Thisvalue is lower than the ionic conductivity of the silver iodobromide
grains of Sample 2 and the activation energy is larger than that ofSample 2.
Accordingly, as the amount of silver iodide in the silver iodobromide phase increases gradually, the ionic conductivity and activationenergy pass through the maximum value and the minimum value.
Decrease of activation energy will relate to the increase of ionic
conductivity. However, we do not have enough information about
the formation energy and the migration energy of interstitial silver
ions in the silver iodobromide grains. These behaviors will be analyzed in a future research.

6. Conclusions
The ionic conductivities of double-structured AgBrI grains withdifferent iodide content in the core and the shell were determined bymeasuring their dielectric loss responses, which were reproduced
quantitatively by the calculations based on Pauly-Schwan/Hanai
theory. Using the calculations based on PS/H theory, we can therefore design the double-structured AgBrI grains that have the ionic
conductivity distribution in the core and the shell suitable for latentimage formation.
Acknowledgments
The authors thank Professor (at that time) Tetsuya Hanai of theInstitute for Chemical Research, Kyoto University for guidance ininterpreting the results of calculation using Pauly-Schwan/Hanai
theory.

25

References
1)
2)

S. Takada, J. Soc. Photogr. Sci. Tech. Jpn., 61, 2 (1998) (in Japanese).
Y. Kume, “A Systematic Survey of Technologies Developed for Color
Negative Films”, National Science Museum Technical Systematization
Survey Report, 17, 351 (2012) (in Japanese).
3) S. Takada, S. Ishimaru, N. Oshima, Fuji Film, Japanese Patent
No.1818914 (in Japanese).
4) S. Urabe, T. Ohzeki, J. Soc. Photogr. Sci. Tech. Jpn., 69, 105 (2006) (inJapanese).
5) S. Takada, H. Ayato, S. Ishimaru, Proceeding of the International Congress of Photographic Science “Review of the Photographic Emulsions
Containing Double Structured Grains,” ed. by F. Granzer and E. Moisar., Koln (Cologne), 1986, 1.1-09, 70.
6) S. Bando, Y. Shibahara, S. Ishimaru, J. Imaging Sci., 29, 193 (1985).
7) S. Takada, J. Soc. Photogr. Sci. Tech. Jpn., 42, 112 (1979) (in Japanese).
8) J. F. Hamilton, “The Theory of the Photographic Process”, 4th-ed., ed. by
T. H. James, Macmillan, New York, (1977), Chap.4 , Sec.I.
9) S. Takada, J. Soc. Photogr. Sci. Tech. Jpn., 44, 81 (1981) (in Japanese).
10) J. Van Biesen, J. Appl. Phys., 41, 1910 (1970).
11) S. Takada, Jpn. J. Appl. Phys., 12, 190 (1973).
12) S. Yamashita, N. Oshima, S. Takada, J. Soc. Photogr. Sci. Tech. Jpn., 77,
318 (2014) (in Japanese).
13) S. Yamashita, N. Oshima, S. Takada, J. Soc. Photogr. Sci. Tech. Jpn., 76,
493 (2013) (in Japanese).
14) J. Pouradier, A. Pailliotet, C. R. Berry “The Theory of the Photographic
Process”, 4th-ed., ed. by T. H. James, Macmillan, New York, (1977),
Chap.1, Sec.I.
15) P. Muller, Phys. Status Solidi., 12, 775 (1965).
16) T. Hanai, “Emulsion Science,” ed. by P. Sherman., Academic Press, London, 1968, Chap. 5.
17) S. Oka, O. Nakata, “Theory of Dielectric Solids”, Iwanami Shoten, Tokyo, 1966, Chap. 4 (in Japanese).
18) S. Iida, K. Oono, H. Kanzaki, H. Kumagai, S. Sawada, “ Physical Constants Table ”, Asakura Shoten, Tokyo, 1978 (in Japanese).
19) S. Yamashita, N. Oshima, S. Takada, K. Kuge, J. Soc. Photogr. Sci. Tech.
Jpn., 78, 174 (2015) (in Japanese).
20) T. Tani, H. Mifune, S. Yamashita, S. Aiba, T. Ohzeki, K. Yamane, J. Imaging Sci. Tech., 51, 202 (2007).
21) G. Cochrane, N. H. Fletcher, J. Phys. Chem. Solid., 32, 2557 (1971).