Preferred orientation control of Bi deposits using experimental strategies

Article abstract of DOI:10.1149/2.103204jes

Based on the experimental strategy of fractional factorial design (FFD) and path of the steepest descentascent (PSDPSA), the preferred orientation ratio of Bi(110)Bi(012) facets of Bi deposits electroplated under a direct-current (dc) mode could be precisely controlled and predicted. The intensity ratio of Bi(110)Bi(012) facets (i.e., the preferred orientation ratio which is denoted as f) was employed as the response variable since this variable was found to be one of the key factors determining the sensitive ability of bismuth-film electrodes (BFEs) to Sn(II). In the FFD study, temperature of the plating bath was identified to be the key factor affecting the preferred orientation ratio of Bi deposits meanwhile f only weakly depended on pH, current density, and stirring rate. From the PSDPSA study, a simple but reliable model for changing the preferred orientation ratio was constructed and the deposit plated at 28°C and pH = 4.25 showed the highest f value. Moreover, BFEs with various f values could be easily prepared and controlled, meanwhile the morphologies of Bi deposits with different f values were also examined in this work.

Full text of DOI:10.1149/2.103204jes

D260
Journal of The Electrochemical Society, 159 (4) D260-D264 (2012)
0013-4651/2012/159(4)/D260/5/$28.00 © The Electrochemical Society
Preferred Orientation Control of Bi Deposits Using
Experimental Strategies
Chien-Hung Lien, Chi-Chang Hu,∗,z Yi-Da Tsai, and David Shan-Hill Wang
Laboratory of Electrochemistry & Advanced Materials, Department of Chemical Engineering, National Tsing Hua
University, Hsin-Chu 30013, Taiwan
Based on the experimental strategy of fractional factorial design (FFD) and path of the steepest descent/ascent (PSD/PSA), the
preferred orientation ratio of Bi(110)/Bi(012) facets of Bi deposits electroplated under a direct-current (dc) mode could be precisely
controlled and predicted. The intensity ratio of Bi(110)/Bi(012) facets (i.e., the preferred orientation ratio which is denoted as f)
was employed as the response variable since this variable was found to be one of the key factors determining the sensitive ability
of bismuth-film electrodes (BFEs) to Sn(II). In the FFD study, temperature of the plating bath was identified to be the key factor
affecting the preferred orientation ratio of Bi deposits meanwhile f only weakly depended on pH, current density, and stirring rate.
From the PSD/PSA study, a simple but reliable model for changing the preferred orientation ratio was constructed and the deposit
plated at 28◦C and pH = 4.25 showed the highest f value. Moreover, BFEs with various f values could be easily prepared and
controlled, meanwhile the morphologies of Bi deposits with different f values were also examined in this work.
© 2012 The Electrochemical Society. [DOI: 10.1149/2.103204jes] All rights reserved.
Manuscript submitted November 15, 2011; revised manuscript received January 16, 2012. Published February 10, 2012.
Bismuth-film electrodes (BFEs) have been used as an alternative
study to extend and control the preferred orientation ratio of Bi de-
posits for future applications.
to replace mercury-film electrodes (MFEs) for the determination of
heavy metal ions since 2000s.1 The most significant advantage of
BFEs is the environmentally friendly property since the toxicity of
bismuth and its salts is negligible.2 However, the unique analytical
ability of BFEs in detecting heavy metal ions, roughly comparable to
that of MFEs, has been attributed to the formation of ‘‘fused alloys’’
with heavy metals for bismuth. This property, analogous to the amal-
gams that mercury forms,3 usually leads to use a stripping solution
containing Bi(III)4 or Bi oxide nanoparticles on substrates5 for sens-
ing heavy metal ions. The former method is generally complicated
because of introducing the detecting solutions into the stripping so-
lution. The second method usually involves the dispersion issue of
Bi oxide nanoparticles onto the substrate for promoting the sensing
ability. Accordingly, understanding the relationship between the mi-
crostructures and the heavy metal ions sensing ability of metallic Bi
films is important for the future applications of BFEs.
Experimental
Bismuth deposits were electroplated from a solution containing
0.06 M Bi(NO3)3 · 5H2O (Hayashi, EP), 0.3 M citric acid (CA,
Shimakyu, EP), 4000 ppm gelatin (from porcine skin, Type A
∼ 300 Bloom (G2500-100G)), 0.3 M ethylenediaminetetraacetic
acid (EDTA, Riedel-deHaen, GA), and variable concentrations of
polyethylene glycol (PEG, MW400, Shimakyu, EP) onto copper
(99.5%, 1.094 × 10−2 cm2, 1.18 × 10−1 cm in diameter) circular plates
which have been deposited with a nickel film (ca. 2 μm). The pre-
treatment procedures of Cu/Ni substrates completely followed our
previous work.12–14 The Cu/Ni substrates, rinsed with deionized wa-
ter, were placed in a 50-mL jacket cell and faced with a dimensionally
stable anode (DSA) to electroplate Bi deposits. The dimensions of the
stirring bar are 1.5 cm in length and 6mm in diameter. The dimensions
of 50-mL jacket cell are 4.5 cm in diameter and 4 cm in height. The pH
of plating baths was adjusted with concentrated HCl or NH4OH. Af-
ter deposition, these electrodes were repeatedly rinsed with deionized
water and finally dried in a vacuum oven at room temperature.
Morphologies of all deposits were examined by a field emis-
sion scanning electron microscope (FE-SEM, Hitachi S-4700).
X-ray diffraction patterns were obtained from an X-ray diffractometer
(CuKα, Ultima IV, Rigaku). All solutions were prepared with deion-
ized water produced by a reagent water system (Milli-Q SP, Japan) at
18 Mꢀ cm and all reagents not specified were Merck, GR. Solution
temperature was maintained at the specified temperature with an accu-
racy of 0.1◦C by means of a water thermostat (Haake DC3 and K20).
There are several methods, such as thermal evaporation,6
electrodeposition,6–9 DC sputtering,10 RF magnetron sputtering,11 and
molecular beam epitaxy,12 etc., for preparing BFEs. From a compari-
son of these methods, electrodeposition is a simple route which shows
the ability for controlling the morphology, roughness, grain sizes, and
preferred orientations of metals and alloys via changing the electro-
plating solutions such as composition,13,14 pH,15 complex agents,16
and additives17,18 as well as the deposition parameters e.g., current
density13 and deposition mode,19–21 etc. However, to date, electrode-
position of bismuth films with good qualities (e.g., uniformity, good
adhesion, etc.) is still recognized as a challenge.22 Moreover, little
literature has been published to establish the relationship between the
microstructure and the metal ion sensing ability of BFEs23 and to con-
trol the morphology and adhesion of Bi films through electroplating,6,7
probably due to the instability of free Bi3+ ions in aqueous media.
Based on the above considerations, this work tries to control the pre-
ferred orientation ratio (denoted as f), Bi(110)/Bi(012) facets, of Bi
deposits through electroplating.
Due to the complicated influences of preparation variables on the
preferred orientation ratio of bismuth deposits and the challenge in
electroplating of bismuth films with good qualities (e.g., uniformity,
good adhesion, etc.), this work employed the fractional factorial de-
sign (FFD) to screen out the key factors affecting the textures of Bi de-
posits significantly, which include pH, current density, concentration
of polyethylene glycol (PEG, MW400), bath temperature, and stirring
rate. Then, using the path of the steepest descent/ascent (PSD/PSA)
Results and Discussion
Fractional factorial design.— For this complicated electroplating
system, the fractional factorial design (FFD) is used to efficiently
screen out the key variables affecting the preferred orientation ratio,
f, of Bi deposits. The main advantage of FFD is that the quantitative
effects of electroplating parameters can be efficiently assessed by
means of limited experiments. Another merit of FFD is the observation
of the influence of each variable at a variety of other variable levels as
well as the interactions among these variables on the response variable
(i.e., the intensity ratio of Bi(110)/Bi(012) facets, f, in this work). The
preferred orientation ratio, f, is defined as follow:
◦
◦
Bi(110)
Bi(012)
I39.7
f =
=
[1]
I27.3
∗
Electrochemical Society Active Member.
z E-mail: cchu@che.nthu.edu.tw
where I indicates the intensity of X-ray diffraction peak.
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Journal of The Electrochemical Society, 159 (4) D260-D264 (2012)
D261
A 2k−1 FFD matrix can be constructed by writing down a basic
design matrix consisting of a full 2k−1 factorial design and then adding
the kth factor by identifying its contrast coefficients from the plus and
minus signs of the highest-order interaction ABC. . . (K-1). For exam-
ple, a 25−1 design with the defining relation, I = ABCDE (introduced
by Box et al.24), shows the following property.
Table I. Factors and levels for the 25−1 fractional factorial
design.
Level
Factor
−
+
E = E · I = E · ABCDE = ABCDE2 = ABCD
[2]
A. pH
4
3
20
25
80
6
B. Current density (mA cm−2
C. PEG concentration (mM)
D. Temperature (◦C)
E. Stirring rate (rpm)
)
30
100
50
Therefore, the 25−1 design can be obtained by writing down a full 24
orthogonal array as the basic design and then equating factor E to the
ABCD interaction.25 In Table II, the low and high levels of A, B, C,
D, and E were denoted as “−” and “+”, respectively. The contrast
coefficients of factor E (i.e., column 6 in Table II) is generated from
the contrast coefficients of factors A, B, C, and D according to Eq. 2.
Thus, the orthogonal contrast coefficients of factor E are equal to that
of its alias, the four-factor interaction of A (pH), B (current density),
C (PEG concentration), and D (bath temperature). As a result, the
observations used to estimate the effect of factor E (stirring rate) are
identical to those used to estimate the four-factor interaction effect.
Hence, the effects of factor E and ABCD interaction are said to be
confounded and indistinguishable.25,26 From the sparsity of effects
principle,25 however, a system is likely to be driven primarily by the
effects of certain main factors and low-order interactions. Therefore,
effects of high-order (e.g., three and higher order) interactions are
generally assumed to be negligible and the effect of factor E can be
isolated from the confounded effects (resolution = V).25
160
There are five electroplating variables in the FFD study: (A) pH,
(B) current density (mA cm−2), (C) concentration of PEG (M), (D)
temperature (◦C), and (E) stirring rate (rpm). In general, the selection
for the factor levels needs brain-storming which includes literature
review, previous experiences, and some preliminary tests in order to
obtain useful information.24–26 For example, the low and high levels
of pH in the plating baths are equal to 4 and 6, respectively, because
the EDTA solubility decreases with decreasing pH while Bi(OH)2+
ions will be formed when the pH value is higher than 6,2 which is
hard to be deposited. In addition, according to our previous work for
factors B and C,23 to suppress the dendrite formation and to make
excellent crystalline quality of Bi films, the current density is set at 3
and 30 mA cm−2 for low and high levels of factor B meanwhile 20
and 100 mM of PEG are selected as the low and high levels of factor C
because PEG is a strong additive adsorbing on the Bi surface to inhibit
the Bi dendrite formation. Moreover, due to the possible formation
of hydrogen bonds among PEG and water molecules, the possible
interaction effect between PEG and temperature has to be considered
since the hydrogen bonds between PEG and H2O molecules are ex-
pected to be broken significantly at higher bath temperatures due to
the more significantly thermal motions of PEG and water molecules.
Hence, the low and high levels of the bath temperature are set at 25
and 50◦C, respectively. The hydrodynamic situation, controlled by
the stirring rate of magnetic bars, generally affects the diffusion of
metallic ions and the growth rate of bismuth crystals, resulting in the
setting for the high and low levels of the stirring rate equal to 160 and
80 rpm, respectively. The fixed levels of these five variables are listed
in Table I meanwhile a 25−1 design matrix with the experimental data
is given in Table II.
From an examination of the results in Table II, f varied from
0.021 to 0.617, indicating that certain factors and/or interactions show
significant effects on the preferred orientation ratio of Bi deposits.
Accordingly, analysis of variance (ANOVA) for the data in Table II
was performed, which is summarized in Table III. ANOVA is derived
from partitioning the sum of squares of total variances (SST) into its
component parts (i.e., sums of square for model and error, SSmodel
and SSE, respectively), which can be calculated on the basis of the
following equations:27
k−1
SST = 2 (yi − y¯)2
[3]
ꢀ
i=1
(Ci )2
2k−1
SSi =
[4]
[5]
SSE = SST − SSmodel
where yi and y¯ are indicative of the ith response and the grand average
of all the observations, respectively. Note that Ci is indicative of the
contrast of factor (or interaction) i, which is the sum of multiplying
Table II. The design matrix and the f value of Bi deposits for
the 25−1 fractional factorial design with the defining relation
I = ABCDE.
Factors
Run
A
B
C
D
E
f
Table III. Analysis of variance for the f value of the Bi deposits
from the 25−1 fractional factorial design.
1
2
3
4
5
6
7
8
−
+
−
+
−
+
−
+
−
+
−
+
−
+
−
+
−
−
+
+
−
−
+
+
−
−
+
+
−
−
+
+
−
−
−
−
−
+
+
+
−
−
−
−
+
+
+
+
−
−
−
−
−
−
−
−
+
+
+
+
+
+
+
+
+
−
−
+
−
+
+
−
−
+
+
−
+
−
−
+
0.484
0.344
0.617
0.337
0.571
0.337
0.482
0.309
0.398
0.070
0.113
0.383
0.093
0.021
0.136
0.446
Source
SS
d.f.
MS
F a
A
B
D
E
AB
AD
AE
BD
ABD
Error
0.028
0.017
0.211
0.010
0.053
0.061
0.031
0.016
0.073
0.024
1
1
1
1
1
1
1
1
1
6
0.028
0.017
0.211
0.010
0.053
0.061
0.031
0.016
0.073
0.004
7.065
4.354
53.418
2.474
13.411
15.357
7.783
9
10
11
12
13
14
15
16
4.048
18.406
Total
0.523
15
a Remark: F0.05(1,6) = 5.99; R2 = 0.955.
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D262
Journal of The Electrochemical Society, 159 (4) D260-D264 (2012)
the observations (i.e., yi) with the appropriate contrast coefficients
(i.e., the plus-minus signs in an appropriate column of the design
matrix). For example, the contrast of factor A is expressed as: CA
= − y1 + y2 − y3 + y4 − y5 + y6 − y7 + y8 − y9 + y10 − y11
+ y12 − y13 + y14 − y15 + y16 = −0.647. In addition, SSi indicates
the sum of square corresponding to factor (or interaction) i. The sum
of SSi with statistical significance is defined as SSmodel. The quantities
MSi = SSi /d fi and MSE = SSE/d ferror are defined as the mean
squares of factor (or interaction) i and the mean square of error,
respectively. The dfi and dferror indicate the degree of freedom for
factor (or interaction) i and error, respectively. In Table III, the test
statistics, F*, defined as MSi/MSE, are employed to test the statistical
significance of each factor or interaction. If the calculated value of F*
is greater than that in the F table at a specific probability level (e.g.,
α = 0.05), a statistically significant factor or interaction is obtained.
After the test, factors A, B, D as well as interactions AB, AD, AE, BD,
and ABD show significant effects on the preferred orientation ratio of
Bi deposits. Note that factor E is considered as a factor with marginal
significance (i.e., its effects is not as important as the effects of factors
A, B, D, and interactions AB, AD, AE, BD and ABD) because its
calculated F* value is somewhat lower than the critical value (F0.05
(1, 6) = 5.99). However, according to the hierarchical principle,24
if a model contains a high-order term (such as AE in this work), it
should also contain all of the lower-order terms that composite it (i.e.,
factor E in this case). Therefore, the model obtained from the ANOVA
contains factor E. Also note that interaction ABD (but not interaction
CE) is also considered here because significant factors easily lead
to significant interactions.25 The multiple correlation coefficient, R2
= 1−(SSE/SST), is the proportion of SST (sum of squares of total
variances) explained by the fitted equation. A R2 value close to 1 means
a good fit to the experiment data. In this work, R2 = 0.955 indicates
an excellent fitting when factors A, B, D, and E as well as interactions
AB, AD, AE, BD, and ABD are considered to be significant. The other
effects (including factor C and the other interactions) were pooled into
the error.
Calculation of the effect estimates for factors and interactions
followed the procedure recommended by Box et al.,24 which is equal
to Ci/2k−2. The effect estimates of factors A–E and interactions with
statistical significance are shown in Figure 1. From Table III and
Figure 1, it is very clear that the sequence of factors/interactions with
respect to decreasing the influence is: D > ABD > AD > AB > AE
>A > B > BD > E. Based on the results of Table III and Figure 1a,
changing the temperature of the plating solution (factor D) from 50 to
25◦C obviously increases the f value from 0.2 to 0.43. In addition, the
low level of factors A (pH = 4) and E (stirring rate = 80 rpm) as well
as the high level of factor B (current density = 30 mA cm−2) can be
used to increase the preferred orientation ratio of Bi deposits. Since
factor C (PEG concentration) is not significant here, the difference in
the f value between the high and low levels of this factor is considered
as an error, probably due to that the PEG concentration at the low level
(20 mM) is high enough. From all the above results and discussion,
the preferred orientation ratio of Bi deposits is strongly affected by
varying the plating temperature but is weakly dependent on the pH
value, current density, and stirring rate.
The significant influences of AB, AD, AE, BD, and ABD interac-
tions on the f value of Bi deposits are shown in Figure 1b. From this
figure, a decrease in pH of the plating solution (Factor A) leads to an
obvious increase in the f value of the deposits when the current density
of electroplating (factor B) is under the low level (3 mA cm−2). How-
ever, when this factor is under the high level (30 mA cm−2), the pH
effect becomes insignificant. The above phenomena reveal the exis-
tence of an interaction between factors A and B, while a deposit with a
higher f value will be obtained when it is plated at a lower current den-
sity in a more acidic solution. Fortunately, from Table III, factor B is a
relatively minor factor in comparing with the effect of interaction AB
although this factor in the high level slightly increases the f value of
the deposits (see Fig. 1a). For interaction AD, a deposit with a higher
f value will be obtained when it is plated at a lower temperature in a
more acidic solution. This trend is consistent with the main effects of
Figure 1. Effects of (a) factors (A) pH, (B) current density (mA cm−2), (C)
PEG concentration (mM), (D) temperature of the plating bath (◦C), and (E)
stirring rate (rpm) and (b) interactions AB, AD, AE, ABD, and BD on the f
value of Bi deposits, where (+) and (−) indicate the high and low levels of
factors/interaction, respectively.
factors A and D. A similar phenomenon is also found for interaction
AE (i.e., a higher f value is obtained for the deposits prepared from a
low level of factor E and a low level of factor A). The ABD interaction
shows that when interaction AB is under the low level, an increase in
the f value will be obtained when factor D is moved from the high level
to the low level. For BD interaction, the influence of factor D on the f
value is more obvious when factor B is under the low level in compar-
ison with that as factor B is under the high level. Moreover, decreasing
the temperature and pH of the plating bath (factors A and D) always
promotes the f value of deposits despite the levels of factors B and E.
This result indicates the monotonous influences of factors A and D on
the f value in this electroplating system, which can be employed as the
reliable variables for controlling the preferred orientation ratio of Bi
deposits.
From the regression analysis of the results in Table II, a fit-
ted polynomial model (including the marginal effect) can be gen-
erated. This model, quantitatively elucidating the effects of all
factors and interactions with statistical significance, is expressed
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Journal of The Electrochemical Society, 159 (4) D260-D264 (2012)
D263
as follow:
f = 0.321 − 0.040xA + 0.032 xB − 0.114 xD − 0.026 xE
+ 0.056 xAxB + 0.063 xAxD + 0.043 xAxE + 0.030 xB xD
+ 0.066 xAxB xD
[6]
where xi are the coded variables for factor i (i.e., A, B, D, and E). The
coded variables, xi, are defined in the standardized form as following:25
xi,H I GH = (Xi,HIGH − Xi,MEAN)/Si (= +1)
xi,LOW = (Xi,LOW − Xi,MEAN)/Si (= −1)
Xi,M E AN = (Xi,HIGH + Xi,LOW)/2
[7]
[8]
[9]
Figure 2. The FE-SEM photographs of Bi deposits with the f value of (a)
1.32, (b) 0.82, (c) 0.56, and (d) 0.01.
Si = (Xi,HIGH − Xi,LOW)/2
[10]
where Xi,HIGH and Xi,LOW are the high and low levels of factor i in the
natural unit, respectively. Eq. 6 is a function of factors A, B, D, and E,
which shows that the f value of deposits will increase with decreasing
temperature (factor D) since the coefficient of factor D is negative
(−0.114). Moreover, the influence of factor D is the highest among all
factors and interactions because the absolute value of its coefficient is
the largest.
of run 4. Based on the results shown in Table IV, the preferred ori-
entation ratio of Bi(110)/Bi(012) facets for Bi deposits can be simply
controlled by varying the pH value, plating temperature, and PEG
concentration from a simple plating bath basically containing 0.06
M Bi(NO3)3 · 5H2O, 0.3 M citric acid, 4000 ppm gelatin, and 0.3 M
EDTA under a constant current density (3 mA cm−2).
Path of the steepest descent/ascent study.— Based on Eq. 6, a
study for the path of the steepest descent/ascent (PSD/PSA) and the
corresponding results are shown in Table IV. The starting point (run
3) is set at the origin of factors A and D (i.e., xA = 0 and xD = 0).
To extend the preferred orientation ratio of Bi deposits, factors A and
D were varied simultaneously with the regular step sizes of factors
A and D equal to 0.5 (in pH) and 6.25◦C (in plating temperature),
respectively. The upper limits of factors A and D (i.e., run 1) are set at
the extreme plating condition for obtaining a deposit with the lowest
f (i.e., pH = 6.0 and plating temperature = 50◦C). The variation in
f with factors A and D is very obvious and almost constant when
pH and temperature of the plating bath are respectively ranged from
6.0 to 4.5 and from 50 to 31.3◦C. This result reveals the reliability
of ANOVA in the FFD study. Note here that in order to obtain the
lowest f value, the direction of the PSD study was slightly modified
(i.e., runs 1 and 2); i.e., the concentration of PEG was increased from
20 to 100 mM. Since the adhesion of Bi deposits becomes poor and
cracks are visible at temperatures equal to/lower than 25◦C, the bath
temperature of 28.1◦C and pH of 4.25 are recommended as the lowest
limits of factors D and A, respectively. According to the above con-
sideration, the step sizes of factors A and D are reduced. Clearly, a
deposit with the highest f value is obtained under the plating condition
Morphology of Bi deposits with different f values.— The mor-
phologies of Bi deposits with the f value varying from 1.32 to 0.01
are shown in Fig. 2. The insets show the morphologies under a lower
magnification. From all insets in Fig. 2, all deposits show uniform
morphologies while the deposit with the lowest f value (Fig. 2d)
seems to be obviously rougher in comparison with the other deposits.
In Fig. 2a, irregular/ellipsoid-like particles between 50 and 100 nm
are visible although the particle boundaries are not very clear. With
decreasing the f value, the particles transform into irregular/triangular
platelets (see Fig. 2b). In Fig. 2c, piling triangular platelets up into
aggregates is visible and sharp edges of crystallites are clearly found.
The piling of metallic rods is very clear in Fig. 2d, resulting in the
formation of many prickly rods with length longer than 600 nm on
this deposit (see inset). All the above results indicate that controlling
the preferred orientation ratio of Bi deposits leads the simultaneous
change in the surface morphology of Bi deposits. The influences of
the preferred orientation ratio of Bi deposits on the sensing ability of
heavy metal ions will be systematically investigated in our next study.
Conclusions
From the FFD study, the preferred orientation ratio of
Bi(110)/Bi(012) facets, f, on Bi deposits is strongly affected by the
plating temperature but only weakly depends on the pH value, current
density, and stirring rate. Moreover, from the analyzes of significant
interaction effects, factors A and D exhibit monotonous influences
on the f value in electroplating Bi deposits, which can be employed
as the reliable variables for controlling the preferred orientation ra-
tio of Bi deposits. This idea has been confirmed in the path of the
steepest descent/ascent study and the preferred orientation ratio of
Bi(110)/Bi(012) facets from 1.32 to 0.01 can be simply controlled by
varying the pH value, plating temperature and PEG400 from a sim-
ple plating bath basically containing 0.06 M Bi(NO3)3 · 5H2O, 0.3 M
citric acid, 4000 ppm gelatin, and 0.3 M EDTA.
Table IV. Dependence of the f value of Bi deposits on pH (factor
A) and temperature (factor D) of the plating bath in the PSD/PSA
study.
Factor
Run
A
D
f
1a
2a
3b
4b
5b
6.0
5.5
5.0
4.5
4.25
50
0.01
0.56
0.82
1.32
0.89
43.8
37.5
31.3
28.1
Acknowledgments
a Factors B, C, and E are 3 mA cm−2, 100 mM, and 80 rpm,
respectively.
The financial support of this work, by the National Science Council
Taiwan and the Low Carbon Energy Research Center of National
Tsing Hua University, is gratefully acknowledged.
b FactorsB, C, and E are 3 mA cm−2, 20mM, and80rpm, respectively.
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D264
Journal of The Electrochemical Society, 159 (4) D260-D264 (2012)
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