Factors influencing the structure of electrochemically prepared α-MnO2 and γ-MnO2 phases

Article abstract of DOI:10.1016/j.electacta.2007.04.095

The α- and γ-phases of MnO₂ prepared by electrolysis of MnSO₄ and M_xSO₄ (where M = Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺ or Mg²⁺) in aqueous solutions at various pH and voltage E_v values under ambient conditions have been systematically studied. The structures of powdery MnO₂ produced are found to depend on the radius of the M^z+ counter cation in addition to the pH and E_v conditions. In order to achieve the α-phase for MnO₂ formation under neutral pH condition, the radius of counter cation must be equal to or greater than 1.41 A?, the size of the K⁺ cation. The relative concentration ratio of [MnO₄^-]_transient/[Mn²⁺], which is related to the pH-E_v conditions, also affects the structure of MnO₂ produced with counter ions smaller than K⁺. For samples prepared in acidified solution with the counter ions of Li⁺, Na⁺ or Mg²⁺ at 2.2 V, the electrolysis products display the γ-MnO₂ phase while those prepared at 2.8 V electrolysis produce a mixture of γ-MnO₂ and α-MnO₂ phases. Single phase of α-MnO₂ is identified in the 5 V electrolysis products. Furthermore, the valence state of manganese was found to decrease as the applied voltage was reduced from 5.0 to 2.2 V. This implies that the lower [MnO₄^-]_transient/[Mn²⁺] ratio or the less oxidative condition is responsible for the non-stoichiometric MnO₂ structure with oxygen deficiency.

Full text of DOI:10.1016/j.electacta.2007.04.095

Electrochimica Acta 52 (2007) 6548–6553
Factors influencing the structure of electrochemically
prepared ␣-MnO2 and ␥-MnO2 phases
H.Y. Lina, Y.P. Suna, B.J. Wengb, C.T. Yanga, N.T. Suena, K.H. Liaoa,
Y.C. Huanga, J.Y. Hoa, N.S. Chongc,∗, H.Y. Tanga,∗
a Department of Applied Chemistry, National Chi-Nan University, Puli, Nantou 545, Taiwan
b Materials and Electro-optics Research Division, Chung-Shan Institute of Science and Technology, Lungtan, Taoyuan 32599, Taiwan
c Department of Chemistry, Middle Tennessee State University, Murfreesboro, TN 37132, United States
Received 15 March 2007; received in revised form 17 April 2007; accepted 17 April 2007
Available online 3 May 2007
Abstract
The ␣- and ␥-phases of MnO2 prepared by electrolysis of MnSO4 and MxSO4 (where M = Li+, Na+, K+, Rb+, Cs+ or Mg2+) in aqueous solutions
at various pH and voltage Ev values under ambient conditions have been systematically studied. The structures of powdery MnO2 produced are
found to depend on the radius of the Mz+ counter cation in addition to the pH and Ev conditions. In order to achieve the ␣-phase for MnO2 formation
+
˚
under neutral pH condition, the radius of counter cation must be equal to or greater than 1.41 A, the size of the K cation. The relative concentration
−
ratio of [MnO4 ]
transient/[Mn2+], which is related to the pH–Ev conditions, also affects the structure of MnO2 produced with counter ions smaller
than K+. For samples prepared in acidified solution with the counter ions of Li+, Na+ or Mg2+ at 2.2 V, the electrolysis products display the ␥-MnO2
phase while those prepared at 2.8 V electrolysis produce a mixture of ␥-MnO2 and ␣-MnO2 phases. Single phase of ␣-MnO2 is identified in the
5 V electrolysis products. Furtherm−ore, the valence state of manganese was found to decrease as the applied voltage was reduced from 5.0 to 2.2 V.
This implies that the lower [MnO4
with oxygen deficiency.
]
transient/[Mn2+] ratio or the less oxidative condition is responsible for the non-stoichiometric MnO2 structure
© 2007 Elsevier Ltd. All rights reserved.
Keywords: Pourbaix diagram; Hollandite; Tunnel structure; EMD; Nano-porous MnO2
1. Introduction
MnO2 minerals have been classified by Turner and Buseck, the
pyrolusite with (1 × 1) structure and the hollandite with (2 × 2)
structure [8,9]. The one-dimensional structures with regular
porous lattices such as 1 × 1 pyrolusite (␤-MnO2), 2 × 2 hollan-
dite (␣-MnO2), and 1 × 1, 1 × 2 intergrowth nsutite (␥-MnO2)
attract attention in the research community because of their
potential applications as octahedral molecular sieve (OMS),
catalyst or battery materials [10–16]. Layered compounds of
buserite and birnessite have been utilized as a precursor for
preparing complex structures [17–19]. The spinel structure of
LiMn2O4 is used as positive electrode materials in the secondary
lithium ion battery [20–23].
Synthesis of layered MnO2 structure can be achieved by
using chemical treatments of manganese ions in basic solu-
tion. For the spinel structure, solid-state thermal treatments
present advantages in controlling the 3D phase formation and
its chemical stoichiometry. In comparison to the 2D and 3D
compounds, the regular one-dimensional structure normally
Black manganese oxide and related manganese-containing
nodules have been discovered on the deep sea floor for a long
time and considered as a rich source of manganese in the Earth’s
crust. Despite numerous chemical and biochemical studies, the
mechanistic details concerning the formation of manganese
oxide remain unknown. In order to characterize these natu-
ral products, various Mn+–MnO2 (i.e. where Mn+ denotes the
counter cation) structures have been continuously studied for the
last 3 decades. The tunnel (1D), layer (2D) and spinel (3D) struc-
tures of MnO2 with different counter cations have been prepared
by different synthesis techniques [1–7]. The one-dimensional
∗
Corresponding authors. Present address: No.1 University Road, Department
of Applied Chemistry, National Chi-Nan University, Puli, Nantou, Taiwan.
Tel.: +886 49 2910 960; fax: +886 49 2917 956.
E-mail address: hytang@ncnu.edu.tw (H.Y. Tang).
0013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2007.04.095

H.Y. Lin et al. / Electrochimica Acta 52 (2007) 6548–6553
6549
requires a multi-step process and is highly sensitive to the
preparation conditions [1,4,8]. For example, ␣-MnO2 samples
prepared by hydrothermal reaction usually depend on a two-
step sequence of ion exchange reaction followed by structure
formation [13,17,24–29]. A precursor with birnessite-type lay-
ered structure is prepared first followed by thermal treatment
in an autoclave reactor to complete the phase transformation.
In such a reaction, the structure of the final product will be
controlled by factors including temperature, pressure, pH and
the counter cation in the solution used for synthesis. The 2 × 2
hollandite structure can be stabilized by counter ions of appro-
priate sizes such as Na+ and K+ in hydrothermal work. Likewise,
the 2 × 5 tunnel structure can be synthesized by hydrothermal
method when larger Rb+ cations are present in the solution [8].
The hydrothermal synthesis of MnO2 has been well established
and is used widely for producing the one-dimensional structure
[4–7,20]. Due to the complexity of hydrothermal reaction, it is
difficult to probe the individual influence of the factors respon-
sible for the structural assembly of the MnO2. Furthermore, the
higher cost of hydrothermal production of MnO2 in a sealed
environment is another concern for industrial mass production.
Samples prepared under atmospheric conditions offer the
advantages in reducing the cost of production by minimizing
process complexity. Thermodynamic and electrochemical prop-
erties of the ␤-MnO2 and ␥-MnO2 have been studied for more
than 50 years [30]. The electrochemically prepared ␥-MnO2
(EMD) is broadly utilized in current battery applications. Sin-
gle phase of ␣-MnO2 prepared by the electrochemical process
has been reported recently [31,32]. In this work, factors influ-
encing the structure formation of ␣-, ␥- and amorphous MnO2
are systematically studied by using different counter cations
and changing the conditions of pH and applied voltages, Ev.
The applied voltages are in the range of 2.2 ꢀ Ev ꢀ 5 V, which
are far from the equilibrium state, and the results are sum-
marized as a pseudo-Pourbaix diagram. The pseudo-Pourbaix
diagram reveals a strong dependence on the identity of the
counter ions and the pH–Ev conditions. It is demonstrated that
the ionic radii of counter ions and the relative concentration ratio
of [MnO4]transient/[Mn2+] are important factors for determining
the structural form of MnO2 produced by the electrochemi-
cal technique. The results allow the construction of a Pourbaix
diagram in the high voltage region and help characterize the
optimal conditions for preparing the ␥-MnO2 and the ␣-MnO2
structures under the ambient conditions of electrochemical
synthesis.
electrode electrolysis setup with a manually controlled voltage
around 5.0 V was adopted.
The electrolysis solution typically consists of 10.0 g
MnSO4·H2O (Merck) and saturated levels of alkali or alkali-
earth MxSO4 salts (where M represents the counter ion of Li+,
Na+, K+, Rb+, Cs+ or Mg2+) dissolved in 150 mL of deionized
water or 4.32 M H2SO4(aq), which are classified as the non-
acidified solution and the acidified solution, respectively. Upon
dissolution of chemicals, electrolysis of the clear solution was
carried out at voltages ranging from 2.2 to 5.0 V. The tempera-
ture of the cell was observed to increase from room temperature
to about 60 ◦C due to the high current density. After electrolysis,
powdery MnO2 sample was harvested by filtration and washed
with deionized water three times.
The averaged oxidation state of manganese was determined
by the potential voltammetric titration method developed by
Suib and coworkers [18]. The chemical stoichiometry of MnO2
samples was determined by the atomic absorption spectroscopy
(AAS) and X-ray powder diffraction patterns of samples were
acquired using a Shimadzu XRD-7000 instrument. TEM and
selected area electron diffraction (SAED) were carried out with
a JEOL II 1200EX transmission electron microscope operated
at 120 kV accelerating voltage.
3. Results and discussion
In Fig. 1, the pH–Ev Pourbaix diagram for
a
manganese–water system shows several thermodynami-
cally stable manganese oxides such as Mn2O3 and MnO2
containing tie line for each half-cell reaction [33]. Standard
half-cell reaction of Mn2+ ion in acidic solution indicates the
MnO4− ion can be generated if the proper oxidation potential is
applied [34]. When the oxidized solution is diluted with water, it
will undergo spontaneous redox reaction and the precipitation of
MnO2 will be observed. In this work, three major experimental
parameters, pH, Ev and counter ion effect, were systematically
studied for their influence on the phase formation of MnO2.
Based on the experimental regime in the pH range of −1 and
2. Experimental
An EG&G 273A potentiostat and a GW Model PR-0875HD
high current power supply were utilized to perform the electrol-
ysis experiments. The electrochemical synthesis was carried out
in the voltage range of 2.2 to 2.8 V in a 250 mL glass cell with the
Ag/AgCl reference electrode and two platinum electrodes. For
electrolysis voltages greater than 2.8 V, a large amount of gas
bubbles could be produced by high voltage electrolysis. Due to
the fact that a reference electrode with gas bubbles interrupting
the electrolyte path would have very high impedance, a two-
Fig. 1. The boundary conditions of the four pH–Ev zones in the
manganese–water Pourbaix diagram that are studied.

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H.Y. Lin et al. / Electrochimica Acta 52 (2007) 6548–6553
Table 1
Correlation of the experimental parameters with the structural phases of the electrochemically prepared MnO2 in water solvent (Zone 1)
Ion
Ion free
Mg2+
Li+
Na+
K+
Rb+
Cs+
˚
Ionic radii (A)
Phase
pHa
None
␥
0.70
␥
0.71
␥
0.97
␥
1.41
␣
1.50
␣
1.73
A
4.52–1.15
3.73–1.77
4.5–1.8
4.45–1.57
4.47–1.88
4.76–1.67
4.33–1.22
A represents the amorphous structure.
a
The range of pH values refers to the measured values at the beginning and the end of electrolysis.
2 and applied voltages ranging from 2.2 to 5.0 V, the Pourbaix
diagram can be illustrated with the four separate zones of pH
and Ev conditions for electrochemical study as shown in Fig. 1:
electrode electrolysis with controlled voltage around 5.0 V. In
our previous work, electrochemical preparation of MnO2 under
Zone 2 conditions displays an unusual phenomenon in which the
structural formation of MnO2 is independent of the counter ion
[30]. These results are quite different with regard to the strong
counter ion dependence of the ␣-MnO2 formation in Zone 1
as compared to the reported hydrothermal work. In Table 2,
the cation/Mn ratios of K+–␣-MnO2 and Li+–␣-MnO2 deter-
mined by AAS are significantly different and reflect that Li+ is
dynamically mobile in tunnel structure as demonstrated by the
solid-state NMR study [32].
Zone 1: 5.0 V (Galvanic), non-acidified solution.
Zone 2: 5.0 V (Galvanic), acidified solution.
Zone 3: 2.2–2.8 V (Potentiostatic), acidified solution.
Zone 4: 2.2–2.8 V (Potentiostatic), non-acidified solution.
3.1. Electrolysis in Zone 1: 5.0 V, non-acidified solution
The MnO2 structure prepared in a non-acidified aqueous
solution is highly dependent on the type of counter ions in the
electrolyteaccordingtotheirionicradii. Table1showstheexper-
imental observations for a series of electrolysis experiments at
applied voltages of 5.0 V that were performed using different
cations for producing MnO2.
3.3. Electrolysis in Zone 3: 2.2–2.8 V, acidified solution
Samples of MnO2 prepared in 4.32 M sulfuric acid solution
with voltage less than 2.8 V show that the structure is depen-
dent upon the applied voltage during synthesis. For samples
prepared with the counter ions of Li+, Na+ or Mg2+ at 2.2 V,
the structure of electrolysis products display the ␥-MnO2 phase
The electrolytic synthesis results in the decomposition of
water accompanied by formation of H+ ions and consequently
the pH will be shifted to a lower value. In the hydrothermal
synthesis of MnO2, inorganic cations display complex or unpre-
dictable behaviors with regard to the relationship between tunnel
structure and cation radius. For instance, Mg2+ tends to stabi-
lize 3 × 3 tunnel, Rb+ have a tendency to form 3 × 5 tunnel
while K+ and NH4+ are believed to be suitable cations for 2 × 2
tunnel structure [4]. However, for the electrochemical synthe-
sis of MnO2, the pore size of the tunnel structure prepared
under ambient conditions is directly controlled by the radius
of counter cation. Samples of MnO2 containing counter ions of
Li+, Na+ or Mg2+ were found to be the polymorph of ␥-MnO2.
At the same pH–Ev setting, the self-assembly of MnO2 struc-
tures in the presence of K+ or Rb+ ions gave rise to the ␣-MnO2
structure as determined by the powder XRD data in Fig. 2. The
scanning and transmission electron micrographs in Fig. 3 show
that the micrometer-sized aggregates of K+-containing ␣-MnO2
were composed of 10–20 nm fibrous crystallites. As the radius of
counter ion is increased, as in the case of Cs+, structural instabil-
ity of MnO2 was noted. An amorphous Cs+–MnO2 structure is
observed in the SAED pattern shown in Fig. 3c. The powder X-
ray diffraction pattern in the inset of Fig. 3c further corroborates
the amorphous structure of the Cs+–MnO2 product.
Fig. 2. PowderX-raydiffractionpatternsofMnO2 powderwithdifferentcounter
ions.
Table 2
The chemical stoichiometry of MnO2 prepared using different electrochemical
potentials and determined by AAS
Atomic ratio
pH–Ev
3.2. Electrolysis in Zone 2: 5 V, acidified solution
4.32 M, 5.0 V
4.32 M, 2.8 V
4.32 M, 2.2 V
K/Mn
Li/Mn
0.0295
0.0028
0.0278
0.0005
0.0302
0.0002
For electrolysis study in the 4.32 M sulfuric acid solution
(pH −0.64), single-phase ␣-MnO2 can be harvested via two-

H.Y. Lin et al. / Electrochimica Acta 52 (2007) 6548–6553
6551
2.2 and 2.8 V potentiostatic experiments. Chemical titration of
samples prepared by different electrolysis voltages of 5.0, 2.8
and 2.2 V shows that the valence states of manganese, with an
experimental error margin of 0.02, are 3.99, 3.92 and 3.87,
respectively. The systematic trend of the decrease in manganese
valence state as a function of applied voltages implies that the
structural stoichiometry of MnO2 is correlated with the concen-
−
tration −ratio of [MnO4
]
transient/[Mn2+] in solution. The lower
[MnO4
]
transient/[Mn2+] ratio or the less oxidative condition
produces the non-stoichiometric MnO2 structure with oxygen
deficiency [30].
3.4. Electrolysis in Zone 4: 2.2–2.8 V, non-acidified solution
A thin passive layer of manganese oxide (MnOx) with lower
manganese valence state is deposited under the conditions of
Zone 4. This MnOx layer has been previously reported [35]. The
highresistanceandreducedcurrenttendtoinhibitthecontinuous
growth of MnOx by potentiostatic electrolysis.
3.5. Construction of pseudo-Pourbaix diagram
The pH–Ev conditions of the four zones and the correspond-
ing phases of electrochemically prepared MnO2 are described
using a pseudo-Pourbaix diagram as shown in Fig. 4. The trends
ofphaseformationreflecttheinfluenceofcounterionandpH–Ev
conditions.
3.6. Influence of counter ions
The results shown in Fig. 4a indicate the influence of the
size of counter ions on the structural formation of MnO2 under
ambient conditions. Single phase of ␣-MnO2 can be obtained in
Zones 1, 2 and 3 when the K+ or Rb+ is selected as the counter
ion. The extra stability of K+–␣-MnO2 has been attributed to the
size effect of the counter ions [36]. In this work, we found that
the Rb+–␣-MnO2 prepared at room temperature demonstrates
the cation size effect similar to its counterpart with the K+ ion.
For Cs+ ion, the greater ionic radius results in the lattice insta-
bility of tunnel structure and consequently the formation of the
amorphous MnO6 framework. No regular tunnel structure with
lattice greater than the 2 × 2 framework has been found in this
work.
Fig. 3. The SEM images with magnification ratios of: (a) 35,000-fold of the
K+-␣-MnO2 prepared in non-acidified solution; (b) HRTEM micrograph of
the K+–␣-MnO2 shows a one-dimensional structure; (c) SAED pattern of
Cs+–MnO2 displaying an amorphous structure (inset: powder XRD pattern of
Cs+–MnO2).
In order to further verify the phenomenon of counter ion
dependence, a series of solution mixtures with molar concen-
tration ratios of K+ to Mg2+ ranging from 1:1 to 1:1000 were
prepared for synthesis under the conditions of Zone 1. The XRD
results clearly display a phase transition from pure ␣-MnO2 to
␥-MnO2 as shown in Fig. 5. Therefore, the counter ion effect
showing the relationship of ionic radius to the MnO2 structure
formation is proven conclusively.
while those prepared at 2.8 V electrolysis produce a mixture
of ␥-MnO2 and ␣-MnO2 phases. This voltage dependence can
be correlated to the difference in relative concentration ratio of
−
[MnO4
higher [MnO4
]
transient/[Mn2+]. The higher applied voltage leads to a
−
]
transient/[Mn2+] ratio that facilitates the 2 × 2
␣-MnO2 lattice formation in acidified solution. Potentiostatic
electrolysis with counter ion of K+ or Rb+ in Zone 3 shows size-
stabilizing effects similar to those in Zone 1, where the ␣-MnO2
is the most stable phase.
3.7. Influence of pH–Ev conditions
In Table 2, the chemical stoichiometries of Li+–␣-MnO2 pre-
pared using different electrochemical voltages show that very
low levels of lithium are present in the MnO2 structure for the
According to the pseudo-Pourbaix diagram in Fig. 4b, the
Li+–␣-MnO2 product can exist only at the region having a high
concentration ratio of [MnO4]transient/[Mn2+] [33]. A fundamen-

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H.Y. Lin et al. / Electrochimica Acta 52 (2007) 6548–6553
Wh−en the Mn2+ ions are electrochemically oxidized to
MnO4 in aqueous solutions, either of the following sponta-
neous redox reactions may take place depending on the pH of
the electrolyte solution [30]:
4MnO4− + 4H+ → 4MnO2 + 3O2(g) + 2H2O
2MnO4− + 3Mn2+ + 2H2O → 5MnO2 + 4H+
(1)
(2)
In a non-acidified solution, the overall reaction of Eq. (1) is
due to the half-cell reduction of MnO4− in Eq. (3) coupled with
half-cell oxidation of water in Eq. (4) [30].
4MnO2 + 8H2O → 4MnO4− + 16H+ + 12e−
−
Eo = 1.692 − 0.0788 pH + 0.0197 log[MnO4
]
(3)
6H2O → 3O2 + 12H+ + 12e−
Eo = 1.228 − 0.0591 pH + 0.0147 pO2
(4)
The electrolysis of water in a non-acidified solution is ener-
getically and kinetically more favored compared to the Mn2+
oxidation. Therefore, the half-cell reactions designated by Eqs.
(3) and (4) account for the predominant redox reaction. The
colorless solution over the course of the electrodeposition exper-
iment and instantaneous deposition of MnO2 indicate the fast
kinetics of MnO4− reduction and rapid water decomposition.
Eq. (2) is the manganese self-redox reaction that can occur
in an acidified solution where the Mn3+ ions and MnO2(s) are
the thermodynamically stable phases [30]. In acidified solution,
half-cell reactions of the MnO4− reduction and the correspond-
ing MnO2 formation are shown in Eqs. (5) and (6).
Fig. 4. The pseudo-Pourbaix diagrams of: (a) K+-containing MnO2 and (b)
Li+-containing MnO2 systems.
2MnO2 + 4H2O → 2MnO4− + 8H+ + 6e−
(5)
3Mn2+ + 6H2O → 3MnO2 + 12H+ + 6e−
Eo = 1.228 − 0.1182 pH + 0.0295 log[Mn2+
tal problem that requires more explanation is the observation that
the MnO2 structure is not a simple function of the applied volt-
age in non-acidified solutions, but more likely depends on the
]
(6)
−
]
transient/[Mn2+].
The overall self-redox reaction shown in Eq. (2)
has th−e characteristics of deep purple color and high
relative concentration ratio of [MnO4
[MnO4
]
transient/[Mn2+] ratio in the electrolyte solution, as well
as a slow rate of MnO2 precipitation. The tie lines of oxidative
reactions represented by Eqs. (4) and (6) in the Pourbaix diagram
can be described as follows [30]:
E = 1.228 − 0.0591pH
and
E = 1.228 − 0.1182pH − 0.0295 log[Mn2+].
The two tie lines of reactions (4) and (6) crossover in the
Pourbaix diagram at a point where the pH −0.5 log[Mn2+] or
the potentials for−oxidative reactions are the same. In other
words, the MnO4 ions may have equal opportunity to oxi-
dize the reactants by Eqs. (4) and (6). Products of Li+–␥-MnO2
and Li+–␣-MnO2 phases should be able to coexist at this par-
ticular pH–Ev setting. Experiments carried out with Li+ counter
ions in the pH range from −0.4 to −0.1 yield the product mix-
tures of ␥-MnO2 and ␣-MnO2 phases. The results shown in
Fig. 5. XRD patterns displaying the phase transformation from ␣-MnO2 to ␥-
MnO2 as a function of different [K+]/[Mg2+] concentration ratio.

H.Y. Lin et al. / Electrochimica Acta 52 (2007) 6548–6553
6553
Fig. 4b are in good agreement with our prediction. The trends of
structural transformation in Fig. 4b reveal that the concentration
ratio of [MnO4
encing structure formation in MnO2 phases with small counter
ions such as Li+. However, in MnO2 structures obtained with
K+ and Rb+ counter cations, the primary factor of a large ionic
radius in ensuring the production the ␣-MnO2 phase was clearly
demonstrated.
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radius of counter ion and [MnO4
]
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electrolytic samples show that the ␣- (2 × 2) and ␥- (1 × 1 and
1 × 2)MnO2 are thermodynamically stable phases in ambient
state. The ionic radius of the counter cation is the primary
factor in determining the structural formation of the MnO6
framework. In non-acidified solution, the ␥-MnO2 can be pre-
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radii. Counter ions such as K+ and Rb+, have ionic radii that
can stabilize the ␣-MnO2 (2 × 2) tunnel structure. However,
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induces the structural instability and gives rise to an amorphous
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concentration ratio of [MnO4
]
transient/[Mn2+] in aqueous solu-
tions, which is another main factor for controlling the structure
of MnO2 produced. In acidified solutions, a high concentra-
−
]
transient/[Mn2+] produces the ␣-MnO2
tion ratio of [MnO4
structure exclusively under the conditions of pH ꢀ −0.64 and
Ev ꢁ 3.0 V.
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The authors appreciate the support and helpful discussion
from Dr. M.K. Wu at Academia Sinica in Taiwan. This work
is sponsored by the ROC National Science Council, Grant No.
NSC 95-2218-E-260-001.
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