Electric field formation during combustion of single metal particles

Article abstract of DOI:10.1149/1.1562936

A strong electric field formed during the initial stage of the combustion of single Zr, Ti, Fe, and Ni particles. The electric field lasted for 20-400 ms and decayed before the particle temperature reached its maximum. A low voltage was generated during the combustion of particles initially surrounded by a thick oxide film or when the ambient oxygen concentration was low. A decrease in the rate of oxygen transport to the reaction zone generated a bipolar signal during the combustion of Zr and Ti and/or electric oscillations of 0.5-10 Hz. Melting of either the reactants, or intermediate or final products annihilated the electrical field. The maximum voltage and current were attained for particles of ～0.8 mm diam. The largest unipolar electric voltage and current were produced during the combustion of either a Zr or a Ti particle (～2 V and ～100 mA). A rapid increase in the rate of temperature rise in Zr and Ti particles followed the annihilation of the electric field. It may have been caused by Joule heating following electric breakdown through the oxide film. A shift from homogeneous to relay-race combustion occurred upon increasing the distance between particles in a row. This shift affected the qualitative features of the generated electric field as well as the temperature at which it formed.

Full text of DOI:10.1149/1.1562936

Journal of The Electrochemical Society, 150 ͑5͒ J9-J16 ͑2003͒
J9
0013-4651/2003/150͑5͒/J9/8/$7.00 © The Electrochemical Society, Inc.
Electric Field Formation during Combustion of Single Metal
Particles
K. S. Martirosyan, I. A. Filimonov,a M. D. Nersesyan, and Dan Lussz
Department of Chemical Engineering, University of Houston, Houston, Texas 77204-4792, USA
A strong electric field formed during the initial stage of the combustion of single Zr, Ti, Fe, and Ni particles. The electric field
lasted for 20-400 ms and decayed before the particle temperature reached its maximum. A low voltage was generated during the
combustion of particles initially surrounded by a thick oxide film or when the ambient oxygen concentration was low. A decrease
in the rate of oxygen transport to the reaction zone generated a bipolar signal during the combustion of Zr and Ti and/or electric
oscillations of 0.5-10 Hz. Melting of either the reactants, or intermediate or final products annihilated the electrical field. The
maximum voltage and current were attained for particles of ϳ0.8 mm diam. The largest unipolar electric voltage and current were
produced during the combustion of either a Zr or a Ti particle ͑ϳ2 V and ϳ100 mA͒. A rapid increase in the rate of temperature
rise in Zr and Ti particles followed the annihilation of the electric field. It may have been caused by Joule heating following
electric breakdown through the oxide film. A shift from homogeneous to relay-race combustion occurred upon increasing the
distance between particles in a row. This shift affected the qualitative features of the generated electric field as well as the
temperature at which it formed.
© 2003 The Electrochemical Society. ͓DOI: 10.1149/1.1562936͔ All rights reserved.
Manuscript submitted February 27, 2002; revised manuscript received October 26, 2002. Available electronically March 20, 2003.
Extensive literature exists on the formation of an electromagnetic
field in gaseous flames.1-4 Several studies have investigated the for-
mation of these fields during the combustion of metal particles used
in propellants, explosives, pyrotechnics, and self-propagating high
temperature synthesis ͑SHS͒. The formation of such fields by the gas
phase detonation or shock waves accompanying the combustion pro-
cess in pyrotechnics and explosives is reported in Ref. 5-7.
Experiments revealed that an electromagnetic field might also
form during combustion in different loose and pressed metal powder
mixtures.8-16 Combustion synthesis of ferromagnetic materials gen-
erated residual spontaneous magnetization of the order of 1-10
␮T.8-10 Temporal current densities of up to 8.3 A/cm2 were observed
in the ambient gas close to the surface during the combustion of
some binary systems Ti-C, Ti-N2 , and Mo-Si.11 An electric field of
up to 1.5 V was created during several solid reaction processes.12-16
We observed weak magnetic fields ͑up to 20 nT͒ during the oxida-
tion of several metal powder mixtures.13-15
The cause of the formation of the electric and associated mag-
netic fields in combusting solids has not yet been established. Nei-
ther is the influence of the electric field on the combustion process
and residual properties of the products predictable. We suggested16
that coupled transport and kinetic rate processes created a charged
double layer ͑dl͒ in single particles. The magnitude, frequency, and
shape of the electromagnetic signal are determined by the factors
affecting the rate of ion diffusion, such as oxygen pressure, sample
density, and reactant particle size.
well as on their combustion rate will facilitate these comparisons.
While Zr and Ti ͑and their oxides͒ do not melt during combustion
under the experimental conditions we used, the other two metals or
their oxides do ͑Ni, FeO͒. Thus, the experiments provide informa-
tion on the impact of melting on the electromagnetic field.
We conducted measurements of the electric voltage evolution
during the combustion of thin wires as they enabled us to exclude
the impact of imperfect particle-electrode contact, which can dis-
guise the intrinsic value. The combustion of a row of Zr particles
was used to study the impact of the contact and interaction between
particles. This study provides the first information on the qualitative
change in the electric charge features upon a transition from quasi-
homogeneous to relay-race combustion.
The study of the combustion of single particles circumvented the
complicating ensemble averaging encountered in measurements of
the electrical signal between two electrodes separated by a large
number of particles and the impact of associated factors, such as
contact between particles and temporal variation of ambient gas
composition and temperature. Moreover, single particle experiments
provide information on the relation between the particle temperature
and the electric charge evolution. The experimental data about the
temporal voltage, current, and temperature generated during the
combustion of a single particle are essential for developing and criti-
cal testing of predictive models of the evolution and features of the
electric potential.
Almost all previous investigators measured the electric voltage
between two electrodes separated by a distance much larger than the
particle size. The only reported single particle experiment17 is of
thermoionic emission of electrons and charged MgOϩ particles
around a burning magnesium pellet.
We report here a study of the evolution of electric potential,
current, and temperature during the combustion of single particles of
four different metals under various operating conditions. The experi-
ments involved simultaneous measurements of the induction time
and temporal electric signal and particle temperature. To provide
data for future critical tests of theoretical predictions we have con-
ducted experiments with two metals whose oxides have a mixed
electronic-ionic conductivity (ZrO2 , FeO͒ and two p-type semicon-
ductors (TiO2 , NiO͒. Extensive data on the ion ͑cation͒ diffusion
and oxygen permeation through these metals and their oxides, as
Experimental
A schematic diagram of the experimental system used to measure
simultaneously the electric potential and temperature during the
combustion of a single metal particle is shown in Fig. 1. The com-
bustion in various oxygen-argon mixtures was conducted in a quartz
tube ͑л 10 and 25 cm long͒. The particle was supported from below
by a S-type ͑Pt-Rh and/or tungsten-rhenium͒ microthermocouple of
about 10 ␮m diam held in a special nonconducting holder. The
thermocouple was much thinner than the particle and its heat capac-
ity significantly smaller than that of the particle. The maximal esti-
mated temperature error was smaller than 1%. Particles with diam-
eter smaller than 0.5 mm were attached to the thermocouple by
organic glue. Two platinum electrodes ͑л 0.1-0.3 mm͒ supported
the particle from both sides and measured the electric field. The
initial contact resistance between the particle and the electrodes was
ϳ0.5 ⍀.
The measured voltage, electric current, and thermocouple read-
ings were transmitted to a multichannel Data Collection System
͑Omega Eng. Inc. Stanford, CT͒ and recorded on a PC. The imped-
ance during voltage and current measurements was 0.25 M⍀ and 0.1
a Permanent address: Institute of Structural Macrokinetics and Materials Science,
Russian Academy of Sciences, Chernogolovka, 142432, Russia.
z E-mail: Dluss@uh.edu
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J10
Journal of The Electrochemical Society, 150 ͑5͒ J9-J16 ͑2003͒
Figure 1. Schematic diagram of the experimental system used for simulta-
neous measurement of the electric potential and temperature during the com-
bustion of a single metal particle.
⍀, respectively. The voltage signal was confirmed by an analog
voltmeter with 2 M⍀ internal resistance.
Most metal particles used in the experiments were spherical and
99ϩ % pure ͑Sigma-Aldrich Chemical Company͒. We have inves-
tigated combustion of both the solid and porous particles. Normally,
metal particles of ϳ0.5-1.8 mm diam and ϳ0.2-20 mg in mass were
used. In some cases, large porous Ti particles of ϳ3.9 mm diam and
ϳ14 mg mass were used. In most cases, a wooden match was used
to initiate the combustion to avoid electric noise. In rare experiments
conducted under constant volume, ignition was initiated by an elec-
trically heated nichrome igniter. The experiments could be con-
ducted in our cell only when the maximum particle temperature was
below ϳ2000°C. At higher temperatures, the particle-electrode or
particle-thermocouple attachments broke during the combustion.
This restricted the size of the Zr and Ti particles, which could be
studied.
We determined in some experiments the electrical field formation
and temperature rise during the combustion of Fe and Ni wires. The
wire ͑0.1-1 mm diam and 2-3 cm length͒ was held between two
conducting supporting electrodes in the quartz reactor. We ignited
the wire center by a wooden match under an oxygen flow of 5
L/min.
A special cell was used to measure the electric charge emission
to the gas adjacent to a burning particle ͑Fig. 2a͒. It consisted of an
Al2O3 ceramic half-cylinder ͑12 cm inner diameter, 3 cm length,
and 0.5 cm thickness͒ that housed the particle supports, electrodes,
and thermocouple. The electric current and voltage were measured
between the particle surface and a 0.1 mm Pt electrode located at a
distance of 0.1-2 mm from the surface. The particle was the negative
electrode.
Another measuring cell ͑Fig. 2b͒ recorded the electrical field
during combustion of a straight row of particles. It consisted of six
to ten metal particles of л 0.2-0.5 mm separated by an equal dis-
tance ͑0-2 mm͒ and squeezed between two 60 mm long platinum
wires of 0.1 mm diam. The distance between these two wires was
smaller than the particles size. A spring kept the wires tight during
combustion and compensated for the thermal expansion.
Single particle experiments showed that the electrical voltage
evolution starts at about 1000°C. The Pt wires were covered with a
thin insulating ͑organic lacquer͒ layer, which evaporates at about
300°C. These wires served as passive electric probes to measure the
voltage generated only by the particles undergoing combustion. The
insulating layer prevented electrical short circuiting between the two
Figure 2. Cells for simultaneous measurement of the electrical field and
temperature. ͑a͒ In the gas-phase near a single particle. ͑b͒ In a row of
particles.
oxide layer prevented short circuiting by the completely combusted
particles. The lacquer layer helped keep the individual particles in
position between the two platinum wires.
Thermogravimetric ͑TG͒ and differential thermal analysis ͑DTA͒
by a TG/DTA-320 thermoanalyzer ͑Seiko Instruments Inc.͒ was
used to prepare pellets with desired thickness of the oxide layer and
to determine the temperature dependence of the phase transforma-
tions. The oxidation products were identified by X-ray diffraction
͑XRD͒ ͑Siemens D-5000͒. The oxide shell thickness was measured
by a microprobe ͑JEOL JAX8600, Japan͒.
Results
We investigated the dependence of the temporal electric potential
formed during the combustion of a single metal particle on its mass
͑size͒, oxygen concentration, and width of an initial exterior oxide
film. Table I summarized some key data about the characteristic
temperatures and electric signal generated during the combustion of
either Zr, Ti, Ni, or Fe single solid particles in an open quartz tube to
which the oxygen mixtures were fed. Solid titanium particles with
diam larger than ϳ1.5 mm could not, but porous spongy particles
could be ignited by a wooden mach. Thus, the data for the Ti particle
with a 3.9 mm diam is for a porous particle.
The combustion was initiated at some location on the particle
surface and then propagated rapidly all over the surface leading to
an abrupt temperature rise. The temperature rise accelerates the re-
action rate. The maximum voltage ϳ2 V was generated by the com-
bustion of either a Zr or Ti particle. It was about one order of
magnitude higher than that during the combustion of the Ni or Fe
Ͻ
electrodes by metal particles with T
300°C and the thick exterior
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Journal of The Electrochemical Society, 150 ͑5͒ J9-J16 ͑2003͒
J11
Table I. Summary of characteristics of the temperature and electric signals generated during the combustion of single metal particles.
Induction
time of
Temperature rising rate, 103 ͑°C/s͒
Maximum
combustion
temperature
(Tb , °C͒
Maximum
reaction rate
temperature
(Tf , °C͒
Duration
of
voltage,
͑ms͒
the
electrical
field
Maximum
voltage
͑V͒
Maximum
current
͑mA͒
Particle size,
ϳл mm
Until
During
signal
After
͑ms͒
signal
signal
0.6
2000
2100
1875
1760
1680
1620
1100
1150
1150
1130
-
28
18
24
30
380
235
30
24
18
40
1020
940
2.4
3.6
4.3
4.0
0.6
1.3
9.1
9.3
7.7
8.4
0.7
1.1
39
42
17
16
-
1.96
1.8
1.8
1.4
0.34
0.25
86
98
80
76
30
28
Zr
Ti
0.8
0.8
3.9a
Fe, 0.6
Ni, 0.5
1050
0.7
a Porous titanium.
particles. This is probably due to the melting that occurred during
the combustion of these particles.
ϳ1.24 V were obtained for a 0.6 mm zirconium particle heated at a
rate of ϳ400°C/s. However, the combustion temperature was
2000°C and the maximum potential was ϳ1.7 V for a heating rate of
800°C/s. The metal particle heating rate by a wooden match could
not exceed ϳ900°C/s.
In all the experiments a small, short temperature drop occurred
before the electric signal formed. We believe that this temperature
drop occurred upon the removal of the wooden match. The initial
increase in the heat release rate following ignition was not sufficient
to compensate for the termination of the external heating by the
match and led to the transient temperature drop.
XRD, and DTA and TG analysis revealed that the combustion of
the Zr and Ti created ZrO2 and TiO2 , respectively. The temperature
at which intense oxidation of Zr and Ti started was higher for large
particles. For example, the ignition temperature of Zr in a oxygen
flow rate of 5 cm3/min was 200 and 460°C for particles with diam of
ϳ5 ␮m and ϳ0.5 mm, respectively.
Figure 3 describes the temperature and voltage evolution during
the combustion of a single Zr and Ti particles. The electric voltage
was generated at a temperature close to the inflection point of the
temporal rising temperature denoted as Tf . The maximal rate of the
chemical reaction and corresponding heat release occurred at this
temperature. The voltage signal generated by the combustion of
those particles is about 2 V. The electric field lasted for about 20 ms.
The maximal current generated during the combustion of Zr and Ti
was 98 and 80 mA, respectively ͑Table I͒. These values largely
exceeded the current measured in the gas phase adjacent to the par-
ticle, which is reported later. The rate of the temperature rise while
the electric signal existed was of the order of ϳ104°C/s. The electric
signal generated by the two metals decayed before the combustion
temperature reached its maximum. The rate of temperature rise in-
creased following the decay of the electric field.
The ignition temperature, Ti , depended on the heating rate and
the particle size. Both the combustion temperature and electric field
increased with increasing rate of particle heating during ignition. A
maximum temperature of ϳ1800°C and a maximum potential of
Figure 4a shows that the voltage generated during the Ti and Zr
particles combustion attained a maximum at some intermediate par-
ticle mass of ϳ1-8 mg. The increase in the particle mass increased
the maximum temperature and led to experimental difficulties due to
the melting of thermocouples and electrodes. The combustion of
large particles of 8-20 mg was very violent and created a liquid
phase that changed the particle shape. The following experiments
for Zr and Ti were conducted with particles, which generated the
maximum electric signal.
Experiments were conducted to determine the impact of the oxy-
gen partial pressure on the magnitude and shape of the voltage sig-
nals. To prepare the oxygen/argon mixtures, a 5 L/min feed of argon
was mixed with another one of oxygen ͑1-12.5 L/min͒. Figure 4b
shows the maximum positive and negative voltage dependence on
the O2 /Ar ratio. Bipolar signals were generated when the O2 /Ar
ratio was smaller than Ͻ0.67. The maximum positive signal during
the combustion of zirconium at different O2 concentrations was
ϩ1.5 V and the maximum negative one was 1.1 V. The difference
between the positive and negative amplitudes of the bipolar signals
increased with increasing O2 /Ar. The negative voltage signal lasted
longer then the positive one at O2 /Ar ratios between 0.28-0.67. At
low O2 /Ar ratio ͑ϳ0.3͒ the combustion was not stable and in some
cases, the combustion was impossible to initiate. The combustion
under these conditions generated weak electrical oscillations with an
amplitude of 60-100 mV at a frequency of ϳ10 Hz. This frequency
depended on the oxygen content. The corresponding combustion
temperatures were about 1400-1700°C. A unipolar positive voltage
signal was generated for O2 /Ar ratios larger than about 0.7.
A thin exterior oxide layer usually covers metal particles stored
in air. For example, the thickness of the oxide shell formed around a
titanium particle is about 10 nm.18 We conducted experiments to
determine the influence of the initial oxide film thickness (hf) on the
shape and magnitude of the electrical potential. We created surface
oxide films of 1-150 ␮m thickness by preoxidation of some Zr and
Figure 3. Temporal voltage and temperature generated by the combustion in
oxygen of a ͑a͒ zirconium and a ͑b͒ titanium particle.
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Journal of The Electrochemical Society, 150 ͑5͒ J9-J16 ͑2003͒
Figure 5. Dependence of the voltage formed on the initial exterior oxide
film thickness during the combustion of a single ͑a͒ Zr particle (л
ϳ 0.8 mm), and ͑b͒ Ti particle (л ϳ 0.8 mm).
Figure 4. ͑a͒ Dependence of the potential induced during the combustion of
Zr and Ti particles on the initial particle mass. ͑b͒ Dependence of the maxi-
mal positive and negative voltage on the O2 /Ar ratio in the ambient gas. No
ms before the temperature reached its maximum of 1340°C.
Ͼ
negative voltage signal is obtained if O2 /Ar
mm.
0.67. Particle diameters Ӎ1.2
Oscillating voltage could be obtained by either decreasing the
oxygen content or increasing the initial oxide film. Typical voltage
oscillations on the surface of a zirconium and titanium particle are
shown in Fig. 7. The ϳ10 Hz oscillatory signal for the Zr particle
was initially positive and then became negative. A similar ϳ10 Hz
oscillatory voltage was obtained for a titanium particle. A decrease
in the ambient oxygen content as well as an increase in the initial
oxide film thickness shifted the temporal voltage from a unipolar
positive signal to a bipolar one and/or to an oscillatory one. This
decrease in the oxygen concentration decreased the positive voltage
amplitude while increasing that of the negative voltage and in-
creased the electric signal duration. In this experiment, the electric
signal decayed after the particle temperature attained its maximum.
The probe shown in Fig. 2a was used to measure the electric field
in the gas at a distance of ϳ0.5 mm from a Zr particle surface. The
Ti particles in a DTA/TG process at a temperature in the range of
200-500°C ͑depending on the particles size͒. The film thickness was
calculated from the thermogravimetrical data, particle size and the
difference in the density of the metal and its oxide. Microscopic
measurements indicated that the oxidation procedure produced films
with a uniform thickness.
Figure 5 describes the dependence of the voltage formed during
the oxidation of either Zr or Ti single particles (л Ӎ 0.8 mm) hav-
ing a film thickness (hf) between 1-60 ␮m. Increasing hf decreased
the electric signal amplitude but increased its duration and affected
its polarity. A zirconium particle with a film thickness of hf
Ӎ 2 ␮m generated a unipolar signal of a ϳ1.42 V that lasted for
Ͼ
ϳ35 ms. With hf
32 ␮m, the voltage signal became bipolar with
a period of ϳ350 ms and amplitudes of ϩ0.37 and Ϫ0.07 V. The
amplitude of the negative voltage was larger for thicker films, i.e.,
for Zr with hf Ӎ 60 ␮m, a voltage with amplitudes of ϩ0.1 V,
Ϫ0.24 V was generated which lasted ϳ870 ms. Qualitatively similar
behavioral features were obtained during the combustion of titanium
particles ͑Fig. 5͒. At hf ϳ 40 ␮m, the negative potential was about
double the positive one and the pulse lasted for ϳ1 s.
We measured simultaneously the temporal temperature and elec-
tric voltage during the combustion of a zirconium particle with a
film thickness ϳ80 ␮m ͑Fig. 6͒. A positive voltage was obtained at
700-740°C, at which the active combustion started. The temperature
rise from ignition to the inflection point took ϳ250 ms. The signal
polarity changed as the temperature increased. A negative voltage of
Ϫ0.8 V was obtained at about ϳ950°C at which an endothermic
reaction ͑probably the Zr ␣ → ␤ phase-transition͒ occurred. The
electric field lasted for about ϳ560 ms while the temperature change
lasted a much longer time. The electrical signal decayed about 20
Figure 6. Temporal voltage and temperature generated by the combustion of
a Zr particle, л Ӎ 0.8 mm, hf ϳ 80 ␮m.
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Journal of The Electrochemical Society, 150 ͑5͒ J9-J16 ͑2003͒
J13
Figure 9. Temporal voltage and temperature generated by the combustion of
a Fe particle л Ӎ 0.6 mm.
Figure 7. Temporal voltage oscillations during the combustion of a Zr and a
Ti particle in different O2 /Ar mixtures: Zr particle (л Ӎ 0.8 mm, hf
ϳ 50 ␮m, O2 /Ar ϭ 0.29), Ti particle (л Ӎ 0.8 mm, hf Ӎ 40 ␮m,
O2 /Ar ϭ 0.33).
decrease at large wire diameter was probably caused by the higher
temperature, which promotes the melting that annihilates the electric
field.
In order to gain an understanding of the interaction between in-
dividual particles we measured the temperature rise and voltage gen-
eration in an array of ten Zr particles of diam D Ӎ 0.2 mm placed in
a row and separated by an equal distance ␦ ͑between 0-2 mm͒ from
each other. When the particles touched each other ignition caused a
quasi-homogeneous combustion. The temperature front moved at a
constant velocity of 3.4 mm/s and the maximum temperature was
1760°C. Temperature profiles at two particles during the quasi-
homogeneous combustion and the corresponding bipolar voltage
signal are shown in ͑Fig. 12a͒. The positive voltage ͑maximum 0.56
V͒ lasted for ϳ90 ms and the negative ͑maximum Ϫ0.56 V͒ for
about 110 ms. An inflection in the temperature profile point existed
at ϳ1100°C.
When the Zr particles (D Ӎ 0.2 mm) were separated by a dis-
tance of 0.5-1 mm, a relay-race combustion mode was obtained. In
this case, heat transfer between adjacent particles led to ignition. A
time delay existed between the ignition of a particle and the extinc-
tion of the one ahead of it in the row ͑Fig. 12b͒. A relay-race com-
bustion with a delay of about 1.5 s was realized using Zr particles
with D ϭ 0.2 mm and ␦ ϭ 0.5 mm. The corresponding combustion
temporal voltage and current exhibited complex oscillations with a
maximum amplitude of ϳ80 mV and a current of up to ϳ1 mA ͑Fig.
8͒.
Figure 9 describes the electric signal and temperature during the
combustion of an iron particle in an oxygen stream of 5 L/min. A
voltage was generated just below the temperature inflection point of
1170°C. Its peak of ϳ0.34 V was much lower than those generated
during the Zr or Ti combustion. The maximum temperature
ϳ1580°C, exceeded the melting temperatures of pure Fe ͑1539°C͒,
FeO oxide ͑1368°C͒, Fe2O3 ͑1562°C͒, and that of Fe3O4 decompo-
sition ͑1538°C͒. The melting changed the particle shape. The tem-
perature plateau of ϳ1370°C was caused by FeO melting, which
annihilated the voltage.
The temporal voltage and temperature generated during the com-
bustion of a Ni single particle is described in Fig. 10. The melting
occurred well before the particle reached its maximum temperature
and decreased the reaction rate, i.e., the rate of the temperature rise.
The partial melting of Ni decreased the heating rate at about
1450°C. The voltage signal oscillated during the oxidation. Since
melting annihilated the electrical voltage, a lower melting tempera-
ture led to a shorter duration of the electrical pulse ͑235 and 380 ms
for Ni and Fe, respectively͒ and a lower maximum of the voltage
signal 0.25 and 0.34 V for Ni and Fe, respectively.
front velocity U ϭ (␦ ϩ D)/␶ was 0.48 mm/s. The temporal
͓
͔
d
temperatures of the particle in the row were similar. The combustion
of the particles generated a positive voltage impulse with an ampli-
tude of 0.25-0.35 V. The average duration of each voltage impulse
was ϳ100 ms.
It is extremely difficult to study the effect of particle size on the
generated voltage in metal particles which melt. Thus, we measured
the voltage generated in wires instead of in particles, which melt
during the combustion. Figure 11 shows that the electric signal gen-
erated by the combustion of iron and nickel wires ͑0.1 up to 1 mm͒
attained a maximum at an intermediate wire diameter. The mono-
tonic voltage increase for small wire diameter was probably due to
the increase in the combustion temperature. The monotonic voltage
Discussion
With thin initial oxide films and high ambient oxygen concentra-
tion the electric potential formed during the initial stage of combus-
Figure 8. Temporal voltage and current generated in the gas phase close to
a Zr particle surface (л Ӎ 1.2 mm).
Figure 10. Temporal temperature and current generated by the combustion
in oxygen of a Ni particle.
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J14
Journal of The Electrochemical Society, 150 ͑5͒ J9-J16 ͑2003͒
mum temperature due to the decreased surface area per unit volume.
The higher temperature led to melting that eliminated the electrical
charge separation and the electrical field.
We believe that an electric dl formed on the particle surface due
to the different diffusion velocities of the charge carriers. This led to
a rapid separation of charges ͑dl͒ within an oxide layer at tempera-
tures around 800°C. The approximate thickness of this diffusion
layer (hd) was of the order
T
dt
ͱ
hd Ӎ
D T͒dt ϭ
D T͒
dT
͓1͔
͑
͑
͵
͵
ͩ ͪ
ͱ
i
i
dT
T
0
where Di is the temperature dependent oxygen diffusion coefficient
and t is time. According to the literature for titanium20,21 Di
ϭ D0i exp(ϪE/RT), where D0i ϭ 1.6 cm2/s, and E ϭ 202 kJ/mol.
The predicted diffusion layer thickness for titanium and a tempera-
ture in the range 800-1400°C is of the order of several micrometers.
The longer duration of the electric impulse at low oxygen con-
centration ͑or thick initial oxide film͒ was caused by the lower com-
bustion temperature that increased the characteristic time of the dif-
fusion controlled combustion. This increase has been confirmed by
simultaneous measurements of the temperature and electric signals
during the combustion of zirconium particle with a film about 100
␮m thick. The ϳ10 Hz oscillations of the electric impulses ͑Fig. 7͒
during the combustion of Zr and Ti were obtained due to the de-
creased oxygen transport to the reaction zone. Following adsorption
on the surface, the oxygen molecules formed on the surface O2Ϫ
ions and electron holes, h ϩ . The different diffusion velocities of
the cations and ions created an electric charge on the particle sur-
face. The oscillations may have been caused by a large difference
between the characteristic time of the oxygen adsorption-desorption
on the particle surface (␶g) and those for diffusion of positive (␶ϩ)
Figure 11. Dependence of the voltage induced during the combustion of Fe
and Ni wires in oxygen on the initial diameter.
tion, and was annihilated at a temperature close to that of the inflec-
tion point, Tf , at which the reaction rate is the largest. The
subsequent temperature rise and reaction did not generate an electric
field. No electric voltage formed when the particle temperature de-
creased. The inflection point of the temporal temperature was much
lower than the melting temperatures of the Zr and Ti particles and
their oxides. The characteristic time of the temperature rise was
about 150 ms while the characteristic time of the Zr intrinsic oxida-
tion reaction is of the order of ϳ1 ms at 500°C.19 This indicates that
the reaction rate was limited by the transport of the oxygen. At high
temperatures, the reaction occurred in a narrow shell that propagated
toward the particle center. The maximum observed electrical poten-
tial and current were ϳ2 V and ϳ100 mA, respectively.
and negative (␶Ϫ) charge carriers in the oxide film. When ␶
The electrical voltage attained a maximum at some intermediate
particle mass ͑Fig. 4a͒ and wire diameter ͑Fig. 11͒. The reason is
that an increase in particle size or wire diameter raised the maxi-
g
Ͼ
ӷ ␶
␶Ϫ, the negative charge carriers diffused faster in the film
ϩ
and a positive electric potential developed on the particle surface.
The lowered concentration of the negative charge carriers on the
surface then reduced the flux of these carriers in the film decreasing
the surface potential and making it negative. After a characteristic
adsorption time ␶g , the surface concentration of the negative carri-
ers was restored and a new oscillation started.
The experiments indicate that oxygen transport to a reaction zone
affected the shape and magnitude of the induced electrical signals
͑Fig. 4b-7͒. This transport may be controlled in two ways. It may be
diminished either by dilution with an inert gas ͑such as argon in our
experiments͒ or by enlarging the thickness of the initial oxide layer
by preliminary oxidation of the particles. The oxygen transport to
the reaction zone affected the range of the particle temperatures. The
diffusion coefficients of the charge carriers in oxide films strongly
depended on the temperature. Variation of the particle temperatures
may have changed the sign of the difference between the diffusion
coefficients of the charge carriers. This may have been the cause for
transforming a unipolar electrical signal into a bipolar one, with a
3-5 times increase of the pulse period ͑Fig. 5͒.
We conjecture that the induction is the period needed to generate
a sufficient charge carrier concentration on the particle surface
(hϩ,O2Ϫ) and for their diffusion through the growing surface oxide
shell. The characteristic induction time (␶i) of the electric field gen-
eration in a single Zr or Ti particle ͑Table I͒ was 18-40 ms. The
induction time for Fe and Ni were much longer than those for Zr and
Ti. The combustion of Fe and Ni caused melting of both the metal
and intermediate products. Thus, formation of the liquid phase an-
nihilated the electric field.
The characteristic scale of the electric field distribution is deter-
mined by the Debye screening length (Dl) that satisfied the
relation21
Figure 12. ͑a͒ Temporal temperature and electric voltage during the quasi-
homogeneous combustion mode of Zr particles (л Ӎ 0.2 mm, ␦ Ӎ 0 mm).
͑b͒ Electric voltage impulses during relay race combustion of a row of Zr
particles (л Ӎ 0.2 mm, ␦ Ӎ 0.5 mm).
kT
1
Dl ϭ
ͱ
͓2͔
4␲e2 N
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Journal of The Electrochemical Society, 150 ͑5͒ J9-J16 ͑2003͒
J15
where k is the Boltzmann’s constant, T is temperature, e is electron
charge, and N is charge carriers concentration. At an average tem-
perature of T ϭ 1200 K, N calculated from data reported in Ref. 22,
23 for chemosorption is about 1021-1022 cmϪ3. The corresponding
Debye screening length is ϳ10 ␮m.
These estimates suggest that unipolar electric signals were gen-
erated when the Debye length Dl ϳ 10 ␮m exceeded the diffusion
film thickness hd . This conclusion is supported by Fig. 5 that shows
a decrease in the amplitude of the voltage pulse and a transition to a
bipolar signal upon an increase in the initial oxide film thickness so
that Dl р hf р hd. When the oxide film was thinner than the Debye
length, charge separation occurred across the whole oxide film. This
generated a maximum number of separated charges and, conse-
quently, a maximum potential. When the oxide film was thicker than
the Debye length, the charge separation occurred over a part of the
oxide film. This decreased the number of separated charges and the
electric potential. This argument is supported by Fig. 5, 6.
The data reported in Table I shows that the temperature of the Zr
and Ti particle rose rapidly following the generation of the electric
signal. That rate of temperature rise of Ϸ104°C/s was more than
four times larger than that before the voltage generation. This
change was not caused by an increase in the particle oxidation rate.
The growing oxide shell increased the resistance to oxygen diffu-
sion, and limited the reaction rate and corresponding heat genera-
tion. A possible explanation is that a high electric charge in the dl
led to an electric breakdown. The corresponding Joule heat dissipa-
tion increased the temperature and the rate of temperature rise. The
following data support the conjecture that an electric breakdown
may have occurred in the oxide shell formed by the metal combus-
tion. During the combustion of Zr and Ti, an electrical current of
80-100 mA and voltage of ␾ Х 2 V, were measured by a 0.1 mm
diam Pt electrode. This implies a current density of ϳ106 A/cm2,
and an electric field strength of 103-104 V/cm for hd Ϸ 1-10 ␮m.
Electric breakdown of oxides was predicted to occur when E
thermal and electric resistances between the particles. These resis-
tances and the coupling among the various rate processes generated
the bipolar electric signal. These experiments indicate that the con-
tact between the particles in a loose powder may have a strong
impact on the characteristics of the measured electric field between
two electrodes.
The current density in the electrodes was computed from the
measured current and the electrode area. Due to the imperfect con-
tacts between the electrodes and the particle it is important to check
whether thermal emission and gas-phase chemical reactions affected
the measured electrical field. The Richardson-Dushman equation28
predicts a thermal emission current density of 5.46 ϫ 10Ϫ2 A/cm2
at 2000 K,11 while we obtained ϳ105 A/cm2 at a similar tempera-
ture. Therefore, thermoemission had a negligible impact in our ex-
periments. Moreover, the electric current of up to 1 mA ͑current
density of 103 A/cm2) measured near the particle surface ͑Fig. 8͒
was negligible compared to that measured on the surface, i.e., the
gas phase chemoionization contribution to the observed electrical
field was small.
Conclusions
The maximum electrical voltage and current ͑ϳ2 V, ϳ100 mA͒
formed during the initial stage of the single particle combustion
͑temperatures in the range of 800-1100°C͒. At thin initial oxide films
and high concentration of ambient oxygen, the electrical field was
annihilated before the combustion was completed, close to the tem-
perature at which the maximum chemical reaction rate was obtained.
The induction time of the voltage generation was 18-40 ms for Zr
and Ti particles and about 1 s for Fe and Ni. When the initial oxide
film was thick or when the ambient oxygen concentration was low
the electric signal persisted till the maximum temperature was
achieved. The chemoionization in the gas phase near the particle
surface and the thermal electron emission contributed negligibly
͑ϳ80 mV, ϳ1 mA͒ to the electric signals in our study.
The electric voltage magnitude and duration strongly depended
on the oxygen transport to the reaction zone. Decreasing the oxygen
concentration in the ambient gas transformed the unipolar 2 V signal
to a bipolar one ͑ϩ0.1 to Ϫ0.8 V͒. Increasing the thickness of the
initial oxide film decreased the rate of oxygen diffusion to the
shrinking reaction core and led to a bipolar potential. Sufficiently
low oxygen transport to the reaction zone generated electric oscilla-
tions with a frequency of 0.5-10 Hz.
We conjecture that the electric field is due to formation of an
electric double charge layer across the oxide film. Adsorption of
oxygen molecules on the surface lead to generation of electron holes
and ions O2Ϫ. The different diffusion velocities of the charge carri-
ers in the oxide shell created a temporal electric charge on the par-
ticle surface.
Complete separation of the electrical charges was estimated to
occur when the oxide film thickness was close to the Debye screen-
ing length. Particles with an initial oxide film of this thickness gen-
erated high unipolar electric voltages. Those with a thicker film
produced a bipolar electric signal and/or oscillations of small ampli-
tude.
5
ϭ 106 V/cm at T р 600 K, and E Ϸ 10 V/cm at T
650
Ͼ
Ϭ 700 K.24,25 We used theoretical predictions26,27 to extrapolate the
above values to higher temperature. This extrapolation predicts that
at the temperature range of 900-1000 K, breakdown will occur for
an electric field strength of 100-1000 V/cm. This value is smaller
than that estimated to exist at these temperatures.
The data about the particle temperature rise at ϳ1000 K in
Table
I
indicates that the corresponding particle heating
rate was Ϸ8 ϫ 103-2 ϫ 104 J/cm3 s because its volumetric
heat capacity was 4-5 J/cm3 K. The Joule heat generation
␴elE2 Ϸ ␴ (␾/hd)2 becomes important when it is of the
el
same order of magnitude. For titanium oxides,
␴
for
el
21
ϭ 1.57 ϫ 105 exp(Ϫ2.27 • 104/T) ⍀Ϫ1 cmϪ1
.
Thus,
␾ ϳ 2 V and hd Ϸ 1-10 ␮m the Joule energy dissipation is of the
order of 43-4300 J/cm3
s at 1000 K
and 5.7 ϫ 103-5.7
ϫ 105 J/cm3 s at 1273 K and consequently should be taken into
account.
The thermal interaction between the Zr particles in the row de-
termined whether their combustion mode was either quasi-
homogeneous or relay-race combustion. The combustion mode af-
fected the electric signal shape as well as the temperature at which
the electric field formed. A quasi-homogeneous combustion mode
was attained when the particles were close to each other ͑small ␦͒.
The duration of the bipolar electric voltage of about ϳ200 ms ͑Fig.
12a͒, was much shorter than the characteristic combustion time
͑ϳ500 ms͒. This electric signal was generated at the maximum com-
bustion temperatures. When the particles were not in close contact
͑large ␦͒ a relay-race combustion mode generated a series of unipo-
lar pulses with a short period of about 100 ms ͑Fig. 12b͒. These
pulses were generated at temperatures 800-1100°C, i.e., close to that
at which the maximum reaction rate was achieved. The frequency
and period of the pulses depended on the initial conditions: D, ␦,
reacting metal, etc. The differences in the signal shape and tempera-
ture of voltage formation may be explained by the existence of
The rate of temperature rise during the combustion of Zr and Ti
particles increased by a factor of more than four after the electric
signal decay. Estimates indicate that electric breakdown may occur
in the thin oxide films and the Joule heat dissipation may contribute
comparably to this temperature rise.
The spacing between particles in a row affected the combustion
mode as well as the magnitude and shape of the electric signal. A
bipolar voltage signal of 200 ms duration was generated in the
quasi-homogeneous combustion mode while a series of unipolar
pulses with about a ϳ100 ms duration were produced by the relay-
race combustion.
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J16
Journal of The Electrochemical Society, 150 ͑5͒ J9-J16 ͑2003͒
2. F. B. Carleton and F. J. Weinberg, Nature (London), 330, 635 ͑1987͒.
Acknowledgment
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We wish to acknowledge the financial support of this research by
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The University of Houston assisted in meeting the publication costs of
this article.
List of Symbols
D
particle diameter, mm
Di oxygen diffusion coefficient, cm2/s
Dl Debye length, ␮m
e
electron charge, C
E
electric strength, V/cm
Ea activation energy kJ/mol
hd diffusion layer thickness, ␮m
hf initial oxide film thickness, ␮m
I
k
m
N
R
t
electric current, mA
Boltzman’s constant
mass of the particle, mg
charge carrier concentration, mol/cm3
gas constant, kJ/mol K
time, s
T
temperature, °C
Tb maximum temperature, °C
Tf inflection point of the temporal temperature, °C
T0 initial temperature, °C
U
Greek
␦
combustion front velocity, mm/s
Distance between the particles, mm
electric conductivity, 1/Ohm cm
␴
el
␶
time delay, s
d
␶
characteristic time of the oxygen adsorption-desorption, s
characteristic diffusion time of positive charge, carriers, s
characteristic diffusion time of negative charge, carriers, s
electric voltage, V
g
␶
ϩ
␶
Ϫ
26. E. Kuffel, W. S. Zaeng, and J. Kuffel, High Voltage Engineering, p. 539,
Butterworth-Heinemann, Oxford, U.K. ͑2000͒.
␾
27. S. Whitehead, Dielectric Breakdown in Solids, p. 271, Clarendon Press, Oxford,
U.K. ͑1951͒.
References
1. J. Lawton and F. J. Weinberg, Electrical Aspect of Combustion, p. 355, Clarendon
Press, Oxford, UK ͑1969͒.
28. T. S. Hutchison and D. S. Barid, The Physics of Engineering Solids, John Wiley
and Sons, London ͑1963͒.
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