Combustion, Explosion, and Shock Waves, Vol. 38, No. 3, pp. 360 364, 2002
Physical Model of Explosive Synthesis of Ultrafine Aluminum Oxide
A. A. Bukaemskii1 UDC 621.762.242 + 662.216.3 + 539.89
Translated from Fizika Goreniya i Vzryva, Vol. 38, No. 3, pp. 121 126, May June, 2002.
Original article submitted October 13, 2000; revision submitted August 30, 2001.
The paper considers a physical model for the explosive synthesis of ultrafine aluminum
oxide, which assumes that in a compression wave the starting material is divided into
layers with different states of aggregation and grain-size compositions. The relation-
ship between the synthesis conditions and the properties of the product is studied. It
is shown that the yield of the ultrafine fraction in the synthesized powder depends on
the conditions of metal oxidation during dispersion, shock-wave parameters, and the
velocity of dispersion of the starting material into the gas medium of the explosion
chamber. Experimental data are used to determine the layer sizes and the constants
characterizing the possibility of vapor-phase oxidation of aluminum during explosive
synthesis. In the coordinates corresponding to the process parameters (yield of the
ultrafine fraction and the masses of the explosive and the starting metal), a synthesis
surface is constructed and optimum parameters for production of ultrafine material
are determined.
Key words: ultrafine aluminum oxide, explosive synthesis, layer-by-layer separation
of material in a compression wave, conditions of synthesis, properties of material.
Ultrafine materials are of considerable interest be- ditions favorable for exactly this combustion regime.
cause of the unusual physicochemical properties of par- A procedure for choosing optimal synthesis parameters
ticles with a characteristic size less than 0.1 µm. The for producing large amounts of ultrafine material and
properties of these materials depend strongly on the characterize the properties of the materials produced
conditions of synthesis [1]; therefore, in spite of the wide was described in [4]. The results obtained suggest that
variety of existing methods, the development of new in a compression wave, the material is separated into
methods of synthesis of ultrafine materials are among layers that differ in the state of aggregation and size of
important scientific and practical problems. the metal particles. These differences determine both
Beloshapko et al. [2] describe a method for synthe- the mechanisms of metal combustion during subsequent
sis of ultrafine metal oxides which employs an explosive dispersion of the metal into the gas medium of the ex-
as an energy carrier. According to the traditional clas- plosive chamber, and, hence, the grain-size characteris-
sification, explosive synthesis belongs to methods based tics of the synthesized materials.
on the  vaporization condensation physical phenom- The present paper considers a physical model of ex-
ena [1]. The starting material (a metal with low bulk plosive synthesis based on the layer-by-layer separation
density) is heated by a shock wave from a contact ex- of a material in a compression wave. The relationship
plosive charge, which is followed by a free high-velocity between the conditions of synthesis and the properties
dispersion and chemical interaction of the material with of the material produced is studied.
the oxygen-containing medium of the explosive cham- The synthesis scheme is described in [4]. The initial
ber.
density of the high explosive (HE) was ÁHE = 1.2 g/cm3
According to [3], the formation of submicron ox- and that of the highly porous medium (PAP-1 alu-
ide particles occurs in vapor-phase metal combustion.
minum powder) was ÁAl = 0.56 g/cm3. The experi-
Hence, in synthesis, it is important to provide for con-
ments were carried out in an explosion chamber with a
volume of 160 dm3. An explosion was initiated in an
1
Physicotechnical Institute, Krasnoyarsk State University,
air medium at an initial pressure of 4 atm.
Krasnoyarsk 660036; [e-mail].
360 0010-5082/02/3803-0360 $27.00 © 2002 Plenum Publishing Corporation
Physical Model of Explosive Synthesis of Ultrafine Aluminum Oxide 361
The paper discusses results of two series of ex-
periments, in which RDX was used as the explosive
and the composition and initial pressure of the gas
medium in the explosion chamber were constant. In the
two series of experiments, we used close ranges of the
main controlled parameter of the synthesis MHE/MAl,
where MHE and MAl are the masses of the HE and
aluminum, respectively. In the first series of experi-
ments, this parameter was varied by changing the initial
mass of aluminum provided that the HE mass was con-
stant (MHE = 12.25 g). In the second series, the mass
of the loaded material was constant (MAl = 60.2 g).
In each experiment, we determined the yield
of the ultrafine fraction of the synthesized powder
· = Md/Mcalc, where Md is the mass of the ultra-
fine powder produced by sedimentation and Mcalc is the
mass of aluminum oxide estimated from the amount of
the initial aluminum and from stoichiometric relations.
The results obtained are shown in Fig. 1a, in which
rass = Rass/RHE (Rass is the radius of the experi-
mental assembly and RHE is the radius of the explo-
sive charge). It is obvious that in each series, the
2
curve of ·(rass) behaves differently. In the experiments
with MHE = const, a distinct maximum is observed
2
for rass H" 12, and the subsequent decrease in the yield of
the ultrafine fraction is observed for large values of rass.
In the experiments with MAl = const, the curve of
2
·(rass) is linear.
Let us consider in detail the process of explosive
synthesis of ultrafine aluminum oxide (Fig. 2a). At a
certain time, a detonation front propagates over the
HE, and a compression shock wave propagates over the
Fig. 1. Yield of the ultrafine fractions of the synthe-
starting material.
sized powder · (a) and ·" (b) versus the relative ra-
As is shown in [5], when RDX with a density
dius of the experimental assembly for MHE = const
of 1.2 g/cm3 is used as the explosive, the starting
(points +) and MAl = const (points " ); solid curves
material at the shock-wave front is compressed to a are calculated data.
nearly monolith density and is heated to the melting
point (Tmelt). The low initial density of the aluminum
powder and the cylindrical symmetry of the experi-
nite the metal upon its subsequent dispersion. Thus,
mental assembly suggest that the shock-pulse ampli-
the material is heated to temperatures below the
tude (P ) and the temperature of the shock-compressed
melting point but above the ignition temperature
layer decrease considerably as the shock wave propa-
(Tign H" 0.8Tmelt [3]). For the starting material, this
gates over the material (Fig. 2b). As a result, at a
layer (II) is bounded by the radii Rliq and Rsol (the sub-
certain thickness of the sample, the temperature of the
script  sol corresponds to the solid state). In this case,
shock-compressed layer Tmelt decreases. Thus, the layer
the shock-compressed material consists of sintered solid
of the shock-compressed material (I) adjacent to the
particles of the aluminum powder heated to tempera-
detonation products is in the liquid state. We denote
tures optimal for their subsequent ignition. Because of
the corresponding radius of the starting material as Rliq.
the size of the aluminum powder particles (H"1 µm), we
During subsequent dispersion, the liquid layer breaks up
classify them as small particles [3] which typically burn
into large metal drops [4].
in the vapor-phase regime, resulting in the formation of
Further decay of the shock wave leads to the
aluminum oxide in the ultrafine state.
fact that at a certain thickness, the temperature of
Layer III of the shock-compressed material consists
the shock-compressed layer becomes insufficient to ig-
of solid particles of aluminum powder, which are heated
362 Bukaemskii
2 2 2
rass > rsol: · = (Ä…I(rliq - 1) + Ä…II(rsol - rliq)
2 2 2
+ Ä…III(rass - rsol))/(rass - 1) (3)
(Ä…I, Ä…II, and Ä…III are the ultrafine fractions of the syn-
thesized powder for each layer, respectively).
We assume that Ä…I 1 because synthesis of ul-
trafine particles during combustion of large aluminum
drops is rather problematic [4]. The value of Ä…II is close
to unity because the most favorable conditions for pro-
duction of ultrafine material are reached in layer II. In
layer III, the shock-compressed material is heated in-
significantly, hence, Ä…III < Ä…II.
2
A curve of ·(rass) is shown schematically in Fig. 2c.
The maximum yield of the ultrafine fraction is reached
for rass = rsol, and for large values of rass, the quantity ·
becomes constant:
2 2
·max = Ä…II + (Ä…I - Ä…II)(rliq - 1)/(rsol - 1); (4)
·(rass ") = Ä…III.
A comparison of Figs. 1a and 2c shows that for the
series of the experiments with MHE = const, the curve
2
of ·(rass) is similar to the modeled one. The character
2
of the curve of ·(rass) for the series of the experiments
with MAl = const is obviously determined by the de-
pendence of the parameter Ä…i on synthesis conditions.
It is obvious that the quantity Ä…i depends on grain-
size characteristics and the state of aggregation of the
material in the layer and on synthesis parameters, for
example, on oxidation conditions. We introduce the
parameter K = MO2/MAl, where MO2 is the amount
Fig. 2. Diagram of the experiment (a) and curves of
of oxygen in the gas volume of the explosion chamber.
shock-compression pressure (b) and the yield of the ul-
2
Figure 1b shows a curve of ·"(rass), where ·" =
trafine fraction of the synthesized powder (c) versus the
radius of the experimental assembly: 1) HE; 2) starting
K·. It can be seen that for both series of experiments
material; 3) compression shock wave. 2
in which rass < 12, the values obtained lie on the same
straight line:
" 2 "
insufficiently for subsequent ignition. However, we may
·" = Ä…II(rass - ²II), (5)
say that the shock-wave action  prepares the material
"
where Ä…" = 1.99 and ²II = 2.14.
II
for combustion, for example, due to partial decomposi-
Using (2) and (5), for ·" = 0 we have
tion of the oxide layer on the surfaces of metal particles.
2 " 2
rass = ²II = rliq(1 - Ä…I/Ä…II) + Ä…I/Ä…II. (6)
This layer of the powder is the first to interact with the
gas phase; therefore, in this case, synthesis of ultrafine
From the experimental data, we can estimate the
aluminum oxide is also possible.
value of the coefficient Ä…I. In the region rliq < rass
We convert to the dimensionless variables rliq, rsol, 2
< rsol, the quantity Ä…I is smaller than ·. For rass = 2.66
and rass, which are the ratio of the corresponding radii
(experiments with MAl = const), we have · = 0.008.
to the radius RHE. It is quite logically to assume that
Taking into account that the coefficients Ä…II and Ä…III
a certain yield of the ultrafine fraction corresponds to
are close to unity, we assume that Ä…I = 0.
each layer of the material. From geometrical considera- 2 "
From Eq. (6), we have rliq = ²II = 2.14. That is,
tions, it is easy to obtain the following relation for ·:
when RDX of bulk density is used as the HE, the radius
rass < rliq: · = Ä…I, (1)
of the aluminum powder sample that enters the liquid
state in the shock wave is equal to Rliq = 1.46RHE.
2
rliq < rass < rsol: · = (Ä…I(rliq - 1)
2 2
For rass > 12, the curve of ·"(rass) is also a straight
2 2 2 "
+ Ä…II(rass - rliq))/(rass - 1), (2) line but its slope changes: Ä…III = 1.24. Obviously, this
Physical Model of Explosive Synthesis of Ultrafine Aluminum Oxide 363
is due to a change of the metal oxidation regime. The
2
value of rsol determined from the intersection of the
two straight lines (see Fig. 1b) is equal to 11.48. Thus,
Rsol = 3.39RHE.
From Eqs. (2) and (5), we obtain
2
Ä…II = Ä…" (rass - 1)(MAl/MO2). (7)
II
From geometrical considerations, we have the following
relationship among the quantities MHE, MAl, and rass:
2
MAl = MHE(ÁAl/ÁHE)(rass - 1). (8)
In the parameter range rliq < rass < rsol from Eqs. (7)
and (8), we have
Ä…II = Ä…" (ÁHE/ÁAl)(MO /MHE)
II 2
"
= Ä…II(ÁHE/ÁAl)(MAl/MHE)(MO /MAl). (9)
2
It can be seen that for the layer bounded by the
radii Rliq and Rsol, the ultrafine fraction of the synthe-
sized powder is determined from the conditions of metal
oxidation during dispersion (MO /MAl), the intensity
2
of shock-wave action (ÁHE/ÁAl), and the velocities of
dispersion of the starting material (MHE/MAl). Obvi-
ously, the physical meaning of the coefficient Ä…" is the
II
probability of vapor-phase aluminum oxidation during
explosive synthesis.
Fig. 3. Yield of the ultrafine fraction of the syn-
For the range of parameters rass > rsol, similar ma-
thesized powder versus the relative radius of the
nipulations yield the relation
experimental assembly: (a) MHE = 10 (1), 15 (2),
"
and 20 g (3); (b) MAl = 50 (1), 60 (2), and
Ä…III = Ä…III(ÁHE/ÁAl)(MAl/MHE)(MO /MAl). (10)
2
70 g (3).
It can be seen that for the series of the experiments
with MHE = const, the values of Ä…II and Ä…III are con-
" 2 2
rass > rsol: · = (MO /MAl)(Ä…III(rass - rsol)
stant and equal to 0.713 and 0.446, respectively. For 2
the series of the experiments with MAl = const, the
" 2 2
+ Ä…II(rsol - rsol)). (16)
value of Ä…II depends on the amount of the HE used and
ranges from 0.096 to 0.713.
Figure 1a shows results of calculations by the above
We finally obtain the following relations for the
formulas. It is obvious that the model proposed agrees
yield of the ultrafine fraction of the synthesized pow-
well with the given experimental data.
der in both series of experiments:
Systems (11) (13) and (14) (16) predict the yield
for MHE = const,
of the disperse fraction depending on the conditions
of synthesis (MHE and MAl, Fig. 3). For the series
rass < rsol: · = 0, (11)
of experiments with MHE = const, the value of ·max
"
rsol < rass < rsol: · = Ä…II(ÁHE/ÁAl)(MO /MHE)
is achieved at rass = rsol, and for the experiments
2
with MAl = const, this value is achieved at rass > rsol.
2 2 2
× (rass - rsol)/(rass - 1), (12)
Moreover, the maximum possible yield of the ultrafine
fraction of the synthesized powder is reached at a value
cr
rass > rsol: · = (ÁHE/ÁAl)(MO /MHE)
2 of MHE that corresponds to the critical diameter of the
HE charge at which steady detonation is still possible.
" 2 2 " 2 2 2
× (Ä…III(rass - rsol) + Ä…II(rsol - rsol))/(rass - 1); (13)
To determine the dependence of the yield of the
ultrafine fraction of the synthesized powder on the HE
for MAl = const,
and aluminum masses, we substitute Eqs. (8) (10) into
rass < rsol: · = 0, (14)
(1) (3):
" 2 2
rsol < rass < rsol: · = Ä…II(MO /MAl)(rass - rsol), (15)
2
364 Bukaemskii
As can be seen from Fig. 4, the most favorable re-
gion for synthesis of the ultrafine material is in the range
cr
of small HE charges (of masses close to MHE). The rec-
ommended range of values is mAl = 0.1 0.5.
We note that the synthesis surface (see Fig. 4) is
constructed for a particular HE  RDX with a density
of 1.2 g/cm3. Special studies [4] showed that RDX is an
optimal HE for the synthesis of ultrafine materials. The
use of more powerful HE (cast and pressed TNT RDX
alloys) leads to an abrupt decrease in the yield of the
ultrafine fraction, which is obviously due to an increase
in the liquid-layer radius Rliq. The use of a less powerful
explosive (AN/TNT) is accompanied by an increase in
the yield of the ultrafine fraction but in this case, the
products are unstable.
The model itself does not impose restrictions on
the type of HE used. This dependence is obviously con-
Fig. 4. Synthesis surface · = ·(mHE, mAl)
tained in the coefficients Ä…II and Ä…III, determining the
shock-wave intensity and the acceleration velocity of the
layer of the starting material [formulas (9) and (10)]. To
find the functional dependence of Ä…II and Ä…III on the
rass < rliq: · = 0; (17)
type of HE, it is necessary to conduct numerous addi-
tional experiments, and this can be a subject for further
rliq < rass < rsol: · = A1/mHE - B1/mAl; (18)
research.
rass > rsol: · = A2/mHE - B2/mAl. (19)
Here mHE = MHE/MO , mAl = MAl/MO , A1 =
2 2
REFERENCES
" " 2
Ä…II(ÁHE/ÁAl), B1 = Ä…II(rliq - 1) and A2 =
" 2 2 " 2
Ä…III(ÁHE/ÁAl), and B2 = Ä…" (rsol - rliq) - Ä…III(rsol - 1).
II 1. I. D. Morokhov, L. I. Trusov, and V. N. Lapovok, Phys-
The synthesis surface of ultrafine aluminum ox-
ical Phenomena in Highly Disperse Media [in Russian],
ide · = ·(mHE, mAl) is given in Fig. 4. The projection
Énergoatomizdat, Moscow (1984).
of the surface onto the plane (mHE, mAl) is bounded by
2. A. G. Beloshapko, A. A. Bukaemskii, and A. M. Staver,
the following straight lines:
 Formation of ultradispersed compounds upon shock
2
wave loading of porous aluminum. Study of particles ob-
mAl = (ÁAl/ÁHE)mHE(rliq - 1), (20)
tained, Combust. Expl. Shock Waves, 26, No. 4, 457 460
(1990).
mAl = 1.125, (21)
3. P. F. Pokhil, A. F. Belyaev, et al., Combustion of Metal
cr
Powders in Reactive Media [in Russian], Nauka, Moscow
mHE = MHE/MO , (22)
2
(1972).
4. A. A. Bukaemskii,  Production of new ultrafine mate-
mHE = 0.33. (23)
rials and investigation of their properties, Candidate s
Equation (21) is obtained from the stoichiometric rela-
Dissertation in Phys.-Math. Sci., Krasnoyarsk (1995).
tion and the condition that the amount of oxygen is suf-
5. A. G. Beloshapko and A. A. Bukaemskii,  Shock adiabat
ficient for complete aluminum oxidation. Equation (22)
of highly porous aluminum, in: Treatment of Materi-
imposes limitations on the minimum permissible HE
als by Pulsed Loading (collected scientific papers), Design
charge, and Eq. (23) limits the maximum HE charge
and Technology Institute of High-Rate Hydrodynamics,
for the explosion chamber used. The synthesis sur-
Novosibirsk (1990), pp. 19 21.
face ·(mHE, mAl) is bounded on the plane (mHE, mAl)
by the straight line (20) because the ultrafine powder is
not formed from the first (liquid) metal layer.
From the synthesis surface constructed by the
model proposed, we can determine the yield of the ultra-
fine fraction of the synthesized powder under specified
experimental conditions (MHE, MAl, and MO ).
2