A study of the mechanochemical synthesis of TlCl nanoparticles by the method of dilution with the final product

Article abstract of DOI:10.1134/S0036024406020051

The kinetics of the solid-state mechanochemical synthesis of the nanosized product (TlCl) in the reaction 2NaCl + Tl₂SO₄ + zNa ₂SO₄ = (z + 1)Na₂SO₄ + 2TlCl was studied experimentlaly. The method used was based on the dilution of the initial mixture of powdered reagents (2NaCl + Tl₂SO₄) with another exchange reaction product (Na₂SO₄) at the optimum theoretically estimated z value, z = z= 11.25. Several special features of the development of this reaction were established. The parameters of the kinetic curve obtained for the mechanochemical synthesis of the desired product were compared with those of the kinetic curve determined theoretically for the model reaction KBr + TlCl + zKCl = (z + 1)KCl + TlBr with z = z ₁ ^* = 13.5. This allowed us to experimentally estimate the mass transfer coefficient in a mechanochemical reactor by mobile milling bodies. This estimate was obtained for the first time. The dynamics of changes in the size of desired product nanoparticles depending on the time of mechanochemical activation in an AGO-2 ball planetary mill was studied. Pleiades Publishing, Inc., 2006.

Full text of DOI:10.1134/S0036024406020051

ISSN 0036-0244, Russian Journal of Physical Chemistry, 2006, Vol. 80, No. 2, pp. 157–163. © Pleiades Publishing, Inc., 2006.
Original Russian Text © F.Kh. Urakaev, V.S. Shevchenko, 2006, published in Zhurnal Fizicheskoi Khimii, 2006, Vol. 80, No. 2, pp. 218–225.
CHEMICAL KINETICS
AND CATALYSIS
A Study of the Mechanochemical Synthesis of TlCl Nanoparticles
by the Method of Dilution with the Final Product
F. Kh. Urakaev1, 2 and V. S. Shevchenko1
1 Institute of Mineralogy and Petrography, Siberian Division, Russian Academy of Sciences,
Universitetskii pr. 3, Novosibirsk, 630090 Russia
E-mail: urakaev@uiggm.nsc.ru
2 Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
Received June 8, 2004
Abstract—The kinetics of the solid-state mechanochemical synthesis of the nanosized product (TlCl) in the
reaction 2NaCl + Tl2SO4 + zNa2SO4 = (z + 1)Na2SO4 + 2TlCl was studied experimentally. The method used
was based on the dilution of the initial mixture of powdered reagents (2NaCl + Tl2SO4) with another exchange
reaction product (Na2SO4) at the optimum theoretically estimated z value, z = z* = 11.25. Several special fea-
tures of the development of this reaction were established. The parameters of the kinetic curve obtained for the
mechanochemical synthesis of the desired product were compared with those of the kinetic curve determined the-
*
oretically for the model reaction KBr + TlCl + zKCl = (z + 1)KCl + TlBr with z = z1 = 13.5. This allowed us to
experimentally estimate the mass transfer coefficient in a mechanochemical reactor by mobile milling bodies. This
estimate was obtained for the first time. The dynamics of changes in the size of desired product nanoparticles
depending on the time of mechanochemical activation in an AGO-2 ball planetary mill was studied.
DOI: 10.1134/S0036024406020051
INTRODUCTION
in an AGO-2 planetary mill under the conditions
described for reaction (1a) [1]. This reaction is similar to
(1a) and satisfies the conditions of synthesizing nanopar-
ticles by the method of dilution with a final product
established in [1]. The solubilities of the initial mixture
components for reaction (1b) were (wt %) 21.925°C for
Na2SO4, 35.8720°C for NaCl, and 4.8720°C for TlCl.
It has been shown in [1] that performing the model
exchange reaction
KBr + TlCl + zKCl = (z + 1)KCl + TlBr
(1‡)
(∆rG° = –12.6 kJ/mol)
Note that exchange mechanochemical reactions in
stoichiometric mixtures of crystalline ionic salts occur
in planetary mills at very high rates. It was, for instance,
shown in [4] that the reaction NaNO3 + KCl = KNO3 +
NaCl was completed in an EI 2 × 150 planetary mill dur-
ing the time of mechanochemical activation τ ≈ 15 min.
It was therefore important to study the influence of the
dilution of the initial stoichiometric mixture of salts
with one of the final products on the rate of the
exchange reaction. Another object of study was the
mechanism of the reaction; that is, how and why do
exchange reactions develop under the conditions of
dilution with a final product? We were also interested in
the size of final reaction product particles formed and
its variations during time τ.
(here, z is the dilution parameter) in practice is impeded
by the presence of substances with low solubilities in
water both on the left- and right-hand sides of (1a)
(TlCl, 0.3525°C wt % and TlBr, 0.0525°C wt %, respec-
tively). Some results of the mechanochemical synthesis
of nanocrystalline powders with particle size ~10 nm in
a water-soluble salt (diluent) matrix were described in
[1, 2]; the final step of the process was washing the
nanoparticles obtained from the diluent. The use of
diluents at the stage of obtaining nanoparticles is nec-
essary to (1) prevent the ignition of combustion reac-
tions in mechanochemical reactors [2, 3] through
decreasing the heat effect of exchange reactions and
(2) decrease the mole (weight, volume) fraction of the
nanosized desired product to suppress the agglomera-
tion of nanoparticles. For this reason, the theoretical
results were checked by performing the reaction
Clearly, the addition of a diluent in large amounts, as
in reaction (1b) that we are considering, should not only
decelerate the exchange process but also completely
stop it after the exhaustion of initial reagent particle
contacts in a mixture under mechanical activation con-
ditions. We, however, did not observe this in experi-
ments [1, 2]. It follows that there is some mass transfer
2NaCl + Tl2SO4 + zNa2SO4
= (z + 1)Na2SO4 + 2TlCl
(∆rG° = –40 kJ/mol)
(1b)
157

158
URAKAEV, SHEVCHENKO
Table 1. Characteristics and salt sample weights for perform-
ing reaction (1b); hardness h is in Mohs (scale from 1 (talc) to
10 (diamond)) and Knoop (in parentheses, kg/mm2) [7] units
where Mi and ρi are the molecular weights and densities
of the reaction mixture components, and RM and RS are
the radii of octahedral and tetrahedral holes in the cubic
or hexagonal close packing of spheres of radius RB. As
is well known, RM = 0.414RB and RS = 0.225RB.
*
*
mi(z1 ) , g mi(z2 ) , g
h
M, g ρ, g/cm
Equation (7) from [1] and Eqs. (2) and (3) can be
used to find the initial weights of component samples
NaCl (i = 1)
58.44 2.165
Tl2SO4 (i = 2)
504.80 6.675
Na2SO4 (i = 3)
142.04 2.663
TlCl (i = 4)
2–2.5 (15.2)
– (–)
1.106
4.832
14.97
4.491
–
1.900
8.206
12.574
7.798
–
*
*
mi(z1 ) and mi(z2 ). The sum Σmi(z*), where i = 1, 2, 3,
gives the optimum weights of the batch mixture for per-
*
forming reaction (1b) in the AGO-2 mill, m(z1 ) =
*
20.77 g and m(z1 ) = 22.68 g. We also obtain
2.5–3 (–)
– (12.8)
*
*
'
*
mb/m(z1 ) = 4.68 and mb/m(z2 ) = 4.28, m m3 (z1 ) =
239.85 7.000
AGO-2 (steel)
'
*
'
1.33 g and m3 (z2 ) = 2.309 g, where m3 is the mass of
diluent Na2SO4 formed additionally in reaction (1b).
4–5 (~300)
–
7.86
According to the hardness h values for the reagents
(NaCl, halite, i = 1; Tl2SO4, thallium sulfate, i = 2) and
the diluent (Na2SO4, thenardite, i = 3), the optimum
dilution conditions for reaction (1b) correspond to the
Note: M , ρ , and m are the molecular weight, density, and weight
i
i
i
of the ith reaction mixture components, respectively.
*
z1 = 11.25 parameter [1], because the hardness of
mechanism (of mixing and transfer of activated parti-
cles) in mechanochemical reactors. Clearly, this mech-
anism can only be related to moving milling bodies,
that is, ball load and rotating planetary mill internal
walls. There should then be some dynamics of changes
in the size of final product particles, from subnanosized
to micron particles characteristic of reactions in stoichi-
ometric salt mixtures. Therefore, there should also exist
optimum time τ that ensures the occurrence of the
exchange reaction to completion and the obtainment of
nanosized desired product particles in the diluent
matrix. Longer mechanical activation should cause the
agglomeration of nanoparticles as a result of mass
transfer. Studies in this area are of timely interest; they
are performed for the first time.
metal sulfates is, as a rule [5–7], higher than that of
metal halides. We were, however, unable to find the
hardness of Tl2SO4 crystals in the literature, and there-
fore used both compositions listed in Table 1 and given
by (2) and (3). Reagent mixtures of kh. ch. (chemically
pure) and ch. (pure, Tl2SO4) grade corresponding to the
*
*
stoichiometric compositions with z = z1 and z = z2
were first ground and homogenized for 1 h in a Fritsch
Pulverisette mill equipped with steel fittings (a mortar
9.45 cm in diameter plus a ball 5.16 cm in diameter).
The size of particles in the initial mixtures was between
0.005 and 0.015 cm according to the optical micros-
copy data. This was much larger than the quasi-equilib-
rium particle size in mechanical activation equal to
1.25 × 10–4 cm [1]. The mechanical activation products
were studied by the standard method of X-ray powder
patterns [4, 8, 9] recorded on a DRON-4 diffractometer
(filtered CuKα radiation) at an angle 2θ sweep rate of
1 deg/min.
EXPERIMENTAL
Detailed conditions of performing exchange reac-
tion (1b) in anAGO-2 steel water-cooled two-drum ball
mill were (also see Table 1 and [1]): steel ball radius
R = 0.2 cm, number of balls N = 401, density of balls
ρ = 7.86 g/cm3, and overall weight of steel ball load
mb = 4πR3Nρ/3 = 97.1 g; τ* is the time necessary for
exchange reaction completion (by 99% or to α = 0.99)
in the AGO-2 mill, and f = 0.189 s–1 is the frequency at
which an arbitrarily selected pair of contacting reagent
particles gets under the shock action of milling bodies.
According to [1], the optimum dilution parameter z = z*
values for reaction (1b) are
The kinetics of reaction (1b) was studied by measur-
ing the conductivity of aqueous solutions of product
samples (1 g per 10 ml of deionized water). The only
product with a low solubility in water was TlCl. This
ensured a fairly high accuracy of measurements based
on a decrease in the conductivity of mechanical activa-
tion product samples with respect to the samples of the
initial homogenized samples. We thoroughly tested this
method by separately determining ammonium thiocy-
anate NH4CNS isomers, namely, pseudohalide and
thiocarbamide (NH2)2CS (molecular nonconducting
crystal), when they were simultaneously present in
solution [10, 11]. A unit for conductivity measurements
was made from a BM507 Impedance Meter, Tesla,
Brno, and a Pt Conductometric Bell type OK-9023
electrode, Radelkis Electrochemical Instrument,
3
3
3
*
z1 = ρ3[2ρ2M1RB – ρ1M2(RM + 2RS)]/ρ1ρ2M3
× (R3M + 2R3S) ≈ 11.25,
(2)
(3)
*
z2 = ρ3(2ρ2M1 – ρ1M2)
× [2R3B + 3(RM3 + 2RS3 )]/RB3 ρ1ρ2M3 ≈ 5.44,
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A STUDY OF THE MECHANOCHEMICAL SYNTHESIS OF TlCl NANOPARTICLES
159
0
1600
f = 0.189, s–1
3200
4800
6400 τ, s
0.8
0.4
fτ*(z*) = 363
fτ*(z*) = 1190
1
z = z* =z*
1
0
302
605
907
1210 fτ
Fig. 1. Degree of completion α(τ, z*) of reaction (1b) in an AGO-2 mill determined from changes in the conductivity of solutions
of mechanical activation products; τ is the activation time and fτ is the frequency at which reagent particles get into the region of
the shock action of milling bodies.
Budapest. The error of measurements was determined
from the following characteristics. The maximum pos-
sible content of TlCl in a sample (of weight m = 1 g)
was 4.491/20.77 ≈ 0.216 g, and that of Tl2SO4
8.206/20.77 ≈ 0.395 g. Water (1 ml) dissolves ~3.5 mg
TlCl and 48.7 mg Tl2SO4. Let us admit that the solubil-
ity of mechanically activated TlCl particles is appexi-
mately ten times lower than that of Tl2SO4, and 1 ml of
water dissolves ~5 mg TlCl (the solubility of mechani-
cally activated salts can exceed their tabulated equilib-
rium solubility [12]). It follows that, at a 1 g sample
weight, 10 ml of water dissolve ~50 mg TlCl and,
assuredly, all the other system components. For this
reason,
*
*
[1], namely, τ*(z1 ) ≈ 1900 s and τ*(z2 ) ≈ 4800 s, to be
sufficient for the completion of reaction (1b). We used
an obviously longer mechanical activation time, τ =
7200 s, in preliminary experiments. It was, however,
found that the reaction was complete (α ≈ 1) only for
the sample with z = z1 , whereas α for the sample with
z = z2 did not exceed ~0.4. The X-ray powder pattern
*
*
*
of the initial sample with z = z1 (Fig. 2a) is the super-
position of the reflections of the initial reagents (NaCl,
e.g., see PDF 77-2064 and Tl2SO4, PDF 7-188) and the
diluent (Na2SO4, PDF 74-2036). However note that a
reflection of the reaction product (TlCl, PDF 6-486) is
detectable already at the homogenization stage (Fig. 2a,
2θ ≈ 33°). The result of the mechanical activation of the
(1) the error in conductivity measurements solely
based on the conductivity of solutions of mechanically
activated samples would be 0.05/0.216 ≈ 23%;
*
sample with z = z1 is shown in Fig. 2b. We see that,
(2) calibration (conductivity curve measurements
for different initial reagent mixture compositions)
allows the error of measurements to be reduced to
(0.05 – 0.035)/0.216 ≈ 7%;
(3) the introduction of the correcting coefficient 2
(averaging over the composition or at reaction half-
completion) allows the accuracy of measurements to be
increased to ~4%.
The diameter of experimental kinetic curve symbols
for reaction (1b) (Fig. 1) corresponds to this error of
measurements.
The results were also roughly controlled using the
X-ray data (the dynamics [9] of the process or the
degree of reaction completion [4] was characterized by
relative changes in the intensities of the main crystal-
line phase reflections).
according to the X-ray data, the reaction (1b) was fully
completed. Subsequent experiments were therefore
*
made using samples with z = z1 = z*.
As the AGO-2 mill had two water-cooled drums
(cooling was essential to obtaining certain specific
results [13]), we expected that the experimental
mechanical activation kinetic curves for reaction (1b)
*
could be constructed using two m(z1 ) loads. The sam-
ples were taken in turn from each drum with interrupt-
ing mechanical activation every 300 s for no more than
1500 s. Sample weights were ~0.3 g, which was very
small compared with the weight of the substance to be
*
activated, m(z1 ) = 20.77 g, and, seemingly, their removal
could not affect the development of reaction (1b). A com-
parison of the degrees α of reaction completion for a
Experimental studies of the kinetics of reaction (1b) sample activated mechanically for 1800 s = 6 × 300 s
encounter certain difficulties. We expected mechanical with six interruptions (α ≈ 0.15) and a sample activated
activation times close to the calculated τ*(z*) values mechanically continuously (α ≈ 0.3), however, showed
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 80 No. 2 2006

160
URAKAEV, SHEVCHENKO
(‡)
1
2
3
4
(b)
2θ(CuKα)
40
35
30
25
20
Fig. 2. X-ray powder patterns of (a) initial reagent mixture for reaction (1b) with z = 11.25 homogenized for 1 h in a Fritsch Pul-
verisette mill and (b) homogenized mixture activated in an AGO-2 mill for 7200 s: (1) NaCl, (2) Tl SO , (3) Na SO , and (4) TlCl.
2
4
2
4
that pauses in mechanical activation [14] influenced the
kinetics of reaction (1b). Subsequent kinetic experi-
ments were therefore performed under continuous
fτ*(z )
fτ*(z )
*
1
*
1
*
fτ*(z1 )[1 – (1 – ξ)
]/(1 – ξ)
= 4.60/Ψ(z1 )Φ* ≈ 105.
Here, Ψ is the mass transfer coefficient, Φ* ≈ 0.65, and
(7)
*
*
mechanical activation conditions using 24 m(z1 ) sam-
ples. This corresponds to the number of experimental
values in Fig. 1.
*
it follows from α(τ = τ*, z1 ) = 0.99 that –ln[1 – α(τ*,
*
z1 )] = 4.60. These values were used in (7) to find
–1
RESULTS AND DISCUSSION
*
fτ*(z1 ) = 363. Using the known frequency f = 0.189 s
at which an arbitrarily selected pair of contacting
reagent particles experiences the shock action of mill-
The following equations describing the kinetic
parameters and kinetic curve of model reaction (1a) in
an AGO-2 mill were obtained in [1]:
*
ing bodies, we obtain τ*(z1 ) = 1920 s (the mechanical
activation time for reaction (1a) to be completed by
99%).
*
*
*
Ψ(z1 ) = N2B(z1 )/N3B(z1 ) = 1/14.8 = 0.0675, (4)
3
ξ(z1 ) = 3g(z1 )d*(z1 )s12(z1 )/4π(RMS + R3B)
In these equations, the only function insufficiently
grounded theoretically or in any experimental way is
Ψ(z), which is a dimensionless function of the dilution
parameter z taking into account mass transfer with
mobile balls in an activated batch mixture, which lines
the surface of milling bodies (balls and mill walls), and
the ensuing formation of new contacts between reagent
*
*
*
*
(5)
(6)
= 0.000697,
*
–ln[1 – α(τ, z1 )]
fτ
fτ
*
= Ψ(z1 )Φ* fτ[1 – (1 – ξ) ]/(1 – ξ) ,
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A STUDY OF THE MECHANOCHEMICAL SYNTHESIS OF TlCl NANOPARTICLES
161
Table 2. Calculations of the mass transfer coefficient Ψ(τ)
as a function of mechanical activation time τ
particles. As far as we know, no works concerned with
mass transfer in mechanochemical reactors have been
published. Clearly, if the kinetic curve is known from
experiment, the Ψ(z*) function can be found from (6) at
any particular α = α' value. Moreover, as distinct from
[1], we can also determine the time dependence Ψ(z*,
τ), that is, the dependence of Ψ(z*) on the time of
mechanical activation åÄ(τ).
τ, s
fτ
α(τ)
Ψ(τ) × 103
900
1200
1500
2100
2400
2700
3000
3300
3900
4200
4800
170
227
283
397
454
510
567
624
737
794
907
0.10
0.16
0.23
0.39
0.47
0.55
0.66
0.72
0.83
0.87
0.93
7.6
6.9
6.5
6.0
5.8
5.6
6.0
0.45
0.55
5.4
5.1
*
Suppose (see (2) and (5)) that ξ(z1 ) ≈ ξ(z*), where
the ξ(z*) parameter is the fraction of the removed vol-
ume V*/V at the shock-frictional contact of a distin-
guished pair of reagent particles, the total volume of the
reagents being V [1], for reaction (1b) that we study.
*
The difference of the ξ(z1 ) and ξ(z*) values is only
caused by an insignificant difference of the densities ρ
and compliances θ = 4(1 – ν2)/E of the reagents in reac-
tions (1a) and (1b); here, E is theYoung modulus and ν
is the Poisson coefficient. Only ρ and θ are different in
*
calculations of V* = d*(z*)s12(z*) [1], where d*(z1 ) is
over this region [Ψ(τ = 300 s) = 0.0065 ≈ Ψ(τ = 600 s) =
0.0058] is smaller than Ψ(τ = 900 s) ≈ 0.0076 (Table 2).
Later, the self-lining and mass transfer by milling bod-
ies should occur with alternating intensities, but this
tendency evens out as the time of mechanical activation
increases. The Ψ(τ) function should therefore tend to
some equilibrium value, which is, unfortunately, diffi-
cult to determine theoretically. We recommend using
Ψeq(τ) = Ψ[α(τeq) = 0.5] ≈ 0.0057 as such a value.
*
the thickness of reaction volume V* and s12(z1 ) is the
area of the shock-frictional contact for the selected pair
of particles.
This allows us (Fig. 1) to estimate the mass transfer
coefficient during mechanical activation Ψ(z*) experi-
mentally for the first time. Indeed, conductometric
measurements show that, after mechanical activation
for approximately τ = τ* = 6300 s, the reaction is com-
plete, and mechanical activation ceases to affect the
results of measurements. Let us use the τ* time of
mechanical activation as an indicator of reaction (1b)
completion by 99%. The following equations and esti-
mate for the Ψ(z*, τ) function then follow from (6)
and (7):
Calculations Based on the X-ray Data
The X-ray powder patterns of the samples that we
used to estimate the kinetics of mechanical activation in
reaction (1b) and the size of coherent scattering D and
strain Y regions in the crystal lattice of the desired nano-
sized product, thallium chloride TlCl, are shown in Fig. 3.
Ψ(z*, τ*) ≈ 7.1(1 – ξ)fτ*(z*)/ fτ*(z*)
It follows from Fig. 1 that α(τ = 2100 s)/α(τ =
1800 s) ≈ 0.31/0.23 ≈ 1.3. For the relative intensities I
of reflections from the TlCl (110) planes (2θ = 32.9°,
d110 = 0.272 nm) and NaCl (200) planes (2θ = 31.7°,
d200 = 0.282 nm), we find (Fig. 3) I(TlCl)/I(NaCl) ≈
1.9 = I(τ = 1800 s) (Fig. 3a) and I(τ = 2100 s) ≈ 2.4
(Fig. 3b). It follows that I(τ = 2100 s)/I(τ = 1800 s) ≈
2.4/1.9 ≈ α(τ = 2100 s)/α(τ = 1800 s), e.g., see [4, 9].
However, an analysis of the kinetic curve α(τ, z*)
shown in Fig. 1 on the basis of the X-ray data is not
that unambiguous. Indeed, the overlap of reflections
of the initial and final components over the 2θ range
studied considerably increases the discrepancy
between the changes in α(τ, z*) determined by the
conductivity and X-ray methods at mechanical activa-
tion times 1800 s < τ < 2100 s. Moreover, the overlap
of reflections of the initial reagents and final products at
(8)
× [1 – (1 – ξ)fτ*(z*)] = 0.0046,
Ψ(τ)
(9)
= –ln[1 – α(τ)](1 – ξ)fτ/Φ* fτ[1 – (1 – ξ)fτ].
According to (8), Ψ(z*, τ*) ≈ 0.0046 at the final stage
of reaction (1b).
Equation (9) is obviously nonlinear. It is therefore
worthwhile to additionally study the Ψ(τ) function. The
Ψ(τ) values calculated over the range of 1 – α(τ) varia-
tions from 0.90 to 0.07 are listed in Table 2. The results
show that the Ψ(τ) function is in all probability
described by a damped sine function. In addition, this
function experiences contraction as time passes.
Such a behavior of Ψ(τ) is easy to explain. Initially short mechanical activation times is very strong and
(during the first 600 s of batch mixture activation), shifts the I(NaCl) maximum to the diffraction angle
grinding and self-lining of milling bodies (the forma- 2θ ≈ 32°. The reflection that does not overlap with the
tion of a compact layer of mechanically activated parti- other reflections of reaction components is that from
cles on the surface of milling bodies) occurs. For this the (111) TlCl plane (Fig. 3). We predominantly used
reason, the mean mass transfer coefficient (≈0.0061) this circumstance.
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 80 No. 2 2006

162
URAKAEV, SHEVCHENKO
(f)
(‡)
(b)
(c)
(d)
(e)
(g)
2θ (CuKα)
2θ (CuKα)
40
37
34
31
28
25
21
40
37
34
31
28
25
21
Fig. 3. Dependences of the dynamics of reaction (1b) and changes in the size of coherent scattering regions on the duration of
mechanical activation τ = (a) 1800 and (b) 2100 s according to the X-ray data. Shown in insets are reflections from the (111) TlCl
plane (2θ = 40.65°) at τ = (c) 600, (d) 900, (e) 3600, (f) 5400, and (g) 300 s.
The sizes D of particles (coherent scattering Gauss equations, respectively. This approximation in
regions) and Y of lattice microdeformations were calcu-
lated from the X-ray data by the well-known methods
[15–17], also see Table 3. These were:
addition uses the integral intensity Bi of the line.
The use of the equation Bcosθ = (0.9Λ/D) + Ysinθ
[15], where Λ = 0.5418 nm is the wavelength of CuKα
radiation, was impeded by the overlap of the (110)
reflections with the corresponding reflections of
Na2SO4 (compare Figs. 2 and 3). On the other hand, the
separation of the D and Y effects using the (222) and
(444) second order reflections was not unambiguous
because of their very low intensities (the reasons for
this may be high dispersity, distortions of the material
and/or its multiphase character, and texture-caused
intensity redistribution [18]). The use of all the methods
described above is as a rule [16] illustrated by unproc-
essed X-ray spectra (reproduced directly from original
(1) The Scherrer equation, which uses the width Bs
at half-height of the X-ray reflection from the (111)
TlCl plane of mechanically activated samples, and the
Warren equation, which uses the standard instrumental
broadening Bst of X-ray reflections; we employed the
half-width of the (222) line of the initial Na2SO4 pow-
der (2θ = 38.6°, d222 = 0.233 nm, also see Fig. 2), whose
2θ and dhkl parameters were close to those of the (111)
TlCl line.
(2) The approximation based on one Voigt line [16],
which assumes that the contributions to the line profile
caused by D and Y are described by the Cauchy and X-ray patterns) such as shown in Figs. 2 and 3.
Table 3. Sizes of coherent scattering regions and TlCl lattice deformations as functions of activation time τ
τ, s
300
600
900
1200
1800
2100
3600
5400
7200
For the (111) reflection by the Scherrer D = 0.9Λ/BcosΘ and Warren B2 = Bs2 – Bs2t equations
B, rad
D, nm
0.0056
26
0.0071
21
0.0078
19
0.0048
31
0.0089
17
0.0073
20
0.0090
16
0.0110
13
0.0029
50
According to Voigt or from the integral intensity of the (111) reflection
Bi, rad
D, nm
Y, %
0.009
47
0.011
28
0.012
24
0.011
30
0.013
34
0.010
48
0.012
80
0.014
80
0.006
85
0.0025
0.0026
0.0028
0.0031
0.0046
0.0038
0.0056
0.0075
0.0077
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 80 No. 2 2006

A STUDY OF THE MECHANOCHEMICAL SYNTHESIS OF TlCl NANOPARTICLES
163
2. F. Miani and F. Maurigh, Encyclopedia of Nanoscience
and Nanotechnology (M. Dekker, New York, 2004).
3. F. Kh. Urakaev, L. Takacs, V. S. Shevchenko, et al.,
Zh. Fiz. Khim. 76 (6), 1052 (2002) [Russ. J. Phys.
Chem. 76 (6), 939 (2002)].
As concerns Table 3, the following comment should
be made (also see [19]). The too low and nonmonoton-
ically changing crystallite size calculated by the Scher-
rer equation without including the effect of microdefor-
mations Y on reflection (111) broadening cannot be
considered correct. The inclusion of Y effects radically
changes the character of D variations toward what can
be expected. At the initial stage of mechanical activa-
tion (during the first 600 s), shock-friction contacts
between reagent particles in the initial mixture predom-
inantly work [1], and the size of coherent scattering
regions is therefore large and close to that characteristic
of traditional mechanochemical reactions [14, 15, 20,
21]. New reagent contacts are formed and the diluent
(Na2SO4) begins to act as τ increases; this decreases the
size of coherent scattering regions. A further increase in
τ should increase the size of coherent scattering regions
because of mass transfer (the formation of contacts
between nanosized particles of the desired reaction
product, TlCl). The D(τ) function therefore has a mini-
mum at τ ≈ 900 s and tends to continuously increase at
τ > 900 s. This also occurs after reaction (1b) is for-
mally completed, at τ > 6300 s.
4. F. Kh. Urakaev and E. G. Avvakumov, Izv. Sib. Otd.
Akad. Nauk SSSR, Ser. Khim. 7 (3), 10 (1978).
5. Mining Encyclopedia, Ed. by E. A. Kozlovskii
(Sovetskaya Entsiklopediya, Moscow, 1984–1991),
Vols. 1–5 [in Russian].
6. L. G. Berry, B. Mason, and R. V. Dietrich, Mineralogy:
Concepts, Descriptions, Determinations, 2nd ed. (Free-
man, San Francisco, 1983; Mir, Moscow, 1987).
7. E. M. Voronkova, B. N. Grechushnikov, G. I. Distler,
et al., Optical Materials for Infrared Technique:
A Handbook (Nauka, Moscow, 1965) [in Russian].
8. F. Kh. Urakaev, V. S. Shevchenko, and T. A. Ketegenov,
Zh. Fiz. Khim. 78 (3), 551 (2004) [Russ. J. Phys. Chem.
78 (3), 480 (2004)].
9. P. N. Kuznetsov, L. I. Kuznetsova, and A. M. Zhizhaev,
Khim. Interesakh Ustoich. Razvit. 10 (1–2), 135 (2002).
10. F. Kh. Urakaev and L. Sh. Bazarov, Zh. Neorg. Khim. 46
(1), 54 (2001) [Russ. J. Inorg. Chem. 46 (1), 47 (2001)].
To summarize, our experimental study of reac-
tion (1b) allowed us to determine the following charac-
teristics of mechanical activation and the preparation of
nanosized systems by the method of dilution with a
final product: the theoretical estimate of the molar dilu-
11. F. Kh. Urakaev, L. Sh. Bazarov, V. S. Shevchenko, et al.,
Koks Khim., No. 8, 26 (2001).
12. F. Kh. Urakaev, E. L. Gol’dberg, and A. F. Eremin, Izv.
Sib. Otd. Akad. Nauk SSSR, Ser. Khim. 17 (6), 22
(1985).
13. M. V. Lukhanin, E. G. Avakumov, and S. I. Pavlenko,
Ogneupory Tekhnicheskaya Keramika, No. 1, 32 (2004).
14. F. Kh. Urakaev, L. Takacs, V. Soika, et al., Khim. Intere-
sakh Ustoich. Razvit. 10 (1–2), 255 (2002).
15. C. Suryanarayana, Prog. Mater. Sci. 46 (1–2), 1 (2001).
*
tion parameter z = z1 = z* = 11.25 was substantiated,
the kinetic curve for the reaction was obtained, the mass
transfer coefficient with mobile milling bodies (ball
load) in an AGO-2 mill was determined, and the size of
coherent scattering regions and crystal lattice microde-
formations in the desired nanosized product TlCl was
calculated.
16. N. S. Belova and A. A. Rempel’, Neorg. Mater. 40 (1),
7 (2004) [Inorg. Mater. 40 (1), 3 (2004)].
17. Th. H. de Keijser, J. I. Langford, E. J. Mittemeijer, et al.,
J. Appl. Crystallogr. 15, 308 (1982).
ACKNOWLEDGMENTS
18. A. N. Ivanov, T. A. Sviridova, E. V. Shelekhov, et al.,
Poverkhnost: Rentgen., Sinkhrotron. Neitron. Issledo-
vaniya, No. 2, 47 (2001).
19. P. N. Kuznetsov, L. I. Kuznetsova, A. M. Zhizhaev, et al.,
Khim. Interesakh Ustoich. Razvit. 12 (2), 193 (2004).
This work was financially supported by the Russian
Foundation for Basic Research (project nos. 05-05-
64572 and 03-03-32271) and the Siberian Division of
the Russian Academy of Sciences (Integration Grant).
20. F. Kh. Urakaev and V. V. Boldyrev, Neorg. Mater. 35 (4),
495 (1999) [Inorg. Mater. 35 (4), 405 (1999)].
REFERENCES
1. F. Kh. Urakaev andV. V. Boldyrev, Zh. Fiz. Khim. 79 (4), 21. F. Kh. Urakaev and V. V. Boldyrev, Powder Technol. 107
651 (2005) [Russ. J. Phys. Chem. 79 (4), 563 (2005)]. (1–2), 93 (2000).
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 80 No. 2 2006