Thermal decomposition of tin tetrachloride based on Cl- and Sn-concentration measurements

Article abstract of DOI:10.1021/jp993985j

The kinetics of the thermal decomposition of tin tetrachloride are studied experimentally and theoretically. Ab initio MO calculations showed that SnCl₄ decomposed into Sn(³P) and four chlorine atoms through four subsequent Sn-Cl bond dissociation channels. Two sets of kinetic experiments are performed using a shock tube equipped with atomic resonance absorption spectroscopy (ARAS). The Rice-Ramsperger-Kassel-Marcus (RRKM) calculations including variational transition state theory are applied. Structural parameters and vibrational frequencies of the reactants and transition states required for the RRKM calculations are obtained from the ab initio MO calculations.

Full text of DOI:10.1021/jp993985j

5246
J. Phys. Chem. A 2000, 104, 5246-5253
Thermal Decomposition of Tin Tetrachloride Based on Cl- and Sn-Concentration
Measurements
Kazuo Takahashi, Andreas Kunz, Dirk Woiki, and Paul Roth*
Institut fu¨r Verbrennung und Gasdynamik, Gerhard-Mercator-UniVersita¨t Duisburg, 47048 Duisburg, Germany
ReceiVed: NoVember 10, 1999; In Final Form: March 7, 2000
The kinetics of the thermal decomposition of tin tetrachloride has been studied experimentally and theoretically.
Ab initio MO calculations showed that SnCl4 finally decomposed into Sn(3P) and four chlorine atoms through
four subsequent Sn-Cl bond dissociation channels. Two sets of kinetic experiments were performed using a
shock tube equipped with atomic resonance absorption spectroscopy (ARAS). Chlorine atoms were first
measured over the temperature range of 1250-1700 K and the total density range of 1.7 × 1018 to 8.9 × 1018
molecules cm-3. The rate coefficient for the initial reaction step, SnCl4 (+M) f SnCl3(2A1) + Cl (+M) (eq
1a), was found to be in the falloff region fairly close to the low-pressure limit under the present conditions.
The second-order rate coefficient based on the Cl-atom measurements was determined to be k1a2nd ) 10-5.37(0.62
exp[-(285 ( 18) kJ mol-1/RT] cm3 molecule-1 s-1 (error limits at the 2 standard deviation level). The second
group of experiments was carried out by detecting tin atoms over the temperature range of 2250-2950 K and
at a total density of 3.2 × 1018 molecules cm-3. The second-order rate coefficients for the subsequent reaction
steps: SnCl2(1A1) (+M) f SnCl(2Π) + Cl (+M) (eq 3a) and SnCl(2Π) (+M) f Sn(3P) + Cl (+M) (eq 4a)
2nd
2nd
were obtained to be k3a ) 10-8.36(0.86 exp[-(310 ( 42) kJ mol-1/RT] cm3 molecule-1 s-1 and k4a
)
10-9.50(0.78 exp[-(265 ( 40) kJ mol-1/RT] cm3 molecule-1 s-1, respectively. The Rice-Ramsperger-Kassel-
Marcus (RRKM) calculations including variational transition state theory were also applied for reactions 1a
and 3a. Structural parameters and vibrational frequencies of the reactants and transition states required for
the RRKM calculations were obtained from the ab initio MO calculations. Energy barriers of the reactions,
E0’s, which are the most sensitive parameters in the calculations, were adjusted until the RRKM rate coefficients
matched the observed ones. These fittings yielded E0,1a ) 326 kJ mol-1 for reaction 1a and E0,3a ) 368 kJ
mol-1 for reaction 3a, in good agreement with the Sn-Cl bond dissociation energies of SnCl4 and SnCl2,
demonstrating that the experimental data for k1a and k3a were theoretically reasonable and acceptable.
Introduction
SnO2 synthesis, e.g., Sn(3P) + O2,4-7 Sn(3P) + N2O,4-6,8 Sn-
(3P) + CO2,4,7 Sn(3P) + hydrocarbons,4 were investigated. As
Tin dioxide (SnO2) is an industrially important material with
the characteristics of high electric conductivity and high
transmissivity.1-3 Its applications range from use as a transparent
electrode in photovoltaic cells, and imaging and display devices,
to use as an energy-conserving coating on windows and light
bulbs. Tin dioxide is also used as a gas sensor, because its
surface resistance is sensitive to gas adsorption. The process
used for SnO2 synthesis depends on the technical application.
When thin films with uniform thickness or fine particles with
uniform size are needed, SnO2 is often produced in high-
temperature gas-phase processes, e.g., chemical vapor deposition
(CVD), high-temperature flow reactors, and flames. However,
the optimum reaction conditions to control these gas-phase
processes still have to be found empirically. To solve this
problem, the knowledge about reaction mechanism and rate
coefficients during the SnO2 synthesis are necessary.
for the Sn precursor reactions, the thermal decompositions of
Sn(CH3)4 and (CH3)2SnCl2 were first studied by Price et al.9,10
in a toluene carrier flow system. The rate coefficients for the
reactions Sn(CH3)4 f Sn(CH3)3 + CH3 and (CH3)2SnCl2 f
CH3SnCl2 + CH3 were determined to be k1st ) 1015.7 exp[-
270 kJ mol-1/RT] and 1013.5 exp[-235 kJ mol-1/RT] s-1 over
the temperature ranges of 803-941 K and 827-961 K,
respectively. In other works,11-13 the kinetics of the Sn(CH3)4
thermal decomposition was reported. However, no kinetic data
for the thermal decomposition of tin tetrachloride, which is the
most important Sn precursor, are published.
In our laboratory, the gas-phase reactions of some metal
chlorides used as Si and Ti precursors were previously
studied.14-16 This series of work is now continued by the thermal
decomposition of SnCl4, which is regarded as a first step to
clarify the reaction mechanism of the SnO2 synthesis from
SnCl4. Possible channels for the thermal decomposition of SnCl4
were theoretically examined by ab initio MO calculations.
Furthermore, two sets of kinetic experiments were performed
using a shock tube equipped with atomic resonance absorption
spectroscopy (ARAS). Chlorine atoms were first measured in
relatively low-temperature experiments to study the kinetics of
the initial reaction step:
Normally, chlorides and organic compounds such as tin
tetrachloride, tetramethyltin, and dimethyldichlorotin are used
as Sn precursors for the gas-phase synthesis. A few kinetic
studies on the reactions of Sn precursors were previously
reported, although numerous reactions of electronically ground-
state tin atoms, which are an intermediate species during the
* Corresponding author. Phone: +49-203-379 3417. Fax: +49-203-
379 3087. E-mail: roth@ivg.uni-duisburg.de.
10.1021/jp993985j CCC: $19.00 © 2000 American Chemical Society
Published on Web 05/13/2000

Thermal Decomposition of Tin Tetrachloride
J. Phys. Chem. A, Vol. 104, No. 22, 2000 5247
SnCl4 (+M) f SnCl3(2A1) + Cl (+M)
(1a)
The second group of experiments was carried out at higher
temperatures by detecting tin atoms to follow the subsequent
reaction steps:
SnCl2(1A1) (+M) f SnCl(2Π) + Cl (+M)
SnCl(2Π) (+M) f Sn(3P) + Cl (+M)
(3a)
(4a)
The Rice-Ramsperger-Kassel-Marcus (RRKM) calculations
including variational transition state theory were also applied
to confirm these experimental results.
Experimental Section
Shock Tube. All experiments were performed behind re-
flected shock waves in a stainless steel shock tube with an
internal diameter of 79 mm. This shock tube consists of a 3.5
m long driver section and a 5.7 m long test section which are
separated by an aluminum diaphragm. The test section was
evacuated by a turbomolecular pump to pressures down to 5 ×
10-7 mbar. Residual gases in the shock tube were analyzed by
a quadrupole mass spectrometer and were found to be practically
free of hydrocarbons. To measure the incident shock velocity,
three gold-resistance-type transducers were placed in the shock
tube wall at 15 cm intervals near the end of the test section.
Temperature and pressure of shock-heated test gas were
calculated from the measured incident shock velocity using
standard methods. Further details of the shock-tube apparatus
are given elsewhere.17,18
Figure 1. Calibration curves for Cl atoms at 134.7 nm (upper part)
and Sn atoms 286.3 nm (lower part). The solid lines are least-squares
fits to the data (see text).
fragments within 10 ns at 2800 K. Therefore, calibration curves
for both diagnostics can be obtained by relating measured
steady-state absorptions to known initial concentrations of CH3-
Cl and Sn(CH3)4. The calibration results are summarized in the
upper part of Figure 1 for Cl atoms and in the lower part for Sn
atoms. The sensitivities are almost equal between the Cl and
Sn atom detection systems. In both cases, the Lambert-Beer
law cannot be applied, due to self-absorption or self-reversal.
Assuming the modified Lambert-Beer equation
Optical System and Calibration. Time-resolved concentra-
tions of electronically ground-state Cl (3p5 2P03/2) and Sn (5p2
3P0) atoms were monitored by atomic resonance absorption
spectroscopy (ARAS). As a light source of Cl atom ARAS, a
microwave discharge lamp (35 W) was used, in which a mixture
of 0.1% Cl2/He was flowing at a pressure of 5 mbar. The
resonant radiation from the lamp passed through two LiF
windows (1 mm thickness) mounted on the shock tube walls at
a position of 1.4 cm apart from the end plate. The transmitted
light was isolated by a 1 m vacuum-UV monochromator
(McPherson GCA-225), which was evacuated to a pressure less
than 2 × 10-7 mbar, and detected by a solar-blind photomul-
tiplier (EMR 542G-08-18). Perpendicular to the Cl atom
detection system, a Sn hollow cathode lamp (Hamamatsu
Photonics L233-50NQ) operated by a pulsed power source, a
25 cm monochromator (Jarrell Ash), and a UV-vis photomul-
tiplier (Hamamatsu Photonics 1P28) were arranged to measure
Sn atom absorption. This crossing optical setup enables us to
monitor Cl and Sn atoms simultaneously. The wavelengths of
the Cl and Sn resonance lines used in the present study were
I
1 - ) 1 - exp{-σ0l[X]γ}
I0
(l is optical path length ()7.9 cm)) the two parameters σ0 and
γ were determined for both atoms by least-squares methods as
follows:
σ0(Cl) ) 10-10.60(0.40 cm1.25 atom-0.75
γ(Cl) ) 0.753 ( 0.031 at 134.7 nm
,
σ0(Sn) ) 10-9.78(0.47 cm1.08 atom-0.69
,
134.7 nm (4s2P3/2 r 3p5 2P03/2) and 286.3 nm (6s3P0 r 5p2
1
γ(Sn) ) 0.694 ( 0.038 at 286.3 nm
3P0), because their sensitivities were the highest of all Cl and
Sn resonance lines.
The fitting curves calculated from these expressions approximate
the experimental data very well; see solid lines in Figure 1.
Measurements and Gases. Two sets of kinetic experiments
were performed in the present study. Chlorine atoms were first
measured at relatively low temperatures to study the kinetics
of the initial reaction step of the SnCl4 thermal decomposition.
The second group of experiments was carried out at higher
temperatures by detecting tin atoms to follow the subsequent
reaction steps. Details of the experimental conditions used are
summarized in Table 1.
Calibration experiments were performed behind reflected
shock waves by using 0.5-4 ppm of CH3Cl/Ar mixtures at
2500-3000 K and 0.05-5 ppm Sn(CH3)4/Ar mixtures at 2800-
3800 K for Cl- and Sn atom ARAS, respectively. Methyl
chloride completely decomposes into CH3 and Cl within 700
µs at 1800 K.19 On the other hand, tetramethyltin finally
decomposes into Sn(3P) and four methyl radicals at high
temperatures through the rate-determining initial step Sn(CH3)4
f Sn(CH3)3 + CH3 and three subsequent fast Sn-C bond
dissociation channels. From the kinetic data,20 99.8% of Sn-
(CH3)4 is calculated to decompose into Sn(3P) and the other
Test gas mixtures of SnCl4 highly diluted in argon were
prepared manometrically in a stainless steel storage cylinder.

5248 J. Phys. Chem. A, Vol. 104, No. 22, 2000
Takahashi et al.
TABLE 1: Experimental Conditions
mole fraction of SnCl4
experiment
Cl atom
measurements
Sn atom
measurements
diluted in Ar/ppm
temp/K
total density/1018 molecules cm-3
reaction
0.2-9
1250-1700
1.7 ( 0.2, 8.9 ( 0.9
initial step in SnCl4
thermal decomposition
subsequent decomposition
steps
0.7-4
2250-2950
3.2 ( 0.5
TABLE 2: Enthalpies of Possible Reaction Channels during
SnCl4 Thermal Decomposition Calculated at MP2/3-21G(d)
Level
reaction channel
∆H°(0 K)/kJ mol-1
SnCl4(+M)
f SnCl3(2A1) + Cl (+M) (1a)
f SnCl2(1A1) + Cl2 (+M) (1b)
362
397
206
432
415
380
680
344
470
SnCl3(2A1)(+M) f SnCl2(1A1) + Cl (+M) (2a)
f SnCl2(3B1) + Cl (+M) (2b)
f SnCl(2Π) + Cl2 (+M) (2c)
SnCl2(2A1)(+M) f SnCl(2Π) + Cl (+M) (3a)
f Sn(1D) + Cl2 (+M) (3b)
SnCl(2Π)(+M)
f Sn(3P) + Cl (+M) (4a)
f Sn(1D) + Cl (+M) (4b)
Purities of the samples used were >99.999% for argon and
>99% for SnCl4. Tin tetrachloride, which is liquid at standard
conditions, was carefully injected and evaporated in a separate
stainless steel vessel.
There was an experimental difficulty that a small amount of
SnCl4 disappeared in the stainless steel storage cylinder due to
adsorption of SnCl4 at the walls. Because of this phenomenon,
the initial concentration of SnCl4 could not be determined
precisely from the partial pressure of SnCl4 introduced. So, just
before every kinetic experiment, a Cl atom measurement was
carried out at high temperatures above 4000 K, in order to check
the gas-phase mole fraction of SnCl4. Chlorine atoms rapidly
increased to reach a constant value immediately after the arrival
of a reflected shock wave. At T > 4000 K, SnCl4 completely
decomposes into Sn(3P) and four chlorine atoms regardless of
reaction pathway or rate. The mole fraction of SnCl4 in the
mixture, X(SnCl4), can be determined by the following formula:
Figure 2. Typical measured concentration profiles of Cl (upper part)
and Sn atoms (lower part) in a SnCl4-Ar mixture heated to a
temperature of 2273 K. The white lines denote profiles calculated by
using the simplified reaction model consisting of reactions 1a, 2a, 3a,
and 4a.
[Cl]ss
[M]
1
4
Additionally, reaction 1b has energy barriers not only for the
forward but also for the reverse directions,24 because reaction
1b proceeds via a three-centered transition state configuration,
resulting in a forward barrier of reaction 1b being higher than
the reaction enthalpy. From this consideration, it can be
concluded that reaction 1b is negligible as the initial step of
the SnCl4 pyrolysis even if the accuracies of the calculated
reaction enthalpies are not so high. Furthermore, the calculations
show that the other Sn-Cl bond dissociation channels (2a), (3a),
and (4a) are the energetically most favorable ones in the
subsequent decomposition pathways so that SnCl4 finally
decomposes into Sn(3P) and four chlorine atoms.
Kinetics of the Initial Decomposition Step. Figure 2 shows
concentration profiles of Cl and Sn atoms in a SnCl4-Ar
mixture at the temperature corresponding to the lower limit of
Sn atom formation. At this temperature, the formation of
chlorine atoms can be divided into two stages: fast Cl atom
formation within 30 µs followed by a relatively slow further
increase. Such behavior can be understood as the rapid formation
of SnCl2(1A1) and two chlorine atoms through reactions 1a and
2a, because the measured Cl atom concentration reaches twice
the initial concentration of SnCl4, and Sn atoms are not detected.
During the subsequent time, reactions 3a and 4a are initiated to
produce both Cl and Sn atoms slowly. This suggestion is
confirmed by the ab initio calculation. As shown in Table 2,
the barrier of reaction 2a is relatively low so that reaction 2a
immediately follows reaction 1a, leading to the formation of
X(SnCl4) )
where [Cl]ss and [M] are the Cl atom concentration at steady
state obtained from the ARAS signal and the total concentration
behind the reflected shock wave, respectively. The adsorption
of SnCl4 on stainless steel surfaces is not very fast. Therefore,
the adsorption on the inner walls of the shock tube during test
gas introduction and shock generation is negligible.
Results and Discussion
Theoretical Examination of Reaction Channels. To exam-
ine possible channels for the thermal decomposition of SnCl4,
thermochemical data for the reactants and products are neces-
sary, which are mostly not available. So, ab initio MO
calculations were performed using the Gaussian 94 program.21
Enthalpies of the possible reaction channels calculated at MP2/
3-21G(d) level are summarized in Table 2. The comparison with
some experimental data22,23 confirms that the MP2/3-21G(d)
calculations systematically overestimate these reaction enthalpies
by 5 to 15%, because of utilizing small basis sets. As found
from Table 2, the reaction enthalpy of Cl formation by reaction
1a is 35 kJ mol-1 lower than that of Cl2 elimination by reaction
1b. This difference results in a ratio of k1b/k1a ) 0.04-0.08 in
the present experimental temperature range, assuming that the
energy barriers of reactions 1a and 1b are equal to their reaction
enthalpies and that both preexponential factors are identical.

Thermal Decomposition of Tin Tetrachloride
J. Phys. Chem. A, Vol. 104, No. 22, 2000 5249
Figure 4. Arrhenius plot of the first-order rate coefficient for reaction
1a. (O) and (b) denote the results measured at [M] ) (1.7 ( 0.2) ×
1018 molecules cm-3 and [M] ) (8.9 ( 0.9) × 1018 molecules cm-3
E0,1a ) 326 kJ mol-1 (see text).
,
respectively. The solid lines show the RRKM results calculated with
Figure 3. Typical measured concentration profiles of Cl (upper part)
and Sn atoms (lower part) in a SnCl4-Ar mixture heated to a
temperature of 1344 K. The white and the two black lines in the upper
part denote profiles calculated by varying the rate coefficient for reaction
1a. Line A being identical with the horizontal axis is the Cl atom
concentration calculated with reactions 1b and S1 (see text).
SnCl2(1A1) + 2Cl from SnCl4. On the other hand, the barrier
of the subsequent reaction 3a is relatively high so that Cl atoms
are slowly formed through reactions 3a and 4a at this temper-
ature.
On the basis of this discussion, shock-tube experiments were
performed at lower temperatures of 1250-1700 K, in order to
study the kinetics of the initial part of the SnCl4 thermal
decomposition. Figure 3 shows typical concentration profiles
of Cl and Sn atoms. Chlorine atoms increase monotonically,
but no tin atoms are detected during the reaction time of about
800 µs. These results show that reactions 3a and 4a have no
influence on Cl-atom formation in this temperature range. As
reaction 2a is considered to be much faster than reaction 1a by
the theory, the steady-state approximation can be applied to the
SnCl3 concentration. Under the present conditions, the Cl atom
concentration at time t, [Cl]t, can be expressed as follows:
Figure 5. Arrhenius plot of the second-order rate coefficient for
reaction 1a. (O) and (b) denote the results measured at [M] ) (1.7 (
0.2) × 1018 molecules cm-3 and [M] ) (8.9 ( 0.9) × 1018 molecules
cm-3, respectively.
squares fit yielded the following Arrhenius expression over the
temperature range of 1250-1700 K:
k1a2nd ) 10-5.37(0.62
×
exp[-(285 ( 18) kJ mol-1/RT] cm3 molecule-1 s-1
[Cl]t ) 2[SnCl4]0{1 - exp(-k1a1stt)}
where the error limits are at the two standard deviation level. If
this expression is assumed to be the low-pressure limit rate
coefficient, the preexponential factor seems to be too large.
Therefore, we can conclude that reaction 1a is in the falloff
region but fairly close to the low-pressure limit.
The first-order rate coefficient for reaction 1a, k1a1st, was
determined by fitting calculated Cl atom concentrations to
observed ones; see three lines in the upper part of Figure 3.
1st
The Arrhenius plot of k1a obtained by this method is shown
in Figure 4, which obviously depends on total concentration
The mixtures of SnCl4 used were highly diluted in argon to
avoid secondary reactions. Although it is most unlikely that side
reactions are of importance under these conditions, the contribu-
tions of some reactions should be discussed here. The side
reactions which may affect the determination of k1a are SnCl4
+ Cl f SnCl3 + Cl2 (S1) and SnCl3 + SnCl3 f products (S2).
Reaction S1 is endothermic and its enthalpy at 0 K is examined
to be 122 kJ mol-1 from the ab initio MO calculations. The
collision theory gives kS1 ) 5.3 × 10-15 and 9.9 × 10-14 cm3
molecule-1 s-1 at 1250 and 1700 K, respectively. Since the
2nd
[M]. So, the second-order rate coefficient k1a calculated by
2nd
the relation k1a ) k1a1st/[M] is plotted in Figure 5. For the
two different total concentrations, the values of k1a2nd follow a
single straight line. This result shows that the rate coefficient
for reaction 1a is fairly close to the low-pressure limit under
the present experimental conditions. However, the experiments
were performed in a relatively narrow range of total density,
so that they did not have enough sensitivity to specify whether
the reaction was in the true low-pressure limit or not. A least-

5250 J. Phys. Chem. A, Vol. 104, No. 22, 2000
Takahashi et al.
maximum concentration of Cl atoms formed during the reaction
time, [Cl]max, is about 1 × 1013 atoms cm-3, the upper limits
for the ratios of reaction rates of reactions S1 and 1a, kS1[Cl]max
/
2nd
k1a [M], can be estimated to be 3 × 10-3 and 8 × 10-5 at
1250 and 1700 K, respectively. This evaluation shows that
reaction S1 is much slower than reaction 1a and therefore
negligible. On the other hand, reaction S2 is exothermic. The
upper limits for the ratios of reaction rates of reactions S2 and
2nd
1a, kS2[SnCl3]max/k1a [M], can also be calculated from the
Lennard-Jones collision frequency and the maximum concentra-
tion of SnCl3 to be in the range of 1 × 10-2 to 2 × 10-5
.
Therefore, both reactions S1 and S2 have no influence on the
determination of k1a.
Figure 6. Typical measured concentration profile of Sn atoms in a
SnCl4-Ar mixture heated at a temperature of 2670 K. The white line
denotes a profile calculated by using the simplified reaction model
consisting of reactions 1a, 2a, 3a, and 4a.
From the ab initio calculations, reaction 1a was examined to
be favored compared to the Cl2-elimination channel (1b). This
theoretical consideration can be confirmed by the measured Cl
atom concentration profiles. If the main initial step of the SnCl4
thermal decomposition is reaction 1b, instead of (1a), the
detected chlorine atoms should be formed through the reaction
Cl2 + M f Cl + Cl + M (S3). As an extreme example, the
rate of reaction 1b is assumed to be much faster than that of
reaction S3. The concentration of Cl atoms formed through
reactions 1b and S3, [Cl]tS3, can then be expressed as follows:
[Cl]tS3 ) 2[SnCl4]0{1 - exp(-kS3[M]t)}
where kS3 is the bimolecular rate coefficient for reaction S3.
The data of kS3 were reported by numerous workers.25-31 Baulch
et al.32 recommended the following Arrhenius expression in their
review article:
kS3 ) 10-10.41 exp[-197 kJ mol-1/RT] cm3 molecule-1 s-1
The time after which the Cl atoms reach 10% of the initial
concentration of SnCl4 can be calculated from this formula to
be 6200 µs at 1344 K. The experimental result is only 130 µs;
see the upper part of Figure 3. This means that the formation
rate of Cl atoms through reactions 1b and S3 is too slow to
explain the measured Cl atom concentration. Therefore, it is
absolutely impossible that reaction 1b is the dominant channel.
The rate coefficient for reaction 1a cannot be compared with
previous data, because it has first been measured in the present
study. A similar kinetic study on the thermal decomposition of
SiCl4 has been performed in our laboratory. Silicon belongs to
the same group (group 14) as tin, so that the mechanism for
the thermal decomposition of SiCl4 is very similar to that of
SnCl4. The second-order rate coefficient for the reaction:
Figure 7. Sum of squared deviation between observed and calculated
Sn atom concentrations as functions of both rate coefficients for
reactions 3a and 4a. 1.1 ppm SnCl4-Ar mixture; T ) 2670 K; P )
1.240 atm.
decomposition of SnCl4 is completed within the reaction time
of about 1000 µs. To determine the rate coefficients for reactions
3a and 4a, Sn atom concentration was calculated based on the
simplified reaction scheme consisting of reactions 1a, 2a, 3a,
and 4a and compared with observed one. As a measure of fitting
quality, the sum of squared deviation between observed and
calculated Sn atom concentrations, F2(k3a,k4a), was calculated
as functions of both rate coefficients k3a and k4a:
SiCl4 (+M) f SiCl3 + Cl (+M)
(Si-1a)
F2(k ,k ) ) {[Sn](t)obs - [Sn](t,k3a,k4a)calc}2 dt
was reported as follows:16
∫
3a 4a
t
2nd
As the value of F2 becomes smaller, the fitting can be judged
to be better. A typical distribution diagram of F2 is shown in
Figure 7. When k3a is fixed at a certain value, the minimum
point for F2, i.e., Fmin2(k3a)fix), can always be found at an
appropriate k4a. Since the absolute values of Fmin2(k3a)fix)
depend on the combination of k3a and k4a, we can simultaneously
determine these rate coefficients from only Sn atom profiles
by determining the minimum point for Fmin2(k3a)fix), as shown
with an arrow in Figure 7.
Sensitivity analyses were performed with k1a, k3a, and k4a
determined in the present study. The CHEMKIN-II33 and
SENKIN34 program codes were used in the calculation. An
example is shown is Figure 8. The Sn atom concentration is
kSi-1a
)
10-6.94 exp[-314 kJ mol-1/RT] cm3 molecule-1 s-1
2nd
The apparent activation energy of kSi-1a is higher than that
of k1a2nd. This tendency can qualitatively be explained by the
difference in dissociation energies between Si-Cl and Sn-Cl
bonds.
Kinetics of the Subsequent Decomposition Steps. To study
the kinetics of the subsequent decomposition reactions 3a and
4a, Sn atom measurements were performed at higher temper-
atures of 2250-2950 K. Figure 6 shows a typical concentration
profile of Sn atoms, which increases gradually to reach finally
the initial concentration of SnCl4. This indicates that the thermal

Thermal Decomposition of Tin Tetrachloride
J. Phys. Chem. A, Vol. 104, No. 22, 2000 5251
Figure 8. Sensitivity analysis of rate coefficients for Sn atom formation
in a SnCl4-Ar mixture heated to a temperature of 2670 K.
Figure 11. Variations of the RRKM high-pressure limit rate coef-
ficients for reaction 1a (upper part) and reaction 3a (lower part) as a
function of distance of the Sn-Cl bond being broken.
TABLE 3: Geometries of the Reactants and Transition
States for the Reactions SnCl4(+Ar) f SnCl3 + Cl(+Ar)
and SnCl2(+Ar) f SnCl + Cl(+Ar)
Figure 9. Arrhenius plot of the second-order rate coefficient for
SnCl4 decomposition
SnCl2 decomposition
reaction 3a measured at [M] ) (3.2 ( 0.5) × 1018 molecules cm-3
.
parameter
reactant transition state reactant transition state
The solid line shows the RRKM result calculated with E0,3a ) 368 kJ
mol-1 (see text).
symmetry
Td
C3ν
C2ν
Cs
r(Sn-Cl*)a/Å
r(Sn-Cl)/Å
2.324
2.324
5.25
2.396
2.396
98.4
5.80
2.410
98.4
2.357
111.5
107.4
(Cl*-Sn-Cl)/deg 109.5
(Cl-Sn-Cl)/deg 109.5
a Cl* means the chlorine atom being removed through the dissocia-
tion reactions.
2250-2950 K:
k3a2nd ) 10-8.36(0.86
exp[-(310 ( 42) kJ mol-1/RT] cm3 molecule-1 s-1
×
k4a2nd ) 10-9.50(0.78
×
exp[-(265 ( 40) kJ mol-1/RT] cm3 molecule-1 s-1
where the error limits are at the two standard deviation level.
2nd
Obviously, both rate coefficients are smaller than k1
.
Figure 10. Arrhenius plot of the second-order rate coefficient for
Numerical calculations based on the kinetic data determined in
the present work can reproduce not only measured Sn atom
concentration, but also Cl atom concentration; see white lines
in Figure 2. This confirms that the SnCl4 thermal decomposition
in the present study can be explained by the simplified reaction
scheme consisting of reactions 1a, 2a, 3a, and 4a.
reaction 4a measured at [M] ) (3.2 ( 0.5) × 1018 molecules cm-3
.
sensitive enough to determine the kinetic data of reactions 3a
and 4a, while the initial decomposition reactions 1a and 2a have
little sensitivity. Furthermore, the ratio of the sensitivities for
rate coefficients k3a and k4a coefficients changes during reaction
time. These are the reasons why k3a and k4a can simultaneously
be determined by the above procedure. Figures 9 and 10 show
Arrhenius plots of the second-order rate coefficients for reactions
3a and 4a, respectively. Least-squares fits resulted in the
following Arrhenius expressions over the temperature range of
RRKM Calculations. In order to evaluate the validity of the
experimental results, RRKM calculations including variational
transition state theory were done for reactions 1a and 3a. The
RRKM unimolecular rate coefficient kRRKM,uni can be expressed
as follows:

5252 J. Phys. Chem. A, Vol. 104, No. 22, 2000
TABLE 4: RRKM Parameters for the Reactions SnCl4(+Ar) f SnCl3 + Cl(+Ar) and SnCl2(+Ar) f SnCl + Cl(+Ar)
SnCl4 decomposition SnCl2 decomposition
transition state transition state
Takahashi et al.
parameter
reactant
reactant
energy barrier of reaction,
E0/kJ mol-1
adjusted
adjusted
reaction path degeneracy, l‡
Lennard-Jones parameters for
the reactants σ/Å and ꢀ/kB/K
Lennard-Jones parameters for
Ar, σ(Ar)/Å and ꢀ(Ar)/kB/K
average downward energy
transferred per collision,
∆E down/cm-1
4
2
4.923, 755
4.804, 512
3.542, 93.3
600
3.542, 93.3
600
moments of inertia for inactive
510.7 (2)
510.4
1178.2 (2)
342.1
1164.1
external rotors/amu Å2
233.3
108.8
1016.0
148.1
moments of inertia for active
511.5
external and internal rotors/amu Å2
335.3 (2)
369 (2)
345
121
99 (2)
205.9
336
vibrational frequencies/cm-1
394 (3)
351
119 (3)
92 (2)
346
338
118
‡
TABLE 5: Arrhenius Expressions of High-Pressure Limit
and Weak Collision Low-Pressure Limit Rate Coefficients
Obtained from RRKM Calculationsa
kBT QR
k
RRKM,uni ) l‡
×
h QRQa
P(E‡) exp(-E‡/RT)
high-pressure limit
low-pressure limit (WC)
A/cm3
Ea/kJ
E0
∞
∑
E‡
RT
exp -
d
∫
(
)
( )
Ea/
0
RT
1 + kr/âckd[M]
reaction A/s-1
kJ mol-1 molecules-1 s-1 mol-1
temp/K
(1a)
(3a)
1016.11
1014.93
316
355
10-7.13
10-8.76
213
285
1250-1700
2250-2950
‡
P(E‡)
QR
∑
kr ) l‡
‡
QR hN(E + E )
a Rate coefficients in the form k ) A exp(-Ea/RT).
0
in Figure 11. The geometries at r1a(Sn-Cl) ) 5.25 Å and r3a-
where l‡ is the reaction path degeneracy; kB and h are the
Boltzmann and Planck constants; QR, QR‡ are partition functions
of the adiabatic rotations for the reactant and the transition state,
respectively; Qa is the partition function of all active modes of
the reactant; E0 is the energy barrier of the reaction at 0 K; âc,
kd are collision efficiency and rate coefficient for collisional
deactivation; ΣP(E‡) is the total number of energy states of the
transition state having energy E‡; and N(E‡+E0) is the density
of energy states for the reactant having energy E ) E‡ + E0.
In this model, the bond-dissociation transition state is treated
as a loosely bound product-like moiety with four characteristics.
First, the vibrational frequencies of SnCl3 (product in reaction
1a) or SnCl (product in reaction 3a) do not change in the
transition state. Second, the two external rotations with the
largest moments are treated as adiabatic. Third, the residual
external rotation and the two degrees of freedom representing
the bending vibrations of the Cl fragment in SnCl3 or SnCl are
treated as completely free active internal rotors with moments
of inertia fixed at that for an isolated SnCl3 or SnCl product.
Fourth, in order to search the structure of the transition state,
the potential energy along the reaction coordinate is modeled
with a Morse potential determined from the frequency repre-
senting the Sn-Cl stretching vibration and the energy barrier
of the reaction, E0. These treatments are widely accepted as a
standard model for simple bond-fission reactions.35-37 The
geometries of SnCl4 and SnCl3 for reaction 1a or SnCl2 and
SnCl for reaction 3a were determined by the MP2/3-21G(d) ab
initio MO calculations. The vibrational frequencies were also
computed at the MP2/3-21G(d) level and scaled by a factor of
RRKM,∞
RRKM,∞
(Sn-Cl) ) 5.80 Å, where the k1a
and k3a
have
minimum values, respectively, were treated as the structures of
the transition states for reactions 1a and 3a. Geometries of the
reactants and transition states are listed in Table 3. All
parameters required for the RRKM calculations are summarized
in Table 4. For each reaction, the energy barrier of the reaction,
E0, which is the most sensitive parameter in the calculations,
was adjusted until the RRKM rate coefficient matched our
experimental data. The average downward energy transferred
per collision, ∆E down, is also unknown. This value ranges from
400 to 800 cm-1 for usual thermal decompositions.39 In this
calculation, the average value (600 cm-1) was used. The value
of ∆E
does not need to be estimated more precisely,
down
because E0 is much more sensitive for the rate coefficient than
∆E and an error due to ∆E is canceled. The solid
down
down
lines in Figures 4 and 9 show the RRKM results calculated with
E0,1a ) 326 kJ mol-1 and E0,3a ) 368 kJ mol-1 for reactions 1a
and 3a, respectively. The fittings to our experimental data are
good for both reactions. Arrhenius expressions of the high-
pressure limit and the weak collision low-pressure limit rate
coefficients obtained from the RRKM calculations are sum-
marized in Table 5.
The values of the energy barriers E0,1a ) 326 kJ mol-1 and
E0,3a ) 368 kJ mol-1 obtained from the fittings are in excellent
agreement with the bond dissociation energies of SnCl4 and
22
SnCl2, D(Cl-SnCl3) ) 314 kJ mol-1 and D(Cl-SnCl) )
370 kJ mol-1 23
These agreements lead to the conclusion that
.
the experimental results for k1a and k3a are also supported by
the RRKM calculations.
0.94 to compensate for known systematic errors.38
The experimental results for k4a cannot be checked with the
RRKM theory, because the theory does not support the thermal
decomposition reactions of diatomic molecules. The relation of
the experimental determined activation energies between reac-
tions 3a and 4a is E3a < E4a. This tendency looks reasonable,
RRKM,∞
The high-pressure limit rate coefficients, k1a
and
k3aRRKM,∞, were calculated as a function of the separation
distance of the Sn-Cl bond, r(Sn-Cl), to determine the
structures of the transition states. A typical example is shown

Thermal Decomposition of Tin Tetrachloride
J. Phys. Chem. A, Vol. 104, No. 22, 2000 5253
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Conclusions
The present study on kinetics of the thermal decomposition
of SnCl4 can be summarized as follows:
(a) SnCl4 finally decomposes into Sn(3P) and four chlorine
atoms through the four subsequent elementary steps: SnCl4-
(+M) f SnCl3(2A1) + Cl(+M) (1a), SnCl3(2A1) (+M) f
SnCl2(1A1) + Cl(+M) (2a), SnCl2(1A1)(+M) f SnCl(2Π) +
Cl(+M) (3a), and SnCl(2Π)(+M) f Sn(3P) + Cl(+M) (4a).
(b) The rate coefficient for reaction 1a was found to be in
the falloff region fairly close to the low-pressure limit. The
second-order rate coefficient was experimentally determined to
be k1a ) 10-5.37(0.62 exp[-(285 ( 18) kJ mol-1/RT] cm3
2nd
molecule-1 s-1 from the initial formation of Cl atoms over the
temperature range of 1250-1700 K.
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Saunders: Philadelphia, PA, 1977; p 270.
(c) The second-order rate coefficients for the subsequent
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reactions 3a and 4a were given to be k3a2nd ) 10-8.36(0.86 exp[-
(310 ( 42) kJ mol-1/RT] cm3 molecule-1 s-1 and k4a
)
2nd
10-9.50(0.78 exp[-(265 ( 40) kJ mol-1/RT] cm3 molecule-1 s-1
by detecting Sn atoms over the temperature range of 2250-
2950 K.
(d) The experimental results for k1a and k3a were also
supported by the RRKM calculations.
Acknowledgment. The authors thank Ms. N. Schlo¨sser and
Mr. L. Jerig for their help in conducting the experiments. One
of the authors (Dr. K. Takahashi) expresses his gratitude to the
Alexander von Humboldt Stiftung for the financial support
during his stay in Germany.
(34) Lutz, A. E.; Kee, R. J.; Miller, J. A. SENKIN: A Fortran Program
for Predicting Homogeneous Gas-Phase Chemical Kinetics with SensitiVity
Analysis; Sandia National Laboratories Report SAND87-8248; Sandia
Laboratories: Albuquerque, NM, 1991.
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