Mechanism and Parameters Controlling the Decomposition Kinetics of Na2SiF6 Powder to SiF4

Article abstract of DOI:10.1002/kin.20999

Sodium hexafluorosilicate (Na₂SiF₆) powder has been used as a silicon source for formation of Si₃N₄ coatings by the hybrid precursor system-chemical vapor deposition (HYSY-CVD) route. The quantitative effect of processing time, temperature, gas flow rate, and process atmosphere (N₂ and N₂:5% NH₃) upon the fractional weight loss during the decomposition of Na₂SiF₆ was studied using a standard L₉ Taguchi experimental design and analysis of variance. The decomposition kinetics of Na₂SiF₆(s) was studied theoretically and experimentally in the temperature range of 550-650°C by applying the shrinking core model. It was found that regardless of atmosphere type, the reaction order is n ≈ 0.12 and that a two-stage mixed mechanism consisting of chemical reaction and boundary layer gas transfer controls the decomposition rate. The determined fractional weight loss during Na₂SiF₆ decomposition in nitrogen atmosphere is about 1.05-1.5 orders of magnitude greater than that in N₂:NH₃. The gas flow rate affects the dissociation activation energy, being of 121, 109, and 94 kJ/mol in N₂ and of 140, 120, and 115 kJ/mol in N₂:NH₃, for the flow rates of 20, 60, and 100 cm³/min, respectively, in both atmosphere types. A good agreement is observed by comparing experimental weight loss data with model predictions.

Full text of DOI:10.1002/kin.20999

Mechanism and Parameters
Controlling the
Decomposition Kinetics of
Na2SiF6 Powder to SiF4
´
N. SOLTANI, M. I. PECH-CANUL, L. A. GONZALEZ, A. BAHRAMI
Centro de Investigacio´n y de Estudios Avanzados del Instituto Polite´cnico Nacional, Cinvestav-Saltillo. Av. Industria
Metalu´rgica No. 1062, Parque Industrial Saltillo-Ramos Arizpe, Ramos Arizpe, Coahuila, 25900, Me´xico
Received 17 November 2015; revised 22 March 2016; accepted 24 March 2016
DOI 10.1002/kin.20999
Published online 27 April 2016 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: Sodium hexafluorosilicate (Na2SiF6) powder has been used as a silicon source
for formation of Si3N4 coatings by the hybrid precursor system-chemical vapor deposition
(HYSY-CVD) route. The quantitative effect of processing time, temperature, gas flow rate,
and process atmosphere (N2 and N2:5% NH3) upon the fractional weight loss during the
decomposition of Na2SiF6 was studied using a standard L9 Taguchi experimental design and
analysis of variance. The decomposition kinetics of Na2SiF6(s) was studied theoretically and
experimentally in the temperature range of 550–650ºC by applying the shrinking core model. It
was found that regardless of atmosphere type, the reaction order is n ࣈ 0.12 and that a two-stage
mixed mechanism consisting of chemical reaction and boundary layer gas transfer controls the
decomposition rate. The determined fractional weight loss during Na2SiF6 decomposition in
nitrogen atmosphere is about 1.05–1.5 orders of magnitude greater than that in N2:NH3. The gas
flow rate affects the dissociation activation energy, being of 121, 109, and 94 kJ/mol in N2 and of
140, 120, and 115 kJ/mol in N2:NH3, for the flow rates of 20, 60, and 100 cm3/min, respectively,
in both atmosphere types. A goodꢀCagreement is observed by comparing experimental weight
loss data with model predictions.
2016
2016 Wiley Periodicals, Inc. Int J Chem Kinet 48: 379–395,
applications, being the most important one its use as Si
source for chemical vapor deposition [1]. Because of
INTRODUCTION
The wide applications of fluorine compounds entail
the need of studying their physicochemical proper-
ties and the mechanisms of the chemical processes
occurring upon heating. The SiF4 species have many
the importance of silicon nitride (Si3N4) in engineer-
ing materials, of its properties and potential applica-
tions at high temperature, as well as in microelectron-
ics and optoelectronics, in recent years there has been
a growing interest in this material from different per-
spectives [2,3]. One of the synthesis routes for silicon
nitride powders is the chemical vapor deposition tech-
nique, using volatile silicon compounds such as SiCl4,
SiH4, SiF4, or related molecular compounds, which
Correspondence to: Martin I. Pech-Canul; e-mail: martin.pech@
cinvestav.mx, martpech@gmail.com.
Supporting Information is available in the online issue at
www.wileyonlinelibrary.com.
ꢀC
2016 Wiley Periodicals, Inc.

380
SOLTANI ET AL.
yield Si3N4 powders upon the gas phase reaction with
ammonia.
There are five methods for production of silicon
tetrafluoride (SiF4) at a laboratory scale: (a) reaction
of elemental silicon with fluorinating agents [4,5] (b)
fluorination of silicon dioxide [6,7], (c) fluorination of
silicon tetrachloride [8–10] (d) decomposing fluorosili-
cic acid with concentrated acids [11], and (e) thermal
dissociation of metal hexafluorosilicates [12,13]. The
obtained SiF4 by the latter method from Na2SiF6 is
of high purity, because the solid by-product, sodium
fluoride, absorbs impurities. The thermal decomposi-
tion of Na2SiF6 offers great opportunities to econom-
ically synthesize Si3N4 as powders, whiskers/fibers,
and films/coatings.
Figure 1 Cross section of a partially dissociated specimen.
Different dissociation mechanisms for Na2SiF6 (s)
to SiF4 (g) in different atmospheres with reaction or-
ders from zero to one have been proposed [14–16].
Vanka and Vachusˇka [14] reported that isothermal de-
composition of Na2SiF6 powder in dry nitrogen is
found to have a reaction order of 2/3, with an acti-
vation energy of 182 kJ/mol in the temperature range
341–413°C and is completely different from that re-
ported by Istomin and coworkers [15]. They reported
that slow removal of gaseous silicon tetrafluoride from
the sample surface was the rate-controlling step, result-
ing in the observed zero-order reaction kinetics. In tests
carried out in Ar atmosphere, Kashiwaya and Cramb
assumed a first-order rate equation. The rate constant
of dissociation was determined as a function of tem-
perature: kc = 87.3 exp (–12,823/T), and the activation
energy for dissociation was 106.6 kJ/mol in a temper-
ature range from 427 to 1347°C. The gas phase mass
transfer did not affect the dissociation reaction [13].
Likewise, from the thermal decomposition of Na2SiF6
sphere-shaped specimens in a reactor open to the ambi-
ent atmosphere, it was determined an order of reaction
of 0.38 and an apparent activation energy of 116.4
1.5 kJ/mol [16].
is regarded as a porous and inert substance, so that
the gas reactants can diffuse from the external sur-
face of the particle to the surface of the unreacted
core. Thus, the unreacted core shrinks as the reaction
proceeds, but the overall particle size essentially re-
mains constant. Although the unreacted shrinking core
model does not precisely represent the whole mecha-
nism of gas–solid reactions, it is accepted as the best
simple model for the majority of reacting gas–solid
systems [18].
Figure 1 shows a schematic representation of the
reaction model presented in this study. For this kind of
reaction, the following five steps occurring in succes-
sion are visualized: (a) diffusion of reactant from the
main body of gas through the gas film to the surface
of the solid, (b) penetration and diffusion of reactant
through the blanket of ash to the surface of the unre-
acted core, (c) reaction on the surface between reactant
and solid, (d) diffusion of gaseous products through the
ash back to the exterior surface of the solid, and (e) dif-
fusion of gaseous products through the gas film back
into the main body of the fluid [19].
In a previous work, it has been found that the de-
composition reaction of Na2SiF6 in nitrogen is of zero
order with activation energy of 156 kJ/mol and a rate-
determining-step given by the chemical reaction it-
self [17]. In the present study, a heterogeneous reac-
tion model was developed to represent the solid–gas
reaction. When the solid reactant is nonporous, the
shrinking particle model and the unreacted shrinking
core model are commonly used. For the shrinking par-
ticle model, reactions are confined at the surface of
the particle. The unreacted shrinking core model is
applied when the reactant is converted into another
solid material leaving behind the unreacted solid. The
converted material, which is sometimes called “ash,”
The final aim of this investigation is coating rice
husk ash (derived from rice husk as a potential re-
inforcement for metal matrix composites) with Si3N4
via the chemical vapor infiltration system [20–23]. The
synthesis of Si3N4 has been conducted at temperature
above 1100ºC through the reaction of nitrogen precur-
sor with SiF4(g) produced during the thermal decom-
position of sodium hexafluorosilicate (Na2SiF6). The
strategic positioning of the Na2SiF6 compacts allows
controlling the decomposition rate in the temperature
range of interest.
Reactions (1)–(3) represent the formation of Si3N4
from ammonia, a mixture of nitrogen–ammonia, and
nitrogen, respectively, indicating the values of their
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DECOMPOSITION KINETICS OF Na2SiF6 POWDER TO SiF4
381
Table I L9 Taguchi Experimental Array Used to Study
the Effect of Processing Parameters on the Dissociation
of Na2SiF6
corresponding Gibbs free energies.
aSiFX(g) + bNH3(g)cSi3N4 + dHF(g) + eH2(g)
Gas Flow
◦
ꢀG1300 C = −843.2 kJ/mol
(1)
Temperature Time
Rate
Precursor
Trial/Run
(°C)
(min) (cm3/min) (N2:NH3)
L1
L2
L3
L4
L5
L6
L7
L8
L9
550
550
550
600
600
600
650
650
650
10
20
40
10
20
40
10
20
40
20
60
100
20
60
100
20
100:0
5:95
100:0
100:0
100:0
5:95
5:95
100:0
100:0
aSiFX(g) + bN2(g) + cNH3(g)dSi3N4 + eHF(g) + fH2(g)
◦
ꢀG1300 C = −584.6 kJ/mol
(2)
aSiFX(g) + bN2(g)cSi3N4 + dF2(g)
60
100
◦
ꢀG1300 C = −18.4 kJ/mol
(3)
Note: Heating and cooling rates were 20°C/min and 20°C/min,
respectively.
It is clear that thermodynamically it is more feasible
to form silicon nitride only in ammonia than in the gas
mixture and in the gas mixture than only in nitrogen.
This outcome can be explained in terms of the thermal
and chemical stabilities of nitrogen and of ammonia.
According to the literature, it is more difficult to disso-
ciate nitrogen than ammonia (ionization potential for
N2 and NH3 are 15.576 and 10.2 eV, respectively) [24].
In addition, the easiness for dissociating NH3 may
be reflected in some extent by the strength of the chem-
ical bonds. At 25°C, the strengths of the H–N and N–N
bonds are 75 and 226.8 kcal/mol, respectively [25]. The
presence of ammonia in even small amounts is enough
for accelerating Si3N4 formation. However, silicon ni-
tride films deposited from ammonia show a large num-
ber of hydrogen radicals incorporated in their structure.
The –SiH radicals formed from the hydrogen atoms in-
corporated in the network may act as charge traps in the
silicon nitride [26,27] and produce a great instability
in the electric characteristics of the devices [28].
ics of Na2SiF6 by systematic variations in processing
time, temperature, gas flow rate, and atmosphere (N2
and N2-NH3). The main goal was to propose a de-
composition mechanism by considering the shrinking
core model. An experimental design (orthogonal ar-
ray L9) by the Taguchi method was also used to study
the quantitative effect of the processing parameters on
the decomposition of Na2SiF6 and establish the opti-
mal conditions to attain complete dissociation. Table I
shows the standard Taguchi orthogonal (L9) array used
in the investigation.
EXPERIMENTAL
In spite the various works devoted to study the de-
composition of Na2SiF6, there are still some discrepan-
cies concerning kinetics, such as the reaction order. It
has also been observed that the kinetic parameters are
dependent on the decomposition conditions, i.e., tem-
perature, atmosphere, heating rate, gas flow rate, etc.
Therefore, new information regarding the influence of
gas type and gas flow rate on the dissociation kinetics,
and the effect of nitrogen atmosphere on the activation
energy for dissociation is still necessary. Moreover, no
previous study based on modeling and experimentation
has reported an elucidation of the steps that make up
the mechanism. Other new contributions of an inves-
tigation would be to study the effect of gas flow rate,
time and temperature, on the porosity in the NaF ash
layer and the influence of the gas flow rate and heating
rate on the decomposition temperature. The aim of this
investigation was to study the decomposition kinet-
Isothermal decomposition tests were performed in
a laboratory reactor consisting of a tubular furnace
(59300 Thermolyne) with an alumina tube (3.1 cm
in diameter × 76 cm long) provided with end-cap
fittings to control the process atmosphere, gas in-
lets (and outlets) to supply the nitrogen precursor as
well as devices to controlling temperature, gas flow
rate, and pressure. The reactor also includes a pow-
der collector and a neutralizer of the gas by-products.
The dissociation tests were conducted using 5 g of
reactant-grade Na2SiF6 (Sigma-Aldrich, Saint Louis,
MO, USA) placed in an alumina boat, positioned in
the center of the reactor, varying temperature in the
range from 550 to 650°C, under N2 and N2-NH3 (5
vol% NH3 balance N2) fed at three flow rates (20, 60,
100 cm3/min). The weight loss was recorded using an
electronic balance with a weight accuracy of 0.0001 g.
The fractional weight loss (x), from each series of
International Journal of Chemical Kinetics DOI 10.1002/kin.20999

382
SOLTANI ET AL.
samples was calculated from the following equation:
thermal tests of Na2SiF6 under various nitrogen flow
rates are presented in Table II. As it can be observed,
upon increasing the heating rate from 5 to 20°C/min,
the initial decomposition temperature augments. On
the other hand, it is apparent that the nitrogen gas flow
rate does not have any effect on the decomposition
(peak) temperature of Na2SiF6.
Weight loss at time (t)
x =
Total weight loss after complete decomposition
(4)
The decomposition kinetics of Na2SiF6 was inves-
tigated by using the shrinking core model, assuming
a specimen constant size. The time constant was ob-
tained from curve-fitting toolbox in Matlab software
(7.10.0-R2010a). The discrepancy between the data
and the estimation model was measured by the sum of
squared errors.
Optimization of Process Parameters
With the aim of determining the percentage of con-
tribution each of the parameters tested to the variabil-
ity in the conversion fraction of Na2SiF6 into gaseous
species, an analysis of variance (ANOVA) was per-
formed. The ANOVA (see Table III) showed that the
parameter that most significantly affects the decompo-
sition of Na2SiF6 is the processing temperature, with
a relative contribution of 51% followed by processing
time and gas flow rate, with relative contributions of
24% and 15%, respectively. The percentage contribu-
tion due to the error term provides an estimate of the
adequacy of the experiment. In this case, the magni-
tude of the error term (7%) suggests that no important
factors were omitted in the design of the experiment.
Figure 3 depicts the main effects of the controllable fac-
tors upon the response variables. According to the main
effects analysis, the use of pure nitrogen (Level 1) and
the high levels (Level 3) of time, temperature, and gas
flow rate enhance the decomposition of sodium hex-
afluorosilicate and the conversion to gaseous species.
Accordingly, the optimum conditions to maximize the
decomposition of sodium hexafluorosilicate are as fol-
lows: nitrogen precursor as atmosphere, gas flow rate
of 100 cm3/min, processing time of 40 min, and pro-
cessing temperature of 650ºC.
Differential thermal and thermogravimetric analy-
ses (DTA/TG) were performed at atmospheric pres-
sure and in a flow of nitrogen using a SDT Q600
(V20.9 build 20) instrument, heating the specimens
up to 700°C and maintaining the specimens under
isothermal conditions. Three heating rate levels (5,
12.5, and 20ºC/min) and three nitrogen flow rates (20,
60, 100 cm3/min) were used to determine the variation
of peak temperature. The reference material was alu-
minum oxide. The starting materials and the decompo-
sition products were identified using a Philips 3040 X-
ray diffractometer . The X-ray diffraction (XRD) pat-
terns were recorded employing Cu Kα radiation (λ =
˚
1.54 A) in the 2θ range of 10–80°, using a scan step
of 0.03°, a voltage of 40 kV, and a current of 30 mA.
The average pore size of reacted Na2SiF6 specimens
was determined by means of a sorptometer (Quan-
tachrome Autosorb1C, Asic-xtcd6) using the principle
of adsorption/desorption of a monolayer of nitrogen
on the surface of the solid, based on the methods of
Brunauer–Emmett–Teller and micropores analysis.
RESULTS AND DISCUSSION
Isothermal Weight-Loss Measurements
Figures 4 and 5 show the effect of temperature on frac-
tional weight loss as a function of reaction time for
two nitrogen precursors under the established gas flow
rates. At a fixed reaction time, the conversion increases
as temperature increases for any gas flow rate and pre-
cursor. At T = 550°C, the reaction rate is too slow to
allow a sufficient conversion into gas species in a rea-
sonable reaction time. At fixed temperature, for higher
gas flow rates, the conversion fraction increases in a
shorter reaction time. By comparing Figs. 4 and 5, it
can be seen that the rate of Na2SiF6 decomposition un-
der the same condition in the presence of N2 is about
1.01–1.5 times greater than that in N2:NH3. The vari-
ous slopes of the fractional weight loss as a function of
time under different gas flow rates show the possibility
of mass transfer control.
Differential Thermal Analysis Results
for Na2SiF6
Figures 2a–2d show the heat flow and weight-loss
curves of Na2SiF6 decomposition at different heating
rates of 5, 12.5, and 20°C/min, respectively, under the
nitrogen gas flow rate of 20 cm3/min. The decomposi-
tion of the salt under all three heating rates is found to
be starting between 548 and 570°C, where an endother-
mic peak is observed in all the heating rates tested. As
it can be seen from Figs. 2b–2d, with increasing the
heating rate from 5 to 20°C/min, the weight of the
samples is reduced just in only one step, suggesting
that the reaction mechanism, at least with the results
obtained within the experimental framework of this
work, is not complex. The results of the differential
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DECOMPOSITION KINETICS OF Na2SiF6 POWDER TO SiF4
383
Figure 2 (a) DTA and TG curves of the thermal decomposition of Na2SiF6 at heating rates of (b) 5, (c) 12.5, and (d) 20°C/min.
Table II Differential Thermal Analysis Results
for Na2SiF6
Reactions of the type A(s) → B(s) + C(g) can be de-
scribed by the following equation:
Nitrogen Flow
Rate (cm3/min)
Heating Rate
(ºC/min)
a
dx
dt
Td
= kxn
(5)
20
5
12.5
20
5
12.5
20
5
12.5
20
548
566
570
548
565
572
548
565
570
where dx/dt is the dissociation rate of the solid
(Na2SiF6), x is the fractional weight loss, n is the em-
pirical order of reaction, and k is the rate constant. A se-
60
ries of plots of log10 (reaction rate) versus log10 xSiF
4
for a constant heating rate of 20ºC/min and tempera-
tures of 550, 600, and 650ºC under different gas flow
rates of N2 and N2:NH3 were constructed. The reaction
orders, which were determined using the differential
method resulted to be in the range of n = 0.12–0.15.
100
aTd: Decomposition temperature of samples at endothermic peak.
International Journal of Chemical Kinetics DOI 10.1002/kin.20999

384
SOLTANI ET AL.
Table III ANOVA Table for Maximizing Conversion Fraction of Na2SiF6 into Gaseous Species
Contribution
Percentage
Number
Factors
DOF
Sum of Squares
Variance
1
2
3
4
5
Temperature
Time
Gas flow rate
Type of gas
Error
2
2
2
1
10
0.38
0.11
0.18
0.022
0.05
0.19
0.05
0.09
0.022
0.005
51
15
24
3
7
in DTA/TG tests) also provide a valuable method for
estimating the reaction order of a particular reaction.
Thus, to confirm the calculated reaction orders, the dif-
ferential thermal technique—by Kissinger [29]—was
used additionally. To quantitatively describe the form
of peak, a “shape index (S)” is defined as the abso-
lute value of the ratio of the slopes of tangents to the
curve at the inflection points [29]. The determination
of this shape index is illustrated in Fig. 6. The re-
action order can thus be calculated by the following
equation:
n = 1.26S1/2
(6)
Shape index = a/b,
where
Figure 3 Main effects of the processing parameters (time,
temperature, gas flow rate, and precursor) on the conversion
fraction of Na2SiF6 into gaseous species (response variable).
ꢀ
ꢀ
ꢁ
ꢁ
d2x
dt2
a =
1
Plots of log10 (reaction rate) versus log10 xSiF for dif-
4
ferent atmospheres, temperatures, and gas flow rates
are presented in Figs. 1 and 2 of the Supporting In-
formation. The differential thermal patterns (obtained
d2x
dt2
b =
2
Figure 4 Experimental fractional weight loss measurements versus time at 550 and 650ºC under N2 atmosphere.
International Journal of Chemical Kinetics DOI 10.1002/kin.20999

DECOMPOSITION KINETICS OF Na2SiF6 POWDER TO SiF4
385
Figure 5 Experimental fractional weight loss measurements versus time at 550, 600, and 650ºC under N2:NH3 atmosphere.
It was found that the results of the differential ther-
mal study from DTA/TG tests are in good agreement
with those obtained using the differential method. The
reaction orders obtained between 0.13 and 0.15. These
results show that the different flow rates, temperature,
and type of nitrogen precursor do not have any effect
on the reaction order and endothermic peak shape.
Representative XRD patterns of specimens after the
thermal treatment in constant gas flow rate and time are
shown in Fig. 7. The XRD patterns reveal the presence
of unreacted Na2SiF6 and of cuboid-shaped NaF as the
only solid reaction product.
Figure 8a is a representative photomicrograph
showing the spherical shape of Na2SiF6 powders be-
fore the thermal treatment. Figure 8b shows the porous
structure of a decomposed Na2SiF6 specimen. Micro-
Figure 6 Method for measuring the magnitude of asym-
metry in an endothermic differential thermal analysis
peak of Na2SiF6 decomposition at a heating rate of 20ºC/min
scopic examination by scanning electron microscopy
(SEM) complemented with energy-dispersive X-ray
for various nitrogen flow rates of (a) 20, (b) 60, and (c) 100
cm3/min.
International Journal of Chemical Kinetics DOI 10.1002/kin.20999

386
SOLTANI ET AL.
Figure 7 XRD patterns of Na2SiF6 decomposed to NaF the thermal treatment.
spectrometry (EDX) analyses showed that the outer
surface of partially reacted specimens is NaF. Also,
by EDX analysis, it was found that the central core of
the powders consists of Na2SiF6. These results together
support the hypothesis that the dissociation process fits
the shrinking core model, in which the core size be-
comes increasingly smaller and the porous surround-
ing layer of (NaF) by-product continuously grows as
the dissociation reaction proceeds (see Fig. 8c). The
backscattered electron signal provided sufficient phase
contrast between the sample and the resin, for phase
identification and image processing of particle cross
sections.
As shown with representative SEM micrographs in
Fig. 9, it is apparent that at a constant gas flow rate
under the same test time, while the use of low temper-
atures gives place to specimens with an open structure,
treating the specimens at high temperatures produces
a finer pore structure.
following assumptions: (1) spherical symmetry, (2)
isothermal particle, (3) the reaction is irreversible, and
(4) no volume change throughout the reaction. Based
on thermodynamic calculations and on previous re-
ports from the literature, the reaction at the spherical
surface is given by [12] the following equation:
Na2SiF6(s) → NaF(s) + SiF4(g)
(7)
The overall process can be explained by three opera-
tive mechanism steps: surface reaction at the unreacted
core surface (che), diffusion of SiF4 in the ash layer of
NaF (dif), mass transfer of SiF4 through the gas film
(external diffusion (ext)). For spherical particles, the
analytic relationship between conversion and reaction
time depends upon the rate-limiting step. However, it
may not be reasonable to consider that one single-step
controls the whole process. Neither the chemical reac-
tion and diffusion nor the gas film diffusion mechanism
can separately explain all the x–t data. If the process is
assumed to be a combination of rate-limiting mecha-
nism such as chemical reaction, diffusion through ash
layer, and external mass transfer, the time t to achieve
a certain degree of conversion x can be calculated as
follows [30]:
Reaction and Elucidation of Controlling
Mechanism
Since microscopic examination and XRD analyses of
partially reacted specimens revealed the presence of
two distinct phases, NaF and Na2SiF6, the overall re-
action was approximated by a single-stage, shrink-
ing core model, based on mass transfer control of the
SiF4 through the reacted shell. The model makes the
t = τche × fche (x) + τdif × fdif (x) + τext × fext (x)
(8)
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DECOMPOSITION KINETICS OF Na2SiF6 POWDER TO SiF4
387
Figure 8 SEM photomicrographs and EDX spectra of the Na2SiF6 salt: (a) before and (b) after the thermal treatment (600ºC
under N2:NH3 flow rate of 60 cm3/min in 40 min) and (c) broken treated particle.
where t is the overall reaction time; τche, τdif, and τext
are time constants; and fche(x), fdif(x), and fext(x) are
conversion functions describing chemical reaction ki-
netics, diffusion, and mass transfer, respectively, given
by [31]:
specimen, n is the reaction order, kg is the mass transfer
coefficient between the fluid and the particle, De is the
effective diffusion coefficient of gaseous reactant in
the ash layer, and ks is a rate constant for the surface
reaction.
CSiF was calculated for the present work by as-
4
ρcR
suming the total pressure of the mixture Pt = 1 atm
and by using the ideal gas law. Pi, Vi, ni,Xi, and T are
the pressure, volume, number of moles, mole fraction,
and temperature of the gas, respectively, and R is the
ideal gas constant.
τext
=
=
(9)
3kgC
SiF4
ρcR2
τdif
(10)
(11)
As it can be seen in Figs. 4 and 5, the fractional
weight loss during the thermal dissociation of Na2SiF6
at constant temperature behaves approximately in a
linear way with time; therefore, the concentration of
SiF4 per minute can be considered constant.
6DeCSiF
4
ρcR
=
ksCn
τche
SiF4
PiVi = niRT, PSiF = CSiF RT
(12)
4
4
where ρc is the molar density of Na2SiF6 in a reacting
particle, R is the initial radius of the specimen, CSiF
is the bulk concentration of SiF4 at the exterior of the
4
Pt = 1, PSiF + PN + PNH = 1
4
2
3
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388
SOLTANI ET AL.
Figure 9 SEM photomicrographs of reacting particle surface at (a) 550, (b) 600, and (c) 650ºC under N2:NH3 flow rate of
60 cm3/min for 40 min.
XSiF + XN + XNH = 1
controlling system, i.e., single mechanism ([fext(x)],
[fche(x)], [fdif(x)]), double mechanism systems ([fext(x)
– fche(x)], [fdif(x) – fext(x)], [fche(x) – fdif(x)]), and triple
mechanism systems ([fext(x) – fche(x) – fdif(x)]) were
considered.
4
2
3
PSiF = XSiF × Pt
4
4
Plots of fractional weight loss versus time for all
tests were constructed. Constant time and standard de-
viations from experimental data can be calculated by
fitting the plot of time versus fractional weight loss to
these equations by considering the single mechanism:
The conversion functions (f(x)) for the different
mechanisms are defined as follows [19,30]:
text
= fext (x) = x
(13)
(14)
τext
tche
= fche (x) = 1 − (1 − x)1/3
t = τextfext x ; t = τchefche x ; t = τdiffdif
( )
( )
x (16)
( )
τche
double mechanism:
tdif
= fdif (x) = 1 − 2 (1 − x) + 3 (1 − x)2/3 (15)
τdif
t = τextfext (x) + τchefche (x) ; t = τchefche (x)
To establish the appropriate controlling mechanism
of Na2SiF6 decomposition, single, double, and triple
+ τdiffdif (x) ; t = τdiffdif (x) + τextfext (x) (17)
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DECOMPOSITION KINETICS OF Na2SiF6 POWDER TO SiF4
389
Table IV Time Constant of Various Mechanisms in One and Multimechanism System under N2 Stream
Time Constant (min)
N2 Flow Rate
(cm3/min)
Temperature (ºC) τche
τdif
τext
τdif & ext
τdif & che
τche & ext
τdif & ext & che
20
550
650
550
650
550
650
739 2,838 220 955 and 277 734 and 625 226 and 24
–2, 17, and 14
53, –117, and 25
–138, 35, and –10
–15, 22, and 15
–6, 51, and 68
–1, 30, and 2
92
88
54
25 and 40
50 and 109
2 and 23
–45 and 138
–85 and 338
–48 and 84
–38 and 295
–6 and 38
24 and 50
89 and 40
4 and 23
71 and 40
3 and 22
60
276
369
125
820 2,960 300
100
155
31
144
30
99
20
22 and 83
16 and 10
Table V Sum of Squared Errors for the Different Mechanisms under a Stream of N2
Sum of Squared Errors
N2 Flow Rate
(cm3/min)
Temperature (ºC)
che
dif
ext
dif & ext
dif & che
che & ext
dif & ext & che
20
550
650
550
650
550
650
2,970
2,550
3,570
4,850
3,740
4,060
3,740
3,080
4,396
5,700
5,383
5,600
3,740
3,750
3,410
3,300
3,100
4,600
86
108
117
46
38
31
84
98
108
16
31
25
4.1
0.5
0.78
0.1
2
102
100
95
10
45
60
100
8.5
40
Table VI Time Constant of Various Mechanisms in Single and Multimechanism System under Stream of NH3:N2
Time Constant (min)
N2:NH3 Flow
Rate (cm3/min) Temperature (ºC) τche τdif τext
τdif & ext
τdif & che
τche & ext
τdif & ext & che
20
550
600
650
550
600
650
550
600
650
157 344 88 56 and 404 –377 and 1,215 250 and 130 146, –409, and 136
329 341 165 29 and 156 –198 and 493
102 94 65 14 and 56 –102 and 207
367 345 203 29 and 189 –268 and 613
71 and 119
24 and 49
151 and 79
27 and 49
12 and 25
90 and 87
14 and 46
6 and 22
–122, 323, and 54
–52, 117, and 25
224, –399, and 312
4, –54, and 24
60
108 100 71
43 39 34
105 217 165 35 and 167
102 119 49
32 31 23
27 and 55
9 and 27
–94 and 203
–160 and 106
–49 and 251
–75 and 162
–15 and 47
–51, 90, and 5
100
183, –218, and 192
–322, 744, and –187
–1, 23, and 7
6 and 52
17 and 12
in N2 and N2-NH3 under a flow rate of 60 cm3/min
at the different test temperatures are presented in
Figs. 10a and 10b.
and triple mechanism:
t = τdiffdif (x) + τextfext (x) + τchefche (x) (18)
As it can be observed in Tables IV and VI, both,
negative and positive time constants resulted from the
calculations. However, since the negative values have
no physical meaning, the combination mechanism with
positive values and minimal deviations (columns 8 in
Tables V and VII) is selected as the one that controls
the decomposition kinetics, namely, the combination
of chemical reaction and external boundary layer gas
transfer.
The calculated parameters (Tables IV and VI) and
mechanism deviation values (Tables V and VII) ob-
tained by considering single and multimechanisms
are shown for both processing atmospheres, N2 and
N2-NH3, correspondingly. However, only the best fit
curves corresponding to the dominant mechanism are
presented. Plots of comparison of the experimental and
predicted fractional weight loss for specimens treated
International Journal of Chemical Kinetics DOI 10.1002/kin.20999

390
SOLTANI ET AL.
Table VII Sum of Squared Errors for the Different Mechanisms under a Stream of N2:NH3
Sum of Squared Errors
N2:NH3 Flow
Rate (cm3/min)
Temperature (ºC)
che
dif
ext
dif & ext
dif & che
che & ext
dif & ext & che
20
550
600
650
550
600
650
550
600
650
111
210
3,074
92
86
12
17
77
11
42
71
41
14
87
297
11.36
210
76
10
60
35
47
0.14
0.32
7.1
0.13
4.9
0.38
0.15
2.5
56.9
297
17
43
13
10
44
35
9
3,028
3,960
3,674
4,001
3,030
3,413
3,602
3,500
4,447
5,470
5,010
5,504
5,700
5,493
4,946
4,704
152
128
503
570
152
540
880
60
100
0.5
Although, for all the experimental systems the re-
action is controlled by both chemical reaction and gas
layer diffusion, the value of external boundary layer
gas transfer resistance to chemical reaction resistance
attributed to the pore diffusion process in the best
fitted plot between the experimental and calculated
data suggests that the diffusion step should be too
fast as to be considered the controlling stage. The ef-
fect of time, temperature, flow rate, and nitrogen pre-
cursor on the average pore diameter was investigated
(Fig. 12). At a fixed reaction time, the average pore
size decreases as temperature increases regardless of
the gas flow rate. This can be visualized in specimens
treated in N2:NH3, where it was observed that at t =
10 min the pore size is larger than at t = 30 min. A pos-
sible explanation to this observation is by the partial
sintering of NaF(s) by-product—which occurs between
640 and 926°C [33]—similarly to that observed in the
calcination of limestone (CaCO3), which decomposes
into (CaO(s)) and CO2(g) [34]. With an increase in tem-
perature and time, CaO sintering occurs, manifested
by a reduction in pore size [35]. In addition, for spec-
imens treated in N2:NH3, at a fixed temperature, with
an increase in the gas flow rates the pore size decreases.
This can be explained in terms of the Kozeny–Carman
equation, which inversely relates the specific surface
area of a material in a porous bed with the flow rate
through a porous media [36,37].
In this specific case, N2 or N2:NH3 pass through
the NaF ash layer (the porous medium). It should be
pointed out that because of the likeness in the viscosi-
ties of N2 and of N2: 5% NH3, similar results were
observed in tests conducted under a stream of nitro-
gen [38].
In light of the previous discussion, it can be con-
cluded that regardless of the pore size in the NaF ash
layer, the decomposition process will take place com-
pletely, and thus the diffusion process does not appear
to be the controlling stage.
ratio (ττ ) suggests that decomposition of Na2SiF6 is
ext
che
mostly governed by reaction at low temperatures (ττ
<
ext
che
1) and by external boundary layer gas transfer at high
τext
τche
temperatures (ττ > 1). In addition, the value of
ext
che
shows that by increasing temperature, the proportion
of gas layer diffusion is larger for higher flow rates, and
the impact of this phenomenon is stronger under nitro-
gen stream. This value at T = 650°C can be changed
by increasing the gas flow rate from 1 to 4 (right-hand
vertical axis) for N2:NH3 and from 2 to 7 for N2 precur-
sor. The values of ks and kg were calculated by Eqs. (6)
and (8), respectively. The influences of temperature
and gas flow rate on the rate constant and mass transfer
coefficient are summarized in Tables VIII and IX.
kg
Figure 11 shows that the value of ratio decreases
ks
by increasing temperature. As discussed before, the
increase in temperature results in increment of equi-
librium conversions. This behavior is essentially at-
tributed to a higher rate constant and to the accelera-
tion of the gas transfer process through the boundary
layer at higher temperature. In addition, it should be
mentioned that both values of ks and kg augment by in-
creasing the gas flow rate for both N2 and N2:NH3 sys-
tem, but ks and kg show the highest values under stream
of nitrogen. An increase in the gas velocity causes a
reduction in the boundary layer thickness [32], and,
consequently, a change in the mass transfer coefficient
and a rapid removal of gaseous silicon tetrafluoride
from the sample surface can be expected as a result a
higher decomposition rate of the salt.
The diffusion mechanism does not appear to have
any effect on the decomposition rate of Na2SiF6. The
highest sum of squared errors (see Tables V and VII)
As the decomposition reaction is a thermally acti-
vated process, the activation energy was determined
International Journal of Chemical Kinetics DOI 10.1002/kin.20999

DECOMPOSITION KINETICS OF Na2SiF6 POWDER TO SiF4
391
Figure 10 Comparison of the experimental and predicted results of double mechanism (ext & che) for samples under stream
of (a) N2:NH3 and (b) N2 with flow rate of 60 cm3/min.
kJ/mol for flow rates of 20, 60, and 100 cm3/min, re-
spectively. It is thus clear that atmosphere plays an im-
using Arrhenius’ equation. While for the tests in
N2:NH3, the activation energies for formation of the
gaseous species from Na2SiF6 are 140, 120, and 115
kJ/mol, in N2 the values of Ea are 121, 109, and 94
portant role in the decomposition kinetics of Na2
SiF
6
and that interestingly, in N2, a lower activation energy
International Journal of Chemical Kinetics DOI 10.1002/kin.20999

392
SOLTANI ET AL.
Table VIII Calculated Effective Parameters of Na2SiF6 Decomposition under N2 Stream
N2 Flow Rate
(cm3/min)
Temperature (°C)
ks (m/min)
kg (m/min)
Ea(kJ/mol)
20
550
650
550
650
550
650
9.4 × 10−7
7.2 × 10−6
1.8 × 10−6
3.46 × 10−5
2.89 × 10−6
5.9 × 10−5
2.01 × 10−7
4.77 × 10−6
2.44 × 10−7
1.14 × 10−6
3.39 × 10−7
1.74 × 10−6
121
60
101
94
100
Table IX Calculated Effective Parameters of Na2SiF6 Decomposition under N2:NH3 Stream
N2:NH3 Flow
Rate (cm3/min)
Temperature (°C)
ks (m/min)
kg (m/min)
Ea (kJ/mol)
20
550
600
650
550
600
650
550
600
650
7.1 × 10−7
2.49 × 10−6
7 × 10−6
1.01 × 10−7
2.6 × 10−7
4.12 × 10−7
1.25 × 10−7
8.62 × 10−7
9.7 × 10−7
1.34 × 10−7
1.32 × 10−6
1.1 × 10−6
140
60
1.3 × 10−6
6.74 × 10−6
1.07 × 10−5
2.1 × 10−6
1.3 × 10−5
2.9 × 10−5
120
115
100
Figure 11 kg/ks and τg/τs versus T under various feeding flow rates of (a) N2 and (b) N2:NH3.
is required than in N2:NH3 (see Fig. 13). However, the
activation energy values reported for an open reactor to
the atmosphere and a reactor operating in argon are 116
and 106 kJ/mol, respectively [1,2], which are lower but
comparable to those obtained with the lowest nitrogen
flow rate (20 cm3/min) used in this study. Vanka and
Vachusˇka [14] proposed a two-stage mechanism for
the decomposition reaction and reported an activation
energy of 182 kJ/mol under dry nitrogen in closed-
system DTA measurements. The differences between
the reported values and the activation energy deter-
mined in the current study clearly show the influence
of test conditions and the need for determination of Ea
values which stand for a variety of applications.
International Journal of Chemical Kinetics DOI 10.1002/kin.20999

DECOMPOSITION KINETICS OF Na2SiF6 POWDER TO SiF4
393
Figure 12 Influence of the gas flow rate on average pore diameters as a function of temperature for (a) 10 min and (b) 30 min,
under N2:NH3 stream.
Figure 13 Arrhenius plot (1/τ vs. 1/T) for the decomposition reaction under various flow rates of (a) N2 and (b) N2:NH3.
temperature (with 51% percentage contribution),
followed by the gas flow rate (24%), by process-
ing time (15%), and finally the type of gas (3%).
The optimal conditions to reach complete disso-
ciation of Na2SiF6 are pure nitrogen as process-
ing atmosphere, temperature of 650°C, process-
ing time of 40 min, and gas flow rate of 100
cm3/min. Maintaining all parameters and levels
constant, using nitrogen, the fractional weight
loss of Na2SiF6 is about 1.05–1.5 orders of mag-
nitude greater than that in N2:5% NH3.
CONCLUSIONS
Based on the previous results and discussion, within the
framework of the experimental design—in the range of
parameters and levels established for this study—it can
be concluded that
•
•
•
Decomposition of Na2SiF6 is a thermally acti-
vated process that can be adequately described
by the shrinking core model, being SiF4(g) and
an ash layer of NaF(s) the dissociation products.
Results from the ANOVA show that the pa-
rameter that most significantly impacts the frac-
tional weight loss of Na2SiF6 is the processing
•
While the decomposition temperature is not af-
fected by the gas flow rate, it is influenced mod-
erately by an increase in the heating rate.
International Journal of Chemical Kinetics DOI 10.1002/kin.20999

394
SOLTANI ET AL.
•
Within the NaF ash layer formed during Na2SiF6
decomposition, porosity decreases with increas-
ing gas flow rate, time, and temperature.
Applying the shrinking core model allowed es-
tablishing that regardless of atmosphere type, de-
composition kinetics fits to a reaction order of
n ࣈ 0.12 and that both chemical reaction
and mass transfer mechanisms govern Na2SiF6
decomposition.
The activation energy for Na2SiF6 dissociation in
N2 resulted to be lower than that in N2:NH3 at
the same flow rates of 20, 60, and 100 cm3/min.
While in N2:NH3 the determined activation ener-
gies are 140, 120 and 115 kJ/mol, in N2 the values
are 121, 109, and 94 kJ/mol, correspondingly.
which can be reduced by
N
T 2
N
ꢂ
ST =
Yi2 −
(A2)
•
•
i=1
The correction factor (CF) is used for calculation of all
sums of squares. It remains constant for all factors as
it composed of fixed quantities (T and N).
T 2
CF =
(A3)
N
The factor sum of squares is calculated by Eq. (A4)
A12
A22
SA =
+
− (CF)
(A4)
NA
NA
1
2
Niloofar Soltani and Amin Bahrami gratefully acknowledge
CONACyT (Consejo Nacional de Ciencia y Tecnolog´ıa, in
Mexico) for granting a doctoral scholarship. Thanks also to
Dr. Francisco Botello Rionda for technical assistance during
the thermogravimetric analysis.
Mean squares (or variance) are simply the sum of
squares per DOF, as
SA
VA =
(A5)
fA
APPENDIX
The percent influence of the factors can now be cal-
culated by comparing the pure sums of squares of the
factors with respect to the total sum of squares, accord-
ing to Eq. (A6)
The Taguchi experimental design, developed by Dr.
Genichi provides a comprehensive understanding of
the individual and combined effects of various design
parameters based on a minimum number of experi-
mental trials. The ANOVA method used in the Taguchi
method is a statistical technique primarily adopted to
evaluate the significance levels of control process pa-
rameters and the response of each parameter. In the
ANOVA, many quantities such as degree of freedom
(DOF), sum of squares, mean of squares, etc. are com-
puted. These quantities and their interrelationships are
defined below, and their mathematical development is
presented.
SA
PA =
(A6)
ST
The percent influence of the error term is calculated
by
Pe = 100 − (PA + PB + PC)
(A7)
BIBLIOGRAPHY
CF = correction
factor
E = error
experimental
F = variance
ratio
n = number of
trials
r = number of
repetitions
P = percent
contribution
F = degree of
freedom
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International Journal of Chemical Kinetics DOI 10.1002/kin.20999