Compensation effect in trichlorosilane synthesis

Article abstract of DOI:10.1016/S0022-328X(03)00610-7

In a recent publication [J. Acker, K. Bohmhammel, J. Phys. Chem. B 106 (2002) 5105], the reactions between transition metal silicides and hydrogen chloride were studied by isothermal calorimetric measurements. The obtained apparent activation energies and pre-exponential factors show clearly a linear dependence that is attributed to the compensation effect. An isokinetic temperature of 696.9±22.1 K was determined. According to Larsson's model of selective energy transfer, a characteristic frequency of 969.3±46.5 cm^-1 is calculated. The occurrence of the compensation effect is discussed in terms of chemisorption, precursor formation, and the involvement of surface species in essential reaction steps.

Full text of DOI:10.1016/S0022-328X(03)00610-7

Journal of Organometallic Chemistry 686 (2003) 151ꢃ157
/
www.elsevier.com/locate/jorganchem
Compensation effect in trichlorosilane synthesis
Jorg Acker a,*, Klaus Bohmhammel b
¨
a Leibniz-Institute for Solid State and Materials Research Dresden, P.O. Box 270116, D-01171 Dresden, Germany
b Department of Physical Chemistry, Freiberg University of Mining and Technology, Leipziger Strasse 29, D-09596 Freiberg, Germany
Received 1 April 2003; accepted 3 June 2003
Abstract
In a recent publication [J. Acker, K. Bohmhammel, J. Phys. Chem. B 106 (2002) 5105], the reactions between transition metal
silicides and hydrogen chloride were studied by isothermal calorimetric measurements. The obtained apparent activation energies
and pre-exponential factors show clearly a linear dependence that is attributed to the compensation effect. An isokinetic temperature
of 696.99
/
22.1 K was determined. According to Larsson’s model of selective energy transfer, a characteristic frequency of 969.39
/
46.5 cmꢀ1 is calculated. The occurrence of the compensation effect is discussed in terms of chemisorption, precursor formation, and
the involvement of surface species in essential reaction steps.
# 2003 Elsevier B.V. All rights reserved.
Keywords: Compensation effect; Trichlorosilane; Direct reaction; Activation energy; Reaction rate; Calorimetry
1. Introduction
transition state by a reduced enthalpy of the transition
state while the free energy remains constant.
Considering that the temperature dependence of rate
constants for a series of closely related reactions
(indexed by i) is valid described by the Arrhenius
equation (Eq. (1))
Another common phenomenon, the isokinetic effect,
is defined by a point of intersection for a family of
Arrhenius lines representing a series of closely related
reactions i in the ln k vs. 1/T plane. A relationship
between compensation and isokinetic effect is found by
rewriting Eq. (2) as
ꢀ
ꢁ
ꢀEA;i
ki ꢁAi exp
(1)
RT
EA;i
ln Ai ꢁ
ꢂln kiso
(3)
then, the linear relationship between the activation
energies EA,i and the logarithm of the pre-exponential
factors ln Ai according to the empiric relationship in Eq.
(2) is denoted as compensation effect.
RTiso
and inserting into Eq. (1) gives finally
ꢀ
ꢁ
1
1
ꢀ
ꢁ
ln ki ꢁln kiso ꢀEA;i
ꢀ
(4)
EA;i
Tiso
RT RTiso
ln Ai ꢁa
ꢂb; a and b are constants
(2)
Deduced from the coordinates of the point of inter-
section in the Arrhenius plane (ln kiso; Tiso) as well as
from a slope of 1/Tiso and an intercept of ln kiso at
The term ‘‘compensation’’ can be explained by the
Eyring theory of reaction: a positive slope in Eq. (2)
corresponds to a decreasing pre-exponential factor
(entropy of the activated complex DS") with decreasing
activation energy (enthalpy of the activated complex
DH"), i.e. a compensation of a loss of freedom in the
EA,i
ꢁ0 in the EA,i vs. ln Ai plane both effects become
/
synonymous, as shown theoretically in detail by Linert
and Jameson [1]. In contradiction, Liu and Guo [2]
showed that compensatory and isokinetic behavior are
not necessarily in relationship to each other.
Compensation effect and isokinetic effect are phe-
nomena which are very often found for homogeneous
and heterogeneous reactions. In spite of the overwhelm-
* Corresponding author. Tel.: ꢂ
4659-452.
E-mail address: j.acker@ifw-dresden.de (J. Acker).
/
49-351-4659-694; fax: ꢂ49-351-
/
0022-328X/03/$ - see front matter # 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0022-328X(03)00610-7

152
J. Acker, K. Bohmhammel / Journal of Organometallic Chemistry 686 (2003) 151ꢃ157
/
ing number of papers dealing with this effect, its origin
and theoretical explanation are still matter of an on-
this paper. He found that the reaction run with different
contact masses (i.e. mixtures between silicon and copper
containing various catalyst precursors and promoters,
such as cuprous chloride, copper chloride, copper oxide;
zinc, tin, and antimony) clearly obey the linearity
between pre-exponential factor and activation energy
according to Eqs. (2) and (3). Recently, Larsson and
Lieske [13] applied Larsson’s model of selective energy
transfer [6] on the data of Refs. [11,12] and calculated an
going debate (for reviews, see Refs. [1ꢃ3]). Few selected
/
concepts with relevance for the present paper are briefly
introduced here.
From point of view of heterogeneous catalysis,
Larsson [4ꢃ6] developed the selective energy transfer
/
model. According to this model, a characteristic single
frequency vibration v of a catalyst system and a
vibration n for the absorbed reactant molecules on the
catalyst are bound together as a damped oscillator of
classical mechanics. As closer the vibration frequency of
the reactant molecules come to the vibration of the
catalyst as more effective is the energy transfer from the
catalyst into the vibrational states of the adsorbed
molecules. The efficiency of energy transfer is linked to
the pre-exponential factor A in Eq. (2). The chemical
reaction of the adsorbed molecule proceeds in case of
isokinetic temperature of 6069
‘‘heat bath’’ frequency of 8509
to an excitation of the SiÃCH3 rocking mode of
/
20 K. The corresponding
/
30 cmꢀ1 was associated
/
catalytically active intermediates at the silicon surface.
Recently, Poco et al. [14] discussed similarities of
compensation behavior in direct synthesis and isokinetic
behavior found in wet chemical anisotropic etching of
silicon in alkaline solutions [15] on a common base as
anisotropic reaction with reaction rates different for the
different crystallographic planes of silicon. Direct synth-
esis [16,17] and copper silicide formation [18,19] (as
dominant step in activation of contact masses by
reaction between silicon and cuprous chloride CuCl)
were found to be anisotropic. The paper by Poco et al.
[14] leads to the interesting statement that ‘‘the aniso-
tropic character of these reactions seems to be respon-
sible for the existence of compensation effect, which
means that more than one active surface are present,
each one related to a crystallographic plane’’.
perfect resonance vꢁ/n. This yields to the following
expression for Tiso
:
Nhcn
2R
Uvꢁn ꢁTiso
ꢁ
ꢁ0:715n
(5)
According to Patterson and Rooney [7] and Rooney
[8] the compensation effect arises from a multi-step
reaction.
kT
kexp
ꢁ
PKK"
(6)
Our present report refers to a recent kinetic study [20]
about the reaction between transition metal silicide
phases and hydrogen chloride by means of calorimetric
methods.
h
In his model of the extended Eyring equation (Eq.
(7)), the equilibrium constant of the activated complex
K" can be separated from the product of the equili-
brium constants K of all preceding reaction steps, like
adsorption or chemisorption. Expanding the term
Q
2. Experimental and kinetic modeling
Q
KK" of Eq. (6) (according to DGi ꢁ
/
RT ln Ki) gives:
X
Kinetic data on direct reactions of silicon (the
reaction between silicon with methyl chloride, hydrogen
chloride or alcohols) are commonly obtained from the
time-dependency of the amount of formed products.
The data presented here are based on the thermokinetic
evaluation of isothermal calorimetric measurements. All
measurements were preformed in a DSC 111 (Setaram,
France). A flow cell is filled with a silicide sample. An
empty flow cell serves as reference cell. A constant flow
of argon is passed through both cells all the time. After
having established a certain temperature and a stable
baseline of heat flow, the reaction is initiated by opening
a sample valve having a reservoir of a constant volume
which is filled with dry hydrogen chloride. The argon
flow introduces the hydrogen chloride into the sample
cell. The heat flow (heat per time) between sample and
reference cell is measured.
DG0 ꢂDG"
X
X
As stated above, compensation occurs for a constant
ꢁ
DH0 ꢂDH" ꢀT(
DS0 ꢂDS")
(7)
aDG0ꢂDG" by an inverse variation between the
enthalpy and entropy.
/
X
X
Therefore, the compensation effect is explained by
D(
DH0 ꢂDH")ꢁTD(
DS0 ꢂDS")
(8)
equilibrium thermodynamics as a balance between a
thermodynamic contribution of the activated complex
and a thermodynamic contribution of all preceding
reaction steps.
Finally, compensatory behavior itself can arise from
adsorption and chemisorption of gases on solids [9,10].
As the first author in silicon chemistry, Lieske et al.
[11,12] reported about the compensation effect in the
reaction between silicon and methyl chloride (Table 1).
This reaction is referred as direct synthesis throughout
An investigation of a silicide phase starts at a
temperature, which is too low for a chemical reaction.
In subsequent runs with fresh samples, the reaction

J. Acker, K. Bohmhammel / Journal of Organometallic Chemistry 686 (2003) 151ꢃ
/157
153
Table 1
Overview about the relevant parameters belonging to isokinetic effect in alkaline etching of silicon and the compensation effect in direct synthesis and
trichlorosilane synthesis
Alkaline etching of silicon
Direct synthesis
Hydrochlorination
Temperature range of experimental data (K)
Range of activation energies (kJ molꢀ1
303ꢃ
31.7ꢃ
/
363
553ꢃ
22.6ꢃ
/
633
95.1
474ꢃ
41.6ꢃ
137.6 to ꢀ19.6
/
877
)
/86.9
/
/196.3
ꢀ/
/
Tiso (K)
Heat bath frequency (cmꢀ1
Reference
628
873
[15]
6039
/
20
30
696.99
/
22.1
a
)
8509
/
969.39
/
46.5
[12,13]
Present study
a
According to Eq. (5).
temperature is increased with each run until the heat
flow signal becomes structured.
This thermokinetic model describes a reaction by a
first-order rate law; therefore, the obtained rate con-
stants are independent from the composition of the
reactants. The resulting activation energies do not have
to be normalized to the stoichiometry of the considered
silicide phase.
Main assumption of the thermokinetic model is that
the entire reaction is valid described by a single rate
constant which has no relationship to the real reaction
mechanism. This criterion is practically satisfied up to
moderate reaction temperatures while a uniform heat
flow peak is obtained. The evaluation fails at the
temperature at which a structured signal (peak splitting
or shoulders) is observed.
A serious argument against the compensation effect is
a lack of reliable experimental data. The used calori-
metric system provides a constant temperature within
0.02 K. But, due to the exothermic reaction the
temperature inside the reaction cell can temporarily
rise up to several Kelvin above the isothermal tempera-
ture. The total error of the measurements, including
reproducibility and data fitting, is below 10% [20].
In order to prevent uncontrolled depletion of silicon,
the amount of silicide sample was chosen in such a way
that always a manifold excess of silicon (depending on
the stoichiometry of the silicide phase) with respect to
hydrogen chloride is given. This ensures furthermore
that only the adjacent metal-rich silicide phase accord-
ing to the phase diagram is formed (one exception exists:
the reaction between NiSi and hydrogen chloride yields
Ni2Si instead of Ni3Si2 due to a nucleation hindrance of
Ni3Si2 below 600 8C [21,22]). Only the expected silicide
phases were found after reaction, metal chlorides were
not formed. The use of defined silicide samples and a
minimal, but controlled depletion of silicon serves as the
necessary condition that all derived kinetic data can be
attributed to the pure silicide phases.
For kinetic evaluation, the heat flow curves of the
reactions are fitted by the AvramiꢃErofeev equation
/
(Eq. (9)), a common thermokinetic model that describes
a spherical grain formation and growth of a new solid
phase in a matrix phase.
dq
rateꢁ ꢁqtotalk t2 eꢀ(kt)
dt
3 1
3
(9)
3
3. Results
The Arrhenius diagram in Fig. 1 shows two activation
energies for each silicide phase, an apparent positive
activation energy at higher temperature and an apparent
negative activation energy at lower temperature (all
experimental results are summarized in Table 2). The
point of intersect defines a characteristic temperature,
denoted as Tstart, which is a unique parameter for a
silicide phase at a given hydrogen chloride partial
pressure. Tstart was identified as parameter to describe
and to compare the reactivity between various silicide
phases [20]. By plotting activation energies vs. pre-
exponential factors for all studied silicide phases (Fig. 2)
the linear dependence is obtained, which is characteristic
for the compensation effect.
Fig. 1. Arrhenius plot of the reaction between various transition metal
silicide phases and hydrogen chloride. (Reprinted with permission
from Ref. [20]. Copyright 2002 American Chemical Society.)

154
J. Acker, K. Bohmhammel / Journal of Organometallic Chemistry 686 (2003) 151ꢃ157
/
Table 2
Kinetic parameters of the reactions between transition metal silicide phases with hydrogen chloride
Silicide
phase
Reaction start tem-
perature, Tstart (8C)
Minimum rate con-
stant ln kmin at Tstart (kJ molꢀ1) (T ꢀ
Tstart
E
Aꢂ(app)
Pre-exponential fac-
tor ln Aꢂ (T ꢀTstart
E
Aꢀ(app)
(kJ molꢀ1) (T B
Tstart
Pre-exponential factor
ln A (T BTstart
/
/
)
/
/
)
)
)
Ni2Si
Cu3Si
270
310
n.d.
ꢀ
/
6.63
49.99
69.89
80.09
/
1.8
4.239
8.119
8.569
/
0.36
0.95
3.94
ꢀ
ꢀ/
/
35.79
44.39
n.d.
/
7.0
ꢀ
ꢀ/
/
14.439
15.439
n.d.
/
1.66
ꢀ
/
6.29
/5.0
/
/
2.4
/0.55
Cu3Siꢂ
/
n.d.
/20.5
/
Zn a
NiSi
FeSi
313
355
418
435
513
ꢀ
/
4.07
4.42
7.33
4.82
5.38
88.19
41.69
186.19
196.39
100.99
/
13.0
14.009
3.559
24.569
28.559
10.089
/
2.53
0.71
1.82
3.70
2.17
ꢀ
/
59.29
59.49
19.69
137.69
115.89
/
5.1
0.6
3.5
17.1
0.7
ꢀ
/
16.229
15.809
10.759
28.199
23.079
/
1.14
0.13
0.71
2.98
0.12
ꢀ
/
/3.9
/
ꢀ
/
/
ꢀ
/
/
Ni3Si
a-FeSi2
NiSi2
ꢀ
/
/9.2
/
ꢀ
/
/
ꢀ
/
/
ꢀ
/
/22.1
/
ꢀ
/
/
ꢀ
/
/
ꢀ/
/15.1
/
ꢀ/
/
ꢀ/
/
The errors are given as 1s. The symbols are: EAꢂ(app)*
/
apparent positive activation energy, EAꢀ(app)*apparent negative activation energy,
/
ln Aꢂ, ln Aꢀ pre-exponential factors belonging to EAꢂ(app) and EAꢀ(app), respectively. ln Aꢂ and ln Aꢀ were not published before. (Reprinted
*
/
with permission from Ref. [20]. Copyright 2002 American Chemical Society.) n.d., not determined.
a
Cu3Si alloyed with 1.5 at.% Zn.
and processes related to an initial bulk depletion. All
these processes are usually attributed to the induction
period of reaction. Therefore, our thermokinetic data
represent initial rate constants of the induction period of
hydrochlorination of transition metal silicides and not
the steady-state period of a continuous silane formation.
In light of this discussion, the turn from negative to
positive apparent activation energies with increasing
temperature, the most remarkable feature in Fig. 1,
becomes understandable. Below Tstart, adsorption/che-
misorption and precursor formation are dominating.
The measured reaction heat increases slightly with
increasing reaction temperature [20]. If the reaction
Fig. 2. Pre-exponential factor*apparent activation energy compen-
sation plot of the data from Table 2 (confidence interval: 95%).
/
temperature comes close to or higher than Tstart
,
4. Discussion
reaction rate and heat of reaction increase stronger.
Above Tstart the measured reaction heat results from the
highly exothermic formation of chlorosilanes (trichlor-
osilane and silicon tetrachloride). Therefore, the reac-
tion of any silicide phase with hydrogen chloride reaches
an identical state at Tstart, at which the formation of
gaseous products just starts. This corresponds to the
model of a characteristic temperature of onset tempera-
ture of reaction mentioned by Galwey [3] as a possible
explanation for the compensation effect.
All activation energies discussed throughout this
paper are apparent activation energies. These are
functions of the activation energies and reaction en-
thalpies of many individual reaction steps. For the
reaction between a silicide phase and hydrogen chloride,
an apparent negative activation energy is a function of
the exothermic adsorption enthalpy and the activation
energy of precursor formation [20]. The Arrhenius-type
temperature dependence of the adsorption equilibrium
4.1. Rate constants, apparent activation energies, and
models
One has to be careful in the interpretation of
thermokinetic data and to ask what effects can cause
the measured calorimetric reaction signal. It depends on
the magnitude of released heat and on the reaction rate,
whether a reaction is or is not detected by a calorimeter
[23]. If a reaction is faster than the response time of the
calorimeter, the signal of reaction is convoluted by the
response function of the calorimeter. A reaction signal is
hardly to separate from the baseline, if the reaction rate
is slow and the reaction heat is too low.
For complex reaction, as in the present case, a
calorimetric signal is caused by the sum of reaction
enthalpies of all proceeding reactions (adsorption or
chemisorption, precursor formation, formation of si-
lanes, etc.). A sudden introduction of hydrogen chloride
to a native silicide sample causes a calorimetric signal
that is mainly determined by processes at the very early
stage of reaction, like chemisorption, surface reactions
constant Kads of hydrogen chloride adsorption (Aads
pre-exponential factor of adsorption, DHads adsorp-
tion enthalpy) and of a rate constant k1 of precursor
formation (k1,0 pre-exponential factor, EA*activa-
*
/
*
/
*
/
/

J. Acker, K. Bohmhammel / Journal of Organometallic Chemistry 686 (2003) 151ꢃ
/157
155
tion energy) gives Eq. (10):
Table 3
SiÃHx vibration modes on Si(1 0 0) in the range between 900 and 800
/
cmꢀ1
d[precursor]
ꢁk1;0Aadspeq eꢀ(DH
dt
adsꢂEA)=RT
(10)
Vibration mode
Scissor
SiÃ
/
H2 (cmꢀ1
)
Sià )
H3 (cmꢀ1
/
If jDHadsjꢀ
energy for T B
with other models to explain negative activation energies
[24ꢃ30]. In case of complex reaction mechanisms, an
/EA then a negative apparent activation
905 [37]
907 [38]
910 [39]
ꢃ/
ꢃ/
ꢃ/
/
Tstart results. This model is consistent
Deformation
Wag, bend
ꢃ
ꢃ/
/
862 [38]
923 [38]
/
equilibrium reaction followed by the rate-determining
step seems to be a general pattern to cause apparent
negative activation energies [20,31].
890 [40]
ꢃ/
The apparent negative activation energies below Tstart
depend linearly on the silicon content of the silicide
phase. In general, an increase of activation barrier with
decreasing metal content indicates that solely the
composition of the silicide phase, namely the metal
constituent, controls this step (in similarity to geometric
effect in bimetallic heterogeneous catalysis [32]). An
exothermic chemisorption of hydrogen chloride on the
silicide surface and exothermic formation of a chlorine-
containing surface reaction layer, i.e. precursor forma-
tion, without liberation of gaseous products were
identified as reactions that cause apparent negative
activation energies [20].
Apparent positive activation energies are high for
silicides with high silicon content (MSi2-type) or high
metal content (M3Si-type), but low for the phases in
between. This led to a model that the silicide surface can
be divided into hydrogen chloride adsorption sites
(metal atoms) and reaction sites (silicon atoms), in
which the crucial step is thought as the spillover from
one site to another yielding to the formation of silylene
precursors [20].
bonds in the crucial reaction step. It has to be
considered that Tstart describes the liberation of chlor-
osilanes originated from precursor states. Possible
mechanisms like reactive desorption, silylene insertion
(Fig. 3) or spillover processes require necessarily an
involvement of SiÃ
vibrations, like that from SiÃ
silicon (between 650 and 200 cmꢀ1) [34ꢃ
active in the region between 900 and 800 cmꢀ1
/
H and SiÃ
/
Cl bonds, even if their
Clx surface species on
36], are not
/
/
.
Finally, there is no reasonable explanation yet, why
the order of silicide phases along the compensation line
varies from negative to positive apparent activation
energies. Lieske et al. [11,12] observed the same phe-
nomena for various contact masses.
Based on the presented results we conclude that
compensatory behavior in direct reactions is related to
the proceeding chemical reactions instead to the element
silicon or to a certain group of transition metals. It
seems that an involvement of two chemically different
surface sites (metal and silicon) and a spillover process
between them are essential. This is basically the same as
pointed out by Poco et al. [14].
As mentioned above and in Section 4.1, the complex
reaction mechanism of the hydrochlorination reaction
may account for a validity of Rooney’s model as well as
for an explanation of the compensation effect in terms
of adsorption of gases on solids. In fact, the derivation
of the model of the apparent negative activation energy
in Eq. (10) follows the same basic principles as Rooney’s
model. Unfortunately, without detailed knowledge of all
reaction steps, their kinetics, and thermodynamics such
a discussion remains qualitatively.
4.2. The compensation effect
Fig. 2 shows a linear relationship between pre-
exponential factors and apparent positive and apparent
negative activation energies for all studied silicide
phases. An isokinetic temperature of Tiso
ꢁ
/
696.9922.1
/
K is obtained (cf. the arithmetic mean over all Tstart is
648.1 K), which is ca. 100 K higher than for direct
synthesis in case of Lieske’s data. As in Ref. [12], Tiso is
located within the range of the reaction temperatures.
Applying Larsson’s model to our data in Fig. 2, we
obtain a characteristic frequency of 9699
region between 1000 and 850 cmꢀ1 is known for SiÃ
scissor bend modes for molecules of SiH2 (999 cmꢀ1
and SiH4 (914 and 975 cmꢀ1) [33], and for vibration
modes of SiÃHx species bound to Si(1 0 0) surfaces
(Table 3).
The coincidence between the characteristic frequency
and the region of SiÃHx species vibration modes does
not necessarily imply that the compensation effect in
trichlorosilane synthesis is exclusively linked to SiÃ
/
46 cmꢀ1. The
H2
/
)
/
/
Fig. 3. Adapted reaction mechanism of dichlorosilane and trichlor-
osilane formation via silylene intermediates according to Lewis et al.
[45].
/
H

156
J. Acker, K. Bohmhammel / Journal of Organometallic Chemistry 686 (2003) 151ꢃ157
/
4.3. One aspect on the role of the solid phase
In direct reactions, the metal is seen as catalyst or its
precursor. But, the details of the mechanism are still
unclear. It had been shown by Ertl and coworkers [41]
that catalytic activity of RuO2 origins from exchanging
and restoring of lattice oxygen atoms. Iron as catalyst in
ammonia synthesis becomes active by incorporation of
nitrogen that leads to a metastable strained lattice
structure at the iron surface [42]. For silicide-catalyzed
hydrodechlorination of silicon tetrachloride it had been
shown that the catalytic activity of the metal arises from
thermodynamically stable transition metal silicide
phases, which are continuously depleted and restored
with silicon while the reaction runs [43,44]. Hence, the
silicide catalyst is a reactant in silicide-catalyzed hydro-
dechlorination and a similar mechanism is thought for
hydrochlorination of silicon in presence of a metal [20].
In direct synthesis, the situation becomes more
Fig. 4. Relationship between the ‘‘hardness’’ (as (TmMꢀ1Vmꢀ2/3 1/2) of
)
the silicide phases and their reaction kinetics (as minimum rate
constant at Tstart) in trichlorosilane synthesis.
We suggest the following interpretation. A high
hardness results from strong bonds between the lattice
constituents. Therefore, the unsaturated bonds at the
surface of the solid should result in a strong attraction
for gaseous molecules and lead to a high coverage of
adsorbed molecules. A high reaction rate follows, if the
reaction rate is proportional to the coverage with
hydrogen chloride.
complex by the use of siliconꢃ
/
copper mixtures. The
state of a metal in a metalꢃsilicon mixture is thermo-
/
dynamically undefined and reactions in the solid phase
(e.g. silicide formation) superimpose silane formation. If
a pure silicide phase is used for reaction, then the solid
phase entering the hydrochlorination is thermodynami-
cally defined. And, if silicon depletion in the reaction is
negligible, then a correlation of the physical and
thermodynamic properties of the silicide phases to their
reaction properties is justified [20]. Therefore, transport
properties of the solid phase (as well as electronic
properties) should play a role for such type of reaction.
In search for frequencies of silicide lattice vibrations
related to Tiso, we have found a correlation between
reaction rate and lattice dynamics. A parameter to
describe the phonon vibration of a solid is the Debye
temperature TDebye. Due to the lack of data for all
studied silicide phases we refer to an equation given in
5. Conclusion
1) Positive and negative apparent activation energies
and pre-exponential factors for reactions of silicide
phases with hydrogen chloride were obtained from
calorimetric measurements.
2) Due to the experimental procedure, the obtained
kinetic parameters represent mainly processes at the
very early stage of reaction, like chemisorption,
surface reactions, and processes related to an initial
depletion of silicon from the bulk silicide phase.
3) Although they reflect different stages of reaction,
apparent positive and apparent negative activation
energies show clearly a compensatory behavior. The
Ref. [46] to calculate this parameter (Tm*
/melting
isokinetic temperature was determined as 696.99
22.1 K, which lies within the range of the reaction
temperatures.
/
point, M *molar mass, Vm*molar volume).
/
/
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Tm
MVm2=3
TDebye ꢁconst
(11)
4) The application of Larsson’s model of selective
energy transfer gives a characteristic frequency of
969.39
/
46.5 cmꢀ1. This frequency might be attrib-
Eq. (11) is based on the equilibrium between lattice
vibration and the kinetic energy of the atoms at Tm.
If one calculates the value of the constant in Eq. (11)
for silicide phases with a known Debye temperature
(NiSi: 497 K [47], 506 K [48]; FeSi: 745 K [49], 694 K
[50], 596 K [51]; FeSi2: 610 K [42]), the individual
constants scatter around the suggested value of 200 K1/2
g1/2 cm molꢀ5/6 [46]. To avoid any confusion about the
value of the constant, in Fig. 4 the value of the
expression in the root of Eq. (11) is plotted vs. the rate
constant at Tstart. The obtained dependence, which is
not fully understood, implies an increasing reaction rate
at Tstart with increasing ‘‘hardness’’ of the silicide lattice.
uted to SiÃ
/
Hx vibrations and their involvement in
the crucial step of reaction. This is in similarity to
result of direct synthesis, in which the characteristic
frequency was related to SiÃ
/CH3 vibrations.
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