Kinetics of the iodide titanium process by the thermal decomposition of titanium tetraiodide

Article abstract of DOI:10.1149/1.1393573

An extensive study of the kinetics of the iodide titanium process, performed in a flow system by the thermal decomposition of titanium tetraiodide over a tungsten filament substrate, is presented in this paper. The influence of the substrate temperature, T_F, and reactant pressure, P_TiI(4)^o, on the process rate has been analyzed. It has been found that the overall process is rate limited by the transfer of gases in the neighborhood of the substrate. In addition, it has been determined that the rate of titanium transfer is modulated at the filament surface by a certain deposition efficiency that depends on reactant pressure and reaction temperature. The available thermodynamic data for the gaseous titanium iodides at high temperatures fail to explain such an efficiency factor, although the calculations described herein indicate that such data are probably incorrect. Eventually, the titanium growth rate results from the noninterfering contributions of titanium deposition and evaporation rates. The overall reaction rate for the process can be expressed as a function of the operational parameters by the following equation: r_G(T_F, P_TiI(4)^o) = 0.9ε_D(T_F, P_TiI(4)^o)P_TiI(4)^oT_F-r_E(T_F) mg cm^-2 min^-1. ε_D represents the determined deposition efficiency and r_E the titanium evaporation rate in vacuum. Owing to the similarities between the iodide process for titanium and zirconium, the general characteristics for the titanium growth kinetics here described are expected to be also fulfilled for the zirconium case.

Full text of DOI:10.1149/1.1393573

Journal of The Electrochemical Society, 147 (7) 2589-2596 (2000)
2589
S0013-4651(99)08-129-X CCC: $7.00 © The Electrochemical Society, Inc.
Kinetics of the Iodide Titanium Process by the Thermal Decomposition
of Titanium Tetraiodide
F. Cuevas,z J. F. Fernández, and C. Sánchez
Departamento Física de Materiales C-IV, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain
An extensive study of the kinetics of the iodide titanium process, performed in a flow system by the thermal decomposition of tita-
nium tetraiodide over a tungsten filament substrate, is presented in this paper. The influence of the substrate temperature, TF, and
reactant pressure, PoTiI4, on the process rate has been analyzed. It has been found that the overall process is rate limited by the trans-
fer of gases in the neighborhood of the substrate. In addition, it has been determined that the rate of titanium transfer is modulat-
ed at the filament surface by a certain deposition efficiency that depends on reactant pressure and reaction temperature. The avail-
able thermodynamic data for the gaseous titanium iodides at high temperatures fail to explain such an efficiency factor, although
the calculations described herein indicate that such data are probably incorrect. Eventually, the titanium growth rate results from
the noninterfering contributions of titanium deposition and evaporation rates. The overall reaction rate for the process can be
expressed as a function of the operational parameters by the following equation: rG(TF, PoTiI ) ϭ 0.9⑀D(TF, PoTiI )PoTiI TF Ϫ rE(TF)
4
4
4
mg cmϪ2 minϪ1. ⑀D represents the determined deposition efficiency and rE the titanium evaporation rate in vacuum. Owing to the
similarities between the iodide process for titanium and zirconium, the general characteristics for the titanium growth kinetics here
described are expected to be also fulfilled for the zirconium case.
© 2000 The Electrochemical Society. S0013-4651(99)08-129-X. All rights reserved.
Manuscript submitted August 30, 1999; revised manuscript received March 6, 2000.
The iodide process was developed by van Arkel and de Boer in
the 1920s of the present century for the production of high-purity
metals.1 This preparation method follows a cyclic behavior in a
closed vessel where elemental iodine acts as a gaseous transport
agent. It starts with the reaction of iodine and impure titanium metal
in excess at a temperature high enough to release volatile metal
iodides. The evolved iodide vapors then contact an incandescent
tungsten filament where they decompose. The filament serves as
growth substrate for the refined metal, whereas the liberated iodine
diffuses back to the impure titanium in order to complete the cyclic
process. The main interest of this method lies in the fact that inter-
stitial gaseous impurities from the crude metal are not transferred to
the deposited material due to the very low reactivity of iodine against
most metal oxides, carbides, and nitrides. A systematic survey of the
many metals that can be purified by the iodide process has been
made by Rolsten.2 This process has been shown to be particularly
suited for the refinement of titanium and zirconium, as a negligible
content of gaseous impurities in both metals is required for their pro-
duction in a ductile condition.
Up to the 1960s, the iodide process was extensively studied due
to the potential use of zirconium and titanium for nuclear and aircraft
applications, respectively. However, owing to the inherent character-
istics of this deposition technique, it was difficult to obtain these
materials on an industrial scale, and active investigation of this tech-
nique almost stopped. At that time, some fundamental physico-
chemical mechanisms of the process remained unclear and, as an
important example, a deep controversy prevailed about the rate-lim-
iting step in the kinetics of metal deposition. Many investigations,
such as those of Holden and Kopelman,3 Runnalls and Pidgeon,4 and
Shelton,5-7 pointed out that the transport of iodide vapors should
determine the process kinetics. On the other hand, the formation of
lower iodides8-10 (namely, TiI3 and TiI2 in the case of titanium depo-
sition) and the reaction between elemental iodine and the crude
metal11,12 have also been stated to influence the kinetics of the
process. Besides, although vapor transport is frequently accepted to
control the overall rate of metal deposition, it has not been estab-
lished whether the slow step is that of the transport of gases between
the crude metal and the filament region or just their transfer in the
close neighborhood of the filament. This lack of knowledge is con-
nected with contradictory observations. Some authors have found
that the metal deposition rate is proportional to the filament surface
area,4,13 whereas others have obtained a null dependence.12,14
Nowadays, several aspects make the research on this process
again valuable. On one hand, the continuous necessity of preparing
high-purity metals to carry out accurate fundamental studies, such
as, for example, the assessment of the Ti-H phase diagram.15,16 On
the other hand, it is now possible to acquire a better understanding
of the iodide process kinetics with the help of the powerful analyti-
cal chemical vapor deposition (CVD) tools that have been developed
in the last thirty years. Additionally, further research on the proper-
ties of titanium tetraiodide is, at present, highly desirable, since this
compound is a promising precursor for the preparation of TiN diffu-
sion barriers to be used in integrated circuits.17
The scope of the present paper is to establish the main character-
istics of the iodide process kinetics. To this end, an extensive research
program on the preparation of iodide titanium was performed in our
laboratory using titanium tetraiodide as starting material.18,19 This
modification of the original process was adopted in the past by Ingra-
ham and Pidgeon20 and Kesler,21 but definite kinetic results were not
obtained at that time. In this way, the process acquires a flow behav-
ior and the problems related to the reaction between the crude titani-
um and iodine (i.e., the formation of lower titanium iodides and sur-
face passivation of the crude titanium) are avoided. Furthermore, the
preparation method becomes, in principle, the easiest example of a
CVD process: the thermal decomposition of a volatile reactant to pro-
duce a solid deposit.22 In order to determine the rate-limiting step of
this process, we have studied the dependence of the titanium growth
rate on the substrate temperature, reactant pressure, and substrate sur-
face area. In a previous publication,23 a detailed description of the
experimental system was given together with a phenomenological
model which allows monitoring of the titanium growth rate from the
variation of the substrate electrical resistance. In that publication, the
dependence of the titanium growth rate on the substrate surface area
was analyzed. It was found that these parameters fulfill a linear
dependence. That result suggested that the titanium growth rate is
controlled by the transfer of gases in the vicinity of the substrate,
however, a more detailed work was said to be prudent to confirm this
statement. Such a work is presented in this paper.
Experimental
The growth of iodide titanium films has been accomplished in a
self-designed CVD reactor made entirely of glass, as dictates the
high reactivity of iodide vapors against most metals. It comprises a
central reaction chamber, where a tungsten substrate is located, and
two side arms to place, respectively, a weighed quantity of TiI4 pow-
der (ϳ1 g) and a gas by-product cooling trap. The tungsten substrate
z
E-mail: fermin.cuevas@glvt-cnrs.fr
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2590
Journal of The Electrochemical Society, 147 (7) 2589-2596 (2000)
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mental setup: the substrate or filament temperature, the reactant
(TiI4) pressure, and the substrate surface area. The dependence of the
process rate, denoted as r, on these parameters for every type of con-
trol is now described and summarized in Table I.
is a ribbon filament of typical dimensions 40 ϫ 2 ϫ 0.025 mm
which is supported to the chamber walls by two thick tungsten elec-
trodes. In addition, two very thin tungsten wires are welded at the fil-
ament edges to perform electrical resistance measurements by the
four-probe method. This apparatus is strongly degassed and vacuum
sealed at ϳ10Ϫ6 Torr.
To start with the deposition process, the TiI4 arm and the reaction
chamber are introduced in a transparent furnace, whereas the cool-
ing arm is attached to a liquid nitrogen reservoir. The TiI4 powder is
then heated to a constant sublimation temperature within the range
380-420 K to generate a certain TiI4 pressure at the inlet of the reac-
tion chamber. Thus, the inlet TiI4 pressure becomes determined by
the vapor pressure of this compound, which is reported to be24
Mass-transport processes present growth kinetics dictated by the
thermodynamic equilibrium constant of the overall chemical reac-
tion. The reaction rate law depends exponentially on the heat of the
overall reaction at constant pressure, ⌬H, and on the inverse of the
substrate temperature, TF. In our case, the whole heterogeneous reac-
tion under study is TiI4(g) r Ti(s) ϩ 4I(g), where ⌬H ϭ
170 kcal/mol. Concerning the dependence of the rate of reaction on
reactant pressure, the process rate varies proportionally with the dif-
ference between the reactant pressure at the reactor inlet, PoTiI4, and
eq,F
the reactant equilibrium pressure at the substrate surface, P
.
TiI
4
log PTiI4(atm) ϭ 39.325 Ϫ 6239/T(K) Ϫ 10.36 log T(K) [1]
Finally, no dependence of the reaction rate on the substrate surface
area should be observed for a mass-transport-controlled process.
In the case of a transfer-controlled process, the reaction rate be-
haves as a power function of the substrate temperature, T mF , where
the exponent, m, varies from Ϫ1/6 to 2. If the reaction rate is sup-
posed to respond to a thermally activated process, an apparent acti-
vation energy, ⌬Ea, within the range 3-8 kcal/mol is obtained.
Regarding the other two operational parameters, the reaction rate is
proportional to PoTiI4 and to the geometric substrate surface area, i.e.,
is not influenced by the substrate roughness.
For a kinetically controlled process, the expression for the reac-
tion rate attends to the occurrence of an activation barrier that is con-
nected with the involved surface reactions. The reaction rate follows
an Arrhenius equation on its temperature dependence, is proportion-
al to PoTiI4, and is dependent on the actual substrate surface area.
The TiI4 sublimation temperature is measured by an externally
clamped NiCr-NiAl thermocouple, the accuracy of which is estimat-
ed to be Ϯ1 K. The described temperature configuration in the whole
system produces a gentle flow of the reactant vapor through the reac-
tion chamber. Next, the filament is electrically lighted to the work-
ing temperature (1400-1850 K) at which the TiI4 vapors undergo
thermal dissociation, and the titanium deposits over the hot filament.
The filament temperature is monitored by optical pyrometry, with an
estimated accuracy of Ϯ20 K. As the titanium growth proceeds, the
electrical current passing through the filament is gradually increased
in order to maintain a constant filament temperature. Simultaneous-
ly, the variation of the filament electrical resistance is monitored and
correlated with the titanium growth rate as described in Ref. 23.
When the TiI4 powder is completely sublimated, the titanium depo-
sition ends. Finally, the reaction chamber is crashed and the filament
is extracted to weigh the grown titanium mass and to determine its
geometrical dimensions. It should be noted that the described proce-
dure implies that every experiment is carried out with distinct reac-
tion chambers which, as far as possible, have identical geometry. A
more detailed description of the experimental apparatus and proce-
dures can be found elsewhere.18,19,23
Results
A complete set of experiments has been conducted in order to
study the dependence of the reaction rate on the filament tempera-
ture, TF, the titanium tetraiodide pressure at the inlet of the reaction
chamber, PoTiI4, and the filament surface area. As mentioned earlier,
the analysis of the r dependence on the filament surface area was
already presented in another publication23 and, therefore, only its
conclusions are quoted in this paper.
Analytical Framework for Kinetic Determination
of CVD Processes
The present kinetical study uses the analytical frame reviewed by
Shaw for CVD processes with open flow systems.25 This frame is
now briefly described to facilitate a straightforward discussion of the
obtained results.
The main data corresponding to both types of experiments here
reported are given in Table II. Nine experiments were carried out at
a constant sublimation temperature of 403 Ϯ 1.5 K, i.e., at PToiI
ϭ
(7 Ϯ 1) 10Ϫ4 atm, for different filament temperatures within4the
range 1410-1830 K. To examine the influence of PoTiI4 on the process
rate, four experiments were run at a constant filament temperature of
1685 Ϯ 10 K, while the TiI4 sublimation temperature, TS, was var-
Shaw points out that any CVD process may be considered to con-
sist of a sequence of consecutive steps. The reactant species under-
go three major steps during the vapor phase growth: (i) transport of
reactants to the growth region, (ii) transfer of reactants from this
region to the substrate surface, and (iii) a complete set of surface
reactions leading to the final material growth. Analogous steps are
followed by the by-products of the chemical reaction in their way
toward the system outlet. The fundamental kinetic principle of this
approach is that if one of these steps is inherently slower than the
others, it determines the overall rate for the process. This step is also
called the rate-limiting step.
The rate-limiting step provides a specific type of control or
regime to the process and determines the kinetic expression for the
rate of reaction. Three different types of control have been observed
to occur in CVD. If the process is limited by the transport step, the
type of control is denoted as mass transport and the rate of reaction
is ruled by thermodynamic laws. If the process is limited by the
transfer step, the process is said to be transfer controlled and is gov-
erned by physical phenomena such as diffusion or convection of
gases. Finally, a process is kinetically controlled when the surface
reactions at the substrate are rate determining and then it becomes
ruled by the kinetics of such chemical reactions.
ied within the range 384-413 K (PoTiI values within the range 2-
4
13 ϫ 10Ϫ4 atm). Some data are lacking for the experiment carried
out at the highest filament temperature, exp 9. This is due to a hot
spot appearing at the filament during its growth, which caused the
failure of the filament. The sublimated TiI4 mass, mTiI , the final
4
grown titanium mass, mTi, and the growth time, tG, are also displayed
in Table II together with the two most important parameters that
Table I. Dependence of reaction rate on selected operation
parameters for CVD processes working under different types
of control.
Type of control
Operating
parameters
Mass transport
Transfer
Kinetic
∆E
∆H
F
a
Substrate
temperature
r ϰ eϪRT
r ϰ eϪRT
F
r ϰ TFm
⌬H ϭ 170
m ϭ [Ϫ1/6 Ϭ 2]
kcal/mol
⌬Ea ϭ [3 Ϭ 8] kcal/mol
Reactant
pressure
r ϰ PoTiI Ϫ PeTqiI,F
r ϰ PoTiI
r ϰ PoTiI
4
4
4
4
In order to find out the type of control that governs a CVD
process, the effect of various operating parameters on the overall
reaction rate is commonly studied. We have focused our attention on
some selected parameters that can be changed at will in our experi-
Substrate
surface area
Independent
Dependent on
geometrical
surface area
Dependent
on actual
surface area
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Journal of The Electrochemical Society, 147 (7) 2589-2596 (2000)
2591
S0013-4651(99)08-129-X CCC: $7.00 © The Electrochemical Society, Inc.
Table II. Growth parameters for the experiments conducted in this investigation.
TF
(K)
TS
(K)
PoTiI
mTiI
(mg)
mTi
(mg)
tG
(min)
rG
⑀
4
G
4
Exp
(10Ϫ4
)
(mg minϪ1 cmϪ2
)
(%)
Experiments conducted at constant reactant pressure: PoTiI4 ϭ (7 Ϯ 1) 10Ϫ4 atm
Exp 1
Exp 2
Exp 3
Exp 4
Exp 5
Exp 6
Exp 7
Exp 8
Exp 9
1410
1435
1485
1545
1590
1630
1680
1770
1830
4031.
402.5
4031.
4031.
403.5
4031.
404.5
401.5
402.5
17.1
16.9
17.1
17.1
17.3
17.1
17.8
16.5
16.9
1240
1085
1060
1020
1835
1130
1290
1845
1830
44.2
45.9
521.
51.2
44.4
62.7
69.6
46.5
115
177
107
175
182
186
182
155
0.31
0.43
0.41
0.58
0.44
0.62
0.68
0.64
41
49
57
58
62
64
63
64
Fused filament
Experiments conducted at constant filament temperature TF ϭ 1685 Ϯ 10 K
Exp 10
Exp 11
Exp 7
1685
1685
1680
1685
384.5
3961.
404.5
4131.
12.1
14.5
17.8
131.
1440
1500
1290
1440
86.9
82.6
69.6
721.
265
115
182
140
0.26
0.49
0.68
1.30
70
64
63
58
Exp 12
a TF: filament temperature, TS: TiI4 sublimation temperature, PoTiI : TiI4 pressure at the reactor inlet, mTiI : TiI4 sublimated mass, mTi: grown titanium
4
mass, tG: growth time, rG: titanium growth rate, and ⑀G: process4efficiency.
result from the process: the rate of titanium growth, rG, and the effi-
ciency of titanium growth, ⑀G. It is worth remarking how these para-
meters are evaluated. The rate of titanium growth is obtained from
the measurement of the variation of the filament electrical resistance
when the experiment is under stable thermodynamic conditions.23 In
other words, this rate is evaluated while the filament temperature and
the reactant pressure are those given in Table II. The measurements
that were obtained at the final stage of the growth are discarded,
since the titanium tetraiodide pressure depletes at that time due to the
finite quantity of the starting material. Concerning the process effi-
ciency, ⑀G values are calculated by dividing the final grown titanium
mass by the titanium sublimated through the reaction chamber in the
form of TiI4, i.e.
reactant pressure on the process rate is subsequently studied and the
kinetic law that describes the overall process rate is finally given.
Determination of the rate-limiting step by varying the filament
temperature.—A detailed analysis of the influence of the filament
temperature on the process reveals that the overall reaction rate is, in
fact, the result of several reaction rates such as the rate of titanium
evaporation, the rate of titanium deposition, and the rate of titanium
transfer. These rates are noted and their characteristics fully ex-
plained as soon as required in the course of the analytical procedure.
Titanium evaporation rate and titanium deposition rate.—The
appearance of hot spots in the experiment conducted at 1830 K can
be related to a fast rate of titanium evaporation at high deposition
temperatures. In fact, as displayed in Fig. 1a, the reported titanium
evaporation rate in vacuum,26 denoted here as rE, acquires a signifi-
cant value in comparison with those of the titanium growth rate at
temperatures above 1700 K. This evaporation rate is an inherent
property of the titanium metal and plays no role on the series of con-
secutive steps that constrain the process kinetics. Therefore, to iden-
tify the rate-limiting step of the iodide process, the study of the rate
of titanium deposition, instead of its growth rate, on the filament
substrate, rD, is more convenient. This rate is written as
100 mTi
⑀G (%) ϭ
[2]
0.0862 mTiI
4
The dependence of rG and ⑀G on the filament temperature and the
reactant pressure at the chamber reaction inlet is plotted in Fig. 1.
The titanium growth rate seems hardly to increase with the filament
temperature (Fig. 1a). No peculiar behavior of this parameter that
could account for filament failure at 1830 K are observed when fil-
ament temperatures approach 1800 K. The intrinsic rate of titanium
evaporation in vacuum26 is also drawn in Fig. 1a since it is used in
the next section to discuss the causes of the filament failure. Fig-
ure 1b displays the variation of the process rate as a function of reac-
tant pressure, PoTiI4, for which a linear-type behavior seems to be
attained. The relationship between the process efficiency and the fil-
ament temperature is depicted in Fig. 1c. This parameter increases
strongly from ϳ40% at 1400 K up to ϳ65% at 1600 K and then
remains essentially constant for higher temperatures. On the other
hand, the process efficiency decreases weakly but continuously from
ϳ70% down to ϳ60% within the analyzed range of reactant pres-
sure PoTiI4, as is illustrated in Fig. 1d.
Ϫ0.5
rD ϭ rG ϩ rE, where rE ϭ 1.84 ϫ 107 TF
Ϫ4
T ]
ϫ 10[7.782Ϫ24275/T Ϫ2.3 ϫ 10
(mg minϪ1 cmϪ2) [3]
F
F
In other words, part of the deposited titanium atoms becomes evap-
orated while the rest gives rise to the filament growth. This new para-
meter, rD, is the significant parameter for the subsequent kinetic
analysis.
The dependence of rD on the filament temperature is displayed in
Fig. 2. rD data have been fitted to the characteristic functions corre-
sponding to the different regimes described in the Analytical frame-
work section. Although the rD values fit well to a power law (depict-
ed by a dotted line), the value of the exponent, m ϭ 3.8, is too high
for a purely transfer-controlled process. To check a possible agree-
ment with exponential laws, the logarithm of the deposition rate is
plotted vs. the absolute reciprocal temperature in the inset of Fig. 2.
This Arrhenius plot follows a good linear behavior, leading to an
apparent activation energy of 11.9 kcal/mol. This value is much
lower than the expected heat for the overall reaction, ⌬H ϭ
170 kcal/mol, and therefore, a purely mass-transport-controlled pro-
cess should be also discarded. Hence, from functional considera-
tions, one could identify the process as kinetically controlled. How-
ever, this conclusion is uncertain because the high filament temper-
Discussion
The main purpose of the following analysis is to establish the
rate-limiting step of the process. To this aim, a right assignment of
the kinetic law that limits the process rate is required. At the end, a
full understanding of the partial reaction rates that are involved in the
overall process and the identification of the limiting one allows for
an expression that describes the overall process rate. To begin with,
we discuss the effect of the filament temperature on the titanium
growth rate and process efficiency, as this operational parameter pro-
vides the key information of the present analysis. The effect of the
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2592
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Figure 1. Titanium growth rate and
process efficiency as a function of the
operational parameters investigated in this
work. (a) Titanium growth rate (᭹) and
reported evaporation rate of titanium in
vacuum (—) as a function of filament tem-
perature. The vertical dashed line stands
for a failed experiment at 1830 K. (b) Vari-
ation of titanium growth rate with reactant
pressure at the reactor inlet. (c) Process
efficiency as a function of filament tem-
perature. (d) Variation of process efficien-
cy with reactant pressure at the reactor
inlet.
atures involved in the iodide process ensure fast rates for typical sur-
face reactions such as gas adsorption and desorption, surface diffu-
sion, or site incorporation. Thus, at the present level of the analysis
procedure, it would be more reasonable to conclude that the iodide
titanium process in our experimental system might be controlled by
a mixture of transfer and mass-transport regimes.
mTi ϩ tGrES
⑀
ϭ
[4]
D
0.0862mTiI
4
where S represents the filament surface area and tG the growth time.
The numerator in Eq. 4 is simply the addition of grown and evapo-
rated titanium masses.
The relationship between the obtained deposition efficiency and
the filament temperature is shown in Fig. 3a. It can be observed that
Deposition efficiency and titanium transfer rate.—In order to get a
deeper insight into the central mechanism that controls the process
kinetics, it seems appropriate to introduce a new efficiency factor:
the deposition efficiency, ⑀D. This parameter stands for the fraction
of titanium that becomes deposited on the filament surface with
respect to the titanium transported through the reaction chamber as
TiI4. Therefore, its definition is analogous to that of the process effi-
ciency regarding the titanium growth rate. The deposition efficiency
can be calculated as
⑀
increases strongly at low temperatures (1400-1500 K), more
D
slowly at intermediate temperatures (1500-1700 K), and ultimately
grows up again strongly at high filament temperatures (1700-
1800 K). The dependence of ⑀D on the filament temperature, at
PoTiI ϭ 7 ϫ 10Ϫ4 atm, can be tentatively fitted within the tempera-
ture4range 1400-1800 K to a polynomial function, as plotted in
Fig. 3a, to be used in further analyses (the General evaluation of the
overall process rate section)
⑀D(TF) ϭ Ϫ109.18 ϩ 0.2076TF Ϫ 1.311 ϫ 10Ϫ4 TF2
ϩ 2.764 ϫ 10Ϫ8 TF3 [5]
The behavior of similar efficiency parameters that are reported in the
literature, either for zirconium (Fig. 3b) or titanium (Fig 3c) deposi-
tion, are also displayed in Fig. 3 for comparison purposes. Figure 3b
shows the variation of the decomposition coefficient with tempera-
ture for ZrI4, as reported by Holden and Kopelman3 and Döring and
Molière,13 at reactant pressures of ϳ10Ϫ9 atm and ϳ10Ϫ6 atm,
respectively. This coefficient is defined in Ref. 3 as the probability
that a given zirconium tetraiodide molecule will decompose upon
impinging once on a hot surface in vacuum. Figure 3c shows the
experimental equilibrium conversion of TiI4 to titanium metal as re-
ported by Kesler21 at reactant pressures of 1.6 and 3.8 ϫ 10Ϫ3 atm.
This conversion factor refers to the fraction of TiI4 which deposits
titanium according to the heterogeneous thermodynamic equilibrium
that takes place in the vicinity of the filament surface. The definition
of the decomposition coefficient given represents a kinetic approach
to this event, while that of the equilibrium conversion attends to a
thermodynamic standpoint. The first case implies the presence of a
transmission coefficient, according to the transition state theory, to
allow for the fact that not every activated complex leads to reac-
tion.27,28 The thermodynamic point of view involves the formation
Figure 2. Titanium deposition rate as a function of filament temperature.
(– – –)The best power fit to the experimental data. Inset: Arrhenius plot of the
same data and best linear fit to the experimental data.
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Journal of The Electrochemical Society, 147 (7) 2589-2596 (2000)
2593
S0013-4651(99)08-129-X CCC: $7.00 © The Electrochemical Society, Inc.
Figure 3. Deposition efficiency as a function of the filament temperature for the iodide process as observed by different authors. (a) Titanium deposition effi-
ciency obtained in this work for a constant reactant pressure at the reactor inlet of PToiI4 ϭ 7 ϫ 10Ϫ4 atm. Best polynomial fit to the experimental data is given.
(b) Decomposition efficiency for the ZrI4 molecule as reported by (᭹) Holden and Kopelman3 and (ᮀ) Döring and Molière.13 (c) Equilibrium conversion of
titanium tetraiodide to titanium at two different TiI4 pressures as reported by Kesler.21
of lower iodides, namely, TiI3, TiI2, and TiI, in chemical equilibrium
with TiI4 and iodine around the filament vicinity. Both approaches
could, in principle, explain the finding of a deposition efficiency in
the iodide process. In the following discussion we try to verify if the
reported thermodynamic knowledge on titanium iodides accounts
for the deposition efficiency observed in this investigation.
The formation of the different gaseous Ti-I species in thermody-
namic equilibrium with solid titanium is given by the following
equations
1
2
[11]
I2 ↔ I
The equilibrium constants for the previous equations were calculat-
ed within the temperature range 1000-2000 K using the thermody-
namic data available in the literature.24,29 Additionally, it is assumed
that a total iodine equivalent pressure P(total I), which is determined
by the incoming vapor, remains invariable at the filament region:
P(total I) ϭ 4PoTiI4. Thus, the following boundary condition should
be satisfied
Ti ϩ 2I2 } TiI4
[6]
[7]
P(total I) ϭ ⌺np(TiIn) ϩ ⌺np(In) ϭ 4PToiI
[12]
4
3
After solving Eq. 6-12 for a certain total iodine equilibrium pressure,
the partial pressures of all Ti-I species can be evaluated. Figure 4a
shows such partial pressures as a function of the reaction tempera-
ture for P(total I) ϭ 10Ϫ4 atm, i.e., the typical value in the iodide
process. This analysis indicates that TiI2 should be the principal
gaseous Ti-containing species in the titanium iodide process for all
operating temperatures. This result is probably incorrect.
Ti ϩ I2 ↔ TiI3
2
Ti ϩ I2 } TiI2
[8]
1
Ti ϩ I2 ↔ TiI
[9]
2
The deposition efficiency for the titanium iodide process can be
now calculated from thermodynamic considerations as
Ti(s) } Ti(g)
[10]
Figure 4. Thermodynamic studies on the
composition of the Ti-I species and Zr-I
species in the iodide process. (a) Partial
pressures of Ti-I species in equilibrium
with Ti(s) as a function of the reaction tem-
perature, according to the present knowl-
edge of the thermodynamic data, for
P(total I) ϭ 10Ϫ4 atm. (b) Deposition effi-
ciency in the iodide process as a function
of reaction temperature as resulting from
(—) thermodynamic calculations at differ-
ent values of total iodine equivalent pres-
sure in comparison with (᭹) experimental
data obtained in this work. (c) Partial pres-
sures of Zr-I species in equilibrium with
Zr(s) as a function of the reaction tempera-
ture, according to the thermodynamic data
before Kleinschmidt et al.30 for P(total I)
ϭ 10Ϫ4 atm. (d) Partial pressures of Zr-I
species in equilibrium with Zr(s) as a func-
tion of the reaction temperature for P(total
I) ϭ 10Ϫ4 atm as reported by Kleinschmidt
et al.30
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2594
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before, this factor represents, from an empirical point of view, the
Po
Ϫ
np(TiIn)
TiI
ratio of deposited titanium to transported titanium through the reac-
tion chamber as TiI4. It should be noted that the TiI4 deposition effi-
ciency is not the rate-limiting step in the iodide process, since very
high values are obtained for ⑀D at the typical operation temperatures
of the process. However, the identification of this factor allows intro-
duction of a new rate parameter, rT, which is denoted as the titanium
transfer rate, which can be expressed as
∑
4
⑀
ϭ
[13]
D
Po
TiI
4
Figure 4b displays the behavior of calculated ⑀D values as a function
of reaction temperature for P(total I) ranging from 10Ϫ7 to 10Ϫ3 atm.
The experimental data obtained in this investigation, corresponding
to a total iodine equivalent pressure of ϳ10Ϫ3 atm, are plotted in the
same figure by solid dots. Several divergences are observed between
experimental and calculated data. In the first place, the experimental
deposition efficiency is much higher than the thermodynamic one
for the same value of P(total I) ϭ 10Ϫ3 atm. Besides, the functional
form for the calculated curves, without any inflection point, differs
notably from the experimental behavior. On the other hand, the ther-
modynamic calculation at least indicates that the deposition effi-
ciency increases as total pressure decreases, in agreement with all
experimental data displayed in Fig. 3.
The above-mentioned discrepancies, together with the observa-
tions pointed out by other authors, may indicate that the reported
thermodynamic data for the titanium iodides at high temperatures
(mostly estimated) are erroneous. The main outcome of these ther-
modynamic considerations, i.e., TiI2 is the principal gaseous Ti-con-
taining species of the process, contradicts the experimental results of
Ingraham and Pidgeon20 and Rolsten.2 The first authors have ob-
served no evidence of sub-iodide formation during the titanium re-
fining at deposition temperatures higher that 1500 K. Likewise, Rol-
sten indicates that for a filament temperature of 1740 K, the gases
removed from the reaction bulb were exclusively I2 and TiI4. A more
recent study of Kleinschmidt et al.30 concerning the thermodynam-
ics of the gaseous zirconium iodides seems, in principle, to clarify
this controversy. They conducted equilibrium calculations with the
data reported at that moment and obtained the partial pressure vs.
temperature configuration given in Fig. 4c for a value of P(total I) ϭ
10Ϫ4 atm. It should be noted that the characteristics of the partial
pressure composition for the Zr-I system and those obtained in this
paper for the Ti-I system (Fig. 4a) are identical. Kleinschmidt et al.
were not convinced of the results derived from the thermodynamic
data available at that time and decided to perform an experimental
study on gaseous equilibria among the zirconium iodides by high-
temperature mass spectrometry. They got significant variations of
the equilibrium constants in the Zr-I system in comparison with the
previous estimations. The new representation of the partial pressures
of Zr-I species for a value of P(total I) ϭ 10Ϫ4 atm after Klein-
schmidt et al. is that in Fig. 4d. Here, ZrI4 becomes the major Zr-
containing species in the process. Furthermore, the intricate varia-
tion between the partial pressures of different compounds in the
operational temperature range (1400-1900) K could account for the
observed inflections in the ⑀D vs. TF relationship.
rD
rT ϭ
[14]
⑀
D
The titanium transfer rate describes the arrival rate of titanium
atoms to the filament, and only a part of them deposits due to an
intrinsic deposition efficiency for the TiI4 molecule. The calculated
data for rT as a function of the filament temperature is plotted in
Fig. 5. Although these data show a considerable dispersion, a slight
increment of rT with the filament temperature is observed. The func-
tional dependence of rT is now analyzed to discern the type of control
that regulates this rate. When rT data are fitted to a power law (dis-
continuous line in Fig. 5) an exponent value of m ϳ 1 is obtained.
Additionally, an apparent activation energy of ⌬Ea ϭ 3.3 kcal/mol is
calculated from the Arrhenius plot illustrated in the inset of Fig. 5.
The notable dispersion of rT data can be attributed to the inevitable
geometric variations of the reaction apparatus that occur from one
experiment to another and to the weak dependence of the titanium
transfer rate with the filament temperature. According to the Shaw’s
review, described previously, this result indicates that the arrival of
titanium atoms to the filament is exclusively controlled by the trans-
fer of gaseous species in the vicinity of the filament, and therefore, a
mass-transport-controlled regime should be definitely discarded for
this process. Therefore, we can conclude that the rate-limiting step in
the iodide process for our experimental configuration is the transfer
of gaseous species just around the filament substrate.
Distinct values of apparent activation energy for the titanium
iodide process are provided in the literature. From the experimental
data reported from Runnalls and Pidgeon,4 concerning the variation
of the titanium growth rate with the filament temperature, an appar-
ent activation energy of 45 kcal/mol can be calculated. Besides,
Ingraham and Pidgeon20 estimate a ⌬Ea value of 92 Ϯ 2 kcal/mol for
the deposition of titanium on a tungsten bar. The disagreement
between the results found by these authors, and also with the one
obtained in this investigation, can be qualitatively explained by the
distinct experimental configurations used in each case. The first
On the basis of the previous discussion, it would be expected that
an experimental determination of the thermodynamic data for the
Ti-I system at high temperatures leads to analogous changes on the
Ti-I equilibrium constants like those reported for the Zr-I system.
Unfortunately, this seems not to be the case. A recent investigation
using mass spectroscopy on the thermodynamic properties of
gaseous lowest titanium iodides31 indicates that the component par-
tial pressures of the gas phase in this system are like those given in
Fig. 4a. Taking into account the close similarities between the prop-
erties of titanium and zirconium iodides, which are reinforced by the
analogous characteristics of the iodide process for both systems, we
believe that such a contrast in their thermodynamic properties is
unlikely. Further investigations on the actual gas composition of Ti-
I species in the vicinity of the filament are becoming indispensable
to clarify the present situation. Such study is at this moment beyond
the scope of this paper.
Although the current status of our knowledge on the thermody-
namic properties of Ti-I species is unsatisfactory, the experimental
results of the present study and those documented in the literature
indicate that an unequivocal deposition efficiency for the titanium
tetraiodide molecule occurs in the iodide process. As mentioned
Figure 5. Titanium transfer rate as a function of filament temperature.
Dashed line stands for a representative linear fit to the experimental data.
Arrhenius plot of the same data is given in the inset figure in which the best
linear fit to the experimental data is depicted by a continuous line.
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Journal of The Electrochemical Society, 147 (7) 2589-2596 (2000)
2595
S0013-4651(99)08-129-X CCC: $7.00 © The Electrochemical Society, Inc.
Figure 6. (a) Deposition efficiency as a
function of reactant pressure at the reactor
inlet for the experiments conducted at a
constant filament temperature of 1685 K.
The best fit of the experimental data to a
polynomial function is depicted by a con-
tinuous line. (b) Titanium transfer rate as a
function of reactant pressure at the reactor
inlet for the experiments conducted at a
filament temperature of 1685 K. The best
fit of the experimental data to a linear
function passing through the origin is
given.
authors carried out the titanium deposition in a closed bulb accord-
rG ϭ rD Ϫ rE
[16]
ing to the conventional cyclic process. Under these circumstances,
the reaction rate between titanium and iodine and the coincidence in
the diffusion pathways for reactants and by-products may contribute
to an increase of the apparent activation energy in comparison with
that of a transfer-controlled process. The second authors used a flow
system equipped with a capillary outlet that precedes the iodine con-
denser. Therefore, Ingraham and Pidgeon conducted their experi-
ments under a regime that becomes strongly determined by the trans-
port of by-products at the system exit, leading to a strong increment
of the apparent activation energy. On the contrary, these impedi-
ments for fast reaction kinetics in the iodide process are avoided in
our experimental system and a lower value for ⌬Ea is obtained.
It has been established that the titanium deposition rate is deter-
mined by the transfer of titanium tetraiodide vapors in the filament
vicinity, rT, (approaching dashed line in Fig. 7) which is modulated
at the filament surface by a certain deposition efficiency, ⑀D. This
efficiency describes the ratio of arriving Ti atoms, in the form of tita-
nium tetraiodide, to the deposited Ti atoms. It depends on both oper-
ational parameters, i.e., filament temperature and reactant pressure.
A unique empirical function can be completed, in agreement with
Eq. 5 and 15, to describe the deposition efficiency
⑀D(TF , PoTiI ) ϭ Ϫ 108.87 ϩ 0.2076TF Ϫ 545PoTiI Ϫ 1.311
4
4
ϫ 10Ϫ4 T F2 ϩ 2.2 ϫ 105 PToiI 2 ϩ 2.764 ϫ 10Ϫ8T F3 [17]
4
Influence of the reactant pressure on the process rate.—A simi-
lar analysis to that presented in the previous section can be applied
to the experiments conducted at constant filament temperature. Con-
sidering the negative contribution of titanium evaporation to the tita-
nium growth rate, the titanium deposition rate and deposition effi-
ciency can be evaluated according to Eq. 3 and 4, respectively, for all
experiments conducted at a constant filament temperature of
1685 K. Afterward, by using Eq. 14, the values for the titanium
transfer rate can also be calculated. The most interesting results
obtained from these calculations are shown in Fig. 6. Figure 6a dis-
plays the deposition efficiency as a function of the reactant pressure
at the reactor inlet. This efficiency decreases with the reactant pres-
sure, in agreement with other authors (Fig. 3b and c), and with ther-
modynamic calculations illustrated in Fig. 4b. The ⑀D values have
been tentatively fitted for subsequent analyses, as depicted by a con-
tinuous line, to the following polynomial function
Taking into account Eq. 3, 14, 16, and 17, the dependence of the tita-
nium growth rate as a function of the operational parameters, TF and
PoTiI4, can be written as
rG(TF, PoTiI ) ϭ ⑀D(TF, PoTiI )rT Ϫ rE(TF)
[18]
4
4
In addition, the titanium transfer rate has been determined to be
proportional to TF and PoTiI as displayed in Fig. 5 and 6c, respec-
4
tively. Hence, the overall reaction rate of the process can be finally
written as
rG(TF, PoTiI ) ϭ k⑀D(TF, PoTiI )PToiI TF Ϫ rE(TF)
[19]
4
4
4
where k is the transfer reaction constant related to the diffusional
properties of the transferring gases. An average value of k equal to
0.9 mg minϪ1 cmϪ2 atmϪ1 KϪ1 has been calculated in order to sat-
isfy simultaneously the rT dependence on TF and PToiI
.
Equation 19 characterizes the overall rate of titani4um growth for
all the experiments carried out in this investigation. This equation is
depicted as a thick continuous line in Fig. 8 and 9 for constant val-
2
⑀D(PoTiI ) ϭ 0.94 Ϫ 545PToiI ϩ 2.2 ϫ 105PoTiI
4
[15]
4
4
The calculated values of the titanium transfer rate vs. the reactant
pressure are plotted in Fig. 6b. If this transfer rate is limited by the
transport of gaseous species in the filament neighborhood, the process
kinetics should be proportional to the reactant pressure, as described
in the Analytical Framework section. Such proportional behavior
seems to be reasonably satisfied in our study, as illustrated in Fig. 6b.
Therefore, it can be concluded that the dependence of the titanium
transfer rate on the reactant pressure at the inlet of the reaction cham-
ber supports the occurrence of a transfer-controlled process.
General evaluation of the overall process rate.—A complete
overview of the whole process from a kinetic standpoint is sketched
in Fig. 7. The rate of titanium growth, rG, over the tungsten filament
is the result of the balance between the rate of titanium deposition,
rD, and the rate of titanium evaporation, rE. Both contributing rates
are considered to be independent and the resulting growth rate can
be simply expressed as
Figure 7. Schematic representation of all reaction rates contributing to the
overall rate of titanium growth at the filament region.
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2596
Journal of The Electrochemical Society, 147 (7) 2589-2596 (2000)
S0013-4651(99)08-129-X CCC: $7.00 © The Electrochemical Society, Inc.
Figure 8. Evolution
of partial reaction
rates (transfer, rT,
deposition, rD, and
evaporation, rE rates)
and overall reaction
rate, rG, as a function
of the filament tem-
perature. The region
of fused filaments,
where rG decreases
with TF, is expressly
indicated. (᭹) Exper-
imental data.
Figure 9. Evolution
of partial reaction
rates (transfer, rT,
deposition, rD, and
evaporation, rE rates)
and overall reaction
rate, rG, as a function
of the reactant pres-
sure at the reactor
inlet. (᭹) Experimen-
tal data.
ues of reactant pressure, PoTiI ϭ 7 ϫ 10Ϫ4 atm, and filament tem-
4
Acknowledgments
perature, TF ϭ 1685 K, respectively. The partial reaction rates, i.e.,
deposition, evaporation, and transfer rates are also displayed in that
figure together with the experimental data for the titanium growth
rate. It can be observed that Eq. 19 describes adequately all the
experimental data. It is worth remarking that the titanium growth
rate increases gradually with the filament temperature till ca. 1800 K
and then starts to decrease. This temperature defines the onset of the
so-called fusion region in which the preparation of iodide titanium
films leads to a nonsuccess. If the growth rate decreases with the fil-
ament temperature, any irregular deposition is favored, because tita-
nium growth is lower at the thinner sections of the filament. Conse-
quently, the temperature of thinner sections increases progressively
and the filament fuses.
Financial support from the Spanish DGICYT (PB96-0084) is
gratefully acknowledged. Technical assistance from F. Moreno and
Segainvex is also recognized.
Universidad Autónoma de Madrid assisted in meeting the publication
costs of this article.
References
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Conclusions
The kinetics of the titanium iodide process has been completely
explained in light of the current CVD analysis frame. To achieve this
goal, a complete set of experiments was carried out in order to study
the influence of filament temperature, reactant pressure, and fila-
ment surface area23 on the titanium growth rate. It can be concluded
from these experiments that the rate-limiting step of the process is
the transfer of gases around the filament vicinity. This type of con-
trol becomes subsequently modulated by the deposition efficiency of
the titanium tetraiodide molecule and the evaporation rate of the
deposited titanium. A thermodynamic evaluation was made in order
to check if the deposition efficiency can be explained by the chemi-
cal equilibrium of Ti-I gases at the filament surface. Such evaluation
seems not to validate this assumption, although the thermodynamic
analysis conducts to inconsistent results. The reported thermody-
namic data for the Ti-I system at high temperatures are questionable,
and future investigations on this field are advisable.
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The experimental titanium growth rate is fully described by the
following equation
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(1991).
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Vol. 1, p. 1, Plenum Press, New York (1974).
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heim (1995).
rG(TF, PoTiI ) ϭ 0.9⑀D(TF, PToiI )PToiI TF Ϫ rE(TF)
4
4
4
The first term represents the rate of titanium deposition on the fila-
ment, while the second term accounts for the evaporation rate. This
equation indicates that the titanium transfer rate is essentially pro-
portional to the filament temperature, which leads to an apparent
activation energy of the process of 3.3 kcal/mol. The previous equa-
tion has a maximum value at 1800 K with respect to the filament
temperature. This feature accounts for the impossibility of perform-
ing iodide titanium experiments at higher temperatures than this
value, owing to the appearance of hot spots in the filament.
30. P. D. Kleinschmidt, D. Cubicciotti, and D. L. Hildenbrand, J. Electrochem. Soc.,
125, 1543 (1978).
31. M. I. Nikitin, N. M. Kosinova, and V. I. Tsirelnikov, Teplofiz. Vys. Temp., 30, 691
(1992).
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