Flow-tube investigation of the high-temperature reaction between BCl3 and NH3

Article abstract of DOI:10.1021/jp981846g

The reaction between BCl₃ and NHs to produce dichloroboramine (Cl₂BNH₂) and HCl was probed using a flow-tube reactor interfaced to a molecular-beam mass-sampling system. A composite method that couples the detailed simulation of the fluid mechanics and chemical reactions occurring in the flow tube to an algorithm for nonlinear least-squares optimization was used to extract the kinetic parameters from the experiment. The rate constant for this gas-phase reaction is k (cm³ mol^-1 s^-1) = 4.21 × 10¹¹ exp[-(8350 cal mol^-1)/(RT)] with an estimated uncertainty of 10-15% over the temperature range 670-920 K. The results indicate that surface reactions involving BCl₃ and NH₃ occur in the flow tube, but their contributions to the observed chemical behavior of the system can be quantified and therefore do not affect the kinetic measurements reported here. In addition, the low-energy barrier to this gas-phase reaction has important implications for the chemical vapor deposition of boron nitride from BCl₃ and NH₃.

Full text of DOI:10.1021/jp981846g

7804
J. Phys. Chem. A 1998, 102, 7804-7812
Flow-Tube Investigation of the High-Temperature Reaction between BCl3 and NH3
Anthony H. McDaniel and Mark D. Allendorf*
Combustion Research Facility, Sandia National Laboratories, LiVermore, California 94551
ReceiVed: April 14, 1998; In Final Form: July 14, 1998
The reaction between BCl3 and NH3 to produce dichloroboramine (Cl2BNH2) and HCl was probed using a
flow-tube reactor interfaced to a molecular-beam mass-sampling system. A composite method that couples
the detailed simulation of the fluid mechanics and chemical reactions occurring in the flow tube to an algorithm
for nonlinear least-squares optimization was used to extract the kinetic parameters from the experiment. The
rate constant for this gas-phase reaction is k (cm3 mol-1 s-1) ) 4.21 × 1011 exp[-(8350 cal mol-1)/(RT)]
with an estimated uncertainty of 10-15% over the temperature range 670-920 K. The results indicate that
surface reactions involving BCl3 and NH3 occur in the flow tube, but their contributions to the observed
chemical behavior of the system can be quantified and therefore do not affect the kinetic measurements
reported here. In addition, the low-energy barrier to this gas-phase reaction has important implications for
the chemical vapor deposition of boron nitride from BCl3 and NH3.
I. Introduction
kcal mol-1
. Although this value is consistent with other
determinations cited by these investigators, their conclusions
are based on measurement techniques that could not resolve
the detailed process chemistry. The experiments of Kwon and
McGee, Avent et al., and others suggest that little if any BCl3
remains intact to adsorb at the growth front under the typical
CVD conditions of excess NH3 and temperatures exceeding
1000 K.
To complicate matters further, the dichloroboramine produced
in reaction 1 is also a Lewis acid, albeit a weaker one than
BCl3 due to the presence of the less electronegative amino group.
As is the case for BCl3, NH3 can donate electrons to the unfilled
boron p-orbital, resulting in further amination:16,19,20
Chemical reactions between Lewis acid-base pairs such as
BX3 (X ) H, F, Cl) and NH3 are of fundamental importance
and have been the subject of intense investigation.1-5 The
resulting complexes (X3B:NH3) are isoelectronic analogues of
organic compounds (X3CCH3) but are unstable solids at room
temperature that possess large dipole moments about the B:N
center.2,5 Furthermore, they readily eliminate HX to form
X2BNH2.6-8 It is these reactions that create a practical synthetic
route to valuable III-V materials such as boron nitride (BN).
The desirable properties of BN, either in hexagonal or
pyrolitic form, have been exploited in a variety of applications,
including corrosion-resistant coatings and ceramic components,9
debonding layers in ceramic-matrix composite materials,10,11 and
coatings on nuclear fuel elements.12 In the majority of these
applications, BN is deposited via chemical vapor deposition
(CVD) processes in which the precursors of choice are boron
trichloride and ammonia.9 Despite the wealth of literature
available on B-N coordination compounds, little is known about
how BCl3 and NH3 are transformed into BN. In 1972, Kwon
and McGee13 reported that BCl3 and NH3 react at room
temperature to form dichloroboramine:
Cl2BNH2 + NH3 f ClB(NH2)2 + HCl
ClB(NH2)2 + NH3 f B(NH2)3 + HCl
(2)
(3)
This fact, coupled with the elimination of HCl from dichloro-
boramine,16,19,20
Cl2BNH2 f ClBNH + HCl
(4)
suggests that the gas-phase chemistry in this system is quite
rich and deserving of a more detailed investigation. It seems
likely that in many cases, BCl3 is not the sole or even the most
abundant boron-containing species that interacts with the BN
surface during deposition.
In this investigation, a molecular-beam mass spectrometer
(MBMS) sampling system interfaced to a high-temperature flow
reactor (HTFR) was used to extract the kinetics of reaction 1
via a conventional discharge-flow approach. Traditional meth-
ods of data reduction have been replaced by a numerical
procedure in which a detailed simulation of the fluid dynamics
and chemistry in the flow reactor is coupled to a nonlinear least-
squares algorithm. This procedure results in a direct determi-
nation of the kinetic parameters that govern the system.
Comparison of our findings with the only other rate constant
reported for reaction 1, that of Kapralova et al.,15 indicates that
BCl3 + NH3 f Cl2BNH2 + HCl
(1)
The reaction products were identified using time-of-flight mass
spectrometry. No mass fragments unique to the Cl3B:NH3
adduct were observed, which is not surprising considering the
difficulty reported by Avent et al.8 in isolating this compound.
Following Kwon and McGee’s report, several other investigators
have documented reaction 1.14-16
These observations cast doubt on the conclusions of several
researchers who state that BN CVD is kinetically limited by
the adsorption of BCl3 or that homogeneous reactions are
unimportant. Patibandla and Luthra17 and Lee et al.18 measured
BN deposition rates and found an activation barrier of 35-40
* Author to whom correspondence should be addressed. E-mail: mdallen@
sandia.gov.
S1089-5639(98)01846-5 CCC: $15.00 © 1998 American Chemical Society
Published on Web 09/15/1998

Reaction between BCl3 and NH3
J. Phys. Chem. A, Vol. 102, No. 40, 1998 7805
Figure 1. Schematic of high-temperature flow reactor (HTFR).
the gas-phase reaction between BCl3 and NH3 is much slower
than previously thought.
the background pressure and serves to minimize beam scattering
and transmission of off-beam gases into the third chamber. This
final chamber houses an electron-impact ionizer, adjustable ion
optics, a mass-spectrometer quadrupole assembly capable of unit
resolution to 500 amu, and a conversion-dynode/electron-
multiplier pair for detection of positive or negative ions (Extrel
C50). The pressure in this chamber is maintained at ∼5 × 10-8
Torr with a 400 L s-1 turbo pump.
The molecular beam originates in the first of the three vacuum
stages as the reactor gases pass from a region of relatively high
pressure (P > 1 Torr) to one of low pressure (Pmax < 2 × 10-5
Torr), through the 125 µm diameter orifice in the sampling
nozzle. The flow exiting the nozzle is supersonic and under-
expanded. By maintenance of a background pressure in the
first (expansion) chamber that is low enough to prevent
continuum flow, complicating shock structures are avoided and
the gas undergoes a smooth transition to free molecular flow.21
Under these conditions, the expansion can be considered ideal
and isentropic. Most importantly, within 2-5 nozzle diameters,
the flow becomes rotationally cold and collisionless, which
“freezes” the chemical composition of the mixture. This allows
transient or short-lived species to be detected as well as stable
compounds.21,22
Prior to electron-impact ionization at 70 eV, the molecular
beam is chopped with a resonant modulator driven at 200 Hz.
The chopper reference and analogue multiplier signals are routed
through a lock-in amplifier (Stanford Research Systems SR510)
where the modulated ion signals are extracted from the dc
baseline. This allows for discrimination between beam gases
and quiescent gases that are present in the quadrupole chamber.
Phase-sensitive detection reduces the ultimate detection limit
to less than 10 ppm at reactor pressures above 5 Torr in a helium
carrier gas.
The reaction of BCl3 with NH3 was investigated at temper-
atures between 670 and 920 K in helium carrier gas at a reactor
pressure of 10.0 ( 0.2 Torr. A few experiments were also
performed with quartz wool inserted into the flow tube to
determine the importance of wall reactions. Anhydrous am-
monia (Scotty Specialty Gases 99.99 wt %), boron trichloride
II. Experiment
Apparatus and Measurements. The experimental apparatus
is depicted in Figure 1 and consists of a high-temperature flow
reactor interfaced to a molecular-beam mass spectrometer. The
HTFR is a water-jacketed steel chamber that contains alumina-
and graphite-felt insulation (not shown), heating elements, a flow
tube, a ceramic heat exchanger, and a translating injector. The
flow tube is constructed of quartz, has an internal diameter of
6.4 cm and an overall length of 112 cm, and is lined with 0.5
mm thick graphite foil to minimize deposition on the tube walls.
Resistive heating elements encircle the tube, creating three
independently controlled heating zones. The injector, also made
of quartz, is mounted on a translating stage that is attached to
the HTFR by a flexible metal bellows.
Mass flow controllers are used to meter all gas feed rates.
Reactants are introduced into the flow tube via the injector and
are dispersed at right angles to the axis of the tube by issuing
through a sparger. Alternate feeds for ammonia and carrier gas
are located at the entrance to the flow tube and at the top of the
translating stage. The reactor exhaust is throttled, allowing for
feedback control of the reactor pressure to any desired setpoint
within the range 1-700 Torr. Power to each heating element
is also under feedback control, using type-K thermocouples in
contact with the outside wall of the flow tube. This results in
a variation in the centerline temperature of (2 K about the
setpoint over the 30 cm length of the tube used to extract kinetic
data. Residence times up to 2000 ms can be achieved by
adjusting the injector position, gas flow rate, pressure, and
temperature.
Gases exiting the flow tube are sampled using the technique
of modulated molecular-beam mass spectrometry (MBMS). The
sampling train consists of three differentially pumped vacuum
stages (see Figure 1). The first chamber houses a 1500 L s-1
turbo pump, adjustable skimmer nozzle assembly, tuning fork
chopper, and molecular-beam entrance aperture. The intermedi-
ate chamber, fitted with a 150 L s-1 turbo pump, further reduces

7806 J. Phys. Chem. A, Vol. 102, No. 40, 1998
McDaniel and Allendorf
(Matheson 99.9 wt %), and helium (Matheson 99.99%) were
fed directly from their respective cylinders and were used
without further purification. Unless indicated otherwise, the
data presented here were collected under the following condi-
tions: a total gas flow rate of either 1280 or 2000 sccm, an
initial BCl3 concentration of 2000 ppm, and a [NH3]/[BCl3] ratio
of 2.25, 3.0, or 4.5. Although unnecessary, given the new
method of data reduction, ammonia was fed in excess to ensure
first-order decay behavior of the BCl3. A typical experimental
run involved positioning the injector at five to ten different
locations within the flow tube, recording the intensity of the
desired ion signals at each position, changing the ammonia
concentration or temperature, and then repeating the injector
motion.
are usually adopted, with convective velocities large enough to
negate axial diffusion. Secondary gas-phase reactions are
neglected, and any heterogeneous chemistry must exhibit first-
order behavior in the primary reactant with a well-determined
rate constant that can be incorporated into the boundary
conditions of the flow equation. Investigators often go to great
lengths in order to satisfy these criteria so that simple ap-
proximations to the flow equation may be used to interpret
experimental data.
Although it is fairly straightforward to maintain the flow
conditions described above for reaction 1 and achieve pseudo-
first-order behavior in the decay of BCl3, secondary loss
mechanisms due to gas-phase and surface reactions cannot be
avoided. The product of the bimolecular reaction between BCl3
and NH3, dichloroboramine (Cl2BNH2), is a Lewis acid that
further interacts with the NH3 (reaction 2) and thereby decreases
its concentration. More importantly, our results show that upon
mixing, BCl3 and NH3 react at the surface, resulting in the loss
of BCl3 that cannot be quantified a priori. These additional
reactions introduce an unacceptable level of uncertainty into
the rate constant for reaction 1 obtained from standard flow-
tube data-reduction techniques, thus requiring an alternative
method for analysis and parameter recovery.
The reactants (BCl3 and NH3) were monitored by their
respective parent-ion signals at mass/charge ratios (m/e) of 116
and 17. The product species, HCl, Cl2BNH2, and diaminochlo-
roborane (ClB(NH2)2), were observed at m/e ratios of 36, 97,
and 43, respectively. Mass flow controllers were used to
calibrate the MBMS sampling system for BCl3, NH3, and HCl.
Calibration factors for the two aminochloroborane species were
calculated from the measured mass balances of hydrogen and
chlorine. The reason for this choice, as opposed to basing the
calibration on boron and/or nitrogen, is that compounds contain-
ing hydrogen and chlorine are least likely to be incorporated
into solid deposits on the reactor walls before detection. The
overall uncertainties in the reported species concentrations for
BCl3, NH3, and HCl are estimated to be (5%. Those for the
aminochloroborane compounds are higher.
Here, we introduce a numerical method similar to the
treatment of Segatz et al.29 for calculating the kinetic constants
from flow-tube data that does not rely on simplifications of the
transport equations. A detailed model of the flow reactor has
been coupled to an iterative procedure for parameter optimiza-
tion to fit the experimental data to a predetermined reaction
mechanism. The optimization program TJMAR130 minimizes
the sum of squares of residuals, using the algorithm developed
by Marquardt,31 to arrive at a best estimate for the Arrhenius
constants. TJMAR1 can solve both linear and nonlinear least-
squares problems with weighted and constrained residual
functions, which are formulated from the experimental data.
An additional source of experimental uncertainty may arise
from mass-discrimination-induced nonlinearities between the
signal intensity and the absolute source density. This is
especially severe for heavily seeded molecular beams of helium
or hydrogen,23 such as those used in flow-tube experiments.
Therefore, to minimize the influence of mass discrimination,
the source densities of reactants were kept small (less than 1%
of the total feed) and all ion signals were normalized to an
internal standard of argon (typically 2000 ppm). As a result,
the mass-sampling system displayed a linear response to the
concentrations of both reactant and product gases present in
the exit stream of the flow tube under all experimental
conditions.
During the optimization, TJMAR1 recursively calls for the
solution of the two-dimensional reacting-flow problem. To
simulate the fluid dynamics and chemistry of the flow tube, we
used the CRESLAF32-34 and CHEMKIN35,36 software packages.
CRESLAF is a Fortran program that predicts the velocity,
temperature, and species profiles in two-dimensional channels
(planar or axisymmetric). The model uses a boundary-layer
approximation to solve the coupled hydrodynamic and species
continuity equations. As such, there must exist a principle flow
direction in which convection dominates diffusive transport, a
criteria that is always met under the laminar-flow conditions of
these experiments. The model accounts for finite-rate gas-phase
and surface chemistries, as well as multicomponent molecular
transport, via the CHEMKIN, SURFACE CHEMKIN, and
transport interpreters,37 respectively. These three software
packages compose a body of subroutines that are linked to
CRESLAF, creating a standard deck from which to calculate
equations of state, chemical production rates, thermodynamic
properties, and mass diffusivities. For a complete discussion
on CRESLAF and the CHEMKIN packages, the reader is
referred to the above literature citations and the references
therein.
Method of Analysis. In a standard flow-tube experiment,
the injector position establishes the residence time for the
reactants by fixing the distance between the detector and the
point at which the primary and secondary reactants are mixed.
Requisite data for a particular condition are collected by
measuring the intensity of some signal that reflects the number
density of the primary reactant as a function of the injector
position. The kinetic parameters governing the transformation
or decay of the measured signal can then be extracted from a
solution to the steady-state transport equation for a single
reaction in a cylindrical duct.24,25 Given the complexity of a
system where the chemistry and fluid dynamics are closely
coupled, it becomes necessary to operate the experiment under
limiting conditions so that data reduction and parameter
extraction are simplified.
Various approximations and numerical procedures have been
formulated in order to evaluate the transport equation, provided
that certain experimental criteria are maintained.26-28 Typically,
the system must exhibit pseudo-first-order behavior in the decay
of the primary reactant, usually accomplished by keeping the
concentration of the secondary reactant in excess of the primary
by an order of magnitude or more. Laminar flow conditions
The numerical treatment of the flow tube is enhanced by an
accurate thermochemical database consisting of all participating
species. Although not a strict requirement for the successful
implementation of CRESLAF/TJMAR1, knowledge of the
thermochemical properties (heats of formation, entropies, and
heat capacities) allows for a more precise determination of the
reverse reaction rates. For all compounds of interest except

Reaction between BCl3 and NH3
J. Phys. Chem. A, Vol. 102, No. 40, 1998 7807
NH3, HCl, and He, the thermochemical properties were taken
from the ab initio work of Allendorf and Melius.20 In this data
set, the results of ab initio electronic structure calculations,
performed at the MP4(SDTQ) level of theory, were coupled
with empirically derived bond-additivity corrections in order
to predict thermochemical quantities. This method is known
as the BAC-MP4 method (for bond-additivity-corrected fourth-
order Møller-Plesset perturbation theory) and has been suc-
cessfully applied to systems of first- and second-row com-
pounds.38,39 The data set we used encompasses 33 molecules
in the B-N-Cl-H system and is believed to be the best and
most complete available. Agreement between calculated heats
of formation and those found in the literature is quite good
(maximum error in the prediction less than (2.6 kcal mol-1).
For NH3, HCl, and He, the requisite data were taken from the
JANAF database.40
Basically, this composite method of reactor simulation and
nonlinear least-squares optimization results in the direct deter-
mination of the kinetic parameters that govern the observed
behavior, within the confines of the gas and surface reactions
included in the model chemistry. This technique has two
principal advantages over the highly specialized treatment
reported by Segatz et al.29 First, the CHEMKIN codes are
designed as a general interface that facilitates the formulation,
solution, and interpretation of problems involving elementary
heterogeneous and gas-phase chemical kinetics in the presence
of a solid surface. As such, with minimal effort, this method
can be adapted to the study of different chemical systems in
reactors of different geometries and flow/chemical complexities.
Second, TJMAR1 allows for parameter optimization over
weighted and constrained fields, which provides more flexibility
in the extraction of rate coefficients.
Figure 2. First-order decay of BCl3 signal as a function of residence
time for various feed ratios of [NH3]/[BCl3] at 10 Torr and 670 K.
Open symbols are data points with error limits at the 95% confidence
interval; lines are the results of CRESLAF/TJMAR1 simulations (see
text).
As a result of the numerical treatment of the flow-tube data,
traditional graphs of the rate constant verses inverse temperature
or rate constant verses NH3 concentration are not necessary. A
benefit of manipulating data in this manner is that uncertainties
in thermal uniformity within the tube and parasitic reactions
that may occur in the gas-phase and on the surface of reactor
walls are no longer a barrier to extracting meaningful rate
constants from flow-tube reactors. Keys to the success of this
method are a well-defined reaction mechanism and an appropri-
ate choice of residual functions to minimize.
Figure 3. First-order decay of BCl3 signal as a function of residence
time for various feed ratios of [NH3]/[BCl3] at 10 Torr and 918 K.
Open symbols are data points with error limits at the 95% confidence
interval; lines are the results of CRESLAF/TJMAR1 simulations (see
text).
III. Results
calculated according to τ - τ0 ) (z - z0)/ u , where z (cm) is
the physical distance between the injector tip and the sampling
nozzle (see Figure 1), u (cm s-1) is the average flow velocity,
and the subscript (0) indicates the initial condition (injector
position closest to detector). It is clear from these figures that
the process is pseudo-first-order in the loss rate of BCl3; it
remains so under all conditions investigated.
HTFR Experiments. The reaction between BCl3 and NH3
was investigated at six temperatures between 670 and 920 K
and at three initial mole fractions of NH3 (4.5, 6.0, and 9.0 ×
10-3), which generated 18 separate conditions from which to
collect rate data. Consistent with earlier investigations of this
system,13-16 we find that BCl3 and NH3 react rapidly over the
entire range of temperatures examined. Three compounds were
detected as products of the reaction: HCl, Cl2BNH2, and ClB-
(NH2)2. It is of interest to note that none of the previous
investigators reported the presence of ClB(NH2)2, probably due
to the lower reactor temperatures and/or lower instrument
sensitivities employed in these studies.
Shown in Figure 2 are the first-order decay curves for the
BCl3 signal as a function of the relative residence time (τ - τ0)
for various initial [NH3]/[BCl3] ratios at 670 K. Illustrated in
Figure 3 are the decay curves measured at 918 K. The open
symbols in these figures are the raw data with error limits
established at the 95% confidence interval, and the solid lines
are the results obtained from the CRESLAF/TJMAR1 analysis.
The residence time relative to an initial injector position was
While the curves in Figures 2 and 3 substantiate the first-
order behavior of the process under study, this observation does
not guarantee that the governing reaction is solely a homoge-
neous process. Both Brown26 and Orkin et al.28 report that a
first-order wall loss would go undetected, meaning that the
behavior of the system would remain linear, but have an
observed slope that is steeper than that expected for a single
gas-phase, bimolecular reaction. Therefore, to test for possible
contamination of our observations by surface reactions, glass
wool was placed in the flow tube. This increased the effective
area exposed to BCl3 and NH3 by a factor of 70; any increase
in the observed decay of the BCl3 signal would immediately
point to an active heterogeneous process.

7808 J. Phys. Chem. A, Vol. 102, No. 40, 1998
McDaniel and Allendorf
TABLE 1: Mole Fractions of Reactant and Product Species
for Various Conditions at a Residence Time of 0.5 s, 10
Torr, and 670 K
TABLE 2: Reaction Mechanism Used in the CRESLAF/
TJMAR1 Calculations
reaction
A
â
E a
mole fraction (× 10-3
)
Gasb
BCl3 + NH3 f
measured (5%a
simulated
4.21 × 1011
3.88 × 1011
0.0
0.0
8350
description
ion
Cl2BNH2 + HCl
Cl2BNH2 + NH3 f
ClB(NH2)2 + HCl
parent
NH3
BCl3
HCl
Cl2BNH2 Cl2BNH2
ClB(NH2)2 B(NH2)2
m/e input
∆
LO
∆
HI
∆
∆
SLO
SHI
18500
+
NH3
17 9.00 -1.37 -2.49 -1.18 -2.59
116 2.00 -1.13 -1.94 -1.08 -1.96
36 0.0 +1.11 +3.62 +1.21 +3.61
97 0.0 +1.01 +0.89 +0.94 +0.82
43 0.0 +0.09 +0.52 +0.05 +0.56
+
Surfacec
BCl3
HCl+
NH3 + * f NH3*
5.00 × 10-2
6.69 × 10-2
0.0
-0.5
0
+
3BCl3 + 4NH3* f
6HCl + Cl2BNH2 +
ClB(NH2)2 + BN(s) + 4*
5240
+
difference (%)b difference(%)
gas-phase
a Units of cal mol-1 b Gas-phase rate constant of the form k ) ATâ
.
atomic balance
input
∆
LO
∆
∆
∆
HI
SLO
SHI
exp[-E/(RT)] in (cm3 mol-1 s-1). c Surface-phase rate constant given
as a sticking coefficient of the form γ ) ATâ exp[-E/(RT)] which is
unitless and in the range (0 e γ e 1). (*) indicates an adsorption site.
Cl
B
N
H
6.00
2.00
9.00
27.0
2.7
1.4
2.0
2.3
-1.9
26.3
6.2
1.5
1.3
29.1
7.2
4.2
1.4
0.8
0.0
1.0
TABLE 3: Species Used in the Equilibrium Calculations
a Uncertainties for Cl2BNH2 and ClB(NH2)2 have not been deter-
mined (see text). (+) indicates gain by reaction; (-) indicates loss by
reaction. (∆LO ) empty flow tube (low surface area), ∆HI ) glass-
wool-packed tube (high surface area), ∆SLO and ∆SHI ) results of
CRESLAF/TJMAR1 simulation (see text). b Values are calculated by
taking the percentage difference between the gas-phase mole fraction
of the element in the input stream and that of the exit. A large positive
value would indicate that the respective atomic element has been
incorporated into a surface deposit.
BCl3
Cl3B:NH3
Cl2BNH2
ClBNH
ClB(NH2)2
B(NH2)3
NH3
NH4Cl (s)
HCl
He
the most significant reactions governing the chemistry of this
system.
Mechanism Development. The model chemistry used in the
simulations is limited to the four reactions listed in Table 2.
The two gas-phase steps, reactions 1 and 2, are discussed in
the Introduction and are the subject of this investigation.
Reactions 3 and 4 are not included in the mechanism because
B(NH2)3 and ClBNH were never detected in the effluent of the
flow tube. We also omit reactions describing the unimolecular
decomposition of BCl3 and NH3 because these processes are
highly activated and would not contribute to the gas-phase
chemistry at the low temperatures and pressures employed in
this investigation.19
For the surface, a simple two-step mechanism was devised
to represent the interactions of NH3 and BCl3 at the gas-solid
interface. This choice was based on the following experi-
mental observations: upon addition of the glass wool (see
Table 1, ∆HI), there is an increase in the net loss of BCl3 and
NH3, a concomitant increase in the production of HCl and
ClB(NH2)2, and an unexpected decrease in the amount of
Cl2BNH2 produced. No new gas-phase species were observed.
There appear to be only two mechanisms consistent with these
observations: (1) a surface reaction(s) that converts NH3 and
Cl2BNH2 to HCl and ClB(NH2)2 or (2) a surface reaction(s)
that converts BCl3 and NH3 to the observed products. The first
pathway, in principle, could deplete Cl2BNH2 and thereby drive
reaction 1 in the forward direction, resulting in an increased
rate of BCl3 loss and a drop in the production of Cl2BNH2.
However, this would be true only if reaction 1 were at
equilibrium.
To test this hypothesis, equilibrium calculations were per-
formed using the STANJAN code developed by Reynolds et
al.41 This program uses the method of “element potentials” to
determine the equilibrium mole fractions of species in ideal
mixtures of one or more phases. The species used in the
equilibrium calculations are listed in Table 3. The molecules
are all stable compounds and represent the most likely moieties
to exist at the temperature and pressure investigated; no reactive
intermediates were considered. Thermochemical data for all
of the compounds except NH4Cl(s), NH3, HCl, and He were
taken from the work of Allendorf and Melius described
previously.20 For the remaining species, the thermochemistry
was again taken from JANAF.40
The results of the experiment are presented in Table 1. Here,
a comparison is made between the mole fractions of five species
measured in the reactor, under identical flow conditions, with
the exception that one set of data was obtained in an empty
tube (low surface area) and the other in a glass-wool-filled tube
(high surface area). The labels ∆LO and ∆HI represent empty-
and filled-tube configurations, respectively. The ∆ operator
gives the difference between outlet and inlet mole fractions.
As such, a “-” sign indicates that a species is consumed by
the reaction, and a “+” indicates that a species is produced.
Comparing ∆LO and ∆HI in Table 1 shows that the consumption
of BCl3 and NH3 increases significantly at the higher surface
area. Consequently, the production rates of HCl and ClB(NH2)2
increase; however, the amount of Cl2BNH2 decreases.
In the lower portion of Table 1, are the results of a mass
balance over the flow tube for the elements (Cl, B, N, and H)
detected in the gas phase. The values listed were calculated
by taking the percentage difference between the mole fraction
of the element in the input stream and that in the exit stream.
Closure of the mass balance, within the experimental uncer-
tainty, is achieved for the ∆LO condition; however, for the ∆HI
state, the elements boron and nitrogen do not balance. The mole
fraction of boron and nitrogen in the exit is much lower than in
the input, which indicates that these two atoms have been
removed from the gas phase, presumably incorporated into solid
deposits on the surfaces within the reactor. The mole ratio of
B/N lost to the surface is nearly 1:1, suggesting that stoichio-
metric BN is being formed.
Clearly, there is a heterogeneous component to the reaction
between BCl3 and NH3. Given that the rate of this reaction
cannot be determined a priori, it then becomes necessary to use
an alternative approach to data reduction so that meaningful
kinetic parameters can be extracted from the experiments.
Posing a well-defined reaction mechanism is important for the
success of the CRESLAF/TJMAR1 method. With the observa-
tions made in the empty and wool-filled reactor, we have
sufficient information to develop a mechanism that describes

Reaction between BCl3 and NH3
J. Phys. Chem. A, Vol. 102, No. 40, 1998 7809
to optimize the rate parameters. With reliable thermochemistry,
a reaction mechanism, and a sufficient number of observations,
the final step in parameter evaluation is to formulate the residual
functions.
The residuals, which are cast into the form of relative errors
and taken as the sum of squares, describe the extent to which
the model predictions deviate from observation. In the interest
of reasonable computation times, we decided to limit NTOT to
36 data points. The most significant experimental results to
fit are the family of decay curves for the BCl3 signal (see Fig-
ures 2 and 3). Another observable that is sensitive to the rates
of gas and surface reactions is the measured ratio of BCl3 to
Cl2BNH2. Given these two data sets, the sum of squares of
residuals (SOR) for the first range (N1) of 18 points, which
represents the decay of BCl3, is defined as:
N1
2
Fi
Yi
Φ1 ) ω1
1 -
(5)
(6)
∑
(
)
i)1
[BCl3]i,1
[BCl3]i,0
Figure 4. Equilibrium mole fractions for various species in the B-N-
Cl-H system as a function of initial [NH3] at 10 Torr, 670 K, and an
initial [BCl3] ) 2000 ppm. The vertical dashed line indicates the
experimental condition.
Fi ) ln
where Φ1 is the SOR for range N1, Yi are the experimental
values, which also take the form of eq 6, ω1 is a weighting
factor, N1 is the number of data points within the range, and
the subscripts (0 and 1) indicate the simulated value obtained
for a reactor with the injector position fully forward (relative
residence time of zero) or fully withdrawn (maximum relative
residence time), respectively.
The SOR for the second range (N2) of 18 data points, which
is a measure of the [BCl3]/[Cl2BNH2] ratio in the exit stream,
is given by
Shown in Figure 4 are the predicted equilibrium mole
fractions as a function of initial NH3 concentration for a constant
temperature (670 K) and pressure (10 Torr). At an [NH3]/[BCl3]
ratio of 4.5, which is similar to the experimental conditions for
the data presented in Table 1, it is clear that Cl2BNH2 is not
the most abundant product. Its equilibrium mole fraction is
dwarfed by those of ClB(NH2)2 and B(NH2)3. The magnitude
of the Cl2BNH2 concentration measured under the conditions
of our flow-tube experiments shows that the system is far from
equilibrium. Thus, the first mechanism described above is
inconsistent with the equilibrium calculations. We therefore
use the second mechanism and assume that NH3 adsorbs on
the surface with a high probability (i.e., relatively large sticking
coefficient) and subsequently reacts with BCl3 via a global
process that results in the formation of gas-phase and solid
products (see Table 2). To reduce the uncertainty associated
with these uncharacterized surface kinetics, a single rate-limiting
coefficient was chosen to represent the net reaction of BCl3 at
the wall. Although this global reaction does not describe the
individual elementary processes that must occur, it will be shown
later that it accurately predicts the behavior of the major gas-
phase species under our experimental conditions.
The rate parameters listed in Table 2 are the final results of
the analysis method and represent the optimal values, in a least-
squares sense, of the kinetic constants. The (â) coefficients
for temperature were held fixed, along with the preexponential
factor (A) for the NH3 adsorption step. The remaining six
coefficients for the two gas-phase and global surface reactions
were optimized to reproduce the experimental observations.
Nonlinear Least-Squares Analysis (CRESLAF/TJMAR1).
As with most least-squares techniques, the total number of
observations (NTOT) should exceed the number of parameters
(K). Here, we are interested in optimizing six rate coefficients
for three reactions (K ) 6). Experimental data, in the form of
species concentration profiles, were collected under 18 different
reactor conditions. In essence, every set of experimental
conditions produced a concentration measurement for each of
the five species listed in Table 1, at a multitude of injector
positions. Therefore, the number of observations can be
extended well beyond the number of experimental conditions,
thus providing a sufficiently large set (NTOT > K) from which
N2
2
Fj
Yj
Φ2 ) ω2
1 -
(7)
(8)
∑
(
)
j)1
[BCl3]j,1
Fj )
[Cl2BNH2]j,1
where Φ2 is the SOR for range N2, Yj are the experimental values
in the form of eq 8, ω2 is a weighting factor, N2 is the number
of data points within the range, and the subscript (1) indicates
the simulated value obtained for a reactor with the injector
position fully withdrawn (maximum relative residence time).
The total SOR minimized by the program is the sum of eqs 5
and 7, ΦTOT ) Φ1 + Φ2.
The objective of this work is to extract a reliable rate constant
for the bimolecular reaction between BCl3 and NH3 (reaction
1). To this end, the SOR for range N1 is given a much greater
priority by the addition of a multiplicative weighting factor (ω1
. 1). An appropriate value for ω1 was determined by
increasing this factor until Φ1 attained a minimum that was
invariant to any further changes in the value of ω1. This point
represents the best possible fit to the measured decay charac-
teristics of BCl3. The robust nature of the numerical procedure
is evidenced by the fact that the predicted pseudo-first-order
rate constant (k, s-1) for the decay of the BCl3 signal does not
vary by more than 2% in the range 1 e ω1 e 106. However,
the overall quality of the fit to the entire data set, represented
by the value of ΦTOT, is strongly influenced by this weighting
factor due to the extreme sensitivity of eqs 7 and 8 to the four
remaining rate parameters in the model chemistry. The best
overall fit to the entire data set is obtained at values of ω1 greater
than 103.

7810 J. Phys. Chem. A, Vol. 102, No. 40, 1998
McDaniel and Allendorf
Figure 6. Sum of squares of residuals (SOR) plotted as a function of
the activation energy for reaction 1. Open symbols are (ΦTOT), which
is the total SOR with the weighting factors removed; solid symbols
are (Φ1/ω1), which is a partial SOR for the residuals defined in eq 5.
Figure 5. Sum of squares of residuals (SOR) plotted as a function of
the preexponential factor for reaction 1. Open symbols are (ΦTOT) which
is the total SOR with the weighting factors removed; solid symbols
are (Φ1/ω1) which is a partial SOR for the residuals defined in eq 5.
In addition to weighting the SOR for range N1, the kinetic
parameters were initially constrained to positive values within
the range 1010-1014 cm3 mol-1 s-1 for the gas-phase preexpo-
nential factors, (0.0-5.0) × 104 for activation energies (EA/R
in K), and 0.0-0.5 for the sticking coefficient prefactor. These
constraints represent limits imposed upon the process by the
stability of the numerical procedure but are quite consistent with
the kinetics under investigation. For example, if the chosen
rate of a reaction is unreasonably fast, the simulation will
consume all of the BCl3 within a very short distance from the
reactor entrance. This leads to integration instabilities that result
in excessively large values of ΦTOT and premature termination
of the program. In a typical numerical experiment, an initial
guess for each of the six parameters was provided; the progress
of the fit was then monitored by examining the value of ΦTOT
.
Once a general pattern for the behavior of the solution space
emerged, the initial guesses were given new values so that
solutions could be approached from different points of origin.
This was done to ensure that the optimized solution was not a
local minimum.
Figure 7. Species concentrations as a function of the injector-nozzle
distance at 771 K, 10 Torr, an initial [BCl3] ) 2000 ppm, and an initial
[NH3] ) 6000 ppm. Symbols are data points and solid lines are
CRESLAF predictions using the full mechanism.
Illustrated in Figure 5 are the SORs as a function of the
prefactor value (A1) for reaction 1. Similarly, in Figure 6 are
the same SORs as a function of the activation energy (E1/R)
for reaction 1. The open symbols are values of ΦTOT, with the
weighting factors ω1 and ω2 removed (ΦTOT ) Φ1/ω1 + Φ2/
ω2), produced by the CRESLAF/TJMAR1 program for runs that
had satisfied the exit criteria and were making no further
progress in the reduction of ΦTOT. The filled symbols are the
corresponding values for Φ1/ω1. It is evident from Figures 5
and 6 that a deep well in the solution field for Φ1/ω1 emerges
near the respective values of 4 × 1011 cm3 mol-1 s-1 and 4.2
× 103 K. The existence of a unique minimum within the
constrained ranges of the kinetic parameters is a good indication
that a meaningful rate constant can be extracted with this
technique. We should reiterate that ΦTOT is a measure of the
quality of the fit to the entire data set and is therefore dependent
upon all six rate parameters associated with the model chemistry.
Thus, small variations in (A1) or (E1/R) should not be interpreted
simulations became unstable, causing the program to halt
prematurely. Each iteration of the program required a minimum
of NTOT (K + 1) reactor simulations, resulting in an excess of
3000 complete reactor simulations per single run. Typical
computation times were on order of 8 h on a Silicon Graphics
Octane workstation.
To verify the accuracy of the model, predictions of species
concentrations exiting the HTFR as a function of injector-nozzle
distance were compared to experiment. Plotted in Figure 7 are
the mole fractions that were measured and predicted for reactions
occurring in an empty flow tube at 771 K, a [NH3]/[BCl3] ratio
of 3.0, and a pressure of 10 Torr. There is excellent agreement
between the CRESLAF/TJMAR1 results and the experimental
data. The figure shows little discernible difference between the
predicted and measured profiles (less than 5%) for NH3, BCl3,
and HCl, which were the three compounds measured with the
highest degree of accuracy. For the two remaining products,
Cl2BNH2 and ClB(NH2)2, the model consistently underpredicts
their rates of formation but not to a significant extent (maximum
deviations of 10 and 36%, respectively). The quality of the
fits is also evident in Figures 2 and 3 and the trends exhibited
by the data in Table 1.
as being responsible for large fluctuations in ΦTOT
.
For each value of ΦTOT less than 102 in Figures 5 and 6, the
convergence to a local minimum was usually attained in 10 or
more iterations. At values of ΦTOT greater than 102, the reactor

Reaction between BCl3 and NH3
J. Phys. Chem. A, Vol. 102, No. 40, 1998 7811
of the simulations are of the empty (i.e., low surface area) reactor
tube. The top dashed line in this figure represents the model
predictions for the gas-phase mechanism (reactions 1 and 2),
omitting any surface chemistry. The solid line is the prediction
resulting from the full mechanism; the solid symbols are data
points with error limits at the 95% confidence interval. It is
clear that the surface reactions increase the decay rate of BCl3,
since the slopes differ by more than 10%. Neglecting the
bimolecular process between BCl3 and NH3 at the wall would
result in a measured rate constant that is too large.
We conclude that the model chemistry proposed in Table 2
is valid for all experimental conditions examined in this work
and that the composite method CRESLAF/TJMAR1 is an
effective tool for extracting the kinetic parameters that govern
the reactions. On the basis of the nonlinear least-squares analy-
sis, the rate constant for reaction 1 is k (cm3 mol-1 s-1) ) 4.21
× 1011 exp[-(8350 cal mol-1)/(RT)] with an estimated accuracy
of 10-15%24 over the temperature range 670-920 K.
Figure 8. First-order decay of BCl3 signal as a function of residence
time at 10 Torr, a reactor temperature of 918 K, an initial [BCl3] )
2000 ppm, and an initial [NH3] ) 9000 ppm. Solid symbols are data
points with error limits at the 95% confidence interval; the solid line
is the result of a CRESLAF simulation using the full mechanism; the
broken line is the result of a CRESLAF simulation devoid of all surface
reactions.
IV. Discussion and Conclusions
Very few researchers have documented the reactions thus far
considered, and only one has reported measuring a rate constant
for reaction 1. Kapralova et al.,15 working at significantly lower
temperatures (345 K) than those used here, measured a rate near
the collision frequency (k ) 6 × 1012 cm3 mol-1 s-1 at 10 Torr,
345 K). This determination is much faster than ours and is
suspect because, at this low temperature, the concurrent deposi-
tion of solid NH4Cl may open heterogeneous routes to BCl3
decomposition. Unfortunately, Kapralova et al. do not provide
sufficient detail in their paper to adequately evaluate their
experiments. The authors only briefly describe the methods
used to mix the reactants. The progress of reaction 1 was
followed by mass spectrometry, but the authors do not state
which mass peaks were monitored.
In their initial investigation, Kapralova et al. mixed nearly
equal portions of BCl3 and NH3 in a small-diameter copper tube
maintained at a temperature of 345 K and a pressure of 1-9
Torr. This technique is identical to that of Kwon and McGee,13
who noted that solid formation was severe enough to clog the
tube after only a few hours. Kapralova also concedes that
heterogeneous reactions could not be avoided, so they adopted
a more elaborate diffusion-flame approach. However, by
keeping the reactor temperature well below the sublimation point
of NH4Cl (Tsub ) 613 K), they could not prevent homogeneous
nucleation of particles in the flow field upstream of their
detector. To add to the uncertainty, Kapralova also describes
a nonlinear, nonmonotonic pressure dependence of the reaction
rate. This trend may be caused by pressure effects on the
particle size distribution of aerosols formed within the reactor,
which would in turn affect the rates of heterogeneous reactions,
rather than by dependence of the bimolecular rate constant on
pressure.
Kapralova’s data also cannot be reconciled with theory. Ab
initio calculations of the transition-state energetics using the
BAC-MP4 method predict an energy barrier to reaction 1 equal
to 13 kcal mol-1 at 298 K.20 This value is 4.7 kcal mol-1 greater
than the energy barrier determined experimentally, which is not
surprising given the likelihood of significant ionic character in
the transition state that cannot be accurately described by the
basis sets employed by the BAC-MP4 method. Nevertheless,
the experimental and theoretical evidence reported here suggests
that a gas-phase reaction between BCl3 and NH3 does not
approach the collision limit even at elevated CVD temperatures.
The energetics of reactions 2 and 3 follow the suppositions
of both Allendorf and Melius20 and Brink et al.4 We observed
In Table 1, ∆LO and ∆SLO represent identical empty-tube
configurations, with the former being experimental and the latter
numerical. Similarly, ∆HI and ∆SHI represent packed-tube con-
figurations. The model reproduces the increased consumption
of BCl3 as well as the increase in production of HCl and ClB-
(NH2)2 that is observed when the reactive surface is augmented
by glass wool. Most noteworthy, however, is that the model
predicts the observed decrease in the concentration of Cl2BNH2.
This is an important subtlety that was not expected, given the
single global surface reaction between BCl3 and NH3 that
dictates the equimolar formation of BN(s), Cl2BNH2, and ClB-
(NH2)2. While it is unlikely that the two aminochloroborane
species would be formed with equal probability on the walls,
this result does indicate that the gas-phase concentration of
Cl2BNH2 depends on a balance between the flux of BCl3 to the
surface and the rate of homogeneous reaction with NH3.
The purpose of using CRESLAF/TJMAR1 to extract the
kinetic parameters from the flow-tube data was to overcome
the uncertainties associated with traditional methods of data
reduction that are induced by secondary reactions occurring in
the gas and on the surface of the reactor walls. With confidence
in the predictive capabilities of the model, it can now be used
to examine the relative effects of processes that may influence
the concentration of BCl3 exiting the HTFR. The first is reaction
2, which depletes the gas phase of both NH3 and the byproduct
of reaction 1 (Cl2BNH2), and the second is the surface reaction
between BCl3 and NH3. We do this numerically by omitting
these reactions and observing the effects on the simulated
behavior of BCl3. A reactor temperature of 918 K was chosen
because these processes are activated and therefore would exert
their greatest influence on the BCl3 concentration at the highest
temperature studied.
The gas-phase reaction between Cl2BNH2 and NH3 has no
observable effect on the decay of the BCl3 signal. This process
is highly activated and therefore is not a significant sink for
NH3; in fact, the surface is the major source of ClB(NH2)2. The
heterogeneous reactions in Table 2, however, are a significant
avenue for consumption of BCl3. Illustrated in Figure 8 are
two curves that represent the simulated first-order decay of the
BCl3 concentration as a function of relative residence time at
an [NH3]/[BCl3] ratio of 4.5 and a temperature of 918 K. All

7812 J. Phys. Chem. A, Vol. 102, No. 40, 1998
McDaniel and Allendorf
(9) Paine, R. T.; Narula, C. K. Chem. ReV. 1990, 90, 73.
smaller quantities of ClB(NH2)2 than Cl2BNH2, indicating that
reaction 2 is slower than reaction 1. The calculated energy
barrier to reaction 2 is 10 kcal mol-1 greater than that of reaction
1, which is consistent with previous findings.16,19 This behavior
is expected as the strength of the Lewis acid decreases upon
substitution of the NH2 group for Cl. According to Brink et
al., the ability of the Lewis acid to accept charge donated from
the Lewis base, and thereby stabilize the resulting complex, will
diminish as amino groups possessing smaller electron affinities
replace the chlorines on boron. An extension of this argument
to the limit of a fully aminated boron would imply that reaction
3 is slower still, which is reasonable considering that no B(NH2)3
was detected.
(10) Fareed, A. S.; Schiroky, G. H.; Kennedy, C. R. DeVelopment of
BN/SiC Duplex Fiber Coating for Fiber-Reinforced Alumina Matrix
Composites Fabricated by Direct Metal Oxidation; Proceedings of the 17th
Annual Conference on Composites and Advanced Ceramic Materials, Cocoa
Beach, FL, 1993.
(11) Cofer, C. G.; Economy, J.; Xu, Y.; Zangvil, A.; Lara-Curzio, E.;
Ferber, M. K.; More, K. L. Comput. Sci. Technol. 1996, 56, 967.
(12) Gu¨ndu¨z, G.; Uslu, I.; Durmazuc¸ar, H. H. Nucl. Technol. 1996, 116,
78.
(13) Kwon, C. T.; McGee, H. A., Jr. Inorg. Chem. 1973, 12, 696.
(14) Pavlovic’, V.; Ko¨tter, H.-R.; Meixner, C. J. Mater. Res. 1991, 6,
2393.
(15) Kapralova, G. A.; Suchkova, T. V.; Chaikin, A. M. MendeleeV
Commun. 1993, 3, 118.
(16) Allendorf, M. D.; Osterheld, T. H. Chemical Reactions in the CVD
of Boron Nitride from BCl3 and NH3. In Proceedings of the XIII
International Conference on Chemical Vapor Deposition; Besmann, T. M.,
Allendorf, M. D., Robinson, M., Ulrich, R. K., Eds.; The Electrochemical
Society Proceedings Series: Pennington, NJ, 1996; Vol. 96, p 16.
(17) Patibandla, N.; Luthra, K. L. J. Electrochem. Soc. 1992, 139, 3558.
(18) Lee, W. Y.; Lackey, W. J.; Agrawal, P. K. J. Am. Ceram. Soc.
1991, 74, 2642.
(19) Allendorf, M. D.; Melius, C. F.; Osterheld, T. H. A Model of the
Gas-Phase Chemistry of Boron Nitride CVD from BCl3 and NH3. In
CoValent Ceramics III: Science and Technology of Non-Oxides; Hepp, A.
F., Kumta, P. N., Sullivan, J. J., Fischman, G. S., Kaloyeros, A. E., Eds.;
Materials Research Society Symposium Proceedings 410; Boston, MA,
1996; p 459.
(20) Allendorf, M. D.; Melius, C. F. J. Phys. Chem. A 1997, 101, 2670.
(21) Miller, D. R. Free Jet Sources. In Atomic and Molecular Beam
Methods; Scoles, G., Ed.; Oxford University Press: New York, 1988; Vol.
1, p 14.
(22) Knuth, E. L. Composition Distortion in MBMS Sampling. In
Applications of Free-Jet, Molecular Beam, Mass Spectrometric Sampling
Proceedings; National Technical Information Service, U.S. Department of
Commerce: Springfield, VA (Distribution Code: UC-1400).
(23) Hsu, W. L.; Tung, D. M. ReV. Sci. Instrum. 1992, 63, 4138.
(24) Howard, C. J. J. Phys. Chem. 1979, 83, 3.
(25) Kaufman, F. Science 1985, 230, 393.
(26) Brown, R. L. J. Res. Natl. Bur. Stand. (U.S.) 1978, 83, 1.
(27) Walker, R. E. Phys. Fluids 1961, 4, 1211.
(28) Orkin, V. L.; Khamaganov, V. G.; Larin, I. K. Int. J. Chem. Kinet.
1993, 25, 67.
(29) Segatz, J.; Rannacher, R.; Wichmann, J.; Orlemann, T.; Dreier, T.;
Wolfrum, J. J. Phys. Chem. 1996, 100, 9323.
(30) Jefferson, T. H. TJMAR1-A Fortran Subroutine for Nonlinear Least
Squares Prameter Estimation; SLL-73-0305; Sandia National Labora-
tories: Albuquerque, NM, 1973.
(31) Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431.
(32) Coltrin, M.; Kee, R. J.; Miller, J. A. J. Electrochem. Soc. 1984,
131, 425.
The results of this study indicate that both homogeneous and
heterogeneous processes play important roles in BN CVD. The
work reported by Patibandla and Luthra17 and Lee et al.18 implies
that reaction 1 is not limiting to the rate of BN deposition, but
this reaction likely plays an important role in determining the
identity of the boron- and nitrogen-containing precursors that
impinge on the growth front. Furthermore, since BN CVD
typically involves high temperatures and excess NH3, the
subsequent reactions outlined in this paper will inevitably
contribute to the formation of these precursors. While the exact
sequence of reactions leading to BN formation from BCl3 and
NH3 is still unknown, our findings create a platform for
launching future investigations. Understanding the reactions
of alternate species such as Cl2BNH2 or ClB(NH2)2 may provide
the insight necessary to develop a full mechanism that in turn,
could be used to develop and optimize BN CVD reactors.
The numerical technique developed here is well suited for
the analysis of kinetic data collected in laminar-flow tubes. A
benefit of using this composite method of simulation and
nonlinear least-squares optimization is that thermal nonunifor-
mity within the tube (radial and axial temperature gradients)
and competing reactions that occur in the gas phase and at the
surface are no longer road blocks to extracting meaningful rate
constants from these reactors. In fact, it is not even necessary
to collect data under pseudo-first-order conditions. This method
is a tool that gives the researcher more latitude in the design
and execution of flow-tube experiments. The example presented
here does not fully establish the utility of such an approach,
due to the limited influences of transport and surface chemistry
on the bimolecular reaction between BCl3 and NH3. However,
other experimental systems often encountered in the study of
chemical vapor deposition reactions that occur at higher
pressures or have more severe heterogeneous character would
clearly benefit from this approach.
(33) Coltrin, M.; Kee, R. J.; Miller, J. A. J. Electrochem. Soc. 1986,
133, 1206.
(34) Coltrin, M. E.; Moffat, H. K.; Kee, R. J.; Rupley, F. M.
CRESLAF: A Fortran Program for Modeling Laminar, Chemically React-
ing, Boundary-Layer Flow in Cylindrical or Planar Channels, version 4.0;
SAND93-0478 UC-401; Sandia National Laboratories: Albuquerque, NM,
1996.
(35) Coltrin, M. E.; Kee, R. J.; Rupley, F. M. Int. J. Chem. Kinet. 1991,
23, 1111.
(36) Coltrin, M. E.; Kee, R. J.; Rupley, F. M.; Meeks, E.; Miller, J. A.
Chemkin-III: A Fortran Chemical Kinetics Package for the Analysis of
Gas-Phase Chemical and Plasma Kinetics; Surface Chemkin-III: A Fortran
Package for Analyzing Heterogeneous Chemical Kinetics at a Solid-
SurfacesGas-phase Interface; SAND96-8216 UC-405 and SAND96-8217
UC-405; Sandia National Laboratories: Albuquerque, NM, 1996.
(37) Kee, R. J.; Dixon-Lewis, G.; Warnatz, J.; Coltrin, M. E.; Miller, J.
A. A Fortran Computer Code Package for the EValuation of Gas-Phase
Multicomponent Transport Properties; SAND86-8246 UC-32, Sandia
National Laboratories: Albuquerque, NM, 1986.
Acknowledgment. This work was supported by the U.S.
Department of Energy, Office of Industrial Technologies,
Advanced Industrial Materials Program.
References and Notes
(1) Zirz, C.; Ahlrichs, R. J. Chem. Phys. 1981, 75, 4980.
(2) Binkley, J. S.; Thorne, L. R. J. Chem. Phys. 1983, 79, 2932.
(3) Haaland, A. Angew. Chem., Int. Ed. Engl. 1989, 28, 992.
(4) Brink, T.; Murray, J. S.; Politzer, P. Inorg. Chem. 1993, 32, 2622.
(5) Jonas, V.; Frenking, G.; Reetz, M. T. J. Am. Chem. Soc. 1994,
116, 8741.
(38) Melius, C. F. BAC-MP4 Method. In Chemistry and Physics of
Energetic Materials; Bulusu, S. N., Ed.; Kluwer Academic Publishers:
Dorderecht, 1990; Vol. 309, p 21.
(39) Ho, P.; Melius, C. F. J. Phys. Chem. 1995, 99, 2166.
(40) Chase, M. W.; Davies, C. A.; Downey, J. R.; Frurip, D. J.;
McDonald, R. A.; Szverud, A. N. J. Phys. Chem. Ref. Data 1985, 14.
(41) Reynolds, W. C. The Element Potential Method for Chemical
Equilibrium Analysis: Implementation in the InteractiVe Program STAN-
JAN; Department of Mechanical Engineering, Stanford University, 1986.
(6) Kroto, H. W.; McNaughton, D. J. Chem. Soc., Dalton Trans. 1985,
1767.
(7) Legon, A. C.; Warner, H. E. J. Chem. Soc., Chem. Commun. 1991,
1397.
(8) Avent, A. G.; Hitchcock, P. B.; Lappert, M. F.; Liu, D.-S.; Mignani,
G.; Richard, C.; Roche, E. J. Chem. Soc., Chem. Commun. 1995, 855.