Chemistry Reference
In-Depth Information
where
c
n
v
is a normalizing constant
g
a
,
s
is the nuclear spin degeneracy of the
n
v
N
level (
g
a
,
s
=
1 for heteronuclear
diatomics)
E
n
v
N
is the term value [cm
−
1
]
h
,
c
,
k
are universal constants
The rotational temperatures have definite physical meaning if the time of rota-
tional relaxation in a certain vibronic state is much smaller than the mean lifetime of
the rotational levels. In this case the rotational distribution of the populations is close
to a Boltzmann distribution, with the temperature
T
rot
(
equal to the translational
temperature
T
of the colliding particles (assuming they have a Maxwell velocity
distribution).
Non-equilibrium population distributions over rotational levels of excited elec-
tronic states of molecules have often been observed in gaseous discharge plasmas
and in flames [177,179,191,192,197]. Their characteristic feature is a large excess of
population in higher rotational levels. Such a non-Boltzmann behavior of the pop-
ulations should be taken into account in the determination of gas temperature from
the low energy part of the distributions (a detailed analysis of various mechanisms
responsible for the effect can be found elsewhere [187,189].
In low-pressure plasmas the radiative lifetimes of rotational levels in excited
vibronic states are often much smaller than those of the rotational relaxation in the
specified excited vibronic states. If this is the case the rotational population distri-
butions [187-190] as well as the corresponding rotational temperatures [177,182] in
the ground and excited vibronic states can be related in the framework of specific
kinetic models. The simplest is the so-called corona-like model which is based on the
assumption of dominant, direct, electron impact excitation and spontaneous decay of
rovibronic levels [182,187-190]. In this case the measurement of an intensity distri-
bution of the rotational structure of emission bands may be used for the determination
of the ground state rotational temperature, which is often close to the gas temperature
[177,178,188,189,192,194,197-199].
In the case of unresolved or partly resolved rotational structure the band shape
has to be calculated theoretically and compared with experimental values to derive
information about temperature. Many papers describe how nitrogen band emission
spectra can be used to determine temperature in low-pressure discharges [179]. Also
at higher pressures such as in barrier discharges, rotational temperatures have been
derived from
N
2
band shapes [186]. Stalder and Sharpless [184] compared experi-
mental and calculated spectral emission of
C
2
Swan band transitions to estimate the
temperature in H
2
-CH
4
plasmas used for thin diamond film deposition.
The possibility of determining the gas temperature from the measured rotational
intensity distributions is directly connected with the applicability of specific theoret-
ical models to the plasma under study. The rates of the required elementary processes
are, as a rule, not known. Therefore, it is not possible even to estimate the applica-
bility
apriori
. So in each particular case it is necessary to accompany the intensity
measurements with supplementary methods of temperature determination (Doppler
broadening, CARS, thermoprobes, etc). The other possibility (especially suitable for
n
,
v
)
