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Transition probabilities for the (0, 0) and (1, 1) bands of the c1Φ-a1Δ system of the TiO molecule
I. Quont. Sptcrrosc. Radial. Transfer.
Vol.IS.pp. 575-577 PergamonPress1975. Printed!n GreatBritain
TRANSITION PROBABILITIES FOR THE (0, 0) AND (1, 1) BANDS OF THE cl@a’A SYSTEM OF THE TiO MOLECULE W. ~YRNICKI Institute of Inorganic Chemistry and Metallurgy of Rare Elements, Technical University of Wro&aw, 50370 Wrochw, Poland (Receioed 1 August 1974) Abstract-Transition probabilities for the (O,O)-and (1, I)-bands of the ~‘0 - a ‘Asystem were determined by analyzing the plasma spectrum produced in an argon plasma-jet. Titaniumoxide was formed during a reaction between TiC1,and O2in Ar. The plasma temperature was calculated either from measured intensities of ArI lines or by the application of Omstein’s method using TiI lines. The values of the transition probabilities for the (0,O)-and (1, I)-bands were found to be 6.6 x 10’ and 4.6 X 10”set-‘, respectively.
INTRODUCTION
molecule have been relative absolute transition probabilities relative transition determined by a number of investigators!‘-” probabilities a-system. intensities belonging to the LY-and p-systems estimated by LINTONand NICHOLLS.“-3’ PRICE, SIJLZMANN and PENNER”~’ have made measurements of the electronic oscillator strengths for the (Y-and -y-systems. In the present work, absolute transition probabilities for the (0,O)-and (1, I)-bands belonging to the /?(c’@ - a’A) system have been measured. VALUES OF
METHOD
The investigated bands of TiO overlapped partially and individual rotational lines in the bands were not resolved. Therefore, a method’” based on measurements of known fractions of the bands was used. The intensity ll:$Tfiof a rotational line in an electronic band system in emission is given by the relation
where L(V) is the line profile, v is the spectral frequency, ni’,fJ’ is the number of emitting molecules in the rotational state J’ of the vibrational level v’ and in the electronic state i’, h is Planck’s constant, v~~$&is the frequency of the rotational line, A::“,$‘,denotes the transition probability from the upper state i’, u’, J to the lower state with the quantum numbers i”, v”, J”. The transition probability A ?$$ for a rotational line belonging to a band is related to the transition probability A!:$ for the band through the expression’“l
where & is the Honl-London factor and v::“,:,is an “average” frequency of the band. It is usually assumed that i’“‘,’ vI”v”J”
z
i’“’
vi”““.
(3)
If rotational lines in a band are not resolved, the sum of intensities of the lines lying in the spectral range from v1 to v2 may be replaced by an integral, viz.
.(I6
W. ~YRNICKI
where I”(v) is the band profile. Applying the Maxwell-Boltzmann distribution law for the relation between the number of emitting molecules n irv’J’ and the total number of the molecules n, one obtains from equations (1) to (4) for LTE the following result:
where
(6)
U=TS.,,exp(-&,F,)
and Qi,, is the internal partition function, gi, is the statistical weight of the electronic state i’, Tic is the electronic term, G,, is the vibrational term, FJ.is the rotational term, c is the velocity of light in vacuum and k is the Boltzmann constant. EXPERIMENTAL
TECHNIQUE
In the present experiments, an argon plasma-jet”’ with a gas mixture containing Ar, TiCl, and O2 at a pressure of 1 atm was used as a light source. The plasma-jet was run with d.c. currents between 400 and 600 amp. The voltage drop between the electrodes was 20 V. TiCI, and O2 were introduced into a’stream of Ar at separate locations. Both TiC14 and O2 were added to the flame outside the inter-electrode area of the plasma-jet to avoid disturbances of the flowing argon stream. The insertion of TiCI, into the jet was made by passing a stream of Ar over liquid titanium tetrachloride. The container with liquid TiCL was immersed in a water bath at a constant temperature of about 70°C. The plasma flowing out of the jet as an axysymmetric stream was protected against contact with the surrounding atmo’sphere by means of a special chamber with quartz windows through which the plasma emission could be recorded. A tungsten ribbon lamp calibrated by pyrometers was used as a source of known absolute spectral radiance. The spectrum of this source was photographed each time on the same plate with the analyzed plasma spectrum under the same circumstances. Calibration curves of the plates were obtained using a platinum-on-quartz 6 step filter. The spectra were recorded in the first order of a Zeiss PGS-2 gratmg spectrograph at a linear dispersion of 7 A/mm using ORWO WP-3 plates. The slit widths were 100 or 80 p. The exposure times for the plasma and the lamp were approximately the same and varied between 30 set and 3 min. The spectra were reduced by means of a Zeiss GII microdensitometer. DETERMINATION
OF TRANSITION
PROBABILITIES
The plasma spectrum was recorded over several cross sections of the plasma stream normal to its axis of symmetry at different positions along this axis. Using an Abel inversion technique,“’ local values of the plasma intensity were calculated and then compared with the tungsten lamp spectrum to obtain absolute intensities. The wavelength regions of TiO for this study extended from 5597 to 5603 A for the (0, 0)-band and from 5629 to 5635 A for the (1, I)-band. Only rotational lines of the R-branches with rotational quantum numbers from J’ = 2 to J’ = 72 for the (0, 0)-band and from J’ = 2 to J’ = 69 for the (1, I)-band have been found in these regions. The plasma-temperature distributions for the cross sections lying closer to the plasma-jet outlet were derived from measurements of absolute intensities of the ArI 4333,4335,4345,4596, and 4702 A lines using known values of the transition probabilities.“” The well-known relation between the absolute intensities of atomic lines, the partial pressures of atoms, and the absolute transition probabilities was then employed to calculate the temperature. The partial pressure of Ar was calculated from the known fraction of argon in the analyzed mixture at a total
Transition probabilities for the TiO molecule
511
pressure of 1 atm. The plasma temperatures in the sections more distant from the plasma outlet were determined by the application of Ornstein’s method,“‘.“’ employing twelve lines of TiI with known transition probabilities.“3’ The calculated temperatures were between 4300 and 9200 K. The total number of the TiO molecules was calculated from the relation nTio=
K,
n-ripe,
(7)
where K, is the equilibrium constant for the reaction TiO = Ti + 0, ltT,is the number density of Ti atoms, and p. is the pressure of 0 atoms. The density of Ti atoms was calculated in the usual way from the experimentally measured absolute intensities of the TiI 5512.5,5514.3 and 5514.5 A lines using known absolute transition probabilities.“” The number of Ti atoms per cm3 was calculated to be between 10” and 1014,depending on the location in the plasma stream and the overall parameters of the experiment. The oxygen pressure p. was determined from the known fraction of O2 in the analyzed mixture, taking into account the reaction of O2= 20. The assumption was made that this pressure was constant in each section and at all radial positions. Calculations of the values of the atomic oxygen pressure, based upon measurements of absolute intensities of the 0 I 4368 and 5436 a lines and known absolute transition probabilities,““’ confirmed this assumption. The pressures of 0 atoms were varied for different experiments between 0.03 and 0.12 atm. The total number of the TiO molecules was found to be between lo8 and lOI per cm3. For the calculations of K,, molecular constants given by PHILLIPS W)were used to determine the dissociation energy of TiO. For all other calculations, spectroscopic data from Ref. (15) were employed. The Hiinl-London factor was expressed according to KOVACS.“@ The values of vi:“,: were assumed to be the band origins. The absolute transition probabilities for the (0, 0)- and (1, 1)-bands of the p-system were found to be 6.6 x IO8and 4.6 X 10”set-‘, respectively. The errors in the transition probabilities were estimated to be about 440 per cent for the (0, O)-band and about 1-50 per cent for the (1, 1)-band. Acknowledgements-The
author is grateful to Dr. A. Czernichowski
for helpful discussions and comments.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
9. 10. 1I. 12. 13. 14. 15. 16.
J. G. PHILLIPS,Astrophys. J. 119, 274 (1954). C. LINTON and R. W. NICHOLLS,J. Phys. B2, 490 (1969). C. LINTONand R. W. NICHOLLS,JQSRT 10, 311 (1970). M. L. PRICE, K. G. P. SULZMANNand S. S. PENNER,JQSRT 11, 427 (1971). M. L. PRICE, K. G. P. SULZMANNand S. S. PENNER,JQSRT 14, 1273 (1974). D. ROBINSONand R. W. NICHOLLS,JQSRT 1, 76 (1960). A. SCHADE,JQSRT 7, 169 (1967). B. BRZOZOWSKI, J. REDA and M. MIKOS, Nizkotemperatumaya Plazma, Trudy Mezhdunarodnogo Simpozyuma po Svoistvam i Primeneniyu Nizkotemperatumoi Plazmy pri XXMezhdunarodnom Kongressepo Teoreticheskoi i Priklodnoi Khimii, p. 595. Moskwa (1%7). W. J. PEARCE,Conf on Extreme/y High Temperatures. Boston, Massachusetts, p. 123. Wiley, New York (1958). W. L. WIESE, M. W. SMITHand B. M. GLENNON,Atomic Transition Probabilities. U.S. Dept. of Commerce, NBS, Washington D.C. Vol. I (1%6), Vol. II (1%9). L. S. ORNSTEINand H. BRINKMANN, Physica 1, 797 (1934). L. S. ORNSTEINand J. KERSTEN,Physica 8, 1124 (1941). C. H. CORLISSand W. R. BOZMANN,Experimental Transition Probabilities for Spectral Lines of Seuenty Elements. U.S. Dept. of Commerce, NBS, Washington, D.C. (1962). J. G. Phillips, Astrophys. J. Suppl. 26, 313 (1973). W. ~YRNICKIand A. CZERNICHOWSKI, Acfa Phys. PO/. A39, 429 (1971). I. KOVACS,Rotational Structure in the Spectra of Diatomic Molecules. Akademiai Kiado, Budapest (1969).
Vol.IS.pp. 575-577 PergamonPress1975. Printed!n GreatBritain
TRANSITION PROBABILITIES FOR THE (0, 0) AND (1, 1) BANDS OF THE cl@a’A SYSTEM OF THE TiO MOLECULE W. ~YRNICKI Institute of Inorganic Chemistry and Metallurgy of Rare Elements, Technical University of Wro&aw, 50370 Wrochw, Poland (Receioed 1 August 1974) Abstract-Transition probabilities for the (O,O)-and (1, I)-bands of the ~‘0 - a ‘Asystem were determined by analyzing the plasma spectrum produced in an argon plasma-jet. Titaniumoxide was formed during a reaction between TiC1,and O2in Ar. The plasma temperature was calculated either from measured intensities of ArI lines or by the application of Omstein’s method using TiI lines. The values of the transition probabilities for the (0,O)-and (1, I)-bands were found to be 6.6 x 10’ and 4.6 X 10”set-‘, respectively.
INTRODUCTION
molecule have been relative absolute transition probabilities relative transition determined by a number of investigators!‘-” probabilities a-system. intensities belonging to the LY-and p-systems estimated by LINTONand NICHOLLS.“-3’ PRICE, SIJLZMANN and PENNER”~’ have made measurements of the electronic oscillator strengths for the (Y-and -y-systems. In the present work, absolute transition probabilities for the (0,O)-and (1, I)-bands belonging to the /?(c’@ - a’A) system have been measured. VALUES OF
METHOD
The investigated bands of TiO overlapped partially and individual rotational lines in the bands were not resolved. Therefore, a method’” based on measurements of known fractions of the bands was used. The intensity ll:$Tfiof a rotational line in an electronic band system in emission is given by the relation
where L(V) is the line profile, v is the spectral frequency, ni’,fJ’ is the number of emitting molecules in the rotational state J’ of the vibrational level v’ and in the electronic state i’, h is Planck’s constant, v~~$&is the frequency of the rotational line, A::“,$‘,denotes the transition probability from the upper state i’, u’, J to the lower state with the quantum numbers i”, v”, J”. The transition probability A ?$$ for a rotational line belonging to a band is related to the transition probability A!:$ for the band through the expression’“l
where & is the Honl-London factor and v::“,:,is an “average” frequency of the band. It is usually assumed that i’“‘,’ vI”v”J”
z
i’“’
vi”““.
(3)
If rotational lines in a band are not resolved, the sum of intensities of the lines lying in the spectral range from v1 to v2 may be replaced by an integral, viz.
.(I6
W. ~YRNICKI
where I”(v) is the band profile. Applying the Maxwell-Boltzmann distribution law for the relation between the number of emitting molecules n irv’J’ and the total number of the molecules n, one obtains from equations (1) to (4) for LTE the following result:
where
(6)
U=TS.,,exp(-&,F,)
and Qi,, is the internal partition function, gi, is the statistical weight of the electronic state i’, Tic is the electronic term, G,, is the vibrational term, FJ.is the rotational term, c is the velocity of light in vacuum and k is the Boltzmann constant. EXPERIMENTAL
TECHNIQUE
In the present experiments, an argon plasma-jet”’ with a gas mixture containing Ar, TiCl, and O2 at a pressure of 1 atm was used as a light source. The plasma-jet was run with d.c. currents between 400 and 600 amp. The voltage drop between the electrodes was 20 V. TiCI, and O2 were introduced into a’stream of Ar at separate locations. Both TiC14 and O2 were added to the flame outside the inter-electrode area of the plasma-jet to avoid disturbances of the flowing argon stream. The insertion of TiCI, into the jet was made by passing a stream of Ar over liquid titanium tetrachloride. The container with liquid TiCL was immersed in a water bath at a constant temperature of about 70°C. The plasma flowing out of the jet as an axysymmetric stream was protected against contact with the surrounding atmo’sphere by means of a special chamber with quartz windows through which the plasma emission could be recorded. A tungsten ribbon lamp calibrated by pyrometers was used as a source of known absolute spectral radiance. The spectrum of this source was photographed each time on the same plate with the analyzed plasma spectrum under the same circumstances. Calibration curves of the plates were obtained using a platinum-on-quartz 6 step filter. The spectra were recorded in the first order of a Zeiss PGS-2 gratmg spectrograph at a linear dispersion of 7 A/mm using ORWO WP-3 plates. The slit widths were 100 or 80 p. The exposure times for the plasma and the lamp were approximately the same and varied between 30 set and 3 min. The spectra were reduced by means of a Zeiss GII microdensitometer. DETERMINATION
OF TRANSITION
PROBABILITIES
The plasma spectrum was recorded over several cross sections of the plasma stream normal to its axis of symmetry at different positions along this axis. Using an Abel inversion technique,“’ local values of the plasma intensity were calculated and then compared with the tungsten lamp spectrum to obtain absolute intensities. The wavelength regions of TiO for this study extended from 5597 to 5603 A for the (0, 0)-band and from 5629 to 5635 A for the (1, I)-band. Only rotational lines of the R-branches with rotational quantum numbers from J’ = 2 to J’ = 72 for the (0, 0)-band and from J’ = 2 to J’ = 69 for the (1, I)-band have been found in these regions. The plasma-temperature distributions for the cross sections lying closer to the plasma-jet outlet were derived from measurements of absolute intensities of the ArI 4333,4335,4345,4596, and 4702 A lines using known values of the transition probabilities.“” The well-known relation between the absolute intensities of atomic lines, the partial pressures of atoms, and the absolute transition probabilities was then employed to calculate the temperature. The partial pressure of Ar was calculated from the known fraction of argon in the analyzed mixture at a total
Transition probabilities for the TiO molecule
511
pressure of 1 atm. The plasma temperatures in the sections more distant from the plasma outlet were determined by the application of Ornstein’s method,“‘.“’ employing twelve lines of TiI with known transition probabilities.“3’ The calculated temperatures were between 4300 and 9200 K. The total number of the TiO molecules was calculated from the relation nTio=
K,
n-ripe,
(7)
where K, is the equilibrium constant for the reaction TiO = Ti + 0, ltT,is the number density of Ti atoms, and p. is the pressure of 0 atoms. The density of Ti atoms was calculated in the usual way from the experimentally measured absolute intensities of the TiI 5512.5,5514.3 and 5514.5 A lines using known absolute transition probabilities.“” The number of Ti atoms per cm3 was calculated to be between 10” and 1014,depending on the location in the plasma stream and the overall parameters of the experiment. The oxygen pressure p. was determined from the known fraction of O2 in the analyzed mixture, taking into account the reaction of O2= 20. The assumption was made that this pressure was constant in each section and at all radial positions. Calculations of the values of the atomic oxygen pressure, based upon measurements of absolute intensities of the 0 I 4368 and 5436 a lines and known absolute transition probabilities,““’ confirmed this assumption. The pressures of 0 atoms were varied for different experiments between 0.03 and 0.12 atm. The total number of the TiO molecules was found to be between lo8 and lOI per cm3. For the calculations of K,, molecular constants given by PHILLIPS W)were used to determine the dissociation energy of TiO. For all other calculations, spectroscopic data from Ref. (15) were employed. The Hiinl-London factor was expressed according to KOVACS.“@ The values of vi:“,: were assumed to be the band origins. The absolute transition probabilities for the (0, 0)- and (1, 1)-bands of the p-system were found to be 6.6 x IO8and 4.6 X 10”set-‘, respectively. The errors in the transition probabilities were estimated to be about 440 per cent for the (0, O)-band and about 1-50 per cent for the (1, 1)-band. Acknowledgements-The
author is grateful to Dr. A. Czernichowski
for helpful discussions and comments.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
9. 10. 1I. 12. 13. 14. 15. 16.
J. G. PHILLIPS,Astrophys. J. 119, 274 (1954). C. LINTON and R. W. NICHOLLS,J. Phys. B2, 490 (1969). C. LINTONand R. W. NICHOLLS,JQSRT 10, 311 (1970). M. L. PRICE, K. G. P. SULZMANNand S. S. PENNER,JQSRT 11, 427 (1971). M. L. PRICE, K. G. P. SULZMANNand S. S. PENNER,JQSRT 14, 1273 (1974). D. ROBINSONand R. W. NICHOLLS,JQSRT 1, 76 (1960). A. SCHADE,JQSRT 7, 169 (1967). B. BRZOZOWSKI, J. REDA and M. MIKOS, Nizkotemperatumaya Plazma, Trudy Mezhdunarodnogo Simpozyuma po Svoistvam i Primeneniyu Nizkotemperatumoi Plazmy pri XXMezhdunarodnom Kongressepo Teoreticheskoi i Priklodnoi Khimii, p. 595. Moskwa (1%7). W. J. PEARCE,Conf on Extreme/y High Temperatures. Boston, Massachusetts, p. 123. Wiley, New York (1958). W. L. WIESE, M. W. SMITHand B. M. GLENNON,Atomic Transition Probabilities. U.S. Dept. of Commerce, NBS, Washington D.C. Vol. I (1%6), Vol. II (1%9). L. S. ORNSTEINand H. BRINKMANN, Physica 1, 797 (1934). L. S. ORNSTEINand J. KERSTEN,Physica 8, 1124 (1941). C. H. CORLISSand W. R. BOZMANN,Experimental Transition Probabilities for Spectral Lines of Seuenty Elements. U.S. Dept. of Commerce, NBS, Washington, D.C. (1962). J. G. Phillips, Astrophys. J. Suppl. 26, 313 (1973). W. ~YRNICKIand A. CZERNICHOWSKI, Acfa Phys. PO/. A39, 429 (1971). I. KOVACS,Rotational Structure in the Spectra of Diatomic Molecules. Akademiai Kiado, Budapest (1969).