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Determination of optical cross-sections for some Na and Li lines with a shock tube
Spectrochimica Acta, Vol. 34B, pp. 283-288 @ Pergamon Press Ltd., lW9. Printed in Great Britain
Determination of optical cross-sections for some Na and Li lines with a shock tube SADAO NAKAJIMA, KYOKO KO~ASAand YOSHIOMARUYAMA Government IndustrialResearch Institute, OSAKAAlidorigaoka1, Ikeda, Osada, Japan (Received 18 December 1978; revised 7 March 1979)
Abstract-The optical cross-sectionfor collisionalbroadeningof the lines NaJ 589.0nm, LiI 670.7 nm and
LiI 610.3 nm by argon was determined by simul~neous measurement of the total absorption and the density of active atoms that were thermally excited in a shock tube. It was found that the method is suitable for both resonance lines and lines originating from transitions between higher excited levels.
1. INTRODUCTION THERE are some papers dealing with the study of spectral line profiles aimed at improving the accuracy of spectroscopic analysis [l-4]. The shape of spectral lines emitted from a hot gas such as a flame or an inductively coupled plasma, where active (emitting or absorbing) atoms are usually sprayed in the perturbing carrier gas or fuel gas, is influenced by several effects namely Doppler, collisional, natural and Stark broadening. Of these only Doppler and collisional broadening are predominant in the above mentioned sources. The optical cross-section of collisional broadening is simply estimated with the aid of the asymptotes of curves of growth (COG) [5-71, that are derived on the basis of the Voigt function [8], by measuring the a parameter through which the width of collisional broadening is combined with the width of Doppler broadening. In generating COG one assumes that the slit width of the spectrometer is wide enough to be considered infinite. At high temperatures, however, the Doppler width for lighter atoms is of the order of 0.1 A and in practice the effective slit width of a spectrometer is not wide enough to cover the whole wing of the spectral lines. Here the effective slit width is defined as the sum of the width of the entrance and exit slits multiplied by the linear dispersion of the spectrometer. There is another disadvantage of the COG method. The efficiency of atomization in a flame may vary with the concentration of the solution sprayed into the flame 191,and the number density of active atoms, especially that in the higher excited states, does not always follow the concentration of the solution. Moreover, LOVETT and PARSONS[lo] suggested that one can not expect COGS to be linear even in the region of higher density where the high-density asymptotes of the COG have a tangent l/2. This paper also describes a method for determining the optical cross-section. The method is based on the simultaneous measurement of the total absorption and the number density of the active atoms excited in a shock tube which is known to be a
[ll G. K.
KIRKBRIGHT. 0. E. TR~CCOLIand S. VEITER,Spe&o&m. Acro 28B, 1 (1973). [ZJ A. GALLAGHER, Phys. Rev. AX2. 133 (1975). Dl H. C. WAGENAARand L. DE GALAN, Spectrvchim. Actu 3OB,361 (1975). [41 B. J. JANSEN,TJ. HOLLAND ERand C. TH. J. ALKEMADE. J. Quant. Spectrosc. Radiat. Transfer 17, 187 (1976). [S] E. HIMNOF, J. Opt. Sot. Am. 47, 151 (1957). 161 E. HINNOV and H. KOHN,L Opt. Sot. Am. 47, 156 (1957). 171 F. W. HOFMANN and H. KOHN,L Opt. Sot. Am. 51,512 (l%l). 181 S. S. PENNERand R. W. KAVANAGH, J. Opt. Sot. Am. 43,385 (1953). f91 D. J. HALLS,Spectrochim. Acta 32B, 397 (1977). [IO] R. J. Lov~ff and M. L. PARSONS, Specfrocirim. Acta 328,421 (1977). 283
284
S.
NAKAJIMA, K. KOSASAand Y. MARUYAMA
convenient light source in the form of a hot gas with a homogeneous distribution of the various species and a known temperature Ill]. The intensity of a spectral line emitted by atoms thermally excited in a homogeneous source is expressed according to Kirchhoff’s law as I = B(T, Y,,)[ A(v) d v = B(T, vO) [l -exp(-K(v)L.)] I
dv.
(1)
In this expression B(T, v,J is the intensity of black-body radiation at the temperature T of the source and the frequency v. in the center of the line, A(v) is the absorptivity of the source at frequency Y, K(v) is the absorption coefficient and L is the thickness of the source in the line of observation. Here, the absorption coefficient K(v) is expressed with Voigt’s function [
(2)
0
-Kg--F
(In 2)“*,
a = 2
*=
(34
Ia’
2(v - vo) (ln AhvD
3112
(3c)
’
Avc= ~($+$}]“*(~n~,
(34
AU,,= z (T)“*
(3d
(In 2)“*.
In the above, e is the electronic charge, m the electronic mass, c the velocity of light in vacuum, n, the number density of the active atoms, f the oscillator strength of the absorption line, k the Boltzmann constant, T the temperature of the gas, m, the mass of active the atoms, mp the mass of the perturber, u the optical cross-section for collisional broadening and n, the density of perturber. The total absorption is defined as A=
Im
[l - exp (-K(v)L)]
-co
dv,
(4)
and is regarded as a function of ndL and a. Hence from the measured values of A and n,,fL, a may be determined by numerical computation of equation (4). The optical cross-section is derived through equations (3a-d). 2.
EXPERIMENTAL
2.1.
Experimental setup 2.1.1. Shock tube. The shock tube is made of a copper tube having a 59 mm i.d. Hydrogen at a pressure of about 7 atm is used as the driver gas to yield shock-waves of Mach-number, M, from 5 to 7. The driven gaq is argon of 99.99% purity. For the
[ill E. L. REELER,SHAO-CHILIN and A. KANTRO~ITZ,J. Appl. Phys. 23, 1390 (1952). [121 A. C. G. MITCHELand M. W. ZEMANSKY, Resonance Radiation and Excited Atoms. Cambridge University Press, New York (1934).
Determination of optical cross-sections for some Na and Li lines with a shock tube
285
optical measurements four plain glass windows, 8 mm in dia., are mounted at 2500 mm from the diaphragm that separates the driver section from the driven section. Metallic sodium or lithium is introduced in the shock tube in the form of ultra-fine powder of less than 0.1 pm in dia. The powder is prepared in a cylinder, 15 cm in dia. and 16 cm high, which is connected to the shock tube with a pipe of 2.5 cm i.d. A valve separates the cylinder from the shock tube. The metal is evaporated in the cylinder with a tungsten heater in argon at reduced pressure. Immediately after the evaporation of the metal, additional argon is led into the cylinder until an adequate pressure is reached so that the gas suspending the fine particles gives the desired pressure in the driven section. The size of the powder particles can be controlled by altering the pressure of argon at which the evaporation is performed [13]. The distribution of active atoms in the shock tube has been examined by KOSASA et al. [14]. When the metal is evaporated at too high pressure, the particle size becomes large and the particles do not disperse evenly in the argon added after the evaporation. Evaporation at too low pressure only causes the metal particles to stick on the wall of the cylinder, thus we cannot introduce a sufficient amount of sample into the shock tube. It has been found that the distribution of active atoms becomes homogeneous if the evaporation pressure is less than 30 torr. The sample was evaporated at a pressure of 20 torr throughout the experiment. The pressure and the temperature of the shock-heated gas are expressed in terms of M by the Rankin-Hugoniot relation [15],
*+%r-1w2+1 (y + 1)2
To and PO are of argon in the y is of heat of the is measured by counting at 180 cm from is also to triggering a flash lamp and N2-laser, which are used to A layout of is given in Fig. 1. 2.1.2. is shown in Fig. 2. to measure a flash lamp, which emits continuum light pulse of 2 psec duration, is at the of the of the of the on the of a 1.5 m concave grating of the is adjusted
FZO-qb
50 .t
180
diffusion pump Fig. 1. Shock tube layout. Ml, M2, M3: pressure gauge, D: diaphragm of 0.2 mm aluminum, T: thermal gauge, W: window, S: sample evaporator, P.S.: power source for evaporation. [13] S. YATSUYA,S. KARUKABE and R. UEDA, hp. J. Appl. Phys. 12, 1675 (1973). [14] K. KOSASA,Y. MARUYAMA and Y. URANO,J. Spect. Sot. hp. 25, 246 (1976). [IS] H. W. LIEPMANN and A. ROSHKO,Elements of Gasdynamics. Wiley, New York (l%O).
S. NAKAJIMA,
286
K. KOSASAand Y. MARUYAMA
Fig. 2. Schematic arrangement of instruments for the optical measurement. F.L.: flash lamp, S.G.: spectrograph, S.P.: spectrophotometer, DEL.1, DEL.2: delay circuit.
50 times the full width at half maximum (FWHM) of a Doppler broadened line calculated for the temperature of the shock-heated gas. A photomultiplier (HTV Type R928) equipped with an emitter follower is used to measure the light intensity. The output is recorded on photographic film with an oscilloscope and a camera. For the measurement of n$L the hook-method [la] is used. In the method a Mach-Zehnder interferometer and a spectrograph are used to produce a set of interference fringes superimposed on the spectrum of the interferometer light source. On account of anomalous dispersion caused by the active atoms, the fringes are distorted to form hook patterns. The relation between nJI_ and the position of hooks is given later. The mirrors and beam splitters of the interferometer are made so as to give nearly the same intensity of light in each branch of the beam splitters is mounted on a adjustable holder so that the inclination and the position of the beam splitter can be adjusted to make the visibility greater than 0.85 on the interferogram. The light source for the hook-method is a dye-laser excited with a NJaser. The firing of the flash lamp and the laser is synchronized with the arrival of the shock-heated gas by means of two delay circuits so that the lamp and the laser operate about 100 set after the passage of shock-front by the window through which the observation is made. Rhodamine 6G, Cresyl Violet and Rhodamine B were used for the measurement of the spectral lines Na I 589.0 nm, Li I 670.7 nm and Li I 610.3 nm respectively. Interferograms are recorded with a 3.5-m Ebert spectrograph. Typical spectrographic and oscilloscopic recordings for Li I 670.7 nm are shown in Figs. 3(a and b).
to
2.2. Measurement of absorption Let the light intensity of the shock-heated gas be 1,. When the gas is irradiated with a background light of intensity Ib, the observed intensity I, in a wavelength interval dh becomes I, dh = I, dh + [l - A(v)]I~ dh. The output of spectrometer
then becomes
I,I,SdA
=I,I$dA
+~/~[l-A(r4ISdA,
where S is the instrumental function of the spectrometer photomultiplier and the amplifier, A is the effective slit width.
1161 W. C.
MARLOW,
(7)
Appl. Opt. 6, 1715 (1%7).
(8) including
that of the
Determination of optical cross-sections for some Na and Li lines with a shock tube
287
Fig. 3. Interferometric (a) and oscilloscopic (b) recordings of the measurement of the LiI 670.7nm line excited at 3573 K. The time scale in (b) is 50 Fsec/div.
Assuming I* and S do not alter in the wavelength I,=I,+1,-I, where the bar, -,
range A, we have
A(v) d& IA
(9)
means an average over A. From equation (9) we have
I
A(v)dA =
A
and by definition the total absorption
(I,+Ib-r;), Ib
,
(10)
is given as
A=CA(ji;;+I,-T;) h2Ib
*
(11)
2.3. Measurement of n,fL For the calculation by means of equation (4) absolute values of n, and f are not necessary if n,fL is known. This fact is important as the reported f-values are often conflicting. The value of n,fL is given in the hook-method by equation n, fL =
rftF2D',
(12)
where A is the wavelength of the spectral line, D is the distance between two hooks and x is the fringe order around the hooks, which is determined from a part of the spectrum that is free of lines. In order to form measurable hooks the fringe order is made about 2000 by inserting a compensator in one of beams of the interferometer. 3. RESULTS AND DISCUSSION We intend in this work to determine
the optical cross-section
for the spectral line
288
S.
NAKAJIMA, K.
KOSASAand Y. MARUYAMA
Li I 610.3 nm because no experimental value has been reported on this line so far, in spite of its frequent use in spectroscopic analysis. The measurements on the resonance lines of sodium and lithium were carried out in order to check the reliability of this method. In order to determine the a-value from nofL and A, an arbitrary a-value is chosen as the starting value. The measured value of n&, and a are substituted in equation (4) and the integration is carried out with the integration limit 50 times the FWHM of the Doppler-width. The resulting A-value is compared with the measured value. If they do not coincide, a is changed a little and the integration is carried out again. This procedure is repeated until the calculated value reaches the measured value within 1% of accuracy. The accuracy of the measured A-value depends on the instability of the intensity of the flash lamp and the error in the A-value is estimated to be 5%. The error in n$L is caused by the error in reading the distance D on the interferogram. The error in D is less than 3%. Hence the error in n&. is about 6% because n,JL is proportional to 0’. Considering the above errors we estimated the error in the u-value to be not more than 12%. The experimental results are shown in Table 1, together with the experimental conditions. In Table 1 a and u are averaged values over five runs. The number density of active atoms is in a range between 1On to 1014cm-3 and that is rather large compared with that in the flame experiments; still we can neglect the collisions between active atoms in the estimation of collisional broadening for the density is only 1110’ of the density of perturbers. Table 1. Experimental parameters and optical cross-sections
(t&l
&
a
( 10-1’cm2)
H.KT [61
H.K.t 171
M.W. ]171
T.H.A ]181
42
30
NaI 7.8 16
589.0 nm 4441 3439
0.13 +-0.01 0.39 * 0.04
29?3 4926
64
59.7
Li I 16
670.7 nm 3573
0.36 -c 0.04
44*5
43
46.5
Li I 8.3 16
610.3 nm 4444 3609
0.58 -c 0.06 1.4820.16
18
153 + 17 209*23
H.K* In an acetylene flame at 2480 K. H.Kt In an acetylene flame at 2500 K. M.W In nitrogen at 573 K. T.H.A In an acetylene flame at 2400 K for Na and in a CO flame at 1970 K for Li.
The measured optical cross-sections seem to have the general tendency of decreasing as the temperature increases. However, they do not follow the T-O.*dependence shown by JENSEN et al. [43. The fact that the perturbers in the present experiment are different from those in the previous works is not sufficient to understand the discrepancy. We are planning another experiment in which active atoms are excited in nitrogen at a wider range of temperature.
Acknowledgements-We would like to thank Mr. S. MATSUIJaAfor his encouragement and interest in the course of the work and Prof. Y. URANOat Kyoto Technical University for his valuable advice in the spectroscopic measurements.
[17] H. MARGENAU and W. W. WATSON,Phys. Rev. 44, 92 (1933). [18] C. V. TRIGT,TJ. HOLLANDER and C. T. J. ALKEMADE,1 Quant. Spectrosc. Radiat. Transfer 5, 813 (1%5).
Determination of optical cross-sections for some Na and Li lines with a shock tube SADAO NAKAJIMA, KYOKO KO~ASAand YOSHIOMARUYAMA Government IndustrialResearch Institute, OSAKAAlidorigaoka1, Ikeda, Osada, Japan (Received 18 December 1978; revised 7 March 1979)
Abstract-The optical cross-sectionfor collisionalbroadeningof the lines NaJ 589.0nm, LiI 670.7 nm and
LiI 610.3 nm by argon was determined by simul~neous measurement of the total absorption and the density of active atoms that were thermally excited in a shock tube. It was found that the method is suitable for both resonance lines and lines originating from transitions between higher excited levels.
1. INTRODUCTION THERE are some papers dealing with the study of spectral line profiles aimed at improving the accuracy of spectroscopic analysis [l-4]. The shape of spectral lines emitted from a hot gas such as a flame or an inductively coupled plasma, where active (emitting or absorbing) atoms are usually sprayed in the perturbing carrier gas or fuel gas, is influenced by several effects namely Doppler, collisional, natural and Stark broadening. Of these only Doppler and collisional broadening are predominant in the above mentioned sources. The optical cross-section of collisional broadening is simply estimated with the aid of the asymptotes of curves of growth (COG) [5-71, that are derived on the basis of the Voigt function [8], by measuring the a parameter through which the width of collisional broadening is combined with the width of Doppler broadening. In generating COG one assumes that the slit width of the spectrometer is wide enough to be considered infinite. At high temperatures, however, the Doppler width for lighter atoms is of the order of 0.1 A and in practice the effective slit width of a spectrometer is not wide enough to cover the whole wing of the spectral lines. Here the effective slit width is defined as the sum of the width of the entrance and exit slits multiplied by the linear dispersion of the spectrometer. There is another disadvantage of the COG method. The efficiency of atomization in a flame may vary with the concentration of the solution sprayed into the flame 191,and the number density of active atoms, especially that in the higher excited states, does not always follow the concentration of the solution. Moreover, LOVETT and PARSONS[lo] suggested that one can not expect COGS to be linear even in the region of higher density where the high-density asymptotes of the COG have a tangent l/2. This paper also describes a method for determining the optical cross-section. The method is based on the simultaneous measurement of the total absorption and the number density of the active atoms excited in a shock tube which is known to be a
[ll G. K.
KIRKBRIGHT. 0. E. TR~CCOLIand S. VEITER,Spe&o&m. Acro 28B, 1 (1973). [ZJ A. GALLAGHER, Phys. Rev. AX2. 133 (1975). Dl H. C. WAGENAARand L. DE GALAN, Spectrvchim. Actu 3OB,361 (1975). [41 B. J. JANSEN,TJ. HOLLAND ERand C. TH. J. ALKEMADE. J. Quant. Spectrosc. Radiat. Transfer 17, 187 (1976). [S] E. HIMNOF, J. Opt. Sot. Am. 47, 151 (1957). 161 E. HINNOV and H. KOHN,L Opt. Sot. Am. 47, 156 (1957). 171 F. W. HOFMANN and H. KOHN,L Opt. Sot. Am. 51,512 (l%l). 181 S. S. PENNERand R. W. KAVANAGH, J. Opt. Sot. Am. 43,385 (1953). f91 D. J. HALLS,Spectrochim. Acta 32B, 397 (1977). [IO] R. J. Lov~ff and M. L. PARSONS, Specfrocirim. Acta 328,421 (1977). 283
284
S.
NAKAJIMA, K. KOSASAand Y. MARUYAMA
convenient light source in the form of a hot gas with a homogeneous distribution of the various species and a known temperature Ill]. The intensity of a spectral line emitted by atoms thermally excited in a homogeneous source is expressed according to Kirchhoff’s law as I = B(T, Y,,)[ A(v) d v = B(T, vO) [l -exp(-K(v)L.)] I
dv.
(1)
In this expression B(T, v,J is the intensity of black-body radiation at the temperature T of the source and the frequency v. in the center of the line, A(v) is the absorptivity of the source at frequency Y, K(v) is the absorption coefficient and L is the thickness of the source in the line of observation. Here, the absorption coefficient K(v) is expressed with Voigt’s function [
(2)
0
-Kg--F
(In 2)“*,
a = 2
*=
(34
Ia’
2(v - vo) (ln AhvD
3112
(3c)
’
Avc= ~($+$}]“*(~n~,
(34
AU,,= z (T)“*
(3d
(In 2)“*.
In the above, e is the electronic charge, m the electronic mass, c the velocity of light in vacuum, n, the number density of the active atoms, f the oscillator strength of the absorption line, k the Boltzmann constant, T the temperature of the gas, m, the mass of active the atoms, mp the mass of the perturber, u the optical cross-section for collisional broadening and n, the density of perturber. The total absorption is defined as A=
Im
[l - exp (-K(v)L)]
-co
dv,
(4)
and is regarded as a function of ndL and a. Hence from the measured values of A and n,,fL, a may be determined by numerical computation of equation (4). The optical cross-section is derived through equations (3a-d). 2.
EXPERIMENTAL
2.1.
Experimental setup 2.1.1. Shock tube. The shock tube is made of a copper tube having a 59 mm i.d. Hydrogen at a pressure of about 7 atm is used as the driver gas to yield shock-waves of Mach-number, M, from 5 to 7. The driven gaq is argon of 99.99% purity. For the
[ill E. L. REELER,SHAO-CHILIN and A. KANTRO~ITZ,J. Appl. Phys. 23, 1390 (1952). [121 A. C. G. MITCHELand M. W. ZEMANSKY, Resonance Radiation and Excited Atoms. Cambridge University Press, New York (1934).
Determination of optical cross-sections for some Na and Li lines with a shock tube
285
optical measurements four plain glass windows, 8 mm in dia., are mounted at 2500 mm from the diaphragm that separates the driver section from the driven section. Metallic sodium or lithium is introduced in the shock tube in the form of ultra-fine powder of less than 0.1 pm in dia. The powder is prepared in a cylinder, 15 cm in dia. and 16 cm high, which is connected to the shock tube with a pipe of 2.5 cm i.d. A valve separates the cylinder from the shock tube. The metal is evaporated in the cylinder with a tungsten heater in argon at reduced pressure. Immediately after the evaporation of the metal, additional argon is led into the cylinder until an adequate pressure is reached so that the gas suspending the fine particles gives the desired pressure in the driven section. The size of the powder particles can be controlled by altering the pressure of argon at which the evaporation is performed [13]. The distribution of active atoms in the shock tube has been examined by KOSASA et al. [14]. When the metal is evaporated at too high pressure, the particle size becomes large and the particles do not disperse evenly in the argon added after the evaporation. Evaporation at too low pressure only causes the metal particles to stick on the wall of the cylinder, thus we cannot introduce a sufficient amount of sample into the shock tube. It has been found that the distribution of active atoms becomes homogeneous if the evaporation pressure is less than 30 torr. The sample was evaporated at a pressure of 20 torr throughout the experiment. The pressure and the temperature of the shock-heated gas are expressed in terms of M by the Rankin-Hugoniot relation [15],
*+%r-1w2+1 (y + 1)2
To and PO are of argon in the y is of heat of the is measured by counting at 180 cm from is also to triggering a flash lamp and N2-laser, which are used to A layout of is given in Fig. 1. 2.1.2. is shown in Fig. 2. to measure a flash lamp, which emits continuum light pulse of 2 psec duration, is at the of the of the of the on the of a 1.5 m concave grating of the is adjusted
FZO-qb
50 .t
180
diffusion pump Fig. 1. Shock tube layout. Ml, M2, M3: pressure gauge, D: diaphragm of 0.2 mm aluminum, T: thermal gauge, W: window, S: sample evaporator, P.S.: power source for evaporation. [13] S. YATSUYA,S. KARUKABE and R. UEDA, hp. J. Appl. Phys. 12, 1675 (1973). [14] K. KOSASA,Y. MARUYAMA and Y. URANO,J. Spect. Sot. hp. 25, 246 (1976). [IS] H. W. LIEPMANN and A. ROSHKO,Elements of Gasdynamics. Wiley, New York (l%O).
S. NAKAJIMA,
286
K. KOSASAand Y. MARUYAMA
Fig. 2. Schematic arrangement of instruments for the optical measurement. F.L.: flash lamp, S.G.: spectrograph, S.P.: spectrophotometer, DEL.1, DEL.2: delay circuit.
50 times the full width at half maximum (FWHM) of a Doppler broadened line calculated for the temperature of the shock-heated gas. A photomultiplier (HTV Type R928) equipped with an emitter follower is used to measure the light intensity. The output is recorded on photographic film with an oscilloscope and a camera. For the measurement of n$L the hook-method [la] is used. In the method a Mach-Zehnder interferometer and a spectrograph are used to produce a set of interference fringes superimposed on the spectrum of the interferometer light source. On account of anomalous dispersion caused by the active atoms, the fringes are distorted to form hook patterns. The relation between nJI_ and the position of hooks is given later. The mirrors and beam splitters of the interferometer are made so as to give nearly the same intensity of light in each branch of the beam splitters is mounted on a adjustable holder so that the inclination and the position of the beam splitter can be adjusted to make the visibility greater than 0.85 on the interferogram. The light source for the hook-method is a dye-laser excited with a NJaser. The firing of the flash lamp and the laser is synchronized with the arrival of the shock-heated gas by means of two delay circuits so that the lamp and the laser operate about 100 set after the passage of shock-front by the window through which the observation is made. Rhodamine 6G, Cresyl Violet and Rhodamine B were used for the measurement of the spectral lines Na I 589.0 nm, Li I 670.7 nm and Li I 610.3 nm respectively. Interferograms are recorded with a 3.5-m Ebert spectrograph. Typical spectrographic and oscilloscopic recordings for Li I 670.7 nm are shown in Figs. 3(a and b).
to
2.2. Measurement of absorption Let the light intensity of the shock-heated gas be 1,. When the gas is irradiated with a background light of intensity Ib, the observed intensity I, in a wavelength interval dh becomes I, dh = I, dh + [l - A(v)]I~ dh. The output of spectrometer
then becomes
I,I,SdA
=I,I$dA
+~/~[l-A(r4ISdA,
where S is the instrumental function of the spectrometer photomultiplier and the amplifier, A is the effective slit width.
1161 W. C.
MARLOW,
(7)
Appl. Opt. 6, 1715 (1%7).
(8) including
that of the
Determination of optical cross-sections for some Na and Li lines with a shock tube
287
Fig. 3. Interferometric (a) and oscilloscopic (b) recordings of the measurement of the LiI 670.7nm line excited at 3573 K. The time scale in (b) is 50 Fsec/div.
Assuming I* and S do not alter in the wavelength I,=I,+1,-I, where the bar, -,
range A, we have
A(v) d& IA
(9)
means an average over A. From equation (9) we have
I
A(v)dA =
A
and by definition the total absorption
(I,+Ib-r;), Ib
,
(10)
is given as
A=CA(ji;;+I,-T;) h2Ib
*
(11)
2.3. Measurement of n,fL For the calculation by means of equation (4) absolute values of n, and f are not necessary if n,fL is known. This fact is important as the reported f-values are often conflicting. The value of n,fL is given in the hook-method by equation n, fL =
rftF2D',
(12)
where A is the wavelength of the spectral line, D is the distance between two hooks and x is the fringe order around the hooks, which is determined from a part of the spectrum that is free of lines. In order to form measurable hooks the fringe order is made about 2000 by inserting a compensator in one of beams of the interferometer. 3. RESULTS AND DISCUSSION We intend in this work to determine
the optical cross-section
for the spectral line
288
S.
NAKAJIMA, K.
KOSASAand Y. MARUYAMA
Li I 610.3 nm because no experimental value has been reported on this line so far, in spite of its frequent use in spectroscopic analysis. The measurements on the resonance lines of sodium and lithium were carried out in order to check the reliability of this method. In order to determine the a-value from nofL and A, an arbitrary a-value is chosen as the starting value. The measured value of n&, and a are substituted in equation (4) and the integration is carried out with the integration limit 50 times the FWHM of the Doppler-width. The resulting A-value is compared with the measured value. If they do not coincide, a is changed a little and the integration is carried out again. This procedure is repeated until the calculated value reaches the measured value within 1% of accuracy. The accuracy of the measured A-value depends on the instability of the intensity of the flash lamp and the error in the A-value is estimated to be 5%. The error in n$L is caused by the error in reading the distance D on the interferogram. The error in D is less than 3%. Hence the error in n&. is about 6% because n,JL is proportional to 0’. Considering the above errors we estimated the error in the u-value to be not more than 12%. The experimental results are shown in Table 1, together with the experimental conditions. In Table 1 a and u are averaged values over five runs. The number density of active atoms is in a range between 1On to 1014cm-3 and that is rather large compared with that in the flame experiments; still we can neglect the collisions between active atoms in the estimation of collisional broadening for the density is only 1110’ of the density of perturbers. Table 1. Experimental parameters and optical cross-sections
(t&l
&
a
( 10-1’cm2)
H.KT [61
H.K.t 171
M.W. ]171
T.H.A ]181
42
30
NaI 7.8 16
589.0 nm 4441 3439
0.13 +-0.01 0.39 * 0.04
29?3 4926
64
59.7
Li I 16
670.7 nm 3573
0.36 -c 0.04
44*5
43
46.5
Li I 8.3 16
610.3 nm 4444 3609
0.58 -c 0.06 1.4820.16
18
153 + 17 209*23
H.K* In an acetylene flame at 2480 K. H.Kt In an acetylene flame at 2500 K. M.W In nitrogen at 573 K. T.H.A In an acetylene flame at 2400 K for Na and in a CO flame at 1970 K for Li.
The measured optical cross-sections seem to have the general tendency of decreasing as the temperature increases. However, they do not follow the T-O.*dependence shown by JENSEN et al. [43. The fact that the perturbers in the present experiment are different from those in the previous works is not sufficient to understand the discrepancy. We are planning another experiment in which active atoms are excited in nitrogen at a wider range of temperature.
Acknowledgements-We would like to thank Mr. S. MATSUIJaAfor his encouragement and interest in the course of the work and Prof. Y. URANOat Kyoto Technical University for his valuable advice in the spectroscopic measurements.
[17] H. MARGENAU and W. W. WATSON,Phys. Rev. 44, 92 (1933). [18] C. V. TRIGT,TJ. HOLLANDER and C. T. J. ALKEMADE,1 Quant. Spectrosc. Radiat. Transfer 5, 813 (1%5).