Temperature and Self-Absorption in an Atmospheric Chromium Arc, and f Values for Near-Infrared Lines of Chromium I, from Spectrometric Measurements with Refrigerated Photomultiplier Tubes':'

Joseph W. Hutchersont Vanderbilt University, Nashville, Tennessee

Bill C. Mundy and Ray Hefferlin Southern Missionary College, Collegedale, Tennessee

A 5-A de arc was struck between pure chromium electrodes in nitrogen at 1 arm. The chromium I excitation temperature, averaged over atoms in the center of the are image, determined by relative emission-line intensities in the near infrared, was found to be (4893 ± 190)°K. The extent of self-absorption was determined from the same lines. Relative f values for 63 lines of chromium I, including the 21 used initially, were determined with precision of 0.33 in log gf. Existing instrumentation and current improvements to the experiment are described.

INTRODUCTION

Since 1956 the Physics Research Projec t at South-

ern Missionary College has been engaged in measur-

ing relative f values or oscillator s trengths for ele- ments of astrophysical interest. The emisslon-line

method has been used, employing a direct-current arc as a source of light. Measurements for the high-ex- citation lines of iron I (Refs. 1-3), t i tanium I (Ref. 4), and manganese I (Ref. 5) have been published:

I t was the purpose of this investigation to pe r fo rm tile same sort of measurements for chromium. The

decision to work with chromium was motivated, to some extent, by the knowledge tha t a sizeable tem- pe ra tu re error existed in the extensive measurements (430 lines) of Hil l and King, 6 which had confused later work with this element. 7-~° This tempera ture error manifests itself in the form of a systematic error

in Hill and King ' s relative f values for higher ex- cited states as compared with those of lower s ta tesJ ,~°

Since the lines of neutra l chromium are more numer- ous in the visual region of the solar spectrum than those of any other element except iron, this element is definitely one of astrophysical interest. I t was de- cided, however, to work in the red and near infrared,

noting, in suppor t of this, t ha t fewer lines in this region have measured f values. Indeed, only 28 chro- mium lines in this region have measurements, most of which have been done by Corliss and Bozman ~ a t

the National Bureau of Standards. Thus, i t was felt

tha t a contribution could be made by measuring f values for lines lacking previous determinations and by checking existing values.

12 Volume 20, Number 1, 1966

I. THEORY

A. Source Temperature

The well-known equation for the intensi ty of a spectral line in energy units per second radiated in all directions by an "op t ica l ly thin l a y e r " of atoms is

Io= A~mN~h,, (1)

where A~m is the Einstein probabi l i ty coefficient for the transit ion f rom state n to state m and N , is the number of atoms in state ~. I f we assume a Bo]tzmann distr ibution for N~, and note the relation 12 between A,,m and the emission f value f , , , of the transition, then we can write

Io = (K'g,,f~m/£ ~) exp ( - E , / K T ) , (2)

where g,~ is the statistical weight of state n, ~ the wavelength of the line, E~ the energy of the uppe r state n, refer red to the ground-state energy of zero, T the average "exc i ta t ion t e m p e r a t u r e " of the source, and K ' is a constant of no interest. Taking common logarithms this becomes

log Io X3/g~f~,.=log K'--504OE,,/T, (3)

where the number 5040 contains the conversion f rom ergs to electron volts and Bol tzman ' s constant. I t can be seen tha t if the f values for a number of lines emitted by the source are known (i.e., previously measured or accurately calculated), and if the relative intensities of these lines are measured then the quan-

t i ty log Io,P/g,~f,,~ may be plotted against E~ for each transition. This plot should be a " s t r a i g h t l i ne" whose slope is -5040 /T and thus it can be used to determine the source "excitation t e m p e r a t u r e . " Fig-

ure 1 is a temperature graph of the sort just de- scribed and was done in connection with the man- ganese experiment.

B. Self-Absorption

Unfortunately, an optically thin source is not com- pletely realizable in most eases and the phenomena of self-absorption and self-reversal often occur. This causes the measured intensity I to be less than Io and consequently points plotted on the graph for lines that have been absorbed or reversed fall below the " s t r a igh t l ine ." This can be seen to be the case for a number of points in Fig. 1. A detailed analysis

- 4

-5

\ T=5340°K

~.< -6 - - ~

-7

-8

l

I :.o

- 9 2

\

3 4 5 7 E. (eV)

~zo. I. ZVfanganese temperature graph. [] E., = 0.0 eV; • E~ =2,1 eV; G E , , = 2 . 3 eV; "4- E , , = 2 . 9 eVi A E ~ = 3 . 8 eV.

of self-absorption of spectrum lines has been done by Cowan and Dielce, 18 which shows that, if we represent the relationship between I and Io (for l ines of known f value) by a graph of log I/Io as a function of log Io, it is found that curves plotted for different ranges of lower energy level E,~ have the proper ty that log I/lo falls off with increasing Io, approaching the slope -½ for lines with resonance profiles (see Fig. 2). The curves drop off less, for a given Io, as multi- plets with higher values of Em are chosen. Figure 2 was done in connection with the t i tanium experi- ment.

0,25

-0.25

- 0.50 ~o

- 0.75

- 1.00

-t .25

-4.50

!

6.0 7.0 8,0 log 70

Fro. 2. Titanium self-absorption graph,

C. Determination of f Values

The above equation which was used to determine the temperature T can be rewrit ten

log g.,,f.~,,~=-logK'+log •0+3 log X+5040 E./T, (4)

and if the temperature can be ascertained as previ- ously described and the unabsorbed intensity Io of various lines emitted by the source can be measured or inferred, then this equation can be used to deter- mine relative log' gf values for these lines.

II. EXPERIMENTAL EQUIPMENT AND METHODS

An arc was struelc between two pieces of metallic chromium of very high pur i ty and operated at 5 A de and 30 V. Figure 3 shows the optimmn electrode shape. The light front the central region of the are was focused on the entrance slit of the spectrograph by a spherical lens. Difficulty was encountered in

Fro. 3. Optimum electrode shape.

APPLIED S P E C T R O S C O P Y 13

mainta ining a suitable are for a sufficiently long time to obtain a complete scan of the wavelength region of interest due to oxidation of the electrodes. A mod- erately successful a t t empt was made to solve this problem by flooding the arc chamber with ni trogen gas.

The intensity measurements were made on a Ja r - rell Ash 3.4-m Mark I I I Eber t spectrograph. The gra t ing employed has 15 000 lines/in. The spect rum was scanned f rom 5900 to 10000 A using an RCA 7102 photomult ipl ier tube which is intended for use in the detection and measurement of red and near-in- f ra red radiation. Because of the low light levels in- volved in operat ing in this region, i t is necessary to mainta in a high signal-to-noise ratio. This is usual ly accomplished by re f r igera t ing the photocell. The cool- ant used was " d r y ice ." The phototube response was recorded on a s t r ipchar t recorder.

Since the system has a different response to sig- nals of the same intensi ty but of different wave- length, it is necessary to calibrate the instrument . This was done by obtaining the response of the sys- tem to a tungsten ribbon-filament lamp whose in- tensi ty as a function of wavelength was calculated by t rea t ing it as a blackbody radia tor of known ef- ficiency. The relative intensities of the various lines emi t ted by the source were then obtained by the relation

Z(X) HNE= (I(X,T~)~A~,/RL~M,) "R~NE, (5)

where R stands for s t r ipchar t reading. The tempera- ture of the lamp TL was measured with an optical pyrometer and corrected to t rue temperature .

III. DISCUSSION OF RESULTS

f values for lines in the wavelength region 6000 to 10 000 A, have been measured pr incipal ly by two groups of investigators. Corliss and Bozman t~ have measured 24 lines with a precision of about 32% and Hill and King ° six lines with a precision of about 50% and three lines to about 25%. (All precisions refer to the 50% confidence level.) The two refer- ences had five lines in common, which af ter normaliza- tion were averaged with weighting according to re- ciprocal o f probable error. Only eight of Hil l and King ' s values were used as compared to 18 of Cor- liss and Bozman 's and five of the eight were weighted approximate ly half as much as Corliss and Bozman ' s measurements. Consequently, i t was fel t tha t our work was not great ly affected by the previously de- scribed systematic error in Hil l and King ' s f values.

In essence our intensi ty measurements on 21 near- in f ra red lines coupled with these measured f values in the l i terature were used to determine the source

- 2

- 5 - - - - -

- - 6

- -7

-- +

\ i

®

• , . ~ 2 POINTS

& 2 POINTS

.... °\o~~P 3 4 5 6 7

E n (eV)

Fie. 4. Graph for determination of temperature of arc. Sym- bols show lower energy level of transition. Q 2.5 eV ~ ~,~ < 3.0 eV; ~ 3.0 eV ~-E~ < 3.5 c-V; [] 3.5 eV ~-E,~; +points not included in least-squares fit.

temperature . F igure 4 shows the t empera ture graph. The slope and intercept and their probable errors were determined by a least-squares fit. The points were weighted according to the following procedure: 2.5 e V ~ E m ~ 3 . 0 eV one weight (seven points) , 3.0 eV~E,~<3.5 eV two weights (five points) , and E,n ~3 .5 eV three weights ( four points) . This weighting was based on the previously mentioned fac t tha t lines with higher values of Em tend to be less af- fected by self-absorption. The tempera ture arr ived at by this procedure was (4893--+190)°K.

Of course, in order to employ the least-squares method, most of the points must be free f rom self- absorption. The data were examined for self-absorp- tion by making the following calculation. The inten- si ty Io tha t each point would represent if i t fell on the " s t r a i g h t l i ne" in the tempera ture plot was

- 2

- 3 3

o

& [ ] [ ] B

8 B ~ & @z~l @ &

®

A A &

5

log I 0

FIG. 5. Graph for examination of data for self-absorption. Symbols show lower energy level of transition. Q 0.94 eV ~-- 2 ~ 1 . 0 3 eV; z~ 2.70 eV-~.E~-~3.07 eV; [] 3.42 e V ~ E ~ --~ 4.37 e ¥ .

14 Volume 20, Number 1, 1966

de te rmined . A p lo t of log I/Io Versus log Io fo r d i f - f e r e n t r anges of lower ene rgy level E , , was made as sugges ted b y the conclus ions d r a w n f r o m the s t u d y of Cowan a n d Dieke. is (See F ig . 5.) I t wi l l be re- cal led f rom F ig . 2 t h a t log I/Io app roaches zero as

log Io app roaches zero. This ind ica tes t h a t fo r smal l Io (i.e., weak l ines) l i t t l e s e l f - abso rp t ion occurs. I n the p lo t for th is e x p e r i m e n t ( F i g . 5) , most of the po in t s fe l l close to the log Io axis, thus i m p l y i n g re la- t ive f r eedom f rom se l f -absorp t ion . This wou ld seem to j u s t i f y the use of the l eas t - squares fit to de ter - mine the exc i t a t ion t e m p e r a t u r e f r o m l ines wi th .E,, -~-2.5 eV and to ind ica t e t h a t the p u r e c h r o m i u m arc is op t i ca l l y th in in the wave leng th r eg ion 6000 to 10 000 £ .

Us ing the t e m p e r a t u r e , j u s t ob ta ined , and i n t e n s i t y measuremen t s , Eq. 4 was used to ca lcu la te r e l a t ive log gf va lues for 63 l ines in the i n t e r v a l 5900 to 10 000 A. (See Table I . ) Twen ty -one of these l ines

were those used to d e t e r m i n e the t e m p e r a t u r e and the o the r 42 lacked a n y p rev ious m e a s u r e m e n t s in the l i t e r a tu re .

The l a rge s t sources of e r ro r in log gf are due to e r ro r s in t e m p e r a t u r e a n d i n t e r c e p t ; thus, the de- t e r m i n a t i o n of an accu ra t e a n d prec ise t e m p e r a t u r e

is i n s t r u m e n t a l in o b t a i n i n g good f va lues b y this method. F i g u r e 6 shows a g r a p h of log gf values in the l i t e r a t u r e (i.e. , those used to de t e rmine the tem- p e r a t u r e ) versus those m e a s u r e d b y the au thors . The a p p r o x i m a t e 45 ° l ine t h r o u g h the po in t s resu l t s whe the r H i l l and K i n g ' s va lues a re l e f t out or not. This p lo t is capab le of i n d i c a t i n g a n y gross e r ro r in the m e a s u r e d or l i t e r a t u r e f values . The slope devia tes m e a s u r a b l y f r o m u n i t y i f an e r roneous t e m p e r a - t u r e is used in c a l c u l a t i n g the f values , and the l ine does no t pass t h r o u g h the o r ig in if an e r roneous i n t e r c e p t is used for the t e m p e r a t u r e g r aph .

I - 4 . . . . . . . . .

F o o

-3 / - - - - 1

- 4 - -

-4 -5 - 2 -I O

LITERATURE Ioq 9'f-VALUES

i~IG. 6. Literature relative log' g/ values versus measured rela- tive ]og gf values for 21 lines used to yield source temperature.

Table I. Relative log gf values for infrared lines of chromium as measured by the author.

~rror in Wavelength Multiplet Literature Measured measured (Angstroms) number log gf log gf log gf 9949.06 226 --0.30 0.31 9900.87 80 -- 1.20 0.30 9734.52 29 -- 1.17 0.28 9730.32 226 --0.39 0.31 9670.48 29 --0.96 0.27 9667.20 29 -- 1.53 0.28 9574.25 29 --0.92 0.31 9571.76 29 --1.72 0.31 9447.00 29 --0.55 0.30 9444.36 29 --1.91 0.3l 9362.06 80 --1.77 0.28 9294.17 29 -- 1.46 0.29 9290.44 29 - 1.01 0.27 9263.97 165 --1.12 0.37 9208.29 165 0.79 0.34 9148.45 165 --1.34 0.32 9035.86 142 --0.66 0.33 9021.69 187 0.14 0.32 9017.10 187 0.33 0.31. 9009.95 187 0.36 0.33 8976.88 142 --0.69 --0.70 0.35 8947.20 142 -0.37 --0.58 0.35 8925.75 142 -- 1.34 0.34 8835.67 142 --1.68 0.37 8636.26 56 --1.94 0.30 8548.83 56 -- 1.58 -- 1.94 0.30 8543.72 56 -- 1.73 0.29 8455.24 56 -- 1.88 -- 1.68 0.28 8450.26 56 -- 1.58 -- 1.48 0.28 8348.28 56 -- 1.40 -- 1.72 0.30 8322.75 298 --0.06 0.33 8290.62 298 --0.18 0.37 8287.38 298 0.15 0.33 8238.29 298 --0.32 0.36 8235.89 298 0.02 0.36 8163.22 298 0.00 0.45 0.33 8084.98 299 -0.21 0.37 7989.36 300 --0.18 0.34 7942.02 300 0.38 0.23 0.33 7910.50 316 1.04 0.38 7908.30 316 0.96 0.39 7462.37 93 0.13 0.22 0.33 7400.23 93 " 0.01 0.10 0.38 7355.94 93 -- 0.05 0.20 0.38 6979.73 222 0.55 0.37 6926.04 222 --0.35 0.41 6925.24 222 --0.36 --0.01 0.37 6924.13 222 --0.17 0.12 0.35 6882.35 222 --0.05 0.25 0.35 6669.257 282 0.14 0.14 0.37 6661.076 282 0.40 0.43 0.34 6643.023 256 --0.40 0.37 6630.015 16 --2.80 --3.16 0.30 6612.17 282 0.21 0.33 6597.556 282 0.05 0.33 6572.90 16 --3.30 --3.34 0.29 6537.921 16 --3.10 --3.30 0.31 6529.197 265 0.08 0.33 6362.874 6 --2.80 --2.73 0.26 6330.101 6 --2.59 --2.50 0.34 6135.759 314 1.30 0.36 6029.28 242 0.3I 0.34 5981.96 185 0.87 0.31

No k n o w n p h y s i c a l p r o p e r t y exp la ins the s ca t t e r

of the po in t s a n d i t is conc luded t h a t i t is r andom . A l l b u t two of these 21 ffwalue m e a s u r e m e n t s agree to w i th in t h e p r o b a b l e e r ro r s wi th those in t h e l i t e ra - ture . As can be seen f r o m Table I the p robab le e r ro r s

in log gff r ange f rom 0.26 to 0.41 a n d ave rage a b o u t 0.33.

APPLIED SPECTROSCOPY 15

In tens i ty measurements in the visible and improved arcs should yield more precise tempera tures and hence more precise f values. Traverses of the arc and the Abel t rans form technique might also be used for this purpose2

IV. CONCLUSION

1. The pure chromium arc in ni trogen at one at- mosphere appears, f rom the data presented, to be optically thin in the near infrared.

2. The tempera ture of this are is approximate ly (4900_+200) °K.

ACKNOWLEDGMENTS

The authors would like to thank Bob McReynolds of the physics depar tment of Southern Missionary College for his work in the construction of the photo- cell cooling appara tus and other hardware, and Pau l Griffin of Oak Ridge National Laboratories for ar- ranging computer reduction of intensi ty data. This work was supported by the National Science Founda- tion.

APPENDIX

Since the work jus t reported has been done, sev- eral a t tempts to improve the exper iment have been made and will now be described. In connection with the effort to obtain a stable, smooth-burning are, which would remain so for the length of time neces- sary to scan the spectrum, fur ther experimentat ion was done with electrodes. Lumps of pure chromium were fused on spectroscopic carbon rods by placing the chromium between the rods and drawing a cur-

-2

~ - 5 . . . .

\ 0 - - - ~

i T= (5600 ± $00)°K

b, : N

iN. .g .1~¢!

I 1¢ o • • •

- 6 - \ 0 ,I 5 4 5 6 7 8 9

E~ (eV)

Fie. 7. Exci tat ion temperature for chromium are in argon at 3 arm.

rent of about 17 A. The chromium melted and on cooling formed a hemisphere on the end of the carbon rod. These electrodes were then placed in a pressure chamber and an arc was struck and operated at approximate ly 3 a tm of argon pressure. These meas- ures resulted in a somewhat improved arc and a scan of the visible spect rum (3500 to 6000 A) was taken using an RCA 7200 photomultiplier . In tens i ty meas- urements were done on 163 lines in this region and a tempera ture graph was constructed using f values measured by Cor l i ss and Bozman. 11 F igure 7 shows this graph. The tempera ture was found to be (5600± 300) °K (about 700°K higher than the are in nitro- gen at 1 arm). Other investigations in the litera- ture 14,1~ indicate tha t the effect of operat ing an are in an inert-gas atmosphere and under increased pres- sure, in both cases, is to raise the temperature .

Also, a much more effective cooling system was designed employing liquid nitrogen as the coolant. The liquid nitrogen is forced by means of gas pres- sure f rom the reservoir through insulated tubing into the copper coils which surround the RCA 7102 tube and out into a dewar flask. This par t icular tube has the p roper ty tha t every six-degree drop in tem- pera ture reduces the dark current by approximate ly a half. Thus, the dark current became almost neg- ligible (of the order of 10 -1~ A) , since the tempera- ture of liquid nitrogen is -196°C as compared to -78°C for " d r y ice ." The visible tube (RCA 7200) was also cooled with liquid nitrogen, but the coolant was forced between concentric copper cylinders which surrounded the tube ra ther than through coils.

Finally, in order to monitor the total light output of the are and thus be able to correct the data for arc flicker, a two-channel recorder was installed with one channel connected to the scanning photocell and the other to an arc-monitor photocell inside the spec- t rograph which received the light reflected f rom a gold thread suspended in the beam of light f rom the entrance slit.

Submitted 23 March 1965

*This paper was presented at the Third National Meeting of the Society for Applied Spectroscopy, 28 September-2 Octo- ber 1964, Clevelsnd, Ohio.

*Present Address: Oak Ridge National Laboratory, Oak Ridge, Tennessee.

1. R. A. Hefferlin, J-. Opt. See. Am. 49, 948 (1959). 2. V. Letfus, J. Opt. Soc. Am. 51, 1151 (1961). 3. R. A. Hefferlin, J. Opt. See. Am. 52, 338 (1962). 4. 1~. A. Hefferlin, B. Cobb, D. Hall, and O. Lehman, Astro-

phys. J. 132, 259 (1960); 133, 354 (1961) (erratum). 5. ~. A. Hefferlin and J. Gearhart, ft. Quant. Speetry. l~adia-

rive Transfer 4, 9 (1964). 6. A. J. Hill and R. B. King, J. Opt. See. Am. 41, 315 (1951).

16 Volume 20, Number 1, 1966

7. C. Charatis and T. D. Wilkerson, Phys. Fluids 5, 1661 (1962).

8. C. W. Allen and A. S. Asaad, Monthly Notices l~oy. Astron. So~. 117, 36 (1957).

9. A. 1~. Sandage and A. J. Hill, Astrophys. J. 118~ 525 (1951).

10. L. Goldberg, E. A. Muller, and ~. I-L Aller~ Astrophys. 3. Suppl. No. 45 (1960).

11. C. I-L Corliss and W. R. ]3ozman, Natl. ~3ur. Stds. (U. S,) Monograph 53 (]963).

12. L. It. Aller~ Astrophysics: The Atmosphere of the Sun and Stars (Ronald Press, New York, 1953), p. 131.

13. I~. D. Cowan and C. tI. Dieko, Revs. Mod. Phys. 20, 418 (1948).

14. O. P. Semenov~ and M. V. Petrov% Transl. No. T-1499 from Izv. Vysshikh Uehebn. Zavedeaii Feijckice 2~ 71 (1961).

15. A. C. Zhiglinskii, A. N. Zaidel, and E. A. Karklinu~ Opt. Spectry. (USSR) 10, 368 (1961).

APPLIED SPECTROSCOPY 17