Spectroscopic flame temperature measurements and their physical significance—V. Experimental determination of relative transition probabilities for 43 Fe I lines in the 3450–3950 Å wavelength region

Spectrochimica Acta,Vol.338, pp.807to 815 PergamonPressLtd.1978.Printed inGreatBritain

Spectroscopic flame temperature measurements and their physical significance-V. Experimental determination of relative transition probabilities for 43 Fe I lines in the 3450-3950 A wavelength region* ISAACREIF,? VELMERA. FASSEL,$RICHARDN. KNISELEYand DENNISJ. KALNICKY Ames Laboratory

and Department

of Chemistry,

Iowa State University,

Ames, IA 50011

(Received 3 December 1976 ; in revised form 13 December 1977)

Abstract-Relative transition probabilities, as measured by the atomic emission spectroscopic technique, have been redetermined for 43 lines of Fe I under experimental conditions that in principle should yield accurate values. The Fe free-atoms are formed in a high temperature environment that has been shown to be isothermal and optically thin under the experimental conditions employed. The temperature of the iron atoms was measured by the reversal method, and the emission measurements were made so that the values obtained were strictly proportional to the line radiances. The high degree of correlation of the values reported with those obtained by the hook method is indicative of the overall reliability of these sets of data.

1.

INTRODUCTION

has been used extensively as a thermometric species for high temperature measurements by spectroscopic techniques because transition probabilities are available for many of its spectral lines, and Fe free-atoms are readily formed in flames, furnaces, and electrical discharges. Although extensive atomic transition probability data are available, there are still disturbing disagreements among the published values. In a previous publication [l] we have shown that a range of about 150 K may be found in flame temperature measurements by the slope method when several well known sets of transition probabilities were used in the calculations. A lack of self-consistency was also shown by the temperatures obtained from two groups of Fe lines when the same set of transition probabilities were employed. The level of disagreement among published values is not unexpected because of the difficulties in fulfilling completely the experimental conditions required for precise measure ments. Because of the need for more accurate values, we have measured relative transition probabilities for 43 Fe lines under experimental conditions that should, in principle, lead to more accurate relative values than many of the measurements in the past. Three important general approaches have been used for measuring transition probabilities of Fe I. Two of these, the hook [2-51 and the total atomic absorption methods [6-81, have been applied to free atoms formed in high t’emperature furnaces. The hook method has also been applied to free-atoms heated in a pressure-driven shock tube [9]. IRON

* Work performed for the U.S. Department of Energy, Basic Energy Science Program, under Contract No. W-7405-eng-82. t On leave from Universidad Central de Venezuela, Caracas. One of the authors (I. R.) acknowledges the financial support of Consejo de De sarrollo Cientifico y Humanistic0 of the Universidad Central de Venezuela. $ Corresponding author. [l] [2]

I. REIF,V. A. FASSEL,and R. N. KNISELEY,Spectrochim.

Actu 31B, 377 (1976). M. S. FRISH, Bull. Crimean Astrophys. Ohs. 31,

V. K. PROKOFIEV,E. I. NIKONOVA, F. P. GROZDEV, and

281 (1964). [3] N. P. PENKIN,J. Quant. Spectrosc. Radiative Transfer 4, 41 (1964). [4] A. K. VALTERSand G. P. STARTSEV,Opt. Spectrosc. 16, 393 (1964) (English translation). [S] F. P. BANFIELDand M. C. E. HUBER, Astrophys. J. 186, 335 (1973). [6] R. B. KING and A. S. KING, Astrophys. J. 87,24 (1938). [7] W. W. CARTER,Phys. Rev. 76,962 (1949). [8] R. B. KING, K. H. OLSEN, and C. H. CORLISS,Astrophys. J. 141, 354 (1965). [9] M. C. E. HUBER and W. H. PARKINSON,Astrophys. J. 172,229 (1972). 807

ISAAC REIF, VELMER A. FASSEL, RICHARD N. KN~SELEYand DENNIS J. KALNICKY

808

Of the two procedures, the hook method is regarded generally as more accurate [lo]. The hook and the atomic absorption procedures, which have utilized furnace production of Fe free-atoms, have been limited to only the strong lines for the hook procedure, and to spectral lines whose absorption transitions are near the ground state for the atomic absorption method. Shock tube heating of Fe I free-atoms extends the application of the hook method to lines with higher excitation energies than those observed with furnace excitation. In emission and lifetime methods [ll-181 a much larger selection of lines may be measured, but the population distribution among the energy levels of the atoms cannot always be specified accurately. In contrast, local thermal equilibrium and an isothermal environment are generally assured when furnace vaporization and excitation are employed and when shock tube heating is employed at sufficiently high electron densities [9]. For accurate relative transition probability measurements by the emission method, it is essential that the following important requirements be met. First, the free atoms should reside in an environment that is in local thermal equilibrium. There is now general agreement that this condition is achieved above the primary reaction zone of high temperature flames burning at itmospheric pressure [19-211. Second, the free atoms observed should reside in an isothermal region. In a recent communication we have demonstrated that the Fe atoms released above the primary reaction zone of N20-C2H2 premixed flames formed on a long path, slot burner exhibit a behavior characteristic of residence in an isothermal zone [22]. Third, the temperature of this zone must be measured accurately; these determinations can be made accurately by the reversal method [23-251. Fourth, integrated line radiances or quantities strictly proportional to these radiances must be measured. This requirement is fulfilled when spectrometer slits are adjusted to produce an instrument function that is significantly larger than the line width [l]. Finally, assurance must be provided that the measured radiances are not affected by self-absorption. This assurance can be obtained by selecting concentration levels that fall within the unit slope of the curves of growth [l]. In this communication we present the result of a redetermination of Fe I relative transition probabilities of 43 lines measured under experimental conditions that satisfy the requirements discussed above to a high degree. 2.

BASIC

EQUATIONS

The radiance emitted by a spectral line under conditions of negligible self-absorption may be expressed by the following equation [26] : [lo]

C. H. CORUSS and B. WARNER, J. Res. NBS 70A (Phys. and Chem.), No. 4,325

(1966).

[ll]

H. M. CROSSWHITE, The Spectrum

Report

of Iron I, Johns

Hopkins

Spectroscopic

No.

13, Baltimore

(1958). [12]

C. H. CORLISS and W. R. BOZMAN, Experimentul Elements, NBS Monograph

Transition

Probabilities

,fiv Spectrcll Lines cd’ Seaem!

53 (1962).

[13]

M. MARC~OSHESand B. F. SCRIBNER,J. Res. NBS 67A (Phys. and Chem.), No. 6,561

[14]

T. ANDERSEN and G. SORENSEN, Astrophys. Letr. 8,39

[15]

J. M. BRIDGES and W. L. WEISE, Astrophgs. J. 161, L71 (1970).

[16]

S. J. WOLNIK, R. 0. BERTHAL, and G. W. WARES, Astrophys. J. 162, 1037 (1970).

[17]

T. GARZ and M. KOCK. Astron. Astrophys. 2,274

(1963).

(1971).

(1969).

1181 J. M. BRIDGES and R. L. KORNBLITH, Astrophys. J. 192, 793 (1974). [19]

T. HOLLANDER, Am. Inst. Aeronaut.

[20]

C. TH. J. ALKEMADE, in Tenth Colloquium

J. 6, 385 (1968). SpecWoscopicum

and M. MARGOSHES, Spartan Books, Washington, [21]

J. 0. RASMUSON. V. A. FASSEL, and R. N. KNISELEY, Spectrochim.

[22]

I. REIF, V. A. FASSEL, and R. N. KNISELEY, Spectrochim.

[23]

W. SNELLEMANand J. A. SMIT,Metrologia

[24]

W. SNELLEMAN.Cornbust.

[25]

W. SNELLEMAN, in Flame

Flume

Emission

DEAN and T. C. RAINS, Marcel [26]

11,453

For a critical review of spectroscopic

by E. R. LIPPINCOT’T

Acta 28B,

365 (1973).

Acta 3OB, 163 (1975).

4, 123 (1968). (1967).

and Atomic

Dekker,

Edited

Internationale,

D.C. (1963).

Absorption

Spectrometry,

Vol. I-Theor),

Edited

by J. A.

New York (1969). flame temperature

V. A. FASSEL, and R. N. KNISEIXY, Spectrochim.

Acra 28B,

measurements, 105 (1973).

the reader is referred to: I. REIF,

Spectroscopic

flame temperature

measurements

Wem)=

and their physical

significance-V

809

& A,, hv, nq 1,

where B(em) is the emitted radiance, A,, is the transition probability, h is Planck’s constant, v, is the frequency of the line, n4 and n, are the number densities of particles in the q level and ground state respectively, gq and go are the statistical weights for these two levels, E, is the excitation energy for the q level, and 1 is the length of the optical path. If the Boltzmann distribution equation is substituted, then B(em) = & Aqphv, p n, emEdk7‘f1, where ge and go are the degeneracies and TJ- is the flame temperature. If accurate values for B(em), T,, 1, and n, could be measured, then the absolute value of the transition probability A,, could be obtained. However, the value of n, in the flame is not known and consequently only relative values can be determined. If equation (2) is applied to two spectral lines and the result rearranged, the following relationship is obtained, , , A 4p _ _no _gq v B’(em) ,-W-EJkTr A 4P n,, gqs v' B(em)

3

where no/no,, is the ratio of the number density of free atoms in the ground state at the two solution concentrations, c, and c,,, which have been found appropriate to yield integrated line radiances, B(em) and B’(em), without appreciable self-absorption. Thus, only values of Tf, n,/nos, and B’(em)/B(em) are needed to obtain relative atomic transition probabilities. As noted previously, accurate flame temperatures can be obtained by means of the reversal technique. Because curves of growth with unit slope have been obtained at all values of the solution concentrations employed, the degree of nebulization and atomization are constants over this concentration range. Thus, the number density of free atoms in the flame is proportional to the solution concentration and the value of no/n,, is given by the ratio of the solution concentrations c,/c,,. The measurement of B’(em)/B(em) requires a spectral response calibration of the spectrometer. If the exit slit used is larger than the entrance slit in the spectrometer, the measured signals or line intensities can be shown (1) to be equal to I g;

= C(v)B(em),

where C(v) =

I meaS (OXN Av 1B:(v,, 7J .

(4)

measis the measured line intensity, 1:::$ is the signal detected when a In this equation, I(,,) calibrated tungsten lamp at a brightness temperature Tb is focused on the spectrometer entrance slit, B~~(v,,~T~)is the spectral radiance of a blackbody source at temperature Tb and frequency v,, Av is the bandpass of the instrument and C(v) is the. spectrometer calibration factor. The ratio of radiances for the two spectral lines can now be written as (5) If these considerations are introduced into equation (3), the following result is obtained for the transition probability ratio

(6)

810

ISAAC R E I F , V E L M E R A .

FASSEL,R I C H A R D

N, KNISELEY and

D E N N I S J. K A L N I C K Y

tr~eq

%

r~

m-

t2.

&

r~

~

-2

f" ~ e,.

~:~ ~t~ ~:~ . . . .

~ .

.

~ r --~-~ ~ o~ oq "z.

.

.

.

.

.

.

¢q

ot~m

Spectroscopic flame temperature measurements and their physical significance-V

8t1

Z ~-~

z~

~z ~

-

~

~

~

~ r~ c~

~

~

~

~

~

~

-

~ .~ r~

r~ c5

u~

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z ~

~

-

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~

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~ ~

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-_

_

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m

W

~ ~ - ~

~ ~

~

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e N

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N~ ~ m m m m m m ~

m m m m m m m

m

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g ~ q i

z

sh[a) 33: 10-t2-~

812

ISAAC

If the expression

is introduced

REIF,VELMERA. FASSEL,RICHARDN. KNISELEYand

for the blackbody

in equation

spectral

radiance,

DENNIS J. KALNICKY

approximated

by Wien’s law,

(5), the final result is

where hv, and hv,,have been substituted by (E, - EP) and (E,, - Eps). Equation used for the calculation of relative transition probabilities.

(6) is

3. EXPERIMENTAL FACILITIES AND PROCEDURES The experimental facilities and operating conditions were the same as those employed in a previous study [22]. The sets of Fe solutions employed were prepared by dissolving pure Fe in HCI followed by dilution to the desired concentration with water. The 43 Fe lines measured possessed sufficient spectral intensity so that the solution concentrations required fell within the operating limits of the nebulizer-burner system. These lines were also free of spectral interferences that might bias the measurements. Curves of growth [l] were determined for each line of interest, the best solution concentration for each one of them was selected, and the spectral line intensities were measured at these concentrations. The spectrometer calibration factors were based on measurements of the spectra of calibrated tungsten strip lamps [ 11. Three independent relative transition probability determinations were performed for Lhree different calibrated tungsten strip lamps and sets of Fe solutions. Each lamp was calibrated [l] several times with the optical pyrometer and an average value was taken. The single determinations for all the lamps did not differ by more than 5 K from the average value. Measurements on the relative intensity of the Fe 373.487 nm line and other lines of interest were alternated to assure accuracy in the transition probability determinations. Because intensity ratios were actually measured, the effect of any fluctuations in the system was minimized. These intensity ratios were measured at least three times and an average value was taken. The reversal temperature determinations were performed on the 371994 nm ground state line. The reversal temperatures did not show any systematic variation with time. within the experimental

error of + 10 K.

4. RESULTS AND DISCUSSION The iron reversal temperatures determined with each of the three lamps were 3084, 3074, and 3077 K. The average values obtained for the relative transition probabilities by means of equation (6) are shown in column 5 of Table 1. The single measurements from the triplicate runs did not deviate by more than 3% from the average value, and most of them differed by 1% or less. For comparative purposes, relative transition probabilities from some recent publications [4,5,9,14-18,27,31] are also shown in Table 1. The uncertainty of the data summarized in Table 1 can be illustrated by calculating the ratio of the relative transition probabilities reported by others to our values. Figure 1 shows these ratios for the data of BRIDGES and KORNBLITH (BK) [18], HUBER and PARKINSON (HP) [9], BANFIELD and HUBER (BH) [5] and CORLISS and TECH (CT) [27]. BRIDGES and KORNBLITH used arc emission measurements. HUBER and PARKINSON used shock-heating in conjunction with the hook method and BANFIELD and HUBER employed high-temperature furnace excitation with the hook method. CORLISS and TECH compiled their transition probabilities from the average of the best data available in the literature at the time their compilation was made. Our values are denoted by RFKK. Since relative transition probability ratios are plotted in Fig. 1, a high correlation between two different sets of transition probabilities will be revealed if a constant value, even though different from one, is obtained for this ratio for a large number of spectral lines. For the CT/RFKK correlation, shown in Fig. lA, only 53:‘; of the ratios fall ratio of 1.6. On the other hand, for the within an arbitrary f 14’>{ of the constant [27] C. M. COHLISSand J. L. TECH, Oscillutor Strengths end Transition NBS Monograph

108 (1968).

Probabilities

,jiw 3288

Lines ot/ Fe 1,

Spectroscopic flame temperature measurements and their physical significance-V

q

I .60 i-

I 60

-

Y

1.40

-

n

1.20

-

350.0

3600

370

0

813

0-i B

3800

390.0

WAVELENGTH (nm)

Fig. 1. Ratios of relative transition probability values reported by CORLISSand TECH (CT), HUBER and BRIDGESand KORNBLITH(BK) to those

and PARKINSON(HP), BANFIELDand HUBER (BH),

measured in this study (RFKK).

BH/RFKK and HP/RFKK and BK/RFKK correlations, shown in Figs. lB, lC, and 1D; 70:/,, 74”/;‘,, and 89% respectively, of the spectral lines fell within + 14% of the respective constant values of 1.05, 1.25 and 1.16. The latter correlations may be viewed as indicative of the overall reliability of the values reported in the present communication and those obtained by HP, BH and BK. Obviously, the best correlations are shown by the BK/RFKK values. 5. EFFECT OF CHOICE OF LINES AND TRANSITION PROBABILITY ON TEMPERATURE VALUES OBTAINED It should be emphasized that even a difference of k 10% in relative transition probability values can lead to significant errors in temperature measurements. For example, if the two-line method is employed with a line pair whose upper energy levels differ by 10,000 cm-’ in a 3000 K temperature source, an error of 100 K may result for f 10% differences in transition probabilities (see Table I in [26]). Larger differences in transition probabilities will naturally result in larger temperature differences. For example, Table 2 shows that temperature differences of as much as 370 K would be obtained by the two-line method if the CT values and those measured in this work were used for the calculations. Because these line pair-transition probability combinations have been previously used or suggested by others [2X, 291 for temperature measurements, the absolute accuracy of the temperatures obtained with these combinations should be viewed with caution. [28] J. D. [29]

WINEFORDNER,C. T. MANSFIELD,and T. J. VICKERS.A&.

Chem. 35, 1611 (1963).

G. F. KIRKBRIGHT,M. SARGENT,and S. VETTER,Spectrochim. Acta

25B, 465 (1970).

814

ISAAC REIF, VELMERA. FASSEL, RICHARD N. KNISELEY and DENNIS J. KALNICKY Table 2. Two-line

temperature

calculations

Temperatures obtained with transition probabilities by This work (K) CT(K)

Line Paris (nm) 373.490~373.7 13 (28) 383.4222389.566 (29) 349.784. 357.010 (29)

2633 2835 3319

3000 3000 3000

The temperature differences between values obtained from different sets of transition probabilities can be significantly reduced when the slope method is employed with spectral emission lines whose transition probabilities are accurately known. Table 3B shows that slope temperature differences of 50 K or less would be obtained for the lo-line sets given in Table 3A if the BK, HP, BP, and RFKK transition probability values were used for the calculations. If, however, the CT values were used, the differences would be as much as 340 K. It is also evident that the differences between the BK, HP, BH, and RFKK slope temperatures are well within the AT error brackets. This is clearly not the case for the CT values. Slope temperatures may, however, show large differences if the lines are chosen rather arbitrarily. For example, Table 4B shows temperatures calculated with the IO-line set given in Table 4A. This set has been proposed previously for flame slope temperature measurements by DEGALAN and WINEFORDNER (DW) [30]. It is evident that large differences in slope temperatures, by as much as 570 K, for the BK and DW comparison, would be obtained if these lines and transition probabilities were used. Comparison with Table 3B also reveals that the AT error bars are about 3-fold greater for the DW slope temperatures of Table 4B than for the BK, HP, and BH values in Table 3B. Slope temperatures and AT brackets obtained with the HP and RFKK relative transition probability data were excluded from Table 4B because of the absence of transition probability data for the Fe 373.332 (for HP) and 374.556 (for RFKK) lines from these compilations. Slope temperature calculated with the eight lines common to the five transition probTable 3A. Data for IO-line sets for slope temperature Relative transition Wavelength (nm) 367.992 370.557 371.994 372.256 373.487 373.713 374.826 374.949 375.824 376.379

Energy levels (cm-‘)

BK/RFKK

27167m 0 27395m 416 268750 27560. 704 33695-6928 27167-m 416 27560 888 34040.-7377 34329-7728 34547 -7986

2000 2200 2400 2600 2800 3000 3200 3400

1980 2180 2370 2570 2760 2960 3150 3350

f f * + f + * +

AT*

HP

15 18 22 25 29 34 38 43

2002 2202 2403 2604 2804 3005 3205 3406

* AT values for the slope temperatures

+ + k + * * f +

1.09 1.04

1.a0 1.05 0.876 0.979 0.962 0.915

1.07

I .0x

1.10 1.19

1.17

ratios CT,‘RFKK 1.55 1.31 1.oo 1.43 1.42 0.916 1.10 1.53 1.75 1.81

comparisons

AT

BH

25 29 35 41 47 54 61 69

2012 2214 2417 2620 2823 3027 3230 3434

are calculated

BH/RFKK

1.22 1.13 1.oo 1.15 0.979 1.00 1.10

1.12 1.06 1.00 1.oo 1.oo 1.oo 1.03 1.05 1.10 1.16

Slope temperatures BK

probability

HP/RFKK

Table 3B. Slope temperature RFKK temperature (K)

comparisons

k k + + + i i f

(K)

AT

CT

26 32 38 44 51 59 67 76

1880, 2055 2228 2400 2570 2737 2903 3066

from one standard

deviation,

AT 48 f 54 + 63 &- 73 + 83 + 95 f 106 + 119 fo.

for the slope of the fit.

Spectroscopic

flame temperature

Table 4A. Emission Wavelength (nm)

371.994 372.256 373.332 373.487 373.713 374.556 374.826 374.949 375.824 376.379

measurements

Relative transition

815

significance-V

line data for Fe I IO-line set suggested

Energy levels (cm-‘)

268750 27560- 704 27666- 888 33695-6928 27167- 416 27395- 704 27560- 888 34040-1317 34329-7728 34547-7986

and their physical

in [30]

probabilities

RFKK

BK

HP

BH

CT

DW*

0.163 0.0505 0.063 0.886 0.143 _____ 0.0904 0.744 0.61 1 0.523

0.163 0.0505 0.0696 0.887 0.143 0.115 0.0927 0.779 0.674 0.608

0.163 0.058 _____ 0.867 0.143 0.108 0.0994 0.798 0.674 0.622

0.163 0.0531 0.0652 0.776 0.140 0.110 0.087 0.681 0.611 0.610

0.163 0.072 0.082 1 1.26 0.131 0.123 0.0998 1.14 I .07 0.948

0.163 0.0262 0.0197 1.40 0.120 0.0745 0.0467 0.956 0.646 0.395

* DECALAN and WINEFORDNER [30] calculated Table 4B. Slope temperature

from the CROSSWHITE data [ 1 I] comparisons

with Fe I IO-line set from [30]

Slope temperatures(K) BH temperature e(K) 2000 2200 2400 2600 2800 3000 3200 3400

BK

AT

CT

AT

1970 2170 2360 2560 2750 2940 3130 3330

If- 16 k 20 k 22 + 26 + 30 f 35 * 41 + 47

1853 2023 2191 2357 2520 2681 2830 2996

DW

It_27 + 32 + 38 k 44 + 50 I56 + 63 + 70

1788 1946 2100 2252 2400 2546 2589 2829

AT f + f + _t + k *

110 130 152 174 198 223 248 275

ability tabulations (excluding the Fe I 373.332 and 374.556 nm lines) are given in Table 5. It is evident that temperatures calculated from this &line subset of Tables 3A and 4A also show large differences, by as much as 450 K, when the values of CT and those chosen by DW are employed. The agreement is much better, with differences less than 37 K when the BK, BH, HP and RFKK (this work) values are employed. The AT error bars are also far smaller for the BH and HP values than those for the CT and DW slope fits. From the above considerations it is clear that spectral emission lines for temperature measurements must be selected carefully to obtain good agreement among several reliable transition probability tabulations and minimal AT’s from the slope fit. (Many other examples of the above types could be cited.) In summary, because the relative transition probabilities reported in Table 1 were measured under experimental conditions that fulfilled all of the experimental requirements to a high degree, the use of carefully chosen subsets of these values in conjunction with other recent tabulations [IS,9,1 S] should lead to increased accuracy of sptctroscopic temperatures measured by the slope or two-line methods. Table 5. R-Line slope temperature RFKK temperature (K) 2000 2200 2400 2600 2800 3000 3200 3400 [30]

comparisons

Slope temperatures(K) BK 1970 2170 2360 2550 2740 2940 3130 3320

AT + 14 & 17 _I 21 + 24 k 28 k 32 f 36 + 41

HP 1987 2184 2381 2578 2775 2971 3167 3363

AT f + + + + k + +

25 30 35 41 48 55 63 71

BH

AT

2002 f 32 2202 + 38 2403 + 47 2603 F 54 2804 & 62 3004+71 3205 ) 81 3405 ) 92

L. DEGALAN and J. D. WINEFORDNER, J. Qume. Spectrosc.

CT

AT

1848 + 41 2017& 49 2184k 57 2348 + 66 251Ok 76 2670 + 85 2827 + 96 2982 k 107

Rudica. Trtrnsfer 7, 703 (1967).

DW

AT

1836k 2003 + 2168 + 2329 + 2489 f 2645 k 2800 + 2952 f

99 118 138 160 182 206 22 I 257