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Comparison of theoretical and experimental atomic fluorescence analytical curves for magnesium
Spectrcchimica Acts, Vol. MB, pp. 161 to 175.
Pergamon Press1971.Printed inNorthern Ireland
Comparison of theoretical and experimental atomic fluorescence analytical curves for magnesium* P. Fysisch Laboratorium,
J. TH. ZF,EGERS
Rijksuniversiteit,
Utrecht,
The Netherlands
and J. D. WINEFORDNER Department of Chemistry, University of Florida, Gainesville, Florida 32601,U.S.A. (Received
1 June 1970)
Abstract-Atomic resonance fluorescence emission was measured as a function of atomic concentration in a flame having known geometrical conditions so that measured curves could be compared to theoretical curves. The measurements were carried out at a single resonance line (Mg 2852 A) with a continuum source as well as with a narrow line source. The parameters necessary to calculate the theoretical fluorescence curves, ie., the line damping parameter, the fluorescence yield factor and the metal concentration in the flame were determined in absolute units by independent, methods. Excellent agreement between calculated and experimental fluorescence curves was found.
EXPERIMENTAL
ANALYTICAL
CURVES IN ATOMIC FLUORESCENCE FLAME SPECTROSCOPY
Introduction ATOMIC fluorescence
flame spectroscopy was introduced in 1964 [l] as an analytical method; since then it has been used for the measurement of a number of metals. Atomic fluorescence flame spectrometry is carried out with either line (hollow cathode lamps, electrodeless discharge tubes) or continuum (xenon arc) background light sources of excitation. For a great number of elements, experimental analytical curves have been measured. Several reviews [2-4] of atomic fluorescence flame spectrometry have been written, and the reader is referred to them for a discussion of previous analytical studies. WINEFORDNER and coworkers [l, 51 have made the first attempt to describe theoretically the shapes of analytical curves. Their theoretical results did not give the correct shape of analytical curves at high metal concentrations, where the fluorescence intensity may be weakened by self-absorption. HOOYMAYERS [S, 71 has given a general explicit expression for the integrated resonance fluorescence intensity as a function of atomic concentration under idealized geometrical conditions. From this expression, curves of growth have been calculated for a number of different values of the line-damping parameter, a, in the limiting cases of a very narrow line * This work was supported by AFOSR(SRC)-OAR
U.S.A.F.
Grant No.Af-AFOSR-69-1685.
[I] J. D. WINEFORDNER and T. J. VICKERS, Anal. Chem. 36, 161 (1964). [2] J. D. WINEFORDNER, V. SVOBODA and L. J. CLINT, Critical Review8 And.
Chem. 1,233 (1970). [3] R. M. DA~NALL and T. S. WEST, A&. Opt. ‘7,1287 (1968). [4] J. D. WINEFORDNER and J. M. USFIELD, Appl. Spectry. Rev. 1, 1 (1967). [5] J. D. WINEFORDNER, M. L. PARSONS, J. M. MANSFIELD and W. J. MCCARTHY, S~ectrochim. Acta 23B, 37 (1967). [6] H. P. HOOYXAXXRS, Ph.D. Thesis, University of Utrecht, Utrecht, The Netherlands [7] H. P. HOOYMAYERS, S~ctrochim. Acta 23B, 567 (1968). 161
(1966).
162
P. J. TH.
ZEEGERSand J. D. WINEFORDNER
source and a continuum source, respectively [7, 81. ALKE~C~ADE [9] has derived qualitatively the shape of analytical fluorescence curves from the curve of growth theory for the limiting cases mentioned and under idealized conditions. From his treatment, he was able to derive exact formulas for the initial and final a,symptotes in terms of the “integral absorption” of a spectral line. No comparison has been made thus far between theory and experiment because fluorescence measurements are usually performed under ill-defined geometrical conditions for the flame shape as well as the optical system. Furthermore, the halfwidth of the background line source does not always meet the requirements set by HOOYMAYERS’ theory [7]. In the present study, the fluorescence curve of growth of Mg at 2852 A was measured under known geometrical conditions which correspond to those assumed in HOOYMAYERS’ theory [7]. In order to calculate the fluorescence curve with a continuum light source, the values of the relevant parameters in absolute units, e.g., radiant fluorescence flux, metal content, the a-parameter and the fluorescence yield factor, were determined. However, only relative measurements with a line source were carried out because of the lack of information concerning the spectral profile and the radiance of the Mg 2852 A resonance line. From the agreement found between calculated and measured curves, it can be concluded that HOOYMAYERS’ theory of fluorescence curves is correct. In addition, measurements were made of fluorescence with a line source for an absorbing layer between source and flame volume called innerfrom which fluorescence emission was radiated (effect of preabsorption; filter effect in fluorimetry) as well as with an absorbing layer between this flame volume and the detector (effect of selfabsorption). Only one element-Mg-was investigated because of the extensive time required to perform the measurements and to analyze the results. The element Mg was chosen because it represented an element thoroughly studied in flames, and so a comparison with previous experimental values of the a-parameter, the quantum yield, and the ratio of peak absorption coefficient to the absorption coefficient for pure DOPPLER broadening could be made. There are no reasons why the approach used is not valid for other elements in various flames.
Theory A square-shaped flame is irradiated by a parallel homogeneous light beam with rectangular cross-section, S = 1-H. This beam intersects the flame axis at right angles (see Fig. 1). The coloured central flame is surrounded by a metal-free mantle flame having the same flame gas composihion in order to guarantee a uniform temperature distribution inside the inner flame. The concentration of metal atoms in the ground state, n, is assumed to be constant at all points in the volume of interest of the coloured flame (I-.L*H or X.L). The fluorescence radiation is observed in a small solid angle, U, in the direction perpendicular to both the irradiating light beam and the flame axis. Hooymayers has presented an exact formula for the observed radiant flux, @‘p (erg set-l), of the fluorescence light emitted from the volume element l-&H in the case [8] P. J. TH. ZEEGERS, R. SMITH, and J. D. WINEFORDKER, Anal. [9] C. TH. J. ALXENADE, Talk given at Atomic Absorption Syrup.,
Chews. 40(13), 26A (1968). Sheffield, England (1969).
Theoretical
and experimcnt,al
atomic
fluorescence AL
L
analytical
curves
for magnesium
163
.
Fig. 1. Cross-sectional ares of the flame of the irradiating light beam B, and of the fluorescence light beam, Or, as seen from above. The colored central flame is indicated. The cross-section of the irradiating light beam and of the fluoresence light beam are determined by the lamp optics and the entrance optics of the monochromator, respectively.
AL = 0 and Al = 0 (see Fig. 1). His formula holds, if re-emission of self-absorbed For the case AL # 0 and Al # 0 the fluorescence radiation may be disregarded. following general relation, which holds for a continuum background as well as for a line source, can be easily derived from HOOYMAYERS’ formula: a& [{I -
- 11 - e=p C-~M~Ll)l dy x
s0
exp [-k(y)(L
a@ - =p -
(1
+
[--lc(~‘)V -
exp
+
AL)11 411
[--k(~Wl)l dy’. (1)
Here B, is the spectral irradiance (i.e., energy per set per cm2 flame area per A) of the source radiation at the front surface of the flame; y is the dimensionless wavelength difference for the absorption process for exciting light, i.e., 2(a - A,)(ln 2)lf2/Ail,, in which 1, stands for the central wavelength of the spectral line observed in the flame (y’ is a similar factor for self-absorption of fluorescence within the illuminated region) and AAD stands for its Doppler half intensity width; Y is the yield factor of fluorescence, defined as the fraction of absorbed energy, that is reemitted as fluorescence radiation; k, (cm-l) is the maximum value of the absorption coefficient, k(y), when only Doppler broadening is present and is related to n according to: Ic = 2(77 In 2)1/2e2&2nf 0
mc2A&,
in whichf is the absorption oscillator strength, c is the velocity of light in vacua, and e and m are electronic charge and mass, respectively. For the limiting case of a continuum light source, we may assume that its spectral
104
P. J. TH. ZEEGERS and J. D. WINEIFORDNER
radiance is independent of wavelength, i.e., B, = B,, and so equation simplified by solving for the dimensionless ratio Po: @R
Fc = ( and substituting
E
)
h’YB,,AI&‘:‘(
G(x) for integrals of the type
Pa =
(
-& 0
>
(1) can be
[G(L + AL) -
s
In 2)-li2 ,{I
-
exp
(3)
F-k(~)41 dy:
G(AL)][G(Z + AZ) -
G(AZ)].
(4)
For a narrow line source, equation (1) can also be simplified by solving for the dimensionless ratio FL @‘p
FL =
m B, dy
SY2( In 2)426& Substituting FL =
G(x) for the appropriate k2
integrals, equation
exp ( -k(lo)AL))P
-
(5)
s0
(1) reduces to :
exp ( -k(~o)L)liG(~
+ A4 -
G(W)
(6)
where k(l,) represents the absorption coefficient at the central wavelength of the background emission line, which is assumed to coincide with the central wavelength m B, dy (in Eq. (5)) equals mBudl, of the absorption line. The term ALD(ln 2)-li2 s0 f0 which is the integrated spectral radiance of the homogeneous exciting light beam. The numerical value of the integral, G, has been tabulated in the literature [lo,1 I] as a function of [nf( In 2)1’2]/[nAi1D] and of the u-parameter, defined as (In 2)1fsA1L/AlD, in which AilL is the Lorentz half width of the absorption line. ALKEMADE [9] using the curve of growth theory described the variation of G(x)[G(x) is the parameter G defined above as a function of the length parameter x] and thus PC and FL as a function of nL for different cases as to AL and AZ. In this paper, only the behaviour of PC and FL at low and high values of nL will be considered. According to HINNOV and KOHN [12]G(x) may be approximated by: G(x) = kox(v)1/2/2,
if
nx --f 0
and by G(x) = [kOax(n)1’2]1/2, if
(7)
nx -+ 03.
(8) Of course, k. is linearly dependent on n, and also on solution concentration over an appreciable range for most atoms. With these approximations, the corresponding equations for Fc and FL can be evaluated and are given in the following section. For a continuum source of excitation and for an atomic vapor at low optical density, i.e., nl + 0 and nL -+ 0, PC is given by: Fc = k,L/2
(9) [lo] P. A. JANSSON and C. L. KOLB, J. Quant. Spectry. Radiative Transfer 8, 1399 (1968). [ll] C. VAN TRIGT,TJ. HOLLANDER and C. TH. J. ALKEMADE, J. Qumt. Spectry. Radiative Transfer 5, 813 (1965). [12]
E. HINNOV and H. KOHN, J. Opt.Soc. Amer. 47, 151, 156 (1957).
Theoretical
and experimental
atomic
and for high optical density, i.e.,
Fa
=
-%tqnp2
fluorescence analytical
165
nl-+ 00 and nL + co, Fc is given by:
[(L + AL) l’s -
if AL = Al = 0, then equation
curves for magnesium
(AL)1’2][Z + AZ)1’2 -
(AZ)1’2]
(10)
(10) reduces to: F
c
=
za
04 I” id
(11)
.
For a narrow line source of excitation, several additional approximations must be made to simplify the final expressions, i.e., low optical densities for absorption (nL -+ 0) : exp [ -k(l,)L] = 1 - k(l,)L, (12) and for high optical densities for absorption 1 Using the approximations is given by:
(nl --+ co):
exp [--k(&)L]
= 1.
(13)
given in equations (7) and (In), FL for the low density case FI, = k(l,)L/2
and using the approximations density case is given by:
(14)
given in equations (8) and (13), FL for the high optical
FL = exp [--b(i.,)AL]a’,Z[k,l(n)1,2]-1/2[(1
+Tr”-
(+yl.
(15)
Experimental
A premixed laminar acetylene-air flame was burned on a Meker-type burner. The square-shaped inner flame was shielded from the surroundings by an outer flame of the same shape, the same composition and the same flame gas velocity. The properties of this flame have been thoroughly studied and are reported elsewhere [13]. Before entering the flame, the pressurized air stream was introduced into a nebulizer for spraying the test solutions into the central part of the flame, as usual. The linearity of the nebulizer was checked by measuring Ca-band emission as a function of solution concentration in absence of ionization [14]. Non-linearity of the nebulizer only occurred if solutions with a concentration higher than 5000 ppm were atomized. All measurements were corrected for this non-linearity. In Fig. 2, a block diagram is given of the optical system which was used for making emission and duplication measurements. This optical fluorescence, absorption, setup and the detection device used were the same as the one described by PEARCE, DE GALAN and WINEFORDNER [15] except for the application of parallel light beams. (The divergence of the light beam from the source was less than 1 degree.) For fluorescence measurements with a continuum light source (xenon arc, XBO 900 [13] P. J. Ta;. ZEEUERS and C. TH. J. ALKFXADE, Comb. Plame 5, 247 (1965). 1141TJ. HOLLANDER, Ph.D. Thesis, University of Utrecht, Utrecht, The Netherlands (1964). [15] S. J. PEARCE, L. DE GALAN and J. D. WINEFORDNER, Spectrochim. Acta 23B, 793 (1968).
P. J.
166
TH. ZEEaEns and J. D. S
ABSORPTION
,
’
-
7
FLUORESCENCE
-
/
LI D,
/ /
WINEFORDNER
A
1
D_
ENTRANCE AorB
OPTICS
I I
A
4 FLAME EMISSION .
.
DUPLICATION
. MON
B!a=x=drnB FLAME
DET
La 4
Fig. 2. Experimental set-up for fluorescence, emission, absorption and duplication S is a light source (xenon arc or electrodeless discharge tube); measurements. L,, L, and L, are lenses; 4, D, and D3 are diaphragms; Ch is a mechanical light chopper; M is a plane mirror; MON is a monochromator; DET is a detector device, consisting of a photo-multiplier, a preamplifier, a 300 Hz lock-in amplifier and a recorder. Emission and duplication measurements were performed with the entrance otpics in arrangement A (flame imaged on monochromator), with a mechanical light chopper just in front of the entrance slit of the monochromator (not indicated in the figure). For the absorption measurements, the source optics, S, L,, D,, D, and Ch, were rotated by 90’ as indicated by the dotted arrow, and M and L, were removed and the entrance optics of the monochromator placed in arrangement B (lens L, at focal length of monochromator). Fluorescence measurements were carried out with the entrance optics either in arrangement A or in arrangement B. In arrangement A, only light from a small part of the flame was detected; in arrangement B, flourescence from a large part was detected.
WIP,
Osram, Berlin, Germany),
only the optical arrangement indicated by position a line source (electrodeless discharge tube, manufactured in the Division of Analytical Chemistry, University of Florida) both arrangements A and B were used. In fluorescence measurements, a light chopper was placed between light source and flame. After rotating the whole optical arrangement between light source and flame over 90” (indicated by the dotted arrow), absorption measurements were made. By focussing the flame on the monochromator slit (position A) and placing a chopper just in front of the monochromator slit, emission curves of growth (analytical curves) and duplication curves could be measured in the usual way (see e.g. HOLLANDER [ll,141). It should be admitted that our set-up for fluorescence measurements does not give the highest possible fluorescence signal with a given lamp and metal concentration in the flame. Therefore, it is not the best arrangement for analytical flame fluorescence spectrometry. Our optical arrangement especially arrangement B, was chosen for theoretical reasons, i.e., in this way, we approached the situation described in Fig. 1 as closely as possible.
B was used; for fluorescence measurements with
Theoretical
and experimental
atomic
fluorescence
analytical
curves
for magnesium
167
EXPERIMENTALPARAMETERS Absolute radiance calibration of the detection device at 2852 A was carried out by measuring the radiation power from a calibrated tungsten strip lamp at a fixed monochromator slit width and slit height. Table Flame
Mg
1. Experimental
parameters
[ 161
1.8 f 0.05 l/min 16.2 f 0.1 l/min 2410 * 10 K k, = (1.07 + 0.05) x 10ea cm-l lppmn = (5.1 f 0.3) 1013 cm3 mol-l k(A,) = (7.0 + 0.4) x lop3 cm-l lppmk(l,)/k, = 0.65 & 0.02 (measured) k,/k, = 0.67 (calculated) a = 0.41 f 0.01 CP, Air T
Y = 0.10 f 0.01 Xenon arc Monochromator
B, (2852 A) = (8.3 & 0.2) x lo* erg set sr-1 cm-2 A-1 Slit area = 1.10 f 0.03 mma Spectral bandwidth = 6.4 + 0.1 A
The slit area was measured by photographing the image of the entrance slit, produced by means of lens L, (see Fig. 2) at the place of the flame. The entrance slit was illuminated from inside the monochromator by placing a light source just behind the exit slit. The slit area used in the fluorescence experiments was found to be l-10 * O-03 mm2. This value agreed with the one that could be calculated directly from the micrometer scale on the slit mechanism. The spectral bandwidth of the monochromator was measured by slowly scanning the emission line of a Mg electrodeless discharge tube. Results from the half-intensity width of the peak trace and from the ratio of line area and peak intensity agreed within 2 per cent,. The spectral bandwidth was found to be 6.4 f O-1 A. Relevant solid angles were calculated as the ratio of the effective area of the imaging lens and the square of the distance from this lens to the light source. From the above results, the spectral radiance (at 2852 A) of the area of the xenon arc used for illuminating the flame was calculated to be (8.3 f 0.2) x lo4 erg set-l sr-1 cm_2 A-1. This value is about a factor of ten lower than the value reported by PRUGGER [1’7]. However, our value refers to the central part of the discharge, whereas in PRUGGER’S measurements, no specific part of the discharge was specified. Therefore, it is possible, that PRUGGER’S value holds for the brightest spot (near the cathode). Cross-sections of light beams were determined photographically. Measured values of these parameters are inserted in the appropriate graphs. The conversion factor of solution concentration (in ppm) into absolute atomic Mg concentration in the flame (i.e., k,l which is linearly dependent on YZ; see Theory) was determined in three independent ways: (i) Curve of growth method [ll, 12, 141: a comparison of the shapes of experimental and calculated emission curves yields a rough value for k,Z and for the a-parameter. [16] p. J. TH. ZEEUERS,W. P.TOWNSEND 243 (1969).
[IT] H. PRUGGER, Spectrochim.
Acta
and J. D. WINEFORDNER,
24B, 197 (1969).
Spectrochim..Acta
24B,
168
P. J. TH. ZEEGERS and J. D. WINEFORDNER
However a more reliable value of the conversion factor may be found from the intersection point (linear) and high density (square root) asymptote in a double-logarithmic plot if the a-parameter is known. The theoretical k,l value at the intersection point can be calculated from equations (7) and (S), (k,Z), = 2-257a. Using the value for the u-parameter found sub (ii) k,l is O-017& 0.002for 1 ppm Mg. (ii) The combinatory method developed by van Trigt e6 al. [l l] : graphical combination of emission curves of growth and duplication curves yields the conversion factor as in this case, the values were: a = O-41$: O-01 well as a value for the a-parameter; and k,Z = O-0161& 0.0003for 1 ppm Mg. (iii) The integrated absorption method [18,191:applied in the range of low absorptions “1 - exp [-k(y)21 dy M k,l: these measurements were carried out with a s narrow slit ythe spectral band width being 0.36A) ; in this case, k,l = O-015f O-001 for 1 ppm Mg. From the average of these results, the value of k,, when spraying a 1 ppm Mg solution into our C,H,-air flame, appeared to be equal to (1.07-j= 0.05)x 10e2cm-l; I was taken as 1.5 cm in these experiments. According to de GALAN et al. [19], k(A,) may be determined from: i.e., where
W,) =
kc(+)(2)(f)(&p
(16)
in which s is the monochromator spectral band in A, uL and ao stand for the fraction of the radiation absorbed in the case of a narrow line source and a continuum source, respectively, when measured with the same low metal concentration. Using the Mg electrodeless discharge, the ratio aL/ac was measured to be 10.9f O-5 and s was found to be 0.36& 0.1i%in these experiments. The other factors in equation (16) being known, k(l,) was calculated to be (7-Of O-4)x 10e3cm-l. It should be pointed out that k(A,) is not necessarily “the peak absorption coefficient”, k,. For example, if the wavelength shift of the peak of the absorption line in the flame is large compared to the width of the background emission line and if the latter line shows no shift, the measured absorption coefficient k(l,) is smaller than the peak absorption coefficient, k,. Collisional broadening of the absorption line in the flame can cause a shift in the absorption line with respect to the background emission line. However, in our experiments with Mg, the measured ratio k(il,)/k,, being 0.65 f 0.04 (see Table l), is almost exactly equal to the theoretical ratio 0.67 [19,20] calculated for a = 0.41,assuming a Voigt profile of the absorption coefficient k(l), Therefore, the measured value of k(&) should hold for the peak absorption coefficient. k,, within close limits. This result may be understood in the following way. The emission line width, Aax, of a Mg electrodeless discharge tube (gas pressure is about 1 mm Hg and the gas temperature is about SOO’K) may be estimated to be 1O-2 A. Because of the low pressure, collisional broadening is expected to be negligible, and so there should be [18] L. DE GALAN and J. D. WINEFORDNER, J. Quunt. Spectry. Radiative Transfer 7,251 (1967). 1191 L. DE GALAN, W. W. MCGEE and J. D. WINEFORDNER, Anal. Chim. Acta 37,436(1967). [20] C. YOUNG, Tables for cakulating the Voight ProjZe, University of Michigan, ORA(1965).
Theoretical
and experimental
atomic fluorescence analytical
curves for magnesium
169
no wavelength shift. When decreasing the output power of the microwave generator, the absorption coefficient did not change noticeably. Therefore, the emission line width is not affected by self-absorption and is determined by Doppler-broadening only. The ratio of collisional line width, A&, to shift, A&, of a spectral line equals about 4 [21,22-j. From the measured value of the u-parameter, 0.41,and the calculated value of AL,, 2.05 x 1O-28, Ale is calculated to be about 1O-2A. In conclusion, A& may be estimated to be 2.5 x 1O-3A, which is only about $ of the emission line width ALE, of the Hg electrodeless discharge tube used. If such a small shift does occur, then it is indeed not to be expected that k(l,) differs much from k,. Furthermore, the agreement between the measured ratio k(l,)/E, and the theoretical vaIue implies that the emission line width is indeed small compared to the absorption line width. Therefore, the condition of a narrow line source is fulfilled in our case of Mg fluorescence with a Mg electrodeless discharge tube as background light source. As pointed out earlier, this condition has to be fulfilled to apply equation (6). DE GALAN et al. [ 191have found for Mg (2852A) in a similar flame the ratio 7c(I,,)/&, to be 0.7.This value agrees well with ours. They have estimated from their k(L,)/k,value and an assumed value for the ratio of the widths of lamp emission and flame absorption line, the a-parameter to be 0.1,with an accuracy of about a factor two. Their value of the a-parameter is certainly wrong. Very probably their assumptions concerning the line width of the emission line are not correct. With the present knowledge of the width of the emission lines from electrodeless discharge tubes and from hollow cathode lamps, this method to determine the a-parameter is inferior to methods based on curve of growth measurements, for a-parameters smaller than 2. It is well-known that the curve of growth alone yields inaccurate a-parameter values, for a-parameters larger than l-5. Therefore, both methods have their own supplementary a-parameter range, in which they may give reliable results. It should be mentioned that DE GALAN’S method, based on the measurement of k(&), also gives wrong results if the absorption and the emission line show different collisional line shifts. For a monochromator as a wavelength selector, PEARCE et al. [15]have shown that the fluorescence yield factor, Y, may be determined from : (17) where iF is the scale deflection in the fluorescence measurements, Aia is the difference in scale deflection recorded in the absorption measurements, Q, is the solid angle of radiation incident on the flame which is determined by position and aperture of lens L, (see Fig. 2),W, is the width in the flame over which fluorescence is measured, and WA is the width of the irradiating light beam. In this measurement, the light source was focused at the center of the flame. Equation (17)holds only if the fluorescence and absorption measurements are carried out with the same setting of monochromator slit width and slit height. Furthermore, in the absorption and in the fluorescence measurements, lens L, should limit the aperture of the entrance optics [al] C. SMITH, Proc. Roy. S’oc. A296, 288 (1967). [22] A. HINDNARSH, D. PETFORD and G. SMITH, Proc. Roy. Sot. &W, 3
296 (1967).
P. J. TE. ZEEGERSand J. D.
170
WINEFORDNER
and the solid angle of the radiation beam incident on the monochromator slit should be larger than the solid angle of the monochromator itself. It is well-known [S, 231 that measurements of Y may be affected by self-absorption. To eliminate this effect, Y was measured as a function of concentration. The true value of Y is then found from a linear extrapolation to zero concentration [23]. The results, presented in Fig. 3, indicate Y = O-10 & 0.01. Values of the most important experimental parameters are summarized in Table 1.
I
I
I
I
50
100
150
200 wm ccKt4g
-
Fig. 3. Measured apparent fluorescence yield factor, Y, as a function of Mg concentration. RESULTS AND DISCUSSION
Pluorescence
curves witha continuum source
Fluorescence curves obtained with a continuum source calculated and measured in absolute units are presented in Fig. 4. The shape of the measured curve and the position of the experimental points along the k&axis agree with theory (see equations (4), (9), and (10)). The measured Po values are 25 per cent lower than the calculated value. In view of the possible systematic errors in the geometrical factors (each $10 per cent), in B, (55 per cent), and in Y (410 per cent), a discrepancy of 25 per cent is reasonable. HOOYMAYERS [7] has proposed to use continuum fluorescence curves for the determination of the a-parameter. This can be done by graphical determination of the intersection point of the low and the high density asymptote in Fig. 4. Combining equations (9) and (10) one gets :
%4)I =
[(L + AE)1’2 - (AL)1’2][(Z + AZ)r’z - (AZ)l’“]
(18)
in which the subscript “I” refers to the intersection point. If (k,Z), is known in absolute measure then the a-parameter may be calculated. However, the experimental curve in Fig. 4 shows from the first point a sublinear behavior. In our experiment, [23] H. P. HOOYMAYERS and P, L. LIJNSE,J. Quant. Spectq.
Radiative
Transfer
9, 995 (1969).
Theoretical
and experimental
atomic
fluorescence analytical
curves for magnesium
17 1
Fig. 4. Fluorescence curves of Mg (I, = 2852 A) measured with and calculated for a continuum light source. The part of the flame from which fluorescence was measured is indicated in the inserted figure. The relevant dimensions are given in mm. This figure presents only the colored central flame, ie., that part of the flame, where Mg atoms were present. Solid lines present the asymptotes of the calculated curve. Dashed lines present the asymptotes of the measured curve.
the signal-to-noise ratio was too poor to define the low density asymptote. The signal-to-noise ratio can be improved by using a flame with less background emission and/or by using a light source with higher intensity. However, in our case, the position of the low density asymptote can only be found by a trial and error method. According to ALKEMADE [9] the incipient deviation of the curve from its initial asymptote can be found in a first order approximation by expanding G(x) (see equa,tion (4) in a series for small values of k,Z:
(19) where k(y) -j-W) which is proportional to k,. in first order approximation
dz///Q/)
dy,
(20)
Using this series expansion, 3’0 (see equation (4)) is given by
++L+1+2AL+2Al)+....
+6(F,)]. 1=fg,I (21)
The relative deviation from linearity, s(Fo), (which is different for different values, is thus approximately (see equations (21) and (9)) given by: 6(F,)
= -4
with S(P0) equal to [(kOZ)asg-
k(y) (L + I + 2AL + 2AZ)
(k,Z),,,]/(k,Z),,,
(here the subscript “asy”
F,(22)
and “exp”
172
I?. J. TH. ZEEGERSand J. D. WINEFORDNER
refer to the asymptotic and the experimental curve, respectively). proportional to k,, equation (22) may be rewritten as: &PC) = --x(&AXC,
Because k(y) is
(23)
with z a proportionality constant that is independent of k,. The asymptote to be found is that straight line with slope equal to 1 having a position along the log (h$)axis such that the incipient deviations from this straight line by the experimental curve fulfills the requirements stated in equation (23). In the usual case that the aparameter is unknown, this line can only be found by trial and error. In our case, z was determined from the calculated curve. The asymptote thus found, is inserted in Fig. 4, together with the calculated (i&Z),,, values. In our case, the first order approximation is sufficient to correct the first three points. Using this procedure, the intersection point of the asymptotes of the experimental curve yields a = 0.42 while the theoretical curve yields a = 0.41. It should be noted that it is difficult to find a consistent value for z if only the experimental curve is available because the experimental error in PC may be of the same order of magnitude as the relative deviation 6(P,). Because of this uncertainty it is expected that an a-parameter determination based on fluorescence measurements will have relative errors equal to or greater than 10 per cent. Therefore, we feel that this method of a-parameter determination cannot compete with other methods such as methods based on emission curves of yrowth and duplication curves. If the a-parameter is known, fluorescence measurements with a continuum source at high metal concentrations for which the asymptote value of -E”ohas been reached may be used for the determination of Y, as has been suggested by HOOYMAYER [7]. The value of Y follows directly from the ratio of the meter deflection corresponding to the re-emitted radiation for high metal concentration and the meter deflection attained when the monochromator is illuminated directly by the continuum light source. These meter deflections have to be measured under identical experimental conditions or, as we did, one has to know all geometrical factors involved. This method yields Y equal to O-08 & 0.02 (see Figs. 4), which is less accurate than the value of Y found earlier, being 0.10 + 0.01 (see Fig. 3). This lower accuracy is mainly caused by the rather unusual geometrical conditions chosen. More favourable conditions may be chosen (i.e., complete illumination of the flame) to produce a higher accuracy. The major advantage of the above method for the determination of Y in contrast to the method used to obtain Fig. 3 is the independence of Y on the metal concentration as long as this concentration is high enough that a point on the high optical density asymptote is measured. However, the accuracy of the measured value decreases with increasing metal concentration as a result of a decrease in the signalto-noise ratio. The signal remains constant, but the noise increases, because the thermal emission increases with metal concentrations. Fluorescence
with a line source
Fluorescence emission of Mg at 2852 A with a Mg electrodeless discharge tube (line source) was only measured in a relative way. The fluorescence emission was measured in two different parts of the illuminated flame volume. In Fig. 5, the
and experimental
atomic
fluorescence analytical
curves for magnesium
10
17 3
100
k, I
------*
Fig. 5. Fluorescence curves of Mg (1 = 2852 A) measured with and calculated for a narrow line source. The part of the flame from which the fluorescence was measured is indicated in the inserted figure. The relevant dimensions are given in mm. For all curves, AZ equals 9.5 mm except for one; this latter curve is indicated by AL = 0 and Al = 0.
results for the case L = O-5 mm and AL = 3 mm are given; these measurements were carried out with the optical arrangement indicated as position A in Fig. 2. In Fig. 6, the results for the case L = 10 mm and AL = 1 mm are given; these results were obtained when the flame was focussed on the entrance slit of the monochromator, i.e., position B in Fig. 2. In both figures, the experimental points are inserted in such a way that t,hey are fitted as well as possible to the calculated curve with AL equal 1
LINE
LIGHT
SOURCE
I
I
I
1
-,/ _ /
.
i
I Id
1 __t
k,l
100
Fig. 6. This figure presents the same type of measurements as Fig. 5. Only in t,his case the ratio AL/L, being 0.1, is quite different from the situation in Fig. 5, where AL/L was equal to 6.
174
P. J. TH. ZEEGERSand J. D. ~VINEFORDNER
; for these conditions, the experimental points agree well with the theoretical curve. Of course, the experimental points were fitted by a shift along the y-axis only because the absolute values of the x-axis values are known. For these experiments, the same solution concentrations were used as in the experiments with the continuum source. The l-value in both experiments wa,s different, being 6.9 and 5 mm for the cont.inuum and the line source, respectively Therefore, the k,lvalues corresponding to the same solution concentration differ by a factor 1.4 in both experiments (compare Fig. 4 to Figs. 5 and 6). 3 and 1 mm, respectively
Preabsorption
and self-absorption
eSfect
Line light sozcrce. In Figs. 5 and 6, calculated curves corresponding to AL-values equal to 0, 0.5, 1, 3, and 5 mm, respectively are also included. These curves indicate very clearly the preabsorption effect, i.e., the influence upon a fluorescence curve of an absorbing layer (AL # 0) in front of the flame part from which fluorescence is measured. First of all, when AL increases the deviation from linearity starts at a lower metal concentration, and secondly, the high density asymptote is never reached. The influence of an absorbing layer between the illuminated flame part and detector, i.e. Al # 0, can be seen by comparing the curves calculated for Al = 0 and Al = 9.5 mm and both for the same AL-value (AL = 0). Such a layer gives rise to an appreciable loss in fluorescence signal (self-absorption effect), even at rather low concentrations. Therefore, in practical fluorescence analysis, it is advantageous to work under such conditions that no preabsorption or self-absorption effect occurs, i.e. AL and Al should be zero. However, it should be noted that the lower limit of detection is not affected by these effects. As can be seen from Fig. 5, especially the curve with AL = 0, a fluorescence curve is not necessarily a monotonous curve with one maximum, as the calculated curves published by HOOYMAYERS [7]. The behavior of a fluorescence curve is brought about by the fact that the fluorescence intensity with a line light source (in case of AL = 0) is determined by two factors (see equation (6)) : (i) [l - exp (-k(&)L)]/k,Z: th is is a constant factor at low k,l values and it decreases with (l~,,l)-~ at high k,l values. (ii) G(Z + AZ) - G(A2); in our case, the double logarithmic plot of this factor consist of three parts successively, having a slope of 1, smaller than 0.5 sometimes even near 0, and -0.5, respectively. The Jc,Irange in which these slopes occur, depends on the a-parameter and the ratio Al/l. The k,Z value at which the factor (i) starts to deviate from linearity and the k,l values at which the factor (ii) changes may produce either a monotonous curve with one maximum (see HOOYMAYER~ [7] Fig. 3), or a curve with several maxima (see Fig. 5). Continuum light source When making measurements with a continuum light source, the preabsorption effect influences the curve in a similar way compared to the line source case with respect to the deviation from linearity. However, a horizontal asymptote is always reached, but the value of the asymptote decreases with increasing AL. These conclusions can easily be drawn from equations (4), (9), and (10).
Theoretical
and experimental
Shape of fluorescence
atomic fluorescence
analytical
curves for magnesium
175
analytical curves
The influence of geometrical factors on the shape of the analytical curve was calculated. It appears that the overshoot (i.e., for k,Z values slightly larger than the intersection value (k,Z),, the value of Fo from the experimental curve is larger than the PC value of the asymptote of the curve at the same k&axis value) decreases gradually and disappears finally with increasing AL and Al. If the curve shows a maximum, t’hen this maximum shifts to lower k&values when AL and/or Al is increased. Whether a maximum in a fluorescence analytical curve with a continuum source will appear is determined by the value of the a-parameter and by geometrical factors. Deviations from the calculated shape of fluorescence curves may occur when the source line is not extremely narrow to the absorption line width, when the lamp radiance shows a spatial inhomogeneity, when the solid angle w is not small, and when a cylindrical flame is used instead of a square-shaped one. ALKEMADE [9] has discussed all these factors. Acknowledgements-Tho authors are indebted to Professor Dr. C. TB. J. ALKEMADE Dr. H. P. HOOYMAYERS for discussion of this work and for their valuable suggestions.
and to
Pergamon Press1971.Printed inNorthern Ireland
Comparison of theoretical and experimental atomic fluorescence analytical curves for magnesium* P. Fysisch Laboratorium,
J. TH. ZF,EGERS
Rijksuniversiteit,
Utrecht,
The Netherlands
and J. D. WINEFORDNER Department of Chemistry, University of Florida, Gainesville, Florida 32601,U.S.A. (Received
1 June 1970)
Abstract-Atomic resonance fluorescence emission was measured as a function of atomic concentration in a flame having known geometrical conditions so that measured curves could be compared to theoretical curves. The measurements were carried out at a single resonance line (Mg 2852 A) with a continuum source as well as with a narrow line source. The parameters necessary to calculate the theoretical fluorescence curves, ie., the line damping parameter, the fluorescence yield factor and the metal concentration in the flame were determined in absolute units by independent, methods. Excellent agreement between calculated and experimental fluorescence curves was found.
EXPERIMENTAL
ANALYTICAL
CURVES IN ATOMIC FLUORESCENCE FLAME SPECTROSCOPY
Introduction ATOMIC fluorescence
flame spectroscopy was introduced in 1964 [l] as an analytical method; since then it has been used for the measurement of a number of metals. Atomic fluorescence flame spectrometry is carried out with either line (hollow cathode lamps, electrodeless discharge tubes) or continuum (xenon arc) background light sources of excitation. For a great number of elements, experimental analytical curves have been measured. Several reviews [2-4] of atomic fluorescence flame spectrometry have been written, and the reader is referred to them for a discussion of previous analytical studies. WINEFORDNER and coworkers [l, 51 have made the first attempt to describe theoretically the shapes of analytical curves. Their theoretical results did not give the correct shape of analytical curves at high metal concentrations, where the fluorescence intensity may be weakened by self-absorption. HOOYMAYERS [S, 71 has given a general explicit expression for the integrated resonance fluorescence intensity as a function of atomic concentration under idealized geometrical conditions. From this expression, curves of growth have been calculated for a number of different values of the line-damping parameter, a, in the limiting cases of a very narrow line * This work was supported by AFOSR(SRC)-OAR
U.S.A.F.
Grant No.Af-AFOSR-69-1685.
[I] J. D. WINEFORDNER and T. J. VICKERS, Anal. Chem. 36, 161 (1964). [2] J. D. WINEFORDNER, V. SVOBODA and L. J. CLINT, Critical Review8 And.
Chem. 1,233 (1970). [3] R. M. DA~NALL and T. S. WEST, A&. Opt. ‘7,1287 (1968). [4] J. D. WINEFORDNER and J. M. USFIELD, Appl. Spectry. Rev. 1, 1 (1967). [5] J. D. WINEFORDNER, M. L. PARSONS, J. M. MANSFIELD and W. J. MCCARTHY, S~ectrochim. Acta 23B, 37 (1967). [6] H. P. HOOYXAXXRS, Ph.D. Thesis, University of Utrecht, Utrecht, The Netherlands [7] H. P. HOOYMAYERS, S~ctrochim. Acta 23B, 567 (1968). 161
(1966).
162
P. J. TH.
ZEEGERSand J. D. WINEFORDNER
source and a continuum source, respectively [7, 81. ALKE~C~ADE [9] has derived qualitatively the shape of analytical fluorescence curves from the curve of growth theory for the limiting cases mentioned and under idealized conditions. From his treatment, he was able to derive exact formulas for the initial and final a,symptotes in terms of the “integral absorption” of a spectral line. No comparison has been made thus far between theory and experiment because fluorescence measurements are usually performed under ill-defined geometrical conditions for the flame shape as well as the optical system. Furthermore, the halfwidth of the background line source does not always meet the requirements set by HOOYMAYERS’ theory [7]. In the present study, the fluorescence curve of growth of Mg at 2852 A was measured under known geometrical conditions which correspond to those assumed in HOOYMAYERS’ theory [7]. In order to calculate the fluorescence curve with a continuum light source, the values of the relevant parameters in absolute units, e.g., radiant fluorescence flux, metal content, the a-parameter and the fluorescence yield factor, were determined. However, only relative measurements with a line source were carried out because of the lack of information concerning the spectral profile and the radiance of the Mg 2852 A resonance line. From the agreement found between calculated and measured curves, it can be concluded that HOOYMAYERS’ theory of fluorescence curves is correct. In addition, measurements were made of fluorescence with a line source for an absorbing layer between source and flame volume called innerfrom which fluorescence emission was radiated (effect of preabsorption; filter effect in fluorimetry) as well as with an absorbing layer between this flame volume and the detector (effect of selfabsorption). Only one element-Mg-was investigated because of the extensive time required to perform the measurements and to analyze the results. The element Mg was chosen because it represented an element thoroughly studied in flames, and so a comparison with previous experimental values of the a-parameter, the quantum yield, and the ratio of peak absorption coefficient to the absorption coefficient for pure DOPPLER broadening could be made. There are no reasons why the approach used is not valid for other elements in various flames.
Theory A square-shaped flame is irradiated by a parallel homogeneous light beam with rectangular cross-section, S = 1-H. This beam intersects the flame axis at right angles (see Fig. 1). The coloured central flame is surrounded by a metal-free mantle flame having the same flame gas composihion in order to guarantee a uniform temperature distribution inside the inner flame. The concentration of metal atoms in the ground state, n, is assumed to be constant at all points in the volume of interest of the coloured flame (I-.L*H or X.L). The fluorescence radiation is observed in a small solid angle, U, in the direction perpendicular to both the irradiating light beam and the flame axis. Hooymayers has presented an exact formula for the observed radiant flux, @‘p (erg set-l), of the fluorescence light emitted from the volume element l-&H in the case [8] P. J. TH. ZEEGERS, R. SMITH, and J. D. WINEFORDKER, Anal. [9] C. TH. J. ALXENADE, Talk given at Atomic Absorption Syrup.,
Chews. 40(13), 26A (1968). Sheffield, England (1969).
Theoretical
and experimcnt,al
atomic
fluorescence AL
L
analytical
curves
for magnesium
163
.
Fig. 1. Cross-sectional ares of the flame of the irradiating light beam B, and of the fluorescence light beam, Or, as seen from above. The colored central flame is indicated. The cross-section of the irradiating light beam and of the fluoresence light beam are determined by the lamp optics and the entrance optics of the monochromator, respectively.
AL = 0 and Al = 0 (see Fig. 1). His formula holds, if re-emission of self-absorbed For the case AL # 0 and Al # 0 the fluorescence radiation may be disregarded. following general relation, which holds for a continuum background as well as for a line source, can be easily derived from HOOYMAYERS’ formula: a& [{I -
- 11 - e=p C-~M~Ll)l dy x
s0
exp [-k(y)(L
a@ - =p -
(1
+
[--lc(~‘)V -
exp
+
AL)11 411
[--k(~Wl)l dy’. (1)
Here B, is the spectral irradiance (i.e., energy per set per cm2 flame area per A) of the source radiation at the front surface of the flame; y is the dimensionless wavelength difference for the absorption process for exciting light, i.e., 2(a - A,)(ln 2)lf2/Ail,, in which 1, stands for the central wavelength of the spectral line observed in the flame (y’ is a similar factor for self-absorption of fluorescence within the illuminated region) and AAD stands for its Doppler half intensity width; Y is the yield factor of fluorescence, defined as the fraction of absorbed energy, that is reemitted as fluorescence radiation; k, (cm-l) is the maximum value of the absorption coefficient, k(y), when only Doppler broadening is present and is related to n according to: Ic = 2(77 In 2)1/2e2&2nf 0
mc2A&,
in whichf is the absorption oscillator strength, c is the velocity of light in vacua, and e and m are electronic charge and mass, respectively. For the limiting case of a continuum light source, we may assume that its spectral
104
P. J. TH. ZEEGERS and J. D. WINEIFORDNER
radiance is independent of wavelength, i.e., B, = B,, and so equation simplified by solving for the dimensionless ratio Po: @R
Fc = ( and substituting
E
)
h’YB,,AI&‘:‘(
G(x) for integrals of the type
Pa =
(
-& 0
>
(1) can be
[G(L + AL) -
s
In 2)-li2 ,{I
-
exp
(3)
F-k(~)41 dy:
G(AL)][G(Z + AZ) -
G(AZ)].
(4)
For a narrow line source, equation (1) can also be simplified by solving for the dimensionless ratio FL @‘p
FL =
m B, dy
SY2( In 2)426& Substituting FL =
G(x) for the appropriate k2
integrals, equation
exp ( -k(lo)AL))P
-
(5)
s0
(1) reduces to :
exp ( -k(~o)L)liG(~
+ A4 -
G(W)
(6)
where k(l,) represents the absorption coefficient at the central wavelength of the background emission line, which is assumed to coincide with the central wavelength m B, dy (in Eq. (5)) equals mBudl, of the absorption line. The term ALD(ln 2)-li2 s0 f0 which is the integrated spectral radiance of the homogeneous exciting light beam. The numerical value of the integral, G, has been tabulated in the literature [lo,1 I] as a function of [nf( In 2)1’2]/[nAi1D] and of the u-parameter, defined as (In 2)1fsA1L/AlD, in which AilL is the Lorentz half width of the absorption line. ALKEMADE [9] using the curve of growth theory described the variation of G(x)[G(x) is the parameter G defined above as a function of the length parameter x] and thus PC and FL as a function of nL for different cases as to AL and AZ. In this paper, only the behaviour of PC and FL at low and high values of nL will be considered. According to HINNOV and KOHN [12]G(x) may be approximated by: G(x) = kox(v)1/2/2,
if
nx --f 0
and by G(x) = [kOax(n)1’2]1/2, if
(7)
nx -+ 03.
(8) Of course, k. is linearly dependent on n, and also on solution concentration over an appreciable range for most atoms. With these approximations, the corresponding equations for Fc and FL can be evaluated and are given in the following section. For a continuum source of excitation and for an atomic vapor at low optical density, i.e., nl + 0 and nL -+ 0, PC is given by: Fc = k,L/2
(9) [lo] P. A. JANSSON and C. L. KOLB, J. Quant. Spectry. Radiative Transfer 8, 1399 (1968). [ll] C. VAN TRIGT,TJ. HOLLANDER and C. TH. J. ALKEMADE, J. Qumt. Spectry. Radiative Transfer 5, 813 (1965). [12]
E. HINNOV and H. KOHN, J. Opt.Soc. Amer. 47, 151, 156 (1957).
Theoretical
and experimental
atomic
and for high optical density, i.e.,
Fa
=
-%tqnp2
fluorescence analytical
165
nl-+ 00 and nL + co, Fc is given by:
[(L + AL) l’s -
if AL = Al = 0, then equation
curves for magnesium
(AL)1’2][Z + AZ)1’2 -
(AZ)1’2]
(10)
(10) reduces to: F
c
=
za
04 I” id
(11)
.
For a narrow line source of excitation, several additional approximations must be made to simplify the final expressions, i.e., low optical densities for absorption (nL -+ 0) : exp [ -k(l,)L] = 1 - k(l,)L, (12) and for high optical densities for absorption 1 Using the approximations is given by:
(nl --+ co):
exp [--k(&)L]
= 1.
(13)
given in equations (7) and (In), FL for the low density case FI, = k(l,)L/2
and using the approximations density case is given by:
(14)
given in equations (8) and (13), FL for the high optical
FL = exp [--b(i.,)AL]a’,Z[k,l(n)1,2]-1/2[(1
+Tr”-
(+yl.
(15)
Experimental
A premixed laminar acetylene-air flame was burned on a Meker-type burner. The square-shaped inner flame was shielded from the surroundings by an outer flame of the same shape, the same composition and the same flame gas velocity. The properties of this flame have been thoroughly studied and are reported elsewhere [13]. Before entering the flame, the pressurized air stream was introduced into a nebulizer for spraying the test solutions into the central part of the flame, as usual. The linearity of the nebulizer was checked by measuring Ca-band emission as a function of solution concentration in absence of ionization [14]. Non-linearity of the nebulizer only occurred if solutions with a concentration higher than 5000 ppm were atomized. All measurements were corrected for this non-linearity. In Fig. 2, a block diagram is given of the optical system which was used for making emission and duplication measurements. This optical fluorescence, absorption, setup and the detection device used were the same as the one described by PEARCE, DE GALAN and WINEFORDNER [15] except for the application of parallel light beams. (The divergence of the light beam from the source was less than 1 degree.) For fluorescence measurements with a continuum light source (xenon arc, XBO 900 [13] P. J. Ta;. ZEEUERS and C. TH. J. ALKFXADE, Comb. Plame 5, 247 (1965). 1141TJ. HOLLANDER, Ph.D. Thesis, University of Utrecht, Utrecht, The Netherlands (1964). [15] S. J. PEARCE, L. DE GALAN and J. D. WINEFORDNER, Spectrochim. Acta 23B, 793 (1968).
P. J.
166
TH. ZEEaEns and J. D. S
ABSORPTION
,
’
-
7
FLUORESCENCE
-
/
LI D,
/ /
WINEFORDNER
A
1
D_
ENTRANCE AorB
OPTICS
I I
A
4 FLAME EMISSION .
.
DUPLICATION
. MON
B!a=x=drnB FLAME
DET
La 4
Fig. 2. Experimental set-up for fluorescence, emission, absorption and duplication S is a light source (xenon arc or electrodeless discharge tube); measurements. L,, L, and L, are lenses; 4, D, and D3 are diaphragms; Ch is a mechanical light chopper; M is a plane mirror; MON is a monochromator; DET is a detector device, consisting of a photo-multiplier, a preamplifier, a 300 Hz lock-in amplifier and a recorder. Emission and duplication measurements were performed with the entrance otpics in arrangement A (flame imaged on monochromator), with a mechanical light chopper just in front of the entrance slit of the monochromator (not indicated in the figure). For the absorption measurements, the source optics, S, L,, D,, D, and Ch, were rotated by 90’ as indicated by the dotted arrow, and M and L, were removed and the entrance optics of the monochromator placed in arrangement B (lens L, at focal length of monochromator). Fluorescence measurements were carried out with the entrance optics either in arrangement A or in arrangement B. In arrangement A, only light from a small part of the flame was detected; in arrangement B, flourescence from a large part was detected.
WIP,
Osram, Berlin, Germany),
only the optical arrangement indicated by position a line source (electrodeless discharge tube, manufactured in the Division of Analytical Chemistry, University of Florida) both arrangements A and B were used. In fluorescence measurements, a light chopper was placed between light source and flame. After rotating the whole optical arrangement between light source and flame over 90” (indicated by the dotted arrow), absorption measurements were made. By focussing the flame on the monochromator slit (position A) and placing a chopper just in front of the monochromator slit, emission curves of growth (analytical curves) and duplication curves could be measured in the usual way (see e.g. HOLLANDER [ll,141). It should be admitted that our set-up for fluorescence measurements does not give the highest possible fluorescence signal with a given lamp and metal concentration in the flame. Therefore, it is not the best arrangement for analytical flame fluorescence spectrometry. Our optical arrangement especially arrangement B, was chosen for theoretical reasons, i.e., in this way, we approached the situation described in Fig. 1 as closely as possible.
B was used; for fluorescence measurements with
Theoretical
and experimental
atomic
fluorescence
analytical
curves
for magnesium
167
EXPERIMENTALPARAMETERS Absolute radiance calibration of the detection device at 2852 A was carried out by measuring the radiation power from a calibrated tungsten strip lamp at a fixed monochromator slit width and slit height. Table Flame
Mg
1. Experimental
parameters
[ 161
1.8 f 0.05 l/min 16.2 f 0.1 l/min 2410 * 10 K k, = (1.07 + 0.05) x 10ea cm-l lppmn = (5.1 f 0.3) 1013 cm3 mol-l k(A,) = (7.0 + 0.4) x lop3 cm-l lppmk(l,)/k, = 0.65 & 0.02 (measured) k,/k, = 0.67 (calculated) a = 0.41 f 0.01 CP, Air T
Y = 0.10 f 0.01 Xenon arc Monochromator
B, (2852 A) = (8.3 & 0.2) x lo* erg set sr-1 cm-2 A-1 Slit area = 1.10 f 0.03 mma Spectral bandwidth = 6.4 + 0.1 A
The slit area was measured by photographing the image of the entrance slit, produced by means of lens L, (see Fig. 2) at the place of the flame. The entrance slit was illuminated from inside the monochromator by placing a light source just behind the exit slit. The slit area used in the fluorescence experiments was found to be l-10 * O-03 mm2. This value agreed with the one that could be calculated directly from the micrometer scale on the slit mechanism. The spectral bandwidth of the monochromator was measured by slowly scanning the emission line of a Mg electrodeless discharge tube. Results from the half-intensity width of the peak trace and from the ratio of line area and peak intensity agreed within 2 per cent,. The spectral bandwidth was found to be 6.4 f O-1 A. Relevant solid angles were calculated as the ratio of the effective area of the imaging lens and the square of the distance from this lens to the light source. From the above results, the spectral radiance (at 2852 A) of the area of the xenon arc used for illuminating the flame was calculated to be (8.3 f 0.2) x lo4 erg set-l sr-1 cm_2 A-1. This value is about a factor of ten lower than the value reported by PRUGGER [1’7]. However, our value refers to the central part of the discharge, whereas in PRUGGER’S measurements, no specific part of the discharge was specified. Therefore, it is possible, that PRUGGER’S value holds for the brightest spot (near the cathode). Cross-sections of light beams were determined photographically. Measured values of these parameters are inserted in the appropriate graphs. The conversion factor of solution concentration (in ppm) into absolute atomic Mg concentration in the flame (i.e., k,l which is linearly dependent on YZ; see Theory) was determined in three independent ways: (i) Curve of growth method [ll, 12, 141: a comparison of the shapes of experimental and calculated emission curves yields a rough value for k,Z and for the a-parameter. [16] p. J. TH. ZEEUERS,W. P.TOWNSEND 243 (1969).
[IT] H. PRUGGER, Spectrochim.
Acta
and J. D. WINEFORDNER,
24B, 197 (1969).
Spectrochim..Acta
24B,
168
P. J. TH. ZEEGERS and J. D. WINEFORDNER
However a more reliable value of the conversion factor may be found from the intersection point (linear) and high density (square root) asymptote in a double-logarithmic plot if the a-parameter is known. The theoretical k,l value at the intersection point can be calculated from equations (7) and (S), (k,Z), = 2-257a. Using the value for the u-parameter found sub (ii) k,l is O-017& 0.002for 1 ppm Mg. (ii) The combinatory method developed by van Trigt e6 al. [l l] : graphical combination of emission curves of growth and duplication curves yields the conversion factor as in this case, the values were: a = O-41$: O-01 well as a value for the a-parameter; and k,Z = O-0161& 0.0003for 1 ppm Mg. (iii) The integrated absorption method [18,191:applied in the range of low absorptions “1 - exp [-k(y)21 dy M k,l: these measurements were carried out with a s narrow slit ythe spectral band width being 0.36A) ; in this case, k,l = O-015f O-001 for 1 ppm Mg. From the average of these results, the value of k,, when spraying a 1 ppm Mg solution into our C,H,-air flame, appeared to be equal to (1.07-j= 0.05)x 10e2cm-l; I was taken as 1.5 cm in these experiments. According to de GALAN et al. [19], k(A,) may be determined from: i.e., where
W,) =
kc(+)(2)(f)(&p
(16)
in which s is the monochromator spectral band in A, uL and ao stand for the fraction of the radiation absorbed in the case of a narrow line source and a continuum source, respectively, when measured with the same low metal concentration. Using the Mg electrodeless discharge, the ratio aL/ac was measured to be 10.9f O-5 and s was found to be 0.36& 0.1i%in these experiments. The other factors in equation (16) being known, k(l,) was calculated to be (7-Of O-4)x 10e3cm-l. It should be pointed out that k(A,) is not necessarily “the peak absorption coefficient”, k,. For example, if the wavelength shift of the peak of the absorption line in the flame is large compared to the width of the background emission line and if the latter line shows no shift, the measured absorption coefficient k(l,) is smaller than the peak absorption coefficient, k,. Collisional broadening of the absorption line in the flame can cause a shift in the absorption line with respect to the background emission line. However, in our experiments with Mg, the measured ratio k(il,)/k,, being 0.65 f 0.04 (see Table l), is almost exactly equal to the theoretical ratio 0.67 [19,20] calculated for a = 0.41,assuming a Voigt profile of the absorption coefficient k(l), Therefore, the measured value of k(&) should hold for the peak absorption coefficient. k,, within close limits. This result may be understood in the following way. The emission line width, Aax, of a Mg electrodeless discharge tube (gas pressure is about 1 mm Hg and the gas temperature is about SOO’K) may be estimated to be 1O-2 A. Because of the low pressure, collisional broadening is expected to be negligible, and so there should be [18] L. DE GALAN and J. D. WINEFORDNER, J. Quunt. Spectry. Radiative Transfer 7,251 (1967). 1191 L. DE GALAN, W. W. MCGEE and J. D. WINEFORDNER, Anal. Chim. Acta 37,436(1967). [20] C. YOUNG, Tables for cakulating the Voight ProjZe, University of Michigan, ORA(1965).
Theoretical
and experimental
atomic fluorescence analytical
curves for magnesium
169
no wavelength shift. When decreasing the output power of the microwave generator, the absorption coefficient did not change noticeably. Therefore, the emission line width is not affected by self-absorption and is determined by Doppler-broadening only. The ratio of collisional line width, A&, to shift, A&, of a spectral line equals about 4 [21,22-j. From the measured value of the u-parameter, 0.41,and the calculated value of AL,, 2.05 x 1O-28, Ale is calculated to be about 1O-2A. In conclusion, A& may be estimated to be 2.5 x 1O-3A, which is only about $ of the emission line width ALE, of the Hg electrodeless discharge tube used. If such a small shift does occur, then it is indeed not to be expected that k(l,) differs much from k,. Furthermore, the agreement between the measured ratio k(l,)/E, and the theoretical vaIue implies that the emission line width is indeed small compared to the absorption line width. Therefore, the condition of a narrow line source is fulfilled in our case of Mg fluorescence with a Mg electrodeless discharge tube as background light source. As pointed out earlier, this condition has to be fulfilled to apply equation (6). DE GALAN et al. [ 191have found for Mg (2852A) in a similar flame the ratio 7c(I,,)/&, to be 0.7.This value agrees well with ours. They have estimated from their k(L,)/k,value and an assumed value for the ratio of the widths of lamp emission and flame absorption line, the a-parameter to be 0.1,with an accuracy of about a factor two. Their value of the a-parameter is certainly wrong. Very probably their assumptions concerning the line width of the emission line are not correct. With the present knowledge of the width of the emission lines from electrodeless discharge tubes and from hollow cathode lamps, this method to determine the a-parameter is inferior to methods based on curve of growth measurements, for a-parameters smaller than 2. It is well-known that the curve of growth alone yields inaccurate a-parameter values, for a-parameters larger than l-5. Therefore, both methods have their own supplementary a-parameter range, in which they may give reliable results. It should be mentioned that DE GALAN’S method, based on the measurement of k(&), also gives wrong results if the absorption and the emission line show different collisional line shifts. For a monochromator as a wavelength selector, PEARCE et al. [15]have shown that the fluorescence yield factor, Y, may be determined from : (17) where iF is the scale deflection in the fluorescence measurements, Aia is the difference in scale deflection recorded in the absorption measurements, Q, is the solid angle of radiation incident on the flame which is determined by position and aperture of lens L, (see Fig. 2),W, is the width in the flame over which fluorescence is measured, and WA is the width of the irradiating light beam. In this measurement, the light source was focused at the center of the flame. Equation (17)holds only if the fluorescence and absorption measurements are carried out with the same setting of monochromator slit width and slit height. Furthermore, in the absorption and in the fluorescence measurements, lens L, should limit the aperture of the entrance optics [al] C. SMITH, Proc. Roy. S’oc. A296, 288 (1967). [22] A. HINDNARSH, D. PETFORD and G. SMITH, Proc. Roy. Sot. &W, 3
296 (1967).
P. J. TE. ZEEGERSand J. D.
170
WINEFORDNER
and the solid angle of the radiation beam incident on the monochromator slit should be larger than the solid angle of the monochromator itself. It is well-known [S, 231 that measurements of Y may be affected by self-absorption. To eliminate this effect, Y was measured as a function of concentration. The true value of Y is then found from a linear extrapolation to zero concentration [23]. The results, presented in Fig. 3, indicate Y = O-10 & 0.01. Values of the most important experimental parameters are summarized in Table 1.
I
I
I
I
50
100
150
200 wm ccKt4g
-
Fig. 3. Measured apparent fluorescence yield factor, Y, as a function of Mg concentration. RESULTS AND DISCUSSION
Pluorescence
curves witha continuum source
Fluorescence curves obtained with a continuum source calculated and measured in absolute units are presented in Fig. 4. The shape of the measured curve and the position of the experimental points along the k&axis agree with theory (see equations (4), (9), and (10)). The measured Po values are 25 per cent lower than the calculated value. In view of the possible systematic errors in the geometrical factors (each $10 per cent), in B, (55 per cent), and in Y (410 per cent), a discrepancy of 25 per cent is reasonable. HOOYMAYERS [7] has proposed to use continuum fluorescence curves for the determination of the a-parameter. This can be done by graphical determination of the intersection point of the low and the high density asymptote in Fig. 4. Combining equations (9) and (10) one gets :
%4)I =
[(L + AE)1’2 - (AL)1’2][(Z + AZ)r’z - (AZ)l’“]
(18)
in which the subscript “I” refers to the intersection point. If (k,Z), is known in absolute measure then the a-parameter may be calculated. However, the experimental curve in Fig. 4 shows from the first point a sublinear behavior. In our experiment, [23] H. P. HOOYMAYERS and P, L. LIJNSE,J. Quant. Spectq.
Radiative
Transfer
9, 995 (1969).
Theoretical
and experimental
atomic
fluorescence analytical
curves for magnesium
17 1
Fig. 4. Fluorescence curves of Mg (I, = 2852 A) measured with and calculated for a continuum light source. The part of the flame from which fluorescence was measured is indicated in the inserted figure. The relevant dimensions are given in mm. This figure presents only the colored central flame, ie., that part of the flame, where Mg atoms were present. Solid lines present the asymptotes of the calculated curve. Dashed lines present the asymptotes of the measured curve.
the signal-to-noise ratio was too poor to define the low density asymptote. The signal-to-noise ratio can be improved by using a flame with less background emission and/or by using a light source with higher intensity. However, in our case, the position of the low density asymptote can only be found by a trial and error method. According to ALKEMADE [9] the incipient deviation of the curve from its initial asymptote can be found in a first order approximation by expanding G(x) (see equa,tion (4) in a series for small values of k,Z:
(19) where k(y) -j-W) which is proportional to k,. in first order approximation
dz///Q/)
dy,
(20)
Using this series expansion, 3’0 (see equation (4)) is given by
++L+1+2AL+2Al)+....
+6(F,)]. 1=fg,I (21)
The relative deviation from linearity, s(Fo), (which is different for different values, is thus approximately (see equations (21) and (9)) given by: 6(F,)
= -4
with S(P0) equal to [(kOZ)asg-
k(y) (L + I + 2AL + 2AZ)
(k,Z),,,]/(k,Z),,,
(here the subscript “asy”
F,(22)
and “exp”
172
I?. J. TH. ZEEGERSand J. D. WINEFORDNER
refer to the asymptotic and the experimental curve, respectively). proportional to k,, equation (22) may be rewritten as: &PC) = --x(&AXC,
Because k(y) is
(23)
with z a proportionality constant that is independent of k,. The asymptote to be found is that straight line with slope equal to 1 having a position along the log (h$)axis such that the incipient deviations from this straight line by the experimental curve fulfills the requirements stated in equation (23). In the usual case that the aparameter is unknown, this line can only be found by trial and error. In our case, z was determined from the calculated curve. The asymptote thus found, is inserted in Fig. 4, together with the calculated (i&Z),,, values. In our case, the first order approximation is sufficient to correct the first three points. Using this procedure, the intersection point of the asymptotes of the experimental curve yields a = 0.42 while the theoretical curve yields a = 0.41. It should be noted that it is difficult to find a consistent value for z if only the experimental curve is available because the experimental error in PC may be of the same order of magnitude as the relative deviation 6(P,). Because of this uncertainty it is expected that an a-parameter determination based on fluorescence measurements will have relative errors equal to or greater than 10 per cent. Therefore, we feel that this method of a-parameter determination cannot compete with other methods such as methods based on emission curves of yrowth and duplication curves. If the a-parameter is known, fluorescence measurements with a continuum source at high metal concentrations for which the asymptote value of -E”ohas been reached may be used for the determination of Y, as has been suggested by HOOYMAYER [7]. The value of Y follows directly from the ratio of the meter deflection corresponding to the re-emitted radiation for high metal concentration and the meter deflection attained when the monochromator is illuminated directly by the continuum light source. These meter deflections have to be measured under identical experimental conditions or, as we did, one has to know all geometrical factors involved. This method yields Y equal to O-08 & 0.02 (see Figs. 4), which is less accurate than the value of Y found earlier, being 0.10 + 0.01 (see Fig. 3). This lower accuracy is mainly caused by the rather unusual geometrical conditions chosen. More favourable conditions may be chosen (i.e., complete illumination of the flame) to produce a higher accuracy. The major advantage of the above method for the determination of Y in contrast to the method used to obtain Fig. 3 is the independence of Y on the metal concentration as long as this concentration is high enough that a point on the high optical density asymptote is measured. However, the accuracy of the measured value decreases with increasing metal concentration as a result of a decrease in the signalto-noise ratio. The signal remains constant, but the noise increases, because the thermal emission increases with metal concentrations. Fluorescence
with a line source
Fluorescence emission of Mg at 2852 A with a Mg electrodeless discharge tube (line source) was only measured in a relative way. The fluorescence emission was measured in two different parts of the illuminated flame volume. In Fig. 5, the
and experimental
atomic
fluorescence analytical
curves for magnesium
10
17 3
100
k, I
------*
Fig. 5. Fluorescence curves of Mg (1 = 2852 A) measured with and calculated for a narrow line source. The part of the flame from which the fluorescence was measured is indicated in the inserted figure. The relevant dimensions are given in mm. For all curves, AZ equals 9.5 mm except for one; this latter curve is indicated by AL = 0 and Al = 0.
results for the case L = O-5 mm and AL = 3 mm are given; these measurements were carried out with the optical arrangement indicated as position A in Fig. 2. In Fig. 6, the results for the case L = 10 mm and AL = 1 mm are given; these results were obtained when the flame was focussed on the entrance slit of the monochromator, i.e., position B in Fig. 2. In both figures, the experimental points are inserted in such a way that t,hey are fitted as well as possible to the calculated curve with AL equal 1
LINE
LIGHT
SOURCE
I
I
I
1
-,/ _ /
.
i
I Id
1 __t
k,l
100
Fig. 6. This figure presents the same type of measurements as Fig. 5. Only in t,his case the ratio AL/L, being 0.1, is quite different from the situation in Fig. 5, where AL/L was equal to 6.
174
P. J. TH. ZEEGERSand J. D. ~VINEFORDNER
; for these conditions, the experimental points agree well with the theoretical curve. Of course, the experimental points were fitted by a shift along the y-axis only because the absolute values of the x-axis values are known. For these experiments, the same solution concentrations were used as in the experiments with the continuum source. The l-value in both experiments wa,s different, being 6.9 and 5 mm for the cont.inuum and the line source, respectively Therefore, the k,lvalues corresponding to the same solution concentration differ by a factor 1.4 in both experiments (compare Fig. 4 to Figs. 5 and 6). 3 and 1 mm, respectively
Preabsorption
and self-absorption
eSfect
Line light sozcrce. In Figs. 5 and 6, calculated curves corresponding to AL-values equal to 0, 0.5, 1, 3, and 5 mm, respectively are also included. These curves indicate very clearly the preabsorption effect, i.e., the influence upon a fluorescence curve of an absorbing layer (AL # 0) in front of the flame part from which fluorescence is measured. First of all, when AL increases the deviation from linearity starts at a lower metal concentration, and secondly, the high density asymptote is never reached. The influence of an absorbing layer between the illuminated flame part and detector, i.e. Al # 0, can be seen by comparing the curves calculated for Al = 0 and Al = 9.5 mm and both for the same AL-value (AL = 0). Such a layer gives rise to an appreciable loss in fluorescence signal (self-absorption effect), even at rather low concentrations. Therefore, in practical fluorescence analysis, it is advantageous to work under such conditions that no preabsorption or self-absorption effect occurs, i.e. AL and Al should be zero. However, it should be noted that the lower limit of detection is not affected by these effects. As can be seen from Fig. 5, especially the curve with AL = 0, a fluorescence curve is not necessarily a monotonous curve with one maximum, as the calculated curves published by HOOYMAYERS [7]. The behavior of a fluorescence curve is brought about by the fact that the fluorescence intensity with a line light source (in case of AL = 0) is determined by two factors (see equation (6)) : (i) [l - exp (-k(&)L)]/k,Z: th is is a constant factor at low k,l values and it decreases with (l~,,l)-~ at high k,l values. (ii) G(Z + AZ) - G(A2); in our case, the double logarithmic plot of this factor consist of three parts successively, having a slope of 1, smaller than 0.5 sometimes even near 0, and -0.5, respectively. The Jc,Irange in which these slopes occur, depends on the a-parameter and the ratio Al/l. The k,Z value at which the factor (i) starts to deviate from linearity and the k,l values at which the factor (ii) changes may produce either a monotonous curve with one maximum (see HOOYMAYER~ [7] Fig. 3), or a curve with several maxima (see Fig. 5). Continuum light source When making measurements with a continuum light source, the preabsorption effect influences the curve in a similar way compared to the line source case with respect to the deviation from linearity. However, a horizontal asymptote is always reached, but the value of the asymptote decreases with increasing AL. These conclusions can easily be drawn from equations (4), (9), and (10).
Theoretical
and experimental
Shape of fluorescence
atomic fluorescence
analytical
curves for magnesium
175
analytical curves
The influence of geometrical factors on the shape of the analytical curve was calculated. It appears that the overshoot (i.e., for k,Z values slightly larger than the intersection value (k,Z),, the value of Fo from the experimental curve is larger than the PC value of the asymptote of the curve at the same k&axis value) decreases gradually and disappears finally with increasing AL and Al. If the curve shows a maximum, t’hen this maximum shifts to lower k&values when AL and/or Al is increased. Whether a maximum in a fluorescence analytical curve with a continuum source will appear is determined by the value of the a-parameter and by geometrical factors. Deviations from the calculated shape of fluorescence curves may occur when the source line is not extremely narrow to the absorption line width, when the lamp radiance shows a spatial inhomogeneity, when the solid angle w is not small, and when a cylindrical flame is used instead of a square-shaped one. ALKEMADE [9] has discussed all these factors. Acknowledgements-Tho authors are indebted to Professor Dr. C. TB. J. ALKEMADE Dr. H. P. HOOYMAYERS for discussion of this work and for their valuable suggestions.
and to