the influence of spectral line profiles
upon analytical curves
ch o
-J O
the influence of spectral line profiles
upon analytical curves
in atomic absorption spectrometry
BIBLIOTHEEK TU Delft P 1950 6227Proefschrift
649666ter verkrijging van de graad van doctor in de techni-sche wetenschappen aan de Technitechni-sche Hogeschool Delft, op gezag van de rector magnificus prof. dr. ir. H. van Bekkum, voor een commissie aangewezen door het college van dekanen, te verdedigen op
woensdag 31 maart 1976 te 16.00 uur.
door
Hendrik Cornells Wagenaar r^^zr^
. . . /C)£-0 6 2 2-7
scheikundig mgenieur i y ^ / geboren te Zaandam
en dan Weer korrelig of kristallijn, zo ook vertonen spektraallijnen een eigen karakter doordat de een aan haar randen saherp begrensd isj terwijl de ander naar een of naar beide zijden hetzij gelijkmatig^ hetzij ongelijkmatig vervloeit of doordat de een ons breed en de ander ons smal toesahijnt.
Het onderzoek dat hier wordt beschreven kon slechts tot stand komen
doordat een aantal collega's daar hun medewerking aan verleenden. Ik denk hierbij vooral aan dr. Ivan Novotny, medewerker aan de Purkyni
Universitelt van Brno en dr. Chris Pickford, thans werkzaam bij Euratom in Ispra. Beide leverden in de periode waarin zij als gast
aan onze Hogeschool verbleven, een waardevolle bijdrage aan de
werk-zaamheden. Ik bewaar aan deze samenwerking bijzonder prettige herin-neringen.
Ook vanuit de technische diensten in het Laboratorium voor
Analyti-sche Scheikunde heb ik veel steun ondervonden. Met name de heren A. van den Berg, F. Bolman en R. Regouw raakten bij het onderzoek
betrokken; ik ben hen veel dank verschuldigd voor de mate waarin en
de wijze waarop zij aan de ontwikkeling van de interferometeropstel-ling hebben bijgedragen.
Een groot deel der resultaten is tussentijds gepubliceerd; dat ik
daartoe steeds kon komen is vooral te danken aan de stimulerende
invloed die lector dr. Leo de Galan op mijn activiteiten uitoefende. De bedoelde publicaties zijn in dit proefschrift, met toestemming
van de uitgever, als hoofdstukken III t/m VI opgenomen.
Ik draag dit proefschrift graag op aan mijn ouders, die mij bij m'n
studie tot grote steun waren en aan Gobi, Sibrenne en Zefanja,
die, naar ik mij voorneem, de aandacht zullen krijgen welke ik gedurende geruime tijd aan lijnprofielen meende te moeten besteden.
chapter I The shape of analytical curves in atomic absorption
spectrometry 1 1. Introduction 1 2. The absorption characteristics of the flame 2
3. The Lambert-Beer law 3 4. Flame and instrument interferences 5
5. Emission radiation from a flame 7 B. Radiation from ho How-cathode lamps 10 7. Literature survey on profile influences 11
chapter II The broadening of spectral lines 14
1. Introduction 14 2. Doppler broadening 15 3. Collision broadening 15 4. The Voigt profile 19 5. Broadening by hyperfine structure 21
6. The interferometric measurement of line profiles 24 chapter III Interferometric measurements of atomic line profiles emitted
by hollow-cathode lamps and by an acetylene-nitrous oxide
flame 28 1 . Introduction 28
2. Theory 29 3. Computer programs 31
4. Experimental 32 5. Results and discussion 37
6. Conclusions 47 chapter IV The interferometric measurements of atomic absorption line
profiles in flames 49 1 . Introduction 49 2. Theory of interferometric measurements of profiles in
flames 50 3. Interferometric measurements of absorption line profiles 52
4. Experimental 54 5. The interferometer instrument function 56
6. Results and discussion 60 chapter V The influence of hollow-cathode lamp line profiles upon
analytical curves in atomic absorption spectroscopy 63
1. Introduction 63 2. Theory 64 3. Experimental 66 4. Calculation procedure 68
5. Influence of lamp current upon emission profiles 68
6. Presentation of the results 71 7. Discussion of the results - 75
copper and silver in atomic absorption spectroscopy 80
1 . Introduction 80 2. Experimental 83 3. Correction for instrument broadening 83
4. The Doppler temperature in the hollow cathode lamp 85 5. The influence of lamp current upon the lamp line profile 86
6. Collisional shift in the air-acetylene flame 89 7. Analytical curves for copper and silver 93
8. Curvature measurements 98
9. Conclusion 100
Summary 101 Samenvatting 103
Chapter I
The shape of analytical curves in atomic absorption spectrometry.
Abstract - Analytical curves in atomic absorption spectroscopy are linear if certain conditions are fulfilled. One of the conditions is flame homogeneity, another proportionality between the number of metal atoms in the flame and the solution concentration, while a third one is related to the wavelength
dependence of the source emission profile and the flame absorption coefficient. A survey of the literature confirms that the shape of spectral lines affects the analytical curve by changing its slope and linearity. Expressions are presented that relate the emission intensity of lines from flames and hollow cathode lamps to the absorption coefficientj they account for self-absorption broadening and self-reversal of lines.
1. INTRODUCTION
The method'of analysis known as atomic absorption spectrometry (AAS) is based upon the reproducible conversion of a metal salt solution into an atomic
vapour, capable of absorbing radiation from an external source at a specific wavelength [1-6]. The conversion into free atoms may be realized by electric heating or by suppletlon of heat from chemical combustion reactions. In this latter case, a flow of gaseous fuel, usually acetylene, is oxidized by premixed air or nitrous oxide on a slot burner. The release of combustion energy
creates a steady flow of burnt gases at high temperature, a flame.
A pneumatic nebulizer is used to convert the solution into an aerosol. The gas stream carries the small droplets into the flame, the solvent evaporates, the remaining salt particles volatilize and the molecules dissociate into
atoms. At the flams temperature of 2500 or 3000 K these atoms are predominantly
[1] A. WALSH, Speatroahim. Aota 7, 108 (1955).
[2] B.V.L'VOV, Atomic Absorption Spectrochemical Analysis, Hilger, London, 1970.
[31 W.J.PRICE, Analytical Atomic Absorption Spectrometry. Heyden, London, 1972. [41 G.F.KIRKBRIGHT and M.SARGENT, Atomic Absorption and Fluorescence
Spectro-scopy, Acad. Press, London, 1974.
[51 J.D.WINEFORDNER, V.SVOBODA and L.J.CLINE, Crit. Rev. Anal. Chem. 1, 233 C1970).
[6] P.J.T.ZEESERS, R.SMITH and J.D.WINEFORDNER, Anal. Chem. 40 (13), 2BA (1968).
in the ground state (energy E Q ) and they can easily absorb radiation of an energy E-|-Eo (E.| is the energy of an excited level) if this is supplied by an
external source of radiation, the hollow cathode lamp (HCL). The HCL radiation
is converted into an electric signal by a detector, situated behind a mono-chromator which selects the appropriate spectral line of wavelength
Xg = hc/(E-|-Eg) from the emission spectrum of the lamp.
The absorption of HCL radiation in the flame can be quantitatively related
to the analyte concentration; this relationship is known as the analytical
curve. Under favourable conditions Beer's law is perfectly obeyed and the analytical curve is straight. In practice, deviations from linearity are
often observed, however. In the following sections (3,4) the causes of non-linearity will be enumerated and discussed. It will be shown that all causes,
except one, can be more or less easily eliminated by improved instrumentation.
The only exception is the influence of spectral line profiles.
For this reason we decided to focus our attention to the direct measurement of line profiles from sources commonly applied in atomic absorption
spectro-metry, namely HCL's and laminar flames on a slot burner. The necessary high wavelength resolution is provided by a Fabry-Perot interferometer. The
measured profiles can be used in the subsequent calculation of analytical
curves. These curves consequently reflect the overall influences of line profiles and do not possess the restrictions inherent to model calculations
(this chapter, section 7 ) . On the other hand, this work deals with a selected number of transitions, mainly restricted by the wavelength limitations imposed
by the interferometer; nevertheless, the results provide a good picture of the
magnitude of profile influence to be expected in analytical AAS.
2. THE ABSORPTION CHARACTERISTICS OF THE FLAME.
In order to obtain a high analytical sensitivity in AAS, flames are used which
are long and narrow. The detector observes a pencil shaped section of that part of the flame, that is lengthwise illuminated by the HCL. The cross-section of
this observed region is determined by the aperture of the optics (in fact, this region consists of two cones with apexes at the slot center and with bases at
the flams edges).
To establish the absorption characteristics of such a flame, the amount of
absorption caused by a fixed metal concentration was measured while the flame was moved accross the HCL light beam. The burner was identical to the one used
in the investigation of spectral line profiles; the burner slot was 0.4 mm wide and 58 mm long. The experiment was repeated in three mutually
A OS 0.4 / JJL
- C _ ^ ,
I -20 0 20 X-displacement, mnn 0 5 y - displacement. m m 0 10 20 z-dlsplacement . m mFig. 1. Absorbance profiles for silver at 328 nm in a C2H2-air flame (1) and for aluminium at 396 nm in an C2H2-N2O flame (2).
the transmitted fraction of lamp radiation] versus the displacement. Two factors determine the local absorbance value: the local density of metal atoms
and, to a lesser extent, the local temperature. Temperature measurements by REIF et al.[71 have recently proved that in a C2H2-N20 flame on a slot burner Isothermal zones exist; absorbance variations should thus mainly be attributed to variations in atom density. Along the line of sight in AAS (x-directlon)
the absorbance curve is quite flat over a large portion of the slot length, it rises slightly towards the outsides and drops sharply to zero at the flame edges. The flame can thus be considered as reasonable homogeneous and (average) values, measured along the line of sight, closely approach the value at the
flat part of the curve. The y and z dimensions of the observed flame region should however be restricted to about 2 mm. If not, gradients in these directions may cause a loss of sensitivity and non-linear analytical curves.
3. THE LAMBERT-BEER LAW.
The reduction of HCL radiation, dl, by absorption in the flame along the
optical axis, between x and x+dx, is proportional to the Incident radiation
intensity I(X) and the atom density n in the small volume with cross section dy.dz between x and x+dx:
-dI(X,x) = k(X,x,y,z)n(x,y,z)I(X,x)dx (1)
The nature of the absorption coefficient k will be fully discussed in Chapter
II. Here, it suffices to state that k depends on the wavelength X and the local
flame temperature T.
To solve the Lambert-Beer equation, gradients in n and T should be absents
the preceding section showed that this is only true if the y and z dimensions are strongly limited. The experiments described in Chapter VI, however, show
that this condition can be realized by reducing the optical aperture. Then,
Eq. 1 becomes:
-dI(X,x] = k(X,x)n(x)I(X,x]dx (2)
Because Fig. 1 shows that the product k-n hardly varies along the x-coordinate,
a relation between the transmitted intensity I(X] and the incident intensity
I(-,(X) can be found by integration over the flame length 1:
I(X) = I|3(X)exp[-k(X)nll (3)
Eq. 3 is valid for each wavelength. However, the signal observed by the detector is the integral over the spectral bandpass selected by the
mono-chromator. An estimate in Chapter II will show that the bandpass exceeds the width of a spectral line emitted by the HCL by at least an order of magnitude.
As long as water is sprayed into the flame (n=0), the read-out signal will be proportional to the integrated HCL intensity:
J = a f'^ I (X)dX (4a)
0 o
where a is a proportionality factor. During aspiration of the analyte:
J = o /^^ I(X)dX (4b)
A convenient representation of these signals is obtained by converting to
common logaritms and substitution of the Lambert-Beer law:
J*^ I (X)exp[-k(X)nlldX
A = -log (5) r I (X)dX
•' 0
It is here that the role of spectral line profiles becomes clear, for a linear relation between absorbance and atom density is only obtained as long as k(X)
does not vary over the wavelength region where I|-,(X) significantly differs from
zero or, in other words, as long as the profile of I (X) is narrow in comparison to the profile of the absorption coefficient k(X).
absorbance and the concentration. This means that a second requirement has to be fulfilled, namely a linear relation between atom density, n, and solution
concentration, c. If the factor B is used to quantify the conversion from solution concentration into free atom density (S=n/c), the Lambert-Beer law (Eq. 5) gets a simple appearance
A = 0.43Bklc = k' Ic (B]
In practice several factors may affect this relation; they are discussed in
the next section.
4. FLAME AND INSTRUMENT INTERFERENCES.
Practical applications of AAS have shown that the shape of the analytical curve is often affected by factors which are not related to spectral line profiles [6, 8-111. The importance of these interferences may vary from case to case, but will generally depend on the type of element, the composition of
solutions, the type of flame, the observation height and the quality and setting of the instrument. They have however, one feature in common: they can be removed one by one either by improving the instrument or by pre-treating the standard solutions. This is in contrast to the influence of
spectral line profiles because no remedy is available to the analyst here. As a consequence, optimum conditions cannot avoid that line profiles determine the ultimate shape of the analytical curve.
(i) Flame interferences.
These interferences affect the proportionality between the solution
concentra-tion of the metal and the atom density in the observed region of the flame. In this respect, vaporization and atomization are the most important steps in the conversion process.
(i.1) Vaporization is not always complete at the height of observation. This is a consequence of the finite time (ms) the desolvated particles require, first to melt and then to vaporize. In a very simplified model,
the vaporization time T is related to the surface of the molten particle
[81 G.J.BASTIAANS and G.M.HIEFTJE, Anal. Chem. 46, 901 (1974).
[91 T.J.VICKERS, L.D.REMINGTON and J.D.WINEFORDNER, Anal. Chim. Aota 36, 42 (19B6).
[10] G.R.KORNBLUM and L.DE GALAN, Speatroahim. Aota 28B, 139 (1973). [11] L.DE GALAN and G.F.SAMAEY, Speatroahim. Aata 248, 679 (1969).
2/3 and thus to the total salt concentration in the solution via T "^ c, , .
tot Only a high salt concentration provides x-values in the order of the rise time of the flame gases. Hence, if vaporization interference is present, it will not affect the linearity of the analytical curve as long as all standard solutions contain the same matrix.
If we suppose that the evaporization of particles of the metal salt MA is
complete, the metal species density n depends linearly on the solution concentration: n "^ c. However, the total metal contents of the flame may only
be partly atomic (density n ) , because ions can be present due to partial ionization (density n„+) or compounds may be formed such as oxides (density
n ) or, in rare cases, salt molecules MA may still be present (density n )
due to incomplete dissociation. Thus:
H T = n^ ^ n^. - n^^ * n^^ C7)
If we suppose that the Lambert-Beer law is fully obeyed, then A "^ n . To
obtain linear analytical curves, we need however A oc c i n (Eq. 6) and this,
of course, will only be true as long as the ratio n /n does not depend on the concentration. The sensitivity will reduce, however, as soon as n +, n ^ or
n notably differ from zero, because a part of the metal is no longer M A
available for atomic absorption. Three cases will be distinguished here,
although in practice combinations of these oases can occur.
(i.2) If we suppose that compound formation is the major interference then n_ = n„ + n^„. If K is the dissociation-equilibrium constant of MX, we
T M MX c
can write n^ = n„[1+n„/K 1. Hence, the ratio n„/n^ is constant as long T M X c M l as the density of the flame gas component X and the temperature are
constant. The result is reduced sensitivity but no curvature.
(1.3) In the case of ionization an equilibrium will exist according to M ^ i M * + e and thus n = n + n^+. Using the Saha equilibrium constant
K. we obtain:
1 1 1 7 2
rn. + — vn. +
"T "- "n " 2"f * 2 ^"f * ^ ^ " M
where n is the contribution to the total electron concentration due to flame gases and to other sample components. Hence, if n is made very
large by adding an ionization suppressing component, then n = n . If,
on the other hand, the metal is easily ionized and no ionization suppressor is added, n_ is very small and n = n + n + = n„ + /K.n„.
In this case n /n is not constant when the concentration is changed and the relation between A and c will be curved.
(i.4) If we suppose that incomplete dissociation of salt molecules MA is the major interference, then n.^ = ri„ + n„.. Because n„ = n. we have
2 T M MA M A
n_ = n + n M/^.. It would appear that here too, n /n varies with the concentration; however, in practice n rvi/'^j^'^n so that n = n .
(ii) Instrument interferences
The important causes of interference in this group are non-absorbed source radiation reaching the detector, and a non ideal light beam geometry in the flame.
(ii.1) Radiation of the resonance wavelength should be the only radiation
reaching the detector. If not, we measure a signal
A = log (I +1 )/(I.+I ) instead of A = logl / I ^ , as a consequence of
o s t s " o t
the non-absorbed contribution I . The analytical curve now obtained, s
will curve and ultimately reach a limiting absorbance given by A = log (I +1 )/I . If bandpass reduction is of no help, the
lim ^ o s s '^ '^
matched scale expansion technique [ll] should be applied to straighten the analytical curve artificially.
(ii.2) A second source of curvature are gradients in the free atom density over the observed flame region (Fig. 7 ) . This can only be eliminated by reduction of the aperture [12]. Commercial instruments do not always meet this requirement because it means a sacrifice in the signal-to-noise ratio.
Summarizing, we can state that non-linearity of analytical curves in practical AAS can be ascribed to a number of causes. Those mentioned here, can be
eliminated and, therefore, offer no principal limitation to the linearity of the analytical curve in AAS.
5. EMISSION RADIATION FROM THE FLAME.
To calculate the influence of spectral lines upon analytical curves (Eq. 5 ] , one should know the emission profile of the HCL, I (X) and the profile of the absorption coefficient k(X) in the flame. The obvious method to obtain infor-mation about k(X) is the measurement of flame emission profiles. In this
section the quantitative relation between k( X) and the emission intensity I(X) is discussed.
The model of a gas in thermodynamic equilibrium is usually employed to [12] Z. VAN GELDER, Speatroahim. Aata 25B, 669 (1970).
describe the equilibrium conditions in an atmospheric flame [13,14]. If a state of thermodynamic equilibrium exists, all dynamic processes which take place in
a flame, such as translation, excitation, ionization, dissociation and
radiation are governed by a unique value of the temperature T.
Because real flames are never completely shielded from the surroundings,
deviations exist. The first one is the loss of energy as a consequence of emission of radiation. In atmospheric nitrogen diluted flames however,
radiation energy is only a small fraction of the total energy contents of the
flame [14]. In such a case, a situation of partial thermodynamic equilibrium may exist, because other equilibria are not neccessarily affected by the absence
of adiabatic walls. A second phenomenon in real flames is often the presence of gradients in partial particle densities and temperature, especially if the
flame is not shielded by a hot gas. If these gradients are strong, one usually
speaks of local thermodynamic equilibrium, indicating that equilibrium conditions are not affected by mass and heat transport, but that these
conditions should be described by local values of T and n.
Experimental verification of the existence of (local) thermodynamic equilibrium is usually obtained by the measurement of temperatures which are
related to different equilibria in the flame. The better these values coincide, the better the state of thermodynamic equilibrium is approached [15-19].
Table 1 shows some results obtained by DE GALAN and SAMAEY [16] for acetylene
flames on a slot burner. These data are of special interest because the
authors' flames are very similar to those applied in the present investigation
on line profiles (e.g. Identical burner).
[13] A.G.GAYDON and H.G.WOLFHARD, Flames, Chapman S Hall, London, 1970.
[14] C.T.J.ALKEMADE and P.J.T.ZEEGERS, Excitation and de-excitation processes
in flames, chapter in Spectrochemical Methods of Analysis, J.D.WINEFORDNER, ed., Wiley, New York, 1971.
[15] I.REIF, V.A.FASSEL and R.N.KNISELEY, Speatroahim. Aata 28B, 105 (1973), 29B, 79 (1974).
[16] L.DE GALAN and G.F.SAMAEY, Speatroahim. Aata 25B, 245 (1970). [17] G.F.KIRKBRIGHT, M.K.PETERS, M.SARGENT and T.S.WEST, Talanta 15, 663
(1968).
[18] W.SNELLEMAN, Ph.D. Thesis, Utrecht (1965).
[19] J.B.WILLIS, J.O.RASMUSON, R.N.KNISELEY and V.A.FASSEL, Speatroahim. Aata 23B, 725 (1968).
Table 1. Exp Flame type C2H2 - N2O C2H2 - air erimental flame Temperatures ( Reversal >27Q0 2450 temperatures [ 16] OK) at 5 mm in the Rot. Vib. 2940 3200 2480 flame. Fe-exc. 2750 2460 loniz. 2950
To the opinion of the authors, the temperatures in Table 1 are sufficiently close to each other, and to data in the literature, to conclude that (partial)
thermodynamic equilibrium exists in the observed region of the flame.
One of the consequences is the applicability of Kirchhoff's law of radiation for each volume in the flame. If In(A) is the blackbody radiation intensity at
b
the temperature T, then the contribution to the radiation intensity emitted
by a flame volume of length dx and unit cross section, is related to the
existing intensity by
dI(A,x) = k(A)n(x)[l^(X) - I(X,x)ldx (8) b
I„(X) and k(X) are independent of the position x because it is reasonable to B
assume that the observed region is isothermal [7 1. To solve Eq, 8, an effective
density can be defined n = (1/1) • / n(x)dx , but weJ<.now from section 2 that local variations in n are small as long as the cross section of the observed
region is limited to a few mm; that means that the effective value n is almost
equal to the true value n. Solving Eq. 8 then gives:
I(X) = I„{1 - Bxp[-k(X)nl]} (9)
In this equation Ip,(A) has been replaced by I because atomic spectral lines from atmospheric flames are sufficiently narrow (<0.01 nm, see chapter II) to
consider I_ wavelength independent. If the product k(A)nl is small, Eq. 9 gives B
in good approximation:
I(X) = I„k(X)nl (10)
•
and the profile of the emission line is identical to the profile of the
absorption coefficient. If the metal atom density n in the flame is raised, the
profile of I(X) starts to broaden (so-called self-absorption broadening) and emission profile measurements no longer simply provide the profile of k(X).
6. RADIATION FROM HOLLOW CATHODE LAMPS
The sources of primary radiation, usually employed in AAS, are sealed-off lamps with 5-10 torr neon pressure, a rod or ring shaped tungsten anode and a
cylindrical hollow cathode [4]. A steady discharge can be sustained at variable
current (usually 3-30 m A ) . The lamp current may be modulated or pulsed. In this investigation however, lamps have been used exclusively in d.c. operation.
The history of stable, high-intensity HCL's is relatively young and hence the knowledge about the conditions in these lamps is correspondingly limited.
Nevertheless, it has been convincingly demonstrated, that the state of the
emitting gas cloud inside the hollow cathode is far from a thermodynamic equilibrium. Whereas in a flame charged particles are of minor significance, in
the HCL they carry the discharge and are responsible for the transfer of energy to neutral particles including metal atoms released by sputtering from the
cathode inner walls. At a pressure of a few torr collisions are relatively
scarce and electrons can be strongly accelerated between two successive collisions. Although a random electron velocity is established in only a few
collisions, the transfer of energy to heavy particles is far less effective. Under stable conditions, the difference in (kinetic] temperatures just causes
the energy transfer to compensate the gain of energy from the electric field.
BUEGER et al. [ 20,21 1 reported electron kinetic temperatures in a high
current HCL of 30.000 K. Gas (kinetic) temperatures are known from line profile
measurements to be much lower, between 300 and 1000 K [this thesis, also 22,23]. Temperatures describing the population of excited electronic energy levels of
metals are found to vary with the excitation energy, roughly between 5000 K for low lying atomic levels to 50.000 K for ionic levels. Metal atoms are
believed to enter the cathode space by sputtering as neutral particles with
low energy. They finally return to the cathode wall or escape by diffusion without being affected by the electric field [20,211. Indeed BRUCE and
HANNAFORD [ 24] found the metal gas (kinetic)temperature to agree with the cathode wall temperature. A Maxwell atomic velocity distribution is therefore
very likely to exist and metal atomic lamp line profiles can consequently yield
the correct gas (kinetic) temperature.
In order to describe the emission intensity, Eq. 9 is usually assumed to hold, although the proportionality constant I_ has no uniform significance
b
[ 2 0 ] P.A.BUEGER and W.SCHEUERMANN, Z. Physik 216, 248 ( 1 9 6 6 ) . [ 2 1 1 P .A.BEUGER and W.FINK, Z. Physik 228, 416 ( 1 9 6 9 ) .
[ 2 2 1 V.P.GOFMEISTER and Y.M. KAGAN,Opt. Speatry 2 5 , 185 ( 1 9 6 8 ) . [ 2 3 ] W.C.KREYE, J. Opt. Soa. Amer. 6 4 , 186 ( 1 9 7 4 ) .
here. In fact each level has its own black-body limit and therefore it is
better to omit the subscript B and use:
I(X) = l''{l-exp[-k(X)nl]} (11)
As in the flame (section 5) I(X) "^ k(X) at low atom density, that means in this case low lamp current. Increasing current causes the profiles I(X) and k(X) to
deviate. The intensity 1(A) initially increases but can never exceed the "blackbody"-limit I .
However, in practice this black-body limit is not reached because before that point the profile has already become deteriorated by self-reversal, visible by the appearance of a decrease in intensity at the central wavelength. Several models have been proposed [25,26] to account for the existence of a
gradient in the excitation temperature. Such calculations usually employ the simple model [12,24,27] which assumes two distinct homogeneous regions to exist, characterized by different values of the product k(A)nl. The second layer does not contribute to the emission and hence the final intensity is given by:
1(A) = I^d-exp [-k(A)nll}-exp[-k'(A)n'l'] (12)
It is clear that the physical significance of this model is very limited, because in practice no distinct layers exist.
7. LITERATURE SURVEY ON PROFILE INFLUENCES.
Since the Introduction of AAS as an analytical tool irf 1955 [ 1 ] , the role of the spectral intensity distribution of the primary source has attracted the
attention of spectroscopists. Several papers have been published [28-30] which deal with the applicability of continuum sources. However, source flicker noise
causes poor limits of detection and the wide bandpass of common monochromators
causes reduced sensitivity and non-linear analytical curves. Proposals [31,32]
[25] R.D.COWAN and G.H.DIEKE, Rev. Mod. Phys. 20, 418 (1948). [28] W.BLEEKER, Z. Physik 52, 808 (1929).
(27 1 H.G.C.HUMAN, Ph.D. Thesis. Pretoria. 1970.
[28 1 V.A.FASSEL, V.G.MOSSOTTI, W.E.L.GROSSMAN and R.N.KNISELEY, Speotrooh-im. Aata 22, 347 (1966).
[29] L.DE GALAN, W.W.McGEE and J.D.WINEFORDNER, Anal. Chim. Aata 3 2 , 436 (1967).
[30] J.H.GIBSON, W.E.L.GROSSMAN and W.D.COOKE, Appl. Speatry 16, 47 (1962). [31] C.VEILLON and P.MERCHANT, Appl. Speatry 27, 361 (1973).
[321 G.J.NITIS, V.SVOBODA and J.D.WINEFORDNER, Speatroahim. Aata 27B, 345 (1972).
to overcome these problems require cumbersome devices and hence are not acceptable in practical AAS. Other authors (27,33 1 investigated the
applicabi-lity of flames as a primary source, thus combining the advantage of continuum
sources (multi-element analysis) with the advantage ot HCL's (narrow lines). Here too, however, detection limits are poor, especially in the U.V. region.
Moreover, the metal density in the primary flame influences the emission profile shape and thus the analytical curve; a higher concentration improves
the detection limit but at the same time reduces sensitivity. The
investi-gations that deal with HCL's as primary sources of radiation are therefore more important for the practice of analytical AAS. A short survey of the most
important studies will be given here.
In one of his early publications, WALSH 11] used an extremely simple model in order to demonstrate the feasibility of AAS as an analytical tool. In this
model the source line is assumed to be infinitely narrow and positioned exactly at the maximum of the absorption coefficient k(0), in the flame, so
that Eq. 5 becomes
A = 0.43k(0)ln
Because of unsufficient knowledge of real profile shapes and because of
limited computer facilities, all early calculations of profile influences are based on line shape models. L'VOV [ 2 1 used a Lorentzian flame absorption
profile to study the consequences of a (shifted) lamp line consisting of two
components. RUBESKA and SVOBODA [34 1 considered the influence of the finite width of the source line, assuming that this line and also the (non-shifted)
absorption profile are Lorentzian shaped; hyperfine structure was supposed to be absent.
An important contribution are the model calculations of VAN GELDER [12 1. This
author successively considered the influence of absorption and
self-reversal in the source line, simple hyperfine structure, light beam geometry in the flame and non-absorbing radiation within the monochromator bandpass.
All these influences were found to contribute to non-linearity of the analytical curve and loss of sensitivity.
The Ph.D. thesis of HUMAN 1271 is devoted to the relation between
analytical sensitivity and conditions of temperature and pressure in the
primary light source. Relative sensitivities were measured with HCL's, high frecuency discharge lamps, flames and an arc and compared with calculated
values, based on two-slab models that account for absorption and
self-[33] C.R.RANN, Speatroahm. Aata 23B, 245, 827 (19B8). [341 I.RUBESKA and V.SVOBODA, Anal. Chim. Aata 32, 253 (1965).
reversal. The author calculated Doppler temperatures between 300 and 600 K from
experimental HCL line profiles. Several years ago YASUDA [35] showed that high HCL currents cause a distortion of the emission profile but the author did not attempt to relate this to changes in absorbance. BRUCE and HANNAFORD [24] used an open hollow cathode to examine the conditions for self-reversal in a
Ca-lamp. Atom densities in an emitting and an absorbing layer (two-slab model) could be calculated. The results were used to calculate analytical curves of calcium, however, without taking the flame line shift into account. This Ca 423 nm line is one of the unique lines whose profile is not influenced by
hyperfine structure. That the presence of hyperfine structure may strongly affect sensitivity was shown by WILLIS [36 1 who calculated the absorbance for several transitions (e.g. Cu 324 nm and Ag 328 n m ) . Because of a lack of experimental data he had to use several approximations, but his results
definitely show that real HCL profiles may cause absorbance values which are two time smaller than those obtained from the WALSH profile model, mentioned at the beginning of this section.
Another approach to the problem of line profile influence was used by L'VOV et al. [37] who evaluated an analytical expression for the calculation of the absorbance in case the hyperfine structure of the transition is known. The assumptions are that the individual components in the lamp line are narrow
in comparison with the flame line (W^LSH model) and that the flame line shift obeys the LINDHOLM theory (38 1 for pure Van der Waals interaction. The
expression slightly overestimates the experimental absorbance observed for low lamp currents and low concentrations. However, an overestimate of 10 percent
at A < 0.2 should be compared with an overestimate of 100 percent in case hyperfine structure and shift are Ignored [361. Of course, the applicability of the L'VOV expression is limited as long as experimental data on ^-values and hyperfine structure are scarce.
The conclusion is that spectral lines certainly influence sensitivity and linearity of the analytical curve as has been demonstrated mainly by model
calculations. However, these model calculations do not provide sufficient information about the magnitude of profile influence in practical cases. The direct measurement of line profiles may therefore provide a link between theory and practice of AAS analysis. , , , •.,,''. . ;
f - - .y,]'^'i [ 3 5 ] K.YASUDA, Anal. Chem. 3 8 , 592 ( 1 9 6 6 ) .
[ 3 6 ] J.B.WILLIS, Speatroahim. Aata 26B, 177 ( 1 9 7 1 ) .
[ 3 7 ] B.V.L'VOV, L.P.KRUGLIKOVA, L.K.POLZIK and D.A.KATSKOV, Speatroahim. Aata. i n p r e s s .
Chapter II
The broadening of spectral lines.
Abstract - The causes of line broadening are discussed. Doppler broadening is shown to exceed the natural width of lines from flames and HCL's by several orders of magnitude. Collision broadening is insignificant in HCL's; hence individual line profiles are about 1 pm wide and Gaussian shaped. In flames, Van der Waals interaction broadening is of the same magnitude as Doppler broadening. The convolution product of the two contributions is a Voigt profile, about 3 pm wide. The profile is shifted to the red when nitrogen is the main flame component. Actual line profiles are often more complex due to the presence of hyperfine structure. The principle of profile measurement through interferometry is briefly discussed.
1. INTRODUCTION
In this chapter the shift and shape of spectral lines will be discussed [1-4]. A spectral line will be considered first as a single, isolated transition free from overlap due to adjacent transitions. Further, we shall assume the source of radiation to be nomogeneous and in thermodynamic equilibrium. The emission intensity is then given by:
1(A) = Ig{l-expl-k(A)nll} (1) In the following sections the influence of the temperature and pressure of a
gas upon the shape of the profile k( A) of an atomic species will be discussed. However, even in the limiting case of T=D. p=0. no infinitely narrow spectral line would be obtained, because the finite duration of a radiation process creates a natural broadening, resulting in a Lorentzian shaped profile k(X) around X :
. ,2
k(A) = k(0) ^ 5 C2)
4(A-A )'^+AA
(1) A.C.G.MITCHELL and M.W.ZEMANSKY, Resonance radiation and excited atoms, Cambridge Univ. Press, 1961.
(21 L.DE GALAN and H.C.WAGENAAR, Meth. Phys. Anal., Sept. 1971. p. 10-31. [3] R.G.BREENE, The shift and shape of spectral lines. Pergamon Press. Oxford.
1961.
[4] J.R.FUHR, W.L.WIESE and L.J.ROSZMAN, Bibliography on atom line shapes and shifts, NBS Special Publ. 366, Washington, 1972.
where AA is the full width at half height of the profile which, for a resonance
transition between states n and m, is related to the transition probability
A through:
nm ^
AA„ = (A^/2irc)A
N nm
o _ .1
Even for values of A as large as 10 s , this natural line width is only
_2 nm ^ •' 10 pm; it will be shown that this is completely negligible in comparison to
the Doppler broadening occurring in flames and HCL's.
2. DOPPLER BROADENING.
A trivial but important reason for line broadening is the variable velocity of radiating particles arising from their thermal motion. Because the absorption coefficient at a wavelength A is proportional to the number of particles with
a specific velocity, the Maxwell velocity distribution yields a Gaussian
profile:
k(A) = k(0)exp{-41n2(A-A^)^/AA^^} (3)
AA is the full width at half height, given by:
AA^ = (81n2«A^jjRT/(Mc^)]^ = 7.16 1 O " ' ' A Q ( T / M ) ^ (4)
In this equation M is the atomic mass. R the universal gas constant and c the speed of light. Within the wavelength range of interest (200-400 nm) we
calculate that the Doppler width is of the order of 1 pm for HCL's (T about 500 K) and 2 pm for flames (T about 2500 K ) . An expression for the peak absorption coefficient k(0) can be found by integrating k(A) over the wave-length and introduction of the oscillator strength f (11 through:
/k(A)dA = Tre^X^f/(mc^) (5)
Hence the maximum of a purely Doppler broadened spectral line is given by:
k(0) = (4TTln2)^'e^X^f/(AA|^mc^) (6)
3. COLLISION BROADENING.
(i) broadening by adiabatio oolliaiona.
Two different theories have been advanced to describe the interaction between
radiating (or absorbing) atoms and surrounding particles [5-8]. The statistical theory considers the average force acting upon the radiating particle, which is
applicable for wavelengths far away from the line centre. For the region around the line centre, that is of primary interest in atomic absorption, the
impact theory provides more reliably results.
This theory considers each encounter between particles as an instantaneous interaction that disturbs the phase of the wave emitted by the radiating atom.
When the variable phase shifts in the wavetrain, resulting from interactions at variable distances, are converted to wavelength variations through a
Fourier analysis [ LINDHOLM, ref. 9] the absorption coefficient is found to be:
A X ^
k(X) = k(Q) 5 ^ (7)
The profile of k(A) is usually denoted as a dispersion or Lorentzian profile
because its shape was first formulated by Lorentz. However, the Lindholm theory also predicts a shift 6 of the complete profile. In flames with a high
nitrogen density (e.g. acetylene with air or N2O), this displacement is found
to be a red shift, thus towards higher wavelength (5 > D ) . By integration of k(A) over the wavelength and insertion of Eq. 5, the peak absorption
coefficient can be found. It yields:
k(0) 2e^X^f/(AX mc^) (8)
where AX is the width of the profile at half height. This width is
proportio-nal to the density of the perturbing particles, thus causing this type of broadening to be much less important in low pressure sources (HCL's) than in
flames. Both the width and the shift 5 depend on the interaction potential which was assumed by Lindholm to be of the form ^ /r , where p is an integer.
Some expressions for the width and shift for various values of p are given in
Table 1. A brief dicsussion will show the order of magnitude in flames and HCL's.
[51 H.MARGENAU, Phys. Rev. 40, 387 (1972).
[6] H. A. LORENTZ, Versl. Amsterdam Aa ad. 14, 518, 577 (1905). [71 E.LINDHOLM, Ph.D. Thesis, Uppsala, 1942.
[8] W.R.HINDMARSH and J.M.FARR, Collision broadening of spectral lines by
neutral atoms. Progress in Quantum Electronics, Vol. 2, Part 3, Pergamon Press, Oxford, 1972.
Table 1. Lindholm's expressions for line shift and line width due to
collision broadening (Eq. 7 ) .
t y p e of I n t e r a c t i o n : c o l l i d i n g p a r t i c l e s : l i n e w i d t h AX l i n e s h i f t & r a t i o 6/AA C P Resonance
S-^
s i m i l a r atoms 2iT^C2NA^/c 0 0 e A f / ( BIT mc) Q u a d r a t i c S t a r kV^'
e l e c t r o n s B . 1 8 C / / V / ^ N A 2 / C 5 . 3 1 C / / 2 V ^ / \ A 2 / C 0.86 <10-^5 cm^ s-^ Van dsr WaalsS-=
a l l 2 . 7 1 C , 2 / V / ^ N A 2 / C D.98C 2 / V / ^ N A 2 / C 0.3B2 M Q - 2 ° cm^ s-^N = concepitration of perturbing particles
V = relative velocity
A = wavelength of the spectral line
c = vacuum velocity of radiation f = oscillator strength
(ii) aollision broadening in flames and HCL's.
The interaction of a radiating atom with other atoms of the same element is known as resonance broadening. If the expression for C is substituted, the
-17
line width at 400 nm is found to be equal to 4'10 'n pm, where n is the atom
density of the radiating element. Now if we aspirate a molar solution at a rate of 0.5 ml/min into a flame with an (expanded) gas flow of 100 1/min, the
15 -3
atom density is found to be 3-10 cm , so that the maximum line width to be expected from resonance broadening is 0.1 pm. This is sufficiently small to be
Ignored [9].
The interaction of a radiating particle with charged particles, notably electrons, is known as Stark broadening. The linear Stark effect is only important for hydrogen lines (and some helium lines). The quadratic Stark effect results from the interaction between charged particles and the dipole
induced in the radiating atom. Unfortunately, there is no general expression
for the constant C in this case, but measurements show that its maximum value
-15 4 7 is about 10 cm /s [10]. With an electron velocity of 10 cm/s at flame
— 1 fi
temperature, the width of a line at 400 nm is then calculated as 10 -n ,pm.
13 -3 ^ As the electron density in a flame is less than 10 cm , Stark broadening is
17 -3 insignificant in flames. In a HCL the total particle density is about 10 cm (for a pressure of 0.01 a t ) . As it is not to be expected that the electrons
constitute more than 1% of the total density, it can be concluded that Stark broadening is also negligible in HCL's [11].
The most important interaction of a radiating particle in a gaseous medium is the Van der Waals interaction between neutral atoms. Although it is
possible to derive an approximate expression for the factor C., this is of b
little help, since the parameters are generally unknown. Again, experiments show [8] that C„ is of the order of 10 cm s , so that with an atomic
5^ -1
velocity of 10 cm s at flame temperatures the width of a line at 400 nm is -18
calculated as 10 -n pm.
17 -3
In HCL's the total particle density is 10 cm at most, so that again the
collision broadening is negligible in comparison to the Doppler-broadening.
We conclude, therefore, that the spectral lines from HCL's are only subject to Doppler broadening and the absorption coefficient is given by Eq. 3. However,
in flames at atmospheric pressure the total particle density is about
i fl — 3
3.10 cm , so that the line width due to Van der Waals broadening is about
2 pm, which is fully comparable to the Doppler width found in the preceding section. The line shift due to Van der Waals interaction in flames is 0.36 times the line width. Experimental ratios from flames supported by air or (\l2D
[this thesis, also 12,13] are often somewhat lower but still of the same sign
which indicates a shift to the red side of the spectrum.
(ill) broadening by quenching collisions.
De-excitation erf metal atoms in flames may proceed during collisions by
transfer of excitation energy to the colliding partner. These quenching
collisions result in a reduction of the mean lifetime of excited states and
hence in line broadening [14]. The consequence is a Lorentz distribution of
k(A) (Eq. 2) and perhaps a width-to-shift ratio similar to those for Van der
[11] C.F.BRUCE and P.HANNAFORD, Speatroahim. Acta 26B, 207 (1971). [12] TJ.HOLLANDER, B.J.JANSEN, J.J.PLAAT and C.TH.J.ALKEMADE, J. Quant.
Speatry. Radiat. Transfer 10, 1301 (1970).
[13] B.V.L'VOV, L.P.KRUGLIKOVA, L.K.POLZIK and D.A.KATSKOV, Speatroahim. Aata. in press.
Waals interaction. The efficiency of the quenching process depends strongly on the internal degrees of freedom of the collision partners. If the colliding particles are mainly molecules like nitrogen, these quenching processes are
strongly favoured [15,16]. Because quenching and radiative de-excitation are competing processes, the quenching contribution to the line width, AA , is
U related to the yield factor of resonance fluorescence Y [12] through:
^ ^ N ^ % = 2 ^ Y f95
If Y = 1, no quenching takes place and Eq. 9 becomes equal to Eq. 7. In atmospheric acetylene flames Y may be as low as 0.1 however, and in that case the line broadening due to quenching cannot be neglected [15,171.
The term AA will therefore be used to indicate the overall collision width, thus including an (unknown) contribution of quenching collisions
(actually plus natural broadening):
AA^ = A A ^ . A A ^ . A A ^ , AA^ . A A^ (10)
4. THE VOIGT PROFILE.
If Doppler broadening and collision broadening both contribute to the profile. and if these mechanisms act independently, the resulting profile is the
convolution product of these contributions, usually denoted as Voigt profile:
k(A) = f ^ k''(A')k^(A-A')dA' (11)
J -co
G L
k (A) and k (A) are the absorption coefficient for Doppler and collision broadening (Eq.'s 3 and 7) respectively. The final expression is simplified by
some substitutions: a = AA /(2S), y = (A'-A„)/3 and v = (A-A -6)/B where c U u g = AX /(2/Tn2), resulting in:
k(A) = k(0)H(a,v) = k(0) f /:: "^P'"^'^^^ (12) a +(v-y)
where k(0). the peak absorption coefficient, is again given by Eq. 6. Thus the profile of the absorption coefficient is determined entirely by the Voigt
[15] C.TH.J.ALKEMADE and P.J.TH.ZEEGERS, Excitation and de-excitation
processes in flames, chapter in Spectrochemical Methods of Analysis,
J.D.Winefordner ed., John Wiley, New York, 1971.
[16] P.L.LIJNSE, Ph.D. Thesis, Utrecht, 1974.
[17] S.J.PEARCE, L.DE GALAN and J.D.WINEFORDNER, Speatroahim. Aata 23B, 793 (1968).
function H(a,v) (Fig. 1 ) . It should be emphasized however, that this function
can not be trusted for the wings of the line profile. As stated, the
convolution implies that the broadening mechanisms act independently. This is not strictly true because Doppler broadening and Van der Waals broadening
both depend on the particle velocity. The actual profile is therefore no longer symmetric [12,18]. However, MIZUSHIMA [19] has shown that this
inter-dependence may be ignored for the central portion of the profile, so that for
the present purpose Eq. 12 is still a good representation (20l.
H(av)
a-vatue v-value
Fig. 1. The Voigt profile H(a,v) as a function of a and v. (Eq. 12).
The Voigt function (Fig. 1) can be used to draw three conclusions:
(1) For a = 0 collision broadening is absent and the profile is identical to the Doppler profile (Eq. 3 ) . With increasing contribution of collision
broadening, the maximum value of the absorption coefficient decreases ' according to:
k(Q)H(a,D) = k(O)H(0,D)exp(a )erfc(a) (13)
where erfc(a) represents the complement error function between 0 and a.
(11) Simultaneously, the width of the profile, AA,, increases, approximately
according to [ 121 :
[18] P.R.BERMAN, J. Quant. Speatry. Radiat. Transfer 12, 1331 (1972). [19] M.MIZUSHIMA, J. Quant. Speatry. Radiat. Transfer 7, 505 (1967).
AX^ = ^ A X ^ . [ ( ^ ) 2 . A X ^ 2 ] ^ (14)
(ill) The relation between the intensity of an emission line 1(A) and the
absorption coefficient is, of course, still given by Eq. 1, thus:
1(A) = I„{l-exp[-k(0)nlH(a,v)l} (15)
Only at low atom density, the profiles I(X) and H(a,v) are identical
(no self-absorption broadening); in that case A X represents the width of the emission profile.
5. BROADENING BY HYPERFINE STRUCTURE
Up to here a spectral line was considered to arise from a single transition. When spectral lines are experimentally observed under high resolution,
however, they often show a composite structure of many lines close together. This phenomenon, denoted as hyperfine structure, can be traced back to the Influence of the atomic nucleus either through its magnetic properties,
characterized by a nuclear spin, or through its mass and volume (isotope shift).
(i) Hyperfine structure due to nuclear spin,
About one third of the stable atomic nuclei have an even number of neutrons and an even number of protons. These nuclei do not possess magnetic properties
and, hence, have a nuclear spin zero. The remaining two third of the stable
atomic nuclei have either an odd number of neutrons or an odd number of protons and possess magnetic properties characterized by a non-zero nuclear
spin quantum number I. The coupling of I with the angular quantum number J gives rise to 21 + 1 or 2J + 1 energy levels (depending on whether I or J is
smaller) specified by a quantum number F.
If the splitting is due purely to magnetic interaction the spacing between adjacent hyperfine levels increases linearly with the F-value of the upper
level (Lande's interval rule), the highest level generally having the highest F-number. If, however, the nuclear spin is greater than \. the nucleus may also have an electric quadrupole moment that can either enhance or oppose the
magnetic splitting, giving rise to minor deviations from the interval rule. The number of hyperfine levels and the number of allowed transitions, derived
from the selection rule AF = 0 or ±1, are unaffected, however.
The relative intensities of hyperfine transitions usually follow the predictions based on Russel-Saunders coupling remarkably well, so that they
®
i = % 0130cm-' - I — 0171 0209 1 tOpmFig. 2. Examples of two relatively large hyperfine splitting patterns.
a) In 410 nm b) Hg 405 nm.
can be derived from the expressions or the tables given in textbooks [211 for normal multiplet transitions by substituting J for L, I for S and F for J. An
115
example is given in fig. 2a, where the resonance line of In is seen to
consist of four hyperfine transitions with relative intensities agreeing with theoretical predictions (100 : 65 : 35 : 100) within the experimental
precision. It is clear that the overall intensity profile of the indium line cannot even be approximated by a Voigt-proflie. Indeed, the line broadening
theory outlined in the preceding sections should be applied to each individual
hyperfine transition separately, whereafter the results may be summed. Since
in Eq. 15 the absorption coefficients must be summed rather than the
intensities, this summation is by no means straightforward in the presence of self-absorption. Thus in case N hyperfine components contribute to the
ultimate profile, Eq. 15 should be replaced by:
21] C.CANDLER, Atomic Spectra and the vector model, Hilger and Watts, London,
N
1(A) = I„{l-exp(-ZkJO)nlH(a.v)]} (16)
Unfortunately, the magnitude of hyperfine splitting cannot be easily
predicted. It depends upon the element and. moreover, upon the transition under consideration. The unequal splitting of the two levels in Fig. 2a forms
an illustrative example. This means that for each transition resource must be
made to studies on hyperfine splitting [4,22,23].
(ii) Hyperfine structure due to isotope shift.
The example of indium is relatively simple since this element consists 115 predominantly of one isotope, the natural composition being 96-5 In and
113
4% In. If, however, an element contains several isotopes in appreciable quantities, a further splitting may be observed since transitions of different
isotopes are mutually displaced.
Isotope shift due to the nuclear mass can be expressed as:
where AA is the wavelength difference for a transition with a wavelength A
between two isotopes with masses M, and M in atomic mass units. When q=1, we have the normal mass effect that displaces the transition of the heavier
isotope towards shorter wavelengths. It is readily seen that the normal mass effect becomes negligibly small for nuclear masses exceeding 30 AMU. In
addition, however, there is a specific mass effect of either positive or
negative sign and of variable magnitude. For transitions involving d-electrons (transition elements) q may range from -20 to +16. For alkali-like
transitions, on the other hand, the specific mass effect is comparable to the normal mass effect. Consequently, the isotope shift due to nuclear mass
effects depends upon the transition involved, although it can usually be
ignored for nuclear masses greater than 150 AMU.
A second cause for Isotope shifts is the nuclear volume effect. When a neutron is added to an atomic nucleus, its charge is distrubuted over a larger
[22] C.E.MOORE, Bibliography on the analysis of optical atomic spectra.
Vol. I-IV, NBS, Washington, 1969.
[23] A.STEUDEL, Optical hyperfine measurements. Chapter in Hyperfine
Interactions, A.J.FREEMAN and R.B.FRANKEL eds.. Academic Press, New York,
volume and the attraction of s-electrons is slightly decreased. Hence, the volume effect is appreciable for transitions involving a jump of an s-electron
and the resulting isotope shift can be of either sign. The volume effect is
negligible for light elements (M < 60 AMU), but it is predominant for heavy elements (M > ISO AMU). For example, for the two indium isotopes the isotope
shift due to the normal mass effect is calculated as 0.03 pm and the specific mass effect is expected to be of the same order of magnitude. The experimental
value of 0.2 pm reported by Jackson [24] is about six times larger,
illustra-ting the influence of the volume effect. Still, this shift is much too small to be noticeable in the spectrum of fig. 2.
An example of the complex pattern obtained when both hyperfine splitting and several isotope shifts are present is shown in fig. 2b for the mercury line at
405 nm [251. ThxS element has six stable isotopes in appreciable quantities,
two of which have an odd number of neutrons and hence show hyperfine splitting. In the spectrum of an ordinary low pressure mercury lamp the
Doppler broadening is such (AA = 0 . 5 pm) that the transitions of the even isotopes cannot be resolved, since their mutual separation is only 0.5 pm.
The hyperfine splitting, however, is much larger, so that all transitions of
the odd isotopes can be resolved.
6. THE INTERFEROMETRIC MEASUREMENT OF LINE PROFILES.
The data in the preceding sections show that flame lines are generally between
3 and 5 pm wide, while HCL lines are often not wider than 1 pm. Undistorted
recording of such profiles is only possible if a spectrometer with a resolution of 0.1 pm is used. Normal grating monochromators fail here; they
integrate radiation over a bandwidth of 5 pm at best. In this section the applicability of the Fabry-Perot interferometer is discussed, its principle of
operation and its limitations [26-28]. Further details about the specific
interferometer used in this investigation can be found in the introductory section of Chapters III-VI.
The principle of operation is shown in fig. 3. An incident ray is reflected
back and forth between two perfectly plane, parallel quartz plates, the inner
[24] D.A.JACKSON, J. Phys. Rad. 18, 459 (1957).
[25 1 D.H.RANK, G.SKORINO, D.P.EASTMAN, G.D.SAKSENA, T.K.McCUBBIN and T.A.WIGGINS, J. Opt. Soa. Amer. 50, 1045 ( 1 9 6 0 ) .
[261 P.JACQUINOT, Rep. Progr. Physics 2 3 , 267 ( 1 9 6 0 ) . [ 2 7 ] R.CHABBAL, J. Reah. C.N.R.S. 2 4 , 137 ( 1 9 5 3 ) .
Fig. 3. Principle of Fabry-Perot interferometry
sides of which are coated with a highly reflective material. The optical path difference between two successively transmitted rays is given by 2ndcosi
where n is the refractive index of the medium between the plates, d is their separation and i is the angle of incidence. In practice, i is very nearly equal to zero and the transmitted rays interfere constructively if
2nd = pA (16)
where p is a whole number, the order of interference.
The interferometer can be characterized by three quantities: the transmittance
T, the free spectral range 0 and the finesse F. Ideally radiation of wave-length A is transmitted at full intensity as soon as Eq. 18 is obeyed. Because of some residual absorption, however, the actual transmittance is less than one and given by T = (1-A/(1-R)] where A and R are the coefficients of
absorption and reflection. The free spectral range 0, is the difference
between wavelengths (A and A-D), transmitted in two successive orders. It 2
follows from Eq. 18 that D = A /2nd.
The resolution of the interferometer A S, is equal to the free spectral
range divided by the finesse F(AS = D/F), so that the resolving power of the interferometer can be increased by either decreasing D or by increasing F. In
practice, the finesse is predominantly limited by the reflection coefficient
of the plate coating and equal to F = IT/R/(1-R) as long as other
contributions are absent. The instrument profile is then described by an
Airy-function A( A) [271. )}c^\ :..<'•..'•:.' '-'•••- '•^''•-'
In the blue region of the spectrum multilayer coatings provide reflection
finesses of about 60 (R=0.95) with a transmittance of 0.2 (A=0.Q3) over a
100-cc
IL 0) 0r
>^c
0
4-<o
(D
>*-n>
cc
8 0
6 0
4 0
2 0
: \ \'Y
\ / /y
useful 1-N
range{
\ iN .
V
Hi.o
0.8 ^
0.6 3
0)0.4 5
o
320
360 400 440
W a v e l e n g t h , n m
-0.2
480
Fig. 4. The transmittance T and reflection finesse F„ of interferometer
plates for the region around 400 nm.
2 9 0
310 330 350
W a v e l e n g t h , n m
370
Fig. 5. The ultimate finesse Fy and Voigt a-values of the instrument
available that provide acceptible finesse and transmittance below 300 nm. Other contributions to the instrument function are: imperfect flatness or adjustment of the plates and the finite width of the circular aperture at the
focal plane (Fig. 3 ) . If these contributions are denoted by P(A) and 0(A), the ultimate instrument function is the convolution product:
S(A) = A(A) « P(A) « 0(A) (18)
The ultimate finesse is of course lower than each of the finesse values which can be attributed to the individual contributions A(A), P(A) and 0(A). Fig. 4 shows the values of T and F versus wavelength for one of the two sets of
plates which were used in the present investigation. The plots are calculated from experimental values of R and A. By limiting the working range to some 75 nm, a reflection finesse better than 50 was always maintained. The ultimate
finesse was found to be 60 at 404 nm and 40 at 435 nm. These data were 1 98
obtained by recording Hg lines (each only 0.4 pm wide) from a discharge
lamp with an interferometer plate separation of 1.0 mm. (note that in that case the instrument profile width exceeds the Hg-line width about four
times.
Fig. 5 shows the change of the ultimate finesse F with wavelength for the
second set of plates. The data were again obtained by recording H g ^ ° lines at small plate separation. The profiles of S(A) were found to closely resemble a Voigt profile (Eq. 1 2 ) . The a-values of these profiles show an increasing Lorentz contribution towards the limits of the useful range.
Close to the centre of this range the instrumental distortion of a true profile 1(A) is insignificant, but at the limits the observed profile (t)(A) starts to deviate from 1(A) according to the convolution (()(A) = S(A) » 1(A).
It is here that the importance of a high finesse becomes manifest. On the one hand, the free spectral range must be chosen large enough to contain the complete line profile, so that D exceeds the line width 3-5 times, or even more if pronounced hyperfine structure is present. On the other hand, the
width of the instrument function S(A) must be almost one order of magnitude smaller than the line width to avoid instrumental distortion. Consequently, the (ultimate) finesse F = D/S, must be better than 20. Hence, the applica-bility of the U.V. set of plates (Fig. 5) is restricted to 31D-34D nm. Outside
this range the finesse is too low and true profiles can only be obtained by deconvolution [29]. The first set of plates (Fig. 4) is applicable from
370 nm to about 450 nm if we require that individual contributions such as F K must be at least two times the ultimate value F .
u
Chapter III
Interferometric measurements of atomic line profiles emitted by
hollow-cathode lamps and by an acetylene-nitrous oxide flame *
Abstract—Source line profiles for eighteen a t o m i c t r a n s i t i o n s of n i n e e l e m e n t s e m i t t e d
bj-l o w - c u r r e n t hobj-lbj-low-cathode bj-l a m p s a n d b y a n a c o t y bj-l o n e - n i t r o u s oxide fbj-lame h a v e been m e a s u r e d w i t h a F a b r ^ r - P e r o t i n t e r f e r o m e t e r . D i s t o r t i o n s c a u s e d b y i n s t r u m e n t b r o a d e n i n g a r e s h o w n t o be neghgible. C o n t r i b u t i o n of self-absorption t o t h e profile w i d t h s is e s t i m a t e d . I n n e a r l y all cases hyperfine s t r u c t u r e h a s a decisive influence u p o n t h e o b s e r v e d profile. F o r t h i r t e e n t r a n s i t i o n s of k n o w n hyperfine s t r u c t u r e t h e e x p e r i m e n t a l c u r v e s a r e c o m p a r e d w i t h c o m p u t e r s i m u l a t e d s p e c t r a using G a u s s i a n functions t o d e r i v e t h e D o p p l e r t e m p e r a t u r e of hollow-c a t h o d e lines a n d Voigt funhollow-ctions t o hollow-calhollow-culate t h e hollow-collision b r o a d e n i n g of flame lines. T h e results s h o w t h a t t h e D o p p l e r t e m p e r a t u r e s of h o l l o w - c a t h o d e lines r a n g e from 400 t o 700°K, t h a t flame lines a r e significantly shifted t o t h e r e d a n d t h a t collision b r o a d e n i n g in t h e flame is fully c o m p a r a b l e t o D o p p l e r b r o a d e n i n g , i.e. t h e o - p a r a m e t e r varies b e t w e e n 0-5 a n d 1-5.
1. INTRODUCTION
T H E PROFILE of atomic spectral lines is of interest in atomic absorption
spectrom-etry. The relative position and shape of the hollow-cathode emission line and the flame absorption line influence the sensitivity of the determination [1-5] and may be a cause of bending of the analytical curve, as has been shown by model calculations [5-7]. Previous information of spectral line profiles in flames has been derived mainty from curve of growth measurements, either in emission [8-10], in absorption [11, 12] or in fluorescence [13]. The major advantage of this technique is its simplicity, both in instrumentation and in the interpretation of the data. I t is, however, an indirect technique and it cannot verify the basic assumption t h a t the line profile can be described by a Voigt function. Also, it cannot measure line shifts or hyperfine structure, which will be shown to be of major importance [2],
[1] C. F . B R U C E , P . H A X N A F O R D , Spectrochim. Acta 2 6 B , 207 (1971). [2] J . B . Vi'ii.i.is, Spectrochim. Acta 26B, 177 (1971).
[3] C. S. R A N N , Spectrochim. Acta 2 3 B , 827 (1968).
[4] L . DE G.AiAN, G. F . S A M A E Y , Anal. Chim. Acta 5 0 , 39 (1970). [5] H . P R U G G E R , Optik 2 1 , 320 (1964).
[6] I. RuBESK-\, V. SvoBODA, Anal. Chim. Acta 3 2 , 253 (1965). [7] Z. VAN G E L D E R , Spectrochim. Acta 25B, 669 (1970). [8] E . HiNNOV, H . KOHN, J. Opt. Soc. Am. 4 7 , 151, 156 (1957). [9] F . W . HoFMANN, H . KoHN, J. Opt. Soc. Am. 5 1 , 512 (1961).
[10] C. VAN T R I G T , T . H O L L A N D E R , C . T . J . A L K E M A D E , J. Quant. Spectr. Radiative Transfer 5, 813 (1965).
[11] W . W . M C G E E , J . D . A V I N E F O R D N E R , J. Quant. Spectr. Radiative Transfer 7, 261 (1967). [12] R . F . B R O W K E R , .1. D . W I N E F O R D N E R , Anal. Chem. 4 4 , 247 (1972).
[13] \V. P . TOWNSEND, D . S. S-MYLY, P . J . T . Z E E G E R S , V . SvOBODA, J . D . WlNEFORDNEK, Spectrochim. Ada 2 6 B , 595 (1971).
"A reprint of H.C.WAGENAAR and L. DE GALAN, Spectrochim.Acta 23B, 157 [1973].
Complete flame line profiles, including shift and asymmetry, have been measured b y Zeeman scanning techniques in order t o calculate collisional interac-tion potentials in flames [14-16]. This technique is greatly complicated by hyper-fine structure in t h e background-sources and is, therefore, of limited applicability.
Direct interferometric measurement of atomic line profiles has been used widely for sources of radiation not amenable to t h e former two techniques, such as arcs [17], transient sources [18] and hollow-cathode lamps [1, 19-22]. I t has found surprisingly little application for flame lines [23]. This technique has t h e advantages of being generally applicable and yielding complete line profiles including line shift and hyperfine structure.
The main disadvantage is t h a t in order to achieve a high resolving power, one pair of interferometer plates can be used over a limited wavelength region only. I t was therefore decided in t h e present study t o measure t h e source line profile of eighteen atomic spectral lines of analytical interest with wavelengths around 400 nm. The sources studied were selected for their interest in analytical atomic absorption spectrometry: commercially available hollow-cathode lamps and a laminar, non-shielded acetylene-nitrous oxide flame generated on a slot burner.
2. T H E O R Y
The theory of atomic spectral lines has been extensively covered in several textbooks [24-26] and t h e essential features have been reviewed in a previous article [27] , which also discusses the measuring techniques mentioned above. For the purpose of this study t h e following conclusions m a y be summarized.
(i) A spectral transition used in atomic absorption spectrometry generally consists of several hyperfine components due t o isotope shift and nuclear spin effects.
(ii) T h e relative intensities of t h e hyperfine components can be predicted from theory, b u t t h e relative positions cannot be predicted a n d are frequently unknown.
[14] H. F . VAN H B E K , Spectrochim. Acta 25B, 107 (1970).
[15] T. HOLLANDER, H . P . BBOIDA, Combust. Flame 13, 63 (1969).
[16] T. HOLLANDER, B . J . JANSEN, J . J . PLAAT, C . T . J . ALKEMADE, J. Quant. Spectr. Radiative Transfer IQ, 1301 (1970).
[17] K. BEROSTEDT, Z. Physik 155, 23 (1959).
[18] G. F . KiBKBBiGHT, M. SABGBNT, Spectrochim. Acta 25B, 577 (1970). [19] K. YASUDA, Anal Chem. 38, 592 (1966).
[20] D. K. DAVIES, J. Appl. Phys. 38, 4713 (1967).
[21] H. G. C. HUMAN, L . R . P . BUTLER, Spectrochim. Acta 25B, 647 (1970).
[22] W. C. K K E E G E , F . L . R O E S L E B , J. Opt. Soc. Am. 60, 1100 (1970).
[23] W. BEHMENBUBG, J. Quant. Spectr. Radiative Transfer 4, 177 (1964).
[24] R . G . B E E E N E , Jr., The shift and shape of spectral lines. Pergamon Press, Oxford (1961). [25] A. UNSOLD, Physik der Sternatmospharen, 2nd edition, Springer, Berlin (1968).
[26] A. C. G. MITCHELL, M . W . ZEMANSKY, Resonance radiation and excited atoms. Cambridge University Press (1961).
[27] L. DE GALAN, H . C . WAGENAAR, Meth. Phys. Anal., Sept. 1971, p . 10-31 (special issue with t h e plenary lectures of the 3rd atomic absorption congress, Paris 1971).
