JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL. 9 131 Theoretical and Practical Limits in Atomic Spectroscopy* Plenary Lecture J. D. Winefordner G. A. Petrucci C. L. Stevenson7 and B. W. Smith Department of Chemistry University of Florida Gainesville FL 3261 1 USA Theoretical expressions are given for the efficiency of detection and the efficiency of measurement for several atomic methods including atomic absorption atomic emission atomic ionization atomic fluor- escence and mass spectrometry where flames plasmas and furnaces are used to produce atoms or ions and in some cases excited atoms and ions. These unique expressions are then used with noise expressions to develop detection limit expressions. Assuming reasonable values of instrumental and spectroscopic parameters efficiencies of detection and measurement and detection limit of atoms in the sample are estimated to within an order of magnitude.Several methods have the capability of being single atom measurement approaches and therefore potentially useful for atom counting. Considerable discussion of noise sources and a comparison of atomic methods with respect to a variety of analytical figures of merit are given. The present fundamental approach is used to predict the future potential of various atomic methods. Keywords Atomic spectroscopy; efficiency of detection; efficiency of measurement; limit of detection; limit of guarantee; shot noise flicker noise The ability to detect atoms1 of a given element in analytical chemistry is largely governed by the signal-to-noise (S/N) ratio of the measurement.Kaiser’72 was the most influential scientist in elevating the limit of detection (LOD) and the limit of guarantee of purity (LOG) to a firm foundation based upon statistical concepts. The LOD corresponds to an S/N=3 and the LOG to an S/N=6. The limit of quantitation (LOQ) corresponds to an S/N= 10. The reciprocal of S/N times 100 is the percentage relative standard deviation (%RSD) of the measurement. The LOD has a low probability of false positives (type I error) 0.14% but a high probability of false negatives (type I1 error) 50% whereas the LOG a more conservative analytical figure of merit has very low probability of a false positive below 0.14% and a low probability of a false negative about 0.14%. In this paper a review or discussion of the statistical concepts of LOD LOG and LOQ will not be given since these have been thoroughly discussed by Kaiser3 and by the present group of but rather the major analytical figures of merit that limit the LOD and LOG will be discussed.These are the efficiency of detection (Ed) and the efficiency of measurement (E,) of the most prominent and/or potentially most analytically useful atomic methods. In addition there will be a discussion of critical background noise sources in each atomic method and how these background and noise levels affect the LOD and LOG and estimations of Ed E the critical noises and the limiting detectable numbers and concen- trations of species. A synopsis will also be given of the atomic methods in terms of their overall detection powers their use in counting atoms their use in analytical chemistry and a biased view of the future of these techniques in analytical chemistry.A glossary of all parameters their definitions and units is given in Appendix I and a definition of all acronyms in Appendix 11. Analytical Figures of Merit Spectral Selectivity Spectral selectivity is not generally an analytical figure of merit although and Fujiwara et aL7 have developed quanti- * Prepared for presentation at the XXVIII Colloquim Spectroscopicurn Internationale (CSI) York UK June 29-July 4,1993. t Present address Advanced Monitoring Development Group Health and Safety Research Div. Oak Ridge National Laboratory Oak Ridge TN 37831-6101 USA. 1 The term atom will be used throughout even though the detected species could be atoms or ions.tative approaches for it. In this paper spectral selectivity will be discussed on a qualitative basis. All atomic methods have inherently high spectral selectivities atomic emission being the poorest and atomic absorption slightly better. Atomic ioniz- ation methods with single-wavelength excitation are somewhat better but are surpassed still by atomic ionization with two- wavelength (two colour) excitation atomic fluorescence with single wavelength excitation and atomic mass spectrometric methods the last three being nearly equivalent. Atomic fluor- escence with two colour excitation has the highest spectral selectivity. The assignment of this order is based on the complexity of the spectrum of each element and the number of independent excitation and/or measurement steps.Efficiency of Detection &d The efficiency of detection first coined by Alkemade8*9 in landmark papers was defined as the probability that a given atom appearing in the probed volume produced an event during the probing time. Since Alkemade was only referring to laser induced fluorescence and laser induced ionization techniques the probed volume was the effective volume irradiated by the laser and ‘observed’ by the detector and the probing time was the duration of a single laser pulse. In addition Alkemade was concerned only with detecting atoms in the absence of extrinsic noise sources. In the present paper the efficiency of detection’@’’ will be defined more generally to include atomic emission atomic absorption and mass spectrometric methods as well as laser induced fluorescence/ionization and will also take into account the presence of extrinsic noise.Therefore the efficiency of detection Ed will be defined here as the probability that a given atom appearing in the probed (measured) volume produces a signal that is detected above the background noise (if any) during the residence time of the atom within the observation region. Note that this definition differs from Alkemade’s in two important aspects (i) &d is defined with respect to a residence time of the atom in the detection volume not simply over a single ‘probing’ of the laser; and (ii) Ed takes into account the need to detect counts due to analyte atoms over the back- ground noise. Thus &d is the probability that a single atom in the detection volume produces a sufficient number of counts to give a signal above the detection limit X,.Efficiency of Measurement E The overall efficiency of meas~rement,~*~’~ E is defined as the probability that a given atom in the sample is detected above132 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL. 9 the background noise in the 'observation' region and so is the counts per atom in the sample per residence time and is also dimensionless. Unlike Ed the value of E is related to analyte concentration in the sample since it accounts for analyte atom losses between the sample and the detection region and for insufficient spatial and temporal probing of the analyte atoms as they appear within the detection volume.The relationship between E and Ed is given"." by Em = EIEVEa,i&TEsEtEd (1) where is the sample introduction efficiency which is less than unity for continuous sample introduction systems such as nebulization of a sample solution into a spray chamber; cV is the sample matrix vaporization efficiency which accounts for vaporization of desolvated particles in nebulization systems and vaporization of solids in systems using discrete samples such as furnaces; &a,i is the efficiency (also called free atom or free ion fraction) of atomization or ionization depending upon the measurement method; E~ is the transport efficiency of the analyte atoms to the detection system; E is the spatial probing efficiency accounting for the fraction of analyte signal being spatially measured; and E is the temporal probing efficiency accounting for the fraction of analyte species within the detection region during interaction with the laser.All efficiencies are dimensionless. The first three efficiencies E E ~ E ~ can be sample and analyte matrix dependent but in the estimations of order of magnitude of values of E no attempt will be made to include sample specific conditions. The fourth and fifth terms E ~ E ~ depend primarily upon how well the observation system views the process spatially and how well the analyte is temporally observed; for example in a pulsed laser fluorescence or ionization experiment it is possible only one in every 100 analyte species is detected with a low repetition rate pulsed laser yielding an E of 1 x Background Noise and Detection Limits Noise is certainly not an analytical figure of merit but does directly affect the LOD LOG and precision and so will be considered in this section.Noise in a measurement can be c l a ~ s i f i e d ~ ~ ~ ~ ~ ~ ' ' as either extrinsic or intrinsic. Extrinsic noise8.9~1s17 is the noise which arises owing to a non-specific background signal that is present even in the absence of analyte. Extrinsic noise sources include for example dark current source light scatter background emission and non- selective detection of atoms/ions in the blank and are generally classified as shot and flicker noises. In a counting experiment it could be possible to reduce all extrinsic noise sources to the extent that the probability of registering one or more counts from the blank is negligible during the measurement time. For such measurement the only noise on the signal is due to the statistical nature of the analyte detection process itself; this is intrinsic noise.Intrinsic noise arises from such sources as the varying number of atoms within the detection region during the measurement and shot noise in analyte signal production. As intrinsic noise arises from the detection of analyte atoms it cannot be removed. Signal noise in extrinsic-limited measurements is due to contri- butions from both extrinsic and intrinsic noise. Since there are no background counts at the intrinsic limit it can be assumed that every count is due to the presence of analyte atoms in the detection region. Thus at the intrinsic noise limit the value of Ed is simply the probability that an atom appearing within the detection volume will produce at least one count.The detection efficiency at the intrinsic limit is a special case and will be denoted by the symbol &do. Likewise E,' is defined as the probability that any analyte atom in the sample will produce one or more counts and can be calculated by using cdo in eqn. (1). The values of Ed' and 8,' are characteristic figures of merit of an analytical method and will be called the intrinsic detection (&do) and measurement (E,,.,') efficiencies. They represent the capability of analyte atoms to produce signal counts regardless of the noise level. Thus while the values of Ed and E provide a means of determining the capability of a method to detect single atoms above the current background noise level (see Appendix 111) the values of &do and E,' allow for a comparison of the signal production probabilities of various analytical methods (independent of the noise level). At the intrinsic limit any detected event is due to the presence of analyte atoms.At a given analyte sensitivity as the noise level increases (owing to extrinsic noise sources) &d will fall below &do and E will correspondingly fall below E,'. This occurs for extrinsic-limited measurements because it is not possible to determine whether a given count is due to analyte signal or extrinsic noise. However with detection techniques which use non-destructive detection (e.g. resonance fluorescence) it is possible that a single atom can give rise to more than one count.For such techniques it is still possible to detect the presence of single atoms in the detection region in the extrinsic noise limit case if the sensitivity (in counts per atoms) is high enough. Destructive techniques like those involving ionization or those involving traps in fluorescence processes can give rise to only one count per atom. The sensitivity Y required to detect single atoms using non- destructive detection at various mean blank signal levels is given in Table 1. Note that for destructive techniques such as mass spectrometry r/( 1 count per atom)=&d' and single atom detection (SAD) is only possible at the intrinsic limit. The second column of Table 1 gives the sensitivity necessary to give a signal probability distribution centered on the signal detection limit Xd (assuming a Poisson distribution).' At this sensitivity it could be claimed that a limit of detection of a single atom is achieved.However this claim might be mislead- ing although single atoms can be detected there is a high probability (approximately 0.5) that atoms passing through the detection region are not detected. A technique which is capable of true SAD as defined by Alkemadesi9 and by the present group of will be capable of detecting each and every atom that passes through the detection region; this corresponds to &d z 1. The necessary sensitivities for non- destructive detection are given in the third column. Destructive detection can only achieve SAD at the intrinsic (LOD) limit with Y z 1 count per atom. More details of SAD theory can be found in refs.10-12. Table 1 Two limits for an SAD experiment. Distribution of back- ground and signal counts assumed to follow a Poisson distributionlG12 Mean blank level/ counts 0.00 0.05 0.25 1 .oo 5.00 10.00 100.00 Y (mean sensitivity)/counts per atom LOD= 1 atom* a G0.0014 1 2 4 5 9 12 32(30)f LOG= 1 atom? p~0.0014 6.6 8.9 12.4 15 23 29 (69)$ * This column gives the mean sensitivity necessary to produce a signal distribution centered at the signal detection limit Xd.10-12 At LOD the probability of false positives a is low but there is a relatively high probability (approximately 0.5) of false negatives p. t This column gives the mean sensitivity required to reduce the false negative probability p to an acceptable level.Note that LOG = 1 atom is necessary to achieve single atom detection (SAD) which is defined as the capability of detecting each and every atom which passes through the detection volume.'0-'2 f The values in parentheses were found by assuming a Gaussian distribution with the appropriate LY and p values. At these higher signal levels the Poisson distribution can be approximated by a Gaussian distribution with p = c2.133 JOURNAL O F ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL. 9 Atomic Methods The atomic methods to be compared in this paper are the following optical emission spectrometry13J4 (OES) in flames (F) and inductively coupled plasmas (ICP); atomic absorption spe~trometryl~.'~ (AAS) in flames and electrothermal atomiz- ers (ETA); laser induced fluorescence spectr~rnetry'~-'~ (LIFS) in flames inductively coupled plasmas glow discharges (GD) electrothermal atomizers and atomic beams (AB); laser induced ionization s p e c t r ~ m e t r y l ~ - ~ ~ J ~ ~ ~ ~ (LIIS) in flames and in flames with introduction by electrothermal vaporization (ETV); res- onance ionization spectromet ry20-24 (RIS) in atomic beams and atomic mass s p e c t r ~ m e t r y ' ~ ~ ~ - ~ ~ (MS) with sample intro- duction via an ICP a GD or an AB.The symbolism for electrothermal vaporization of a sample into a flame with two colour (TC) (two different excitation wavelengths) excitation of laser induced ionization spectrometry would be ETV-F-TC- LIIS. Other combinations result by similarly combining other systems and will be used in this paper.No review of the theoretical basics instrumentation and applications of the individual atomic methods will be given here. It will be assumed that the reader is familiar with the general aspects of the individual methods or if not familiar the reader is referred to the appropriate references cited previously. Estimation of Detection Limits The requirement for SAD (also see Appendix 111) is that &d % 1. It is also possible to calculate detection limits using &do and E,' values even in cases when &do< 1. For both destructive and non-destructive detection the following can be written N,= YNA (2) where N = number of detected count events during t (measurement time) or z (counts) Y = sensitivity (counts per atoms) and NA=number of analyte atoms detected in the sample during the atom residence time in the region of observation.The probability of an analyte atom producing one (or more) counts is given by &do (3) where Ati is the interaction time (s). The meaning of $s (counts s-l) depends on whether destructive or non-destructive detec- tion is For non-destructive detection & is the mean flux of detected events; for destructive detection $s is the reciprocal of the mean detection time once the atom has entered the detection region. For OES AAS and CW AFS Ati=z the residence time for the atom in the observation region. For pulsed (laser) source methods LIFS LIIS RIS RIMS etc the following can be written 0 - 1 -e-@sAti &d - Ed0(1)= 1 -e-@-qAtl (4) where &do( 1) is the &d value for one single laser pulse and Atl is the laser pulse width.If zfi < 1 and z,>> At then &do = &do( 1 );A is the laser repetition rate (s-l). However if there are p probings (where p = z f i and zfi> 1) per atom residence time in the detection region then &do@) is given by where &do(p)=&dO for p pulses. It should be noted that &do( 1) is identical with the Alkemades.9 definition of Ed. It is clear that the sensitivity of measurement Y is given by (6) &do(p)=f-[ 1 -&do(1)lp ( 5 ) Y = &I&V&,,i&T&,&t&dO counts per atom for destructive methods (LEI RIMS RIS etc.) and for non- destructive CW methods such as AAS OES and CW and pulsed laser fluorescence methods where &do<< 1 and by for non-destructive pulsed methods (LIF) where &do > 0.05. Y = &I&Vea,i&T&s&t$sAtlp counts per atom (7) To be detected the analyte atoms must produce a large enough signal N so that Note that this value is given for single atoms in the second column in Table 1 for various mean blank z values.The LOD in atoms in the sample N is given by (9) Xd - xb NL=- Y This equation provides a link between the LOD (in terms of numbers of atoms) and E,' as long as the &d and values used to determine N are calculated at the intrinsic noise limit i.e. &d=&dO and E,=E,O. Eqn. (9) is valid for the extrinsic as well as the intrinsic noise limits with only the numerator changing depending upon the noise type. For example for the case of the background shot noise limit the numerator Xd - Xb becomes three times the square root of the number of back- ground counts during the species residence time or measure- ment time i.e.3 X where 3 is the confidence factor as - defined by Kaiser. G Evaluation of cdo and 8,' for Atomic Methods In Table 2 expressions for &do for various atomic methods are given. In Tables 3-6 estimations of &do and E,' for the various atomic methods are given. Such estimates have never been given in a consistent manner for the major analytical atomic methods. All values used for the various parameters for each atomic method are given at the end of each table. The values for the parameters represent in all cases possible magnitudes for existing experimental systems. The intent here is to estimate &do and 8,' values that are possible with each atomic method under good operating conditions.It would of course be impos- sible to give an exhaustive listing of &do and &,O values for all possible conditions. It should also be pointed out that certain liberties were taken with the choice of parameters; for example it was assumed for the ICP-OES case that all of the atomic species were in the correct form (atoms or ions) when in fact this fraction ( E ~ ) could be much less than unity for certain elements. In addition for consistency and simplicity an atom residence time of 1 ms was chosen for all cases except for ETA where 1 s was chosen. Also only two hypothetical resonance lines (200 and 500 nm) were chosen for ICP-OES F-OES and AAS and only two flame temperatures (2000 and 3000 K) and one plasma temperature (6000 K) were assumed.For the laser based and the MS methods only a single set of reasonable (except for the optimistic selection of a 3000 Hz tunable laser) conditions were chosen to minimize the number of cases possible. In the case of the AB (in LIFS RIS and RIMS) it was assumed that the atoms produced in the furnace (ETA) were either excited (and fluoresced) or ionized immediately adjacent to the furnace orifice so that E ~ E = 1. If a true atomic beam is produced and excited/ionized down-field from the orifice E~E,<<I resulting in much smaller &do and E,O values and much larger N and cL values. The reader is encouraged to estimate &do and em0 values for their own specific atomic systems. Estimation of Magnitudes of Extrinsic Noises in Atomic Methods The intrinsic noise limit at the detection limit exceeds the extrinsic noise if the following equation is valid (Poisson distribution of analyte signal is assumed) next < (NL&rn0)li2 (10) It should be pointed out that in reality the intrinsic noise limit is achieved when there is no extrinsic noise not simply when the intrinsic noise on the signal exceeds the extrinsic134 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL.9 Table 2 Specific expressions for &do for atomic methods*? I( I Optical emission spectrometry (0ES)- Ed" = [ 1 -exp(-4Ezrrem~el?d)l 4 ~ = Vex& I1 Atomic absorption spectrometry (AAS)$- A Narrow line source if EPL<EpSat &do = [ -exp(-$ATr)I B Broad line or pseudo-continuum source if EplC<Eppt -exp(-#Azr)I 111 Pulsed laser induced resonance Juorescence spectrometry (LIFS)*+ A Single-colour excitation )= -exp(-gA,lAtirflrdrel)l B Two-colour excitation &do( = [ -exp(-g'Au,l,Atiyfl?d'l,l)l IV Pulsed laser induced ionization spectrometry ('LIIS)*k A Single-colour excitation B Two-colour excitation1 -exp(-g'ku,iAtiqdr,l)l C Two-photon (single wavelength) excitation1 [ -exp(-~Z,hEpz((nu,)A~i~drel)l V Pulsed resonance ionization spectrometry (two or more colour excitation) *F VI Mass spectrometry (MS)- * The parameter p accounts for the probing of the same atom in a pulsed laser experiment by more than one laser pulse.p = 1 if residence time of the atom times the laser repetition rate is < 1.However if that product exceeds unity then eqn. ( 5 ) is used; e.g. p would be 3 if the residence time of an atom is 1 ms and a 3000 Hz repetition rate laser is used ( 1 x lop3 x 3 x 103=3 pulses per atom). ? See Appendix I for definition of all parameters and their units. $ Line source = hollow cathode lamp; pseudo-continuum source = xenon arc lamp with spectrometer. ij Assumptions for &d expressions for LIFS LIIS and RIS. The laser is assumed to be broad band i.e. its spectral profile is larger than the absorption profile of the atoms in all the atomizers considered. In addition the rate equations approach was used15 to derive the expressions and the laser is assumed to be characterized by a rectangular temporal profile. For the ion yield expressions recombina- tion between ions and electrons was neglected.In all expressions both the first and second (where applicable) transitions are considered to be optically saturated during the entire interaction time. For LIFS no metastable states are considered. 1 Assumes no collisional or radiational losses from level u'. 11 The relationship between the absorption cross-section (iA and the Einstein coefficient of spontaneous emission Aul is given by where A& is the absorption FWHM which is assumed to be Lorentzian. noise level. Otherwise the atomic system is limited by extrinsic noise. For all atomic methods near the limit of detection "background' shot or flicker extrinsic noise will be limiting. 'The 'background' or 'blank' refers to all non-analyte noises such as those due to background emission background related to the source of excitation detector etc.Background shot noise It& only on the magnitude of the rate of background detected events Ri (count s-') and the time of measurement. For a CW detection system and one residence time and for a pulsed dete'ction ~ y s t e r n ~ ~ ~ ~ where Atg is the gate width of the detection system andfi and z are as defined above. For the case of ETA cells z is 1 s. Typical extrinsic noise estimates are given in Table 7. For the case of extrinsic noise it should be stressed that 'background' shot noise predominates at low background fluxes (photon s-l) but 'background' flicker noise (tb flicker factor for background emission or t flicker factor for source emission) predominal es at high background fluxes.Comparison of Absolute and Relative Detection Limits In Table 8 a theorei:ical comparison of detection limits NL (absolute number of atoms at detection limit) and cL (concen- trational detection limit in mass of analyte divided by mass of sample; for example 1 x lo-'' is a part per trillion) is given for the various atomic methods with several cell and/or source types and the limiting nine sources. The theoretical possibility of atom counting with each method is also given. It should be stressed that the masses of sample assumed for the various sample introduction devices have been liberally chosen; for example a mass of 1 x g for all nebulization and ETV experiments (an asp:iration rate of 6 ml min-' for zr= 1 ms) was chosen.For all furnaces (ETA) a sample mass of 0.1 g was assumed during the atom residence time of 1 s and for the GD and AB a sample mass of 1 x lop9 g was assumed to be sputtered vaporized atomized and/or ionized and/or atom- ized during each millisecond (7 = 1 ms). In Table 9 an experimental comparison of atomic methods for solution samples is given. The reader should also refer to the excellent review by Sjostrom and M a ~ c h i e n . ~ ~ Conclusions Based Upon 8 2 E,' NL cL and Noise Estimates The estimations given in Tables 3-9 for &do E,' noise NL and cL should be used only in comparing one method with another. If one wishes to estimate any of these parameters for a given system then specific values of the parameters must be used. However several conclusions can be made.and E,' for OES AAS and a variety of other atomic systems are given. It is clear that even if &do were unity and extrinsic noise were absent NL would slill exceed unity since cm0<<1 because of atomic losses probing inefficiencies detection inefficiencies etc. (2) The values of ,:do and E,' for OES for atoms in the ICP and for visible emission lines can approach values of 1 x lop5 and 1 x lo-' respectively and for AAS for both hollow cathode lamp and xenon arc spectrometer excitation can approach values of 1 x lop7 for flames and 1 x lop3 for furnaces (ETAS). Despite the rather impressive detection and measure- ment efficiencies in OES and in AAS the 'background' noise levels in both cases limit the calculated values of NL and cL to values consistent with experimental results.(1) For the first time expressions to estimateJOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL. 9 135 Table 3 conditions at end of table) for a measurement time (z,) of 1 ms Order of magnitude values of efficiency of detection and efficiency of measurement for optical emission spectrometry (see experimental 2000 K (flame) 3000 K (flame) 6000 K (plasma) 6000 K (plasma) (NEB) (NEB) (NEB) (ETV) &do Emo Ed0 Emo Ed Emo Ed Em0 i,Jnm A&' 200 1 105 2 x 10-15 1 x 10-19 3 x 10-13 2 x 10-14 5 x 10-5 5 x 10-l0 1 x 1 10-5 1 106 2 10-20 1 10-21 3 10-15 2 1 0 - l ~ 5 x 1 0 - l ~ 5 x 1 0 - l ~ 1 x 1 x 10-l0 1 106 2 10-22 1 3 x 10-1~ 2 x 1 0 - l ~ 5 x 1 0 - l ~ 5 x 1 0 - l ~ 1 x 1 0 - l ~ 1 x 1 0 - l ~ 1 ~ 1 0 9 4x10-9 2 x 10-10 5 x 10-7 3 10-5 8 x lop6 8 x lop8 2 10-4 2 x 10-6 1 106 4 x 10-11 2 x 10-12 5 x 10-9 3 x lo-'' 8 x lop8 8 x lo-'' 2 x 2 x 10-5 500 1 x 104 4 x 2 x 5 x lo-" 3 x lo-'' 8 x lo-'' 8 x 2 x lo-' 2 x lo-'' Notes Conditions for 0ES13,17,29-32 3 x (500 nm 2000 K) 4 x lo-" (200 nm 3000 K); 6 x lo-' (500 nm 3000 K) 6 x 1 x lo8 s-' (highly probable transition) 1 x lo6 s-' (less probable transition) 1 x lo4 s-l (improbable transition) 0.001 cm x 1 cm x 0.01 sr 4nsr 0.1 z = 1 ms 1 0.05 (F); 0.01 (ICP); 1 (ETV) 1 (F or ICP) 1 (F or ICP) 1 (F or ICP with nebulization) (200 nm 2000 K); 5 x (200 nm 6000 K); 1 x lop3 (500 nm 6000 K) cm2=8 x 1 (ETA-ICP-AES) Order of magnitude values of efficiency of detection and efficiency of measurement for atomic absorption spectrometry (see experimental conditions at end of table) for a measurement time (2,) of 1 ms HCL XeS A1,Jnm A,JsC1 (F) 200 1 x 108 5 x 10-7 5 x 10-9 5 x 10-11 500 1 x 105 5 x 10-7 5 x 10-9 5 x 10-11 1 x 106 1 x 104 1 x 106 1 x 104 &do (ETA) E,' (F) E,' (ETA) 5 x 3 x lo-'' 5 x 5 x 3 x 10-l0 5 x 5 x 1 0 - 4 3 x 10-5 5 x 10-4 5 x 10-5 3 10-12 5 x 10-5 5 10-4 3 10-5 5 x 10-4 5 x 10-5 3 x 10-12 5 x 10-5 &do (F) &do (ETA) E,' (F) E,' (ETA) 5 x 10-9 5 x 3 x 10-1° 5 x 5 x lo-" 5 x 3 10-12 5 x 10-5 5 10-13 5 10-10 3 x 10-14 5 x i o - l o 5 x 5 x 10-3 3 x 10-7 5 x 10-3 5 x 10-5 5 x 10-5 3 10-9 5 x 10-5 5 x lo-'' 5 x 3 10-11 5 x 10-7 Notes Conditions for AAS133'7,31*32 A = 1 x lo's-' (highly probable transition) 1 x lo6 s - l (less probable transition); 1 x lo4 s-l (improbable transition). oA = 1 x t = T,= 1 ms (F); t,= 1 s (ETA) A = 200 and 500 nm E = 1 = 0.05 (F); E,= 1 (ETA) cV = E ~ = E = E ~ = 1 (HCL or XeS) cV = cT=l and ~ = ~ ~ = 0 . 0 1 Sb = 1 cm2; WH=0.001 cm2 T,=0.5 Ijdqel=0.1 xtL = 5x10-'cm2 EpLc= 1 x 10l6 photons sK1 cm-2 nm-l at 500 nm EpLc= 1 x photons s-l cm-' nm-l at 200 nm Sb = 1 cm2 WH = 0.001 cm2 T = 0.5 AA = 0.01 nm qdqel = 0.1 xtc = 5 ~ 1 0 - ~ c m ~ n m cm2 (Aul = 1 x lo8 s- l) 1 x 10- l4 (Aul = 1 x lo6 s -') and 1 x cm2 (Au1 = 1 x lo4 s-l).HCL EpL = 1 x lo1' photons s-l cmP2 (z 100 pW cm-2) at 200 or 500 nm XeS (3) The wide range of cdo and emo (and N and cL) and values for OES result because of the Boltzmann distribution of excited states and therefore the significant variation in the fraction of species excited vex with temperature. (4) The narrow range of cdo and emo (and N and cL) values for AAS is based on the rather constant transition probability or absorption cross-section for resonance absorption lines.( 5 ) Of the LIFS and LIIS techniques considered here SAD in the sample is theoretically possible by several LIFS (ETA GD AB) methods. These are methods theoretically capable of single atom counting as shown in Table 8. In fact the intrinsic noise limit is theoretically achieved in those techniques. Certainly SAD in the sample has not yet been achieved but the predictions are encouraging and intriguing. The great variations in c values for single atoms (see Table 8 e.g. LIFS methods have N z 1 atom and cL z 1 x lop2' whereas RIMS and MS (AB) have N L z 1 atom and c L z 1 x is owing to the amount of sample introduced within one atom residence time (0.1 g for ETA and 1 x g for GD and AB).Certainly ETA-LIFS appears to be the simplest method with the greatest potential for achieving near SAD. The new method ETV-F- LIIS should achieve detection limits ( N ) of z 1 x 103-1 x lo4 atoms with c values of 1 x 10-15-1 x like ETA-LIFS ETV-F-LIIS is a relatively simple approach for both solid and solution samples. Of the remaining LIFS techniques GD-LIFS has the greatest potential since it should achieve detection136 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL. 9 Table5 experimental conditions at end of table) for a measurement time of 1 ms for all methods except those involving the ETA ( 1 s) Order of magnitude values of efficiency of detection and efficiency of measurement lor several pulsed laser atomic methods (see Method LIFS (SC)$ LIFS (TC)$ LIIS (SC)\i LIIS (TC)/I LIIS (TP)JJ RIS (TC)** Bp=l x 106s-l Bp= 1 x 1O'O s-l Edo 30 Hz laser*? 5 x 10-4 5 10-4 5 x 10-4 5 10-4 2 x 10-4 2 x 10-4 2 x 10-4 2 x 10-4 0.02 0.01 5 x 10-3-5 x lo-' 1 .o 1 .o 0.01 4 x 10-3 1.0 3000 Hz laser*? 2 x 10-3 2 x 1 0 - 3 2 x 10-3 2 x 10-3 0.8 (1.5) 6 x lop3 6 x lop3 6 x lop3 0.6 (1.0) 6 x lop3 1 .o 1 .o 0.03 2 x 10-2-2 x 10-4 0.0 1 1 .o 30 Hz laser*? 5 x lo-' 5 x lo+ 3 x 10-7 2 x 10-4 5 x 10-4 2 x 10-7 2 x 2 x 8 x 2 x 3 x 10-'-3 x lo-' 5 x 10-4 5 x 10-4 5 x 4 x 0.01 3000 Hz laser"? 1 x 10-4 2 x 10-3 2 x 10-3 3 x 10-5 2 x 0.8 (1.5) 6 x lo-' 6 x lob3 0.6 6 x ( 1.0) 5 x 1 x 10-3-1 x 10-5 2 x 10-3 1 .o 0.01 1 .o Notes * For fi = 30 Hz and z = 1 ms p = 1 since AT < 1 for all nebulization cases (F ICP) and the GD and AB and p = 30 for the ETA.t For J; = 3000 Hz and zr = 1 ms p =AT = 3 for (F ICP) nebulization cases and for the GD and AB and 3000 for the ETA. $ Conditions for g = 0.5; g'=0.3 Ad Ati zr vfl = 1 x 10' s-1; A,*,,= 1 x lo8 s-' = At,=1 x lo-' s = 1 ms (F ICP GD AB); z = 1 s (ETA) = wfi i22,T0/47dfl= 1 X lo-' VdVel = 1x10-' &a,i = 1 El EV = 1 E r = 1 Ei Et = 0.05 (F); 0.01 (ICP); 1 (GD ETA AB) = 1 x = 1 (30 Hz or 3000 Hz laser) for ETA (30 Hz pulsed laser) and Et= 1 (3000 Hz pulsed laser) for F ICP GD and AB Es = 1 (GD F ICP AB ETA) 9 Measurement time is 1 ms (q). 7 Measurement time is 1 s (tm). 11 Conditions for L I I S ' ~ * ~ O g = 0.5; g'=0.3 kui g2ph Ati V d v e l = 1 &a = 1 EV = 1 Es = 1 Zum = 1x108s-' g = 0.5 A tl v d v e l = 1 Ea = 1 El = 1 EV = 1 ET = 1 Es = 1 = 1 x lo6-1 x 10' s-'; ZUm= 1 x lo8 s-'; ku,i= 1 x 10" s-' = At,= 1 x lo-' s = 1 x cm4 s; E (A,,)= 1 x lo2' photons s - l cm-2 (100 W cmP2) El = 0.05 (F); 1 (ETV-F) ET = 1 ( F or ETV-F) ** Conditions for R I S ' ' S ~ ~ Buipui(Aui) = 1 x lo6 s-' and 1 x 101os-l = At,= 1 x lo-' s Ei = 1 x lop2 (30 Hz pulsed laser); 1 (3000 Hz pulsed laser) limits of near single atoms with concentrations of 0.1-1 pptr in solid samples is simple and could possibly be improved dramatically if the GD cell design minimized dilution and loss of the atomic vapour.( 6 ) It should be stressed that of the LIFS approaches the sensitivity Y in counts per atom exceeds unity (parenthetical values in Table 5) only twice and is only 1.5 in those cases.In other words the sensitivity requirements for SAD (LOG) as shown in Table 1 are not achieved in those two cases or in any method consid,ered in this paper. However it should be possible to achieve a Y>> 1 in LIFS as long as the transition probability is z 1 x lo8 s-' if the residence time of the atom within the observation region is long as in ETAS and if the laser interaction time (Atl) is increased. In the latter instance if it is assumed that At is only increased to 100 ns instead of 10 ns then Y would be 15 instead of 1.5 for the two cases in Table 5 where Y is listed as 1.5. Of course if more efficient collection of the fluorescence and detection of fluorescenceJOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL.9 137 Table6 Order of magnitude values of efficiency of detection and efficiency of measurement for several atomic spectrometric methods (see experimental conditions at end of table) for measurement time of 1 ms Ed &mO Method Cell 1 x QPMS NEB-ICP 1.0 TOFMS RIMS Continuous wave Pulsed ETV-ICP GD AB AB 1.0 1 .o 0.01 4 x lo-’ (30 Hz)* 0.01 (3000 Hz)* 1.0 (30 Hz)t 1.0 (3000 Hz)t ~~ 1 x 10-4 1 x 10-4 1 x 10-4 4 x 10-5 (30 HZ)* 0.01 (3000 Hz)* 0.01 (30 Hz)t 1.0 (3000 HzH Notes ~ $ 2 5 2 7 ci = 1 (ICP for many elements) ci qdqel = = 0.01 (GD for many elements) = 0.1 (AB for many elements electron impact) El Ev = 1 E = 1 (ICP); 1 (GD); 1 (AB) E ET = 1 x (ICP-QPMS); 1 x (GD-QPMS); 1 x lo-’ (TOFMS) E = 1 EV = 1 E = 0.01 E = 0.01 (ICP); 1 (GD AB); 1 (ETV) = 1 (QPMS TOFMS); E,< 1 for ITMS and ICRMS qdqel = E I = 1 ET = 1 = 1 (CW RIMS); 1 x lo-’ (30 Hz pulsed laser); 1 (3000 Hz pulsed laser) * Bp= 1 x lo6 s-l.t B p = 1 x 1o’O s-l. photons were achieved this would also increase Y. Therefore non-destructive LIFS methods deserve careful attention for achieving the ultimate goal of SAD. (7) The AB-RIS technique is also theoretically capable of N L % 1 atom and atom counting as shown in Table 8. However the concentration detection limit cL is much poorer (x 0.1 pptr) than the values for LIFS because of the low sample introduc- tion rate in RIS. Of the MS methods only AB-RIMS (with a TOFMS)” and possibly AB-MS are capable of SAD (N,= 1 atom) but both have corresponding cL values of ~ 0 .1 pptr because of the low sample introduction rate. The other MS methods theoretically achieve better detection limits (0.1 pptr for NEB-ICP-MS and 0.1 ppq for ETV-ICP-MS) but cannot achieve SAD because of the losses occurring in the transfer process (cT<<l). The major difficulty with the AB-MS method involving an ideal atomic beam AB produced some distance from the ion source/ion trap is the significant loss in transport ( E ~ ) and spatial probing ( E J of the atoms/ions produced. Falk17 proposed the use of a TOFMS in an AB-MS system and estimated an overall measurement efficiency of the order of = l x 10-5-1 x The use of a TOFMS rather than a QPMS enables this approach to be a truely multi-element method. However no experimental results are yet available.and E,’ values represent maximum values and the NL and cL values represent minimum values in many cases since the efficiency of producing the species of concern (atom or ions) was chosen to be unity for all methods the best case scenario. This assumption is particularly severe in the case of a flame cell where compound formation and ionization can greatly reduce the atomic species e.g. Zr W Hf Os Mo and V in the former case and Na K Rb and Cs in the latter case. If the values of E or ci were known then the E ~ ’ E,’ N and cL values could be readily corrected. The efficiency of vaporization E ~ was also assumed to be unity for all methods which again will be too high for some samples introduced into flames and to a lesser extent for some samples introduced into ETVs and ETAS.The other efficiencies were (8) The less sample and analyte dependent and so their values will be more accurate except possibly for E ~ . Finally in those cases where analyte is transferred from and ETV to a cell e.g. ETV- F-LEIS the E ~ which was assumed to be unity may also be considerably less for some samples. (9) The NL values in this manuscript differ to some extent from those given by Stevenson and Winefordner.” The reasons for this are as follows (i) in this paper all N values were obtained from estimates of the noise and the sensitivity Y and efficiency of measurement E,’ for each method by the general approach given in eqns. (2)-( 9) whereas in ref. 11 the approach differed greatly depending upon the noise source; (ii) in this paper all N values are given for a single atom residence time whereas in ref.11 more arbitrary times were chosen; therefore the N and cL values and their ranges are more consistent than those given in ref. 11; (iii) in this paper values of E ~ E ~ E ~ E E ~ E ~ are given whereas in ref. 11 this product was assumed to be unity in most cases; (iu) in this paper the intrinsic efficiencies of detection and measurement for each atomic method were estimated whereas in ref. 11 this was not done; and (v) in this paper more efforts were taken to be consistent and fair with regard to choice parameters for all atomic methods whereas in ref. 11 the NL values were taken from a number of references. Nevertheless ref. 11 as well as this paper are valuable resources to use in estimating the detection power of atomic methods.(10) It should be stressed that the solution techniques of flame and ICP OES AAS LIFS and LIIS suffer by an additional factor of about 100 when solid samples are to be analysed. Solids commonly require grinding weighing 1 part solid to 100 parts solvent and dissolving. A direct solids approach neglecting the difficulties of solid standards is faster and does not suffer in loss in detection power owing to dilution but does posses difficulties with standardization. The direct solids approaches involve ETA (solutions can also be used) GD (dried solutions can also be used) AB and AT (furnaces with solids or dried solutions can be used),138 Table 7 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL.9 Estimates of extrinsic noise magnitudes near the LOD in atomic method^^^-^^ ‘Background’ noise counts Method OES AAS LIFS LIF LIIS RIS RIMS MS Cell F ETA F ICP ETA (2000 K) ETA (3000 K) GD AB F AB AB ICP GD Source F ICP ICP HCL HCL XeS XeS HCL HCL PL (SC or TC) PL (SC or TC) PL (SC or TC) PL (SC or TC) PL (SC or TC) PL (SC or TC) PL (SC or TC) PL (TC) TC CL TC PL (TC) TC Noise type BES BES BES SBS SBF SBS 200 nm SBS 500nm SBF 200 nm SBF 500 nm ETA BEF 2000 K 200 nm 2000 K 500 nm ETA BEF 3000 K 200 nm 3000 K 500 nm BES 30 Hz 3000 Hz BES 30 Hz 3000 Hz BES 200 nm 30 Hz 200 nm 3000 Hz 500 nm 30 Hz 500 nm 3000 Hz 200 nm 30 Hz 200 nm 3000 Hz 500 nm 30 Hz 500 nm 3000 Hz DN 30 Hz 3000 Hz DN 30 Hz 3000 Hz BCS 3000 Hz 1 x A 3000 Hz 1 x lO-’A DN 30 Hz 3000 Hz DN 30 Hz 1 x A 30 HZ 1 x 10-9 A DN 30 Hz 3000 Hz DN DN z,=1 s 30 800 5000 1 x 104 5 x 105 5 x 103 2 x 105 1 x 105 1 x lo8 0.25 8 x lo2 80 1 104 0.02 0.2 0.5 5 1 x 10-4 i x 10-3 0.5 5.5 0.009 0.09 8 80 1 x 10-4 1 x 10-3 8 x lop4 8 x lop3 2.5 x 103 a x 104 77 8 x f03 1 1 1 1 1 1 1 z,=1 ms 1 .o 25 5 300 50 2 x lo2 6 x lo3 I 103 1 x 105 8 x 25 2 3 x 10’ 0.0006 0.006 0.005 0.15 3 x 3 x 10-5 3 x 10-4 3 x 10-3 0.01 5 0.16 0.25 2.5 3 x 3 x 10-5 4 x 10-5 4 x 10-4 3 x 103 80 2 3 x f02 8 x 8 x lop3 0.03 8 x 8 x 0.03 0.03 Notes Typical ‘Background’ levels in cells sources detectors Flame2’ (1 not in OH bands or in CN CH C2 bands; photon radiance would be higher by =:.LO-fold in spectral regions of these bands) BpAz 1 x loll photons s-’ cm-2 sr-l nm-I (conventional C2H,-air flame) Typical spectrometer conditions WH = 0.001 cm2 sZE = 0.01 sr; A1 = 0.01 nm To = 0.5; qdqe = 0.1; 4; = 0.01 Background count rate x 5 x 10’ s - ’ ICP30 BpAz 1 x 1014 photons s-’ cm-’ sr-l nm-‘ Typical spectrometer conditions same as for flame Background count rate z 5 x lo5 s-l E TA3’ BpAz 1 x 1014 photons s-l cmP2 sr-l nm-‘ at 500 nm and 2000 K BpAz2 x 10l6 photons s-’ cmP2 sr-l nm-‘ at 500 nm and 3000 K BpAz 7 x lo1’ photons s-’ cm-’ sr-l nm-’ at 200 nm and 3000 K BpAx5 x lo6 photons s-l cm-2 sr-’ nm-’ at 200 nm and 2000 K Typical spectrometer conditions same as for flame Background count rate = 5 x lo5 s-’ at 500 nm and 2000 K Background count rate= 1 x 10’ s - l at 500 nm and 3000 K Background count rate = 0.03 s-’ at 200 nm and 2000 K Background count rate=4 x lo3 s-l at 200 nm and 3000 KJOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL.9 139 Table 7 (continued) GD No absolute B values could be found. Based on relative measurements of signals to background levels in HCLs the values of BPn should be < 1 x lo7 photons s-l cm-2 sr-l nm-' at all wavelengths between atomic lines of the fill gas and the elemental species in the gas phase. Using spectrometer conditions for the flame case above the background count rate should therefore be ~ 0 . 0 5 s-l PMTdetector Electron multiplier count rate33-35 1-3 s-l Flame background current20'21 Optogalvanic detector x 1 x 10lO-1 x 1013 s-l for H2 based to C2H2 based flames Source count rate (AAS) HCL? B P z l x 1013-1 x 1014 photons s-l cm-2 sr-l nm-I Typical spectrometer conditions WH = 0.001 cm2 R = 0.1 sr T = 0.5 qdqel =O.1 tS = 0.001 HCL EPL= 1 x 1013 photons s-' cm-2 Xenon arc lamp3' BPA (200 nm)x2 x photons s-' cm-2 sr-l nm-' BPn (500 nm)x2 x 10" photons s-' cm-2 sr-' nm-' Typical spectrometer conditions WH = 0.001 cm' R = 0.001 sr To = 0.5 A& = 0.01 nm q&.l= 0.1 5 = 0.01 Xenon arc E = 2 x 10"-2 x 1OI2 photons s-l cm-' nm-' Source scatter count rates (LIFS)15,16 Laser scatter and environmental fluorescence count rates are assumed to be less than cell background emission count rates and are neglected. This is an excellent assumption if the experimental system is optimized for negligible laser scatter for low fluorescence optics assuming proper baffling is used as well as measurement of atomic fluorescence in the UV Typical pulsed laser conditions Ati = Atl = 1 x f; = 30 or 3000 Hz Atg= 1 x lo-' s Dark count rate x 1 x 10'-1 x lo2 s-l Table 8 Theoretical comparison of several atomic methods Method OES I1 AAS** LIFStT LIIS$$ RIS$§ RIMS$§ MS% Cell NEB-F NEB-ICP ETV-ICP NEB-F ETA NEB-F NEB-ICP ETA ETA GD AB NEB-F ETV-F NEB-F AB AB NEB-ICP ETV-ICP GD AB Source HCL XeS HCL XeS XeS SC TC SC TC SC TC SC TC SC TC SC TC TC TP TC TC Noise limit BES BEF BEF SBS SBS (200 nm) SBS (500 nm) SBF SBF (200 nm) SBF (500 nm) BES BES BES BES DN DN BCS BCS BCS BCS DN DN DN DN DN DN Atom counting* No No No No No No No No No No No Yes Yes Yes Yes No No No No No Yes No No No Yes Theoretical N (atoms)tS 1 x lo8-1 x 10l8 1 x 108-1 x 1014 1 x 107-1 x 1013 1 x 1010-1 x 10'4 1 x 1011-1 x 1015 1 x 109-1 x 1013 1 x 1011-1 x 1015 1 x 1011-1 1015 1 x 102-1 x 104 1 x 104-1 x 106 1 x 10l2-1 x 10l6 x 1 x loo-1 x 10' % 1 x loo-1 x lo1 % 1 x loo-1 x lo1 %l x loo 1 x 107-1 x 1011 1 x 105-1 x 107 1 x 103-1 x 106 1 100-1 103 1 x 104 1 x 103 M 1 x 100-1 x 103 1 x lo6-1 x lo8 z 1 x loo-1 x lo2 1 x lo6 Theoretical cL (fraction)$§l 1 x 10-lo-1 1 x 10-10-1 x 10-4 1 x 10-11-1 x 10-5 1 x 10-8-1 x 10-4 1 x 10-7-1 x 10-3 1 x 10-6-1 x 1 x 10-"-1 x 1 x 10-'O-1 x lo+ 1 x 10-lo-1 x 1 x 10-16-1 x 10-14 1 x 10-14-1 x 10-12 1 x 10-13-1 x 10-12 1 10-13 1 10-11-1 x 10-7 1 x 10-13-1 x 10-11 1 x 10-15-1 x 10-12 1 x 10-l2-1 x 10-1° x 1 x 10-13-1 x 10-10 x 1 x 10-13-1 x 10-10 1 x 10-l2 1 x 10-14 1 x 10-'O 1 x 10-13-1 x 10-10 % 1 x 10-21-1 x % 1 x 10-21-1 x _ _ _ _ _ _ _ _ _ _ _ _ ~ ~ ~ ~ ~ ~~ ~ * Yes means atom counting is theoretically possible if NL= 1 x 10' (unity). -f Values of N and cL (rounded to decades) calculated using eqn.( 5 ) with values of E from Tables 3-6 and noises from Table 7 assuming a single atom/ion residence time measurement. $ For those cases where the calculated N for the extrinsic noise limit was < 1 atom NL is reported to be x 1 atom since the intrinsic noise takes over as N approaches 1 atom. Q cL= NL x 60/6 x A where A is the relative atomic mass of the analyte. The detection limit cL is a fraction 1 x is 1 pptr; N is the number of detectable atoms within the observation time 60 is the assumed relative atomic mass of the atom and m is the mass of sample. For the flame and ICP 6 ml of sample are assumed to be nebulized in 1 min giving a sample mass of 0.1 g sC1 or 1 x g in 1 ms.For the ETA the sample mass is assumed to be 0.1 g (100 pl of an aqueous sample). For the ETV a sample mass of g is assumed to be present during one residence time. For the GD and AB the sample mass is assumed to be 1 x g introduced in one residence time. 7 If the value of NL is so large as to make c,> 1 NL was limited to the value making c unity. 11 The range of NL and cL for OES values is dependent mainly on the temperature of the flame or plasma the wavelength of the transition and ** The range of N and cL values for AAS is dependent mainly on the range of A,] (or oA) values for the absorption transition. tt The range of NL and cL values for LIFS depends mainly on the values of the laser repetition frequency the noise source and the residence $$ The range of N and c values for LIIS depends mainly on the laser repetition frequency values and the background current shot noise.the value of A,]. time for an atom. @ The single values for RIS RMS and MS are a result of choosing one noise level and optimized ionization systems.140 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL. 9 Table 9 Experimental comparison of several atomic methods for solution samples Selectivity Matrix Range of Multi- - LOD*/ Sample RSD Method ng ml-l LODt/pg volumeipl ( O h ) Elemental$ Isotope§ isotopq elements I/ element8 F-AAS 100- 104 104-108 5 x 103-104 1 G N S M N 1 o -2- 102 10 - 4- 100 5-100 3 G N S M N 10 - lo2 103-106 5 x 103-104 G 1 F N M A Y ETA-LIFS 10-~-10 10-~-10-l 1-50 5 E N S M N ICP-LIFS 10- '-lo2 103-107 5 x 103-104 5 G N S M N F-LIIS 10-4-102 100-106 5 103-104 5 G N H M N ICP-MS 10 - 3- 100 10-104 5 x 103-104 G I E Y M A Y ETV-ICP-MS 10-4-100 10- 6-10-2 5-100 3 E Y M A Y GD-MS 1oo-1o3 10-~-10O 10-~-10 5 G Y S A Y ETA-RIMS 10-~-10 10-~-10-~ 10-~-10 5 E Y VS A Y ETA-RIS 10-~-10 1 0 - ~ - i o - ~ 10-~-10 5 E Y S A Y ETA-A AS ICP-OES * LOD =Limit of detection in concentration units.All values rounded to nearest decade. LOD = Limit of detection in absolute amount; 10 ml sample volumes assume for all flame and ICP nebulization cases and 10 pl assumed for all ETA and ETV cases and 1 pl for GD-MS. All values rounded to nearest decade. 1 E = Excellent G =good and F =fair. §N=No and Y=yes. 7 VS =Very small S = small M =moderate and H = high. 11 M =Mostly metals and A = almost all elements.( 11) The only present technique which is truly multi-element is ICP-OES. However ICP-MS and GD-MS are rapid sequen- tial multi-element approaches. The quadrupole (QP) mass spectrometer has been by far the most popular system for ICP-MS. The ion trap (IT) and the ion cyclotron resonance (ICR) mass spectrometers have dynamic range difficulties as well as difficulties with handling high flow rate of ions (1 x 10l6 argon ions s-l; a 1 ppm solution of some analyte will contrib- ute about 1 x lo1' analyte ions s - ~ ) . ~ ~ Therefore it is difficult to envision the routine analytical use of ITMS or ICRMS for the QPMS in ICP-MS. The time-of-flight mass spectrometer (TOFMS) has the capability for rapid multi-element analysis but so far has a duty factor problem; Hieftje27 believes this problem can be overcome. Interfacing the GD to the IT or ICR could lead to a substantial improvement in the through- put i.e.&,' could approach &do. (12) The reader might note that laser ablation (vaporization) was not included with the ICP-MS. The calculated detection limits NL and cL for those cases should be similar to those using the GD-MS since the sample introduction rate of ~1 ngms-l of the laser ablation is similar to the use of GD. Also no calculated detection limits NL and cL are given for GD-OES laser ablation of sample with transfer to ICP-OES or laser ablation-excitation-emission where the laser vaporizes the sample and the vapour enters into a plasma formed by the laser interaction with the surface.In the case of GD-OES FANES;' HA-FANES,40 FAPES,41 and the laser produced plasma excitation sources the essential characteristics namely the electronic excitation temperature of the plasma and the background spectral radiance are not well known negating calculations of &do E,' NL and cL. In the case of laser ablation of the sample with transfer to the ICP-OES the values of E,' NL and cL should be similar to those for ETV-ICP-OES. (13) Several other atomic methods including ETA coherent forward scatter spectrometry flame or ETA degenerate four wave mixing ETA intracavity laser atomic absorption spec- trometry flame concentration modulation atomic absorption spectrometry and flame-ring down laser as well as electrother- mal OES have also not been considered in this paper because the authors felt they were not viable analytical atomic methods.However all of the above flame and furnace-based methods except for electrothermal OES will have similar &do E,' NL and cL values to FAAS and ETAAS depending upon the atom cell. Electrothermal OES will have poorer NL and cL values than ETAAS for all elements except possibly for those with resonance line having wavelengths longer than z 500 nm because of the high black-body emission. (14) A novel technique which could have future analytical utility and which has been omitted from the estimations of E ~ ' E,O NL and cL is atom trap (AT) LIFS.14 No experimental results for analytical AT-LIFS have been published and so the analytical future of this method is still questionable.In addition the technique would appear to suffer considerable losses owing to transport (E:) and spatial (E,) efficiencies much like the AB-MS and the ion trap based methods [see items (7) and (ll)]. (15) The atomic techniques listed in Tables 5 and 6 are all fairly spectrally selective. Even so AB-RIMS certainly has the highest selectivity and ETA-LIFS (TC) most likely has the second highest spectral selectivity although ETV-F-LIIS ICP-MS F-LIIS (TC) ETA-LIFS (SC) and AB-RIS (TC) are a close third. Electrothermal AAS and ICP-OES are certainly less spectrally selective but the vast literature available for virtually all analytes in all sample types minimizes such difficulties. (16) The atomic technique with the greatest freedom from matrix interferences is certainly ICP-OES although ETAAS is a close second and the LIFS techniques using ETA fall in this same category.Glow discharge LIFS and GD-MS have been found25 to exhibit minimal matrix interferences and would fall third in this comparison. Some matrix interferences problems are encountered with ICRMS; but many have been overcome or accounted for with proper choice of experimental conditions Certainly all flamc-based methods including AAS LIIS and LIFS have matriK interferences which are also well docu- mented in the literature. Insufficient data are available on techniques using PLB or AT to know the extent of such matrix interferences. (17) It would seem based upon the above conclusions that ICP-OES and ETAAS will continue to be used for years to come as a back-ulp for ICP-MS or as stand-alone techniques known for their simplicity and reliability and low cost of equipment and operation.Certainly ICP-MS will continue to grow as the premier multi-element method; the next major improvement will probably involve improved operation for the rapid simultaneous analysis of 20 or more elements based upon a true 'multi-element' measurement approach (e.g. ICP-MS with a TOFMS).27 Up till now the outstanding detection limits ( ~ 0 . 1 - 1 fg) in ETV-ICP-MS have been obtained with single ion monitoring. Considerably poorer detection limits result if for example 20 elements are to be measured in the same sample. This degradation in detection limits does not occur in ICP-OES when using the direct reader approach with photomultipliers or a CCD array detector.The laser-based techniques all single element approaches willJOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL. 9 141 continue to find use primarily for the determination of selected elements at concentrations below the LOD of ICP-OES ETAAS and ICP-MS or in small sample amounts (sub- microgram samples) where the number of analyte atoms is below NL or cL for the three conventional approaches. Such samples can be found,'* for example in the environmental biological forensic high-purity materials geological and nuclear areas. (18) The introduction of sample as particles molecular vapour atoms or ions into the atom/ion 'cell' and the type of atom/ion 'cell' are and will undoubtedly remain the research areas of greatest activity.Certainly the use of hybrid techniques will continue to flourish because of the possibility of optimizing atom/ion production as well as excitation. This research was supported by DOE-DEOFGOS-88ER- 13881. Professor Winefordner was unable to present the paper at the XXVIII CSI owing to illness. Appendix I = total surface area of emission (cm') = total surface area of fluorescence (cm2) = Einstein coefficient of spontaneous emission from level u to level 1 (s-') = Einstein coefficient of spontaneous emission from level u' to level 1' (the primes indicate uppermost laser populated level resulting from two colour excitation) (s-') = Einstein coefficient of spontaneous emission from level u to level m (a metastable level) (s-l) = photon radiance of a source or a cell back- ground (photons s-' cm-' sr-' nm-') = radiative ionization rate (s-l) for the transition between level u and the ionization continuum induced by the laser radiation tuned at Aui of spectral energy density pui (J cm-3 Hz-l).BUi is the Einstein coefficient for stimulated absorp- tion (J-' cm3 Hz s-') Definition of all Symbols with Units Aem Afl All1 All,*! Aum BPk Buipui(Aui) Bui where a(A) is the cross section (cm2) c is the velocity of light (cm s-I) Aui is the wavelength of transition (cm) and h is the Planck constant (J s) C = speed of light (3 x 10" cm s-') CL = limiting detectable analyte concentration Ei Ell EpSat Ep(Auv) (fraction) = ionization energy of atom (eV) = energy of upper energy level (J) = saturation irradiance (photons s-' crnd2) = photon irradiance of photoionization laser in two-photon ionization (photons s-' cm-') = photon irradiance of line source (photons s-' cm-2) = photon spectral irradiance of continuum source at All (photons s-' cm-') = frequency of laser (source) pulsing (s-') = the statistical weight of level i (dimensionless) E,L EPIC f; gi g = (A) (dimensionless) g' = (gl + ::+ gu,) (dimensionless) H = slit (or aperture) height (cm) h = Planck constant (6.7 x J s) k = Boltzmann constant (1.38 x J K-l) kui ku'i = 'effective' collisional ionization rate coefficients from levels u into the ionization continuum (s- I); 'effective' here means that in collision- dominated systems this coefficient cannot be referred to a single level u since collisions might be effective in redistributing the excited atoms between neighboring levels; u' represents the level reached by the second excitation step (s-') ku,m = total collisional deactivation rate from level u to level m (s-l) K = 4.83 x 10'' T3'2[Z(T)A+/Z(T)A] x 10-5040Ei,/T next = extrinsic ('background') noise in an atomic ne = electron number density ( ~ m - ~ ) = background shot noise for CW (source) system %hPU = background shot noise for pulsed (source) N = noise level (counts) Ne = number of detected (signal) count events (counts) NA = number of analyte atoms measured during one residence time (atoms) NL = limiting detectable number of atomic species in the sample (dimensionless) P = number of laser pulses during atom residence time (minimum value of p = 1 even if temporal efficiency is less than unity) (dimensionless) = probability that signal is at least equal to or greater than as assigned value (dimensionless) = rate of detected events (detected electrons per second) due to phenomenon i (s-') = cross sectional area of source beam (cm2) = transmittance of optical (spectrometer) system = temperature of emission source (K) = slit-width (or aperture) (cm) = mean of one blank measurement (counts) = signal limit of detection (counts) = signal limit of guarantee (counts) = signal counts (counts) = total signal level (counts) method (counts) cw nsh system P Ri Sb TO Ts W Xb Xd xg XS xt Y = sensitivity of method (counts per atom in = electronic partition function for temperature T Z(T) Z(T)A Zum (dimensionless) - sample) (dimensionless) Z(T),+ = Z(T) for atom A and ion A' respectively (dimensionless) = (=Aum + kum) total deactivation rate coefficient for atoms from level u to metastable level m taking into account radiative (Aum) and quench- ing (/cum) transitions (s-') a P 4 Ati = probability of a type I error (false positives) = probability of a type I1 error (false negative) = gate or aperture width of boxcar detector (s) = interaction time.This time is defined as the probing time of the process (fluorescence and ionization) and is given by the laser pulse duration since a pulsed laser is assumed here whose duration does not exceed 1 ps (s) (dimensionless) (dimensionless) = laser pulse width (s) = absorption line full width at half maximum = 'source' line full width at half maximum or = efficiency of atomization/ionization of analyte = efficiency of detection of event X (photons or = same as &d defined at intrinsic noise limit (nm) spectral bandpass of spectrometer (nm) in the cell or source (dimensionless) ions) (dimensionless) (dimensionless)JOURNAL OF ANALYTICAL ATOMIC SPIECTROMETRY MARCH 1994 VOL.9 = efficiency of sample introduction (dimen- sionless) = efficiency of overall measurement process accounting for losses of atoms or ions and for spatial and temporal probing of the atoms (dimensionless) = same as E defined at intrinsic noise limit (dimensionless) = efficiency of nebulization of nebulizer systems (dimensionless) = efficiency of vaporization of analyte containing material (dimensionless) = efficiency of probing analyte in observation region = E,E (dimensionless) = spatial probing efficiency accounting for inefficient spatial excitation (dimensionless) = temporal probing efficiency accounting for inefficient temporal excitation (dimensionless) = transport efficiency of analyte to observation (detection) region (dimensionless) = detection efficiency of the photons reaching the PMT in emission or fluorescence or of the ion produced in ionization experiments (dimensionless) = efficiency of electronics counts per photoelec- tron (dimensionless) = efficiency of thermal excitation of atoms (or ions) in cell gJZ(T)e-EukT (dimensionless) = collection efficiency in emission spectrometry = WHQE T0/47rAe (dimensionless) = collection efficiency in fluorescence spec- trometry = WHQF T0/4nA (dimensionless) = wavelength of l+u or u-rl transition (cm) = true mean = flicker factor for source (dimensionless) = flicker factor for background (dimensionless) = 3.1418 ...= spectral energy density for transition u+i = true standard deviation = absorption cross-section (cm2) = absorption cross-section for the two photon excitation process (cm4 s) = residence time of atom (ion) in observation region (s) = absorption photoelectron count rate (counts due to absorption/s atom) = emission photoelectron count rate (counts due to emission/s atom) = photoelectron count rate due to laser process (counts per atom) = throughput for spectrometric system with line source = WHToVdVel assuming entrance optics matched to spectrometric optics (cm2) = throughput for spectrometric system with con- tinuum source = WHToVdVel assuming entrance optics matched to spectrometric optics (cm2 nm) (J cm-3 Hz-l) = solid angle of collection of emission (sr) = solid angle of collection of fluorescence (sr) Appendix I1 HA-FANES = Hollow anode FANES LIFS = Laser induced (enhanced) fluorescence spec- tronietry (also LEAFS) LIIS = Laser induced (enhanced) ionization spec- trornetry (also LEIS) MS = Mass spectrometry OES RIMS RIS = Resonance ionization spectrometry Cells/sources terminology AB = Atomic beam AT = Atom trap cw = Continuous wave operation CWL = CMT tunable laser ETA = electrothermal atomization ETV = electrothermal vaporizer F = Flame GD = Glow discharge HCL = Hollow cathode lamp ICP = Indiuctively coupled plasma NEB = Nebulizer PL = Pulsed laser PU XeS Laser terminology sc = Single colour excitation TC TP Mass spectrometry terminology IT = Ion trap ICR = Ion cyclotron resonance = Quadrupole = Time-of-flight QP TOF Other terms AFOM = Analytical figure of merit BCS = Background current shot noise BEF = Background emission flicker noise BES = Background emission shot noise CCD = Charge coupled device DN = Detector noise INT = Intrinsic noise LOD = Limit of detection LOG = Limit of guarantee LOQ = Limit of quantitation PMT = Photomultiplier tube RSD = Rclative standard deviation SAD = Single atom detection SBF SBS uv = Ultraviolet = Optical (atmic or ionic) emission spectrometry = Resonance ionization mass spectrometry = Pulsed operation = Xenon continuum source Spectrometer = Two-colour excitation (through real levels) = Two-photon excitation (through virtual level) = Source background flicker noise = Source background shot noise Appendix 111 Requirements for SAD The general requirement for an SAD method is that the method detects ea’ch and every atom with near The SAD methods are only applicable to the laser based methods.An SAD method is therefore a method in which where P is the probability of a false negative and Ed is defined as Definitions of Acronyms AAS = Atomic absorption spectrometry where P ( X 3 x d ) is the probability that the measured signal FANES exceeds or equals the detection limit. At the intrinsic limit x d = l count therefore &d becomes &do and E becomes E ~ ’ FAPES = Furnace atomization plasma emission which gives the probability that an atom will produce a signal count.The probabilities &do and gmo do not change even if the Methods terminology Ed P(xt 3 x d ) (A2) = (Hollow cathode) furnace atomization using non-thermal excitation spectrometry spectrometryJOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1994 VOL. 9 143 extrinsic noise increases. The application of the above general requirement for SAD differs for the cases of destructive detec- tion (e.g. LIIS RIS and RIMS) and non-destructive detection (e.g. LIFS). To achieve SAD with a destructive detection method a single atom can only give rise to one count at most. The detection efficiency is thus the binomial probability of success namely that an atom will be ionized during the laser interaction time Ati.This probability is given by a Poisson process. However the only way the SAD requirement can be reached is for the intrinsic noise limit i.e. xd to be equal to 1. Thus for true SAD using a laser based ionization method the following two conditions must hold P(X > 0) <a (A31 (A4) y = 1 -,-@ti> 1 - ' P where is the number of detected events per atom per unit time and Ati is the laser-atom interaction time. To achieve SAD with a non-destructive detection method the guaranteed detection limit X is used; X is defined as the probability of a variable in a distribution with mean X being less than xd being negligible i.e. less than a desired probability fl (false negative). If both background and signal are described by Poisson probability distributions it is easy to assign values of Xd and X for any value of Xb by using tables of Poisson values.The procedure in determining these signal limits is as follows. From the values of xb X is chosen so that P(Xb>Xd)%M. With this value of Xd a Poisson distribution is found such that P(X 2 X,) % P. 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Liang D. C. and Blades M. W. Spectrochim. Acta Part B 1989 44 1059. Paper 3/04012G Received July 9 1993 Accepted August 24 1993