208 Analyst March 1979 Vol. 104 $9. 208-223 Mechanism of Atom Excitation in Carbon Furnace Atomic-emission Spectrometry D. Littlejohn and J. M. Ottaway Department of Pure and Applied Chemistry Universit,y of Strathclyde Cathedral Street Glasgow G I 1XL By consideration of electronic and vibrational excitation temperatures and the ionisation temperature it is demonstrated that local thermal equilibrium (LTE) is established under the practical analytical conditions of interrupted gas flow in which commercial carbon furnace atomisers are used as emission sources. The electron concentration is shown to1 be derived from thermionic emission from the carbon tube and calculated values of 5.2 x 1O1O cm-3 at 2558 K and 1.3 x 101l cm-3 at 2766 K are reported. The processes that contribute to the establishment of LTE are considered in detail and it is suggested that molecular collisions make the major contribution to atomic excitation under all conditions but that radiation absorption may be significant when a monatomic gas is used as purge gas and when molecules are present as impurities at concentrations of only 0.01 7,.Keywords Atom emission ; carbon furnace atomisation ; excitation mechanism ; electifon concentration ; local thermal equilibrium The original introduction of electrothermal atomisers now used extensively in analytical atomic-absorption and -emission spectrometry can be traced back to the work of A. S. King in 1905 and 1908.132 He designed a resistively heated electrothermal atomiser in order to measure emission spectra of atoms arid molecules in a source which was free from the electrical action of the current carrying vapour of an arc or spark and where the complicated and often unknown chemical reactions of a combustion flame could be avoided.The measurement of atomic- and molecular-emission spectra generated by thermal energy alone in a source closely approximating to thermodynamic equilibrium rendered the King furnace of great value in the study of a number of fundamental spectroscopic proce~ses.l-~ The King furnace has been used more recently in a number of other fundamental studies. R. B. King and co-workers used furnace-emission intensity measurements at known temperatures to calculate relative gf values for a number of atomic species,6 and determined the distribution of CN molecules amongst the vibrational and rotational energy levels in a calculation of the relative vibration transition probabilities of the CN violet bands.' In studies of the vapour pressure and heat of sublimation of graphite Brewer and co-~orkers*9~ measured the emission spectrum of C in a King furnace and calculated the dissociation energy of gaseous C,.During their studies the vapour-phase temperature was measured using zirconium line-reversal at 473.95 nm. For a tube-wall temperature of 2973 K they obtained a vapour-phase temperature of 2963 5 20 K which was also in agreement with the C Swan band rotational temperat~re.~ The existence of thermal equilibrium within the electrically heated furnace was thus confirmed. Despite the information derived from such studies of the King furnace no applications of this type of atomiser in analytical emission spectrometry were reported at that time.The first analytical applications of a modified atomiser incorporating arc atomisation were reported only in 1959 and involved atomic-absorption measurements.10 Since then and notably in recent years the development of electrothermal atomisers for use in atomic-absorption analysis has advanced rapidly,ll but it is only since 1975 that the possibility of using a furnace as an analytical emission source has been advanced12913 and as yet only a limited number of analytical procedures have been described.14-lg Commercially available furnace atomisers are resistively heated like the King furnace, and it might therefore be expected that they would also act as thermal emission sources.However differences in the design and operation of modern atomisers compared with the King furnace may cause deviations from thermal equilibrium during the analysis time. There has to date been no evaluation for a furnace of the relative importance of the various excitation processes known to populate atomic energy states. The King furnace wa LITTLE JOHN AND OTTAWAY 209 generally enclosed and sealed and either operated at high pressures up to 16 atm,3 or at pressures below 1 atm.5-9 Samples introduced into the furnace were spread in bulk along the hot section of the tube often fusing to the carbon surface for the lifetime of the tube. The furnace was usually operated at the desired temperature for 10-15 min to allow equi-librium to be attained before emission measurements were taken over a further period of several minutes8 In modern analytical carbon furnace atomic-absorption and -emission spectrometry however transient signals are measured when both the tube temperature and the concentration of atoms are changing rapidly.Under these conditions there is a net transport of energy and mass through the system and an inhomogeneous temperature distribution exists. The chemical species in the furnace never reach over-all equilibrium as in the King furnace and atomisation is carried out under non-isothermal conditions. However if the rates of transport and temperature change are small compared with the rate at which energy is partitioned over the different degrees of freedom a state of equi-librium can be established for each volume element of the furnace in each small time interval.Each volume element at any instant can then be assigned a local temperature and local thermal equilibrium (LTE) can be achieved for each volume element in each small interval of time. A knowledge of the vapour temperature and how this relates to the change in wall temperature is of fundamental importance in emission spectrometry as the intensity of the analytical signal is related directly to the temperature which controls (under LTE) the distribution of the analyte species amongst the various energy levels. To understand the processes that control this distribution it is necessary to ascertain both the magnitude of the apparent source temperature and the effect of the temperature gradient on the measured emission intensity.In most instances the influence of the temperature gradient will be a function of the distribution of atoms along the tube at any instant of time. In contrast, in atomic-absorption spectrometry where resonance lines are employed for most analyses under normal experimental conditions the magnitude of the vapour temperature and the severity of the temperature gradient are less significant spectroscopically provided that the furnace temperature is high enough to maintain the atomic vapour. However the vapour temperature will affect the absorption (and emission) signals because of the tempera-ture dependence of physical parameters such as the degree of dissociation of molecular species and the residence time of atoms in the furnace.To investigate these processes and to assess whether LTE is established during the time required for the measurement of atomic-absorption signals a number of have compared vapour-phase temperatures with tube-wall temperatures measured at different times during atomisation. In most instances two-line atomic-absorption methods have been applied to estimate the vapour temperature from electronic excitation temperature calculations and these and other methods have been reviewed recently.20-22 The results of these investigations show a marked lack of agreement on the relationship between vapour and furnace-wall temperatures which is significant if the occurrence of LTE is to be con-firmed. Adams and Kirkbright23 reported that the excitation temperature of indium in a Perkin-Elmer HGA-2000 furnace increased with increase in the furnace-wall temperature, achieved a maximum similar to the temperature of the wall at the time of peak absorbance and finally decreased to a value that was up to 700 K lower than the final wall temperature.More recently Sturgeon and Chakrabarti20 found that excitation temperatures calculated from indium gallium iron and tin absorption signals in a Perkin-Elmer HGA-2100 furnace and a Varian Techtron CRA-63 atomiser rose to a maximum that occurred a t a different time to the absorption maximum The excitation temperature varied with the volatility of the thermometric species and was always lower than the tube-wall temperature by as much as 1300 K (indium). In contrast Matou~ek~~ reported vapour-phase temperatures in a Varian CRA-63 mini-furnace that were 300 K higher than the wall temperature over most of the absorption signal.He used a nickel two-line atomic-absorption procedure and this discrepancy was traced subsequently to the use of erroneous gf literature values.22 When corrected values were applied the average vapour temperature was found to lag behind the maximum wall temperature by only 50-100 K.22 Van den Broek et aZ.22 have suggested that the differences observed in the literature vapour temperature calculations for different elements can often be attributed to random and systematic errors in the methods used. From measurements of the vapour temperatures of both a Perkin-Elmer HGA-2100 furnac 210 LITTLEJOHN AND OTTAWAY MECHANISM OF ATOM EXCITATION AnaZyst VoZ.104 and a Varian CRA-63 mini-furnace using the same nickel line-pair as Matousek,= they proposed22 a model for heat transfer that indicates that in the absence of convective flow through a furnace the gas temperature will follow the wall temperature of the heated furnace to within a few degrees. Electronic excitation temperatures based on emission measurements have also been reported and show closer agreement with the furnace-wall temperature than those based on atomic-absorption methods. Alder et aZ.26 calculated the electronic excitation temperature of iron by a two-line atomic-emission procedure using a Perkin-Elmer HGA-70 furnace. The temperature was calculated for the time of the peak emission signal and was found to be of the order of 2450 K when the temperature of the furnace wall was 2420 K.Hutton2s employed iron two-line atomic-emission and “slope techniques”21 as well as two-line atomic absorption procedures involving indium and gallium to measure the vapour temperature in argon nitrogen and helium in a Perkin-Elmer HGA-72 furnace at the time of maximum atomic-emission or -absorption signals. He concluded that the vapour temperature lagged behind the wall temperature by up to 250 K and that the difference was greatest in helium and least in argon. A subsequent investigation using iron electronic excitation temperature measurements indicatedz1 that the vapour temperatures in argon nitrogen and helium were only 80-150 K lower than the wall temperature at the tube centre throughout the duration of the emission signal.Temperatures measured using the same procedure with an HGA-2200 furnace operated with maximum power heating and temperature control have also indicated2’ close agreement between the vapour-phase temperature and the furnace-wall temperature at the centre of the tube. Although some of the above results are conflicting the balance of recent experimental data supports the view that LTE does exist during carbon furnace atomisation. The supporting evidence is however derived solely from studies of atomic species. In order to confirm the existence of LTE more conclusively we have extended the application of emission measurements to molecular and ionic species and present electronic and vibrational excitation temperatures and ionisation temperatures obtained from a detailed study using the Perkin-Elmer HGA-72 and -74 furnace atomisers.Our results support the view that a thermal process or processes seem adequate to explain analyte emission intensities. 21v25 The mechanism responsible for the establishment of a Boltzmann distribution of energy under different experimental conditions has also been examined. The relative importance of electron and molecular collisions and radiative processes are assessed in a kinetic study of sodium atom excitation and an explanation is offered for the observation21 that similar atomic-emission intensities are obtained in argon and nitrogen furnace gases. In addition the electron concentration during furnace atomisation has been calculated using Saha’s equation and the result shown to be consistent with the hypothesis that electrons are generated from thermionic emission from the graphite surface.Experimental Reagents Standard solutions were prepared from reagents of the highest purity available and distilled water was used at all times. Stock solutions of each element (1000 pg ml-1) were prepared by dissolving the appropriate amount of sulphate or nitrate salt in distilled water with the addition of sufficient nitric or sulphuric acid to give a final acid concentration of 10-2~. Working solutions of the required concentration were prepared from the stock standard solutions as required. Research-grade argon (99.996% purity) was used as the furnace purge gas. Apparatus Two instrumental systems were used for the measurements reported in this paper.A Perkin-Elmer HGA-72 carbon furnace atomiser was mounted in a Perkin-Elmer 306 atomic-absorption/emission spectrometer and coupled to a Servoscribe RE 541.20 strip-chart recorder. This was used for the measurement of (;) nickel atomic emission for calcula-tion of the electronic excitation temperature and (ii) barium calcium europium strontium and ytterbium atom and ion emission for calculation of the ionisation temperature and electron concentration. The operation of this system for measurement of atomic emissio March 1979 I N CARBON FURNACE ATOMIC-EMISSION SPECTROMETRY 211 has been described previously.12.21 Standard HGA-72 graphite tubes were used. Solutions of the required concentration were transferred to the centre of the carbon tube using a 50-pl Oxford micropipette and were then dried for 40 s at 373 K and atomised for 10-13 s at maximum power which gave a final temperature of approximately 2700 K under argon gas-stop conditions.The PE 306 monochromator slit was set to give a band pass of 0.2 nm in the ultraviolet and 0.4 nm in the visible region and emission signals were recorded at a chart speed of 2 cm s-l. A Perkin-Elmer HGA-74 carbon furnace atomiser mounted in a Perkin-Elmer 360 atomic-absorption/emission spectrometer and coupled to the Servoscribe RE 541.20 strip-chart recorder was used to measure the Av = 0 series CN band emission of the B2C+ -+ X2C+ violet system for calculation of the vibrational excitation temperature. Standard HGA-74 graphite tubes were used. The operation of this system for measurement of furnace-emission signals is similar to that of the HGA-2200 which has been described previou~ly.~~ A small volume of nitrogen was introduced into the furnace with the argon purge gas to allow formation of CN molecules.This was achieved either by mixing 1-2% nitrogen with the argon supply or by operating the furnace with the end windows removed to allow ingress of atmospheric nitrogen. Both methods gave signals of sufficient magnitude and stability to permit the measurement of CN emission over the time required to scan the wavelength region of interest from 382 to 390nm. The HGA-74 was operated at maximum power under a continuous argon gas flow for 90 s. A maximum tube temprature of 2700 K was obtained within 8 s and remained constant for the duration of the measurement period.The CN band emission was scanned using the PE 360 wavelength drive at a rate of 5 nm min-l. The spectrometer slit width was set to give a spectral band pass of 0.2 nm with reduced slit height and the emission signals were recorded at a chart speed of 1 cm min-l. For measurements of atomic and ionic emission the spectrometers were adjusted to the required wavelength using the appropriate hollow-cathode lamp. In all instances suitable choice of slit height and aperture stops reduced the amount of tube-wall radiation directly entering the monochromator to a minimum. Residual background emission signals were recorded under the same conditions as the atomic- and ionic-emission measurements. The background emission at the time of the maximum of the combined analyte and background signal was then subtracted to give the net maximum atom- or ion-emission signal.The methods employed in the calculation of the spectroscopic temperatures presented in this paper are described in the Results and Discussion section. The values obtained are compared with the tube-wall temperatures measured with an Ircon series 1100 automatic optical pyrometer the design and application of which have been described elsewhere.21 Results and Discussion The processes reponsible for the excitation and de-excitation of atoms ions and molecules in arcs sparks flames and other emission sources have been well characterised by many workers (see for example references 28-34 and the literature cited therein). Excitation mechanisms have been classified28 into radiative processes collisions with electrons atoms and molecules and chemical reactions and in any specific source one or some combination of these processes may make a significant contribution.The relative importance of these processes in stimulating atomic emission from a carbon or tungsten tube atomiser has not been considered previously. If as appears likely from the earlier work cited above local thermal equilibrium is confirmed for electrothermal atomisation then one or more of these processes must be responsible for establishing LTE. It seems unlikely therefore that the chemical processes that often produce suprathennal atomic emission in combustion flames will be important. However photoreactions involving dissociation and excitation by continuum radiation from the walls and two-body exothermic exchange reactions of gaseous carbon with molecular oxides could conceivably take place under particular conditions.Similarly although the furnace system does not exhibit the electrical action of highly ionised vapours the concentration of electrons and their signifi-cance in the excitation of atoms has yet to be investigated. In order to eliminate these possible but unlikely excitation processes it is important to obtain conclusive evidence of the existence of local thermal equilibrium in the furnace during the initial few seconds of Atoms produced in a graphite furnace exist in a chemically inactive system 212 LITTLEJOHN AND OTTAWAY MECHANISM OF ATOM EXCITATION Analyst VoZ. 104 atomisation and to calculate the concentration of electrons in the furnace atmosphere in the same period.Local Thermal Equilibrium For a gas to be in complete thermodynamic equilibrium it is required that the various gaseous components of the system be in equilibrium mutually and with respect to the surroundings. This will normally prevail only in an enclosure whose walls and interior have a uniform temperature with respect to radiation and internal and although a situation closely approximating to this can exist under certain conditions for the King furnace,7s9 modern commercial electrothermal atomisers do not fulfil this criterion. How-ever as previously mentioned local thermal equilibrium can be established within a furnace during the normal atomisation period.This will be characterised for each volume element of the source by the following c~nditions~ls~~ (a) the velocity distribution of all species in all energy levels satisfies Maxwell’s equation; (b) for each chemical species the relative population of energy levels conforms to Boltzmann’s distribution law; (c) the degree of ionisation of each species is described by Saha’s equation; and (d) the radiation density is consistent with Planck’s law. Local thermal equilibrium can be shown to exist if the same value of temperature deter-mines each of the above conditions at the same time in each volume element. In real sources with concentration and thermal gradients it is impossible to consider each volume element individually and a collective measurement is obtained.This usually involves the measure-ment of the combined radiation emission from each volume element and the value of the resulting apparent temperature depends on the distribution of atoms along the temperature gradient of the s o u r ~ e . ~ ~ ~ ~ ~ As most of the atoms and molecules in an electrothermal tube furnace have similar mass and atmospheric pressure is normally used translational energy will be partitioned by collisions almost instantaneously and it can therefore be assumed that the velocity distri-bution will be given by Maxwell’s formula. The experimental determination of the trans-lational (or kinetic) temperature is possible from Doppler half-widths but is known to be fairly inaccurate3’ and is not considered further here. The likelihood of LTE existing in the graphite tube furnace is enhanced by the presence of the tube-wall enclosure which is the source of all energy subsequently transferred to the vapour phase.In most emission sources condition (d) above concerning Planck’s radiation density is not fulfilled and deviations from LTE can exist because radiation emitted by vapour species is not compensated for by absorption of an equal amount of radiation from the surroundings. In many sources where the molecular concentration is high and collisional processes of excitation and de-excitation predominate the effect of this outward radiation loss is minimal. Departures from L‘TE through radiative dis-equilibrium have, however been observed for hydrogen - argon and for a low current d.c. arc operated in an atomic gas (see p.126 of reference 32). In a previously reported s t ~ d y 3 ~ we have shown that the spectral distribution of energy from a graphite tube atomiser closely fulfils the requirements of Planck’s radiation law. A temperature of 2553 K was calculated from the spectral distribution of the graphite tube continuum when the wall temperature as measured by the optical pyrometer was 2603 K at the tube centre and a temperature of 2534 K was obtained from the intensity of wall radiation scattered by the components of the vapour phase when the wall temperature was measured at 2573 K. In this investigation we considered LTE criteria (b) and (c) above by comparing electronic and vibrational excitation temperatures and the ionisation temperature with corresponding tube-wall temperatures in order to ascertain whether LTE holds during the initial few seconds of atomisation when both atomic-absorption and atomic-emission signals are recorded.Excitation ternperatu~es31~32s37~~~ The wavelength-integrated emission intensity measured by a spectrometer when an atom or molecule undergoes a radiative transition from an energy level Ex to a lower energy state Ey can be expressed by hc L I = KAz,Nx x - x - hzv 47 March 1979 IN CARBON FURNACE ATOMIC-EMISSION SPECTROMETRY 213 where I is the intensity over the total line width K is a machine constant Ax is the Einstein transition probability Nx is the concentration of atoms or molecules in the upper energy level A,* is the wavelength of the transition L is the source length in the direction of viewing and h and c have their usual meanings and values.If the species in question are thermally distributed amongst the various electronic vibra-tional and rotational levels Nx can be replaced with where k is Boltzmann's constant g is the statistical weight of the upper energy level N is the total species concentration in all states and B(T) is the partition function or the state sum41 and is defined as where the subscripts denote the excited states and zero the ground state. Combining equations (1) and (2) gives which can be rearranged to In ("> = In (K'N,) - - E X kT * * gxA xv where K' covers all of the constants in equation (4) including the partition function B(T), which is approximately constant for the species of interest over the temperature range discussed here.42 The value of ln(K'Nt) will vary during the atomisation cycle of a furnace because N,, the total concentration of atoms in the tube varies but will be constant for all lines of an element at any specific instant.Hence by measuring the relative intensity of a series of spectral lines at different times during atomisation it is possible to calculate T the electronic excitation temperature at each moment from the slope of In (Lk,) - against E, if the energy levels are populated in accordance with the Boltzmann equation. The atomic-emission signals of the nickel lines listed in Table I were measured in duplicate with respect to time using the HGA-72/PE 306 system. A 50-pl aliquot of a 0.5 pg ml-l nickel solution was used in each instance.At this concentration self-absorption effects were observed to be negligible. Correction factors for the slight variation in the spectro-meter spectral response at different wavelengths were applied to the mean of the recorded intensities. The slope temperatures were then calculated as illustrated in Fig. l ( a ) at various times during atomisation from the least squares calculation of the slope of the graph TABLE 1 NICKEL LINES EMPLOYED FOR THE MEASUREMENT OF THE ELECTRONIC EXCITATION TEMPERATURE BY THE SLOPE METHOD43 Wavelength h/nm Energy levels/eV log, gA / A 305.08 4.088-0.025 5.35 341.48 3.655-0.025 5.24 342.37 3.832-0.2 12 4.72 343.36 3.635-0.025 4.72 344.63 3.705-0.109 4.98 349.30 3.657-0.109 5.0 214 LITTLE JOHN AND OTTAWAY MECHANISM OF ATOM EXCITATION AnaZyst VoZ.104 3.0 3.4 3.8 4.2 €,,lev V + Es- E,/eV Variation of the intensity of carbon furnace emission signals with excitation and ionisation energy in a calculation of (a) nickel electronic excitation temperature (HGA-72) wall temperature a t the centre 2 670 K and slope temperature 2 568 f 143 K; (b) CN vibrational excitation temperature (HGA-74) wall temperature a t the centre 2 700 K and slope temperature 2 491 & 143 K ; and (G) ionisation temperature (HGA-72) wall temperature at the centre 2 700 K and slope temperature 2 603 jl 174 K. Measurements made in argon at maximum power (999 units). Electronic and ionisation temperature calculated from atomic and ionic emission intensities recorded with inter-rupted gas flow at 4 and 6 s respectively from the start of atomisation.Fig. 1. of In (”-> against E,. The gJ values employed were those described by C o r l i s ~ ~ ~ as the best recommended values for the nickel lines in question. g J m The calculated temperatures at various times up to -9 s during atomisation in Fig. 2 are slightly lower than the equivalent wall temperatures at the centre of the tube owing to the temperature gradient along the carbon surface and are in agreement with our previous studies using iron as the thermometric species in Perkin-Elmer HGA-7221 and HGA-220027 furnaces. The error bars in the observed temperatures were obtained by the method of least squares and represent one standard deviation of the points from the straight line, taking into account variations in sample introduction signal measurement and errors in the 6 + 8 9 ’ Tirnels Fig.2. Variation with time oi the wall temperature a t the centre of an HGA-72 graphite tube atomiser (-) with the electronic excitation temperature (@) calculated from the nickel atomic emission. Atomisation a t maximum power (999 units) in argon with interrupted gas flow March 1979 I N CARBON FURNACE ATOMIC-EMISSION SPECTROMETRY 215 gxA values. Close agreement between tube-wall and electronic excitation temperature was also reported by Van den Broek et aZ.,22 who used a nickel two-line atomic-absorption procedure to calculate the vapour temperatures of a Varian CRA-63 mini-furnace and a Perkin-Elmer HGA-2100 atomiser. When molecules are used as the thermometric species the excitation temperature can be calculated from rotational and vibrational spectra.This requires the replacement of the transition probability Ax# in equation (4) by the expression 167~3 1 . # A = - x- x s 3 4 & gx where E, is the permittivity of a vacuum and S is the line strength which by definition is the square of the electric dipole transition moment.41 Rotational lines of certain molecules, such as OH and CN are nearly always observed as impurities in emission sources but high resolution is required to resolve the rotational s t r u c t ~ r e . ~ ~ ~ ~ * Vibrational bands of un-resolved rotational character can however be used easily to calculate the vibrational excitation temperature. In this instance the line strength S is replaced by the vibrational transition probability pvsvI calculation of which requires a knowledge of the dependence of the electronic transition moment on internuclear distance.46 Equation (4) can then be expressed in the form which on rearrangement (7) becomes where K" includes all of the constants in the previous equations and Ev2 is the energy of the upper vibrational level of the transition of interest.Emission spectra of a number of molecules formed during carbon furnace atomisation were described in detail by Hutton et aZ.46 Of those molecules which are easily observed CN seemed the most suitable and equation (8) was applied to the vibrational spectra of the Av = 0 sequence of the B2C+ -+ X2C+ band system given in Table 11. The CN emission was measured using an HGA-74 atomiser operated at maximum power with argon gas flow, using the wavelength drive of the spectrometer (PE 360) to scan the bands in the 385-390-nm region.As with the vibrational spectra of many diatomic molecules the bands overlap strongly and it was necessary to extrapolate the tail of each band to the maximum of the adjacent band to subtract the overlapping background intensity and obtain the net emission intensity of each band. With these reduced band-head intensities a graph of In ?$) zle~syszcs Eva was constructed as illustrated in Fig. l ( b ) and the vibrational excita-tion temperature calculated. A period of approximately 90s was necessary to scan the wavelength region required, TABLE I1 BANDS OF THE CN VIOLET B2 C+ -+ X 2 C+ SYSTEM EMPLOYED FOR THE MEASUREMENT O F THE VIBRATIONAL EXCITATION TEMPERATURE BY THE SLOPE METHOD4' Wavelength/ Energy levels/ Relative vibrational Band nm eV transition probabilities 010 388.34 3.198-0.0 1000 1,1 387.14 3.462-0.253 880 282 386.19 3.720-0.503 790 3,3 386.47 3.973-0.750 74 216 LITTLEJOHN AND OTTAWAY MECHANISM OF ATOM EXCITATION Analyst VoE.104 and to maintain reproducible and measurable CN emission over this time nitrogen impurities were continuously introduced at a constant rate into the furnace with the argon gas flow by operating the atomiser without the end windows to allow ingress of air. As the furnace was also operated at constant temperature the CN bands were therefore measured under equilibrium conditions. The residence time of the nitrogen in the furnace is however, relatively short and the establishment of equilibrium conditions therefore needs to be rapid.Temperatures calculated by this procedure give little information about changes in the vapour temperature during the initial few seconds of atoniisation normally used for analysis, but do give an indication of the influence of tube-temperature gradient on the vapour-phase temperature. Because the measured emission intensity is a combination of the photons emitted from each small volume element of the furnace and the intensity from each section is dependent on its temperature and atom or molecule content the deviation of the apparent vapour temperature from that of the carbon wall at the tube centre will depend on the distribution of species along the tube-temperature gradient.Under the conditions normally used for analytical atomic-emission studies i.e. interrupted gas flow (or gas stop) the concentration of atoms etc. will always be greatest at the tube centre but for the procedure used for the measurement of CN an almost even distribution will exist along the tube. The vibrational excitation temperature of 2491 & 143 K calculated from the slope in Fig. l ( b ) is about 200 K lower than the wall temperature at the tube centre. Although this is a greater deviation than that observed for the nickel atorn measurements the difference is relatively small considering that the ends of the tube and the carbon cones will be of the order of lo00 K or lower when the centre of the tube is at 2700 K. This suggests that an apparent temperature gradient of only a few hundred degrees from the centre to a few millimetres from the ends of the carbon tube will be effective in determining the intensity of atomic or molecular emission from an electrothermal atomiser depending on the concentration gradient therein.This argument will be developed elsewhere47 in a consideration of tube design and temperature on the intensity of atomic-emission signals. As far as the present work is concerned measurements of the vibrational excitation temperature of CN indicate a thermal population of energy levels and support the contention that LTE is attained during carbon furnace atomisation. Ionisation tempe~atu~e~7~4~~@ is represented by Saha's equation for the ionisation equilibrium between the atoms and ions of one element where N, Ni and N are the concentrations of atoms ions and electrons respectively, B(T)u and B(T) are the partition functions of atom and ion V is the ionisation potential, m is the mass of the electron and the other terms have their usual meanings and values.The intensity of the ionic emission can be expressed in a similar manner to that for atomic emission and combination of equation (4) for each species with equation (9) yields the relationship where subscripts s and t refer to the upper and lower energy levels of the ionic transition. Equation (10) requires that the emission intensities of an atom and ion line be measured for a series of elements or line pairs. At any instant in time during atomisation the ternpera-ture and hence 1.5 1nT will be constant and a graph of the left-hand side of equation (10) veYsus V + Es - E for each element or line pair will be a straight line of slope +l/kT, from which the ionisation temperature can be calculated.Emission signals were measured with respect to time in duplicate for each of the atom and ion line pairs shown in Table 111, using the HGA-72/PE 306 system at maximum furnace power and with interrupted argo March 1979 Element Eu Yb Ca Crt Sr Ba IN CARBON FURNACE ATOMIC-EMISSION SPECTROMETRY TABLE I11 ATOM AND ION LINE PAIRS EMPLOYED FOR THE CALCULATION OF THE IONISATION TEMPERATURE49 Ionisation Wavelength/ Energy levels/ potential/ Line nm eV eV gA x 10-8/s I 321.281 3.858-0.0 5.67 9.6 I1 420.505 2.949-0.0 3.2 I 377.010 5.433-2.144 6.20 8.6 I1 369.4 19 3.356-0.0 0.74 I 430.253 4.781-1.899 6.11 7.1 I1 393.367 3.152-0.0 0.91 I 445.673 4.683-1.899 6.11 7.5 I1 393.367 3.152-0.0 0.91 I 496.226 4.346-1.848 5.69 4.8 I1 407.771 3.04 1-0.0 0.66 I 611.076 3.219-1.190 5.21 5.2 I1 614.172 2.723-0.704 0.38 21’7 Concentration of solution*/ pg ml-I 5 50 40 40 10 20 * Injections of 50 p1.gas flow. Similar spectrometer conditions were applied for the measurement of the atom and ion signals of each pair. Wavelengths were chosen to give emission intensities of a similar order of magnitude for both species at concentrations giving negligible self-absorption. Atom and ion lines of similar wavelength were employed where possible to minimise errors in the correction for variations in spectrometer spectral response.The ionisation temperature was calculated at various times during atomisation as illustrated in Fig. l ( c ) and the collated results shown in Fig. 3 compared reasonably well with the tube-wall temperature at the corresponding time. The error bars signify the random errors for the derived temperatures as calculated with a programmable calculator by applying the method of least squares. The errors appear to be acceptable for the procedure con-sidering the number of measurements contributing to each calculation. 2 600 2 200 -1 ’ 6ooe$-- 3 4 5 6 j 8- 9 I 0 1’1 1; Time/s Variation with time of the wall temperature at the centre of an HGA-72 graphite tube atomiser (-) with the ionisation tempera-ture (*) calculated from the atomic and ionic emission of calcium, barium strontium europium and ytterbium.Atomisation a t maximum power (999 units) in argon with interrupted gas flow. Fig. 3. Electron concentration Once the ionisation temperature at any point during atomisation has been calculated, the abscissa of the above graph of equation (10) can be used to calculate the value of N, 218 LITTLE JOHN AND OTTAWAY MECHANISM OF ATOM EXCITATION Analyst VoZ. 104 the natural level of electrons in the furnace at the same time. The electron concentration was found to range from 5.2 x 1O1O ~m-~ at 2558 K to 1.3 x loll ~ m - ~ at 2766 K. The errors in the electron concentrations at each point during atomisation were calculated from a knowledge of the error in the slope (and hence the abscissa) and the temperature.The errors were found to vary between hO.9 and k l . 9 orders of magnitude for all the points considered. This appears to be acceptable for the procedure used considering the degree of extrapolation required to obtain the abscissa and the dependence of the calculation of electron concentration on temperature (see p. 173 of reference 31). No comparative values for the electron concentration in electrothermal atomisers have been reported. It is unlikely that furnace electrons will be produced through the ionisation of vapour phase carbon species as the ionisation potentials of CN C C, C, etc. are of the order of 11 eV or higher.50 Graphite however has a comparatively low thermionic work function and an indication of the concentration of electrons produced by thermionic emission as the tube surface is heated is given by the expression51 2 (2nm,kT) 5 -w N = .. . . (11) where W is the work function for carbon 4.6 eV. At 2760 K the value of 2.7 x 101 cm-3 obtained from equation (11) compares reasonably well with the value obtained above from Saha's equation and is within experimental error. Although trace impurities of sodium, potassium and other easily ionised elements present in the furnace material or purge gas will add to the partial pressure of electrons the concentration will be much smaller (10s cm-,) than that produced by thermionic emission,2o which hence seems the only viable source of electrons. Conclusion From the preceding discussions it appears that conditions closely approximating LTE are achieved in a carbon furnace during atomisation excitation and ionisation of atomic and molecular species.The evidence presented above appears conclusive at least for the presently available commercial systems investigated. Although the measurement of thermal emission from a carbon furnace precludes excitation by suprathermal chemiluminescence mechanisms confirmation of a Boltzmann distribution of energy does not in itself identify the relative contributions of the remaining processes in establishing thermal equilibrium. To obtain information on the most likely mechanism or mechanisms it is necessary to consider the kinetics and practical rate of each process under normal atomisation conditions. Atom Excitation Mechanism The competing processes that are likely to excite metal atoms (or ions )electronically in a graphite tube atomiser are therefore (a) collisions with electrons involving transfer of the translational energy from electrons (b) collisions with molecules with transfer of the vibra-tional and rotational energy of molecules (c) discrete absorption of radiation from the tube-wall continuum.These processes can be expressed in the form of equations as follows: M+e- +M*+e- . . . . (124 M + X Y + M * + X Y . . (12b) M + h v +M* . . (124 where e represents an electron M and M* a metal atom in the ground and excited states, respectively XY a molecule where X may or may not be the same as Y and hv is a photon of discrete energy. The excitation rate equations for these processes can then be described respectively as Ratee = ke[e-][M] .. . . (13a March 1979 IN CARBON FURNACE ATOMIC-EMISSION SPECTROMETRY 219 Rate, = kxY[XY][M] . . . . (13b) where k is the rate coefficient or constant for each process and k includes a term accounting for the radiation density. It is generally accepted that monatomic species show low efficiency in the electronic excitation of metal atoms,% which would be expected from classical mechanics and this process is not considered further in this discussion. However owing to their much smaller mass and larger mean velocity under thermal conditions electrons are expected to be considerably more efficient than inert gas atoms in the (de-)population of atomic electronic states that lie several electronvolts above the ground state% and so have been considered.Gilmore et aZ.,29 in a review of atomic and molecular excitation mechanisms tabulated rate coefficients for excitation de-excitation and excitation energy transfer for a number of reactions but in general investigations involving metal atom species have been limited to the alkali metals. For all the processes described above expressions were available that allowed calculation of the rate coefficients for the excitation of the sodium resonance line at 589.00 nm. These calculations are used in the following discussion as an illustrative example, using a typical furnace temperature of 2500 K. As the concentration of sodium is a constant whichever process is considered values of Rate/[Na] will be calculated in each instance and compared. Electron collisions T by averaging over a Maxwellian distribution of electron energy giving28 The excitation rate constant ke can be obtained under thermal conditions at temperature where E is the energy of the excited state in this instance 2.1 eV for sodium and uTHB is the effective cross-section at energies greater than the threshold required for excitation and is of the order of 2.3 x 10-15 crn2.5 Substitution for the other constants in equation (14) and T = 2500 K gives a value for he of 4.4 x cm3 s-l.An alternative expression for ke was derived by Gilmore et based on the integration of Zapes~chnyi’s~~ cross-sections over a Maxwell velocity distribution for several temperatures and fitting the data for sodium by an Arrhenius function of temperature The resulting equation was ke = 6 x 10-10To.6exp (-2y) ____ which was shown to fit well over a wide temperature range from 1500 to 20000 K.With this relationship a value of 3.6 x cm3 s-l is obtained for ke at 2500 K in reasonably close agreement to the alternative value above. Taking a value for ke of 4.4 x cm3 s-l and the value of the electron concentration of 3.1 x 1011 CM-~ calculated as produced by thermionic emission at 2500 K equation (13a) gives a value for Ratee/[Na] of 14 s-1. The alternative value of ke would result in a smaller value of Rate,/Na and the above value may be considered as a possible maximum. Molecular collisions The concentration of molecules such as N, O, CN C, etc. present in a graphite tube atomiser during the production and excitation of metal atoms depends greatly on the conditions of operation such as inert gas used and temperature and the design of the furnace.Two conditions will therefore be considered that can be taken as the extremes of the maximum and minimum molecular content normally encountered in practical analysis. When an atomiser is operated in a nitrogen atmosphere the concentration of molecules will be totally dominated by N at a level of about 3 x lo1* molecules ~ r n - ~ at 1 atm and 2500 K. Mental1 et aZ.53 have calculated the rate coefficient for excitation of sodium b 220 LITTLEJOHN AND OTTAWAY MECHANISM OF ATOM EXCITATION APtaZyst Vol. 104 nitrogen to be approximately k, 10-lo cm3 s-l att temperatures between 2 100 and 2800 K. These two figures combined give a value of Ratel\~,(~~~.)[Na] from equation (13b) of 3 x lo8 s-l.When a monatomic gas such as argon is used as purge gas in an enclosed furnace system like the IL 555 atomiser the molecular concentration arises from nitrogen and oxygen present as impurities in the gas and from desorption from the furnace material at elevated temperatures. The argon normally used in this laboratory contains 0.004% impurity, which if it is assumed to be exclusively 0 and N, gives about 1014 molecules cm-3. In addition at room temperature a level of at least 1014 molecules cm- of nitrogen and oxygen will be adsorbed on the surface of the atomiser when opened to the air.54 On desorption, during atomisation this will add a further 5 x 1014 molecules ~ m - ~ to the furnace volume. At 2500 K the partial pressure of C species will be approximately 10-7 atm,55 giving 3 x loll C molecules ~ m - ~ .This is increased at 3000 K. to 3 x lo1* molecules ~ m - - ~ atm) and only at this temperature would the concentration approach that of the nitrogen and oxygen. As optimum atomic-emission signals are normally measured for sodium and many other elements at temperatures less than 3000 K,56 it is unlikely that excitation by C will be significant unless the rate constant for such excitation is very large. The fact that LTE exists at temperatures a t which the concentration of C species is very low suggests that this process cannot be the major excitation medhanism. A value for the rate constant for the excitation of sodium by oxygen was not available. The minimum concentration of molecules under these conditions is therefore expressed exclusively as N and is assigned a value of 5 x 1014 ~ m - ~ .The collision cross-section of 0 at 2000 K (given on p. 48 of reference 28) suggests that oxygen will be at least as effective as nitrogen as a molecular species capable of exciting metal atoms. The rate of excitation at this minimum concentration of molecules expressed as nitrogen and given by equation (13b) RateN2,,,,,,/[Na] will be 5 x lo4 s-l. Photon absorption Unlike other emission sources a graphite or tungsten tube atomiser will fulfil the con-ditions of "detailed balance" for radiative processes irrespective of the concentration of analyte present as loss of photons through atomic ionic or molecular emission will be balanced by absorption of the tube-wall black-body radiation at discrete energies.The rate constant for radiational excitation kRAD can be expressed as (reference 28, P. 64) where f is the oscillator strength for absorption and PA is the spectral volume density of the radiation field. For a graphite tube atorniser PA rn PA the black-body radiation density which is given by Wien's approximation of Planck's law39 as 87Thc PAb = - x e!xp A5 The oscillator strength f can be expressed in terms of the Einstein transition probability for emission A, by (reference 28 p. 17) Substitution of equations (17) and (18) for PA andf into equation expression for kR,D : . . (18) (16) produces a simplifie March 1979 IN CARBON FURNACE ATOMIC-EMISSION SPECTROMETRY 221 The magnitude of (g2/gl)A2 is of the order of 108 s,49 giving for the sodium resonance line at 589.0 nm a value of RateaAD/[Na] approaching 5.8 x 103 s-1 at 2500 K.Using data available in the literature it has been possible to calculate the reaction rates for processes (12a) (12b) and (1%) for the sodium resonance transition at 589.00 nm. Similar data for all the processes do not seem to be available for any other atom or transition. The reaction rates for the sodium transition at 2500 K are compared in Table IV and additional values computed for 2 100 and 2 800 K are given. These temperatures represent the extremes of the temperature interval over which the nitrogen rate coefficient of 1O1O cm3 s-l can be applied. A number of conclusions can be derived from these figures regarding the mechanism of sodium excitation and atomic excitation generally in a carbon furnace atomiser.When nitrogen is used as the furnace purge gas excitation and de-excitation of all species will be dominated by N molecular collisions. Although the temperature dependence of electron concentration greatly increases the rate of electron excitation from 2100 to 2800 K it is unlikely that electron collisions will be a significant excitation process at the temperatures at which emission signals are normally measured (less than 3000 K) irrespective of the pressure or composition of the furnace gas. (C) When a monatomic gas such as argon is used as purge gas at temperatures approach-ing 3000 K in an enclosed furnace the contribution of photon absorption can become similar to that of nitrogen molecular impurities.In open furnaces the contribution of photon absorption is less significant than in a closed furnace owing to the increased ingress of atmospheric nitrogen. A lack of detailed information regarding the temperature variation of the N collision-rate constant leads to an unexpected trend of reduced rate with increased temperature (Table IV) for nitrogen collisions. This trend may in fact be erroneous but it will not affect the conclusions drawn above over the most useful temperature range of presently available carbon furnace atomisers. (A) (B) (D) TABLE IV RATES OF REACTIONS FOR PHYSICAL PROCESSES OF SODIUM EXCITATION AT DIFFERENT TEMPERATURES OF 2 100,2500 AND 2800 K Rate/ [Na]/s-l r n 7 Process 2100 K 2500 K 2800 K Electron collisions .. 3.08 x 1.39 x lo1 4.43 x 102 Nitrogen collisions maximum . . 3.5 x lo8 3.0 x los 2.6 x 108 Nitrogen collisions minimum . . -5 x lo4 -5 x 104 -5 x 104 Photon absorption . . 9.0 x 102 5.8 x 103 1.7 x 104 Although the excitation of atomic and molecular species in nitrogen can be up to lo4 times faster than in argon (owing to the greater concentration of N,) similar emission intensities are measured in both gases at the same furnace temperature.21 This is explained by the principle of “detailed balance” that applies to all processes in conditions of local thermal equilibrium. “Detailed balance” states that the total number of atoms or other species leaving an excited state per second by any process (collision radiation etc.) just equals the number arriving in that state per second by the exact reverse process.34 Hence, in nitrogen the de-excitation rate will be also about lo4 times faster than in argon.In carbon furnace atomic-emission spectrometry reduction of the molecular concentration from 100% nitrogen to approximately O.Olyo does not appear to disturb conditions of local thermal equilibrium as indicated previously by a comparison of atomic-emission intensities in argon and nitrogen gases. In contrast departures from LTE arise in a d.c. arc operated in an inert gas with less than 1% molecular impurity and infrathermal emission is en-countered in combustion flames of low molecular concentration (see pp. 126131 of reference 32). This can be understood from a comparison of the number of molecular collisions that a metal atom suffers during the average residence time in the observation zone of each source.At atmospheric pressure the number of collisions between sodium and nitroge 222 LITTLEJOHN AND OTTAWAY MECHANISM OF ATOM EXCITATION Analyst VoZ. 104 is about 109 s-1 at 2500 KS (assuming 100% nitrogen). The residence time of a metal atom in an air - acetylene flame or d.c. arc is of the order of millisecond^,^^ and therefore each sodium atom will take part in 105-106 collisions in this time. At 2000 K at least one out of every 105 colliding molecules has an energy of about 3 eV,34 and the collision frequency therefore seems sufficient to establish an equilibrium population of the excited state. At lower nitrogen concentrations this is less likely to be true. However the residence time of metal atoms in a HGA-72 furnace operated with interrupted gas flow is about 1 s,57 and therefore even at nitrogen concentrations as low as O .O l ~ o sodium and other atoms will still make 105-106 collisions with nitrogen molecules while present in the furnace atmosphere. The existence of LTE under such conditions is therefore likely even without the contribution of tube-wall radiation. It is also interesting to note that when the molecular concentration, in a d.c. arc or combustion flame falls below the level at which molecular collisions dominate all other processes departures from thermal populations arise through radiative disequi-librium as photons emitted by atoms are not balanced by the absorption of photons at an equal rate from the radiation field.In a furnace atomiser the semi-enclosure of the tube wall which radiates as a black body ensures that radiative disequilibrium does not occur and LTE is maintained. Similar conclusions to the above will apply to most furnace tube atomisers operated under interrupted gas flow conditions including those made from other materials such as tungsten. The thermionic work function for tungsten 4.52 eV,50 is similar to that of carbon and will give a similar electron concentration and Kirchoff’s law2* ensures that an approximate black body radiation density will exist in the tungstein-tube atomiser. The conclusions reached above may not necessarily apply under conditions of convective gas flow where vapour-phase temperatures may differ substantially from tube-wall temperatures.22 The work described in this paper indicates that the graphite furnace is unique amongst emission sources in that local thermal equilibrium exists under normal working conditions.In achieving this state molecular collisions appear to make the major contribution but radiation absorption may be of minor importance when argon is used as purge gas. Although some of the fundamental properties of the King furnace have been known for many years, the possibility of applying the technique of furnace emission more widely in analytical chemistry is only now being investigated in detail. While the carbon furnace remains a relatively cool source compared with other currently available emission sources the signal to background ratios signal stabilities and atom residence times are such that very low detection limits have already been achieved for a wide range of elements,27@ and spectral interferences are much reduced in complexity.The fundamental origin of the observed emission signals established in this paper will contribute to the development of the technique, and to considerations of the most suitable design of atomisation source. The authors thank the Salters’ Company for the award of a Scholarship to D.L. and The Royal Society for the award of a research grant to J.M.O. for the purchase of the HGA-72 atomiser. The gift of the HGA-74/PE 360 system by the British Steel Corporation, Ravenscraig Works and helpful discussions with many colleagues particularly C. Th. J. Alkemade are also gratefully acknowledged.1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 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Received June 12th 1978 Accepted October llth 197