Analyst February 1983 Vol. 108 pp. 145-152 145 Intensities of Some Spectral Lines from Hollow-cathode Lamps Christopher Howard Marjorie E. Pillow and Edward B. M. Steers* and Donald W. Ward School of Applied Physics The Polytechnic of North London Holloway London N 7 8013 Cathodeon L t d . Nu$eld Road Cambridge CB4 1TF The relationship between spectral line intensity 1 and discharge current i is examined as part of an investigation of low pressure (1-20 Torr) hollow-cathode discharges in neon for various cathode dimensions. An equation, I = Ai ( 1 + Ci)/(l + Bi) deduced by balancing likely excitation and de-excitation processes can be fitted within the limits of experimental accuracy to measured I versus i graphs. Here A depends on one-stage excitation C on the relative importance of two- and one-stage excitation and B on the relative importance of collisional and radiative de-excitation.The values of B and C for individual lines and their dependence upon pressure and upon cathode dimensions together with the possible role of self-absorption are discussed. Keywords Hollow cathodes ; excitation pyocesses ; spectral intensity ; neon Hollow-cathode discharges have been used for many years for the production of intense, narrow spectral lines and in more recent years have been extensively employed in analytical atomic spectroscopy mainly as sealed lamps forming the line source in atomic-absorption spectroscopy but also as a demountable source for samples in emission spectroscopy. Despite this the details of the excitation processes are as yet imperfectly understood; this paper presents some preliminary results from a continuing extensive study of hollow-cathode lamps.In hollow-cathode and other low-pressure low-current sources thermodynamic equilibrium does not exist and the populations of the excited states of the carrier gas and of the atoms sputtered from the cathode cannot be characterised by a “temperature.” A possible method of studying excitation processes under actual discharge conditions is the investigation of the relationship between the intensity of specific spectral lines and the discharge current. In this paper a theoretical interpretation of such relationships with physically significant parameters, is deduced by balancing excitation and de-excitation processes and shown to be in good agreement with experimental results for a number of Ne I and Ne I1 lines.Discussion of the intensity of spectral lines emitted by sputtered cathode atoms is reserved for later work; whilst most of the applications of hollow-cathode lamps involve such lines their intensities depend on two further processes (the sputtering of the atoms and the diffusion and excitation of the sputtered atoms) and can only be considered satisfactorily when the basic processes occurring in the carrier gas have been established. I n a review on hollow-cathode discharges Pillowl has pointed out that whilst in the lamps now used for atomic-absorption spectroscopy and emission spectroscopy the cathode is typically of 3 mm bore most of the published work on the physical properties of hollow-cathode discharges (electron energy distributions field strengths etc.) has been carried out using much larger cathodes (10-30 mm bore).The results presented in this paper are part of a wider investigation currently in progress which includes the effects of cathode dimensions and carrier gas pressure on the electrical and spectral properties of the discharge. The “similarity principle” predicts that geometrically similar discharge tubes typified by linear dimensions d, d would exhibit the same electrical behaviour if the gas pressures used PI P2 were such that P,d = P2d2. This is unlikely to hold exactly in instances where as in a hollow cathode, photo-emission has a significant role in cathode emission; however it was found here that a large cathode at low pressures gave results closely resembling those for a smaller cathode at correspondingly higher pressure.It is clear from a visual examination of a hollow-cathode discharge that the intensity varies within the cathode; previous workers such as Lompe et aZ.2 and Kagan and c o - ~ o r k e r s ~ - ~ have shown that the radial intensity distribution varies greatly with pressure and from line to * To whom correspondence should be addressed 146 HOWARD et al. INTENSITIES OF SOME Analyst Vol. 108 line and that this can be linked with electron energy distributions. This variable intensity distribution complicates the measurement of line intensity; three approaches may be used a small image on the spectrometer slit may be used to give the total intensity; with a larger image the intensity from a diametral or other slice may be recorded; and by restricting the slit height a particular region of the discharge (frequently the axial region) may be studied.In the present investigations radial intensity distributions were recorded so that total, diametral and axial intensities could be derived. The results in this paper are based on axial intensities recorded as discussed below. Experimental Some preliminary measurements were made using sealed hollow-cathode lamps from Cath-odeon Ltd. Some of these were of routine manufacture and some were provided specifically for this work. The majority of the work was carried out using a demountable hollow-cathode lamp (Fig. 1 ) ; the experimental chamber formed part of a specially designed metal high-vacuum system which could be evacuated to Torr for the de-gassing of the hollow-cathode chamber.After de-gassing a charge of research-grade neon could be introduced at the desired pressure and gas purity maintained with a non-evaporable getter (Societa Appar-ecchi Electtrici e Scientifici Stl71TM). Various sizes of mild-steel cathodes were used with a stainless-steel ring anode. Mica and glass screens were used to prevent unwanted discharges. All the intensity measurements were made using a 0.8 m focal lengthf/10 Ebert mono-chromator (Philips) with a 1200 lines mm-l grating used in the first order and an EM1 9789QA photomultiplier. The signal was amplified and recorded on a Honeywell Brown chart recorder. An image of the central plane of the cathode was focused on the entrance slit of the monochromator using two plane mirrors and a concave mirror operated close to its axis.The magnification of the system was adjusted according to the cathode size and this influenced the solid angle accepted from the source. The radial intensity distribution was recorded by rotating the concave mirror slightly by a slow mechanical drive to scan the diameter of the cathode image horizontally across a short slit (height about one tenth of the image diameter). The centre of the image yielded the “axial intensities.” Cathode dimensions Bore/mm Depth/mm 3 10 6 20 15 50 Fig. 1. Sectional view of demountable hollow-cathode lamp. A Stainless-steel ring anode; C cathode; G getter; L insulated lead-throughs M mica disc Q, fused quartz viewport; S, S, glass sheaths; S, fused silica sheath; V connection to high-vacuum system February 1983 SPECTRAL LINES FROM HOLLOW-CATHODE LAMPS Results and Discussion Experimental Results 147 In the preliniinary experiments with a sealed iron hollow-cathode lanip axial intensity versus current graphs were plotted for a number of spectral lines and showed a wide variety of form; typical graphs are shown in Fig.2. For Ne I lines a linear graph was obtained for a few lines with upward curvature for some others but many showed pronounced downward curvature even when self-absorption was not likely. Ne I1 lines usually gave a straight line or upward curving graph whilst the spectral lines of the cathode material showed very pronounced upward curvature. Similar results were obtained for copper and molybdenum cathodes.20 15 VI t 3 .l- .-2 2 .= 10 -e i 5 0 ilmA Fig. 2. Experimental intensity ( I ) vettius current (2) graphs for a sealed iron hollow-cathode lamp (cathode 3 mni bore 10 mm deep). The arbitrary intensity units differ for each line. Wavelength 1 Ne I 363.4; 2 Xe I 470.9; 3 Ne I 665.2; 4 Ne I 614.3; 5 Ne I1 337.4; and 6 Fe I 382.7 nm. On the basis of this survey the spectral lines listed in Table I (and for Ne I lines sliown 011 the energy level diagram Fig. 3) were chosen for more detailed study with different cathode dimensions at various gas pressures in the demountable discharge lamp. The radial intensity distributions were recorded in all instances and were compatible with other published pressure has a marked effect on these distributions whilst for most lines current has a very limited effect.Accordingly axial intensities have been considered for this first treatment of the results. Smooth trends were observed with pressure and cathode size. TABLE I NEON LINES STUDIED IN DETAIL (OR REFERRED TO IN THIS PAPER) Species A/nm Transition Upper level/eV N e I . . . . 363.4 4p[+lo + 3s’[8]! 20.3 470.9 5d[$]! -+ 3~5$!,~ 21.0 588.2 3p’[Q] + 3s[1&]; 18.7 614.3 3p[13l2 += 3s[l&]O 18.6 665.2* 3p[Ql0 -+ 3s’[+]; 18.7 585.2 3p’[+] -+ 3s [2]1 19.0 Ne I1 . . . . 337.4* 3d 4D3,2 + 3p 4D,,2 21.6 + 34.9 348.1 3~”~P,,,-t 3s” ‘ S ) 21.6 + 37.7 348.2 3p ‘P*” + 3s 2P3,2 21.6 + 31.4 * Sealed lamps only 148 Analyst Vol. 108 Theoretical Interpretation In a paper that gives probably the most extensive previous coverage of intensity current relationships MushalO used a log - log plot for his results; he obtained very approximately straight lines of differing gradients but there is no physical reason suggested for the various fractional powers obtained.Computer curve-fitting techniques showed that power laws were not adequate to describe the present results and the basic processes involved were therefore, considered in detail. For a discharge in a steady state the population of an excited state is determined by a balance between the rates of radiative and collisional processes. The latter depend upon the number density (No) of atoms in the ground state the number density (n) of electrons their velocity and energy distributions and the relevant excitation and de-excitation cross-sections; n is related to the current density i / S (S being the effective cross-sectional area of discharge) by the equation ;/S = nvd.The electron drift velocity ud will be approximately constant at a given pressure if the voltage across the relevant section of the discharge is constant; hence for a given pressure and discharge configuration n will be approximately proportional to i. HOWARD et al. INTENSITIES OF SOME 16.8 16.6 An excited level Ex (Fig. --M I I -M lonisation 22.0 1 k k Ground state 0 Fig. 3. Partial energy level diagram for Ne I showing transitions discussed in the text. Note the expanded sections of the energy scale. M denotes the meta-stable levels.Wavelengths in nano-metres. 4) may be populated from the ground state E in a single step by 00 electron collisions and the rate of this process will be proportional to NoJn(E)v(E)QOz(e)de where n(E) is the number density of electrons of energy E and velocity u(e) and Qoz(E) is the excitation cross-section from the ground state to level x for such electrons. This expression can be written as No ni?jox. The rate at which the level x is de-populaled by radiation will be N,/T where T is the radiative lifetime of the state and its value is independent of the collision processes. February 1983 SPECTRAL LINES FROM HOLLOW-CATHODE LAMPS t 149 Fig. 4. Excitation (single- and two-stage) and de-excitation pro-cesses. If these were the only processes determining the steady condition it would follow that N = No nvQ0,7 and hence that N is proportional to n and therefore to current.In such an instance the intensity of a line originating from level x should be proportional to current. A two-stage process via an intermediate level E may also be possible and by similar reasoning this would give an additional excitation rate proportional to No n2 v Qoz v Qyx and line intensity would include a term proportional to the square of the current and could be written I = ai + pi2. For lines in the spectrum of a neutral atom the two-stage process is possible if metastable levels exist as in neon to provide a suitable intermediate levely. For a singly ionised spec-trum the level y might be the ground state of the ion or a metastable state of the neutral atom or ion.Whilst the expression I = ai + piz gave an adequate description of the behaviour of some Ne I1 lines it was not generally satisfactory for the upward curving lines; moreover the major-ity of the Ne I lines showed a downward curvature at least under some conditions; this curvature was more marked for lines with higher upper levels for which collisional de-excitation, either to the ground state or to adjacent states becomes more probable. The rate for colli-sional de-excitation to the ground state is N n$, and the total collisional de-excitation rate is N n qxz. Balancing rates of single and two-step excitation processes against rates of collisional de-excitation and radiative de-excitation leads to the expression - -Hence it can be shown that I = Ai(1 + Ci)/(l + Bi) where A depends on the magnitude of single-step excitation B on the relative importance of collisional and radiative de-excitation and C on the relative importance of two-stage and single-stage excitation.Application to Experimental Results The above expression has been fitted to the results from the demountable hollow-cathode tube in which the pressure was independent of current using both graphical and least-squares methods. The agreement is very satisfactory for many examples as illustrated in Figs. 5-8, with the deduced values of the constants listed in Table 11. In some instances where the cathode dimensions and pressure used led to very low axial intensities the experimental scatter was too large for satisfactory fitting and additional experimental work is being carried out.For lines showing pronounced downward curvature ( A 363.3 470.9 and 585.2 nm) good fits are obtained with a large value of B and with C having a smaller value appreciably different, however from zero. The relative magnitudes of B and C are certainly significant and it is clear that for these lines collisional de-excitation is very important and there is a small amoun 150 HOWARD et al. INTENSITIES OF SOME Analyst Vol. 108 of two-step excitation. The absolute values of the constants are less well defined with the current ranges used in this preliminary investigation; it can be seen from the equation that as the current increases the ratio of the constants becomes more important than the absolute values and further work is in progress to extend the current range to lower values and to obtain more accurate results for the lower intensities.30 25 v) 4- 'C 20 .- L- 1 5 -- 2 40 ---/x'x X / YM 10 0 5 10 15 20 ilmA Fig. 5. Intensity Z I ~ Y S U S current graph for demountable hollow-cathode lamp. The lines arc graphs of 1 = Ai (1 + Cz)/(l + Bi), with the values of the constants derived by a least-squarcs fit (sce Table 11) ; the symbols indicate experimental results. The arbitrary intensity units are constant for a given wave-length and cathode size. Wavelength Nc I, 363.4 nm. Cathode 3 mrn bore 10 mm deep. Pressures A 3.5; B 5 ; C 7.5; D 10; and 141 20 Torr. Where the I 'UCYSUS i graph shows upward curvature the fit is often rather less satisfactory, but it appears that for Ne 11 lines the best fit occurs for B zero whilst for Ne I lines a small non-zero value of B is required for a good fit.iImA Fig. 6. As Fig. 5. Wavelength Ne I, 363.4 nm. Cathode 15 mm bore 50 mm deep. Prcssures A 1 ; B. 2; and C, 5 Torr February 1983 SPECTRAL LINES FROM HOLLOW-CATHODE LAMPS 151 Where the experimental data yield a straight line A is accurately determined but whilst it is clear that B and C are approximately equal they cannot be determined uniquely and such data have not been analysed in detail. From Table I1 it can be seen that for h 363.4 nm there is a smooth variation of A and B with pressure for the small cathode (3 mm bore x 10 mm depth) and almost constant values for the large cathode (15 x 50) whilst for h 470.9 nm a marked variation with pressure occurs in the large cathode.Such apparently erratic behaviour is not surprising as the excitation and de-excitation cross-sections depend on electron energy in differing ways for various spectral lines, and changing the pressure has a marked effect on the axial electron energy distribution as is shown by the variation in radial intensity distributions. The detailed reasons for these trends in A B and C are still under consideration. 0 5 10 15 20 ilmA Fig. 7. As Fig. 5. Wavelength Ne I, 470.9 nm. Cathode 15 mm bore 50 mm deep. Pressures A 1 ; B 2 ; and C , 5 Torr. Effect of Self-absorption In neon the visible and near ultraviolet spectra are due to transitions between highly excited levels and resonance transitions lie in the vacuum ultraviolet region.However two of the lower levels involved in the visible and ultraviolet spectra are metastable (Fig. 3) and appreciable populations of metastables could lead at higher currents to self-absorption or self-reversal of transitions to these levels and hence reduced intensity. In this work two such lines ( A 614.3 and 588.2 nm) originally chosen for their upward curvature consistently yielded I versus i graphs that were slightly S-shaped (Fig. 2). In a separate experiment the profiles of these lines emitted from sealed lamps recorded using a pressure-scanned Fabry Perot inter-ferometer showed at high currents self-absorption and self-reversal the magnitude of which depended on the lamp used and was not observed for lines with non-metastable lower levels.0 5 10 15 2c ilmA Fig. 8. As Fig. 5 . Wavelength Ne 11, 348.1 nm. Cathode 6 mm bore 50 mm deep. Pressures A 2.5; B 5; and C, 7.5 Torr 152 HOWARD PILLOW STEERS AND WARD It has been shown further that with a sealed lamp the ratio of the intensities of lines A 614.3 and 630.4 nm (from the same upper level and the former terminating on a metastable level) varies with current by a factor if (1-yi) implying a metastable concentration proportional to current; y is an experimentally determined constant that varies with the particular lamp used. Appli-cation of such a factor can account for the S shape of curves and further work on this will be carried out on the demountable system. TABLE I1 VALUES OF CONSTANTS A B AND C FROM I VERSUS i GRAPHS Cathode Species X/nm (bow x depth)/mm Pressure/Torr A arbitrary units* l3IrnA-I N e I 363.4 3 x 10 3.5 39 1.6 5 15 0.6 7.5 10 0.4 10 6.5 0.3 20 3.0 0.2 16 x 50 N e I 470.9 15 x 50 Ne I1 .. 348.1 6 x 20 1 2 5 1 2 5 2.5 5 7.5 8.1 0.5 3.0 0.5 0.5 0.5 17 0.9 5.7 0.6 1.2 0.3 1.5 0.03 0.28 0.00 0.07 0.00 C/mA-I 0.05 0.04 0.04 0.05 0.02 0.07 0.08 0.08 0.04 0.02 0.00 0.04 0.12 0.20 * Arbitrary units constant for a given line and cathode. Conclusions The expression I = Ai(1 + Ci)/(l + Bi) derived for the dependence of intensity on current, is shown to hold for a number of spectral lines under a wide range of experimental conditions in hollow-cathode discharges. I t is suggested that the values of A B and C can be used to characterise the behaviour of individual spectral lines in a discharge and interpreted in terms of the processes controlling this behaviour.Some preliminary work has shown that the expression can also be fitted to the different I zleysuus i graphs obtained for spectral lines from a positive column discharge. Experimental work on hollow-cathode and positive-column dis-charges is continuing with measurements over a wider current range to yield more reliable determinations of the constants and to link them where possible with excitation cross-sections. The work described formed part of an SERC CASE project with Cathodeon Ltd.; C. H. thanks the Science and Engineering Research Council for a studentship. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. References Pillow M. E. Spectrochim. Acta Part B 1981 36 821. Lompe A. Seeliger R. and Wolter E. Ann. Phys. (Leipzig) 1939 36 9. Borodin V. S. Gerasimov G. N. and Kagan Yu. M. Sou. Phys. Tech. Phys. 1967 12 283. Gofmeister V. P. and Kagan Yu. M. o p t . Spectrosc. (USSR) 1968 25 185. Gofmeister V. P. and Kagan Yu. M. Rev. Roum. Phys. 1968 13 19. Gofmeister V. P. and Kagan Yu. M. Opt. Spectrosc. (USSR) 1969 26 379. Gofmeister V. P. Desai S. K. and Kagan Yu M. 9th Int. Conf. Phenomena Ioniz. Gases 1969, Howorka F. and Pohl M. 2. Naturforsch Teil A 1972 27 1425. Kuen I. Howorka F. and Stori H. Phys. Rev. Sect. A 1981 23 829. Musha T. J . Phys. SOC. Jpn. 1962 17 1440. contributed papers p. 167. Received September 9th 1982 Accepted October 18th 198