Anal. Chem. 1980, 52, 1049-1053 (1 1) L. C . Bate, S. E. Lindberg. and A. W. Andren, J . Radioanal. Chem., 32, 125 (1976). ( 12) M.Gallorini, M. dicasa, R. Stella, N. Genova, and E. Orvini, J , Radioanal. Chem., 32, 17 (1976). (13) D. R. Myron, S. H. Givand, and F. H.Nielsen, J . Agric. Food Chem., 25, 297 (1977). (14) A. R. Byrne and L. Kosta, J . Radioanal. Chem., 44, 247 (1978). (15) R. Cornelis, L. Mees, J. Hoste, J. Ryckebusch, J. Versieck, and F. Barbier, "Nuclear Activation Techniques in the Life Sciences 1978", IAEA. Vienna. 1979. D 165. (16) A . J. Blotcky, C. Falcone, V . A. Medina, E. P. Rack, and D. W. Hobson, Anal. Chem., 51, 178 (1979). (17) P. J. Cali, Anal. Chem., 48, 802A (1976). (18) H. J. M. Bowen, At. Energy Rev., 13, 451 (1975). (19) Standard Reference Material 1571, National Bureau of Standards, Washington, D.C., 1976.
1049
(20) R. A. Nadkarni and G. H. Morrison, J . Radioanal. Chem., 43, 347 (1978). (21) "Handbook of Chemistry and Physics", 59th ed., CRC Press, Florida, 1978, p F-199. (22) C . 0. Ingamells and P. Switzer, Taianta, 20, 547 (1973). (23) G. Herdan, "Small Particle Statistics", Butterworths, London, 1960, p 81. (24) A. D. Wilson, Analyst(London). 89, 18 (1964). (25) C. 0. Ingamells, Talanta, 21, 141 (1974). (26) J. J. M. de Goeij, K. J. Volkers, P. S.Tjioe, and J. J. Kroon, Radiochem. Radioanal. Lett., 35 (3). 139 (1978).
RECEIVED for review September 17, 1979. Accepted February 19, 1980. The support of the Daell Foundation is gratefully This paper was presented in part at the 7th Nordic Trace Element Conference in Vejle, Denmark, 1979.
Microwave Attenuation Determination of Electron Concentrations in Graphite and Tantalum Tube Electrothermal Atomizers R. E. Sturgeon* and S. S. Berman Division of Chemistry, Analytical Section, National Research Council of Canada, Ottawa, Ontario, Canada K 1 A OR9
Satish Kashyap Division of Electrical Engineering, Electromagnetic Engineering Section, National Research Counci/ of Canada, Ottawa, Ontario, Canada, K I A OR9
The concentratlons of free electrons generated in a graphite and tantalum tube atomizer were determined by microwave attenuation measurements. The electron concentration is shown to be derived from thermionic emission from the atomizer surface and measured values range from 2.5 X 10" ~ K in the graphite ~ m at- 2470 ~ K to 7.8 X 10" ~ m at- 3000 furnace and from 1.1 X 10" ~ m at- 2413 ~ K to 8.7 X I O ' ' at 2743 K in the tantalum tube furnace. Application of the Saha equation indicates that analyte ionization in the graphite furnace is negligible for those elements having ionization potentials greater than 4.6 eV.
Ionization interferences are frequent and often severe in high temperature flames used for atomic absorption and atomic emission spectrometry (1-3). Although the problem has long been recognized and suitably treated in flame spectroscopy, the question of whether or not ionization interference occurs in electrothermal atomizers has not been satisfactorily resolved (4-7). Recent experimental data (8-12) suggest that local thermal equilibrium is achieved in tube type furnaces under the conditions of interrupted purge gas flow. Although the maximum temperatures experienced by the atomic vapor in electrothermal atomizers are lower than those attained in a nitrous oxide-acetylene flame, sufficient thermal energy is available through collisional excitation processes ( 1 2 ) to populate upper electronic energy levels lying as much as 5.28 eV above the ground state (5). As a number of elements have ionization potentials of this order of magnitude, it is reasonable to assume that ionization of metal vapors may occur in these devices. Ottaway and Shaw (5)and Epstein et al. (7)have confirmed this assumption through measurement of both barium ion absorption (5)and emission (5. 7) and the suppression of these 0003-2700/80/0352-1049$01 O O / O
signals following addition of excess cesium ( 5 ) or potassium ( 7 ) to the analyte. Although there is no doubt as to the existence of such ionic species, disagreement arises as to the extent of ionization. Ottaway and Shaw (5) concluded that ionization was negligible, based on the observation that suppression of barrium ion absorption does not lead to a simultaneous increase in neutral atom barium atomic absorption or emission. Based on the relative increase in barium neutral atom emission following suppression of ionization by addition of potassium to the analyte, Epstein et al. (7) concluded that barium was 35% ionized in the HGA-2100 furnace. Whereas Ottaway and Shaw ( 5 ) used a HGA-72 furnace and maximum atomization temperature of 2300 "C, Epstein et al. (7) used a HGA-2100 furnace and an atomization temperature of 2700 "C. The 400 "C increase in temperature experienced by the atomic vapor in the HGA-2100 could possibly account for the conflicting conclusions drawn by these researchers. It is well known that ionization is a mass acticln process and in the simplest case can be described by the following equations:
M+M++e a, =
(1) (2)
nM+/nh.l
(3)
n, = n e , + n g i log
a1 ~- CL;
1
=
3 log T 2
-
-
3040 ~
T
v + log
ZI
--
z,
-
log n ,
+
15.684 (4) where cy, is the degree of ionization, rz is the number density of the species indicated by the subscript, e-, and e-j are electrons derived from ionization of the metal and other sources within the furnace, respectively, V is the ionization potential (eV), T the absolute temperature, and Z, and 2, the partition functions for the atom and ion, respectively. I t is 1980 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 5 2 , NO. 7 , JUNE 1980
evident from the Saha equation (Equation 4) that the electron density has a n important effect on the degree of ionization. Increasing ne-by a factor of 10 has roughly the same depressing effect on cyl as reducing the temperature by 1000 K (13). Sturgeon and Chakrabarti (14) suggested that a significant partial pressure of electrons may be generated in an electrothermal atomizer by thermionic emission from the incandescent surface of the atomizer. Consideration of the equilibrium:
Cn(4
+
Cn+w + e-
(5)
for a graphite atomizer yields an expression for the number density of generated electrons (15, 16):
I
VA R I A 8 L E AT T € V U ATOR '\
32.7 G i z
FURNACE
MI C7CYrAV E SOJRCE
5 3 m p e Eeom Crys.01 3erec.c. RESCk4YT 33r'ITY
ne = [ 2 ( 2 ~ r n , k T ) ~ f ~ / / h ~ ] e - @ / ~(~6 ) Figure 1. Schematic of measurement system
where me is the mass of the electron, h is Boltzmann's constant, h is Planck's constant and p the work function (4.6 eV The collision frequency between electrons and other molecules for graphite). At 3000 K, ne is approximately 1.5 x 1013~ m - ~ . (inert gas in this case) may be estimated from the kinetic This value may be compared to electron concentrations of 10" theory of gases, Le., cm-3 in a clean unsalted air-acetylene flame a t 2500 K ( 1 7 ) v = (~/2rn,kT)'~'p~P (9) and 1 X 1013cm-3 in a similar flame into which 1 M solution of C s N 0 3 was aspirated (18). Clearly, such an additional where p is the molecular diameter and P the gas pressure. For source of electrons would contribute to suppression of ioniargon sheath gas used in these experiments p = 2.86 X lo-@ zation of the analyte. cm (24) and over the temperature range 2500-3000 K (used Recently, Littlejohn and Ottaway (12) measured the ioniin these experiments), u varies from 5.8 X 10" to 5.3 X 10" zation temperature of the vapor generated in a HGA-72 5-l respectively. With a microwave source frequency of 32.70 furnace and, from Saha's equation, calculated the electron GHz (used in these experiments), o = 20.5 X 10'O s-'. Using concentration. Values of 5.2 X 10" cm-3 and 1.3 X 10" cm-3 a n average value of u , the term ( v 2 + 0 2 ) / v = 8.1 X 10" s were obtained a t 2558 and 2766 K, respectively. These values Thus, the expression for ne given in Equation 8 simplifies to: compare reasonably well with those calculated from Equation nE= 1.76 X 1 0 1 2 ( $ / d ) (10) 6, assuming that electrons are produced solely by thermionic emission. Although trace impurities of sodium, potassium, This equation was used to calculate electron concentrations a n d other easily ionized elements present in the furnace from measurements of p. material or purge gas will contribute to the electron supply, Application of Equation 10 to the calculation of electron the concentration will be much smaller (loe cm-3) than that density from microwave attenuation measurements assumes produced by thermionic emission (14). No comparative values that the microwave radiation traverses the transition region for electron concentration in electrothermal atomizers have between air and the hot furnace gases (between the end of been reported. In this connection, we propose to measure the the source waveguide horn and the hottest section of the electron concentration generated in both a heated graphite atomic vapor) without reflection. This is a reasonable asatomizer and a tantalum tube atomizer by an independent sumption since i t is well known that no reflection normally method based on the attenuation of microwave radiation by occurs if the transition between two media of different elecfree electrons (19). With such information a more compretrical properties is a gradual one (15). This is the case here hensive investigation of ionization in these devices can be since there is a transition region of the order of one wavelength undertaken. between the entrained air-argon mixture at room temperature and the hottest slab of Ar gas in the center of the furnace. THEORY Additionally, the electron concentrations detected in the T h e determination of electron concentrations from microfurnace (discussed below) are sufficiently low t h a t the rewave attenuation data has been extensively used to investigate flection coefficient for the incident radiation is negligible (22), chemical reactions involving ionized components in comi.e., the furnace does not approach the properties of a black bustion flames (15, 16, 19-22). T h e principles of the microbody, The third source of potential nonspecific attenuation wave attenuation method are given in (20,22,and 23) and will is the variation of the electrical conductivity of the furnace not be repeated here. The attenuation in dB, of the intensity with temperature (as the furnace tube is, of course, acting as of a n electromagnetic wave (frequency f , by free electrons is a waveguide). The electrical resistivity of tantalum changes almost independent of frequency (15) and is given by the by a factor of 9 as the temperature varies from 300 to 3000 following expression: K (25) while that for graphite changes by a factor of 2 over this same temperature range (25). Calculation (see Appendix) shows that such variations in electrical resistivity contribute negligibly to the microwave signal attenuation. Additionally, the effects of temperature changes on the dimensions of the where ne is the electron density ( ~ m - ~e )the , electronic charge furnace tube (thermal expansion) contribute negligibly to the (ESU), c the velocity of light (cm s?), u the collision frequency measured changes in microwave signal attenuation. of electrons (s-l), o the angular frequency of the radiation (27rfl EXPERIMENTAL and d the absorption path length (cm). Upon rearrangement, Apparatus. The experimental arrangement is shown in Figure an expression for the electron density as a function of the 1. A Perkin-Elmer HGA-2200 atomizer was used. The quartz attenuation per unit length may be obtained: end windows and their brass mounts were removed and the furnace was secured to an optical rail, as described elsewhere (26). Radiation from the microwave source (model 697C sweep generator, Hewlett-Packard, Palo Alto, Calif.) was directed into the
'.
ANALYTICAL CHEMISTRY, VOL. 52, NO. 7, JUNE 1980
a
b
c
d
e
(d)
f
(b)
1051
9
Tantalum t u b e furnace assembly. (a) brass waveguide; 4 cm long, 0.5-cm i.d., 1.4-cm o.d., tapered to 0.071 X 0.036 cm rectangular port with 1.9 X 1.9 cm flange tapped for screw mount. (b) Ta washer; 0.85-cm i.d., 1.3-cm o.d., 0.2 cm thick. (c) Commercial graphite furnace cone; i.d. enlarged to 0.85 cm. (d) Ta collar; 1.0-cm 0 . d . tapered to 0.85-cm o.d., 0.6-cm i.d., 0.65 cm long. (e) Ta tube; 2.9 cm long, 0.63-cm o.d., 0.57-cm i.d. (f) Commercial graphite furnace cone; i.d. enlarged to 0.85 cm. (g) Brass waveguide; 6.5 cm long, dimensions a s in (a) Figure 2.
electrothermal atomizer through a brass waveguide directional coupler (model R752C Hewlett-Packard, internal dimensions: 7.112 X 3.556 mm) terminated by an outer, circular brass transmitting horn which was machined to fit into the end window guides of the atomizer. The transition from a rectangular to circular cross-section within the waveguide was continuous throughout the length of the brass horns. The receiving horn on the opposite side of the atomizer was identical to the transmitting horn. The attenuated signal was passed through a variable attenuator (Hewlett-Packard, model R382A) and onto a crystal detector (Hewlett-Packard, model R422A) terminating in a 5 0 4 load resistor (Hewlett-Packard,model 11523A). Both the incident power and the attenuated power (a crystal detector was also placed on the directional coupler leading t o the transmitting horn) were measured with a standing wave ratio meter (S.W.R. HewlettPackard, model 415E). The oscillator frequency was measured using a type U410AF resonant cavity (F-R machine works, Woodside, N.Y.) located directly before the variable attenuator. The sweep oscillator was mounted on adjustable blocks; all other apparatus (except the S.W.R. meter) was rigidly attached to the optical rail. Measurements were carried out using both conventional Perkin-Elmer pyrolytic graphite coated tubes mounted in the furnace and with a tantalum tube machined to fit the furnace. The dimensions of the tantalum tube and associated tantalum fittings (washers and collar inserts) are shown in Figure 2. With such an arrangement, graphite was effectively eliminated from the observation volume of the furnace. In order t o achieve this, the graphite furnace cones were modified to accept the interior tantalum tube support collars and exterior tantalum washers were pressed onto the protruding edge of the support collars. The tantalum tube, 2.9 cm long, was fabricated from 5.7-mm i.d. tubing of 0.30-mm wall thickness (Fansteel Metals, Chicago Ill.) No sample injection port was required for these experiments. It was found that the tantalum tube tended to collapse more quickly at high temperatures if an injection port was present. The electrical resistance of the furnace assembly was measured using a digital multimeter (Keithley, model 160B) and found to be 17 mQ for both the tantalum and graphite tube assemblies. The steady-state surface temperature of both furnace tubes was measured at each temperature setting of the power supply using a calibrated automatic optical pyrometer, series 1100 (Ircon Inc., Niles, Ill.). Procedure. The waveguide-furnace-detector system was aligned for maximum power throughput with the furnace at room temperature. The frequency of the source, measured with the resonant cavity, was 32.72 GHz. The incident power was arbitrarily set at some reference value using the S.W.R. meter, allowing the stability of the source to be monitored for any short term drift using the crystal detector which was mounted on the source waveguide directional coupler. No source drift was encountered. The transmitting and receiving horns were located in the window ports of the furnace but not in physical contact with the furnace. If physical contact was made, a large amount of noise pickup occurred during the heating of the furnace, rendering measurements with the S.W.R. meter impossible to make. Attenuation measurements were taken using a null technique whereby the attenuation of the variable attenuator was decreased from an upper, arbitraty reference value (set with a cold furnace). This was in order to balance the decrease in the detected power level on the S.W.R. meter and maintain the crystal detector output a t a steady value as the furnace temperature increased. The measured decrease in attenuation required to achieve this null point at the steady-state temperature of the furnace was a measure of the attenuation of the microwave signal by free electrons generated in the furnace.
TEMPERATURE, K
Variation of electron concentration with temperature. (A) Calculated for Ta tube assuming thermionic emission (Equation 6). (B) Calculated from experimental data for Ta tube (Equation 9). (C) Calculated for graphite tube assuming thermionic emission (Equation 6). (D) Calculated from experimental data for graphite tube (Equation 9). Estimated error bars are shown for each experimental point Flgure 3.
The furnace was operated in the purge gas interrupt mode (15 s ) using argon sheath gas.
RESULTS AND DISCUSSION Electron Concentration. Graphite Furnace. T h e concentration of electrons in the graphite furnace was found t o ~ 2470 ) K t o 7.8 vary from 2.5 X 10" cm-3 (f0.2 X 10" ~ m - at x lo1*cm-3 (f0.5 X 10l2~ m - a~t 3000 ) K. T h e measured source attenuation varied between 0.14 0.01 dB and 4.4 f 0.3 dB over this temperature range. Figure 3 shows the variation of electron concentration with temperature. The experimentally measured values, computed from Equation 10, are compared t o the theoretical concentrations which are assumed t o be derived solely from thermionic emission (calculated from Equation 6). The temperature data were obtained by measuring, with the automatic optical pyrometer, the intensity of black body radiation emitted from the interior surface of the furnace through the sample injection port. These surface temperatures for the graphite furnace are accurate t o within 30-40 "C over the temperature range displayed in Figure 3 (i.e., < f 2 % , (14)). At least three replicate measurements of the source attenuation were made a t each furnace temperature setting. T h e average attenuation obtained for each temperature exhibited a relative standard deviation of < f 6 % at temperatures above 2700 K and degraded to f8.570 a t temperatures below 2700 K. It is evident from Equation 10 that the greatest source of error introduced into the calculation of n, is contributed by the uncertainty in the value of d-the path length over which attenuation occurs. An unambiguous measurement of this quantity is extremely difficult because of the large thermal gradients which develop along the length of the furnace tube as well as the concentration distribution of vapor phase species throughout the tube ( 1 4 , 2 7 ) . Any measure of the attenuation path length thus becomes quite arbitrary. This, however, is not too serious a problem since the critical factor is the accuracy with which the total attenuation pd, has been measured. An uncertainty of even 50% in the estimation of the
*
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ANALYTICAL CHEMISTRY, VOL 52, NO 7, JUNE 1980
path length would not significantly affect the order of magnitude of the electron concentration. With the graphite tube, t h e path length was estimated as the distance between the "burn rings" on the extremities of a tube which had undergone repeated high temperature firings in the absence of an inert sheath gas. This procedure yielded a value of 1 cm for d and can be justified on the grounds that this central portion of the tube is t h e hottest and thus should contain most of the electrons which bring about attenuation of the microwave beam. Comparison of the theoretical and experimental curves in Figure 3 shows that the theoretical and experimental values of ne agree within a factor of 2 over the temperature range studied. I t can be concluded that the electrons must be produced by thermionic emission since no analyte was added to the furnace. T h e ionization of impurity atoms such as sodium and potassium present in the sheath gas contribute negligibly to the electron concentration (14) and ionization of the Ar sheath gas is negligible. Although attenuation measurements were taken after about 10 s heating of the furnace, a small but continuously increasing attenuation was noted as long as power was supplied to the furnace. A reasonable interpretation of this observation is that the hottest, central region of the furnace continues to spread in length, thus slowly increasing the attenuation path length. T h e attenuation path length, a', (Equation 10) is no doubt, a temperature dependent parameter. Once a steadystate temperature a t the center of the furnace has been established, the magnitude of a' will be determined by the central temperature and by the efficiency of water cooling of the contacts a t the extremities of the tube. I t is only fortuitous, perhaps, t h a t the experimental and theoretical values of n, obtained in the graphite furnace agree to within less than a factor of five. Tantalum Furnace. T h e concentration of electrons in the tantalum furnace system ranged from 1.0 x 10" cm (*0.1 x 10l2 cm-') to 8.7 x 10l2 cm-3 (f0.3 X 10" ern-?) over the temperatures 2413 to 2743 K. The measured source attenuation varied from 0.60 =k 0.06 d B to 4.9 0.2 d B over this temperature range. Figure 3 shows the variation of' electron concentration with temperature. The experimentally measured values, computed from Equation 10, are compared to the theoretical concentrations which are assumed to be derived solely from thermionic emission (calculated from Equation 6, 4~~ = 4.2 eV (28)). Temperature data were obtained with the optical pyrometer. Because emission from the exterior surface of the tube wall was monitored, a spectral emissivity of 0.4 was used to correct for pyrometer response (29). At 2.700 K.the error introduced by assuming that the spectral emissivity is 0.5 or 0.3 instead of 0.4 is approximately 100 "C (30). Because of the differences in electrical resistivity between the tantalum and graphite tubes, the temperature calibration on the furnace power supply could not be used even as a rough guide for the tantalum tube system. A temperature of 1800 "C read from the power supply resulted in the tantalum tube attaining a temperature of 2470 "C. If the furnace power supply was set for a temperature above 2000 "C, the tantalum tube would begin to soften (m.p. T a = 3269 K (28)) and, because of its compression fit between the furnace contacts, the tube wall would begin to flow and buckle a t the center. An estimate of the attenuation path length was obtained from a measurement of the length of such a melted portion of a tantalum tube whose temperature had been raised to -3000 K. A path length of 1 cm was taken. Comparison of the theoretical and experimental curves in Figure 3 shows that the experimental values of ne agree within a factor of 2 of the theoretical values (excluding the anoma-
'
*
IT
x IO', K-'
Figure 4. Variation of (In ne - 3 / 2 In T ) with T-'. ( 0 )Graphite tube.
(A)Tantalum tube. Error bars are shown for each experimental point
lously low value of the last experimental point). T h e agreement is excellent, considering the possibly large errors introduced into the temperature measurements. As with the graphite tube, it may be concluded that the source of these electrons is their thermionic emission from the tantalum tube walls. Work F u n c t i o n s . The thermionic work function, 4, of each surface can be calculated from Equation 6 using the experimentally determined values of ne and T . A plot of (In ne - 312 In 2') against T' is shown in Figure 4 for both tantalum and graphite. The work functions, calculated from the slopes of a least squares fit of the data, are 3.8 f 0.1 and 3.3 & 0.3 eV for graphite and tantalum, respectively. (The quoted uncertainties reflect only the goodness of fit of the data to a straight line and are not intended to represent the accuracy to which the work functions are determined.) These work functions are to be compared to the recommended literature values of 4.6 eV for graphite (reported values ranging from 4.00-4.84 eV (28)) and 4.2 eV for tantalum (reported values ranging from 4.03-4.19 eV (28)). Although the work function of graphite determined in this study lies close to the range of acceptable values, that for tantalum is distinctly lower than any reported data. A possible explanation for this discrepancy lies with the error in measurement of the temperature of the tantalum tube. Although a constant emissivity of 0.4 was selected as a correction coefficient for the pyrometer response, the spectral emissivity of the surface changes with temperature (29). I t is evident from Figure 3 that if the highest temperature coordinate of the experimental data point was actually 100 K lower than plotted, a superior exponential fit would be obtained. Similarly, a greater slope (hence, larger work function for tantalum) would be obtained from Figure 4 if the temperature data were roughly correct in the low range but suffered an increasingly positive error as the tube temperature increased. Analyte Ionization. Sufficient thermal energy is available within the graphite furnace to promote the ionization of elements having ionization potentials below about 5.3 eV ( 5 ) . Because of large thermal gradients, however, such excitation is confined to the center of the furnace where tube wall and vapor temperatures are highest. As electron concentrations, derived from thermionic emission from the tube surface, are also greatest a t the center of the furnace, suppression of ionization should occur due to the buffering action exerted by these electrons (Equation 1 and 4). T h e Saha equation (Equation 4)can be used to calculate the degree of ionization
ANALYTICAL CHEMISTRY, VOL. 52, NO. 7, JUNE 1980
of barium (ionization potential = 5.21 eV) in the HGA-2200 furnace. T h e appearance temperature of barium is 2200 K (31);the maximum ion population occurs at much higher temperatures, on the order of 3000 K. For the purposes of calculation of aia temperature of 3000 K can be assumed. At 3000 K, the electron concentration at the center of the furnace (where ionization is expected to be greatest) should be 1.5 X 1013~ m - ~ Taking . the ion:atom partition function ratio equal to 0.7 at 3000 I< (32), the degree of ionization of barium should be approximately 6%. In contrast to this, the degree of ionization of barium in an unbuffered chemical flame at 3000 K is an order of magnitude greater ( I ) . In practice, the effect of ionization should be even smaller than the 6% calculated above because of the different time and temperature dependences of atom and ion populations within the furnace. Maximum ion concentration occurs a t a time when only a small portion of the free atom concentration is present in the furnace ( 5 ) . Within the precision of analytical measurement available with electrothermal atomizers (=5%), the extent of ionization of barium should be negligible. This conclusion is in agreement with that drawn by Ottaway and Shaw ( 5 ) . From a theoretical point of view, ionization should be negligible for those elements having ionization potentials above 4.5 eV (the thermionic work function of graphite) in tube type graphite furnaces or above 4.2 eV (thermionic work function of tantalum) in tube type tantalum furnaces. Only Cs, K, and R b should be susceptible to ionization interference with electrothermal atomization.
ACKNOWLEDGMENT T h e authors thank C. L. Chakrabarti for loan of the optical pyrometer.
APPENDIX T h e variation of electrical conductivity of the waveguide (furnace tube) with temperature can be shown to contribute negligibly to the measured change in microwave signal strength upon passage through the furnace. The attenuation due to finite conductivity of the tube is given by (33):
where ,B is the attenuation in Nepers m-], i ~ '= 2xf0,f 0 is the source frequency (32.7 X lo9 Hz), CT is the conductivity (mho m-l), p o the permeability of free space (47r X lo-' Henrys m '), a is the radius of the tube (3 X m), 2, the free space impedance (120 T ohms), f, the cut-off frequency for the dominant mode in the circular waveguide (29.3 X lo9 Hz) and P ' = 1.841 for the dominant mode in the circular waveguide. Substitution of all experimental constants into Equation A-1 yields an expression relating the attenuation to conductivity of the furnace tube: (A-2)
1053
T h e conductivity of tantalum varies from 8.3 X lo6 mho m-l at 300 K to 9.6 X lo5 mho m-l at 3000 K (25, p 623); that for graphite varies from 2.0 X lo5 mho a t 300 K to 1.0 X lo5 mho at 3000 K (25, p 145). Substituting these values into Equation A-2 shows that, in the absence of other absorption processes, the attenuation of the microwave beam as a result of changes in the conductivity of the furnace amounts to 0.06 d B in the tantalum tube and 0.08 d B in the graphite tube (for 1-cm path lengths). This increased attenuation, above that given by the free electrons, contributes negligibly to the measurements made over the temperature range employed here.
LITERATURE CITED Manning, D. C.; Capacho-Delgado, L. Anal. Chim. Acta 1966, 36, 312. Kornblum, G. R.; d e a l a n , L. Spectrochim. Acta, Part6 1973, 28, 139. L'Vov, B. V., "Atomic Absorption Spectrochemical Methods of Analysis"; Hilger: London, 1970; p 188. Bancroft, M. F.; Schleicher, R. G.; Smith, S. 6.;Ernrnel, R. H.; Hwang, J. Y. Presented at the 2nd Federation of Analytical Chemistry and Spectroscopy Societies (FACSS) conference, Indianapolis, Ind., Oct. 6-10, 1975, paper #203. Ottaway, J. M.; Shaw, F. Analyst(London) 1976, 101, 582. Schrenk, W. G.; Everson, R. T. Appl. Spectrosc. 1975, 29. 41. Epstein, M. S.; Rains, T. C.; O'Haver, T. C . Appl. Spectrosc. 1976, 30, 324. Littlejohn. D.; Ottaway, J. M. Analyst (London) 1978, 103. 595. Van den Broek, W. M. G. T.; de Galan, L.; Matousek, J. P.; Czobik, E. J. Anal. Chim. Acta 1978, 100, 121. Alder, J. F.; Samuel, A . J.; Snook, R. D. Spectrochim. Acta, Part 6 1976, 3 1 , 509. Littlejohn, D.; Ottaway, J. M. Anal. Chim. Acta 1978, 98, 279. Littlejohn, D.; Ottaway, J. M. Analyst (London) 1979, 104, 208. Boumans, P. W. J. M. "Theory of Spectrochemical Excitation"; Hilger: London, 1966; p 166. Sturgeon. R. E.; Chakrabarti. C. L. Spectrochim. Acta, Part 6 1977, 32, 231. Shuler, K. E.; Webber, J. J . Chem. Phys. 1954, 22 491. Page, F. M.; Wooley, D. E. Combust. Flame 1974, 2 3 , 121. Alkemade. C. T. J. Ph.D. thesis, University of Utrecht, The Netherlands; 1954, p 141. Hofmann. F. W.; Kohn, H.; Schneider, J. J . Opt. SOC.Am. 1961, 57, 508. Sugden, T. M. Discuss. Faraday SOC. 1955, 19, 68 Andrew, E . R.; Axford. D. W. E.; Sugden, T. M. Trans. Faraday SOC. 1948, 4 4 , 427. Sugden, T. M.; Wheeler, R. C. Discuss. Faraday SOC. 1955, 19, 76. Schneider, J.; Hofmann, F. W. Phys. Rev. 1959, 716, 244. Adler, F. P. J , Appl. Phys. 1949, 2 0 , 1125. Moore, W. J. "Physical Chemistry". 4th ed.; Prentice-Hall: Englewood Cliffs, N.J., 1972; p 229. "Handbook of Thermophysical Properties of Solid Materials". Goldsmith, A.; Waterman, T. E., Hirschhorn, H. J., Eds.; Macmillar Co.: New York. 1961; VoI. 1 . Sturgeon, R. E.; Berman, S. S.; Desaulniers, A.; Russell, D. S. Anal. Chem. 1979, 5 1 , 2364. Sturgeon, R. E. Anal. Chern. 1977, 49, 1255A. "Handbook of Chemistry and Physics", 54th ed.. Weast, R . C., Ed.; C.R.C. Press: Cleveland, Ohio, 1973: p E-80. "Metals Reference Book", Smithells, C. J., Ed.; Butterworth: London, 1962; VoI. 2, p 725. Ircon, Automatic Optical Pyrometer, series 1100, Operations Manual, Ircon Inc., Skokie, IiI., 1978. Campbell, W. C.; Ottaway, J. M. Talanta 1974, 2 1 . 837. Acta. de Galan. L.: Smith.. R.:. Wineforner. J. D. Soectrochim. ~. Part 6 ~,~ 1968, 23, 521. Collin, R. E. "Foundations for Microwave Engineering"; McGraw-Hill, Inc.: Canada. 1966; p 110. ~
~
RECEIVED for review December 13, 1979. Accepted February 27. 1980.
