and
G S S S ,=~ 0.39 VF
.L/"J=P
(A61
1RJ
J=l
Dividing Equation A5 by Equation 12, the ratio is found to be 0 . 7 0 m . The identical ratio is obtained upon dividing Equation A6 by Equation 13. Because B must exceed R J F by a factor usually chosen to be 100 (in order to have detector noise limitation in the SLS and SSS cases), the multiplex gain is a t least 7 times larger than in the photon noise limited situation. Even so, this increased multiplex gain may still be less than unity, thus yielding a multiplex disadvantage. For example, for Case I in the text
G S S S ,=~ 6.2 X lo1
2; l=P
2 RJ
1=1
Thus if Ei,=p RJ is less than 3.8 X lo5 B, GSLS,~will exceed unity and a multiplex advantage will exist over the SLS system. If B were equal to 50 sP1,then ZIZf' RJ would have to exceed 1.9 X lo7 s-l in order for a multiplex disadvantage to occur. Thus, the existence of a multiplex advantage in F T S for the ith spectral component depends strongly on the total radiation flux reaching the detector, just as in the photon noise limited cases in the text. For Case I1 in the text,
GSLS,~= 6.2
X 10'
d s ]=1
RJ
and so unless E?,=? R, > 3.8 X lo3 B , G S S S ,will ~ exceed unity and a multiplex advantage will exist over the SSS system. For the case of B = 50 s-l, the average count rate
in the interferogram would have to exceed 1.9 X lo5 s-l to produce a multiplex disadvantage. A count rate of this magnitude is often observed even on a single channel spectrometer; thus it is not as likely that a multiplex advantage would exist.
LITERATURE CITED (1) (2) (3) (4) (5) (6)
P. Jacquinot, Rep. Prog. Phys., 23,267 (1960). J. Connes, Rev. Opt., Theor. Instrum., 40, 45 (1961). J. Connes, Rev. Opt., Theor. Instrum., 40, 116 (1961). J. Connes, Rev. Opt., Theor. lflstrum., 40, 171 (1961). J. Connes, Rev. Opt., Theor. lnstrum., 40, 231 (1961). G. A. Vanasse and H. Sakai, in "Progress in Optics VI", E. Wolf, Ed., North Holland, Amsterdam, 1967, p 263. (7) H. A. Gebbie and R. Q. Twiss, Rep. Prog. Phys., 29, 729 (1966). (8)A. Girard and P. Jacquinot, in "Advanced Optical Techniques", A. C. S. Van Heel, Ed., North Holland, Amsterdam, 1967. (9) A. S. Filler, J. Opt. SOC.Am., 63, 589 (1973). (10) J. D. Winefordner, R. Avni. T. L. Chester, J. J. Fitzgerald, L. P. Hart, D. J. Johnson, and F. W. Plankey, Spectrochim. Acta, Part E, in press. (1 1) R. Herrmann and C. T. J. Alkemade, "Chemical Analysis by Flame Photometry", P. T. Gilbert, Jr., translator, Interscience Publishers, New York, 1963. (12) J. A. Decker, Appl. Opt.. I O , 510 (1971). (13) F. W. Plankey, L. P. Hart, T. H. Glenn, and J. D. Winefordner, Anal. Chem., 46, 1000 (1974). (14) G. Horlick and W. K . Yuen. Anal. Chem., 47, 775A (1975). (15) T. L. Chester and J. D. Winefordner, Spectrochim. Acta, Part B, in press (16) D. J. Johnson, F. W. Plankey. and J. D. Winefordner, Can. J. Spectrosc., 19, 151 (1974). (17) D. J. Johnson, F. W. Plankey, and J. D. Winefordner. Anal. Chem., in press.
T. L. Chester J. J. Fitzgerald J. D. Winefordner* Department of Chemistry University of Florida Gainesville. Fla. 32611
RECEIVEDfor review October 6, 1975. Accepted December 17, 1975. This research supported by AF-AFOSR-74-2574.
Mass Spectrometric Determination of Hydrogen Thermally Extracted from Titanium Sir: Attention should be called to a report published in June 1973 entitled, "Determination of Hydrogen in Milligram Quantities of Titanium and its Alloys" ( I ) , in which interfering reactions could be studied. The accuracy of the method was equivalent to t h a t of the certified value of NBS T i standard used to test the method. I t also shows about the same standard deviation as the method presented by Powell, Postma, Cook, Tucker, and Williamson (2). In the method presented by Powell e t al., hydrogen is evolved a t 930 "C in an evacuated chamber which is open into the detection chamber of a mass spectrometer (Le., a residual gas analyzer). The output a t mass 2 of the mass spectrometer is a function of the rate of hydrogen removal from the sample and the pumping rates involved with the various parts of the system. The hydrogen content is obtained via integration of the output by means of an analog computer. Powell et al. found 30 i 6 ppm hydrogen in NBS Ti Standard Reference Material Number 352 which is certified to contain 32 f 2 ppm hydrogen. They attribute the large uncertainty in the results to the difficulty in determining when the output returns to zero. The fundamental cause for the inaccuracy is the slow and/or incomplete extraction of the hydrogen. This trouble is avoided by the method described in Ref. ( I ) . In it, a triple stage mercury diffusion pump is used to maintain a low pressure in the extraction chamber (at 800 "C) by transfer-
ring the extracted gases to the expansion volume of a mass spectrometer. The maximum attainable vacuum of this pump was stated by the manufacturer to be Torr (1.3 X N/m2). Hence, we believe the hydrogen pressure over the Ti should not be greater than l o w 6 Torr (1.3 x lo-* N/m2) especially when hydrogen desorption is complete. The amount of hydrogen is determined via batch collection process. A second collection is usually close to the blank value. Quantitative extraction is assured when the blank value is obtained. Our experience indicates that the extraction is quantitative from Ti wires with diameters ranging from 0.25 to 1.25 mm in 15 to 45 min, respectively. T h e design of the extraction chamber facilitates the addition and removal of Ti samples without an increase in the interference due to air components. Thin samples of NBS Ti Standard Reference Material Number 354 which has certified hydrogen content of 215 & 6 ppm were analyzed. The mean value of 9 analyses was 216 ppm hydrogen with a standard deviation of 5 ppm. T o attain this accuracy, several interfering factors mkst be controlled; for instance, the temperature of the specimen. When Ti is heated above 800 "C, a metallic film forms in the cooler parts of the extraction chamber; this is accompanied by a loss of hydrogen. High blanks are usually observed in subsequent work unless the film is destroyed. Evidently the freshly f x m e d titanium film sorbs some hydroANALYTICAL CHEMISTRY. VOL. 48, NO. 4, APRIL 1976
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783
gen which later desorbs. Titanium evaporation is minimized by extracting the hydrogen a t the lowest temperature (800 "C) that permits quantitative extraction in a relatively short time. It is estimated that the hydrogen content when extraction is complete to be less than 0.5 ppm. This estimate is based on the work of Albrecht and Mallett (3). Their expression for the hydrogen solubility in Ti is: log10 -= 2020 - 0.723 pl/* T where S is the solubility in ppm, p is the partial pressure in microns, T i s the absolute temperature. Other factors involve the high reactivity of T i at elevated temperatures. At 800 "C, titanium reacts with a number of substances to produce extraneous hydrogen. High blanks are obtained (Ref. I ) when hydrogen-free titanium (
