data show that the plasma levels of I and 11 were measurable through the 48th hour, whereas I11 was not detected until 30 hours. Plasma levels of I, 11, and 111 (Table VI) were obtained from another subject following chronic administration of Librium. The subject received 10-mg oral doses three times a day for 21 days, and a single 30-mg oral dose once a day thereafter. Levels of I, 11, and I11 were measured at one and two hours post each 30-mg dose on days 22, 26, 30, 34, and 36. These samples were analyzed by the DPP assay and the standard spectrofluorometric assay (3). Excellent correlation of data was obtained using the two methods. The correlation coefficient for compounds I, 11, and 111 were 0.92,0.91, and 0.88,'respectively.
ACKNOWLEDGMENT The authors wish to extend thanks to Herbert Spiegel, Director of the Clinical Biochemistry Laboratory, for providing the fluorometric data presented in this manuscript and to Thomas Daniels for the drawings of the figures presented. Received for review November 9, 1973. Accepted February 4, 1974. This material was presented as a preliminary communication at the Eastern Analytical Symposium, Atlantic City, N.J., October 1972,.and in American Laboratory, 5, (9), 23 (1973). The manuscript was presented in its entirety at the 166th National Meeting of the American Chemical Society, Chicago, Ill., August 1973.
Internal Normalization Techniques for High Accuracy Isotope Dilution Analyses- Application to Molybdenum and Nickel in Standard Reference Materials L. J. Moore, L. A. Machlan, W. R. Shields, and E. L. Garner Analytical Chemistry Division, lnstitute for Materials Research, National Bureau of Standards, Washington, D.C. 20234
General exact equations and iteration techniques have been developed for internal normalization to eliminate the effect of thermal fractionation from isotope ratio measurements, and therefore isotope dilution analyses, by thermal ionization mass spectrometry. The techniques are applicable to more than 20 elements, and have been extensively applied to the determination of Mo in ore concentrates (55% Mo) and silicate trace standards (50 and 500 ppm Mo). The standard deviations of all internally corrected Mo isotope ratio measurements were < 0 . 1 % . The Mo sample size was 40 pg, but normalization techniques should apply to pg and smaller samples with a more sensitive ion detection system. Procedures are described for the chemical separation of Mo from matrix interferences and for the mass spectrometric analysis of Mo. Application of the techniques to Ni in three pollution Standard Reference Materials is described.
The thermal emission of ions of a polynuclidic element in a mass spectrometer is accompanied by fractionation of the isotopes, resulting in an observed value(s) for the isotope ratio(s) that is not representative of the isotopic composition of the sample. Investigators have observed for a number of elements that the amount of fractionation, or change in the ratio, is linear with mass and therefore proportional to the difference between the masses (1-3). Various approaches have been used to correct for the fractionation effect based on the assumption of linearity with mass as inferred by these observations. (1) W. R. Shields, T. J. Murphy, E. J . Catanzaro, and E. L. Garner, J. Res. Nat. Bur. Stand., Sect. A, 70, 193-197 (1966). (2) D . A. Papanastassiou and G. J . Wasserburg, Earth Planet. Sci. Lett., 5 , 361-376 (1969). (3) C. M. Stevens, Int. J. Mass Spectrom. Ion Phys., 8, 251-257 (1972),
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ANALYTICAL CHEMISTRY, VOL. 46, NO. 8 , JULY 1974
Double spiking has been employed, with varying degrees of success, to provide this correction by adding two separated isotopes to a polynuclidic element and using the measured fractionation of the known double spiked ratio as a lever to correct the observed ratios for isotopic fractionation (4-6). This technique has been applied to U (7), P b (8), Ca (9),Ba (IO),and Mo ( I I , 12). To make absolute isotope ratio measurements, the isotopic analysis technique is rigorously standardized to permit a correction to be made for the effect of fractionation. In this manner, very precise ratio determinations ( t s 500 "C to the metal. The vigorous reduction in H2 of a real sample appears to result in a gray mixture of the partially reduced MoOz oxide, and metallic Mo. Further heating during analysis in the mass spectrometer results in a post-analysis residue that is completely metallic in appearance. High purity zone-refined Re ribbon (0.001 inch X 0.030 inch) was selected as the support material, since a roughly 10-fold decrease in background Mo was observed over regular Re ribbon. No detectable (= - I , S,W,C,
R
=’=
+ N , W,C, + N,W,C, + N,W,C, + N,W,C,
(2)
where R1 = Normalizing isotope ratio; Rz = Isotope dilution ratio; I1 = Number of atoms of Isotope 1; I2 = Number of atoms of Isotope 2; 13 = Number of atoms of Isotope 3 and 14 = Number of atoms of Isotope 4 (Either can be specified as separated isotope); SI = Atom fraction of 11 in spike; Sz = Atom fraction of 1 2 in spike; Sa = Atom fraction of 13 in spike; S4 = Atom fraction of I 4 in spike; NI= Atom fraction of 11 in natural; Nz = Atom fraction of I2 in natural; N3 = Atom fraction of 13 in natural; N4 = Atom fraction of 1 4 in natural; W, = Weight spike, grams; W, = Weight natural, grams; C, = Concentration spike, pmol/gram; and C, = Concentration natural, pmol/gram. Eliminating ( W, C,)/( W,C,) between Equations 1 and 2, a general equation of the form
results. A fractionation factor, a , can be defined for the normalizing ratio as (4) where R1* = The observed R1 and R1 = theoretical, or unfractionated, ratio. Since it is assumed that the filament fractionation of the isotopes is proportional to the difference between the isotopic masses, the correction factor to be applied to the ID ratio can be written as a linear function of a (a generalization of Long’s (14) approach):
where n = Mass range of the normalizing isotopes and m = Mass range of the isotope dilution isotopes. In the process of surface or thermal ionization, the isotopes of a given element are evaporated and ionized at a rate which is a function of the mass of a particular isotope. For example, if one accepts the Rayleigh distillation model for isotope evaporation ( 2 4 ) , then the observed ratio of a “light” to “heavy” isotope will vary as the square root of the ratio of the masses, resulting in an apparent depletion of the lighter isotope in the observed ratio. In any event, if a correction factor derived from one ratio (normalizing ratio) is to be applied to a second ratio (ID ratio), an accounting must be made for the possibility that the two ratios observed may have the lighter isotope in either the numerator or denominator, so that the correction factor derived for the normalizing ratio is applied either in the same or opposite sense to the ID ratio. To illustrate that all possible fractionation directions are considered, it is observed’ that only four combinations are possible for the normalizing and ID ratios: (24) A. Eberhardt, R. Delwiche, and J. Geiss, Z. Naturforsch. A , 19, 736-740 (1964).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 8, JULY 1974
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For Case I, f ( a ) is applied in the same direction as a :
where Rz* = The observed RZ and Rz = Theoretical, or unfractionated ratio. For Case II,f ( a )is applied in the inverse:
By substituting ~ R I *for RI ( = Il/Ip) and either f(a).R2* (Case I) or [ l / ( f ( a ) )Rp* ] (Case 11) for R2 (= 13/14)into Equation 3, and solving for CY two general quadratic equations result: case I: a2[R,*R~*(N2S4 - N4S,)] a[R,*(N4S1- NlS,)
+
;(
+
- ~)R,*R,*(N,s, - N , S J +
:(
- I)RI*(N4Sl- N , S J
=0
(8)
Case 11: a2[Rl*(N,S3- N3S2)1+ a[(;)Ri*R,*(N4S, - N,s,)
+
Each of the equations can be solved for a using the formula for a quadratic solution:
cy=
+ +
ba c = 0 -b f [ b 2 - ~ U C ] ” ~
aa2
110)
2a
Although two roots, or solutions result, the useful root is the one obtained by adding the value ( b 2 - 4 U C ) ~ to ’ ~ -b. ~
Isotope Comp., Atom %
where Since the other parameters on the right-hand side of Equation 1 are known, the value of C, permits the calculation of an approximate theoretical R1. An “approximate”a is then defined a s a = RI/R1*. If / ( a ) from Equation 5 is then applied in the proper direction to Rp*, a new value can be calculated for C, followed by a new a , R1 and f ( a ) , etc., until the value of a converges. It has been observed in the current work that three iterations are usually sufficient for a difference of
