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A Methodology for the isotopic characterization of natural uranium to be used as reference material for thermal ionization mass spectrometry
international Journal of Mass Spectrometry and Ion Processes, 98 (1990) 99-106
99
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
A METHODOLOGY FOR THE ISOTOPIC CHARACTERIZATION OF NATURAL URANIUM TO BE USED AS REFERENCE MATERIAL FOR THERMAL IONIZATION MASS SPECTROMETRY
R.F. CRETELLA,
R.A. LUKASZEW,
J.G. MARRERO
and R. SERVANT*
Mass Spectrometry Division-Analytical Chemistry Department, National Commission on Atomic Energy (CNEA), Av. de1 Libertador 8250 (1429). Buenos Aires (Argentina)
(First received 2 August 1989; in final form 19 October 1989)
ABSTRACT Owing to natural variations in the abundance of 235Uand 234U,nuclear grade UJO,, with a natural isotopic composition was analyzed by thermal ionization mass spectrometry (TIMS) and characterized (i.e. mean isotopic ratio values, 95% confidence limit) to be used as isotopic reference material. The mass discrimination bias factor was calculated for the aforementioned situation using isotopic reference materials within the range U-002 to U-015 for the 235U:238Uisotopic ratio (R5,8) and with the isotopic reference materials U-005, U-010, U-015 and U-900 for the 234U:235Uisotopic ratio (R4,5). As the variances obtained for the isotopic ratio measurements were not constant in the investigated range, weighted least-squares regression analysis was applied. The atomic weight of U calculated for the sample was consistent with the accepted value published by the Commission on Atomic Weights and Isotopic Abundances from IUPAC.
INTRODUCTION
It has been stated in the literature that the natural abundance of 235Uvaries [ 11.Very small variations in R5,* have been observed, prior to the discovery of the natural reactor which occurred at the Oklo mine in the Republic of Gabon, West Africa [2], and could be attributed entirely to isotopic fractionation by natural geochemical processes. In addition, it has been stated that there are significant differences in the 234Uconcentration of unaltered uranium ore concentrates produced in various parts of the world. A spread of 7.5% of the average 234U assay was found among concentrates from 16 processing mills around the world. Although this variation is substantial it is small compared with that reported for specific minerals [3,4]. * Author to whom correspondence 0168-1176/90/$03.50
should be addressed.
0 1990 Elsevier Science Publishers B.V.
100
The aforementioned situation led to the isotopic characterization of an Argentine, nuclear grade U,O, production batch with a natural isotopic composition rather than accepting the best measurement from a single natural source published by the Commission on Atomic Weights and Isotopic Abundance from the International Union of Pure and Applied Chemistry (IUPAC)
PI. DISCUSSION
The determination of the absolute abundance and atomic weight of any element to a high level of accuracy requires the development of highly precise chemical assays and mass spectrometric procedures [6]. Good analytical procedures are based upon (a) a knowledge of the source of bias, (b) establishing control of the various parameters and (c) selecting an optimum combination of parameters that is uniform and reproducible for each analysis. Garner et al. [7] determined that for the isotopic analysis of uranium by TIMS, over the range of ratios represented by the isotopic standards SRMs U-050 to U-930 from the NBS, the bias is independent of the isotopic composition while for the range of ratios represented by the isotopic standards U-050 to U-005 from the NBS, non-ohmic response and the R-C response of the measuring circuit make point calibration for each standard mandatory. For the TIMS analysis of uranium samples Stephens et al. [8] recommend that the certified standard with an enrichment nearest to the enrichment of the samples should be analyzed at least once during each shift. If a suitable certified standard is not available, the quality control laboratory should retain a sufficient quantity of an appropriate uranium dioxide production batch preferably in powder form. This batch should be characterized initially to give reliable estimates of the isotopic composition (mean values and 95% confidence limit). Subsequently, samples from this designated batch can serve as an “in house” standard. Alternatively a standard may be blended from NBS reference materials; however, this is expensive. The present contribution describes the procedure followed to obtain a standard for uranium with a natural isotopic composition, according to the aforementioned recommendation proposed by Stephens et al. [8]. EXPERIMENTAL
DETAILS
The spectrometer used was a single focusing Nuclide 12-90 SU instrument, characterized by the following features: a single-sample thermal ionization source, a 15 inch radius, a 90” magnetic sector, a Faraday cup and an electron
101 TABLE I Certified and measured values for the 235U:238Uisotopic ratio (R,,*) Reference
&, (certified)
Rsis (measured)
U-002 (IAEA) U-005 (NBS) U-010 (NBS) U-01 5 (NBS) U3 OS (CNEA)
0.002049 0.004919 0.010140 0.015565 -
0.002018 0.004867 0.010221 0.015744 0.007287
1.3 2.0 1.9 4.2 3.2
x x x x x
10-9 10-9 1o-9 1O-9 10m9
multiplier. The measurement of the observed isotopic ratios (Robs)depends on (a) the chemical preparation procedure of the sample, (b) the loading procedure of the sample on the evaporating filament and (c) the measuring procedure. Reproduction of these procedures is essential to obtain reproducible values of Robs for different filament loads. Standard procedures have been developed at the Mass Spectrometry Division in the National Commission on Atomic Energy, Argentina (CNEA) over many years [9], as explained below. The sample to be isotopically characterized was nuclear grade U308 from Argentina, with a natural isotopic composition. Four standards were measured for RS,8. Three were the isotopic reference materials U-005, U-010 and U-01 5 from the NBS. The fourth, U-002 (IAEA), was calibrated in an interlaboratory test organized by the International Atomic Energy Agency (IAEA). For R4,5 the standards used were U-005, U-010, U-01 5 and U-900 from the NBS, which had a certified R4,5 value within the natural range for this isotopic ratio. The standard procedure followed at the CNEA Mass Spectrometry Division (Argentina) for the determination of the uranium isotopic ratios used a triple filament rhenium source. The analyzed uranium solutions from the sample and the standards had a 5 mg U ml-’ concentration in 1 M nitric acid. From the respective solutions 5 ~1 were loaded onto the sample filaments. The mass spectrometric procedure consisted of four determinations (four filament loads) of Rsls performed for each isotopic reference material and for the sample to be characterized. Each determination involved a set of 16 measurements of the 235Uand 238Upeaks through the peak-jumping procedure. The same method was followed for R4,5. The results shown in Tables 1 and 2 refer the measured values to the mean of the mean of four independent filament loadings. The total standard deviation combines the external standard deviation of four independent loadings and the internal standard deviation of a set of 16 measurements within one loading through the use of a test for statistical consistency [lOI.
102 TABLE
2
Certified
and measured
values for the 234U:235U isotopic
ratio (R4,5)
Reference
R4,5 (certified)
R4,J (measured)
2 &o1
U-005 U-010 U-015 U-900 U30s
0.004454 0.005390 0.005547 0.008622
0.005040 0.005269 0.005504 0.008648 0.007347
2.4 2.2 5.6 6.6 2.4
(NBS) (NBS) (NBS) (NBS) (CNEA)
x x x x x
1O-9 1o-9 1O-9 1o-9 10m9
CALCULATIONS
As the range of isotopic ratios analyzed in the present work was below the range for which the mass discrimination bias factor (k) can be considered independent of the isotopic ratio [6], it was decided to find out the relationship between this factor and the certified isotopic ratio (I&) for the analyzed isotopic reference materials. As the variances obtained for the isotopic ratio measurements were not constant in the investigated range, it was decided to apply weighted least-squares regression analysis. With this procedure the regression equation is obtained, potential outliers are flagged and confidence bands around the predicted values are calculated [I I]. The equation thus obtained for Rsls in the analyzed standards was Robs= -4.254
x 1O-5 + 1.01242 x R,,,,
(1)
with a regression coefficient r = 0.99996. This is an empirical equation and valid for this particular measurement procedure and for the particular investigated range of isotopic ratios. As we define the mass discrimination bias factor k as R
k=P
(2) 5/8,cert
it follows from Eqs. (1) and (2) that k=
R 5/8,obs
x
1*01242
R 5,Qo&+ 4.254 x lO-5
(3)
where we can see that the influence of the y axis intercept in Eq. 1 decreases for increasing isotopic ratios, corroborating the observations of Garner et al. [71. The influence of the y axis intercept is 0.5% for uranium with a natural isotopic composition. There has been recognition in the chemical literature that variance is usually not constant in chemical analyses [ 12-151.
103 TABLE 3 Coefficient of variation (CV) vs. the 235U:23*Uisotopic ratio Reference
Rsls (measured)
Log be
CV
Log cv
u-002 u-005 u-010 u-015
0.002018 0.004867 0.010221 0.015744 0.007287
- 2.695 -2.313 - 1.991 - 1.803 -2.137
1.79 0.92 0.43 0.41 0.77
0.253 - 0.036 - 0.367 - 0.387 -0.114
u3os
Franke et al. [12] have employed a standard deviation function directly proportional to concentration, and Smith and Mathews [13] assumed a standard deviation directly proportional to the signal. Geerlings and Koch [16] and Gonzalez [17] have informed us that the coefficient of variation for a given isotopic ratio R, is proportional to Rio.’ for a wide range of R,. The coefficient of variation (CV) is defined as
cv+
x 100
(4)
I/J
where stat is the total standard deviation for each measurement. This relationship was also investigated in the present report, and it was found that the least-squares regression of log CV vs. log R5,8 yielded the equation log CV = - 1.652 - 0.707 x log R5,*
(5)
with a regression coefficient r = 0.997, indicating that CV is proportional to R;‘.’ in the investigated range (Table 3). For the sample to be calibrated, the “certified” value calculated with Eq. (1) for the 235U:238Uisotopic ratio, with a 95% confidence interval is R5/8+ $+ -
= 0.007242 + 0.000054 .
where R5,8IS the mean value for the four determinations, t corresponds to the Student coefficient for the n - 1 degrees of freedom and n is the number of determinations (Table 4). As can be seen, the sample value is located in the middle of the isotopic range that was investigated for the obtention of Eq. (1). To complete the isotopic analysis for this sample, the 234U:235Uisotopic ratio has to be considered. The weighted least-squares regression analysis was applied to Robs vs. &,, for R4,5in the standards. The equation thus obtained was Robs =
-4.04412
x 1O-4 + 1.05382 x R,,,
(6)
104 TABLE 4 Measured and calculated values for the 235U:238Uisotopic ratio in the sample to be characterized (U, 0,) R5,*(measured)
R s/s a
Upper limit
Lower limit
0.00726199 0.00737001 0.00726919 0.00724690
0.0072176 0.0073243 0.0072247 0.0072027
0.0072562 0.0073629 0.0072672 0.0072427
0.0071793 0.0072861 0.0071827 0.0071630
“Calculated applying Eq. 1.
with a regression coefficient Y= 0.9990. The same considerations about the empirical character of this equation as for Eq. (1) are valid. For the sample to be characterized, the application of the last equation yielded R4,5values along with the upper and lower limits, which are shown along with the observed values in Table 5. Thus, the calibrated value calculated for R4,5 was
R4,5 + f+ n
= 0.007356 f 0.000073
and the symbols have the same meaning as for the R, g case. To calculate the absolute isotopic abundances, the i 34U isotope has to be referred to the 238Uisotope. Thus --R4/8 = R4,5 x Rsle = 0.0000532715 and Sk, = R:,s x
&t,4,5
+
2
R4,5
x
&,,,t~
=
1.7 x lo-l3
TABLE 5 Measured and calculated values for the 234U:23sUisotopic ratio in the sample to be characterized (U, 0,) &
(measured)
0.00741845 0.00733997 0.00728739 0.00734177
%,Sa
Upper limit
Lower limit
0.0074234 0.0073489 0.0072990 0.0073506
0.0076170 0.0074650 0.0074045 0.0074845
0.0072473 0.0072432 0.0072029 0.0072287
“Calculated applying Eq. 6.
105 TABLE 6 Isotopic abundances Isotope
U-234 U-235 U-238
in the sample to be characterized (U,O,) Abundance Atom percent
Weight percent
0.00529 + 0.00005 0.719 f 0.005 99.276 f 0.005
0.00520 rf: 0.00005 0.710 f 0.005 99.285 + 0.005
and therefore
R4,8 +3
= 0.0000533
* 0.0000066
From the calibrated values obtained for R5,* and R4,8 the isotopic abundances were calculated with a 95% confidence interval. The results obtained are shown in Table 6. The atomic weight of uranium was calculated for the sample and was found to be 238.03 ) 0.02. This value is in agreement with the accepted value published by the Commission on Atomic Weights and Isotopic Abundances from the International Union of Pure and Applied Chemistry [5]. Thus, the isotopic characterization was completed, and the sample could be considered an “in house” working standard for uranium with natural composition. CONCLUSIONS
Owing to natural variations in the isotopic composition of uranium it was decided to characterize an Argentine, nuclear grade U,O, production batch with a natural isotopic composition. The methodology proposed in the present report fulfilled the requirements of providing reliable estimates for the isotopic composition (mean values and 95% confidence limit) for the U,O, sample. The use of expensive enriched isotopes was thus circumvented. In addition, the use of isotopic reference materials from the NBS was minimized, because they were used only once for the determination of the mass discrimination bias factor. The obtained values for the isotopic abundances were used to calculate the atomic weight of uranium which was in agreement with the accepted value published by the Commission on Atomic Weights and Isotopic Abundances from the IUPAC.
106 REFERENCES 1 G.A. Cowan and H.H. Adler, Geochim. Cosmochim. Acta, 40 (1976) 1487. 2 R. Naudet and C. Renson, Rtsultats des Analyses Systematiques de Teneurs Isotopiques de l’uranium, Proc. Int. Symp. Oklo Phenomenom, Libreville, IAEA-SM-240/23. Proceedings of an International Symposium on the Oklo Phenomenom, Libreville, Gabon, West Africa, 23-27 June, 1975. 3 R.F. Smith and J.M. Jackson, USAEC Report KY-581, 1969. 4 J.N. Rosholt, E.N. Itarshman, W.R. Shields and E.L. Garner, Econ. Geol., 59 (1964) 570. 5 N.E. Holden, R.L. Martin and I.L. Barnes, J. Appl. Chem., 56 (1984) 675. 6 L.P. Dunstan, J.W. Gramlich and I.L. Barnes, J. Res. Natl. Bur. Stand., 85 (1980) 1. 7 E.L. Garner, L.A. Machlan and W.R. Shields, Natl. Bur. Stand. Spec. Pub]., 260-27 (1971). 8 F.B. Stephens, R.G. Gutmacher, K. Ernst, J.E. Harrar and S.P. Turel, Report NUREG-75/ 010, 1975. 9 R. Cretella, J. Dal Favero and R. Servant, Report CNEA PQ/Q/QA-33, 1980. 10 R.J. Jones, Selected Measurement Methods for Plutonium and Uranium in the Nuclear Fuel Cycle, USAEC, TID-7029, 1963. 11 J.S. Garden, D.G. Mitchell and W.N. Mills, Anal. Chem., 52 (1980) 2310. 12 J.P. Franke, R.A. Zeeuw and R. Hakkert, Anal. Chem., 50 (1978) 1374. 13 E.D. Smith and D.M. Mathews, J. Chem. Educ., 44 (1967) 757. 14 L.M. Schwartz, Anal. Chem., 51 (1979) 723. 15 D. Rodbard, R.H. Lenox, H.L. Wray and D. Ramseth, Chin. Chem. (Winston-Salem, N.C.), 22 (1978) 350. 16 E. Geerling and L. Koch, Report EUR-3949, 1976. 17 0. Gonzalez, Private communication, CNEA, 1978.
99
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
A METHODOLOGY FOR THE ISOTOPIC CHARACTERIZATION OF NATURAL URANIUM TO BE USED AS REFERENCE MATERIAL FOR THERMAL IONIZATION MASS SPECTROMETRY
R.F. CRETELLA,
R.A. LUKASZEW,
J.G. MARRERO
and R. SERVANT*
Mass Spectrometry Division-Analytical Chemistry Department, National Commission on Atomic Energy (CNEA), Av. de1 Libertador 8250 (1429). Buenos Aires (Argentina)
(First received 2 August 1989; in final form 19 October 1989)
ABSTRACT Owing to natural variations in the abundance of 235Uand 234U,nuclear grade UJO,, with a natural isotopic composition was analyzed by thermal ionization mass spectrometry (TIMS) and characterized (i.e. mean isotopic ratio values, 95% confidence limit) to be used as isotopic reference material. The mass discrimination bias factor was calculated for the aforementioned situation using isotopic reference materials within the range U-002 to U-015 for the 235U:238Uisotopic ratio (R5,8) and with the isotopic reference materials U-005, U-010, U-015 and U-900 for the 234U:235Uisotopic ratio (R4,5). As the variances obtained for the isotopic ratio measurements were not constant in the investigated range, weighted least-squares regression analysis was applied. The atomic weight of U calculated for the sample was consistent with the accepted value published by the Commission on Atomic Weights and Isotopic Abundances from IUPAC.
INTRODUCTION
It has been stated in the literature that the natural abundance of 235Uvaries [ 11.Very small variations in R5,* have been observed, prior to the discovery of the natural reactor which occurred at the Oklo mine in the Republic of Gabon, West Africa [2], and could be attributed entirely to isotopic fractionation by natural geochemical processes. In addition, it has been stated that there are significant differences in the 234Uconcentration of unaltered uranium ore concentrates produced in various parts of the world. A spread of 7.5% of the average 234U assay was found among concentrates from 16 processing mills around the world. Although this variation is substantial it is small compared with that reported for specific minerals [3,4]. * Author to whom correspondence 0168-1176/90/$03.50
should be addressed.
0 1990 Elsevier Science Publishers B.V.
100
The aforementioned situation led to the isotopic characterization of an Argentine, nuclear grade U,O, production batch with a natural isotopic composition rather than accepting the best measurement from a single natural source published by the Commission on Atomic Weights and Isotopic Abundance from the International Union of Pure and Applied Chemistry (IUPAC)
PI. DISCUSSION
The determination of the absolute abundance and atomic weight of any element to a high level of accuracy requires the development of highly precise chemical assays and mass spectrometric procedures [6]. Good analytical procedures are based upon (a) a knowledge of the source of bias, (b) establishing control of the various parameters and (c) selecting an optimum combination of parameters that is uniform and reproducible for each analysis. Garner et al. [7] determined that for the isotopic analysis of uranium by TIMS, over the range of ratios represented by the isotopic standards SRMs U-050 to U-930 from the NBS, the bias is independent of the isotopic composition while for the range of ratios represented by the isotopic standards U-050 to U-005 from the NBS, non-ohmic response and the R-C response of the measuring circuit make point calibration for each standard mandatory. For the TIMS analysis of uranium samples Stephens et al. [8] recommend that the certified standard with an enrichment nearest to the enrichment of the samples should be analyzed at least once during each shift. If a suitable certified standard is not available, the quality control laboratory should retain a sufficient quantity of an appropriate uranium dioxide production batch preferably in powder form. This batch should be characterized initially to give reliable estimates of the isotopic composition (mean values and 95% confidence limit). Subsequently, samples from this designated batch can serve as an “in house” standard. Alternatively a standard may be blended from NBS reference materials; however, this is expensive. The present contribution describes the procedure followed to obtain a standard for uranium with a natural isotopic composition, according to the aforementioned recommendation proposed by Stephens et al. [8]. EXPERIMENTAL
DETAILS
The spectrometer used was a single focusing Nuclide 12-90 SU instrument, characterized by the following features: a single-sample thermal ionization source, a 15 inch radius, a 90” magnetic sector, a Faraday cup and an electron
101 TABLE I Certified and measured values for the 235U:238Uisotopic ratio (R,,*) Reference
&, (certified)
Rsis (measured)
U-002 (IAEA) U-005 (NBS) U-010 (NBS) U-01 5 (NBS) U3 OS (CNEA)
0.002049 0.004919 0.010140 0.015565 -
0.002018 0.004867 0.010221 0.015744 0.007287
1.3 2.0 1.9 4.2 3.2
x x x x x
10-9 10-9 1o-9 1O-9 10m9
multiplier. The measurement of the observed isotopic ratios (Robs)depends on (a) the chemical preparation procedure of the sample, (b) the loading procedure of the sample on the evaporating filament and (c) the measuring procedure. Reproduction of these procedures is essential to obtain reproducible values of Robs for different filament loads. Standard procedures have been developed at the Mass Spectrometry Division in the National Commission on Atomic Energy, Argentina (CNEA) over many years [9], as explained below. The sample to be isotopically characterized was nuclear grade U308 from Argentina, with a natural isotopic composition. Four standards were measured for RS,8. Three were the isotopic reference materials U-005, U-010 and U-01 5 from the NBS. The fourth, U-002 (IAEA), was calibrated in an interlaboratory test organized by the International Atomic Energy Agency (IAEA). For R4,5 the standards used were U-005, U-010, U-01 5 and U-900 from the NBS, which had a certified R4,5 value within the natural range for this isotopic ratio. The standard procedure followed at the CNEA Mass Spectrometry Division (Argentina) for the determination of the uranium isotopic ratios used a triple filament rhenium source. The analyzed uranium solutions from the sample and the standards had a 5 mg U ml-’ concentration in 1 M nitric acid. From the respective solutions 5 ~1 were loaded onto the sample filaments. The mass spectrometric procedure consisted of four determinations (four filament loads) of Rsls performed for each isotopic reference material and for the sample to be characterized. Each determination involved a set of 16 measurements of the 235Uand 238Upeaks through the peak-jumping procedure. The same method was followed for R4,5. The results shown in Tables 1 and 2 refer the measured values to the mean of the mean of four independent filament loadings. The total standard deviation combines the external standard deviation of four independent loadings and the internal standard deviation of a set of 16 measurements within one loading through the use of a test for statistical consistency [lOI.
102 TABLE
2
Certified
and measured
values for the 234U:235U isotopic
ratio (R4,5)
Reference
R4,5 (certified)
R4,J (measured)
2 &o1
U-005 U-010 U-015 U-900 U30s
0.004454 0.005390 0.005547 0.008622
0.005040 0.005269 0.005504 0.008648 0.007347
2.4 2.2 5.6 6.6 2.4
(NBS) (NBS) (NBS) (NBS) (CNEA)
x x x x x
1O-9 1o-9 1O-9 1o-9 10m9
CALCULATIONS
As the range of isotopic ratios analyzed in the present work was below the range for which the mass discrimination bias factor (k) can be considered independent of the isotopic ratio [6], it was decided to find out the relationship between this factor and the certified isotopic ratio (I&) for the analyzed isotopic reference materials. As the variances obtained for the isotopic ratio measurements were not constant in the investigated range, it was decided to apply weighted least-squares regression analysis. With this procedure the regression equation is obtained, potential outliers are flagged and confidence bands around the predicted values are calculated [I I]. The equation thus obtained for Rsls in the analyzed standards was Robs= -4.254
x 1O-5 + 1.01242 x R,,,,
(1)
with a regression coefficient r = 0.99996. This is an empirical equation and valid for this particular measurement procedure and for the particular investigated range of isotopic ratios. As we define the mass discrimination bias factor k as R
k=P
(2) 5/8,cert
it follows from Eqs. (1) and (2) that k=
R 5/8,obs
x
1*01242
R 5,Qo&+ 4.254 x lO-5
(3)
where we can see that the influence of the y axis intercept in Eq. 1 decreases for increasing isotopic ratios, corroborating the observations of Garner et al. [71. The influence of the y axis intercept is 0.5% for uranium with a natural isotopic composition. There has been recognition in the chemical literature that variance is usually not constant in chemical analyses [ 12-151.
103 TABLE 3 Coefficient of variation (CV) vs. the 235U:23*Uisotopic ratio Reference
Rsls (measured)
Log be
CV
Log cv
u-002 u-005 u-010 u-015
0.002018 0.004867 0.010221 0.015744 0.007287
- 2.695 -2.313 - 1.991 - 1.803 -2.137
1.79 0.92 0.43 0.41 0.77
0.253 - 0.036 - 0.367 - 0.387 -0.114
u3os
Franke et al. [12] have employed a standard deviation function directly proportional to concentration, and Smith and Mathews [13] assumed a standard deviation directly proportional to the signal. Geerlings and Koch [16] and Gonzalez [17] have informed us that the coefficient of variation for a given isotopic ratio R, is proportional to Rio.’ for a wide range of R,. The coefficient of variation (CV) is defined as
cv+
x 100
(4)
I/J
where stat is the total standard deviation for each measurement. This relationship was also investigated in the present report, and it was found that the least-squares regression of log CV vs. log R5,8 yielded the equation log CV = - 1.652 - 0.707 x log R5,*
(5)
with a regression coefficient r = 0.997, indicating that CV is proportional to R;‘.’ in the investigated range (Table 3). For the sample to be calibrated, the “certified” value calculated with Eq. (1) for the 235U:238Uisotopic ratio, with a 95% confidence interval is R5/8+ $+ -
= 0.007242 + 0.000054 .
where R5,8IS the mean value for the four determinations, t corresponds to the Student coefficient for the n - 1 degrees of freedom and n is the number of determinations (Table 4). As can be seen, the sample value is located in the middle of the isotopic range that was investigated for the obtention of Eq. (1). To complete the isotopic analysis for this sample, the 234U:235Uisotopic ratio has to be considered. The weighted least-squares regression analysis was applied to Robs vs. &,, for R4,5in the standards. The equation thus obtained was Robs =
-4.04412
x 1O-4 + 1.05382 x R,,,
(6)
104 TABLE 4 Measured and calculated values for the 235U:238Uisotopic ratio in the sample to be characterized (U, 0,) R5,*(measured)
R s/s a
Upper limit
Lower limit
0.00726199 0.00737001 0.00726919 0.00724690
0.0072176 0.0073243 0.0072247 0.0072027
0.0072562 0.0073629 0.0072672 0.0072427
0.0071793 0.0072861 0.0071827 0.0071630
“Calculated applying Eq. 1.
with a regression coefficient Y= 0.9990. The same considerations about the empirical character of this equation as for Eq. (1) are valid. For the sample to be characterized, the application of the last equation yielded R4,5values along with the upper and lower limits, which are shown along with the observed values in Table 5. Thus, the calibrated value calculated for R4,5 was
R4,5 + f+ n
= 0.007356 f 0.000073
and the symbols have the same meaning as for the R, g case. To calculate the absolute isotopic abundances, the i 34U isotope has to be referred to the 238Uisotope. Thus --R4/8 = R4,5 x Rsle = 0.0000532715 and Sk, = R:,s x
&t,4,5
+
2
R4,5
x
&,,,t~
=
1.7 x lo-l3
TABLE 5 Measured and calculated values for the 234U:23sUisotopic ratio in the sample to be characterized (U, 0,) &
(measured)
0.00741845 0.00733997 0.00728739 0.00734177
%,Sa
Upper limit
Lower limit
0.0074234 0.0073489 0.0072990 0.0073506
0.0076170 0.0074650 0.0074045 0.0074845
0.0072473 0.0072432 0.0072029 0.0072287
“Calculated applying Eq. 6.
105 TABLE 6 Isotopic abundances Isotope
U-234 U-235 U-238
in the sample to be characterized (U,O,) Abundance Atom percent
Weight percent
0.00529 + 0.00005 0.719 f 0.005 99.276 f 0.005
0.00520 rf: 0.00005 0.710 f 0.005 99.285 + 0.005
and therefore
R4,8 +3
= 0.0000533
* 0.0000066
From the calibrated values obtained for R5,* and R4,8 the isotopic abundances were calculated with a 95% confidence interval. The results obtained are shown in Table 6. The atomic weight of uranium was calculated for the sample and was found to be 238.03 ) 0.02. This value is in agreement with the accepted value published by the Commission on Atomic Weights and Isotopic Abundances from the International Union of Pure and Applied Chemistry [5]. Thus, the isotopic characterization was completed, and the sample could be considered an “in house” working standard for uranium with natural composition. CONCLUSIONS
Owing to natural variations in the isotopic composition of uranium it was decided to characterize an Argentine, nuclear grade U,O, production batch with a natural isotopic composition. The methodology proposed in the present report fulfilled the requirements of providing reliable estimates for the isotopic composition (mean values and 95% confidence limit) for the U,O, sample. The use of expensive enriched isotopes was thus circumvented. In addition, the use of isotopic reference materials from the NBS was minimized, because they were used only once for the determination of the mass discrimination bias factor. The obtained values for the isotopic abundances were used to calculate the atomic weight of uranium which was in agreement with the accepted value published by the Commission on Atomic Weights and Isotopic Abundances from the IUPAC.
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