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Determination of magnesium at trace levels by isotope dilution
701
SHORT COMMUNICATIONS Talanta,
Vol.24,pp.701-703. Pergamon Press,1977hmtedm GreatBritsm.
DETERMINATION OF MAGNESIUM AT TRACE LEVELS BY ISOTOPE DILUTION S. K. AGGARWAL, V. D. KAVIMANDAN, H. C. JAIN and C. K. MATHEWS Radiochemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay 400 085, India
(Received 13 January 1977. Accepted 28 May 1977) Summary-A mass spectrometric method for the isotopic analysis of magnesium and its determination at low concentrations in the presence of an excess of other elements is described. The lowest level at which magnesium was determined was 1 ppm with a precision and error f 1%.
An accurate method for the determination of magnesium at low concentrations in the presence of au excess of other elementsbecame necessary when the element was proposed as a tracer for the input accountability of plutonium in fuel-reprocessing plants. is2 A number of techniques, including gravimetry, titrimetry, spectrophotometry and emission spectrography, have been used for the determination of magnesium 3,4 but they do not have the accuracy or the sensitivity required for this application. Because isotope dilution analysis offers high sensitivity, selectivity and accuracy in such measurements,5p6 the mass spectrometric method was developed for the accurate determination of trace levels of magnesium. This has made it possible to use the magnesium tracer technique for the determination of the total amount of plutonium in the accountability tanks of reprocessing plants and to check the volume calibration of these tanks with an error of less than l%.’ In isotope dilution analysis, the concentration of an element is determined by increasing the relative abundance of one of its isotopes by adding a known amount of this element enriched in this isotope (spike) and measuring the increased abundance. If R’, RsP and RM are the relative abundances of two isotopes in the sample (S), spike (Sp) and mixture (M) respectively, then the concentration of the element in the sample is given by c
S
where C is concentration, Wis weight and the summation is over all the isotopes of the element (in this case magnesium). There are several reports on the determination of the isotopic composition of magnesium. The pioneering work of Dempster’ and that of White and Cameron,* whose results are often accepted as the best estimates for the isotopic abundances in natural magnesium, was done with use of electron-impact ion sources, but this is not suitable for the present purpose as the magnesium would have to be converted into the gaseous state. If a thermionic source is used isotope fractionation becomes a serious problem,’ and erroneous conclusions on the variation of isotopic abundances in natural magnesium have been arrived at because of the fractionation effects.” Some workers have used binding agents such as uranyl nitrate, beryllium oxide and amorphous carbon for loading magnesium on the filaments.9-11 The National Bureau of Standards has standardized a method for the isotope abundance measurement of magnesium, using uranyl nitrate as a binding, agent,” and reported that strict control of filament temperatures
was necessary to minimize the effects of isotope fractionation. In the present work, we have used a thermionic source. Significant fractionation was observed when magnesium was analysed by loading the sample on the filament in the nitrate form. This prompted a search for a compound which would give rise to negligible fractionation effects. Magnesium chloride was found to be suitable. This paper reports the standardization of the conditions for the isotopic analysis of magnesium and the procedure for the measurement of magnesium concentration down to the ppm level. EXPE’RIMENTAL
The instrument used was a Varian MAT CH-5 mass spectrometer with a thermionic source. It had a resolution of 425 (on 10% valley definition) measured at around mass 238 and an abundance sensitivitv of 105. Rhenium ribbons (0.04 x 0.7 x 8 mm) were used -as sample and ionization filaments. Isotopic analysis
A drop of the magnesium solution in suitable chemical form (chloride in’most of this work) was taken on a Teflon sheet, evaporated to very small volume, transferred by means of a capillary onto the sample filament of a prebaked double-filament assembly and evaporated to dryness. The filament assembly was introduced into the mass spectrometer and the isotope abundance measured after adjustment of the temperatures of the vaporizing and ionizing filaments. The heating pattern depended on the chemical nature of the sample. The procedure for analysing magnesium in the chloride form is as follows. Time from start, min O-2 2-15 15-20
2(r30
Operation The ionizing-filament current is set at about 2 A. The ionizing-filament current is increased slowly step&e to about 5 A. The Re+ sienal is found and focused. If this signal (for mass number 187) is greater or less than 10 mV (at SEM gain = 5 x lo4 and grid-leak resistance = 10’ ohm, i.e., an ioncurrent of 2 x lo-id A), the ionizing-filament current is readjusted to give a IO-mV signal for i8’Re+. The sample filament is heated with a current of 1 A apd the Mg+ signal is found and focused. Initially the signal decays and then becomes almost steady.
702 30 onwards
SHORT COMMUNICATIONS
Data recording begins. If the signal is less than 30 mV (i.e., 6 x lo-“‘A), the samplefilament current is further increased and data recorded as soon as a steady ion-current is obtained.
Concentration measurement using the isotope dilution technique
The concentration of magnesium in demineralized water, commercial nitric acid and nuclear grade uranium oxide was determined. In each case a weighed portion of sample solution was taken (UOs was first dissolved in acid) and mixed with a suitable weight of the 26Mg-enriched spike solution, which had already been calibrated. The mixed solution was evaporated to dryness and converted mto the chloride form by repeated evaporation with 8M hydrochloric acid. Magnesium was separated from most of the impurities by passing the solution through an anionexchange column (Dowex 1 x 8, 20@4OOmesh); the magnesium appeared in the eluate and was collected in a clean glass vial, evaporated to dryness and dissolved in 0.5-1M hydrochloric acid for mass spectrometric analysis. To avoid contamination the acids and water used were doubly distilled in quartz, the glassware was leached with nitric acid and the filaments were prebaked in vacuum. RESULTS AND DISCUSSION
Isotope abundance measurements Isotopic analysis of magnesium as the nitrate. Mass spectrometric analysis of magnesium was carried out several times with the sample loaded in the nitrate form and the sample size (2O-3Opg of Mg), sample composition (pure magnesium nitrate) and acidity of the loading solution (about 0.5M nitric acid) were kept constant. The ionizing filament was heated with a current of 5-6 A (adjusted to give the same peak height for Re+ ions) and the samplefilament current varied from 1.5 to 2.5 A. However, significant isotope fractionation occurred and it was not possible to find a filament current that would give reproducible results. Choice of a suitable magnesium compound for isotopic analysis. A search was made for a more smtable magnesium compound than the nitrate. Magnesium nitrate decomposes at around 600K to magnesium oxide which has a melting point of 3073 K and hence would have to be heated to very high temperatures to give sufficient vapour pressure at the ionizing filamenti Isotope fractionation is enhanced at such high temperatures. The carbonate and sulphate also decompose to the oxide at relatively low temperatures. Magnesium chloride, however, has a relatively low melting point and a vapour pressure of 10m4atm at 1000 K.“’ The comparatively low evaporation temperature and high molecular weight of the species evaporated both minimize isotope fractionation. Hence magnesmm chloride was chosen as a suitable compound. Isotopic analysis of magnesium as the chloride. A sample
Table 2. Comparison of 26Mg/24Mg isotope ratios obtained with sample loaded in the nitrate and chloride forms 26Mg/24Mg ratio Sample
Magnesium nitrate
Magnesium chloride
1
0.8431 0.8405 0.8535 0.8596 0.6901 0.6901 1.1855 1.1903 0.1355 0.1376 0.1392
0.8472 0.8457 0.8455
2 3 4
* 1, 2 and 3 are synthetic samples, 4 is a natural magnesium sample. size of 1&2Opg of magnesium was found to be optimal. It was observed that magnesium ions could be obtained in many cases by heating only the ionization filament. However, the procedure finally adopted consisted of heating the ionizing filament with a current of 5-6 A (the temperature being adjusted by monitoring the Re+ signal) with the sample-filament current varied from 1.2 to 1.8 A. This gave good reproducibility and no detectable isotope fractionation was observed with sample filament currents up to 1.8 A. Typical results are given in Tables 1 and 2. As can be seen from Table 1, there is no significant variation in s6Mg/s4Mg isotope ratios as the sample filament temperature is varied within a reasonable range, thus making it possible to obtain reproducible results. Table 2 shows that more reproducible values can be obtained by loading as the chloride than as the nitrate. The results obtained for the isotopic composition of natural magnesium were “Mgjz4Mg = 0.1247 and 26Mg/24Mg = 0.1352, the relative standard deviation being about 0.5% in both cases. Mass discrimination factor (mdf). The absolute isotope ratios are obtained from the observed values by applying a correction factor called the mass discrimination factor (mdf) which is usually determined by analysing isotopic standards. As no isotopic standard for magnesium was readily available, the overall mass discrimmation was determmed by analysing natural magnesium samples. The *6Mg/24Mg ratio was used for calculating the mdf. as the use of two isotopes with the greatest mass separation gives the maximum sensitivity for determination of the bias. The overall mdf per mass unit was found to be 1.0157 f 0.0015. That this bias is essentially due to the use of an electron multiplier was confirmed by comparison with results obtained with a Faraday-cup detector, from which little bias is expected. It was found that the electron multiplier
Table 1. Variation in s6Mg/s4Mg isotope ratio with sample-filament (magnesium loaded as chloride) Samplefilament current A 1.2 1.3 1.4 1.5 1.6 1.7 1.8
0.6743 0.6754 1.1445 1.1411 0.1354 0.1359 0.1354
temperature
26Mg/24Mg ratio Sample 1
Sample 2
1.807 f 0.008 1.819 + 0.009 1.819 : 0.008 1.822 & 0.010 1.800 f 0.010 1.802 + 0.005
Sample 3 1.701 ) 0.009
1.836 ) 1.846 k 1.848 f 1.846 f
0.008 0.009 0.006 0.008
1.703 + 0.012 1.710 + 0.009 1.719 + 0.007
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gave a value which was 1.0282 + 0.0064 times that obtained with the Faraday cup, giving 1.0141 f 0.0032 as the mdf per mass unit. This value is close enough to the observed mdf; hence there can be no doubt that isotope fractionation effects are negligible. Moreover, in concentration measurement the mass discrimination factor is cancelled because spike calibration is also carried out by isotope dilution. When the variation in the isotopic composition of different natural magnesium samples is studied. the mdf is not important.
signal which can be detected above background). The sensitivity, precision and accuracy may be compared with the sensitivity of 0.1 ppm and precision of about 10% at the I-ppm level in spectrographic measurements.i5,i6 Acknowledgements-The authors are thankful to Dr. M. V. Ramanash, Head of the Radiochemistry Division, for his interest in this work. Thanks are also due to their colleagues m the Mass Spectrometry Group who have helped at various stages of this work. REFERENCES
Table 3. Estimation of magnesium in various samples
Sample Demineralized water Nitric acid (commercial grade) Uranium (UsO,)
Mean value, ppm
Estimated error, %
RSD, %
6.34 1.16
0.8 0.6
0.1 1.0
3.30
0.6
0.9
1. C. K. Mathews, H. C. Jain, S. A. Chitambar, V. D. Kavimandan and S. K. Aggarwal, BARC-809, 1975. 2. C. K. Mathews, H. C. Jain, V. D. Kavimandan and S. K. Aggarwal. Safeguarding Nuclear Materials, Vol. II, p. 485. IAEA, Vienna, 1976. 3. A. I. Vogel, A Text Book of Quantitative Inorganic Analysis, 3rd Ed., Longmans, London, 1964. 4. G. H. Morrison, Trace Analysis, Interscience, New York, 1965. 5. C. K. Mathews, J. Sci. Ind. Res. (India), 1970, 30, 297. 6. S. A. Chitambar and C. K. Mathews, Z. Anal. Chem., 1975. 214, 9.
CONCENTRATION
MEASUREMENTS
Results on the concentration measurement of magnesium in various samples are given in Table 3. The errors arise from uncertainty in the isotope ratio measurement and in the measurement of portions of sample and spike solution used. In the isotope ratio measurement, there can be random and systematic errors. The systematic errors arising from isotope fractionation and mass discrimination were shown above to be negligible. The error in measurement of fractions used for isotope dilution was negligible (less than 0.1%) since the fractions were weighed. The total error stated is based on error propagation and equation (1). The precision is also given, as the relative standard deviation (RSD). The lowest level of magnesium estimated in the present work was 1 ppm (precision and accuracy f 1%). The method is, however, much more sensitive and should be able to determine magnesium at levels down to 1 part in 10” (this is an estimate based on the lowest
I. A. J. Dempster, Phys. Rev., 1921. 18, 421. 8. J. R. White and A. E. Cameron, lbrd., 1948, 74, 991. 9. A. C. Daughtry, D. Perry and M. Williams, Geochim. Cosmochim. Acta, 1962, 26, 857. 10. E. J. Catanzaro and T. J. Murphy, J. Geophys. Res., 1966, 71, 1271. 11 M. Shima, Bull. Chem. ‘Sot. Japan, 1964. 37, 284. 12. E. J. Catanzaro, T. J. Murphy, E. L. Garner and W. R. Shields, J. Res. Natl. Bur. Stds. A., 1966, 70, 453. 13. Y. S. Touloukian. Thermophysica2 Properties of High Temperature Materials, Plenum Press, New York, 1973. 14. I. Barin and D. Knacke, Thermochemical Properties of Inorganic Substances, Springer-Verlag, Heidelberg, 1973. 15. B. D. Joshi, T. R. Bangia and A. G. I. Dalvi, Z. Anal. Chem., 1972, 260, 107. 16. Idem, Ibid., 1973, 266, 125.
SHORT COMMUNICATIONS Talanta,
Vol.24,pp.701-703. Pergamon Press,1977hmtedm GreatBritsm.
DETERMINATION OF MAGNESIUM AT TRACE LEVELS BY ISOTOPE DILUTION S. K. AGGARWAL, V. D. KAVIMANDAN, H. C. JAIN and C. K. MATHEWS Radiochemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay 400 085, India
(Received 13 January 1977. Accepted 28 May 1977) Summary-A mass spectrometric method for the isotopic analysis of magnesium and its determination at low concentrations in the presence of an excess of other elements is described. The lowest level at which magnesium was determined was 1 ppm with a precision and error f 1%.
An accurate method for the determination of magnesium at low concentrations in the presence of au excess of other elementsbecame necessary when the element was proposed as a tracer for the input accountability of plutonium in fuel-reprocessing plants. is2 A number of techniques, including gravimetry, titrimetry, spectrophotometry and emission spectrography, have been used for the determination of magnesium 3,4 but they do not have the accuracy or the sensitivity required for this application. Because isotope dilution analysis offers high sensitivity, selectivity and accuracy in such measurements,5p6 the mass spectrometric method was developed for the accurate determination of trace levels of magnesium. This has made it possible to use the magnesium tracer technique for the determination of the total amount of plutonium in the accountability tanks of reprocessing plants and to check the volume calibration of these tanks with an error of less than l%.’ In isotope dilution analysis, the concentration of an element is determined by increasing the relative abundance of one of its isotopes by adding a known amount of this element enriched in this isotope (spike) and measuring the increased abundance. If R’, RsP and RM are the relative abundances of two isotopes in the sample (S), spike (Sp) and mixture (M) respectively, then the concentration of the element in the sample is given by c
S
where C is concentration, Wis weight and the summation is over all the isotopes of the element (in this case magnesium). There are several reports on the determination of the isotopic composition of magnesium. The pioneering work of Dempster’ and that of White and Cameron,* whose results are often accepted as the best estimates for the isotopic abundances in natural magnesium, was done with use of electron-impact ion sources, but this is not suitable for the present purpose as the magnesium would have to be converted into the gaseous state. If a thermionic source is used isotope fractionation becomes a serious problem,’ and erroneous conclusions on the variation of isotopic abundances in natural magnesium have been arrived at because of the fractionation effects.” Some workers have used binding agents such as uranyl nitrate, beryllium oxide and amorphous carbon for loading magnesium on the filaments.9-11 The National Bureau of Standards has standardized a method for the isotope abundance measurement of magnesium, using uranyl nitrate as a binding, agent,” and reported that strict control of filament temperatures
was necessary to minimize the effects of isotope fractionation. In the present work, we have used a thermionic source. Significant fractionation was observed when magnesium was analysed by loading the sample on the filament in the nitrate form. This prompted a search for a compound which would give rise to negligible fractionation effects. Magnesium chloride was found to be suitable. This paper reports the standardization of the conditions for the isotopic analysis of magnesium and the procedure for the measurement of magnesium concentration down to the ppm level. EXPE’RIMENTAL
The instrument used was a Varian MAT CH-5 mass spectrometer with a thermionic source. It had a resolution of 425 (on 10% valley definition) measured at around mass 238 and an abundance sensitivitv of 105. Rhenium ribbons (0.04 x 0.7 x 8 mm) were used -as sample and ionization filaments. Isotopic analysis
A drop of the magnesium solution in suitable chemical form (chloride in’most of this work) was taken on a Teflon sheet, evaporated to very small volume, transferred by means of a capillary onto the sample filament of a prebaked double-filament assembly and evaporated to dryness. The filament assembly was introduced into the mass spectrometer and the isotope abundance measured after adjustment of the temperatures of the vaporizing and ionizing filaments. The heating pattern depended on the chemical nature of the sample. The procedure for analysing magnesium in the chloride form is as follows. Time from start, min O-2 2-15 15-20
2(r30
Operation The ionizing-filament current is set at about 2 A. The ionizing-filament current is increased slowly step&e to about 5 A. The Re+ sienal is found and focused. If this signal (for mass number 187) is greater or less than 10 mV (at SEM gain = 5 x lo4 and grid-leak resistance = 10’ ohm, i.e., an ioncurrent of 2 x lo-id A), the ionizing-filament current is readjusted to give a IO-mV signal for i8’Re+. The sample filament is heated with a current of 1 A apd the Mg+ signal is found and focused. Initially the signal decays and then becomes almost steady.
702 30 onwards
SHORT COMMUNICATIONS
Data recording begins. If the signal is less than 30 mV (i.e., 6 x lo-“‘A), the samplefilament current is further increased and data recorded as soon as a steady ion-current is obtained.
Concentration measurement using the isotope dilution technique
The concentration of magnesium in demineralized water, commercial nitric acid and nuclear grade uranium oxide was determined. In each case a weighed portion of sample solution was taken (UOs was first dissolved in acid) and mixed with a suitable weight of the 26Mg-enriched spike solution, which had already been calibrated. The mixed solution was evaporated to dryness and converted mto the chloride form by repeated evaporation with 8M hydrochloric acid. Magnesium was separated from most of the impurities by passing the solution through an anionexchange column (Dowex 1 x 8, 20@4OOmesh); the magnesium appeared in the eluate and was collected in a clean glass vial, evaporated to dryness and dissolved in 0.5-1M hydrochloric acid for mass spectrometric analysis. To avoid contamination the acids and water used were doubly distilled in quartz, the glassware was leached with nitric acid and the filaments were prebaked in vacuum. RESULTS AND DISCUSSION
Isotope abundance measurements Isotopic analysis of magnesium as the nitrate. Mass spectrometric analysis of magnesium was carried out several times with the sample loaded in the nitrate form and the sample size (2O-3Opg of Mg), sample composition (pure magnesium nitrate) and acidity of the loading solution (about 0.5M nitric acid) were kept constant. The ionizing filament was heated with a current of 5-6 A (adjusted to give the same peak height for Re+ ions) and the samplefilament current varied from 1.5 to 2.5 A. However, significant isotope fractionation occurred and it was not possible to find a filament current that would give reproducible results. Choice of a suitable magnesium compound for isotopic analysis. A search was made for a more smtable magnesium compound than the nitrate. Magnesium nitrate decomposes at around 600K to magnesium oxide which has a melting point of 3073 K and hence would have to be heated to very high temperatures to give sufficient vapour pressure at the ionizing filamenti Isotope fractionation is enhanced at such high temperatures. The carbonate and sulphate also decompose to the oxide at relatively low temperatures. Magnesium chloride, however, has a relatively low melting point and a vapour pressure of 10m4atm at 1000 K.“’ The comparatively low evaporation temperature and high molecular weight of the species evaporated both minimize isotope fractionation. Hence magnesmm chloride was chosen as a suitable compound. Isotopic analysis of magnesium as the chloride. A sample
Table 2. Comparison of 26Mg/24Mg isotope ratios obtained with sample loaded in the nitrate and chloride forms 26Mg/24Mg ratio Sample
Magnesium nitrate
Magnesium chloride
1
0.8431 0.8405 0.8535 0.8596 0.6901 0.6901 1.1855 1.1903 0.1355 0.1376 0.1392
0.8472 0.8457 0.8455
2 3 4
* 1, 2 and 3 are synthetic samples, 4 is a natural magnesium sample. size of 1&2Opg of magnesium was found to be optimal. It was observed that magnesium ions could be obtained in many cases by heating only the ionization filament. However, the procedure finally adopted consisted of heating the ionizing filament with a current of 5-6 A (the temperature being adjusted by monitoring the Re+ signal) with the sample-filament current varied from 1.2 to 1.8 A. This gave good reproducibility and no detectable isotope fractionation was observed with sample filament currents up to 1.8 A. Typical results are given in Tables 1 and 2. As can be seen from Table 1, there is no significant variation in s6Mg/s4Mg isotope ratios as the sample filament temperature is varied within a reasonable range, thus making it possible to obtain reproducible results. Table 2 shows that more reproducible values can be obtained by loading as the chloride than as the nitrate. The results obtained for the isotopic composition of natural magnesium were “Mgjz4Mg = 0.1247 and 26Mg/24Mg = 0.1352, the relative standard deviation being about 0.5% in both cases. Mass discrimination factor (mdf). The absolute isotope ratios are obtained from the observed values by applying a correction factor called the mass discrimination factor (mdf) which is usually determined by analysing isotopic standards. As no isotopic standard for magnesium was readily available, the overall mass discrimmation was determmed by analysing natural magnesium samples. The *6Mg/24Mg ratio was used for calculating the mdf. as the use of two isotopes with the greatest mass separation gives the maximum sensitivity for determination of the bias. The overall mdf per mass unit was found to be 1.0157 f 0.0015. That this bias is essentially due to the use of an electron multiplier was confirmed by comparison with results obtained with a Faraday-cup detector, from which little bias is expected. It was found that the electron multiplier
Table 1. Variation in s6Mg/s4Mg isotope ratio with sample-filament (magnesium loaded as chloride) Samplefilament current A 1.2 1.3 1.4 1.5 1.6 1.7 1.8
0.6743 0.6754 1.1445 1.1411 0.1354 0.1359 0.1354
temperature
26Mg/24Mg ratio Sample 1
Sample 2
1.807 f 0.008 1.819 + 0.009 1.819 : 0.008 1.822 & 0.010 1.800 f 0.010 1.802 + 0.005
Sample 3 1.701 ) 0.009
1.836 ) 1.846 k 1.848 f 1.846 f
0.008 0.009 0.006 0.008
1.703 + 0.012 1.710 + 0.009 1.719 + 0.007
SHORT
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gave a value which was 1.0282 + 0.0064 times that obtained with the Faraday cup, giving 1.0141 f 0.0032 as the mdf per mass unit. This value is close enough to the observed mdf; hence there can be no doubt that isotope fractionation effects are negligible. Moreover, in concentration measurement the mass discrimination factor is cancelled because spike calibration is also carried out by isotope dilution. When the variation in the isotopic composition of different natural magnesium samples is studied. the mdf is not important.
signal which can be detected above background). The sensitivity, precision and accuracy may be compared with the sensitivity of 0.1 ppm and precision of about 10% at the I-ppm level in spectrographic measurements.i5,i6 Acknowledgements-The authors are thankful to Dr. M. V. Ramanash, Head of the Radiochemistry Division, for his interest in this work. Thanks are also due to their colleagues m the Mass Spectrometry Group who have helped at various stages of this work. REFERENCES
Table 3. Estimation of magnesium in various samples
Sample Demineralized water Nitric acid (commercial grade) Uranium (UsO,)
Mean value, ppm
Estimated error, %
RSD, %
6.34 1.16
0.8 0.6
0.1 1.0
3.30
0.6
0.9
1. C. K. Mathews, H. C. Jain, S. A. Chitambar, V. D. Kavimandan and S. K. Aggarwal, BARC-809, 1975. 2. C. K. Mathews, H. C. Jain, V. D. Kavimandan and S. K. Aggarwal. Safeguarding Nuclear Materials, Vol. II, p. 485. IAEA, Vienna, 1976. 3. A. I. Vogel, A Text Book of Quantitative Inorganic Analysis, 3rd Ed., Longmans, London, 1964. 4. G. H. Morrison, Trace Analysis, Interscience, New York, 1965. 5. C. K. Mathews, J. Sci. Ind. Res. (India), 1970, 30, 297. 6. S. A. Chitambar and C. K. Mathews, Z. Anal. Chem., 1975. 214, 9.
CONCENTRATION
MEASUREMENTS
Results on the concentration measurement of magnesium in various samples are given in Table 3. The errors arise from uncertainty in the isotope ratio measurement and in the measurement of portions of sample and spike solution used. In the isotope ratio measurement, there can be random and systematic errors. The systematic errors arising from isotope fractionation and mass discrimination were shown above to be negligible. The error in measurement of fractions used for isotope dilution was negligible (less than 0.1%) since the fractions were weighed. The total error stated is based on error propagation and equation (1). The precision is also given, as the relative standard deviation (RSD). The lowest level of magnesium estimated in the present work was 1 ppm (precision and accuracy f 1%). The method is, however, much more sensitive and should be able to determine magnesium at levels down to 1 part in 10” (this is an estimate based on the lowest
I. A. J. Dempster, Phys. Rev., 1921. 18, 421. 8. J. R. White and A. E. Cameron, lbrd., 1948, 74, 991. 9. A. C. Daughtry, D. Perry and M. Williams, Geochim. Cosmochim. Acta, 1962, 26, 857. 10. E. J. Catanzaro and T. J. Murphy, J. Geophys. Res., 1966, 71, 1271. 11 M. Shima, Bull. Chem. ‘Sot. Japan, 1964. 37, 284. 12. E. J. Catanzaro, T. J. Murphy, E. L. Garner and W. R. Shields, J. Res. Natl. Bur. Stds. A., 1966, 70, 453. 13. Y. S. Touloukian. Thermophysica2 Properties of High Temperature Materials, Plenum Press, New York, 1973. 14. I. Barin and D. Knacke, Thermochemical Properties of Inorganic Substances, Springer-Verlag, Heidelberg, 1973. 15. B. D. Joshi, T. R. Bangia and A. G. I. Dalvi, Z. Anal. Chem., 1972, 260, 107. 16. Idem, Ibid., 1973, 266, 125.